From cd5d8d2a8016c1ae8e83ed8663f960d7f7c63bdc Mon Sep 17 00:00:00 2001 From: rdelhaye <38891240+rdelhaye@users.noreply.github.com> Date: Fri, 18 May 2018 13:56:47 +0100 Subject: [PATCH 001/170] Add files via upload Added/extended three forms of Tanaka method, with flexibility for with/without errors. --- pycurious/curie.py | 150 +++++++++++++++++++++++++++++++++++++++++++-- 1 file changed, 145 insertions(+), 5 deletions(-) diff --git a/pycurious/curie.py b/pycurious/curie.py index 9620438..925d77c 100644 --- a/pycurious/curie.py +++ b/pycurious/curie.py @@ -211,14 +211,153 @@ def radial_spectrum(self, subgrid, taper=np.hanning, scale=0.001, **kwargs): for i in range(0, nbins): mask = np.logical_and(kk >= kbins[i], kk <= kbins[i+1]) - rr = 2.0*np.log(FT[mask]) + #rr = np.log(np.sqrt(FT[mask]))(2*np.pi) + rr = np.log(np.sqrt(FT[mask])) S[i] = rr.mean() k[i] = kk[mask].mean() sigma2[i] = np.std(rr)/np.sqrt(rr.size) return S, k, sigma2 - + def Tanaka(self, S, k, sigma2,kmin=0.05, kmax=0.2): + """ + Compute weighted linear fit of S over spatial frequency window kmin:kmax + + Parameters + ---------- + S : Power spectrum of signal (see radial spectrum), expected in ln(sqrt(S)) form + k : Wavenumber + sigma2 : Errors of S + kmin,kmax : Minimum and maximum spatial frequencies to fit. Ideally low frequency, straight-ish line + + Returns + ----------- + Zb : Estimated Curie point depth, as per Tanaka et al, 1999 + eZb : Error of Zb + : No geothermal gradient, trivial to estimate. + : Possible to extend, return fitted components? + """ + sf=k/(2.0*np.pi) + S2=np.log(np.exp(S)/sf) + + mask2=np.logical_and(sf >=kmin,sf <=kmax) + X=sf[mask2] + Y=S[mask2] + E=np.log(np.exp(sigma2[mask2])/X) + TL= sum(X/(E**2))*sum(Y/(E**2)) - sum((np.multiply(X,Y)/(E**2))*sum(1/(E**2))) + BL= (sum(X/(E**2)))**2 - (sum((X**2)/(E**2))*sum(1/(E**2))) + Ztr=TL/BL + btr= (sum(np.multiply(X,Y)/E**2) -Ztr*(sum(X**2/E**2) ))/(sum(X/E**2)) + eZtr=np.sqrt( sum(1/E**2)/ ( sum(X**2/E**2)*sum(1/E**2)-(sum(X/E**2))**2 )) + + Y2=np.log(np.exp(S[mask2])/X) + TL= sum(X/(E**2))*sum(Y2/(E**2)) - sum((np.multiply(X,Y2)/(E**2))*sum(1/(E**2))) + BL= (sum(X/(E**2)))**2 - (sum((X**2)/(E**2))*sum(1/(E**2))) + Zor=TL/BL + bor= (sum(np.multiply(X,Y2)/E**2) -Zor*(sum(X**2/E**2) ))/(sum(X/E**2)) + eZor=np.sqrt( sum(1/E**2)/ ( sum(X**2/E**2)*sum(1/E**2)-(sum(X/E**2))**2 )) + Zb=2*Zor-Ztr + eZb=2*eZor+eZtr + return Zb, eZb + + def Tanakac(self, S, k, sigma2,kmin=0.05, kmax=0.2,k2min=0.05, k2max=0.2): + """ + Compute weighted linear fit of S over spatial frequency window kmin:kmax + + Parameters + ---------- + S : Power spectrum of signal (see radial spectrum), expected in ln(sqrt(S)) form + k : Wavenumber + sigma2 : Errors of S + kmin,kmax : Minimum and maximum spatial frequencies to fit. Ideally low frequency, straight-ish line + + Returns + ----------- + Zb : Estimated Curie point depth, as per Tanaka et al, 1999 + eZb : Error of Zb + : No geothermal gradient, trivial to estimate. + : Possible to extend, return fitted components? + """ + sf=k/(2.0*np.pi) + S2=np.log(np.exp(S)/sf) + #print(sf) + mask2=np.logical_and(sf >=kmin,sf <=kmax) + #print(mask2) + X=sf[mask2] + Y=S[mask2] + E=sigma2[mask2] + TL= sum(X/(E**2))*sum(Y/(E**2)) - sum((np.multiply(X,Y)/(E**2))*sum(1/(E**2))) + BL= (sum(X/(E**2)))**2 - (sum((X**2)/(E**2))*sum(1/(E**2))) + Ztr=TL/BL + btr= (sum(np.multiply(X,Y)/E**2) -Ztr*(sum(X**2/E**2) ))/(sum(X/E**2)) + eZtr=np.sqrt( sum(1/E**2)/ ( sum(X**2/E**2)*sum(1/E**2)-(sum(X/E**2))**2 )) + + mask2=np.logical_and(sf >=k2min,sf <=k2max) + X=sf[mask2] + Y2=np.log(np.exp(S[mask2])/X) + E=np.log(np.exp(sigma2[mask2])/X) + TL= sum(X/(E**2))*sum(Y2/(E**2)) - sum((np.multiply(X,Y2)/(E**2))*sum(1/(E**2))) + BL= (sum(X/(E**2)))**2 - (sum((X**2)/(E**2))*sum(1/(E**2))) + Zor=TL/BL + bor= (sum(np.multiply(X,Y2)/E**2) -Zor*(sum(X**2/E**2) ))/(sum(X/E**2)) + eZor=np.sqrt( sum(1/E**2)/ ( sum(X**2/E**2)*sum(1/E**2)-(sum(X/E**2))**2 )) + Zb=2*Zor-Ztr + eZb=2*eZor+eZtr + #return Zb, eZb + return Zb, eZb, Ztr, Zor + + def Tanakab(self, S, k, kmin=0.05, kmax=0.2): + """ + Compute unweighted linear fit of S over spatial frequency window kmin:kmax + + Parameters + ---------- + S : Power spectrum of signal (see radial spectrum), expected in ln(sqrt(S)) form + k : Wavenumber + kmin,kmax : Minimum and maximum spatial frequencies to fit. Ideally low frequency, straight-ish line + + Returns + ----------- + Zb : Estimated Curie point depth, as per Tanaka et al, 1999 + eZb : Error of Zb + : No geothermal gradient, trivial to estimate. + : Possible to extend, return fitted components? + """ + sf=k/(2.0*np.pi) + S2=np.log(np.exp(S)/sf) + + mask2=np.logical_and(sf >=kmin,sf <=kmax) + X=sf[mask2] + Y=S[mask2] + TL= X.size*sum(X*Y)-(sum(X)*sum(Y)) + BL=X.size*sum(X**2)-(sum(X)**2) + Ztr=TL/BL + + + Y2=np.log(np.exp(S[mask2])/X) + TL= X.size*sum(X*Y2)-(sum(X)*sum(Y2)) + BL=X.size*sum(X**2)-(sum(X)**2) + Zor=TL/BL + Zb=2*Zor-Ztr + return Zb + + #TL= sum(X/(E**2))*sum(Y/(E**2)) - sum((np.multiply(X,Y)/(E**2))*sum(1/(E**2))) + #BL= (sum(X/(E**2)))**2 - (sum((X**2)/(E**2))*sum(1/(E**2))) + #Ztr=TL/BL + #btr= (sum(np.multiply(X,Y)/E**2) -Ztr*(sum(X**2/E**2) ))/(sum(X/E**2)) + #eZtr=np.sqrt( sum(1/E**2)/ ( sum(X**2/E**2)*sum(1/E**2)-(sum(X/E**2))**2 )) + + #Y2=np.log(np.exp(S[mask2])/X) + #TL= sum(X/(E**2))*sum(Y2/(E**2)) - sum((np.multiply(X,Y2)/(E**2))*sum(1/(E**2))) + #BL= (sum(X/(E**2)))**2 - (sum((X**2)/(E**2))*sum(1/(E**2))) + #Zor=TL/BL + #bor= (sum(np.multiply(X,Y2)/E**2) -Zor*(sum(X**2/E**2) ))/(sum(X/E**2)) + #eZor=np.sqrt( sum(1/E**2)/ ( sum(X**2/E**2)*sum(1/E**2)-(sum(X/E**2))**2 )) + #Zb=2*Zor-Ztr + #eZb=2*eZor+eZtr + #return Zb, eZb + + def azimuthal_spectrum(self, subgrid, taper=np.hanning, scale=0.001, theta=5.0, **kwargs): """ Compute azimuthal spectrum for a square grid. @@ -239,8 +378,9 @@ def azimuthal_spectrum(self, subgrid, taper=np.hanning, scale=0.001, theta=5.0, S : Azimuthal spectrum k : wavenumber [rad/km] theta : angles + sigma2 : variance of S """ - import radon + from pycurious import radon data = subgrid nr, nc = data.shape nw = nr @@ -256,6 +396,7 @@ def azimuthal_spectrum(self, subgrid, taper=np.hanning, scale=0.001, theta=5.0, dtheta = np.arange(0.0, 180.0, theta) sinogram = radon.radon2d(data, np.pi*dtheta/180.0) S = np.zeros((dtheta.size, kbins.size)) + sigma2 = np.zeros((dtheta.size, kbins.size)) # control taper if taper is None: @@ -266,8 +407,7 @@ def azimuthal_spectrum(self, subgrid, taper=np.hanning, scale=0.001, theta=5.0, nk = 1 + 2*kbins.size for i in range(0, dtheta.size): PSD = np.abs(np.fft.fft(vtaper*sinogram[:,i], n=nk)) - S[i,:] = 2.0*np.log( PSD[1:kbins.size+1] ) - + S[i,:] = np.log( np.sqrt(PSD[1:kbins.size+1] )) return S, kbins, dtheta From cfcf273c6bac36bc718d0098571d3579dbb3d7e5 Mon Sep 17 00:00:00 2001 From: rdelhaye <38891240+rdelhaye@users.noreply.github.com> Date: Fri, 18 May 2018 14:37:49 +0100 Subject: [PATCH 002/170] Add files via upload Code to generate synthetic magnetic anomaly data for Curie point depth analysis/comparison. --- tests/Bouligand_forward.py | 155 +++++++++++++++++++++++++++++++++++++ 1 file changed, 155 insertions(+) create mode 100644 tests/Bouligand_forward.py diff --git a/tests/Bouligand_forward.py b/tests/Bouligand_forward.py new file mode 100644 index 0000000..68c6e1d --- /dev/null +++ b/tests/Bouligand_forward.py @@ -0,0 +1,155 @@ +## Code to generate test magnetic data for testing of PyCurious methods +## Converted from MATLAB code by R Delhaye. +#Original code: +#Claire Bouligand +#03-19-2007 +#05-09-2014 +#Modified to use less memory + +import numpy as np +import matplotlib.pyplot as plt +import pycurious +import time + +start_time=time.time() +cm=1.e-7 + +########################################################## +#A VERIFIER: multiplier facteur cm par 4*pi +## TO VERIFY: multiplication factor "cm for 4*pi" +########################################################### +## Degree of fractal +b=-3 +## Dimension of pixels (km), should be multiples of the smallest +dlx=1.0 +dly=1.0 +dlz=1.0 +dl=min([dlx,dly,dlz]) +dx=dlx/dl +dy=dly/dl +dz=dlz/dl + +#nombre de pixels +## Number of pixels. +nx=305 +ny=305 +nz=16 +nmax=int(max([nx*dx,ny*dy,nz*dz])) + +#texte="dimensions x : %d / y : %d / z : %d" % (nx*dlx,ny*dly,nz*dlz) +#print(texte) +#disp(texte) + +#Parametres de l'aimantation +## Parameters of magnetisation +#M1=1 # aimantation moyenne = 1 A/m ## Average magnetisation +#M2=10^(0.25) # std de l'aimantation = 10^(0.25) A/m ## Standard dev of +#magnetisation +M1=0 +M2=0.2 +#prof sommet zt # Depth Zt +zt=0.305 +#prof base zb ## Depth Zb +zb=zt+nz*dlz + +############################################################ +#GENERATION DE LA DISTRIB 3D D'AIMANTATION FRACTAL +#A PARTIR VOLUME DE DIM ID. (nmax,dl) SELON X, Y ET Z + +M=np.zeros((nmax,nmax,nmax)) +l=[0,(nmax-1)*dl,dl] + +#x=np.arange(0,dlx*(nx-1),dlx) +#y=np.arange(0,dly*(nx-1),dly) +#z=np.arange(0,dlz*(nx-1),dlz) + +df=1/(nmax*dl) +dfx=1/(nx*dlx) +dfy=1/(ny*dly) +dfz=1/(nz*dlz) + +#Center indices of matrix = Nyquist +c=(nmax+1)/2 +f=np.zeros((int(np.floor((nmax+1))),1)) +fx=np.zeros((int(np.floor((nmax+1))),1)) +fy=np.zeros((int(np.floor((nmax+1))),1)) +fz=np.zeros((int(np.floor((nmax+1))),1)) +for i in range(0,int(np.floor((nmax+1)/2))-1): + f[i]=(i)*df +for i in range(int(np.floor((nmax+1)/2))-1,int(nmax)): + f[i]=-1*(nmax-i)*df +for i in range(0,int(np.floor((nx+1)/2))-1): + fx[i]=(i)*dfx +for i in range(int(np.floor((nx+1)/2))-1,int(nx)): + fx[i]=-1*(nx-i)*dfx +for i in range(1,int(np.floor((ny+1)/2))-1): + fy[i]=(i)*dfy +for i in range(int(np.floor((ny+1)/2))-1,int(ny)): + fy[i]=-1*(ny-i)*dfy +for i in range(1,int(np.floor((nz+1)/2))-1): + fz[i]=(i)*dfz +for i in range(int(np.floor((nz+1)/2))-1,int(nz)): + fz[i]=-1*(nz-i)*dfz + +# Normal distribution +M=M2*np.random.randn(nmax,nmax,nmax)+M1 + +Mf=np.fft.fftn(M) +for i in range(0,nmax-1): + for k in range(0,nmax-1): + for l in range(0,nmax-1): + Mf[i,k,l]=Mf[i,k,l]*((f[i])**2+(f[k])**2+(f[l])**2+0.0000001)**(b/4) +## DC correction - not needed in python, req. in MATLAB +##Mf(1,1,1)=mean([Mf(2,1,1) Mf(1,2,1) Mf(1,1,2)]) + +Mi=np.fft.ifftn(Mf) +TFANO=np.zeros((nx,ny), dtype=np.complex) +ANO=np.zeros((nx,ny), dtype=np.complex) +#input("Press Enter to continue.") +## executes fine up to here. +for k in range(0,nz): + TFHM=np.fft.fft2(Mi[:,:,k]) + z1=zt+k*dlz + z2=z1+dlz +# disp(z1) +# disp(z2) + for i in range(0,nx): + for j in range(0,ny): + fH=float(np.sqrt((fx[i])**2+(fy[j])**2)) + TFANO[i,j]=TFHM[i,j]*2*np.pi*cm*(np.exp(-2*np.pi*fH*z1)-np.exp(-2*np.pi*fH*z2)) + ANO=ANO+np.fft.ifft2(TFANO) + +print("--- %s seconds ---" % (time.time() - start_time)) + +x=np.arange(0.5,0.5+dlx*(nx),dlx)*1000 +y=np.arange(0.5,0.5+dly*(nx),dly)*1000 +fid=open("test_mag_data.txt","w+") +for i in range(0,nx): + for j in range(0,ny): + fid.write(' '.join([str(x[i]),str(y[j]),str(np.real(ANO[i,j])),"\n"])) + +fid.close() +#plt.pcolor(np.real(ANO)) +#plt.show() +#clear TFHM TFANO + +#figure (7) +## RD - PROBLEM! "Data inputs must be real". Trying abs(), or real() +##pcolor(ANO) +#pcolor(log10(abs(ANO))) +#shading flat +#colorbar + +##Sauvegarde carte : +#ncol=nx #Number of columns +#nrow=ny #Number of rows +#xleft=x(1) #x coordinate for left hand corner of grid +#dx=dlx #delta x +#yleft=y(1) #y coordinate for left hand corner of grid +#dy=dly #delta y +#gridC=ANO + +##save carte_synth_format.mat ncol nrow xleft yleft dx dy gridC +##save carte_synth.mat b M1 M2 dlx dly dlz zt zb MM2 ANO + + From 7f7cfefe5d6c96e24dfe751a5f250f1a1d7f21a9 Mon Sep 17 00:00:00 2001 From: rdelhaye <38891240+rdelhaye@users.noreply.github.com> Date: Fri, 18 May 2018 14:43:19 +0100 Subject: [PATCH 003/170] Create readme.txt --- Scripts/readme.txt | 1 + 1 file changed, 1 insertion(+) create mode 100644 Scripts/readme.txt diff --git a/Scripts/readme.txt b/Scripts/readme.txt new file mode 100644 index 0000000..4f724d2 --- /dev/null +++ b/Scripts/readme.txt @@ -0,0 +1 @@ +This is a directory by RDelhaye to contain various scripts for testing & execution of CPD codes From 9db2a2cf99108025b7e0ba51d764b3c91e9b362b Mon Sep 17 00:00:00 2001 From: rdelhaye <38891240+rdelhaye@users.noreply.github.com> Date: Fri, 18 May 2018 14:45:05 +0100 Subject: [PATCH 004/170] Add files via upload Collection of scripts from RDelhaye. Included are mag_grid2.npz (compressed Tellus aeromag data as of 18/05/2018), and tst_data.npz, a synthetic data set from the Bouligand_forward.py code. --- Scripts/BFwdTest.py | 154 ++++++++++++++++++++++++++++++ Scripts/CPD_Pts_find.sh | 6 ++ Scripts/IapetusCheck.py | 138 +++++++++++++++++++++++++++ Scripts/LinearFitScratch.py | 182 ++++++++++++++++++++++++++++++++++++ Scripts/RobTest.py | 122 ++++++++++++++++++++++++ Scripts/RosettePlot.sh | 20 ++++ Scripts/mag_grid2.npz | Bin 0 -> 3931407 bytes Scripts/tst_data.npz | Bin 0 -> 343823 bytes 8 files changed, 622 insertions(+) create mode 100644 Scripts/BFwdTest.py create mode 100644 Scripts/CPD_Pts_find.sh create mode 100644 Scripts/IapetusCheck.py create mode 100644 Scripts/LinearFitScratch.py create mode 100644 Scripts/RobTest.py create mode 100644 Scripts/RosettePlot.sh create mode 100644 Scripts/mag_grid2.npz create mode 100644 Scripts/tst_data.npz diff --git a/Scripts/BFwdTest.py b/Scripts/BFwdTest.py new file mode 100644 index 0000000..8ae3dfd --- /dev/null +++ b/Scripts/BFwdTest.py @@ -0,0 +1,154 @@ +import numpy as np +import matplotlib.pyplot as plt +import pycurious +# %matplotlib inline + +#xmin = 600000. +#xmax = 660000. +#ymin = 780000. +#ymax = 835000. + +#nx = int((xmax - xmin)/200.) +#ny = int((ymax - ymin)/200.) +#xcoords, dx = np.linspace(xmin, xmax, nx, retstep=True) +#ycoords, dy = np.linspace(ymin, ymax, ny, retstep=True) +#xq, yq = np.meshgrid(xcoords, ycoords) +# importing the data and gridding is time consuming +# see if the grid exists first, otherwise proceed gridding +# ORIGINAL +# try: + # with np.load('mag_grid.npz') as f: + # mag_grid = f['data'] +# except: + # from scipy.interpolate import griddata + # # import data X | Y | Z | nT + # xc, yc, zc, mag = np.loadtxt('./mag2.xyz', dtype=np.float32, unpack=True) + # mag_grid = griddata(np.column_stack([xc, yc]), mag, (xq, yq)) + # # save grid + # np.savez_compressed('mag_grid.npz', data=mag_grid) + +# NEW +try: + # with np.load('mag_grid.npz') as f: + # with np.load('mag2.npz') as f: + with np.load('tst_data.npz') as f: + print('tst_data.npz found...') + mag_grid = f['data'] + xmin = f['xm'] + xmin = xmin[()] + xmax = f['xM'] + xmax = xmax[()] + ymin = f['ym'] + ymin = ymin[()] + ymax = f['yM'] + ymax = ymax[()] + + # print(mag2[:,0]) + # xc, yc, zc, mag = mag2 + # mag_grid = griddata(np.column_stack([mag2[:,0], mag2[:,1]]), mag2[:,3], (xq, yq)) +except: + print('making tst_data.npz...') + from scipy.interpolate import griddata + # import data X | Y | Z | nT + xc, yc, mag = np.loadtxt('./test_mag_data.txt', dtype=np.float32, unpack=True) + xmin = np.nanmin(xc[0]) + xmax = np.nanmax(xc[-1]) + ymin = np.nanmin(yc[0]) + ymax = np.nanmax(yc[-1]) + + nx = int((xmax - xmin)/1000.) + ny = int((ymax - ymin)/1000.) + #print(xmin,xmax,ymin,ymax,nx,ny) + xcoords, dx = np.linspace(xmin, xmax, nx, retstep=True) + ycoords, dy = np.linspace(ymin, ymax, ny, retstep=True) + xq, yq = np.meshgrid(xcoords, ycoords) + mag_grid = griddata(np.column_stack([xc, yc]), mag, (xq, yq),method='nearest') + #mag_grid = griddata(np.column_stack([mag2[:,0], mag2[:,1]]), mag2[:,3], (xq, yq),method='nearest') + # save grid + np.savez_compressed('tst_data.npz', data=mag_grid,xm=xmin,xM=xmax,ym=ymin,yM=ymax) + +#print(mag_grid.shape,xmin,xmax,ymin,ymax) +#plt.imshow(mag_grid, extent=(xmin, xmax, ymin, ymax), origin='lower') +#plt.show() +#exit() + + +## plt.imshow(mag_grid, extent=(xmin, xmax, ymin, ymax), origin='lower') +## initialise CurieGrid object +grid = pycurious.CurieGrid(mag_grid, xmin, xmax, ymin, ymax) + + +## Let's not!' +## let's pick a point in the centre of the study area +xpt = xmin + (xmax-xmin)/2 +ypt = ymin + (ymax-ymin)/2 + +subgrid = grid.subgrid(xpt, ypt, 125000.) +S, k, sigma2 = grid.radial_spectrum(subgrid, taper=None) + +DK=0.025 +nb=20 +hmap=np.zeros((nb,nb)) +ZT=np.zeros((nb,1)) +ZO=np.zeros((nb,1)) +for j in range(1,nb,1): + for l in range(1,nb,1): + print((j-1)*0.05, (j)*0.05,(l-1)*0.05, (l)*0.05) + Zb,eZb, Ztr, Zor = grid.Tanakac(S, k, sigma2,(j-1)*DK, (j)*DK,(l-1)*DK, (l)*DK) + hmap[j,l]=Zb + ZO[l]=Zor + ZT[j]=Ztr + +fig2 = plt.figure(figsize=(8,8)) +ax2 = fig2.add_subplot(111, xlabel=r'$\nu$ window of $\Phi/|k|$ (km$^{-1}$)', ylabel=r'$\nu$ window of $\Phi$') +#im2 = ax2.imshow(np.clip(hmap,-30,-10), extent=[0., (nb+1)*DK, 0., (nb+1)*DK], aspect=1) +im2 = ax2.imshow(np.clip(hmap,-30,-10), extent=[0., 0.5, 0., 0.5], aspect=1) +fig2.colorbar(im2, label='CPD') +plt.title('Heatmap of CPD') +plt.savefig('Heatmap.jpg') +plt.show() + + + + +#f.write(str(xpt)) +# compute radial spectrum + +Zb,eZb = grid.Tanaka(S, k, sigma2,kmin=0.05, kmax=0.25) + +print(Zb,eZb) +#exit() + +#print(xpt,ypt) +## get a subsection of the grid +#subgrid = grid.subgrid(xpt, ypt, 50000.) +#print(subgrid.shape) +## compute radial spectrum +#S, k, sigma2 = grid.radial_spectrum(subgrid, taper=None) +## fig, (ax1, ax2) = plt.subplots(1,2,figsize=(12,4)) +## ax1.plot(k, abs(S)) +##ax2.plot(sf, abs(S)) +#Zb,eZb = grid.Tanaka(S, k, sigma2,kmin=0.05, kmax=0.2) +#print(Zb,eZb) + +## INSTEAD +## Let's read a central point from file pts.xy +#cx,cy=np.loadtxt('pts.xy',unpack=True) +#f=open("CPD_pts.txt","w+") +#for xpt, ypt in zip(cx,cy): + ### get a subsection of the grid + #subgrid = grid.subgrid(xpt, ypt, 75000.) + #if subgrid.shape[0] != subgrid.shape[1]: + #continue + ##f.write(str(xpt)) + ## compute radial spectrum + #try: + #S, k, sigma2 = grid.radial_spectrum(subgrid, taper=None) + #Zb,eZb = grid.Tanaka(S, k, sigma2,kmin=0.05, kmax=0.2) + ##print(xpt,ypt,Zb,eZb) + #f.write(' '.join([str(xpt),str(ypt),str(Zb),str(eZb),"\n"])) + #except: + #print('Error for ',xpt,ypt) + ##break + +#f.close() diff --git a/Scripts/CPD_Pts_find.sh b/Scripts/CPD_Pts_find.sh new file mode 100644 index 0000000..c21b3c7 --- /dev/null +++ b/Scripts/CPD_Pts_find.sh @@ -0,0 +1,6 @@ +#!/bin/bash +gmtset PROJ_SCALE_FACTOR 0.999820 +x0= +y0= + +# Find SW point that's on land \ No newline at end of file diff --git a/Scripts/IapetusCheck.py b/Scripts/IapetusCheck.py new file mode 100644 index 0000000..61ad335 --- /dev/null +++ b/Scripts/IapetusCheck.py @@ -0,0 +1,138 @@ +import numpy as np +import matplotlib.pyplot as plt +import pycurious +# %matplotlib inline + + +#nx = int((xmax - xmin)/200.) +#ny = int((ymax - ymin)/200.) +#xcoords, dx = np.linspace(xmin, xmax, nx, retstep=True) +#ycoords, dy = np.linspace(ymin, ymax, ny, retstep=True) +#xq, yq = np.meshgrid(xcoords, ycoords) +# importing the data and gridding is time consuming +# see if the grid exists first, otherwise proceed gridding +# ORIGINAL +# try: + # with np.load('mag_grid.npz') as f: + # mag_grid = f['data'] +# except: + # from scipy.interpolate import griddata + # # import data X | Y | Z | nT + # xc, yc, zc, mag = np.loadtxt('./mag2.xyz', dtype=np.float32, unpack=True) + # mag_grid = griddata(np.column_stack([xc, yc]), mag, (xq, yq)) + # # save grid + # np.savez_compressed('mag_grid.npz', data=mag_grid) + +# NEW +try: + # with np.load('mag_grid.npz') as f: + # with np.load('mag2.npz') as f: + with np.load('mag_grid2.npz') as f: + print('mag_grid2.npz found...') + mag_grid = f['data'] + xmin = f['xm'] + xmin = xmin[()] + xmax = f['xM'] + xmax = xmax[()] + ymin = f['ym'] + ymin = ymin[()] + ymax = f['yM'] + ymax = ymax[()] + + # print(mag2[:,0]) + # xc, yc, zc, mag = mag2 + # mag_grid = griddata(np.column_stack([mag2[:,0], mag2[:,1]]), mag2[:,3], (xq, yq)) +except: + print('making mag_grid2.npz...') + from scipy.interpolate import griddata + # import data X | Y | Z | nT + with np.load('mag2.npz') as f: + print('mag2.npz found...') + mag2 = f['mag2'] + # xc, yc, zc, mag = np.loadtxt('./mag2.xyz', dtype=np.float32, unpack=True) + print(mag2[0,]) + xmin = np.nanmin(mag2[:,0],axis=0) + xmax = np.nanmax(mag2[:,0],axis=0) + ymin = np.nanmin(mag2[:,1],axis=0) + ymax = np.nanmax(mag2[:,1],axis=0) + + nx = int((xmax - xmin)/200.) + ny = int((ymax - ymin)/200.) + print(xmin,xmax,ymin,ymax,nx,ny) + xcoords, dx = np.linspace(xmin, xmax, nx, retstep=True) + ycoords, dy = np.linspace(ymin, ymax, ny, retstep=True) + xq, yq = np.meshgrid(xcoords, ycoords) + mag_grid = griddata(np.column_stack([mag2[:,0], mag2[:,1]]), mag2[:,3], (xq, yq),method='nearest') + # save grid + np.savez_compressed('mag_grid2.npz', data=mag_grid,xm=xmin,xM=xmax,ym=ymin,yM=ymax) + +#print(mag_grid.shape,xmin,xmax,ymin,ymax) +#plt.imshow(mag_grid, extent=(xmin, xmax, ymin, ymax), origin='lower') +#plt.show() +#exit() + + + + +## plt.imshow(mag_grid, extent=(xmin, xmax, ymin, ymax), origin='lower') +## initialise CurieGrid object +grid = pycurious.CurieGrid(mag_grid, xmin, xmax, ymin, ymax) + + +## Let's not!' +## let's pick a point in the centre of the study area +#xpt = xmin + (xmax-xmin)/2 +#ypt = ymin + (ymax-ymin)/2 +#print(xpt,ypt) +## get a subsection of the grid +#subgrid = grid.subgrid(xpt, ypt, 50000.) +#print(subgrid.shape) +## compute radial spectrum +#S, k, sigma2 = grid.radial_spectrum(subgrid, taper=None) +## fig, (ax1, ax2) = plt.subplots(1,2,figsize=(12,4)) +## ax1.plot(k, abs(S)) +##ax2.plot(sf, abs(S)) +#Zb,eZb = grid.Tanaka(S, k, sigma2,kmin=0.05, kmax=0.2) +#print(Zb,eZb) + +f=open("iap_rosette.txt","w+") +xpt=632781 +ypt=805755 + ## get a subsection of the grid +subgrid = grid.subgrid(xpt, ypt, 75000.) +#if subgrid.shape[0] != subgrid.shape[1]: +# continue + #f.write(str(xpt)) + # compute radial spectrum +#try: +S, k, dtheta = grid.azimuthal_spectrum(subgrid, taper=None, scale=0.001, theta=5.0) + +# plot +#fig = plt.figure(figsize=(12,3)) +#ax1 = fig.add_subplot(111, xlabel='wavenumber (rad/km)', ylabel='theta ($^{\circ}$)') +#im1 = ax1.imshow(S, extent=[k.min(), k.max(), dtheta.min(), dtheta.max()], aspect=0.025) +#fig.colorbar(im1, label='Azimuthal spectrum') +#plt.show() + +for t in range(dtheta.size): + Zb= grid.Tanakab(S[t,:], k, kmin=0.05, kmax=0.2) + f.write(' '.join([str(dtheta[t]),str(Zb),"\n"])) +#print(Zb) + +#S, k, sigma2 = grid.radial_spectrum(subgrid, taper=None) + #Zb,eZb = grid.Tanaka(S, k, sigma2,kmin=0.05, kmax=0.2) + #print(xpt,ypt,Zb,eZb) + #f.write(' '.join([str(xpt),str(ypt),str(Zb),str(eZb),"\n"])) +#except: +# print('Error for ',xpt,ypt) + + + + +#cx,cy=np.loadtxt('pts.xy',unpack=True) + + + + + +f.close() diff --git a/Scripts/LinearFitScratch.py b/Scripts/LinearFitScratch.py new file mode 100644 index 0000000..ebcd90c --- /dev/null +++ b/Scripts/LinearFitScratch.py @@ -0,0 +1,182 @@ +import numpy as np +import matplotlib.pyplot as plt +import pycurious +try: + # with np.load('mag_grid.npz') as f: + # with np.load('mag2.npz') as f: + with np.load('mag_grid2.npz') as f: + print('mag_grid2.npz found...') + mag_grid = f['data'] + xmin = f['xm'] + xmin = xmin[()] + xmax = f['xM'] + xmax = xmax[()] + ymin = f['ym'] + ymin = ymin[()] + ymax = f['yM'] + ymax = ymax[()] +except: + print('making mag_grid2.npz...') + from scipy.interpolate import griddata + # import data X | Y | Z | nT + with np.load('mag2.npz') as f: + print('mag2.npz found...') + mag2 = f['mag2'] + print(mag2[0,]) + xmin = np.nanmin(mag2[:,0],axis=0) + xmax = np.nanmax(mag2[:,0],axis=0) + ymin = np.nanmin(mag2[:,1],axis=0) + ymax = np.nanmax(mag2[:,1],axis=0) + + nx = int((xmax - xmin)/200.) + ny = int((ymax - ymin)/200.) + print(xmin,xmax,ymin,ymax,nx,ny) + xcoords, dx = np.linspace(xmin, xmax, nx, retstep=True) + ycoords, dy = np.linspace(ymin, ymax, ny, retstep=True) + xq, yq = np.meshgrid(xcoords, ycoords) + mag_grid = griddata(np.column_stack([mag2[:,0], mag2[:,1]]), mag2[:,3], (xq, yq),method='nearest') + # save grid + np.savez_compressed('mag_grid2.npz', data=mag_grid,xm=xmin,xM=xmax,ym=ymin,yM=ymax) + +grid = pycurious.CurieGrid(mag_grid, xmin, xmax, ymin, ymax) + + + + +xpt=632781 +ypt=805755 + ## get a subsection of the grid +subgrid = grid.subgrid(xpt, ypt, 75000.) + +S, k, sigma2 = grid.radial_spectrum(subgrid, taper=None) + + +#ax1.plot(k, abs(S)) +# ok, let's plot the interval derivatives of dS/dk +Sn=np.log(np.exp(S)/(k/(2.0*np.pi))) +dS = np.zeros((S.size-1, 1)) +dSn = np.zeros((S.size-1, 1)) +dk = np.zeros((S.size-1, 1)) +#print(S.size,dS.size) +def running_mean(x, N): + cumsum = np.cumsum(np.insert(x, 0, 0)) + return (cumsum[N:] - cumsum[:-N]) / float(N) +for x in range(dS.size): + dS[x]=(abs(S[x+1])-abs(S[x]))/(k[x+1]-k[x]) + dSn[x]=(abs(Sn[x+1])-abs(Sn[x]))/(k[x+1]-k[x]) + dk[x]=(k[x+1]+k[x])/2 + #print(dS) + #break + #print(str((S(x+1)-S(x))/(k(x+1)-k(1)))) +# let's compute variance over the same 5 pts... +dSm=running_mean(dS,5) +dSnm=running_mean(dSn,5) +var=np.zeros(dSm.size) +varn=np.zeros(dSm.size) +for x in range(var.size): + var[x]=np.var(dS[x:x+5]) + varn[x]=np.var(dSn[x:x+5]) +#print(var) +#ax2.plot(dk,dS,dk[2:-2],dSm) +plt.figure(figsize=(20,12)) +plt.subplot(2,3,1) +plt.plot(k/(2.0*np.pi),S/(2.0*np.pi)) +plt.title('$\Phi$') +plt.subplot(2,3,2) +plt.plot(dk/(2.0*np.pi),dS/(2.0*np.pi),dk[2:-2]/(2.0*np.pi),dSm/(2.0*np.pi)) +plt.title('$\partial\Phi/\partial k$') +plt.legend(['Original','5pt mean']) +plt.subplot(2,3,3) +plt.plot(dk[2:-2]/(2.0*np.pi),var) +plt.title('$\sigma^2(\partial\Phi/\partial k($') +plt.subplot(2,3,4) +plt.plot(k/(2.0*np.pi),Sn/(2.0*np.pi)) +plt.title('$\Phi/|k|$') +plt.xlabel('Spatial Frequency') +plt.subplot(2,3,5) +plt.plot(dk/(2.0*np.pi),dSn/(2.0*np.pi),dk[2:-2]/(2.0*np.pi),dSnm/(2.0*np.pi)) +plt.title('$\partial(\Phi/|k|)/\partial k$') +plt.legend(['Original','5pt mean']) +plt.xlabel('Spatial Frequency') +plt.subplot(2,3,6) +plt.plot(dk[2:-2]/(2.0*np.pi),varn) +plt.title('$\sigma^2(\partial(\Phi/|k|)/\partial k($') +plt.xlabel('Spatial Frequency') +plt.savefig('dSpectra.jpg') + +f2, ax2 = plt.subplots(1,1,figsize=(12,4)) +ax2.plot(k/(2.0*np.pi),S/(2.0*np.pi),k/(2.0*np.pi),np.log(np.exp(S)/(k/(2.0*np.pi)))/(2.0*np.pi)) +plt.xlabel('Spatial Frequency$') +plt.legend(['$\Phi$','$\Phi/|k|$']) +plt.title('Spectra') +plt.savefig('Spectra.jpg') +#plt.show() +#exit() +#ax4.plot(k/(2.0*np.pi),np.log(np.exp(S)/(k/(2.0*np.pi)))/(2.0*np.pi)) + + +#print(k/(2.0*np.pi)) +DK=0.05 +nb=48 +hmap=np.zeros((nb,nb)) +ZT=np.zeros((nb,1)) +ZO=np.zeros((nb,1)) +for j in range(1,nb,1): + for l in range(1,nb,1): + #print((j-1)*0.05, (j)*0.05) + Zb,eZb, Ztr, Zor = grid.Tanakac(S, k, sigma2,(j-1)*DK, (j)*DK,(l-1)*DK, (l)*DK) + hmap[j,l]=Zb + ZO[l]=Zor + ZT[j]=Ztr + +fig2 = plt.figure(figsize=(8,8)) +ax2 = fig2.add_subplot(111, xlabel='$k$ window of $\Phi/|k|$', ylabel='$k$ window of $\Phi$') +#im2 = ax2.imshow(np.clip(hmap,-30,-10), extent=[0., (nb+1)*DK, 0., (nb+1)*DK], aspect=1) +im2 = ax2.imshow(np.clip(hmap,-30,-10), extent=[0., 0.5, 0., 0.5], aspect=1) +fig2.colorbar(im2, label='CPD') +plt.title('Heatmap of CPD') +plt.savefig('Heatmap.jpg') + +fig4 = plt.figure(figsize=(12,6)) +ax5 = fig4.add_subplot(111,xlabel='k', ylabel='Z (km)') +nk=np.linspace(0, nb*DK, nb) +ax5.plot(nk,ZT,nk,ZO) +plt.legend(['Z_t','Z_o']) +plt.ylim(-40,0) +plt.savefig('Z_dist.jpg') + +plt.show() +#plt.clim(-50,0) +#exit() + + + + + + + + + + + +### INSTEAD +### Let's read a central point from file pts.xy +#cx,cy=np.loadtxt('pts.xy',unpack=True) +#f=open("CPD_pts.txt","w+") +#for xpt, ypt in zip(cx,cy): + ### get a subsection of the grid + #subgrid = grid.subgrid(xpt, ypt, 75000.) + #if subgrid.shape[0] != subgrid.shape[1]: + #continue + ##f.write(str(xpt)) + ## compute radial spectrum + #try: + #S, k, sigma2 = grid.radial_spectrum(subgrid, taper=None) + #Zb,eZb = grid.Tanaka(S, k, sigma2,kmin=0.05, kmax=0.2) + ##print(xpt,ypt,Zb,eZb) + #f.write(' '.join([str(xpt),str(ypt),str(Zb),str(eZb),"\n"])) + #except: + #print('Error for ',xpt,ypt) + ##break + +#f.close() diff --git a/Scripts/RobTest.py b/Scripts/RobTest.py new file mode 100644 index 0000000..416c906 --- /dev/null +++ b/Scripts/RobTest.py @@ -0,0 +1,122 @@ +import numpy as np +import matplotlib.pyplot as plt +import pycurious +# %matplotlib inline + +#xmin = 600000. +#xmax = 660000. +#ymin = 780000. +#ymax = 835000. + +#nx = int((xmax - xmin)/200.) +#ny = int((ymax - ymin)/200.) +#xcoords, dx = np.linspace(xmin, xmax, nx, retstep=True) +#ycoords, dy = np.linspace(ymin, ymax, ny, retstep=True) +#xq, yq = np.meshgrid(xcoords, ycoords) +# importing the data and gridding is time consuming +# see if the grid exists first, otherwise proceed gridding +# ORIGINAL +# try: + # with np.load('mag_grid.npz') as f: + # mag_grid = f['data'] +# except: + # from scipy.interpolate import griddata + # # import data X | Y | Z | nT + # xc, yc, zc, mag = np.loadtxt('./mag2.xyz', dtype=np.float32, unpack=True) + # mag_grid = griddata(np.column_stack([xc, yc]), mag, (xq, yq)) + # # save grid + # np.savez_compressed('mag_grid.npz', data=mag_grid) + +# NEW +try: + # with np.load('mag_grid.npz') as f: + # with np.load('mag2.npz') as f: + with np.load('mag_grid2.npz') as f: + print('mag_grid2.npz found...') + mag_grid = f['data'] + xmin = f['xm'] + xmin = xmin[()] + xmax = f['xM'] + xmax = xmax[()] + ymin = f['ym'] + ymin = ymin[()] + ymax = f['yM'] + ymax = ymax[()] + + # print(mag2[:,0]) + # xc, yc, zc, mag = mag2 + # mag_grid = griddata(np.column_stack([mag2[:,0], mag2[:,1]]), mag2[:,3], (xq, yq)) +except: + print('making mag_grid2.npz...') + from scipy.interpolate import griddata + # import data X | Y | Z | nT + with np.load('mag2.npz') as f: + print('mag2.npz found...') + mag2 = f['mag2'] + # xc, yc, zc, mag = np.loadtxt('./mag2.xyz', dtype=np.float32, unpack=True) + print(mag2[0,]) + xmin = np.nanmin(mag2[:,0],axis=0) + xmax = np.nanmax(mag2[:,0],axis=0) + ymin = np.nanmin(mag2[:,1],axis=0) + ymax = np.nanmax(mag2[:,1],axis=0) + + nx = int((xmax - xmin)/200.) + ny = int((ymax - ymin)/200.) + print(xmin,xmax,ymin,ymax,nx,ny) + xcoords, dx = np.linspace(xmin, xmax, nx, retstep=True) + ycoords, dy = np.linspace(ymin, ymax, ny, retstep=True) + xq, yq = np.meshgrid(xcoords, ycoords) + mag_grid = griddata(np.column_stack([mag2[:,0], mag2[:,1]]), mag2[:,3], (xq, yq),method='nearest') + # save grid + np.savez_compressed('mag_grid2.npz', data=mag_grid,xm=xmin,xM=xmax,ym=ymin,yM=ymax) + +#print(mag_grid.shape,xmin,xmax,ymin,ymax) +#plt.imshow(mag_grid, extent=(xmin, xmax, ymin, ymax), origin='lower') +#plt.show() +#exit() + + + + +## plt.imshow(mag_grid, extent=(xmin, xmax, ymin, ymax), origin='lower') +## initialise CurieGrid object +grid = pycurious.CurieGrid(mag_grid, xmin, xmax, ymin, ymax) + + +## Let's not!' +## let's pick a point in the centre of the study area +#xpt = xmin + (xmax-xmin)/2 +#ypt = ymin + (ymax-ymin)/2 +#print(xpt,ypt) +## get a subsection of the grid +#subgrid = grid.subgrid(xpt, ypt, 50000.) +#print(subgrid.shape) +## compute radial spectrum +#S, k, sigma2 = grid.radial_spectrum(subgrid, taper=None) +## fig, (ax1, ax2) = plt.subplots(1,2,figsize=(12,4)) +## ax1.plot(k, abs(S)) +##ax2.plot(sf, abs(S)) +#Zb,eZb = grid.Tanaka(S, k, sigma2,kmin=0.05, kmax=0.2) +#print(Zb,eZb) + +## INSTEAD +## Let's read a central point from file pts.xy +cx,cy=np.loadtxt('pts.xy',unpack=True) +f=open("CPD_pts.txt","w+") +for xpt, ypt in zip(cx,cy): + ## get a subsection of the grid + subgrid = grid.subgrid(xpt, ypt, 75000.) + if subgrid.shape[0] != subgrid.shape[1]: + continue + #f.write(str(xpt)) + # compute radial spectrum + try: + S, k, sigma2 = grid.radial_spectrum(subgrid, taper=None) + Zb,eZb = grid.Tanaka(S, k, sigma2,kmin=0.05, kmax=0.2) + #print(xpt,ypt,Zb,eZb) + f.write(' '.join([str(xpt),str(ypt),str(Zb),str(eZb),"\n"])) + except: + print('Error for ',xpt,ypt) + #break + +f.close() diff --git a/Scripts/RosettePlot.sh b/Scripts/RosettePlot.sh new file mode 100644 index 0000000..64d5fc7 --- /dev/null +++ b/Scripts/RosettePlot.sh @@ -0,0 +1,20 @@ +#!/bin/bash + +oFile='RosetteTest.ps' + +# Several plots... +# plot of theta vs CPD + +J=' -JX8c/6c' +R=' -R0/180/-35/-15' +psbasemap $J $R -Ba30/a10g5::neWS -K > $oFile +cat iap_rosette.txt | psxy -R -J -O -K -W2p,blue>> $oFile +echo '90 -35 Azimuth (@+o@+)' | pstext -R -J -O -K -N -Ya-1.25c >> $oFile +echo '0 -25 CPD (km)' | pstext -R -J -O -K -N -F+a90 -Xa-1.25c >> $oFile + +psbasemap $J -R0/2/-35/-15 -B/a10g5::neWS -O -K -Y10c >> $oFile +echo '1 -23.7 -19.7 -22.3 -24.48 -29.09' | psxy -R -J -EY -G127 -O -K >> $oFile +echo '1 -23.7 -19.7 -22.3 -24.48 -29.09' | psxy -R -J -Sc0.2c -G127 -O -K >> $oFile + +# box & whisker +# fancy rosette...? \ No newline at end of file diff --git a/Scripts/mag_grid2.npz b/Scripts/mag_grid2.npz new file mode 100644 index 0000000000000000000000000000000000000000..b8565d34d35d8d994604b9abf423148177ae5e90 GIT binary patch literal 3931407 zcmYhidpwiGqcT3-`$_b_woDw9*=8(T-UDcdSBQ3^?tsd&*$rP-Lc%WSLUz3{yHG~ zocha5`bxCSj^SS~NWA|Y@pKPy*Ypd3t|6fh?Z>l(*Y1_%efR(V=KY&zo^BSKXHOlr z_>~=XCUVNBLg8+OlZ~Z~uW6aRZ%TWv#_`zI&*=}+OKR^^O72})y>o8Uw%p)Ef_>pC zZwn44=X|)l=a;pc09x-)HKqh-MA8@ycuJqo;|$%cbw&k9Hf8`-{h5*Tbt}$&bg3xD z)apof3=Mi=eyQXTpVIf1xQ&mLo!#0B;Q_Soi~bv2@& z;~BbBGlgcb4%x4}xQO3qR66u$QH9kmg|E9J<)#XgqvYndG94%ED-|$oB#RO`Rip)x 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| 0 {Scripts => Examples/Scripts}/RosettePlot.sh | 0 {Scripts => Examples/Scripts}/mag_grid2.npz | Bin {Scripts => Examples/Scripts}/readme.txt | 0 {Scripts => Examples/Scripts}/tst_data.npz | Bin {examples => Examples}/british_isles.py | 0 {examples => Examples}/british_isles_parallel.py | 0 .../british_isles_parallel_sensitivity.py | 0 .../british_isles_parallel_windows.py | 0 13 files changed, 0 insertions(+), 0 deletions(-) rename {Scripts => Examples/Scripts}/BFwdTest.py (100%) rename {Scripts => Examples/Scripts}/CPD_Pts_find.sh (100%) rename {Scripts => Examples/Scripts}/IapetusCheck.py (100%) rename {Scripts => Examples/Scripts}/LinearFitScratch.py (100%) rename {Scripts => Examples/Scripts}/RobTest.py (100%) rename {Scripts => Examples/Scripts}/RosettePlot.sh (100%) rename {Scripts => Examples/Scripts}/mag_grid2.npz (100%) rename {Scripts => Examples/Scripts}/readme.txt (100%) rename {Scripts => Examples/Scripts}/tst_data.npz (100%) rename {examples => Examples}/british_isles.py (100%) rename {examples => Examples}/british_isles_parallel.py (100%) rename {examples => Examples}/british_isles_parallel_sensitivity.py (100%) rename {examples => Examples}/british_isles_parallel_windows.py (100%) diff --git a/Scripts/BFwdTest.py b/Examples/Scripts/BFwdTest.py similarity index 100% rename from Scripts/BFwdTest.py rename to Examples/Scripts/BFwdTest.py diff --git a/Scripts/CPD_Pts_find.sh b/Examples/Scripts/CPD_Pts_find.sh similarity index 100% rename from Scripts/CPD_Pts_find.sh rename to Examples/Scripts/CPD_Pts_find.sh diff --git a/Scripts/IapetusCheck.py b/Examples/Scripts/IapetusCheck.py similarity index 100% rename from Scripts/IapetusCheck.py rename to Examples/Scripts/IapetusCheck.py diff --git a/Scripts/LinearFitScratch.py b/Examples/Scripts/LinearFitScratch.py similarity index 100% rename from Scripts/LinearFitScratch.py rename to Examples/Scripts/LinearFitScratch.py diff --git a/Scripts/RobTest.py b/Examples/Scripts/RobTest.py similarity index 100% rename from Scripts/RobTest.py rename to Examples/Scripts/RobTest.py diff --git a/Scripts/RosettePlot.sh b/Examples/Scripts/RosettePlot.sh similarity index 100% rename from Scripts/RosettePlot.sh rename to Examples/Scripts/RosettePlot.sh diff --git a/Scripts/mag_grid2.npz b/Examples/Scripts/mag_grid2.npz similarity index 100% rename from Scripts/mag_grid2.npz rename to Examples/Scripts/mag_grid2.npz diff --git a/Scripts/readme.txt b/Examples/Scripts/readme.txt similarity index 100% rename from Scripts/readme.txt rename to Examples/Scripts/readme.txt diff --git a/Scripts/tst_data.npz b/Examples/Scripts/tst_data.npz similarity index 100% rename from Scripts/tst_data.npz rename to Examples/Scripts/tst_data.npz diff --git a/examples/british_isles.py b/Examples/british_isles.py similarity index 100% rename from examples/british_isles.py rename to Examples/british_isles.py diff --git a/examples/british_isles_parallel.py b/Examples/british_isles_parallel.py similarity index 100% rename from examples/british_isles_parallel.py rename to Examples/british_isles_parallel.py diff --git a/examples/british_isles_parallel_sensitivity.py b/Examples/british_isles_parallel_sensitivity.py similarity index 100% rename from examples/british_isles_parallel_sensitivity.py rename to Examples/british_isles_parallel_sensitivity.py diff --git a/examples/british_isles_parallel_windows.py b/Examples/british_isles_parallel_windows.py similarity index 100% rename from examples/british_isles_parallel_windows.py rename to Examples/british_isles_parallel_windows.py From 8395d53d6a90d2bf1f90dd24216edb41eb4c62c1 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Mon, 25 Jun 2018 21:25:10 +0100 Subject: [PATCH 006/170] Defragmented some of the legacy code and new Notebooks --- .../Notebooks/Ex1-Plot-power-spectrum.ipynb | 269 +++++++++++++++++ ...-Compute-Curie-depth-Tanaka-approach.ipynb | 101 +++++++ ...mpute-Curie-depth-Bouligand-approach.ipynb | 236 +++++++++++++++ .../Notebooks/Ex3-Optimisation-routine.ipynb | 109 +++++++ .../Ex4-Mapping-Curie-depth-EMAG2.ipynb | 69 +++++ .../Notebooks/Ex5-parallel-processing.ipynb | 41 +++ pycurious/__init__.py | 2 +- pycurious/curie.py | 278 +++++++++--------- pycurious/optimise.py | 7 +- 9 files changed, 963 insertions(+), 149 deletions(-) create mode 100644 Examples/Notebooks/Ex1-Plot-power-spectrum.ipynb create mode 100644 Examples/Notebooks/Ex2a-Compute-Curie-depth-Tanaka-approach.ipynb create mode 100644 Examples/Notebooks/Ex2b-Compute-Curie-depth-Bouligand-approach.ipynb create mode 100644 Examples/Notebooks/Ex3-Optimisation-routine.ipynb create mode 100644 Examples/Notebooks/Ex4-Mapping-Curie-depth-EMAG2.ipynb create mode 100644 Examples/Notebooks/Ex5-parallel-processing.ipynb diff --git a/Examples/Notebooks/Ex1-Plot-power-spectrum.ipynb b/Examples/Notebooks/Ex1-Plot-power-spectrum.ipynb new file mode 100644 index 0000000..4334a06 --- /dev/null +++ b/Examples/Notebooks/Ex1-Plot-power-spectrum.ipynb @@ -0,0 +1,269 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Example 1 - Plot power spectra\n", + "\n", + "`PyCurious` offers convenience functions to extract the radial power spectrum. This has been derived analytically by Bouligand *et al.* 2009.\n", + "\n", + "In this notebook we plot the radial power spectrum using the analytical expression, and compare it to the spectrum computed from a synthetic magnetic anomaly. (This can be generated from `Bouligand_forward.py` in the `tests` directory.)\n", + "\n", + "### Contents\n", + "\n", + "- [Analytical solution](#Analytical-solution)\n", + "- [Radial power spectrum](#Power-spectrum-from-FFT)\n", + "- [Azimuthal power spectrum](#Azimuthal-power-spectrum)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "\n", + "import pycurious" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Analytical solution\n", + "\n", + "The analytic solution to the power spectrum is given in Equation 4 of [Bouligand *et al.*, 2009](http://doi.wiley.com/10.1029/2009JB006494).\n", + "\n", + "where the shape of the curve depends on 4 variables:\n", + "\n", + "- $\\beta$ - a fractal parameter\n", + "- $z_t$ - top of magnetic sources\n", + "- $\\Delta z$ - thickness of the magnetic layer\n", + "- $C$ - a field constant" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# wavenumber range\n", + "k = np.linspace(1e-3, 3, 10000)\n", + "\n", + "# Bouligand 2009 parameters\n", + "beta = 3.0\n", + "zt = 1.0\n", + "dz = 20.0" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# plot Bouligand et al. 2009 curves\n", + "\n", + "fig, (ax1, ax2, ax3) = plt.subplots(1,3, figsize=(14,8),)\n", + "\n", + "# vary zt\n", + "for zti in np.arange(0.0, 2.5, 0.5):\n", + " S = pycurious.bouligand2009(beta, zti, dz, k)\n", + " S -= S.max()\n", + " ax1.semilogx(k, S, label=r'$z_t$ = {} km'.format(zti))\n", + "\n", + "# vary dz\n", + "for dzi in [10., 20., 50., 100., 200.]:\n", + " S = pycurious.bouligand2009(beta, zt, dzi, k)\n", + " S -= S.min()\n", + " ax2.semilogx(k, S, label=r'$\\Delta z$ = {} km'.format(dzi))\n", + "\n", + "# vary beta\n", + "for betai in np.arange(0, 5, 1):\n", + " S = pycurious.bouligand2009(betai, zt, dz, k)\n", + " S -= S[-1]\n", + " ax3.semilogx(k, S, label=r'$\\beta$ = {}'.format(betai))\n", + "\n", + "ax1.set_ylim(-20, 0)\n", + "ax2.set_ylim(0, 20)\n", + "\n", + "ax1.legend()\n", + "ax2.legend()\n", + "ax3.legend()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Radial power spectrum\n", + "\n", + "The radial power spectrum is computed from a square window of the magnetic anomaly. Methods to select window sizes and compute the Fast Fourier Transform (FFT) belong to the `CurieGrid` object.\n", + "\n", + "`CurieGrid` achieves the following purposes:\n", + "\n", + "- Upward continuation\n", + "- Reduction to the pole\n", + "- Compute the radial power spectrum using FFT\n", + "\n", + "The shape of the radial power spectrum is heavily dependent on window size. Resolution of long wavelength features require large windows.\n", + "\n", + "> Suggestion: use a window size **> 4 times** the maximum Curie depth." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# load magnetic anomaly\n", + "mag_data = np.loadtxt(\"../data/test_mag_data.txt\")\n", + "\n", + "nx, ny = 305, 305\n", + "\n", + "x = mag_data[:,0]\n", + "y = mag_data[:,1]\n", + "d = mag_data[:,2].reshape(ny,nx)\n", + "\n", + "xmin, xmax = x.min(), x.max()\n", + "ymin, ymax = y.min(), y.max()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# initialise CurieGrid object\n", + "grid = pycurious.CurieGrid(d, xmin, xmax, ymin, ymax)\n", + "\n", + "# pick the centroid\n", + "xpt = 0.5*(xmin + xmax)\n", + "ypt = 0.5*(ymin + ymax)\n", + "\n", + "window_size = 304e3\n", + "subgrid = grid.subgrid(xpt, ypt, window_size)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# compute radial power spectrum\n", + "S, k, sigma2 = grid.radial_spectrum(subgrid)\n", + "\n", + "\n", + "# plot radial power spectrum\n", + "fig = plt.figure()\n", + "ax1 = fig.add_subplot(111, xlabel=\"wavenumber (rad/km)\", ylabel=\"radial power spectrum\")\n", + "ax1.plot(k, S, '-o')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The default taper is the hanning filter (see [`numpy.hanning`](#hanning) for more details), but other functions can be passed to taper, or simply set it to `None`." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "S, k, sigma2 = grid.radial_spectrum(subgrid, taper=None)\n", + "\n", + "\n", + "fig = plt.figure()\n", + "ax1 = fig.add_subplot(111, xlabel=\"wavenumber (rad/km)\", ylabel=\"radial power spectrum\")\n", + "ax1.plot(k, S, '-o')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Azimuthal power spectrum\n", + "\n", + "The azimuthal spectrum computes the FFT on a square window that is polarised at a range of radii. This is useful to explore linear trends in the magnetic anomaly that may align with a particular foliation or strike direction.\n", + "\n", + "```python\n", + "azimuthal_spectrum(subgrid, theta=5.0)\n", + "```\n", + "\n", + "`theta` controls the thickness of each azimuth (in degrees)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "S, k, theta = grid.azimuthal_spectrum(subgrid, theta=20.0)\n", + "\n", + "fig = plt.figure()\n", + "ax1 = fig.add_subplot(111, ylabel=r'azimuth $\\theta$', xlabel='wavenumber (rad/km)')\n", + "im1 = ax1.pcolor(k, theta, S)\n", + "fig.colorbar(im1, label='radial power spectrum')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plotting each azimuth on the power spectrum-wavenumber axis highlights the different in slope for different polarisations of the magnetic anomaly." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig = plt.figure()\n", + "ax1 = fig.add_subplot(111, xlabel=\"wavenumber (rad/km)\", ylabel=\"radial power spectrum\")\n", + "\n", + "for i, angle in enumerate(theta):\n", + " ax1.plot(k, S[i], label=r'$\\theta = {}^\\circ$'.format(angle))\n", + "\n", + "ax1.legend(bbox_to_anchor=(1,1))\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.15" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Examples/Notebooks/Ex2a-Compute-Curie-depth-Tanaka-approach.ipynb b/Examples/Notebooks/Ex2a-Compute-Curie-depth-Tanaka-approach.ipynb new file mode 100644 index 0000000..3a861d2 --- /dev/null +++ b/Examples/Notebooks/Ex2a-Compute-Curie-depth-Tanaka-approach.ipynb @@ -0,0 +1,101 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Example 2a - Compute Curie depth (Tanaka approach)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "\n", + "import pycurious" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# load x,y,anomaly\n", + "mag_data = np.loadtxt(\"../data/test_mag_data.txt\")\n", + "\n", + "nx, ny = 305, 305\n", + "\n", + "x = mag_data[:,0]\n", + "y = mag_data[:,1]\n", + "d = mag_data[:,2].reshape(ny,nx)\n", + "\n", + "xmin, xmax = x.min(), x.max()\n", + "ymin, ymax = y.min(), y.max()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# initialise CurieOptimise object\n", + "grid = pycurious.CurieOptimise(d, xmin, xmax, ymin, ymax)\n", + "\n", + "# pick the centroid\n", + "xpt = 0.5*(xmin + xmax)\n", + "ypt = 0.5*(ymin + ymax)\n", + "\n", + "window_size = 304e3\n", + "subgrid = grid.subgrid(xpt, ypt, window_size)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "S, k, sigma2 = grid.radial_spectrum_log(subgrid)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "pycurious.tanaka1999(S, k, sigma2)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.15" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Examples/Notebooks/Ex2b-Compute-Curie-depth-Bouligand-approach.ipynb b/Examples/Notebooks/Ex2b-Compute-Curie-depth-Bouligand-approach.ipynb new file mode 100644 index 0000000..ab84e0e --- /dev/null +++ b/Examples/Notebooks/Ex2b-Compute-Curie-depth-Bouligand-approach.ipynb @@ -0,0 +1,236 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Example 2b - Compute Curie depth (Bouligand approach)\n", + "\n", + "Bouligand *et al.* (2009) formulated an expression for the radial power assuming a fractal model for crustal magnetisation (see [Ex1-Plot-power-spectra](./Ex1-Plot-power-spectrum.ipynb) for analytic solution), which depends on 4 parameters:\n", + "\n", + "- $\\beta$ - a fractal parameter\n", + "- $z_t$ - top of magnetic sources\n", + "- $\\Delta z$ - thickness of the magnetic layer\n", + "- $C$ - a field constant\n", + "\n", + "These parameters can be fitted to the radial power spectrum computed from FFT to determine Curie depth ($z_\\mathrm{curie} = z_t + \\Delta z$).\n", + "\n", + "### Contents\n", + "\n", + "- [Plot radial power spectrum](#Plot-radial-power-spectrum)\n", + "- [Optimise parameters](#Optimise-parameters)\n", + "- [Varying window sizes](#Varying-window-sizes)\n", + "- [Add prior constraints](#Add-prior-constraints)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "\n", + "import pycurious" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# load x,y,anomaly\n", + "mag_data = np.loadtxt(\"../data/test_mag_data.txt\")\n", + "\n", + "nx, ny = 305, 305\n", + "\n", + "x = mag_data[:,0]\n", + "y = mag_data[:,1]\n", + "d = mag_data[:,2].reshape(ny,nx)\n", + "\n", + "xmin, xmax = x.min(), x.max()\n", + "ymin, ymax = y.min(), y.max()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Plot radial power spectrum\n", + "\n", + "The radial power spectrum is computed from a square window of the magnetic anomaly. Methods to select window sizes and compute the Fast Fourier Transform (FFT) belong to the `CurieGrid` object. We apply the default `np.hanning` taper to the power spectrum as in [Ex1-Plot-power-spectrum](#./Ex1-Plot-power-spectrum.ipynb)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "grid = pycurious.CurieOptimise(d, xmin, xmax, ymin, ymax)\n", + "\n", + "# pick the centroid\n", + "xpt = 0.5*(xmin + xmax)\n", + "ypt = 0.5*(ymin + ymax)\n", + "\n", + "window_size = 304e3\n", + "subgrid = grid.subgrid(xpt, ypt, window_size)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "S, k, sigma2 = grid.radial_spectrum(subgrid)\n", + "\n", + "# plot radial power spectrum\n", + "plt.plot(k, S, '-o')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Optimise parameters\n", + "\n", + "The `optimise` routine determines the Curie parameters ($\\beta, z_t, \\Delta z, C$) by minimising the misfit between the analytic power spectum and the computed power spectrum. Optimisation is handles by the nonlinear least-squares algorithm implemented in `scipy.optimize.minimize`.\n", + "\n", + "```python\n", + "optimise(window, xc, yc, beta=3.0, zt=1.0, dz=20.0, C=5.0)\n", + "```\n", + "\n", + "These are sane defaults to initiate the optimisation, however, values close to the final solution will result in faster convergence and stability." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "beta, zt, dz, C = grid.optimise(window_size, xpt, ypt)\n", + "print(\"beta = {:.2f}\\n zt = {:.2f}\\n dz = {:.2f}\\n C = {:.2f}\".format(beta,zt,dz,C))\n", + "\n", + "Sb = pycurious.bouligand2009(beta, zt, dz, k, C)\n", + "\n", + "# plot radial power spectrum - compare analytic against computed\n", + "plt.plot(k, S, '-o')\n", + "plt.plot(k, Sb, linewidth=2)\n", + "\n", + "print(\"\\nCurie depth is {:.2f} km\".format(zt + dz))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Varying window sizes\n", + "\n", + "Here, we observe the effect decreasing the window size has on the optimisation of Curie parameters. The number of points in the power spectrum decrease with smaller window sizes, particularly at low wavenumbers (long wavelengths). This significantly reduces the quality of Curie depth determinations for window sizes less than 200 km.\n", + "\n", + "As a rule of thumb, the window size should be > 4 times the maximum possible Curie depth that could be resolved from a study area." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "# window size in kilometres\n", + "window_size_range = [304e3, 200e3, 100e3, 50e3]\n", + "\n", + "\n", + "fig = plt.figure()\n", + "ax1 = fig.add_subplot(111)\n", + "\n", + "for i, window_size in enumerate(window_size_range):\n", + " \n", + " # compute radial power spectrum\n", + " subgrid = grid.subgrid(xpt, ypt, window_size)\n", + " S, k, sigma2 = grid.radial_spectrum(subgrid)\n", + " ax1.plot(k, S, '-o', color='C{}'.format(i))\n", + " \n", + " # optimise Curie variables\n", + " beta, zt, dz, C = grid.optimise(window_size, xpt, ypt)\n", + " print(\"beta = {:.2f}\\n zt = {:.2f}\\n dz = {:.2f}\\n C = {:.2f}\\n\".format(beta,zt,dz,C))\n", + " \n", + " Sb = pycurious.bouligand2009(beta, zt, dz, k, C)\n", + " ax1.plot(k, Sb, color='C{}'.format(i), linewidth=2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Add prior constraints\n", + "\n", + "Spurious Curie depth values can often be obtained if windows of the magnetic anomaly do not contain long wavelengths. This often arises from selecting too small a small window size, but can also occur from uncorrected artefacts in the magnetic anomaly, or simply the absence of magnetic minerals close to the surface of the crust.\n", + "\n", + "Adding *a priori* information on $\\beta, z_t, \\Delta z, C$ can reduce the incidence of anomalous values. $\\beta$ and $C$ vary at long wavelengths, and $z_t + \\Delta z$ should be within the range of 10-40 km if we assume the Curie depth is equivalent to the 580$^\\circ$C isotherm. Adding prior information to any (or all) of these parameters penalises spurious values using a standard $\\ell_2$-norm misfit function.\n", + "\n", + "```python\n", + "add_prior(beta=(3.0,0.5), zt=(0.0,0.1), dz=(20.0,10.0), C=(5,2.5))\n", + "```\n", + "\n", + "A combination of priors can be added with $(\\mu, \\sigma)$ pairs. Currently, only Gaussian distributions are supported. `reset_priors()` removes all prior information." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "grid.reset_priors()\n", + "grid.add_prior(beta=(3.0,0.01))\n", + "\n", + "fig = plt.figure()\n", + "ax1 = fig.add_subplot(111, xlabel=\"wavenumber (rad/km)\", ylabel=\"radial power spectrum\")\n", + "\n", + "for i, window_size in enumerate(window_size_range):\n", + " \n", + " # compute radial power spectrum\n", + " subgrid = grid.subgrid(xpt, ypt, window_size)\n", + " S, k, sigma2 = grid.radial_spectrum(subgrid)\n", + " ax1.plot(k, S, '-o', color='C{}'.format(i), label='{} km window size'.format(window_size*1e-3))\n", + " \n", + " # optimise Curie variables\n", + " beta, zt, dz, C = grid.optimise(window_size, xpt, ypt)\n", + " print(\"beta = {:.2f}\\n zt = {:.2f}\\n dz = {:.2f}\\n C = {:.2f}\\n\".format(beta,zt,dz,C))\n", + " \n", + " Sb = pycurious.bouligand2009(beta, zt, dz, k, C)\n", + " ax1.plot(k, Sb, color='C{}'.format(i), linewidth=2)\n", + " \n", + "ax1.legend()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.15" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Examples/Notebooks/Ex3-Optimisation-routine.ipynb b/Examples/Notebooks/Ex3-Optimisation-routine.ipynb new file mode 100644 index 0000000..f65ce73 --- /dev/null +++ b/Examples/Notebooks/Ex3-Optimisation-routine.ipynb @@ -0,0 +1,109 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Example 3 - Optimisation routine\n", + "\n", + "In Examples 2a and 2b we computed the Curie depth for a single point using a fixed window. Here, we use `CurieOptimise` object to compute the Curie depth over an entire magnetic anomaly.\n", + "\n", + "`CurieOptimise` inherits all methods from `CurieGrid` in addition to:\n", + "\n", + "- iteratively evaluate the Curie depth across the magnetic anomaly\n", + "- add priors to limit spurious Curie depth determinations\n", + "- optimise Curie depth parameters using constraints from an objective function\n", + "\n", + "### Contents\n", + "\n", + "- [The inverse problem](#The-inverse-problem)\n", + "- [Iterate across magnetic anomaly](#Iterate-across-magnetic-anomaly)\n", + "- [Compare Bouligand to Tanaka](#Compare-Bouligand-to-Tanaka)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "\n", + "import pycurious" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# load x,y,anomaly\n", + "mag_data = np.loadtxt(\"../data/test_mag_data.txt\")\n", + "\n", + "nx, ny = 305, 305\n", + "\n", + "x = mag_data[:,0]\n", + "y = mag_data[:,1]\n", + "d = mag_data[:,2].reshape(ny,nx)\n", + "\n", + "xmin, xmax = x.min(), x.max()\n", + "ymin, ymax = y.min(), y.max()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# initialise CurieOptimise object\n", + "grid = pycurious.CurieOptimise(d, xmin, xmax, ymin, ymax)\n", + "\n", + "window_size = 200e3\n", + "xc_list, yc_list = grid.create_centroid_list(window_size)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The inverse problem\n", + "\n", + "It is notoriously difficult to estimate uncertainties from Curie depth determinations. Intuitively, the fewer points in the power spectrum should result in higher uncertainty, but it is difficult to quantify these uncertainties in practise. For [Bouligand *et al.*, 2009](http://doi.wiley.com/10.1029/2009JB006494) it is difficult to determine the values of $\\beta$ and $\\Delta z$ since both control the slope of the power spectrum at low wavenumbers. Similarly, for [Tanaka *et al.*, 1999](http://linkinghub.elsevier.com/retrieve/pii/S0040195199000724) the lower and upper ranges of the power spectrum used to compute $z_b$ and $z_t$ is highly subjective and can result in significantly different Curie depths.\n", + "\n", + "Here, we aim to assess the uncertainty of Curie depth determinations using a sensitivity analysis. The approach we outline here is not necessarily the most statistically robust methodology, but it is intended as a practical way forward to compute Curie depth while considering the high degree of uncertainty." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.15" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Examples/Notebooks/Ex4-Mapping-Curie-depth-EMAG2.ipynb b/Examples/Notebooks/Ex4-Mapping-Curie-depth-EMAG2.ipynb new file mode 100644 index 0000000..cf13045 --- /dev/null +++ b/Examples/Notebooks/Ex4-Mapping-Curie-depth-EMAG2.ipynb @@ -0,0 +1,69 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Example 4 - Mapping Curie depth from EMAG2\n", + "\n", + "Using global compilations of the magnetic anomaly, such as EMAG2, means there is no limitation on window sizes. The mapping module in *PyCurious* has several functions to simplify:\n", + "\n", + "1. Translating between Coordinate Reference Systems (CRS)\n", + "2. Griding scattered point data\n", + "3. Importing and exporting Geotiffs\n", + "\n", + "These can be accessed from `pycurious.mapping`\n", + "\n", + "This requires some extra dependencies:\n", + "\n", + "- pyproj\n", + "- pyepsg\n", + "- cartopy (for visualisation)\n", + "\n", + "which can be installed via `pip`\n", + "\n", + "```bash\n", + "pip install [--user] pyproj pyepsg cartopy\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "\n", + "import pycurious\n", + "\n", + "import cartopy.crs as ccrs\n", + "import cartopy.feature as cfeature\n", + "import cartopy.io.shapereader as shpreader" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.15" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Examples/Notebooks/Ex5-parallel-processing.ipynb b/Examples/Notebooks/Ex5-parallel-processing.ipynb new file mode 100644 index 0000000..d22f644 --- /dev/null +++ b/Examples/Notebooks/Ex5-parallel-processing.ipynb @@ -0,0 +1,41 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Example 5 - Parallel processing\n", + "\n", + "`CurieParallel` inherits from `CurieOptimise`, which, in turn, inherits from `CurieGrid`" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.15" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/pycurious/__init__.py b/pycurious/__init__.py index 547711f..31932e4 100644 --- a/pycurious/__init__.py +++ b/pycurious/__init__.py @@ -1,5 +1,5 @@ # -*- coding: utf-8 -*- -from .curie import CurieGrid, bouligand2009, maus1995 +from .curie import CurieGrid, bouligand2009, tanaka1999, maus1995 from .optimise import CurieOptimise from .parallel import CurieParallel from .mapping import transform_coordinates, grid, trim \ No newline at end of file diff --git a/pycurious/curie.py b/pycurious/curie.py index 925d77c..f52db81 100644 --- a/pycurious/curie.py +++ b/pycurious/curie.py @@ -178,17 +178,13 @@ def radial_spectrum(self, subgrid, taper=np.hanning, scale=0.001, **kwargs): # control taper - if taper is None: + if type(taper) == type(None): vtaper = 1.0 else: - vtaper = np.ones((nr, nc)) rt = taper(nr, **kwargs) ct = taper(nc, **kwargs) - - for col in range(0, nc): - vtaper[:,col] *= rt - for row in range(0, nr): - vtaper[row,:] *= ct + xq, yq = np.meshgrid(ct, rt) + vtaper = xq*yq dx_scale = self.dx*scale dk = 2.0*np.pi/(nw - 1)/dx_scale @@ -200,9 +196,9 @@ def radial_spectrum(self, subgrid, taper=np.hanning, scale=0.001, **kwargs): kbins = np.arange(dk, dk*nw/2, dk) nbins = kbins.size - 1 - S = np.zeros(nbins) - k = np.zeros(nbins) - sigma2 = np.zeros(nbins) + S = np.empty(nbins) + k = np.empty(nbins) + sigma2 = np.empty(nbins) i0 = int((nw - 1)//2) nw_range = np.arange(0, nw) @@ -211,151 +207,79 @@ def radial_spectrum(self, subgrid, taper=np.hanning, scale=0.001, **kwargs): for i in range(0, nbins): mask = np.logical_and(kk >= kbins[i], kk <= kbins[i+1]) - #rr = np.log(np.sqrt(FT[mask]))(2*np.pi) - rr = np.log(np.sqrt(FT[mask])) + rr = 2.0*np.log(FT[mask]) S[i] = rr.mean() k[i] = kk[mask].mean() sigma2[i] = np.std(rr)/np.sqrt(rr.size) return S, k, sigma2 - def Tanaka(self, S, k, sigma2,kmin=0.05, kmax=0.2): - """ - Compute weighted linear fit of S over spatial frequency window kmin:kmax - - Parameters - ---------- - S : Power spectrum of signal (see radial spectrum), expected in ln(sqrt(S)) form - k : Wavenumber - sigma2 : Errors of S - kmin,kmax : Minimum and maximum spatial frequencies to fit. Ideally low frequency, straight-ish line - - Returns - ----------- - Zb : Estimated Curie point depth, as per Tanaka et al, 1999 - eZb : Error of Zb - : No geothermal gradient, trivial to estimate. - : Possible to extend, return fitted components? - """ - sf=k/(2.0*np.pi) - S2=np.log(np.exp(S)/sf) - - mask2=np.logical_and(sf >=kmin,sf <=kmax) - X=sf[mask2] - Y=S[mask2] - E=np.log(np.exp(sigma2[mask2])/X) - TL= sum(X/(E**2))*sum(Y/(E**2)) - sum((np.multiply(X,Y)/(E**2))*sum(1/(E**2))) - BL= (sum(X/(E**2)))**2 - (sum((X**2)/(E**2))*sum(1/(E**2))) - Ztr=TL/BL - btr= (sum(np.multiply(X,Y)/E**2) -Ztr*(sum(X**2/E**2) ))/(sum(X/E**2)) - eZtr=np.sqrt( sum(1/E**2)/ ( sum(X**2/E**2)*sum(1/E**2)-(sum(X/E**2))**2 )) - - Y2=np.log(np.exp(S[mask2])/X) - TL= sum(X/(E**2))*sum(Y2/(E**2)) - sum((np.multiply(X,Y2)/(E**2))*sum(1/(E**2))) - BL= (sum(X/(E**2)))**2 - (sum((X**2)/(E**2))*sum(1/(E**2))) - Zor=TL/BL - bor= (sum(np.multiply(X,Y2)/E**2) -Zor*(sum(X**2/E**2) ))/(sum(X/E**2)) - eZor=np.sqrt( sum(1/E**2)/ ( sum(X**2/E**2)*sum(1/E**2)-(sum(X/E**2))**2 )) - Zb=2*Zor-Ztr - eZb=2*eZor+eZtr - return Zb, eZb - - def Tanakac(self, S, k, sigma2,kmin=0.05, kmax=0.2,k2min=0.05, k2max=0.2): - """ - Compute weighted linear fit of S over spatial frequency window kmin:kmax - - Parameters - ---------- - S : Power spectrum of signal (see radial spectrum), expected in ln(sqrt(S)) form - k : Wavenumber - sigma2 : Errors of S - kmin,kmax : Minimum and maximum spatial frequencies to fit. Ideally low frequency, straight-ish line - - Returns - ----------- - Zb : Estimated Curie point depth, as per Tanaka et al, 1999 - eZb : Error of Zb - : No geothermal gradient, trivial to estimate. - : Possible to extend, return fitted components? - """ - sf=k/(2.0*np.pi) - S2=np.log(np.exp(S)/sf) - #print(sf) - mask2=np.logical_and(sf >=kmin,sf <=kmax) - #print(mask2) - X=sf[mask2] - Y=S[mask2] - E=sigma2[mask2] - TL= sum(X/(E**2))*sum(Y/(E**2)) - sum((np.multiply(X,Y)/(E**2))*sum(1/(E**2))) - BL= (sum(X/(E**2)))**2 - (sum((X**2)/(E**2))*sum(1/(E**2))) - Ztr=TL/BL - btr= (sum(np.multiply(X,Y)/E**2) -Ztr*(sum(X**2/E**2) ))/(sum(X/E**2)) - eZtr=np.sqrt( sum(1/E**2)/ ( sum(X**2/E**2)*sum(1/E**2)-(sum(X/E**2))**2 )) - - mask2=np.logical_and(sf >=k2min,sf <=k2max) - X=sf[mask2] - Y2=np.log(np.exp(S[mask2])/X) - E=np.log(np.exp(sigma2[mask2])/X) - TL= sum(X/(E**2))*sum(Y2/(E**2)) - sum((np.multiply(X,Y2)/(E**2))*sum(1/(E**2))) - BL= (sum(X/(E**2)))**2 - (sum((X**2)/(E**2))*sum(1/(E**2))) - Zor=TL/BL - bor= (sum(np.multiply(X,Y2)/E**2) -Zor*(sum(X**2/E**2) ))/(sum(X/E**2)) - eZor=np.sqrt( sum(1/E**2)/ ( sum(X**2/E**2)*sum(1/E**2)-(sum(X/E**2))**2 )) - Zb=2*Zor-Ztr - eZb=2*eZor+eZtr - #return Zb, eZb - return Zb, eZb, Ztr, Zor - - def Tanakab(self, S, k, kmin=0.05, kmax=0.2): + + def radial_spectrum_log(self, subgrid, taper=np.hanning, scale=0.001, **kwargs): """ - Compute unweighted linear fit of S over spatial frequency window kmin:kmax - + Compute the radial spectrum for a square grid. + Parameters ---------- - S : Power spectrum of signal (see radial spectrum), expected in ln(sqrt(S)) form - k : Wavenumber - kmin,kmax : Minimum and maximum spatial frequencies to fit. Ideally low frequency, straight-ish line - + subgrid : window of the original data + : (see subgrid method) + taper : taper function (np.hanning is default) + : set to None for no taper function + scale : scaling factor to get k into rad/km + : (0.001 by default) + args : keyword arguments to pass to taper + Returns - ----------- - Zb : Estimated Curie point depth, as per Tanaka et al, 1999 - eZb : Error of Zb - : No geothermal gradient, trivial to estimate. - : Possible to extend, return fitted components? + ------- + S : Radial spectrum + k : wavenumber in rad/km + sigma2 : variance of S """ - sf=k/(2.0*np.pi) - S2=np.log(np.exp(S)/sf) - - mask2=np.logical_and(sf >=kmin,sf <=kmax) - X=sf[mask2] - Y=S[mask2] - TL= X.size*sum(X*Y)-(sum(X)*sum(Y)) - BL=X.size*sum(X**2)-(sum(X)**2) - Ztr=TL/BL - - - Y2=np.log(np.exp(S[mask2])/X) - TL= X.size*sum(X*Y2)-(sum(X)*sum(Y2)) - BL=X.size*sum(X**2)-(sum(X)**2) - Zor=TL/BL - Zb=2*Zor-Ztr - return Zb - - #TL= sum(X/(E**2))*sum(Y/(E**2)) - sum((np.multiply(X,Y)/(E**2))*sum(1/(E**2))) - #BL= (sum(X/(E**2)))**2 - (sum((X**2)/(E**2))*sum(1/(E**2))) - #Ztr=TL/BL - #btr= (sum(np.multiply(X,Y)/E**2) -Ztr*(sum(X**2/E**2) ))/(sum(X/E**2)) - #eZtr=np.sqrt( sum(1/E**2)/ ( sum(X**2/E**2)*sum(1/E**2)-(sum(X/E**2))**2 )) - - #Y2=np.log(np.exp(S[mask2])/X) - #TL= sum(X/(E**2))*sum(Y2/(E**2)) - sum((np.multiply(X,Y2)/(E**2))*sum(1/(E**2))) - #BL= (sum(X/(E**2)))**2 - (sum((X**2)/(E**2))*sum(1/(E**2))) - #Zor=TL/BL - #bor= (sum(np.multiply(X,Y2)/E**2) -Zor*(sum(X**2/E**2) ))/(sum(X/E**2)) - #eZor=np.sqrt( sum(1/E**2)/ ( sum(X**2/E**2)*sum(1/E**2)-(sum(X/E**2))**2 )) - #Zb=2*Zor-Ztr - #eZb=2*eZor+eZtr - #return Zb, eZb + + data = subgrid + nr, nc = data.shape + nw = nr + + if nr != nc: + warnings.warn("subgrid is not square {}".format((nr,nc)), RuntimeWarning) + + + # control taper + if type(taper) == type(None): + vtaper = 1.0 + else: + rt = taper(nr, **kwargs) + ct = taper(nc, **kwargs) + xq, yq = np.meshgrid(ct, rt) + vtaper = xq*yq + + dx_scale = self.dx*scale + dk = 2.0*np.pi/(nw - 1)/dx_scale + + # fast Fourier transform and shift + FT = np.abs(np.fft.fft2(data*vtaper)) + FT = np.fft.fftshift(FT) + + kbins = np.arange(dk, dk*nw/2, dk) + nbins = kbins.size - 1 + + S = np.empty(nbins) + k = np.empty(nbins) + sigma2 = np.empty(nbins) + + i0 = int((nw - 1)//2) + nw_range = np.arange(0, nw) + iy, ix = np.meshgrid(nw_range, nw_range) + kk = np.hypot((ix - i0)*dk, (iy - i0)*dk) + + for i in range(0, nbins): + mask = np.logical_and(kk >= kbins[i], kk <= kbins[i+1]) + rr = np.log(np.sqrt(FT[mask])) + S[i] = rr.mean() + k[i] = kk[mask].mean() + sigma2[i] = np.std(rr)/np.sqrt(rr.size) + + return S, k, sigma2 def azimuthal_spectrum(self, subgrid, taper=np.hanning, scale=0.001, theta=5.0, **kwargs): @@ -378,7 +302,6 @@ def azimuthal_spectrum(self, subgrid, taper=np.hanning, scale=0.001, theta=5.0, S : Azimuthal spectrum k : wavenumber [rad/km] theta : angles - sigma2 : variance of S """ from pycurious import radon data = subgrid @@ -593,6 +516,71 @@ def bouligand2009(beta, zt, dz, kh, C=0.0): return Phi1d +def tanaka1999(S, k, sigma2, kmin_range=(0.05, 0.2), kmax_range=(0.05, 0.2)): + """ + Compute weighted linear fit of S over spatial frequency window kmin:kmax + + Parameters + ---------- + S : Power spectrum of signal (see radial spectrum), expected in ln(sqrt(S)) form + k : Wavenumber + sigma2 : Errors of S + kmin,kmax : Minimum and maximum spatial frequencies to fit. Ideally low frequency, straight-ish line + + Returns + ----------- + Zb : Estimated Curie point depth, as per Tanaka et al, 1999 + eZb : Error of Zb + : No geothermal gradient, trivial to estimate. + : Possible to extend, return fitted components? + """ + def compute_coefficients(X, Y, E): + X2 = X**2 + Y2 = Y**2 + E2 = E**2 + + XY = np.multiply(X, Y) + XE2sum = np.sum(X/E2) + YE2sum = np.sum(Y/E2) + rE2sum = np.sum(1.0/E2) + X2E2sum = np.sum(X2/E2) + Y2E2sum = np.sum(Y2/E2) + + TL = XE2sum*YE2sum - np.sum(XY/E2*rE2sum) + BL = XE2sum**2 - X2E2sum*rE2sum + + Z = TL/BL + b = (np.sum(XY/E2) - Z*X2E2sum)/XE2sum + dZ = np.sqrt( rE2sum/(X2E2sum*rE2sum - XE2sum) ) + return Z, b, dZ + + + sf=k/(2.0*np.pi) + S2=np.log(np.exp(S)/sf) + + # mask low wavenumbers + kmin, kmax = kmin_range + mask1 = np.logical_and(sf >=kmin, sf <=kmax) + X1 = sf[mask1] + Y1 = S[mask1] + E1 = sigma2[mask1] + + # mask high wavenumbers + kmin, kmax = kmax_range + mask2 = np.logical_and(sf >=kmin, sf <=kmax) + X2 = sf[mask2] + Y2 = np.log(np.exp(S[mask2])/X2) + E2 = np.log(np.exp(sigma2[mask2])/X2) + + # compute top and bottom of magnetic layer + Ztr, btr, dZtr = compute_coefficients(X1, Y1, E1) + Zor, bor, dZor = compute_coefficients(X2, Y2, E2) + + Zb = 2.0*Zor - Ztr + dZb = 2.0*dZor - dZtr + return abs(Zb), dZb + + def maus1995(beta, zt, kh, C=0.0): """ Calculate the synthetic radial power spectrum of diff --git a/pycurious/optimise.py b/pycurious/optimise.py index 120e0e1..5c136a7 100644 --- a/pycurious/optimise.py +++ b/pycurious/optimise.py @@ -33,7 +33,8 @@ def __init__(self, grid, xmin, xmax, ymin, ymax): self.reset_priors() # lower / upper bounds - lb = np.zeros(4) + # [beta, zt, dz, C] + lb = [0.0, 0.0, 0.0, None] ub = [None]*len(lb) bounds = list(zip(lb,ub)) self.bounds = bounds @@ -111,14 +112,14 @@ def min_func(self, x, Phi_exp, kh): We purposely ignore all warnings raised by the bouligand2009 function because some combinations of input parameters will trigger an out-of-range warning that will crash the minimiser - when this occurs we overwrite the misfit with a very large number + when this occurs we set the misfit to a very large number """ beta, zt, dz, C = x with warnings.catch_warnings() as w: warnings.simplefilter("ignore") Phi_syn = bouligand2009(beta, zt, dz, kh, C) - misfit = np.linalg.norm(Phi_exp - Phi_syn) + misfit = self.objective_function(Phi_syn, Phi_exp, 1.0) if not np.isfinite(misfit): misfit = 1e99 else: From 3606daa9c99dcebc86221450b5736e5d5f3dd6b6 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Mon, 25 Jun 2018 22:26:56 +0100 Subject: [PATCH 007/170] Random fractal model - beta = 3 - dz = 10 --- Examples/data/test_mag_data.txt | 93025 ++++++++++++++++++++++++++++++ 1 file changed, 93025 insertions(+) create mode 100644 Examples/data/test_mag_data.txt diff --git a/Examples/data/test_mag_data.txt b/Examples/data/test_mag_data.txt new file mode 100644 index 0000000..7f59a38 --- /dev/null +++ b/Examples/data/test_mag_data.txt @@ -0,0 +1,93025 @@ 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+304500.0 275500.0 -3.942610792132017e-07 +304500.0 276500.0 6.515617580151788e-07 +304500.0 277500.0 9.122197966506269e-07 +304500.0 278500.0 3.642314207521848e-07 +304500.0 279500.0 1.575049146677057e-07 +304500.0 280500.0 1.0684481761193174e-06 +304500.0 281500.0 1.7338803666311594e-06 +304500.0 282500.0 1.5873266925368805e-06 +304500.0 283500.0 1.530732745779759e-06 +304500.0 284500.0 1.3923587994756964e-06 +304500.0 285500.0 1.9413361958436677e-06 +304500.0 286500.0 2.7209012479894167e-06 +304500.0 287500.0 2.9681175970467628e-06 +304500.0 288500.0 2.3638253676786033e-06 +304500.0 289500.0 1.9322548166243845e-06 +304500.0 290500.0 1.8323036137370268e-06 +304500.0 291500.0 1.85897742899941e-06 +304500.0 292500.0 2.476816592475855e-06 +304500.0 293500.0 3.675830071166784e-06 +304500.0 294500.0 4.457683808654705e-06 +304500.0 295500.0 4.216248019097752e-06 +304500.0 296500.0 4.1756142031569495e-06 +304500.0 297500.0 3.7219243240592216e-06 +304500.0 298500.0 3.4442187022402667e-06 +304500.0 299500.0 3.185036600351722e-06 +304500.0 300500.0 2.5253382862641192e-06 +304500.0 301500.0 2.130102591676184e-06 +304500.0 302500.0 2.0773364175386353e-06 +304500.0 303500.0 1.832989843244632e-06 +304500.0 304500.0 1.6319181000261058e-06 From 5bdee393fb2845dcbbd3efc42f08a22119d511a2 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Sat, 7 Jul 2018 23:02:36 +0100 Subject: [PATCH 008/170] Updated jupyter notebooks --- ...mpute-Curie-depth-Bouligand-approach.ipynb | 1 + .../Notebooks/Ex3-Optimisation-routine.ipynb | 136 ++++++++++++- .../Ex4-Mapping-Curie-depth-EMAG2.ipynb | 187 +++++++++++++++++- .../Notebooks/Ex5-parallel-processing.ipynb | 10 +- pycurious/optimise.py | 184 ++++++++++++----- 5 files changed, 458 insertions(+), 60 deletions(-) diff --git a/Examples/Notebooks/Ex2b-Compute-Curie-depth-Bouligand-approach.ipynb b/Examples/Notebooks/Ex2b-Compute-Curie-depth-Bouligand-approach.ipynb index ab84e0e..edcd2ed 100644 --- a/Examples/Notebooks/Ex2b-Compute-Curie-depth-Bouligand-approach.ipynb +++ b/Examples/Notebooks/Ex2b-Compute-Curie-depth-Bouligand-approach.ipynb @@ -189,6 +189,7 @@ "outputs": [], "source": [ "grid.reset_priors()\n", + "\n", "grid.add_prior(beta=(3.0,0.01))\n", "\n", "fig = plt.figure()\n", diff --git a/Examples/Notebooks/Ex3-Optimisation-routine.ipynb b/Examples/Notebooks/Ex3-Optimisation-routine.ipynb index f65ce73..b3d2a8c 100644 --- a/Examples/Notebooks/Ex3-Optimisation-routine.ipynb +++ b/Examples/Notebooks/Ex3-Optimisation-routine.ipynb @@ -17,7 +17,7 @@ "### Contents\n", "\n", "- [The inverse problem](#The-inverse-problem)\n", - "- [Iterate across magnetic anomaly](#Iterate-across-magnetic-anomaly)\n", + "- [Sensitivity analysis](#Sensitivity analysis)\n", "- [Compare Bouligand to Tanaka](#Compare-Bouligand-to-Tanaka)" ] }, @@ -50,7 +50,10 @@ "d = mag_data[:,2].reshape(ny,nx)\n", "\n", "xmin, xmax = x.min(), x.max()\n", - "ymin, ymax = y.min(), y.max()" + "ymin, ymax = y.min(), y.max()\n", + "\n", + "# initialise CurieOptimise object\n", + "grid = pycurious.CurieOptimise(d, xmin, xmax, ymin, ymax)" ] }, { @@ -59,11 +62,12 @@ "metadata": {}, "outputs": [], "source": [ - "# initialise CurieOptimise object\n", - "grid = pycurious.CurieOptimise(d, xmin, xmax, ymin, ymax)\n", + "# get centroids\n", "\n", "window_size = 200e3\n", - "xc_list, yc_list = grid.create_centroid_list(window_size)" + "xc_list, yc_list = grid.create_centroid_list(window_size, spacingX=10e3, spacingY=10e3)\n", + "\n", + "print(\"number of centroids = {}\".format(len(xc_list)))" ] }, { @@ -74,7 +78,127 @@ "\n", "It is notoriously difficult to estimate uncertainties from Curie depth determinations. Intuitively, the fewer points in the power spectrum should result in higher uncertainty, but it is difficult to quantify these uncertainties in practise. For [Bouligand *et al.*, 2009](http://doi.wiley.com/10.1029/2009JB006494) it is difficult to determine the values of $\\beta$ and $\\Delta z$ since both control the slope of the power spectrum at low wavenumbers. Similarly, for [Tanaka *et al.*, 1999](http://linkinghub.elsevier.com/retrieve/pii/S0040195199000724) the lower and upper ranges of the power spectrum used to compute $z_b$ and $z_t$ is highly subjective and can result in significantly different Curie depths.\n", "\n", - "Here, we aim to assess the uncertainty of Curie depth determinations using a sensitivity analysis. The approach we outline here is not necessarily the most statistically robust methodology, but it is intended as a practical way forward to compute Curie depth while considering the high degree of uncertainty." + "Here, we aim to assess the uncertainty of Curie depth determinations using a sensitivity analysis. The approach we outline here is not necessarily the most statistically robust methodology, but it is intended as a practical means to compute Curie depth whilst considering its uncertainty.\n", + "\n", + "First we find the best model with no priors to evaluate the heterogeneity in the signal we extract from the magnetic anomaly. We use the commonly used $\\ell_2$-norm objective function to calculate misfit." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# no priors\n", + "grid.reset_priors()\n", + "\n", + "beta, zt, dz, C = grid.optimise_routine(window_size, xc_list, yc_list)\n", + "\n", + "# plot results\n", + "fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2, 2, sharex=True, sharey=True, figsize=(10,10))\n", + "\n", + "sc1 = ax1.scatter(xc_list, yc_list, c=beta)\n", + "sc2 = ax2.scatter(xc_list, yc_list, c=zt)\n", + "sc3 = ax3.scatter(xc_list, yc_list, c=dz)\n", + "sc4 = ax4.scatter(xc_list, yc_list, c=C)\n", + "\n", + "fig.colorbar(sc1, ax=ax1, label=r\"$\\beta$\")\n", + "fig.colorbar(sc2, ax=ax2, label=r\"$z_t$\")\n", + "fig.colorbar(sc3, ax=ax3, label=r\"$\\Delta z$\")\n", + "fig.colorbar(sc4, ax=ax4, label=r\"$C$\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Sensitivity analysis\n", + "\n", + "The sensitivity analysis requires defining a prior distribution to sample from. The default is a Gaussian normal distribution,\n", + "\n", + "$$\n", + "P(\\mathbf{m}) = \\frac{1}{\\sqrt{2\\pi} \\sigma_p} \\exp \\left( \\frac{-\\mathbf{m}^2}{2 \\sigma_p^2} \\right)\n", + "$$\n", + "\n", + "but other distributions can be defined from the `scipy.stats` module. We repeat the inversion multiple times, sampling different values from $P(\\mathbf{m})$ to evaluate the uncertainty in each variable. Note: $\\mathbf{m}$ is the variables $\\beta, z_t, \\Delta z, C$ for the Bouligand approach or $z_t, z_b $ for the Tanaka approach.\n", + "\n", + "Prior distributions are added by\n", + "\n", + "```python\n", + "from scipy import stats\n", + "beta_p = stats.norm(3.0, 1.0)\n", + "grid.add_prior(beta=beta_p)\n", + "```\n", + "\n", + "and can be accessed from a dictionary:\n", + "\n", + "```python\n", + "prior = grid.prior_pdf['beta'] # stats.norm object\n", + "prior = grid.prior['beta'] # stats.norm object arguments (3.0, 1.0)\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from scipy import stats\n", + "\n", + "beta_p = stats.norm(3.0, 1.0)\n", + "zt_p = stats.norm(0.0, 1.0)\n", + "dz_p = stats.norm(12.0, 8.0)\n", + "C_p = stats.norm(-17.0, 5.0)\n", + "\n", + "grid.add_prior(beta=beta_p, zt=zt_p, dz=dz_p, C=C_p)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# number of simulations to run for each centroid\n", + "nsim = 10\n", + "\n", + "beta, zt, dz, C = grid.sensitivity_routine(nsim, window_size, xc_list, yc_list)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig = plt.figure(figsize=(16,4))\n", + "\n", + "\n", + "for i, (label, var) in enumerate([('beta', beta), ('zt', zt), ('dz', dz), ('C', C)]):\n", + " \n", + " # prior distribution\n", + " prior = grid.prior_pdf[label]\n", + " p, sigma_p = prior.mean(), prior.std()\n", + " \n", + " # posterior distribution\n", + " P, sigma_P = var[:,0].mean(), var[:,1].mean()\n", + " post = stats.norm(P, sigma_P)\n", + " \n", + " x_samples = np.linspace(p-2*sigma_p, p+2*sigma_p, 100)\n", + " \n", + " # plot pdf\n", + " ax = fig.add_subplot(1,4,i+1, xlabel=label)\n", + " ax.plot(x_samples, prior.pdf(x_samples), label=\"prior\")\n", + " ax.plot(x_samples, post.pdf(x_samples), label=\"posterior\")\n", + " ax.legend()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The precision of the values are properly resolved " ] }, { diff --git a/Examples/Notebooks/Ex4-Mapping-Curie-depth-EMAG2.ipynb b/Examples/Notebooks/Ex4-Mapping-Curie-depth-EMAG2.ipynb index cf13045..32d8b56 100644 --- a/Examples/Notebooks/Ex4-Mapping-Curie-depth-EMAG2.ipynb +++ b/Examples/Notebooks/Ex4-Mapping-Curie-depth-EMAG2.ipynb @@ -22,9 +22,16 @@ "\n", "which can be installed via `pip`\n", "\n", - "```bash\n", + "```shell\n", "pip install [--user] pyproj pyepsg cartopy\n", - "```" + "```\n", + "\n", + "### Contents\n", + "\n", + "- [Import EMAG2 data](#Import-EMAG2-data)\n", + "- [Interpolate onto grid projection](#Interpolate-onto-grid-projection)\n", + "- [Compute Curie depth](#Compute-Curie-depth)\n", + "- [Compare to reference models](#Compare-to-reference-models)" ] }, { @@ -43,6 +50,182 @@ "import cartopy.feature as cfeature\n", "import cartopy.io.shapereader as shpreader" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Import EMAG2 data\n", + "\n", + "The latest data can be downloaded from the [NOAA web page](https://www.ngdc.noaa.gov/geomag/emag2.html) in CSV format. Download it to a local directory (may take some time).\n", + "\n", + "Once loaded, we trim the data to a region of interest - being careful to allow some buffer to accommodate the maximum window size. We save this to a compressed `.npz` file to avoid the costly repitition of reloading the same data in the future." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "filedir = '/path/to/directory/'\n", + "\n", + "try:\n", + " with np.load(filedir+'EMAG2_V3_20170530.npz') as f:\n", + " mag_data = f['data']\n", + "except:\n", + " mag_data = np.loadtxt(filedir+'EMAG2_V3_20170530.csv', delimiter=',', usecols=(2,3,4,5,7))\n", + " lon_mask = mag_data[:,0] > 180.0\n", + " mag_data[lon_mask,0] -= 360.0\n", + " np.savez_compressed(filedir+'EMAG2_V3_20170530.npz', data=mag_data.astype(np.float32))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# filter NaNs\n", + "mag_data = mag_data[mag_data[:,4] != 99999.]\n", + "mag_data = mag_data[mag_data[:,4] != -888.]\n", + "mag_data = mag_data[mag_data[:,4] != -999.]\n", + "\n", + "# print min/max\n", + "mincols = mag_data.min(axis=0)\n", + "maxcols = mag_data.max(axis=0)\n", + "\n", + "fmt = \"min/max {:5.2f} -> {:5.2f}\"\n", + "for col in xrange(mag_data.shape[1]):\n", + " print(fmt.format(mincols[col], maxcols[col]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Interpolate onto grid projection\n", + "\n", + "We choose an arbitrary section of the Earth's surface and a suitable projection. PyCurious handles transformation between different CRS using a EPSG reference code. EMAG2 is in lons and lats (in decimal degrees), which we want to convert into eastings and northings (in metres). For this example, we transform WGS84 coordinates (EPSG:4326) to the IRENET95 projection (EPSG:2157)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# grid extent - grid of the British Isles in Irenet 95 grid projection\n", + "xmin = 250000.0\n", + "xmax = 1400000.0\n", + "ymin = 200000.0\n", + "ymax = 1500000.0\n", + "extent_grid = [xmin, xmax, ymin, ymax]\n", + "\n", + "# extent on the sphere (WGS84)\n", + "extent_sphere = pycurious.mapping.convert_extent(extent_grid, epsg_in=4326, epsg_out=2157)\n", + "\n", + "# map extent - should be narrower than extent_sphere\n", + "extent_map = [-10.8, 2, 49.5, 59]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "dx, dy = 1e3, 1e3 # 1 km resolution\n", + "nx, ny = int(round((xmax-xmin)/dx)), int(round((ymax-ymin)/dy))\n", + "\n", + "# interpolate onto grid extent (for computation)\n", + "mag_grid = grid(mag_data[:,:2], mag_data[:,3], extent, shape=(ny,nx), epsg_in=4326, epsg_out=2157)\n", + "\n", + "# interpolate onto extent on the sphere (for mapping)\n", + "mag_sphere = grid(mag_data[:,:2], mag_data[:,3], extent_sphere, shape=(ny,nx))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "proj = ccrs.UTM(30)\n", + "\n", + "fig = plt.figure(figsize=(12,10))\n", + "ax = plt.axes(projection=proj)\n", + "ax.set_extent(map_extent)\n", + "ax.coastlines(resolution='50m', linewidth=1.5)\n", + "ax.gridlines()\n", + "\n", + "im1 = ax.imshow(mag_sphere, extent=extent_sphere, transform=ccrs.PlateCarree(),\n", + " vmin=-200, vmax=200, zorder=0)\n", + "\n", + "fig.colorbar(im1, label='nT')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Compute Curie depth\n", + "\n", + "For this example we use the Bouligand *et al.*, 2009 approach we outlined in [Ex3-Optimisation-routine](#./Ex3-Optimisation-routine.ipynb)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "grid = pycurious.CurieOptimise(mag_grid, xmin, xmax, ymin, ymax)\n", + "\n", + "# centroid spacing of 20 km\n", + "xc_list, yc_list = grid.create_centroid_list(100e3, spacingX=20e3, spacingY=20e3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Compare to reference models\n", + "\n", + "A global Curie depth reference model has been created by [Li *et al.*, 2017](https://www.nature.com/articles/srep45129), which is a useful resource to compare these results. Download the supplementary material from the open access [article](https://www.nature.com/articles/srep45129#supplementary-information) to the same directory as EMAG2." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "li_cpd = np.loadtxt(filedir + 'Li_2017_curiedepth.txt')\n", + "li_cpd = li_cpd[~np.isnan(li_cpd[:,2])]\n", + "\n", + "li_grid = pycurious.grid(li_cpd[:,:2], li_cpd[:,2], extent_sphere, shape=(ny,nx))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "proj = ccrs.UTM(30)\n", + "\n", + "fig = plt.figure(figsize=(12,10))\n", + "ax = plt.axes(projection=proj)\n", + "ax.set_extent(map_extent)\n", + "ax.coastlines(resolution='50m', linewidth=1.5)\n", + "ax.gridlines()\n", + "\n", + "im1 = ax.imshow(li_grid, extent=extent_sphere, transform=ccrs.PlateCarree(),\n", + " cmap='BrBG', zorder=0, vmin=10, vmax=40)\n", + "\n", + "fig.colorbar(im1, label='km')" + ] } ], "metadata": { diff --git a/Examples/Notebooks/Ex5-parallel-processing.ipynb b/Examples/Notebooks/Ex5-parallel-processing.ipynb index d22f644..ff77b96 100644 --- a/Examples/Notebooks/Ex5-parallel-processing.ipynb +++ b/Examples/Notebooks/Ex5-parallel-processing.ipynb @@ -6,7 +6,15 @@ "source": [ "# Example 5 - Parallel processing\n", "\n", - "`CurieParallel` inherits from `CurieOptimise`, which, in turn, inherits from `CurieGrid`" + "`CurieParallel` inherits from `CurieOptimise`, which, in turn, inherits from `CurieGrid`. Parallelism is handled by MPI via the Python interface, `mpi4py`.\n", + "\n", + "```bash\n", + "pip install [--user] mpi4py\n", + "```\n", + "\n", + "This requires an MPI implementation, such as [OpenMPI](https://www.open-mpi.org) or [MPICH](http://www.mpich.org/downloads), to be installed on the system.\n", + "\n", + "The parallel scheme operates by dividing a grid equally among processors with a shadow region equal to the maximum window size. This ensures that windows are not clipped close to the boundaries of the domain on any given processor." ] }, { diff --git a/pycurious/optimise.py b/pycurious/optimise.py index 5c136a7..22e13bf 100644 --- a/pycurious/optimise.py +++ b/pycurious/optimise.py @@ -3,6 +3,7 @@ import numpy as np from scipy.optimize import minimize from scipy.special import polygamma +from scipy import stats try: range=xrange except: pass @@ -44,23 +45,39 @@ def __init__(self, grid, xmin, xmax, ymin, ymax): def add_prior(self, **kwargs): """ Add a prior to the dictionary (tuple) - Available priors are beta, zt, dz, C + Assumes a normal distribution or + define another distribution from scipy.stats + Usage ----- add_prior(beta=(p, sigma_p)) + add_prior(beta=scipy.stats.norm(p, sigma_p)) """ for key in kwargs: if key in self.prior: prior = kwargs[key] - self.prior[key] = prior + if type(prior) == tuple: + p, sigma_p = prior + pdf = stats.norm(p, sigma_p) + elif type(prior) == stats._distn_infrastructure.rv_frozen: + pdf = prior + else: + raise ValueError("Use a distribution from scipy.stats module") + + # add prior PDF to dictionary + self.prior_pdf[key] = pdf + self.prior[key] = list(pdf.args) + else: raise ValueError("prior must be one of {}".format(self.prior.keys())) + def reset_priors(self): self.prior = {'beta':None, 'zt':None, 'dz':None, 'C':None} + self.prior_pdf = {'beta':None, 'zt':None, 'dz':None, 'C':None} def objective_routine(self, **kwargs): @@ -81,14 +98,24 @@ def objective_routine(self, **kwargs): for key in kwargs: val = kwargs[key] if key in self.prior: - prior = self.prior[key] - if type(prior) == tuple: - c += self.objective_function(val, prior[0], prior[1]) + prior_args = self.prior[key] + if prior_args is not None: + c += self.objective_function(val, *prior_args) return c - def objective_function(self, x, x0, sigma_x0): + def objective_function(self, x, x0, sigma_x0, *args): """ Objective function used in objective_routine + + Parameters + --------- + x : float, ndarray + x0 : float, ndarray + sigma_x0 : float, ndarray + + Returns + ------- + misfit : float """ return np.linalg.norm((x - x0)/sigma_x0)**2 @@ -134,20 +161,20 @@ def optimise(self, window, xc, yc, beta=3.0, zt=1.0, dz=20.0, C=5.0, taper=np.ha Parameters ---------- - window : size of window in metres - xc_list : centroid x values shape(l,) - yc_list : centroid y values shape(l,) - beta : fractal parameter (starting value) - zt : top of magnetic layer (starting value) - dz : thickness of magnetic layer (starting value) - C : field constant (starting value) + window : float - size of window in metres + xc : float - centroid x values + yc : float - centroid y values + beta : float - fractal parameter (starting value) + zt : float - top of magnetic layer (starting value) + dz : float - thickness of magnetic layer (starting value) + C : float - field constant (starting value) Returns ------- - beta : fractal parameters - zt : top of magnetic layer - dz : thickness of magnetic layer - C : field constant + beta : float - fractal parameters + zt : float - top of magnetic layer + dz : float - thickness of magnetic layer + C : float - field constant """ if type(process_subgrid) == type(None): @@ -179,25 +206,23 @@ def optimise_routine(self, window, xc_list, yc_list, beta=3.0, zt=1.0, dz=20.0, Use this routine to iteratively improve the precision of various parameters (see notes) - - CAUTION! Priors will be altered at the end of this routine! Parameters ---------- - window : size of window in metres - xc_list : centroid x values shape(l,) - yc_list : centroid y values shape(l,) - beta : fractal parameter shape(l,) - zt : top of magnetic layer shape(l,) - dz : thickness of magnetic layer shape(l,) - C : field constant shape(l,) + window : float - size of window in metres + xc_list : ndarray shape(l,) - centroid x values + yc_list : ndarray shape(l,) - centroid y values + beta : float - fractal parameter + zt : float - top of magnetic layer + dz : float - thickness of magnetic layer + C : float - field constant Returns ------- - beta : fractal parameters shape(l,) - zt : top of magnetic layer shape(l,) - dz : thickness of magnetic layer shape(l,) - C : field constant shape(l,) + beta : ndarray shape(l,) - fractal parameters + zt : ndarray shape(l,) - top of magnetic layer + dz : ndarray shape(l,) - thickness of magnetic layer + C : ndarray shape(l,) - field constant Notes ----- @@ -237,28 +262,85 @@ def optimise_routine(self, window, xc_list, yc_list, beta=3.0, zt=1.0, dz=20.0, return Bopt, ztopt, dzopt, Copt - def _prioritise(self, mask, **kwargs): + def sensitivity_routine(self, nsim, window, xc_list, yc_list, beta=3.0, zt=1.0, dz=20.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs): """ - Calculate mean and stdev for beta, zt, dz, C that were provided - in optimise_routine and set as priors. - - mask selects entries that are within the window size + Iterate through a list of centroids to compute the mean and + standard deviation of beta, zt, dz, C by perturbing their + prior distributions (if provided by the user - see add_prior). + + Parameters + ---------- + nsim : int - number of Monte Carlo simulations + window : float - size of window in metres + xc_list : ndarray shape(l,) - centroid x values + yc_list : ndarray shape(l,) - centroid y values + beta : float - starting fractal parameter + zt : float - starting top of magnetic layer + dz : float - starting thickness of magnetic layer + C : float - starting field constant Returns - ---------- - x0 : initial x variables + ------- + beta : ndarray shape(l,2) - fractal parameters (mean, stdev) + zt : ndarray shape(l,2) - top of magnetic layer (mean, stdev) + dz : ndarray shape(l,2) - thickness of magnetic layer (mean, stdev) + C : ndarray shape(l,2) - field constant (mean, stdev) + """ - self.reset_priors() - x0 = np.array([3.0, 1.0, 20.0, 5.0]) - - for i, key in enumerate(['beta', 'zt', 'dz', 'C']): - array = kwargs[key] - if type(array) == np.ndarray or type(array) == list: - marray = array[mask] - v = np.mean(marray) - dv = np.std(marray) - if dv != 0.0: - self.prior[key] = (v, dv) - x0[i] = v - - return x0 + + n = len(xc_list) + + if n != len(yc_list): + raise ValueError("xc_list and yc_list must be the same size") + + + # storage vectors for centroids (mean, std) + Bopt = np.empty((n,2)) + ztopt = np.empty((n,2)) + dzopt = np.empty((n,2)) + Copt = np.empty((n,2)) + + # storage vectors for nsim + Bsim = np.empty(nsim) + ztsim = np.empty(nsim) + dzsim = np.empty(nsim) + Csim = np.empty(nsim) + + + use_keys = [] + for key in self.prior_pdf: + prior_pdf = self.prior_pdf[key] + if prior_pdf is not None: + use_keys.append(key) + + + for i in range(0, n): + xc = xc_list[i] + yc = yc_list[i] + + for sim in range(0, nsim): + + # randomly generate new prior values within PDF + for key in use_keys: + prior_pdf = self.prior_pdf[key] + self.prior[key][0] = prior_pdf.rvs() + + + # run the optimisation routine + Bsim[sim], ztsim[sim], dzsim[sim], Csim[sim] = self.optimise(window, xc, yc,\ + beta=beta, zt=zt, dz=dz, C=C,\ + taper=np.hanning, process_subgrid=None, **kwargs) + + # store mean, stdev pairs + Bopt[i] = np.mean(Bsim), np.std(Bsim) + ztopt[i] = np.mean(ztsim), np.std(ztsim) + dzopt[i] = np.mean(dzsim), np.std(dzsim) + Copt[i] = np.mean(Csim), np.std(Csim) + + + # restore priors + for key in use_keys: + prior_pdf = self.prior_pdf[key] + self.prior[key] = list(prior_pdf.args) + + return Bopt, ztopt, dzopt, Copt From 23642c357ce20b49f1c8fb3b9603eb3bf1e3e7b0 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Sun, 8 Jul 2018 23:16:34 +0100 Subject: [PATCH 009/170] Ex4 Notebook improvements --- Examples/Notebooks/Ex4-Mapping-Curie-depth-EMAG2.ipynb | 9 ++++++--- 1 file changed, 6 insertions(+), 3 deletions(-) diff --git a/Examples/Notebooks/Ex4-Mapping-Curie-depth-EMAG2.ipynb b/Examples/Notebooks/Ex4-Mapping-Curie-depth-EMAG2.ipynb index 32d8b56..4e7fbea 100644 --- a/Examples/Notebooks/Ex4-Mapping-Curie-depth-EMAG2.ipynb +++ b/Examples/Notebooks/Ex4-Mapping-Curie-depth-EMAG2.ipynb @@ -139,10 +139,10 @@ "nx, ny = int(round((xmax-xmin)/dx)), int(round((ymax-ymin)/dy))\n", "\n", "# interpolate onto grid extent (for computation)\n", - "mag_grid = grid(mag_data[:,:2], mag_data[:,3], extent, shape=(ny,nx), epsg_in=4326, epsg_out=2157)\n", + "mag_grid = pycurious.mapping.grid(mag_data[:,:2], mag_data[:,3], extent, shape=(ny,nx), epsg_in=4326, epsg_out=2157)\n", "\n", "# interpolate onto extent on the sphere (for mapping)\n", - "mag_sphere = grid(mag_data[:,:2], mag_data[:,3], extent_sphere, shape=(ny,nx))" + "mag_sphere = pycurious.mapping.grid(mag_data[:,:2], mag_data[:,3], extent_sphere, shape=(ny,nx))" ] }, { @@ -183,7 +183,10 @@ "grid = pycurious.CurieOptimise(mag_grid, xmin, xmax, ymin, ymax)\n", "\n", "# centroid spacing of 20 km\n", - "xc_list, yc_list = grid.create_centroid_list(100e3, spacingX=20e3, spacingY=20e3)" + "xc_list, yc_list = grid.create_centroid_list(200e3, spacingX=20e3, spacingY=20e3)\n", + "print(\"number of centroids = {}\".format(len(xc_list)))\n", + "\n", + "beta, zt, dz, C = grid.optimise_routine(window_size, xc_list, yc_list)" ] }, { From a586ec6a59047db30b64ea8b5c9ffe6a00962999 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Mon, 9 Jul 2018 16:29:23 +0100 Subject: [PATCH 010/170] Reduce int -> float operations --- tests/Bouligand_forward.py | 22 +++++++++++----------- 1 file changed, 11 insertions(+), 11 deletions(-) diff --git a/tests/Bouligand_forward.py b/tests/Bouligand_forward.py index 68c6e1d..d039a07 100644 --- a/tests/Bouligand_forward.py +++ b/tests/Bouligand_forward.py @@ -12,14 +12,14 @@ import time start_time=time.time() -cm=1.e-7 +cm=1e-7 ########################################################## #A VERIFIER: multiplier facteur cm par 4*pi ## TO VERIFY: multiplication factor "cm for 4*pi" ########################################################### ## Degree of fractal -b=-3 +b=-3.0 ## Dimension of pixels (km), should be multiples of the smallest dlx=1.0 dly=1.0 @@ -33,7 +33,7 @@ ## Number of pixels. nx=305 ny=305 -nz=16 +nz=10 nmax=int(max([nx*dx,ny*dy,nz*dz])) #texte="dimensions x : %d / y : %d / z : %d" % (nx*dlx,ny*dly,nz*dlz) @@ -63,10 +63,10 @@ #y=np.arange(0,dly*(nx-1),dly) #z=np.arange(0,dlz*(nx-1),dlz) -df=1/(nmax*dl) -dfx=1/(nx*dlx) -dfy=1/(ny*dly) -dfz=1/(nz*dlz) +df=1.0/(nmax*dl) +dfx=1.0/(nx*dlx) +dfy=1.0/(ny*dly) +dfz=1.0/(nz*dlz) #Center indices of matrix = Nyquist c=(nmax+1)/2 @@ -77,19 +77,19 @@ for i in range(0,int(np.floor((nmax+1)/2))-1): f[i]=(i)*df for i in range(int(np.floor((nmax+1)/2))-1,int(nmax)): - f[i]=-1*(nmax-i)*df + f[i]=-1.0*(nmax-i)*df for i in range(0,int(np.floor((nx+1)/2))-1): fx[i]=(i)*dfx for i in range(int(np.floor((nx+1)/2))-1,int(nx)): - fx[i]=-1*(nx-i)*dfx + fx[i]=-1.0*(nx-i)*dfx for i in range(1,int(np.floor((ny+1)/2))-1): fy[i]=(i)*dfy for i in range(int(np.floor((ny+1)/2))-1,int(ny)): - fy[i]=-1*(ny-i)*dfy + fy[i]=-1.0*(ny-i)*dfy for i in range(1,int(np.floor((nz+1)/2))-1): fz[i]=(i)*dfz for i in range(int(np.floor((nz+1)/2))-1,int(nz)): - fz[i]=-1*(nz-i)*dfz + fz[i]=-1.0*(nz-i)*dfz # Normal distribution M=M2*np.random.randn(nmax,nmax,nmax)+M1 From 1e70fc759cb6ed8609bf80b0bfc738c30397810a Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Mon, 9 Jul 2018 18:00:53 +0100 Subject: [PATCH 011/170] Updated examples for Bouligand approach Left room for Rob to add Tanaka optimisation strategy in Ex3-Optimisation-routine.ipynb --- .../Notebooks/Ex1-Plot-power-spectrum.ipynb | 58 +++++++++++++++---- ...mpute-Curie-depth-Bouligand-approach.ipynb | 23 ++++++-- .../Notebooks/Ex3-Optimisation-routine.ipynb | 2 +- pycurious/optimise.py | 6 +- 4 files changed, 70 insertions(+), 19 deletions(-) diff --git a/Examples/Notebooks/Ex1-Plot-power-spectrum.ipynb b/Examples/Notebooks/Ex1-Plot-power-spectrum.ipynb index 4334a06..a8484bb 100644 --- a/Examples/Notebooks/Ex1-Plot-power-spectrum.ipynb +++ b/Examples/Notebooks/Ex1-Plot-power-spectrum.ipynb @@ -8,7 +8,7 @@ "\n", "`PyCurious` offers convenience functions to extract the radial power spectrum. This has been derived analytically by Bouligand *et al.* 2009.\n", "\n", - "In this notebook we plot the radial power spectrum using the analytical expression, and compare it to the spectrum computed from a synthetic magnetic anomaly. (This can be generated from `Bouligand_forward.py` in the `tests` directory.)\n", + "In this notebook we plot the radial power spectrum using the analytical expression, and the spectrum computed from a synthetic magnetic anomaly. (This can be generated from `Bouligand_forward.py` in the `tests` directory.)\n", "\n", "### Contents\n", "\n", @@ -36,14 +36,21 @@ "source": [ "## Analytical solution\n", "\n", - "The analytic solution to the power spectrum is given in Equation 4 of [Bouligand *et al.*, 2009](http://doi.wiley.com/10.1029/2009JB006494).\n", + "The analytic solution to the power spectrum is given in Equation 4 of [Bouligand *et al.*, 2009](http://doi.wiley.com/10.1029/2009JB006494),\n", + "\n", + "$$\\begin{align}\n", + "\\Phi_{B1D}(|k|)=&C-2|k|z_t-|k|\\Delta z-\\beta \\ln (|k|)\\\\\n", + "&+\\ln\\left[\\int_0^\\infty\\left(\\cosh(|k|\\Delta z)-\\cos(k_z\\Delta z)\\right)\\left(1+\\left(\\frac{k_z}{|k|}\\right)^2\\right)^{-1-\\frac{\\beta}{2}}\\text{d}k_z\\right]\n", + "\\end{align}$$\n", "\n", "where the shape of the curve depends on 4 variables:\n", "\n", "- $\\beta$ - a fractal parameter\n", "- $z_t$ - top of magnetic sources\n", "- $\\Delta z$ - thickness of the magnetic layer\n", - "- $C$ - a field constant" + "- $C$ - a field constant\n", + "\n", + "We vary each of the parameters below to observe the different shapes of the power spectra." ] }, { @@ -55,7 +62,7 @@ "# wavenumber range\n", "k = np.linspace(1e-3, 3, 10000)\n", "\n", - "# Bouligand 2009 parameters\n", + "# Bouligand 2009 test parameters\n", "beta = 3.0\n", "zt = 1.0\n", "dz = 20.0" @@ -113,7 +120,13 @@ "\n", "The shape of the radial power spectrum is heavily dependent on window size. Resolution of long wavelength features require large windows.\n", "\n", - "> Suggestion: use a window size **> 4 times** the maximum Curie depth." + "> Suggestion: use a window size **> 4 times** the maximum Curie depth.\n", + "\n", + "Let's compare the computed radial power spectrum with random fractal noise from the test data that was generated from `Bouligand_forward.py` with the following parameters:\n", + "\n", + "- $\\beta$ = 3.0\n", + "- $z_t$ = 0.305 km\n", + "- $\\Delta z$ = 10 km" ] }, { @@ -122,7 +135,7 @@ "metadata": {}, "outputs": [], "source": [ - "# load magnetic anomaly\n", + "# load magnetic anomaly - i.e. random fractal noise\n", "mag_data = np.loadtxt(\"../data/test_mag_data.txt\")\n", "\n", "nx, ny = 305, 305\n", @@ -135,6 +148,20 @@ "ymin, ymax = y.min(), y.max()" ] }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "## Plot random fractal noise\n", + "\n", + "fig = plt.figure()\n", + "ax1 = fig.add_subplot(111)\n", + "im1 = ax1.imshow(d)\n", + "fig.colorbar(im1, label='nT')" + ] + }, { "cell_type": "code", "execution_count": null, @@ -161,11 +188,15 @@ "# compute radial power spectrum\n", "S, k, sigma2 = grid.radial_spectrum(subgrid)\n", "\n", + "# analytic formulation\n", + "Sb = pycurious.bouligand2009(3.0, 0.305, 10.0, k, -18)\n", + "\n", "\n", "# plot radial power spectrum\n", "fig = plt.figure()\n", "ax1 = fig.add_subplot(111, xlabel=\"wavenumber (rad/km)\", ylabel=\"radial power spectrum\")\n", "ax1.plot(k, S, '-o')\n", + "ax1.plot(k, Sb)\n", "plt.show()" ] }, @@ -173,7 +204,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The default taper is the hanning filter (see [`numpy.hanning`](#hanning) for more details), but other functions can be passed to taper, or simply set it to `None`." + "**Choice of taper**\n", + "\n", + "The default taper is the hanning filter (see [`numpy.hanning`](#hanning) for more details), but other functions can be passed to taper, or simply set it to `None`. There is a significant offset in the power spectrum with tapering functions, however, it is the *slope* of the spectrum with wavenumber that is most important when it comes to determining Curie depth." ] }, { @@ -183,12 +216,17 @@ "outputs": [], "source": [ "\n", - "S, k, sigma2 = grid.radial_spectrum(subgrid, taper=None)\n", + "S1, k1, sigma2 = grid.radial_spectrum(subgrid, taper=None)\n", + "S2, k2, sigma2 = grid.radial_spectrum(subgrid, taper=np.hanning)\n", + "S3, k3, sigma2 = grid.radial_spectrum(subgrid, taper=np.hamming)\n", "\n", "\n", "fig = plt.figure()\n", "ax1 = fig.add_subplot(111, xlabel=\"wavenumber (rad/km)\", ylabel=\"radial power spectrum\")\n", - "ax1.plot(k, S, '-o')\n", + "ax1.plot(k1, S1, '-o', label='none')\n", + "ax1.plot(k2, S2, '-o', label='hanning')\n", + "ax1.plot(k3, S3, '-o', label='hamming')\n", + "ax1.legend()\n", "plt.show()" ] }, @@ -198,7 +236,7 @@ "source": [ "## Azimuthal power spectrum\n", "\n", - "The azimuthal spectrum computes the FFT on a square window that is polarised at a range of radii. This is useful to explore linear trends in the magnetic anomaly that may align with a particular foliation or strike direction.\n", + "The azimuthal spectrum computes the FFT on a square window that is polarised at a range of radii. This is useful to explore linear trends in the magnetic anomaly that may align with a particular foliation or strike orientation.\n", "\n", "```python\n", "azimuthal_spectrum(subgrid, theta=5.0)\n", diff --git a/Examples/Notebooks/Ex2b-Compute-Curie-depth-Bouligand-approach.ipynb b/Examples/Notebooks/Ex2b-Compute-Curie-depth-Bouligand-approach.ipynb index edcd2ed..e09af69 100644 --- a/Examples/Notebooks/Ex2b-Compute-Curie-depth-Bouligand-approach.ipynb +++ b/Examples/Notebooks/Ex2b-Compute-Curie-depth-Bouligand-approach.ipynb @@ -101,7 +101,7 @@ "The `optimise` routine determines the Curie parameters ($\\beta, z_t, \\Delta z, C$) by minimising the misfit between the analytic power spectum and the computed power spectrum. Optimisation is handles by the nonlinear least-squares algorithm implemented in `scipy.optimize.minimize`.\n", "\n", "```python\n", - "optimise(window, xc, yc, beta=3.0, zt=1.0, dz=20.0, C=5.0)\n", + "optimise(window, xc, yc, beta=3.0, zt=1.0, dz=10.0, C=5.0)\n", "```\n", "\n", "These are sane defaults to initiate the optimisation, however, values close to the final solution will result in faster convergence and stability." @@ -162,7 +162,9 @@ " print(\"beta = {:.2f}\\n zt = {:.2f}\\n dz = {:.2f}\\n C = {:.2f}\\n\".format(beta,zt,dz,C))\n", " \n", " Sb = pycurious.bouligand2009(beta, zt, dz, k, C)\n", - " ax1.plot(k, Sb, color='C{}'.format(i), linewidth=2)" + " ax1.plot(k, Sb, color='C{}'.format(i), linewidth=2, label=\"window size = {}km\".format(window_size/1e3))\n", + "\n", + "ax1.legend()" ] }, { @@ -176,10 +178,19 @@ "Adding *a priori* information on $\\beta, z_t, \\Delta z, C$ can reduce the incidence of anomalous values. $\\beta$ and $C$ vary at long wavelengths, and $z_t + \\Delta z$ should be within the range of 10-40 km if we assume the Curie depth is equivalent to the 580$^\\circ$C isotherm. Adding prior information to any (or all) of these parameters penalises spurious values using a standard $\\ell_2$-norm misfit function.\n", "\n", "```python\n", - "add_prior(beta=(3.0,0.5), zt=(0.0,0.1), dz=(20.0,10.0), C=(5,2.5))\n", + "from scipy import stats\n", + "\n", + "# define normal distributions\n", + "beta_p = stats.norm(3.0, 1.0)\n", + "zt_p = stats.norm(0.0, 1.0)\n", + "dz_p = stats.norm(10.0, 8.0)\n", + "C_p = stats.norm(10.0, 10.0)\n", + "\n", + "# add to grid object\n", + "grid.add_prior(beta=beta_p, zt=zt_p, dz=dz_p, C=C_p)\n", "```\n", "\n", - "A combination of priors can be added with $(\\mu, \\sigma)$ pairs. Currently, only Gaussian distributions are supported. `reset_priors()` removes all prior information." + "A combination of priors can be added. `reset_priors()` removes all prior information." ] }, { @@ -190,7 +201,9 @@ "source": [ "grid.reset_priors()\n", "\n", - "grid.add_prior(beta=(3.0,0.01))\n", + "from scipy import stats\n", + "beta_p = stats.norm(3.0, 0.01)\n", + "grid.add_prior(beta=beta_p)\n", "\n", "fig = plt.figure()\n", "ax1 = fig.add_subplot(111, xlabel=\"wavenumber (rad/km)\", ylabel=\"radial power spectrum\")\n", diff --git a/Examples/Notebooks/Ex3-Optimisation-routine.ipynb b/Examples/Notebooks/Ex3-Optimisation-routine.ipynb index b3d2a8c..ae40d98 100644 --- a/Examples/Notebooks/Ex3-Optimisation-routine.ipynb +++ b/Examples/Notebooks/Ex3-Optimisation-routine.ipynb @@ -80,7 +80,7 @@ "\n", "Here, we aim to assess the uncertainty of Curie depth determinations using a sensitivity analysis. The approach we outline here is not necessarily the most statistically robust methodology, but it is intended as a practical means to compute Curie depth whilst considering its uncertainty.\n", "\n", - "First we find the best model with no priors to evaluate the heterogeneity in the signal we extract from the magnetic anomaly. We use the commonly used $\\ell_2$-norm objective function to calculate misfit." + "First we find the best model with no priors to evaluate the heterogeneity in the signal we extract from the magnetic anomaly. We use the commonly used $\\ell_2$-norm objective function to calculate misfit. The objective function can be accessed (and modified) under `grid.objective_function`" ] }, { diff --git a/pycurious/optimise.py b/pycurious/optimise.py index 22e13bf..74152e0 100644 --- a/pycurious/optimise.py +++ b/pycurious/optimise.py @@ -154,7 +154,7 @@ def min_func(self, x, Phi_exp, kh): return misfit - def optimise(self, window, xc, yc, beta=3.0, zt=1.0, dz=20.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs): + def optimise(self, window, xc, yc, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs): """ Find the optimal parameters of beta, zt, dz, C for a given centroid (xc,yc) and window size. @@ -199,7 +199,7 @@ def process_subgrid(subgrid): return res.x - def optimise_routine(self, window, xc_list, yc_list, beta=3.0, zt=1.0, dz=20.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs): + def optimise_routine(self, window, xc_list, yc_list, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs): """ Iterate through a list of centroids to compute the optimal values of beta, zt, dz, C for a given window size. @@ -262,7 +262,7 @@ def optimise_routine(self, window, xc_list, yc_list, beta=3.0, zt=1.0, dz=20.0, return Bopt, ztopt, dzopt, Copt - def sensitivity_routine(self, nsim, window, xc_list, yc_list, beta=3.0, zt=1.0, dz=20.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs): + def sensitivity_routine(self, nsim, window, xc_list, yc_list, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs): """ Iterate through a list of centroids to compute the mean and standard deviation of beta, zt, dz, C by perturbing their From 17913e5ef07e9cdabfe261fd43aa4e5899a3f2ac Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Tue, 10 Jul 2018 11:58:25 +0100 Subject: [PATCH 012/170] New mapping function to export GeoTIFFs --- .../Ex4-Mapping-Curie-depth-EMAG2.ipynb | 132 +++++++++++++++--- pycurious/__init__.py | 2 +- pycurious/curie.py | 3 +- pycurious/mapping.py | 120 +++++++++++----- 4 files changed, 201 insertions(+), 56 deletions(-) diff --git a/Examples/Notebooks/Ex4-Mapping-Curie-depth-EMAG2.ipynb b/Examples/Notebooks/Ex4-Mapping-Curie-depth-EMAG2.ipynb index 4e7fbea..efaebcc 100644 --- a/Examples/Notebooks/Ex4-Mapping-Curie-depth-EMAG2.ipynb +++ b/Examples/Notebooks/Ex4-Mapping-Curie-depth-EMAG2.ipynb @@ -31,7 +31,8 @@ "- [Import EMAG2 data](#Import-EMAG2-data)\n", "- [Interpolate onto grid projection](#Interpolate-onto-grid-projection)\n", "- [Compute Curie depth](#Compute-Curie-depth)\n", - "- [Compare to reference models](#Compare-to-reference-models)" + "- [Compare to reference models](#Compare-to-reference-models)\n", + "- [Export GeoTIFF](#Export-GeoTIFF)" ] }, { @@ -59,7 +60,22 @@ "\n", "The latest data can be downloaded from the [NOAA web page](https://www.ngdc.noaa.gov/geomag/emag2.html) in CSV format. Download it to a local directory (may take some time).\n", "\n", - "Once loaded, we trim the data to a region of interest - being careful to allow some buffer to accommodate the maximum window size. We save this to a compressed `.npz` file to avoid the costly repitition of reloading the same data in the future." + "Once loaded, we trim the data to a region of interest - being careful to allow some buffer to accommodate the maximum window size. We save this to a compressed `.npz` file to avoid the costly repitition of reloading the same data in the future.\n", + "\n", + "**EMAG2_V3_20170530.csv**\n", + "\n", + "- Column 1: i ; grid column/longitude index\n", + "- Column 2: j ; grid row/latitude index\n", + "- Column 3: LON ; Geographic Longitude WGS84 (decimal degrees)\n", + "- Column 4: LAT ; Geographic Latitude WGS84 (decimal degrees)\n", + "- Column 5: SeaLevel ; Magnetic Anomaly Value at Sea Level(nT)\n", + "- Column 6: UpCont ; Magnetic Anomaly Value at continuous 4km altitude (nT)\n", + "- Column 7: Code ; Data Source Code (see table below)\n", + "- Column 8: Error ; Error estimate (nT)\n", + "\n", + "Code 888 is assigned in certain cells on grid edges where the data source is ambiguous and assigned an error of -888 nT\n", + "\n", + "Code 999 is assigned in cells where no data is reported with the anomaly value assigned 99999 nT and an error of -999 nT" ] }, { @@ -68,7 +84,7 @@ "metadata": {}, "outputs": [], "source": [ - "filedir = '/path/to/directory/'\n", + "filedir = '/path/to/emag2'\n", "\n", "try:\n", " with np.load(filedir+'EMAG2_V3_20170530.npz') as f:\n", @@ -87,7 +103,7 @@ "outputs": [], "source": [ "# filter NaNs\n", - "mag_data = mag_data[mag_data[:,4] != 99999.]\n", + "mag_data = mag_data[mag_data[:,3] != 99999.]\n", "mag_data = mag_data[mag_data[:,4] != -888.]\n", "mag_data = mag_data[mag_data[:,4] != -999.]\n", "\n", @@ -106,7 +122,9 @@ "source": [ "## Interpolate onto grid projection\n", "\n", - "We choose an arbitrary section of the Earth's surface and a suitable projection. PyCurious handles transformation between different CRS using a EPSG reference code. EMAG2 is in lons and lats (in decimal degrees), which we want to convert into eastings and northings (in metres). For this example, we transform WGS84 coordinates (EPSG:4326) to the IRENET95 projection (EPSG:2157)." + "We choose an arbitrary section of the Earth's surface and a suitable projection. PyCurious handles transformation between different CRS using a EPSG reference code. EMAG2 is in lons and lats (in decimal degrees), which we want to convert into eastings and northings (in metres). For this example, we transform WGS84 coordinates (EPSG:4326) to the IRENET95 projection (EPSG:2157).\n", + "\n", + "**The power spectrum must be in eastings & northings to compute the power spectrum in rad/km.**" ] }, { @@ -116,14 +134,14 @@ "outputs": [], "source": [ "# grid extent - grid of the British Isles in Irenet 95 grid projection\n", - "xmin = 250000.0\n", - "xmax = 1400000.0\n", - "ymin = 200000.0\n", - "ymax = 1500000.0\n", + "xmin = 0.0\n", + "xmax = 1900000.0\n", + "ymin = 0.0\n", + "ymax = 1700000.0\n", "extent_grid = [xmin, xmax, ymin, ymax]\n", "\n", "# extent on the sphere (WGS84)\n", - "extent_sphere = pycurious.mapping.convert_extent(extent_grid, epsg_in=4326, epsg_out=2157)\n", + "extent_sphere = pycurious.mapping.convert_extent(extent_grid, epsg_in=2157, epsg_out=4326)\n", "\n", "# map extent - should be narrower than extent_sphere\n", "extent_map = [-10.8, 2, 49.5, 59]" @@ -135,11 +153,11 @@ "metadata": {}, "outputs": [], "source": [ - "dx, dy = 1e3, 1e3 # 1 km resolution\n", + "dx, dy = 1e3, 1e3 # 1 km grid resolution\n", "nx, ny = int(round((xmax-xmin)/dx)), int(round((ymax-ymin)/dy))\n", "\n", "# interpolate onto grid extent (for computation)\n", - "mag_grid = pycurious.mapping.grid(mag_data[:,:2], mag_data[:,3], extent, shape=(ny,nx), epsg_in=4326, epsg_out=2157)\n", + "mag_grid = pycurious.mapping.grid(mag_data[:,:2], mag_data[:,3], extent_grid, shape=(ny,nx), epsg_in=4326, epsg_out=2157)\n", "\n", "# interpolate onto extent on the sphere (for mapping)\n", "mag_sphere = pycurious.mapping.grid(mag_data[:,:2], mag_data[:,3], extent_sphere, shape=(ny,nx))" @@ -155,7 +173,7 @@ "\n", "fig = plt.figure(figsize=(12,10))\n", "ax = plt.axes(projection=proj)\n", - "ax.set_extent(map_extent)\n", + "ax.set_extent(extent_map)\n", "ax.coastlines(resolution='50m', linewidth=1.5)\n", "ax.gridlines()\n", "\n", @@ -182,13 +200,50 @@ "source": [ "grid = pycurious.CurieOptimise(mag_grid, xmin, xmax, ymin, ymax)\n", "\n", - "# centroid spacing of 20 km\n", - "xc_list, yc_list = grid.create_centroid_list(200e3, spacingX=20e3, spacingY=20e3)\n", + "window_size = 400e3\n", + "\n", + "# centroid spacing of 50 km\n", + "xc_list, yc_list = grid.create_centroid_list(window_size, spacingX=50e3, spacingY=50e3)\n", "print(\"number of centroids = {}\".format(len(xc_list)))\n", "\n", + "\n", "beta, zt, dz, C = grid.optimise_routine(window_size, xc_list, yc_list)" ] }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "curie_depth = zt + dz\n", + "centroids = np.column_stack([xc_list, yc_list])\n", + "\n", + "curie_depth_sphere = pycurious.mapping.grid(centroids, curie_depth, extent_sphere, (ny,nx), epsg_in=2157, epsg_out=4326)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": false + }, + "outputs": [], + "source": [ + "proj = ccrs.UTM(30)\n", + "\n", + "fig = plt.figure(figsize=(12,10))\n", + "ax = plt.axes(projection=proj)\n", + "ax.set_extent(extent_map)\n", + "ax.coastlines(resolution='50m', linewidth=1.5)\n", + "ax.gridlines()\n", + "\n", + "im1 = ax.imshow(curie_depth_sphere, extent=extent_sphere, transform=ccrs.PlateCarree(),\n", + " cmap='BrBG', vmin=10, vmax=40, zorder=0)\n", + "\n", + "fig.colorbar(im1, label='nT')" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -201,7 +256,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "li_cpd = np.loadtxt(filedir + 'Li_2017_curiedepth.txt')\n", @@ -220,7 +277,7 @@ "\n", "fig = plt.figure(figsize=(12,10))\n", "ax = plt.axes(projection=proj)\n", - "ax.set_extent(map_extent)\n", + "ax.set_extent(extent_map)\n", "ax.coastlines(resolution='50m', linewidth=1.5)\n", "ax.gridlines()\n", "\n", @@ -229,6 +286,45 @@ "\n", "fig.colorbar(im1, label='km')" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Export GeoTIFF\n", + "\n", + "The GeoTIFF format contains projection information, which makes it ideal for GIS applications such as [QGIS](https://www.qgis.org/en/site/)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "pycurious.mapping.export_geotiff(\"my-curie-depth.tiff\", curie_depth_sphere, extent_sphere, epsg=4326)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can also import a GeoTIFF using the `mapping` module. the `import_geotiff` function prints a wealth of information on the reference spheriod and the projection of the GeoTIFF, including EPSG code." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "GTiff, GTextent = pycurious.mapping.import_geotiff(\"my-curie-depth.tiff\")\n", + "\n", + "print(GTextent)\n", + "print(GTiff.shape)" + ] } ], "metadata": { @@ -247,7 +343,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", - "version": "2.7.15" + "version": "2.7.12" } }, "nbformat": 4, diff --git a/pycurious/__init__.py b/pycurious/__init__.py index 31932e4..bcb2dc3 100644 --- a/pycurious/__init__.py +++ b/pycurious/__init__.py @@ -2,4 +2,4 @@ from .curie import CurieGrid, bouligand2009, tanaka1999, maus1995 from .optimise import CurieOptimise from .parallel import CurieParallel -from .mapping import transform_coordinates, grid, trim \ No newline at end of file +from .mapping import * \ No newline at end of file diff --git a/pycurious/curie.py b/pycurious/curie.py index f52db81..10b7f02 100644 --- a/pycurious/curie.py +++ b/pycurious/curie.py @@ -268,8 +268,7 @@ def radial_spectrum_log(self, subgrid, taper=np.hanning, scale=0.001, **kwargs): sigma2 = np.empty(nbins) i0 = int((nw - 1)//2) - nw_range = np.arange(0, nw) - iy, ix = np.meshgrid(nw_range, nw_range) + ix, iy = np.mgrid[0:nw,0:nw] kk = np.hypot((ix - i0)*dk, (iy - i0)*dk) for i in range(0, nbins): diff --git a/pycurious/mapping.py b/pycurious/mapping.py index 63efc79..73692c9 100644 --- a/pycurious/mapping.py +++ b/pycurious/mapping.py @@ -16,6 +16,28 @@ def transform_coordinates(x, y, epsg_in, epsg_out): return pyproj.transform(proj_in, proj_out, x, y) +def convert_extent(extent_in, epsg_in, epsg_out): + """ + Transform extent from epsg_in to epsg_out + + Parameters + ---------- + extent_in : bounding box [minX, maxX, minY, maxY] + epsg_in : CRS of extent + epsg_out : CRS of output + + Returns + ------- + extent_out : bounding box in new CRS + """ + xmin, xmax, ymin, ymax = extent_in + xi = [xmin, xmin, xmax, xmax] + yi = [ymin, ymax, ymin, ymax] + xo, yo = transform_coordinates(xi, yi, epsg_in, epsg_out) + extent_out = [min(xo), max(xo), min(yo), max(yo)] + return extent_out + + def trim(coords, data, extent, buffer_amount=0.0): """ Grid a smaller section of a large dataset taking into @@ -58,7 +80,6 @@ def trim(coords, data, extent, buffer_amount=0.0): return coords_trim, data_trim - def grid(coords, data, extent, shape=None, epsg_in=None, epsg_out=None, **kwargs): """ Grid a smaller section of a large dataset taking into @@ -100,7 +121,7 @@ def grid(coords, data, extent, shape=None, epsg_in=None, epsg_out=None, **kwargs xtextent = [xtmin, xtmax, ytmin, ytmax] # trim data - buffer = 1% - coords_trim, data_trim = trim(coords, data, xtextent, 0.01) + coords_trim, data_trim = trim(coords, data, xtextent, 0.05) if type(epsg_in) != type(None): @@ -133,45 +154,74 @@ def grid(coords, data, extent, shape=None, epsg_in=None, epsg_out=None, **kwargs return vq -def optimise_surfaces(surface1, surface2, sigma): +def import_geotiff(file_path): """ - Optimise the misfit between surface1 and surface2 - - surface1 and surface2 are normalised between 0 and 1 - and their residual is minimised, weighted by sigma + Import a GeoTIFF to a numpy array and prints + information of the Coordinate Reference System (CRS) Parameters ---------- - surface1 : starting surface (can be flat) - surface2 : surface to match to - sigma : uncertainty of fitting coefficients + file_path : path to the GeoTIFF Returns ------- - surface3 : optimised surface - - Notes - ----- - The Krylov method uses a Krylov approximation for the - inverse Jacobian as it is suitable for large problems + data : 2D numpy array + extent : extent in the projection of the GeoTIFF + e.g. [xmin, xmax, ymin, ymax] """ - from scipy.optimize import root - - def objective_function(x, x0, sigma_x0): - return (x - x0)**2/sigma_x0**2 - - sigma = sigma.ravel() - - s1 = surface1.flatten() - s1 -= s1.min() - s1 /= s1.max() - - s2 = surface2.flatten() - s2 -= s2.min() - s2 /= s2.max() + from osgeo import gdal, osr - # starting point should be at prior - x0 = s1 - - sol = root(objective_function, x0, method='krylov') - return sol.x.reshape(surface1.shape) + gtiff = gdal.Open(file_path) + data = gtiff.ReadAsArray() + gt = gtiff.GetGeoTransform() + gtproj = gtiff.GetProjection() + + inproj = osr.SpatialReference() + inproj.ImportFromWkt(gtproj) + + gtextent = (gt[0], gt[0] + gtiff.RasterXSize*gt[1], + gt[3] + gtiff.RasterYSize*gt[5], gt[3]) + + # print projection information + print(inproj) + + # this closes the geotiff + gtiff = None + + return np.flipud(data), gtextent + + +def export_geotiff(file_path, array, extent, epsg): + """ + Export a GeoTIFF from a numpy array projected in a + predefined Coordinate Reference System (CRS) + + Parameters + ---------- + file_path : str, path to write the GeoTIFF + array : 2D numpy array + extent : extent in the projection of the GeoTIFF + e.g. [xmin, xmax, ymin, ymax] + epsg : int, CRS of the GeoTIFF + + """ + from osgeo import gdal, osr + # import ogr, gdal, osr, os + + cols = array.shape[1] + rows = array.shape[0] + + xmin, xmax, ymin, ymax = extent + spacingX = (xmax - xmin)/cols + spacingY = (ymax - ymin)/rows + + driver = gdal.GetDriverByName('GTiff') + outRaster = driver.Create(file_path, cols, rows, 1, gdal.GDT_Byte) + outRaster.SetGeoTransform((xmin, spacingX, 0, ymin, 0, spacingY)) + outband = outRaster.GetRasterBand(1) + outband.WriteArray(array) + outRasterSRS = osr.SpatialReference() + outRasterSRS.ImportFromEPSG(epsg) + outRaster.SetProjection(outRasterSRS.ExportToWkt()) + outband.FlushCache() + return \ No newline at end of file From 82eb33dd8670b0ba798fe9aca6b63672c7b9c0b6 Mon Sep 17 00:00:00 2001 From: Robert Delhaye Date: Thu, 12 Jul 2018 17:16:49 +0100 Subject: [PATCH 013/170] Updated Jupyter notebooks. Ex2a essentially complete. Ex4 in progress. --- .../Notebooks/Ex1-Plot-power-spectrum.ipynb | 2 +- ...-Compute-Curie-depth-Tanaka-approach.ipynb | 144 +++++++++++++++-- ...mpute-Curie-depth-Bouligand-approach.ipynb | 152 ++++++++++++++++-- .../Notebooks/Ex3-Optimisation-routine.ipynb | 16 +- pycurious/curie.py | 4 +- 5 files changed, 291 insertions(+), 27 deletions(-) diff --git a/Examples/Notebooks/Ex1-Plot-power-spectrum.ipynb b/Examples/Notebooks/Ex1-Plot-power-spectrum.ipynb index 4334a06..9db4fde 100644 --- a/Examples/Notebooks/Ex1-Plot-power-spectrum.ipynb +++ b/Examples/Notebooks/Ex1-Plot-power-spectrum.ipynb @@ -261,7 +261,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", - "version": "2.7.15" + "version": "2.7.15rc1" } }, "nbformat": 4, diff --git a/Examples/Notebooks/Ex2a-Compute-Curie-depth-Tanaka-approach.ipynb b/Examples/Notebooks/Ex2a-Compute-Curie-depth-Tanaka-approach.ipynb index 3a861d2..d7c515d 100644 --- a/Examples/Notebooks/Ex2a-Compute-Curie-depth-Tanaka-approach.ipynb +++ b/Examples/Notebooks/Ex2a-Compute-Curie-depth-Tanaka-approach.ipynb @@ -4,12 +4,44 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Example 2a - Compute Curie depth (Tanaka approach)" + "# Example 2a - Compute Curie depth (Tanaka approach)\n", + "Tanaka *et al.* (1999) based their method upon an expression for the radial power spectrum that assumes random magnetisation of the crust, and a radially averaged power spectra $\\Phi_{\\Delta T}(|k|)$:\n", + "\n", + "$$(1) \\Phi_{\\Delta T}(|k|)=Ae^{-2|k|Z_t}(1-e^{-|k|(Z_b-Z_t)})^2$$\n", + "\n", + "where:\n", + " - $k$ - spatial wavenumber ($k=2\\pi/\\lambda$, where $\\lambda$ is wavelength).\n", + " - $Z_t$ - top of assumed magnetic source.\n", + " - $Z_b$ - bottom of assumed magnetic source.\n", + " - ($Z_b-Z_t$ is hence the thickness of the magnetic source)\n", + "\n", + "For wavelengths less than twice the source thickness, this simplifies to:\n", + "\n", + "$$(2) \\ln [\\Phi_{\\Delta T}(|k|)^{1/2}] = \\ln B-|k|Z_t $$\n", + "\n", + "where $B$ is another constant. Conversely, (1) can be rewritten, with $Z_o$ as the centroid depth of the magnetic source:\n", + "\n", + "$$(3) \\Phi_{\\Delta T}(|k|)^{1/2} = Ce^{-|k|Z_o}(e^{-|k|(Z_t-Z_o)}-e^{-|k|(Z_b-Z_o)}) $$\n", + "\n", + "For long wavelengths, where $2d$ is the magnetic source thickness:\n", + "$$(4) \\Phi_{\\Delta T}(|k|)^{1/2} = Ce^{-|k|Z_o}(e^{-|k|(-d)}-e^{-|k|(-d)})\\approx Ce^{-|k|Z_o}2|k|d $$\n", + "\n", + "$$ \\ln \\{\\Phi_{\\Delta T}(|k|)^{1/2}/|k|\\}=\\ln D-|k|Z_o $$\n", + "\n", + "\n", + "Estimates of $Z_t$ and $Z_o$ can be estimated from Equations (2) and (5), and hence the base of the magnetic source (assumed to be at the Curie point depth):\n", + "\n", + "$$(6) Z_b=Z_o-(Z_t-Z_o) = 2Z_o-Z_t $$\n", + "\n", + "### Contents\n", + "\n", + "- [Plot radial power spectrum](#Plot-radial-power-spectrum)\n", + "- [Compute CPD Estimate](#Compute-cpd-estimate)" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 10, "metadata": {}, "outputs": [], "source": [ @@ -22,7 +54,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": {}, "outputs": [], "source": [ @@ -39,14 +71,23 @@ "ymin, ymax = y.min(), y.max()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Plot radial power spectrum\n", + "The radial power spectrum is computed from a square window of the magnetic anomaly. Methods to select window sizes and compute the Fast Fourier Transform (FFT) belong to the `CurieGrid` object. We apply the default `np.hanning` taper to the power spectrum as in [Ex1-Plot-power-spectrum](#./Ex1-Plot-power-spectrum.ipynb)." + ] + }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# initialise CurieOptimise object\n", "grid = pycurious.CurieOptimise(d, xmin, xmax, ymin, ymax)\n", + "#grid = pycurious.CurieGrid(d, xmin, xmax, ymin, ymax)\n", "\n", "# pick the centroid\n", "xpt = 0.5*(xmin + xmax)\n", @@ -58,22 +99,103 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 35, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0,0.5,u'$\\\\ln(\\\\Phi_{\\\\Delta T}(|k|)^{1/2})/(2\\\\pi)$')" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "S, k, sigma2 = grid.radial_spectrum_log(subgrid)\n", + "\n", + "# Plot of power spectrum, as function of spatial frequency\n", + "plt.plot(k/(2*np.pi), S/(2*np.pi), '-o')\n", + "plt.title('Power Spectrum')\n", + "plt.xlabel(r'$|k|/(2\\pi)$ [km$^{-1}$]')\n", + "plt.ylabel(r'$\\ln(\\Phi_{\\Delta T}(|k|)^{1/2})/(2\\pi)$')" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0,0.5,u'$\\\\ln(\\\\Phi_{\\\\Delta T}(|k|)^{1/2}/|k|)/(2\\\\pi)$')" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ - "S, k, sigma2 = grid.radial_spectrum_log(subgrid)" + "Sn=np.log(np.exp(S)/k)\n", + "plt.plot(k/(2*np.pi), Sn/(2*np.pi), '-o')\n", + "plt.title('Power Spectrum, weighted by k')\n", + "plt.xlabel(r'$|k|/(2\\pi)$ [km$^{-1}$]')\n", + "plt.ylabel(r'$\\ln(\\Phi_{\\Delta T}(|k|)^{1/2}/|k|)/(2\\pi)$')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Compute CPD Estimate\n", + "As described above, once the power spectrum (and weighted spectrum) are computed, then the gradient of linear fits of certain wavenumber/spatial frequency windows can be taken as estimates of $Z_t$ and $Z_o$. The weighted linear fitting of the respective spectral window is implemented in the `CurieGrid` parent class as `tanaka1999`, and takes the spectrum, wave number, and spectrum error as inputs. The function also has functionality to pass specific spectral windows for each spectra, however, the default is to consider spatial frequencies of 0.05 - 0.2 (recalling that $k$, the wavenumber, is proportional to the spatial frequency $\\nu$ by $k=2\\pi\\nu$).\n", + "\n", + "\n", + "The function has two returns: the estimate of $Z_b$, and the propagated uncertainty $\\varepsilon_{Zb}$." ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 43, "metadata": { "scrolled": true }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Zb estimate: 23.35771952, +/- 6.77365143 km\n" + ] + } + ], "source": [ - "pycurious.tanaka1999(S, k, sigma2)" + "[Zb,ezb]=pycurious.tanaka1999(S, k, sigma2)\n", + "print('Zb estimate: '+np.array2string(Zb)+', +/- '+np.array2string(ezb)+' km')" ] } ], @@ -93,7 +215,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", - "version": "2.7.15" + "version": "2.7.15rc1" } }, "nbformat": 4, diff --git a/Examples/Notebooks/Ex2b-Compute-Curie-depth-Bouligand-approach.ipynb b/Examples/Notebooks/Ex2b-Compute-Curie-depth-Bouligand-approach.ipynb index ab84e0e..418efa5 100644 --- a/Examples/Notebooks/Ex2b-Compute-Curie-depth-Bouligand-approach.ipynb +++ b/Examples/Notebooks/Ex2b-Compute-Curie-depth-Bouligand-approach.ipynb @@ -25,7 +25,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ @@ -38,7 +38,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -66,7 +66,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": {}, "outputs": [], "source": [ @@ -82,9 +82,30 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "S, k, sigma2 = grid.radial_spectrum(subgrid)\n", "\n", @@ -109,9 +130,32 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "beta = 0.00\n", + " zt = 1.31\n", + " dz = 107.74\n", + " C = 0.00\n", + "\n", + "Curie depth is 109.05 km\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "beta, zt, dz, C = grid.optimise(window_size, xpt, ypt)\n", "print(\"beta = {:.2f}\\n zt = {:.2f}\\n dz = {:.2f}\\n C = {:.2f}\".format(beta,zt,dz,C))\n", @@ -138,9 +182,46 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "beta = 0.00\n", + " zt = 1.31\n", + " dz = 107.74\n", + " C = 0.00\n", + "\n", + "beta = 0.00\n", + " zt = 1.36\n", + " dz = 146.33\n", + " C = 0.00\n", + "\n", + "beta = 0.00\n", + " zt = 1.45\n", + " dz = 19.95\n", + " C = 0.00\n", + "\n", + "beta = 0.00\n", + " zt = 1.53\n", + " dz = 20.00\n", + " C = 0.00\n", + "\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "\n", "# window size in kilometres\n", @@ -184,9 +265,56 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "beta = 3.01\n", + " zt = 0.50\n", + " dz = 0.65\n", + " C = 0.00\n", + "\n", + "beta = 2.99\n", + " zt = 0.76\n", + " dz = 0.54\n", + " C = 0.00\n", + "\n", + "beta = 3.00\n", + " zt = 0.62\n", + " dz = 0.34\n", + " C = 0.00\n", + "\n", + "beta = 3.00\n", + " zt = 0.86\n", + " dz = 20.00\n", + " C = 0.00\n", + "\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "grid.reset_priors()\n", "grid.add_prior(beta=(3.0,0.01))\n", @@ -228,7 +356,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", - "version": "2.7.15" + "version": "2.7.15rc1" } }, "nbformat": 4, diff --git a/Examples/Notebooks/Ex3-Optimisation-routine.ipynb b/Examples/Notebooks/Ex3-Optimisation-routine.ipynb index f65ce73..661c666 100644 --- a/Examples/Notebooks/Ex3-Optimisation-routine.ipynb +++ b/Examples/Notebooks/Ex3-Optimisation-routine.ipynb @@ -83,6 +83,20 @@ "metadata": {}, "outputs": [], "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Parameter Exploration of Spectral Analysis method (Tanaka)\n", + "\n", + "Due to the deterministic approach that [Tanaka *et al.*, 1999](http://linkinghub.elsevier.com/retrieve/pii/S0040195199000724) uses for estimating $Z_b$, the uncertainties returned by `CurieGrid.tanaka1999` are the simple results of error propagation from the initial spectra uncertainties. It should also be noted that the spectra uncertainties represent the variance within the sampled sector of the 2D FFT, and may comprise both noise and anisotropic signal.\n", + "\n", + "We present here several tests of the `CurieGrid.tanaka1999` function in order to explore how the input parameters affect the resulting Curie point depth estimates. In particular, we consider the following:\n", + "1. Effect of magnetic data window size (i.e., domain of magnetic data before computing FFT).\n", + "2. Effect of where in $k$-space is specific window used, separately for both the power and $k$-weighted power spectra (i.e., which $k$ do we consider?).\n", + "3. Effect of $k$-space window size (i.e., how much of the $k$-domain do we consider?).\n" + ] } ], "metadata": { @@ -101,7 +115,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", - "version": "2.7.15" + "version": "2.7.15rc1" } }, "nbformat": 4, diff --git a/pycurious/curie.py b/pycurious/curie.py index f52db81..b2c988b 100644 --- a/pycurious/curie.py +++ b/pycurious/curie.py @@ -280,8 +280,8 @@ def radial_spectrum_log(self, subgrid, taper=np.hanning, scale=0.001, **kwargs): sigma2[i] = np.std(rr)/np.sqrt(rr.size) return S, k, sigma2 - - + + def azimuthal_spectrum(self, subgrid, taper=np.hanning, scale=0.001, theta=5.0, **kwargs): """ Compute azimuthal spectrum for a square grid. From 27f42320f4c5f803a72ccf4ee218d22f2f9a40ed Mon Sep 17 00:00:00 2001 From: Robert Delhaye Date: Thu, 12 Jul 2018 17:19:01 +0100 Subject: [PATCH 014/170] Updated Jupyter notebooks. Ex2a essentially complete. Ex4 in progress. --- .../Ex1-Plot-power-spectrum-checkpoint.ipynb | 269 +++++++++++++ ...rie-depth-Tanaka-approach-checkpoint.ipynb | 223 +++++++++++ ...-depth-Bouligand-approach-checkpoint.ipynb | 364 ++++++++++++++++++ .../Ex3-Optimisation-routine-checkpoint.ipynb | 123 ++++++ ...x2a-Compute-Curie-depth-Tanaka-approach.py | 35 ++ Examples/Notebooks/Ex2a.py | 39 ++ 6 files changed, 1053 insertions(+) create mode 100644 Examples/Notebooks/.ipynb_checkpoints/Ex1-Plot-power-spectrum-checkpoint.ipynb create mode 100644 Examples/Notebooks/.ipynb_checkpoints/Ex2a-Compute-Curie-depth-Tanaka-approach-checkpoint.ipynb create mode 100644 Examples/Notebooks/.ipynb_checkpoints/Ex2b-Compute-Curie-depth-Bouligand-approach-checkpoint.ipynb create mode 100644 Examples/Notebooks/.ipynb_checkpoints/Ex3-Optimisation-routine-checkpoint.ipynb create mode 100644 Examples/Notebooks/Ex2a-Compute-Curie-depth-Tanaka-approach.py create mode 100644 Examples/Notebooks/Ex2a.py diff --git a/Examples/Notebooks/.ipynb_checkpoints/Ex1-Plot-power-spectrum-checkpoint.ipynb b/Examples/Notebooks/.ipynb_checkpoints/Ex1-Plot-power-spectrum-checkpoint.ipynb new file mode 100644 index 0000000..9db4fde --- /dev/null +++ b/Examples/Notebooks/.ipynb_checkpoints/Ex1-Plot-power-spectrum-checkpoint.ipynb @@ -0,0 +1,269 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Example 1 - Plot power spectra\n", + "\n", + "`PyCurious` offers convenience functions to extract the radial power spectrum. This has been derived analytically by Bouligand *et al.* 2009.\n", + "\n", + "In this notebook we plot the radial power spectrum using the analytical expression, and compare it to the spectrum computed from a synthetic magnetic anomaly. (This can be generated from `Bouligand_forward.py` in the `tests` directory.)\n", + "\n", + "### Contents\n", + "\n", + "- [Analytical solution](#Analytical-solution)\n", + "- [Radial power spectrum](#Power-spectrum-from-FFT)\n", + "- [Azimuthal power spectrum](#Azimuthal-power-spectrum)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "\n", + "import pycurious" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Analytical solution\n", + "\n", + "The analytic solution to the power spectrum is given in Equation 4 of [Bouligand *et al.*, 2009](http://doi.wiley.com/10.1029/2009JB006494).\n", + "\n", + "where the shape of the curve depends on 4 variables:\n", + "\n", + "- $\\beta$ - a fractal parameter\n", + "- $z_t$ - top of magnetic sources\n", + "- $\\Delta z$ - thickness of the magnetic layer\n", + "- $C$ - a field constant" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# wavenumber range\n", + "k = np.linspace(1e-3, 3, 10000)\n", + "\n", + "# Bouligand 2009 parameters\n", + "beta = 3.0\n", + "zt = 1.0\n", + "dz = 20.0" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# plot Bouligand et al. 2009 curves\n", + "\n", + "fig, (ax1, ax2, ax3) = plt.subplots(1,3, figsize=(14,8),)\n", + "\n", + "# vary zt\n", + "for zti in np.arange(0.0, 2.5, 0.5):\n", + " S = pycurious.bouligand2009(beta, zti, dz, k)\n", + " S -= S.max()\n", + " ax1.semilogx(k, S, label=r'$z_t$ = {} km'.format(zti))\n", + "\n", + "# vary dz\n", + "for dzi in [10., 20., 50., 100., 200.]:\n", + " S = pycurious.bouligand2009(beta, zt, dzi, k)\n", + " S -= S.min()\n", + " ax2.semilogx(k, S, label=r'$\\Delta z$ = {} km'.format(dzi))\n", + "\n", + "# vary beta\n", + "for betai in np.arange(0, 5, 1):\n", + " S = pycurious.bouligand2009(betai, zt, dz, k)\n", + " S -= S[-1]\n", + " ax3.semilogx(k, S, label=r'$\\beta$ = {}'.format(betai))\n", + "\n", + "ax1.set_ylim(-20, 0)\n", + "ax2.set_ylim(0, 20)\n", + "\n", + "ax1.legend()\n", + "ax2.legend()\n", + "ax3.legend()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Radial power spectrum\n", + "\n", + "The radial power spectrum is computed from a square window of the magnetic anomaly. Methods to select window sizes and compute the Fast Fourier Transform (FFT) belong to the `CurieGrid` object.\n", + "\n", + "`CurieGrid` achieves the following purposes:\n", + "\n", + "- Upward continuation\n", + "- Reduction to the pole\n", + "- Compute the radial power spectrum using FFT\n", + "\n", + "The shape of the radial power spectrum is heavily dependent on window size. Resolution of long wavelength features require large windows.\n", + "\n", + "> Suggestion: use a window size **> 4 times** the maximum Curie depth." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# load magnetic anomaly\n", + "mag_data = np.loadtxt(\"../data/test_mag_data.txt\")\n", + "\n", + "nx, ny = 305, 305\n", + "\n", + "x = mag_data[:,0]\n", + "y = mag_data[:,1]\n", + "d = mag_data[:,2].reshape(ny,nx)\n", + "\n", + "xmin, xmax = x.min(), x.max()\n", + "ymin, ymax = y.min(), y.max()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# initialise CurieGrid object\n", + "grid = pycurious.CurieGrid(d, xmin, xmax, ymin, ymax)\n", + "\n", + "# pick the centroid\n", + "xpt = 0.5*(xmin + xmax)\n", + "ypt = 0.5*(ymin + ymax)\n", + "\n", + "window_size = 304e3\n", + "subgrid = grid.subgrid(xpt, ypt, window_size)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# compute radial power spectrum\n", + "S, k, sigma2 = grid.radial_spectrum(subgrid)\n", + "\n", + "\n", + "# plot radial power spectrum\n", + "fig = plt.figure()\n", + "ax1 = fig.add_subplot(111, xlabel=\"wavenumber (rad/km)\", ylabel=\"radial power spectrum\")\n", + "ax1.plot(k, S, '-o')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The default taper is the hanning filter (see [`numpy.hanning`](#hanning) for more details), but other functions can be passed to taper, or simply set it to `None`." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "S, k, sigma2 = grid.radial_spectrum(subgrid, taper=None)\n", + "\n", + "\n", + "fig = plt.figure()\n", + "ax1 = fig.add_subplot(111, xlabel=\"wavenumber (rad/km)\", ylabel=\"radial power spectrum\")\n", + "ax1.plot(k, S, '-o')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Azimuthal power spectrum\n", + "\n", + "The azimuthal spectrum computes the FFT on a square window that is polarised at a range of radii. This is useful to explore linear trends in the magnetic anomaly that may align with a particular foliation or strike direction.\n", + "\n", + "```python\n", + "azimuthal_spectrum(subgrid, theta=5.0)\n", + "```\n", + "\n", + "`theta` controls the thickness of each azimuth (in degrees)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "S, k, theta = grid.azimuthal_spectrum(subgrid, theta=20.0)\n", + "\n", + "fig = plt.figure()\n", + "ax1 = fig.add_subplot(111, ylabel=r'azimuth $\\theta$', xlabel='wavenumber (rad/km)')\n", + "im1 = ax1.pcolor(k, theta, S)\n", + "fig.colorbar(im1, label='radial power spectrum')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plotting each azimuth on the power spectrum-wavenumber axis highlights the different in slope for different polarisations of the magnetic anomaly." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig = plt.figure()\n", + "ax1 = fig.add_subplot(111, xlabel=\"wavenumber (rad/km)\", ylabel=\"radial power spectrum\")\n", + "\n", + "for i, angle in enumerate(theta):\n", + " ax1.plot(k, S[i], label=r'$\\theta = {}^\\circ$'.format(angle))\n", + "\n", + "ax1.legend(bbox_to_anchor=(1,1))\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.15rc1" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Examples/Notebooks/.ipynb_checkpoints/Ex2a-Compute-Curie-depth-Tanaka-approach-checkpoint.ipynb b/Examples/Notebooks/.ipynb_checkpoints/Ex2a-Compute-Curie-depth-Tanaka-approach-checkpoint.ipynb new file mode 100644 index 0000000..d7c515d --- /dev/null +++ b/Examples/Notebooks/.ipynb_checkpoints/Ex2a-Compute-Curie-depth-Tanaka-approach-checkpoint.ipynb @@ -0,0 +1,223 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Example 2a - Compute Curie depth (Tanaka approach)\n", + "Tanaka *et al.* (1999) based their method upon an expression for the radial power spectrum that assumes random magnetisation of the crust, and a radially averaged power spectra $\\Phi_{\\Delta T}(|k|)$:\n", + "\n", + "$$(1) \\Phi_{\\Delta T}(|k|)=Ae^{-2|k|Z_t}(1-e^{-|k|(Z_b-Z_t)})^2$$\n", + "\n", + "where:\n", + " - $k$ - spatial wavenumber ($k=2\\pi/\\lambda$, where $\\lambda$ is wavelength).\n", + " - $Z_t$ - top of assumed magnetic source.\n", + " - $Z_b$ - bottom of assumed magnetic source.\n", + " - ($Z_b-Z_t$ is hence the thickness of the magnetic source)\n", + "\n", + "For wavelengths less than twice the source thickness, this simplifies to:\n", + "\n", + "$$(2) \\ln [\\Phi_{\\Delta T}(|k|)^{1/2}] = \\ln B-|k|Z_t $$\n", + "\n", + "where $B$ is another constant. Conversely, (1) can be rewritten, with $Z_o$ as the centroid depth of the magnetic source:\n", + "\n", + "$$(3) \\Phi_{\\Delta T}(|k|)^{1/2} = Ce^{-|k|Z_o}(e^{-|k|(Z_t-Z_o)}-e^{-|k|(Z_b-Z_o)}) $$\n", + "\n", + "For long wavelengths, where $2d$ is the magnetic source thickness:\n", + "$$(4) \\Phi_{\\Delta T}(|k|)^{1/2} = Ce^{-|k|Z_o}(e^{-|k|(-d)}-e^{-|k|(-d)})\\approx Ce^{-|k|Z_o}2|k|d $$\n", + "\n", + "$$ \\ln \\{\\Phi_{\\Delta T}(|k|)^{1/2}/|k|\\}=\\ln D-|k|Z_o $$\n", + "\n", + "\n", + "Estimates of $Z_t$ and $Z_o$ can be estimated from Equations (2) and (5), and hence the base of the magnetic source (assumed to be at the Curie point depth):\n", + "\n", + "$$(6) Z_b=Z_o-(Z_t-Z_o) = 2Z_o-Z_t $$\n", + "\n", + "### Contents\n", + "\n", + "- [Plot radial power spectrum](#Plot-radial-power-spectrum)\n", + "- [Compute CPD Estimate](#Compute-cpd-estimate)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "\n", + "import pycurious" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# load x,y,anomaly\n", + "mag_data = np.loadtxt(\"../data/test_mag_data.txt\")\n", + "\n", + "nx, ny = 305, 305\n", + "\n", + "x = mag_data[:,0]\n", + "y = mag_data[:,1]\n", + "d = mag_data[:,2].reshape(ny,nx)\n", + "\n", + "xmin, xmax = x.min(), x.max()\n", + "ymin, ymax = y.min(), y.max()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Plot radial power spectrum\n", + "The radial power spectrum is computed from a square window of the magnetic anomaly. Methods to select window sizes and compute the Fast Fourier Transform (FFT) belong to the `CurieGrid` object. We apply the default `np.hanning` taper to the power spectrum as in [Ex1-Plot-power-spectrum](#./Ex1-Plot-power-spectrum.ipynb)." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "# initialise CurieOptimise object\n", + "grid = pycurious.CurieOptimise(d, xmin, xmax, ymin, ymax)\n", + "#grid = pycurious.CurieGrid(d, xmin, xmax, ymin, ymax)\n", + "\n", + "# pick the centroid\n", + "xpt = 0.5*(xmin + xmax)\n", + "ypt = 0.5*(ymin + ymax)\n", + "\n", + "window_size = 304e3\n", + "subgrid = grid.subgrid(xpt, ypt, window_size)" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0,0.5,u'$\\\\ln(\\\\Phi_{\\\\Delta T}(|k|)^{1/2})/(2\\\\pi)$')" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "S, k, sigma2 = grid.radial_spectrum_log(subgrid)\n", + "\n", + "# Plot of power spectrum, as function of spatial frequency\n", + "plt.plot(k/(2*np.pi), S/(2*np.pi), '-o')\n", + "plt.title('Power Spectrum')\n", + "plt.xlabel(r'$|k|/(2\\pi)$ [km$^{-1}$]')\n", + "plt.ylabel(r'$\\ln(\\Phi_{\\Delta T}(|k|)^{1/2})/(2\\pi)$')" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0,0.5,u'$\\\\ln(\\\\Phi_{\\\\Delta T}(|k|)^{1/2}/|k|)/(2\\\\pi)$')" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "Sn=np.log(np.exp(S)/k)\n", + "plt.plot(k/(2*np.pi), Sn/(2*np.pi), '-o')\n", + "plt.title('Power Spectrum, weighted by k')\n", + "plt.xlabel(r'$|k|/(2\\pi)$ [km$^{-1}$]')\n", + "plt.ylabel(r'$\\ln(\\Phi_{\\Delta T}(|k|)^{1/2}/|k|)/(2\\pi)$')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Compute CPD Estimate\n", + "As described above, once the power spectrum (and weighted spectrum) are computed, then the gradient of linear fits of certain wavenumber/spatial frequency windows can be taken as estimates of $Z_t$ and $Z_o$. The weighted linear fitting of the respective spectral window is implemented in the `CurieGrid` parent class as `tanaka1999`, and takes the spectrum, wave number, and spectrum error as inputs. The function also has functionality to pass specific spectral windows for each spectra, however, the default is to consider spatial frequencies of 0.05 - 0.2 (recalling that $k$, the wavenumber, is proportional to the spatial frequency $\\nu$ by $k=2\\pi\\nu$).\n", + "\n", + "\n", + "The function has two returns: the estimate of $Z_b$, and the propagated uncertainty $\\varepsilon_{Zb}$." + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Zb estimate: 23.35771952, +/- 6.77365143 km\n" + ] + } + ], + "source": [ + "[Zb,ezb]=pycurious.tanaka1999(S, k, sigma2)\n", + "print('Zb estimate: '+np.array2string(Zb)+', +/- '+np.array2string(ezb)+' km')" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.15rc1" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Examples/Notebooks/.ipynb_checkpoints/Ex2b-Compute-Curie-depth-Bouligand-approach-checkpoint.ipynb b/Examples/Notebooks/.ipynb_checkpoints/Ex2b-Compute-Curie-depth-Bouligand-approach-checkpoint.ipynb new file mode 100644 index 0000000..418efa5 --- /dev/null +++ b/Examples/Notebooks/.ipynb_checkpoints/Ex2b-Compute-Curie-depth-Bouligand-approach-checkpoint.ipynb @@ -0,0 +1,364 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Example 2b - Compute Curie depth (Bouligand approach)\n", + "\n", + "Bouligand *et al.* (2009) formulated an expression for the radial power assuming a fractal model for crustal magnetisation (see [Ex1-Plot-power-spectra](./Ex1-Plot-power-spectrum.ipynb) for analytic solution), which depends on 4 parameters:\n", + "\n", + "- $\\beta$ - a fractal parameter\n", + "- $z_t$ - top of magnetic sources\n", + "- $\\Delta z$ - thickness of the magnetic layer\n", + "- $C$ - a field constant\n", + "\n", + "These parameters can be fitted to the radial power spectrum computed from FFT to determine Curie depth ($z_\\mathrm{curie} = z_t + \\Delta z$).\n", + "\n", + "### Contents\n", + "\n", + "- [Plot radial power spectrum](#Plot-radial-power-spectrum)\n", + "- [Optimise parameters](#Optimise-parameters)\n", + "- [Varying window sizes](#Varying-window-sizes)\n", + "- [Add prior constraints](#Add-prior-constraints)" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "\n", + "import pycurious" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# load x,y,anomaly\n", + "mag_data = np.loadtxt(\"../data/test_mag_data.txt\")\n", + "\n", + "nx, ny = 305, 305\n", + "\n", + "x = mag_data[:,0]\n", + "y = mag_data[:,1]\n", + "d = mag_data[:,2].reshape(ny,nx)\n", + "\n", + "xmin, xmax = x.min(), x.max()\n", + "ymin, ymax = y.min(), y.max()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Plot radial power spectrum\n", + "\n", + "The radial power spectrum is computed from a square window of the magnetic anomaly. Methods to select window sizes and compute the Fast Fourier Transform (FFT) belong to the `CurieGrid` object. We apply the default `np.hanning` taper to the power spectrum as in [Ex1-Plot-power-spectrum](#./Ex1-Plot-power-spectrum.ipynb)." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "grid = pycurious.CurieOptimise(d, xmin, xmax, ymin, ymax)\n", + "\n", + "# pick the centroid\n", + "xpt = 0.5*(xmin + xmax)\n", + "ypt = 0.5*(ymin + ymax)\n", + "\n", + "window_size = 304e3\n", + "subgrid = grid.subgrid(xpt, ypt, window_size)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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R15BIL1AASLh60kTLaYEZke6mAJBwpWmiACmrvNpYudx4Xq0AkS6lNFAJFVVdNIqqiYp0BlUDldiCB/mm3UcYz09W3b+0mihcWJV0aCDLyKFc6Psi0h5qAUhF9S45GSaTTnHr9Vm+dzB3Xosik9bsY5FGa/lEMDO7y8zczK6I2D5lZmPFr92NOKe0RiOqg+Ynp/jWgRMXdCdpEFmkvWJ3AZnZVcAq4ESF3fLuvjzuuaT1FvZnYrcAKlH5aZH2aUQL4OvAl4DO7UuSGQtLE033GXPSjUkgU/lpkfaJ9b/YzNYAOXc/XGXX2WY2amYHzGwozjmltcKqiW7/ret4Ycuvs2Pt8rrTRkup/LRIe1XtAjKzx4H5IZvuBe6h0P1TzfvcPWdm7wf2m9lz7v7jiPOtA9YBLFq0qIZDS7OFLTUZvA/UlS5a6t5PfUgDwCJtNOMsIDNbBvxPYKL41pXAKWCFu/+0ws/9N+ARd/9utXMoC6g7BOmdufH8BeWkw6QMgvpzKjst0lj1ZAE1LA3UzI4Dg+7+atn7c4EJd3+7mCX0f4A17v5CtWMqAHSvJcN7IgeF0imLrECqCWUi8bR9PQAzGzSz+4ovPwSMmtlh4AlgWy0Pf+luUYO7KYt++MO7E8pUXkKk+TQRTJoirJREJp2qe6xAXUMi9Wl7C0AkLHuotOhcrVR2WqR51AKQlqq3yFwgZca0u2oIiVShFoB0rPLy07XOIphyP7cQzfpdYwxsfkytApGY1AKQths5lOOuBw9Hpo1GMQrTzzVOIPIutQCkqwwNZPnaZ6+re2WyIFxonEBkZtQCkI5ROqEsDrUIJMm0IIx0pdKSE3HWIQhaBMExRSScuoCkI8VZrB4Kaw3c9eBhdQuJVKAWgHSk4Df30iUkP/bBeTxx9DS58fy5AeBKptwjl6kMjqXlKSXJNAYgXamezCEDZlWoPxRQHSLpBcoCkp5XT+aQQ9WHP6gOkSSPAoB0rfJJZY2gdYolSTQGIF2tNHNopmUmymmdYkkKtQCkZwQtgjjLVAL0makbSBJBAUB6ykxnFZcKsocUBKTXqQtIek7QJbRp9xHG85PnbUv3GZfMnsX4xOS5dNBvP/XyBdlEwTyC0ZdeU7qo9CylgUpPC8pLVHqAV1q+slwQQM5MTGo9Y+lIKgUhUlQ6SBxlYX+m5rITk9POmYlCqyJoNaj0hHQrjQFI4sUtOwEqPSHdSS0ASbzgt/aZrElQqlLpCXURSSfSGIBIUaPmEUSVnlCpCWkFlYIQmYFGzSOIKj2hUhPSaRQAREo0Yh5BJRorkE6iLiCREKXpo33FdM9y/Zk0b5+dnlGXkdJJpVla1gVkZpvMLGdmY8WvmyL2u9HMjpnZi2Y2HOecIq0wNJDlyeGP83+3fSq0RZBJp9h089Uz7jKqlE6q1oG0SiOygL7u7n8YtdHMUsB/An4NOAk8bWa73f2FBpxbpOnCFqcp/029EYPH8G4XUel5RZqlFWmgK4AX3f0nAGb2Z8AaQAFAukalCWWNSiMNTLmzftcYX3n4CJ+6doFKUUjTNGIQ+E4ze9bM7jezuSHbs8DLJa9PFt8LZWbrzGzUzEZPnz7dgMsTab6oweNMOsVv37BoRoPKZyYm+daBE+TG8ziFLqL1u8YY2PyYuomkIaq2AMzscWB+yKZ7gf8MbKGQ+bYF+Brw+TgX5O47gZ1QGASOcyyRVqrUVTT4vssb1kII0klLz1lJLfWQJJkalgVkZouBR9z9mrL3fxXY5O6ri6/vBnD3rdWOqSwg6SWNmmhWrlIWUdg5M+kUW29ZpiDQo1qZBbSg5OVvAs+H7PY08AEzW2JmFwGfA3bHOa9INypdwtKAbH+GHWuXs2Pt8tjrF0B4FtH2vccuCDha9lICcQeB/72ZLafQBXQc+D0AM1sI3OfuN7n7WTO7E9gLpID73f1IzPOKdKVKg8lh6xfUKz85xfpdY2zfe4wNq5dGLm+ZG88zciinVkDCaSKYSAcZOZRr2FhBJp1idrrv3HyDsO3qCuo9qgUk0qWisonSfUZfnfPN8pNTuDtRP6auIFE5aJEOE5VNBPVPOBvPn624PaqLSJJBAUCkA1UaK9i+9xi58fy57J9URK2iUn0G0yG7OLB4eM95GUTlaaMf++A8TUbrURoDEOkBI4dyfHHXWM1rG4dJ9xnplDExOV1xP40ddDaNAYgkzNBANtbDHwoF6qo9/EElrXuJAoBIj8j2Z1p2rmD5SwWB7qYAINIjalncPu5qZ6WCOQeLh/ewctt+BYMupDEAkR4SDODmxvMYnNctlEmnuPX6LN87mGt4OYpAMNisRW7ap54xAAUAkR4VVQSuNEi0ytw5aTZ++moFghZQABCRmkQVqJuT7mNy2kMXt5+pIHsIKi+uI/HUEwA0D0AkwSqVsA6bD/Dtp16ecZmK/OQUX9w1xqyUnQssQQG70muR1lELQERq1syS1l/77HUKAg2geQAi0hSlJa2ByDpD9QqWwdRqZ62lFoCIxFI6qBxk/5RnINVLg8Yzp0FgEWm7uKWt033GJbNnMT4xqcHiOqgLSETaLqq0da0mp50zE5M4hcFidRE1nloAItJUI4dyrN811tBjBhPOKlUxTWqLQV1AItJRVm7bHzrxLO5YQSVJrVqqLiAR6ShhdYoy6RRfX7ucHWuX059JN/ycWvGsOk0EE5GmqzThLNjeyPWQA7nx/LkxA3UPXUhdQCLSMZox0SzdZ2CcV9ail7uH1AUkIl2pdKKZURjk/e0bFsXqIgqraaTuoQK1AESkK1QqdR1H+drK2S5fB7llWUBmtgn458Dp4lv3uPujIfsdB94EpoCztV6cAoCIRAmbgRz82QxhqaedqNUB4Bfu/odV9jsODLr7q/UcXwFAROrRrGJ1YTq1XIXKQYtIIpVmGzV7wZszE5NdX8q6EYPAd5rZs2Z2v5nNjdjHgcfM7KCZrat0MDNbZ2ajZjZ6+vTpSruKiFxgaCDLk8MfZ8fa5TMuQ1Gr/OQUdz14+ILyFCOHcqzctp8lHb5ectUuIDN7HJgfsule4ADwKoUH/BZggbt/PuQYWXfPmdl7gX3Av3L3H1W7OHUBiUgcpeUh+po4PgDvdgkBod1QreoyakspCDNbDDzi7tdU2W8TNYwbgAKAiDRO1PhAMLjbqMyi4HhRmh0IWjYGYGYL3P2V4svfBJ4P2edioM/d3yx+vwrYHOe8IiL1qjYbGQhdBvOJo6frSj2t9PCHwtjB+l1jfOXhI20fRI6bBfSnwHIKfy/Hgd9z91fMbCFwn7vfZGbvB75f/JFZwP9w96/Wcny1AESkkzS6XEUzZiSrGqiISJM0OtU0ZcY//shV51oapRPSZjLfQGmgIiJNEjyQN+0+wnh+Mvbxptz51oET572GQiG7ZqeZqhaQiEidhgayjG1cVVMpa4txnmbXLFIAEBGZoWqBoBFrHpxq4oQ2dQGJiMQ0NJCtuizlTNc8WNifadZlKwCIiDRKEAgqbYfwiWJhMukUG1Yvbdj1lVMAEBFpoSAIVGsJtKLqqAKAiEiLRbUEWr1SmQKAiEgb1DIzudkUAERE2qTamEGzKQ1URCShFABERBJKAUBEJKEUAEREEkoBQEQkoTq6HLSZnQZequNHrqCwRGU30z10Bt1DZ9A91O997j6vlh07OgDUy8xGa62D3al0D51B99AZdA/NpS4gEZGEUgAQEUmoXgsAO9t9AQ2ge+gMuofOoHtoop4aAxARkdr1WgtARERq1JUBwMxuNLNjZvaimQ2HbH+Pme0qbn/KzBa3/iorq+Eebjez02Y2Vvz6QjuuM4qZ3W9mPzOz5yO2m5n9x+L9PWtmH271NVZTwz181MxeL/kMvtzqa6zGzK4ysyfM7AUzO2Jm/zpkn47+LGq8h47+LMxstpn9pZkdLt7DV0L26bznkrt31ReQAn4MvB+4CDgM/ErZPv8S+Gbx+88Bu9p93TO4h9uBb7T7Wivcwz8EPgw8H7H9JuAHFNbEvgF4qt3XPIN7+CjwSLuvs8o9LAA+XPz+UuCvQ/4tdfRnUeM9dPRnUfy7vaT4fRp4CrihbJ+Oey51YwtgBfCiu//E3d8B/gxYU7bPGuBPit9/F/iEmVkLr7GaWu6ho7n7j4DXKuyyBvjvXnAA6DezBa25utrUcA8dz91fcfdnit+/CfwVUF5fuKM/ixrvoaMV/25/UXyZLn6VD7B23HOpGwNAFni55PVJLvzHcm4fdz8LvA78nZZcXW1quQeAW4tN9u+a2VWtubSGqfUeO92vFpv1PzCzq9t9MZUUuxQGKPz2WaprPosK9wAd/lmYWcrMxoCfAfvcPfJz6JTnUjcGgKR4GFjs7tcC+3j3NwdpnWcoTKu/DvgjYKTN1xPJzC4Bvgesd/c32n09M1HlHjr+s3D3KXdfDlwJrDCza9p9TdV0YwDIAaW/DV9ZfC90HzObBVwG/LwlV1ebqvfg7j9397eLL+8Drm/RtTVKLZ9TR3P3N4Jmvbs/CqTN7Io2X9YFzCxN4cH5gLs/FLJLx38W1e6hWz4LAHcfB54Abizb1HHPpW4MAE8DHzCzJWZ2EYXBlN1l++wGbit+/xlgvxdHXjpE1Xso66O9mUK/aDfZDfxOMQPlBuB1d3+l3RdVDzObH/TRmtkKCv9fOukXCYrX91+Av3L3/xCxW0d/FrXcQ6d/FmY2z8z6i99ngF8Djpbt1nHPpa5bE9jdz5rZncBeCtk097v7ETPbDIy6+24K/5j+1MxepDDI97n2XfGFaryH3zezm4GzFO7h9rZdcAgz+zaFzIwrzOwksJHCwBfu/k3gUQrZJy8CE8DvtudKo9VwD58B/oWZnQXywOfa/R82xErgnwHPFfufAe4BFkHXfBa13EOnfxYLgD8xsxSF4PSguz/S6c8lzQQWEUmobuwCEhGRBlAAEBFJKAUAEZGEUgAQEUkoBQARkYRSABARSSgFABGRhFIAEBFJqP8PZWZHFAN/gXEAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "S, k, sigma2 = grid.radial_spectrum(subgrid)\n", + "\n", + "# plot radial power spectrum\n", + "plt.plot(k, S, '-o')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Optimise parameters\n", + "\n", + "The `optimise` routine determines the Curie parameters ($\\beta, z_t, \\Delta z, C$) by minimising the misfit between the analytic power spectum and the computed power spectrum. Optimisation is handles by the nonlinear least-squares algorithm implemented in `scipy.optimize.minimize`.\n", + "\n", + "```python\n", + "optimise(window, xc, yc, beta=3.0, zt=1.0, dz=20.0, C=5.0)\n", + "```\n", + "\n", + "These are sane defaults to initiate the optimisation, however, values close to the final solution will result in faster convergence and stability." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "beta = 0.00\n", + " zt = 1.31\n", + " dz = 107.74\n", + " C = 0.00\n", + "\n", + "Curie depth is 109.05 km\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "beta, zt, dz, C = grid.optimise(window_size, xpt, ypt)\n", + "print(\"beta = {:.2f}\\n zt = {:.2f}\\n dz = {:.2f}\\n C = {:.2f}\".format(beta,zt,dz,C))\n", + "\n", + "Sb = pycurious.bouligand2009(beta, zt, dz, k, C)\n", + "\n", + "# plot radial power spectrum - compare analytic against computed\n", + "plt.plot(k, S, '-o')\n", + "plt.plot(k, Sb, linewidth=2)\n", + "\n", + "print(\"\\nCurie depth is {:.2f} km\".format(zt + dz))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Varying window sizes\n", + "\n", + "Here, we observe the effect decreasing the window size has on the optimisation of Curie parameters. The number of points in the power spectrum decrease with smaller window sizes, particularly at low wavenumbers (long wavelengths). This significantly reduces the quality of Curie depth determinations for window sizes less than 200 km.\n", + "\n", + "As a rule of thumb, the window size should be > 4 times the maximum possible Curie depth that could be resolved from a study area." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "beta = 0.00\n", + " zt = 1.31\n", + " dz = 107.74\n", + " C = 0.00\n", + "\n", + "beta = 0.00\n", + " zt = 1.36\n", + " dz = 146.33\n", + " C = 0.00\n", + "\n", + "beta = 0.00\n", + " zt = 1.45\n", + " dz = 19.95\n", + " C = 0.00\n", + "\n", + "beta = 0.00\n", + " zt = 1.53\n", + " dz = 20.00\n", + " C = 0.00\n", + "\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "# window size in kilometres\n", + "window_size_range = [304e3, 200e3, 100e3, 50e3]\n", + "\n", + "\n", + "fig = plt.figure()\n", + "ax1 = fig.add_subplot(111)\n", + "\n", + "for i, window_size in enumerate(window_size_range):\n", + " \n", + " # compute radial power spectrum\n", + " subgrid = grid.subgrid(xpt, ypt, window_size)\n", + " S, k, sigma2 = grid.radial_spectrum(subgrid)\n", + " ax1.plot(k, S, '-o', color='C{}'.format(i))\n", + " \n", + " # optimise Curie variables\n", + " beta, zt, dz, C = grid.optimise(window_size, xpt, ypt)\n", + " print(\"beta = {:.2f}\\n zt = {:.2f}\\n dz = {:.2f}\\n C = {:.2f}\\n\".format(beta,zt,dz,C))\n", + " \n", + " Sb = pycurious.bouligand2009(beta, zt, dz, k, C)\n", + " ax1.plot(k, Sb, color='C{}'.format(i), linewidth=2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Add prior constraints\n", + "\n", + "Spurious Curie depth values can often be obtained if windows of the magnetic anomaly do not contain long wavelengths. This often arises from selecting too small a small window size, but can also occur from uncorrected artefacts in the magnetic anomaly, or simply the absence of magnetic minerals close to the surface of the crust.\n", + "\n", + "Adding *a priori* information on $\\beta, z_t, \\Delta z, C$ can reduce the incidence of anomalous values. $\\beta$ and $C$ vary at long wavelengths, and $z_t + \\Delta z$ should be within the range of 10-40 km if we assume the Curie depth is equivalent to the 580$^\\circ$C isotherm. Adding prior information to any (or all) of these parameters penalises spurious values using a standard $\\ell_2$-norm misfit function.\n", + "\n", + "```python\n", + "add_prior(beta=(3.0,0.5), zt=(0.0,0.1), dz=(20.0,10.0), C=(5,2.5))\n", + "```\n", + "\n", + "A combination of priors can be added with $(\\mu, \\sigma)$ pairs. Currently, only Gaussian distributions are supported. `reset_priors()` removes all prior information." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "beta = 3.01\n", + " zt = 0.50\n", + " dz = 0.65\n", + " C = 0.00\n", + "\n", + "beta = 2.99\n", + " zt = 0.76\n", + " dz = 0.54\n", + " C = 0.00\n", + "\n", + "beta = 3.00\n", + " zt = 0.62\n", + " dz = 0.34\n", + " C = 0.00\n", + "\n", + "beta = 3.00\n", + " zt = 0.86\n", + " dz = 20.00\n", + " C = 0.00\n", + "\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "grid.reset_priors()\n", + "grid.add_prior(beta=(3.0,0.01))\n", + "\n", + "fig = plt.figure()\n", + "ax1 = fig.add_subplot(111, xlabel=\"wavenumber (rad/km)\", ylabel=\"radial power spectrum\")\n", + "\n", + "for i, window_size in enumerate(window_size_range):\n", + " \n", + " # compute radial power spectrum\n", + " subgrid = grid.subgrid(xpt, ypt, window_size)\n", + " S, k, sigma2 = grid.radial_spectrum(subgrid)\n", + " ax1.plot(k, S, '-o', color='C{}'.format(i), label='{} km window size'.format(window_size*1e-3))\n", + " \n", + " # optimise Curie variables\n", + " beta, zt, dz, C = grid.optimise(window_size, xpt, ypt)\n", + " print(\"beta = {:.2f}\\n zt = {:.2f}\\n dz = {:.2f}\\n C = {:.2f}\\n\".format(beta,zt,dz,C))\n", + " \n", + " Sb = pycurious.bouligand2009(beta, zt, dz, k, C)\n", + " ax1.plot(k, Sb, color='C{}'.format(i), linewidth=2)\n", + " \n", + "ax1.legend()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.15rc1" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Examples/Notebooks/.ipynb_checkpoints/Ex3-Optimisation-routine-checkpoint.ipynb b/Examples/Notebooks/.ipynb_checkpoints/Ex3-Optimisation-routine-checkpoint.ipynb new file mode 100644 index 0000000..661c666 --- /dev/null +++ b/Examples/Notebooks/.ipynb_checkpoints/Ex3-Optimisation-routine-checkpoint.ipynb @@ -0,0 +1,123 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Example 3 - Optimisation routine\n", + "\n", + "In Examples 2a and 2b we computed the Curie depth for a single point using a fixed window. Here, we use `CurieOptimise` object to compute the Curie depth over an entire magnetic anomaly.\n", + "\n", + "`CurieOptimise` inherits all methods from `CurieGrid` in addition to:\n", + "\n", + "- iteratively evaluate the Curie depth across the magnetic anomaly\n", + "- add priors to limit spurious Curie depth determinations\n", + "- optimise Curie depth parameters using constraints from an objective function\n", + "\n", + "### Contents\n", + "\n", + "- [The inverse problem](#The-inverse-problem)\n", + "- [Iterate across magnetic anomaly](#Iterate-across-magnetic-anomaly)\n", + "- [Compare Bouligand to Tanaka](#Compare-Bouligand-to-Tanaka)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "\n", + "import pycurious" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# load x,y,anomaly\n", + "mag_data = np.loadtxt(\"../data/test_mag_data.txt\")\n", + "\n", + "nx, ny = 305, 305\n", + "\n", + "x = mag_data[:,0]\n", + "y = mag_data[:,1]\n", + "d = mag_data[:,2].reshape(ny,nx)\n", + "\n", + "xmin, xmax = x.min(), x.max()\n", + "ymin, ymax = y.min(), y.max()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# initialise CurieOptimise object\n", + "grid = pycurious.CurieOptimise(d, xmin, xmax, ymin, ymax)\n", + "\n", + "window_size = 200e3\n", + "xc_list, yc_list = grid.create_centroid_list(window_size)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The inverse problem\n", + "\n", + "It is notoriously difficult to estimate uncertainties from Curie depth determinations. Intuitively, the fewer points in the power spectrum should result in higher uncertainty, but it is difficult to quantify these uncertainties in practise. For [Bouligand *et al.*, 2009](http://doi.wiley.com/10.1029/2009JB006494) it is difficult to determine the values of $\\beta$ and $\\Delta z$ since both control the slope of the power spectrum at low wavenumbers. Similarly, for [Tanaka *et al.*, 1999](http://linkinghub.elsevier.com/retrieve/pii/S0040195199000724) the lower and upper ranges of the power spectrum used to compute $z_b$ and $z_t$ is highly subjective and can result in significantly different Curie depths.\n", + "\n", + "Here, we aim to assess the uncertainty of Curie depth determinations using a sensitivity analysis. The approach we outline here is not necessarily the most statistically robust methodology, but it is intended as a practical way forward to compute Curie depth while considering the high degree of uncertainty." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Parameter Exploration of Spectral Analysis method (Tanaka)\n", + "\n", + "Due to the deterministic approach that [Tanaka *et al.*, 1999](http://linkinghub.elsevier.com/retrieve/pii/S0040195199000724) uses for estimating $Z_b$, the uncertainties returned by `CurieGrid.tanaka1999` are the simple results of error propagation from the initial spectra uncertainties. It should also be noted that the spectra uncertainties represent the variance within the sampled sector of the 2D FFT, and may comprise both noise and anisotropic signal.\n", + "\n", + "We present here several tests of the `CurieGrid.tanaka1999` function in order to explore how the input parameters affect the resulting Curie point depth estimates. In particular, we consider the following:\n", + "1. Effect of magnetic data window size (i.e., domain of magnetic data before computing FFT).\n", + "2. Effect of where in $k$-space is specific window used, separately for both the power and $k$-weighted power spectra (i.e., which $k$ do we consider?).\n", + "3. Effect of $k$-space window size (i.e., how much of the $k$-domain do we consider?).\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.15rc1" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Examples/Notebooks/Ex2a-Compute-Curie-depth-Tanaka-approach.py b/Examples/Notebooks/Ex2a-Compute-Curie-depth-Tanaka-approach.py new file mode 100644 index 0000000..2b263c7 --- /dev/null +++ b/Examples/Notebooks/Ex2a-Compute-Curie-depth-Tanaka-approach.py @@ -0,0 +1,35 @@ +import numpy as np +import matplotlib.pyplot as plt +#matplotlib inline +import pycurious + + +# load x,y,anomaly +mag_data = np.loadtxt("../data/test_mag_data.txt") + +nx, ny = 305, 305 + +x = mag_data[:,0] +y = mag_data[:,1] +d = mag_data[:,2].reshape(ny,nx) + +xmin, xmax = x.min(), x.max() +ymin, ymax = y.min(), y.max() + +# initialise CurieOptimise object +#grid = pycurious.CurieOptimise(d, xmin, xmax, ymin, ymax) +grid = pycurious.CurieGrid(d, xmin, xmax, ymin, ymax) + +# pick the centroid +xpt = 0.5*(xmin + xmax) +ypt = 0.5*(ymin + ymax) + +window_size = 304e3 +subgrid = grid.subgrid(xpt, ypt, window_size) + +print(type(subgrid)) +print(type(grid)) +S, k, sigma2 = grid.radial_spectrum(subgrid) +print(np.size(S)) +S, k, sigma2 = grid.radial_spectrum_log(subgrid) +#S, k, sigma2 = grid.radial_spectrum_log(subgrid) diff --git a/Examples/Notebooks/Ex2a.py b/Examples/Notebooks/Ex2a.py new file mode 100644 index 0000000..416c4ed --- /dev/null +++ b/Examples/Notebooks/Ex2a.py @@ -0,0 +1,39 @@ +import numpy as np +import matplotlib.pyplot as plt +#matplotlib inline +import pycurious + + +# load x,y,anomaly +mag_data = np.loadtxt("../data/test_mag_data.txt") + +nx, ny = 305, 305 + +x = mag_data[:,0] +y = mag_data[:,1] +d = mag_data[:,2].reshape(ny,nx) + +xmin, xmax = x.min(), x.max() +ymin, ymax = y.min(), y.max() + +# initialise CurieOptimise object +#grid = pycurious.CurieOptimise(d, xmin, xmax, ymin, ymax) +grid = pycurious.CurieGrid(d, xmin, xmax, ymin, ymax) + +# pick the centroid +xpt = 0.5*(xmin + xmax) +ypt = 0.5*(ymin + ymax) + +window_size = 304e3 +subgrid = grid.subgrid(xpt, ypt, window_size) + + +S, k, sigma2 = grid.radial_spectrum(subgrid) +#print(S) +S, k, sigma2 = grid.radial_spectrum_log(subgrid) +#print(S) +#S, k, sigma2 = grid.radial_spectrum_log(subgrid) + + +zb=pycurious.tanaka1999(S, k, sigma2) +print(zb) \ No newline at end of file From 177e435a7ec8dd1dc2fa564a06b92afb313b77a1 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Tue, 17 Jul 2018 18:13:07 +0100 Subject: [PATCH 015/170] Updated Ex4 Notebook with importing/exporting data --- .../Ex4-Mapping-Curie-depth-EMAG2.ipynb | 26 +++++++++++++------ 1 file changed, 18 insertions(+), 8 deletions(-) diff --git a/Examples/Notebooks/Ex4-Mapping-Curie-depth-EMAG2.ipynb b/Examples/Notebooks/Ex4-Mapping-Curie-depth-EMAG2.ipynb index efaebcc..a420a5a 100644 --- a/Examples/Notebooks/Ex4-Mapping-Curie-depth-EMAG2.ipynb +++ b/Examples/Notebooks/Ex4-Mapping-Curie-depth-EMAG2.ipynb @@ -38,7 +38,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "import numpy as np\n", @@ -81,10 +83,12 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ - "filedir = '/path/to/emag2'\n", + "filedir = '/mnt/ben_raid/'\n", "\n", "try:\n", " with np.load(filedir+'EMAG2_V3_20170530.npz') as f:\n", @@ -124,13 +128,15 @@ "\n", "We choose an arbitrary section of the Earth's surface and a suitable projection. PyCurious handles transformation between different CRS using a EPSG reference code. EMAG2 is in lons and lats (in decimal degrees), which we want to convert into eastings and northings (in metres). For this example, we transform WGS84 coordinates (EPSG:4326) to the IRENET95 projection (EPSG:2157).\n", "\n", - "**The power spectrum must be in eastings & northings to compute the power spectrum in rad/km.**" + "> **IMPORTANT:** The power spectrum must be in eastings & northings to compute the power spectrum in rad/km." ] }, { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "# grid extent - grid of the British Isles in Irenet 95 grid projection\n", @@ -150,7 +156,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "dx, dy = 1e3, 1e3 # 1 km grid resolution\n", @@ -213,7 +221,9 @@ { "cell_type": "code", "execution_count": null, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "curie_depth = zt + dz\n", @@ -311,7 +321,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We can also import a GeoTIFF using the `mapping` module. the `import_geotiff` function prints a wealth of information on the reference spheriod and the projection of the GeoTIFF, including EPSG code." + "We can also import a GeoTIFF using the `mapping` module. the `import_geotiff` function prints a wealth of information on the reference spheriod and the projection, including EPSG code." ] }, { From f4d095ee8b97e1a8214290b671eab56b1b2c5a0d Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Thu, 26 Jul 2018 22:04:57 +0100 Subject: [PATCH 016/170] export / import geotiff now working correctly --- pycurious/mapping.py | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/pycurious/mapping.py b/pycurious/mapping.py index 73692c9..6ade59a 100644 --- a/pycurious/mapping.py +++ b/pycurious/mapping.py @@ -179,8 +179,8 @@ def import_geotiff(file_path): inproj = osr.SpatialReference() inproj.ImportFromWkt(gtproj) - gtextent = (gt[0], gt[0] + gtiff.RasterXSize*gt[1], - gt[3] + gtiff.RasterYSize*gt[5], gt[3]) + gtextent = (gt[0], gt[0] + gtiff.RasterXSize*gt[1],\ + gt[3], gt[3] + gtiff.RasterYSize*gt[5]) # print projection information print(inproj) @@ -188,7 +188,7 @@ def import_geotiff(file_path): # this closes the geotiff gtiff = None - return np.flipud(data), gtextent + return data, gtextent def export_geotiff(file_path, array, extent, epsg): @@ -216,7 +216,7 @@ def export_geotiff(file_path, array, extent, epsg): spacingY = (ymax - ymin)/rows driver = gdal.GetDriverByName('GTiff') - outRaster = driver.Create(file_path, cols, rows, 1, gdal.GDT_Byte) + outRaster = driver.Create(file_path, cols, rows, 1, gdal.GDT_Float64) outRaster.SetGeoTransform((xmin, spacingX, 0, ymin, 0, spacingY)) outband = outRaster.GetRasterBand(1) outband.WriteArray(array) From 0a34e01de113b00a80f68713639f5442ae6fc7d4 Mon Sep 17 00:00:00 2001 From: Robert Delhaye Date: Fri, 27 Jul 2018 13:32:35 +0100 Subject: [PATCH 017/170] Ex2a Notebook updated --- ...rie-depth-Tanaka-approach-checkpoint.ipynb | 70 +++++++++++++++---- 1 file changed, 56 insertions(+), 14 deletions(-) diff --git a/Examples/Notebooks/.ipynb_checkpoints/Ex2a-Compute-Curie-depth-Tanaka-approach-checkpoint.ipynb b/Examples/Notebooks/.ipynb_checkpoints/Ex2a-Compute-Curie-depth-Tanaka-approach-checkpoint.ipynb index d7c515d..f94a1a1 100644 --- a/Examples/Notebooks/.ipynb_checkpoints/Ex2a-Compute-Curie-depth-Tanaka-approach-checkpoint.ipynb +++ b/Examples/Notebooks/.ipynb_checkpoints/Ex2a-Compute-Curie-depth-Tanaka-approach-checkpoint.ipynb @@ -41,7 +41,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ @@ -54,7 +54,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -81,7 +81,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ @@ -99,7 +99,7 @@ }, { "cell_type": "code", - "execution_count": 35, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -108,7 +108,7 @@ "Text(0,0.5,u'$\\\\ln(\\\\Phi_{\\\\Delta T}(|k|)^{1/2})/(2\\\\pi)$')" ] }, - "execution_count": 35, + "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, @@ -116,7 +116,7 @@ "data": { "image/png": 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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -135,7 +135,7 @@ }, { "cell_type": "code", - "execution_count": 31, + "execution_count": 6, "metadata": {}, "outputs": [ { @@ -144,7 +144,7 @@ "Text(0,0.5,u'$\\\\ln(\\\\Phi_{\\\\Delta T}(|k|)^{1/2}/|k|)/(2\\\\pi)$')" ] }, - "execution_count": 31, + "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, @@ -152,7 +152,7 @@ "data": { "image/png": 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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -175,12 +175,12 @@ "As described above, once the power spectrum (and weighted spectrum) are computed, then the gradient of linear fits of certain wavenumber/spatial frequency windows can be taken as estimates of $Z_t$ and $Z_o$. The weighted linear fitting of the respective spectral window is implemented in the `CurieGrid` parent class as `tanaka1999`, and takes the spectrum, wave number, and spectrum error as inputs. The function also has functionality to pass specific spectral windows for each spectra, however, the default is to consider spatial frequencies of 0.05 - 0.2 (recalling that $k$, the wavenumber, is proportional to the spatial frequency $\\nu$ by $k=2\\pi\\nu$).\n", "\n", "\n", - "The function has two returns: the estimate of $Z_b$, and the propagated uncertainty $\\varepsilon_{Zb}$." + "The function has two tuple returns: the gradient estimate, intercept and errors of $Z_t$ and $Z_o$. The gradient and errors can then be passed into the `CurieGrid.ComputeTanaka` method to obtain estimates of $Zb$ and $\\varepsilon Zb$." ] }, { "cell_type": "code", - "execution_count": 43, + "execution_count": 7, "metadata": { "scrolled": true }, @@ -189,13 +189,55 @@ "name": "stdout", "output_type": "stream", "text": [ - "Zb estimate: 23.35771952, +/- 6.77365143 km\n" + "Zb estimate: 17.80614059, +/- 2.02467493 km\n" ] } ], "source": [ - "[Zb,ezb]=pycurious.tanaka1999(S, k, sigma2)\n", - "print('Zb estimate: '+np.array2string(Zb)+', +/- '+np.array2string(ezb)+' km')" + "[(Ztr,btr,dZtr), (Zor, bor, dZor)]=pycurious.tanaka1999(S, k, sigma2)\n", + "[Zb,eZb]=pycurious.ComputeTanaka(Ztr, dZtr, Zor, dZor)\n", + "print('Zb estimate: '+np.array2string(Zb)+', +/- '+np.array2string(eZb)+' km')" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0,0.5,u'$\\\\ln(\\\\Phi_{\\\\Delta T}(|k|)^{1/2}/|k|)/(2\\\\pi)$')" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# make two plots with Z-lines overlain.\n", + "# Plot of power spectrum, as function of spatial frequency\n", + "fig, (ax1, ax2) = plt.subplots(1,2, figsize=(16,6),)\n", + "\n", + "ax1.plot(k/(2*np.pi), S/(2*np.pi), '-bo',k/(2*np.pi),(Ztr*k/(2*np.pi)+btr)/(2*np.pi),'r-')\n", + "#ax1.title('Power Spectrum')\n", + "ax1.set_xlabel(r'$|k|/(2\\pi)$ [km$^{-1}$]')\n", + "ax1.set_ylabel(r'$\\ln(\\Phi_{\\Delta T}(|k|)^{1/2})/(2\\pi)$')\n", + "\n", + "ax2.plot(k/(2*np.pi), Sn/(2*np.pi), '-o',k/(2*np.pi),(Zor*k/(2*np.pi)+bor)/(2*np.pi),'r-')\n", + "ax2.set_xlabel(r'$|k|/(2\\pi)$ [km$^{-1}$]')\n", + "ax2.set_ylabel(r'$\\ln(\\Phi_{\\Delta T}(|k|)^{1/2}/|k|)/(2\\pi)$')\n" ] } ], From 5d254463a3d0bef9eadb03ad9a2183cc4b775a6c Mon Sep 17 00:00:00 2001 From: Robert Delhaye Date: Fri, 27 Jul 2018 13:47:26 +0100 Subject: [PATCH 018/170] Ex2a Notebook updated --- ...-Compute-Curie-depth-Tanaka-approach.ipynb | 70 +++++++++++++++---- 1 file changed, 56 insertions(+), 14 deletions(-) diff --git a/Examples/Notebooks/Ex2a-Compute-Curie-depth-Tanaka-approach.ipynb b/Examples/Notebooks/Ex2a-Compute-Curie-depth-Tanaka-approach.ipynb index d7c515d..f94a1a1 100644 --- a/Examples/Notebooks/Ex2a-Compute-Curie-depth-Tanaka-approach.ipynb +++ b/Examples/Notebooks/Ex2a-Compute-Curie-depth-Tanaka-approach.ipynb @@ -41,7 +41,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ @@ -54,7 +54,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -81,7 +81,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ @@ -99,7 +99,7 @@ }, { "cell_type": "code", - "execution_count": 35, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -108,7 +108,7 @@ "Text(0,0.5,u'$\\\\ln(\\\\Phi_{\\\\Delta T}(|k|)^{1/2})/(2\\\\pi)$')" ] }, - "execution_count": 35, + "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, @@ -116,7 +116,7 @@ "data": { "image/png": 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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -135,7 +135,7 @@ }, { "cell_type": "code", - "execution_count": 31, + "execution_count": 6, "metadata": {}, "outputs": [ { @@ -144,7 +144,7 @@ "Text(0,0.5,u'$\\\\ln(\\\\Phi_{\\\\Delta T}(|k|)^{1/2}/|k|)/(2\\\\pi)$')" ] }, - "execution_count": 31, + "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, @@ -152,7 +152,7 @@ "data": { "image/png": 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\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -175,12 +175,12 @@ "As described above, once the power spectrum (and weighted spectrum) are computed, then the gradient of linear fits of certain wavenumber/spatial frequency windows can be taken as estimates of $Z_t$ and $Z_o$. The weighted linear fitting of the respective spectral window is implemented in the `CurieGrid` parent class as `tanaka1999`, and takes the spectrum, wave number, and spectrum error as inputs. The function also has functionality to pass specific spectral windows for each spectra, however, the default is to consider spatial frequencies of 0.05 - 0.2 (recalling that $k$, the wavenumber, is proportional to the spatial frequency $\\nu$ by $k=2\\pi\\nu$).\n", "\n", "\n", - "The function has two returns: the estimate of $Z_b$, and the propagated uncertainty $\\varepsilon_{Zb}$." + "The function has two tuple returns: the gradient estimate, intercept and errors of $Z_t$ and $Z_o$. The gradient and errors can then be passed into the `CurieGrid.ComputeTanaka` method to obtain estimates of $Zb$ and $\\varepsilon Zb$." ] }, { "cell_type": "code", - "execution_count": 43, + "execution_count": 7, "metadata": { "scrolled": true }, @@ -189,13 +189,55 @@ "name": "stdout", "output_type": "stream", "text": [ - "Zb estimate: 23.35771952, +/- 6.77365143 km\n" + "Zb estimate: 17.80614059, +/- 2.02467493 km\n" ] } ], "source": [ - "[Zb,ezb]=pycurious.tanaka1999(S, k, sigma2)\n", - "print('Zb estimate: '+np.array2string(Zb)+', +/- '+np.array2string(ezb)+' km')" + "[(Ztr,btr,dZtr), (Zor, bor, dZor)]=pycurious.tanaka1999(S, k, sigma2)\n", + "[Zb,eZb]=pycurious.ComputeTanaka(Ztr, dZtr, Zor, dZor)\n", + "print('Zb estimate: '+np.array2string(Zb)+', +/- '+np.array2string(eZb)+' km')" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0,0.5,u'$\\\\ln(\\\\Phi_{\\\\Delta T}(|k|)^{1/2}/|k|)/(2\\\\pi)$')" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# make two plots with Z-lines overlain.\n", + "# Plot of power spectrum, as function of spatial frequency\n", + "fig, (ax1, ax2) = plt.subplots(1,2, figsize=(16,6),)\n", + "\n", + "ax1.plot(k/(2*np.pi), S/(2*np.pi), '-bo',k/(2*np.pi),(Ztr*k/(2*np.pi)+btr)/(2*np.pi),'r-')\n", + "#ax1.title('Power Spectrum')\n", + "ax1.set_xlabel(r'$|k|/(2\\pi)$ [km$^{-1}$]')\n", + "ax1.set_ylabel(r'$\\ln(\\Phi_{\\Delta T}(|k|)^{1/2})/(2\\pi)$')\n", + "\n", + "ax2.plot(k/(2*np.pi), Sn/(2*np.pi), '-o',k/(2*np.pi),(Zor*k/(2*np.pi)+bor)/(2*np.pi),'r-')\n", + "ax2.set_xlabel(r'$|k|/(2\\pi)$ [km$^{-1}$]')\n", + "ax2.set_ylabel(r'$\\ln(\\Phi_{\\Delta T}(|k|)^{1/2}/|k|)/(2\\pi)$')\n" ] } ], From 14f33961608db670f3467acc150f5409d1bad344 Mon Sep 17 00:00:00 2001 From: Robert Delhaye Date: Fri, 27 Jul 2018 13:47:58 +0100 Subject: [PATCH 019/170] Ex3, Tanaka tests added --- .../Notebooks/Ex3-Optimisation-routine.ipynb | 233 +++++++++++++++++- 1 file changed, 227 insertions(+), 6 deletions(-) diff --git a/Examples/Notebooks/Ex3-Optimisation-routine.ipynb b/Examples/Notebooks/Ex3-Optimisation-routine.ipynb index 661c666..b69ba53 100644 --- a/Examples/Notebooks/Ex3-Optimisation-routine.ipynb +++ b/Examples/Notebooks/Ex3-Optimisation-routine.ipynb @@ -23,7 +23,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ @@ -36,7 +36,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -55,7 +55,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": {}, "outputs": [], "source": [ @@ -93,9 +93,230 @@ "Due to the deterministic approach that [Tanaka *et al.*, 1999](http://linkinghub.elsevier.com/retrieve/pii/S0040195199000724) uses for estimating $Z_b$, the uncertainties returned by `CurieGrid.tanaka1999` are the simple results of error propagation from the initial spectra uncertainties. It should also be noted that the spectra uncertainties represent the variance within the sampled sector of the 2D FFT, and may comprise both noise and anisotropic signal.\n", "\n", "We present here several tests of the `CurieGrid.tanaka1999` function in order to explore how the input parameters affect the resulting Curie point depth estimates. In particular, we consider the following:\n", - "1. Effect of magnetic data window size (i.e., domain of magnetic data before computing FFT).\n", - "2. Effect of where in $k$-space is specific window used, separately for both the power and $k$-weighted power spectra (i.e., which $k$ do we consider?).\n", - "3. Effect of $k$-space window size (i.e., how much of the $k$-domain do we consider?).\n" + "1. Effect of where in $k$-space is specific window used, separately for both the power and $k$-weighted power spectra (i.e., which $k$ do we consider?).\n", + "2. Effect of $k$-space window size (i.e., how much of the $k$-domain do we consider?). It is important to note that increasing the $k$-bandwidth also stabilises the estimation by increasing the statistics of the spectrum portion.\n", + "3. Effect of magnetic data window size (i.e., domain of magnetic data before computing FFT).\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "#Default set up\n", + "grid = pycurious.CurieOptimise(d, xmin, xmax, ymin, ymax)\n", + "xpt = xmin + (xmax-xmin)/2\n", + "ypt = ymin + (ymax-ymin)/2" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": {}, + "outputs": [], + "source": [ + "# 1) Where in k-space do we locate window?\n", + "ws=304e3\n", + "subgrid = grid.subgrid(xpt, ypt, ws)\n", + "S, k, sigma2 = grid.radial_spectrum_log(subgrid, taper=None)\n", + "# Number of bins to divide k-range into\n", + "nb=10\n", + "hmap=np.zeros((nb*nb,3))\n", + "# k-range divided between 0 (i.e., DC), and 0.3 (i.e., spatial wavelengths of ~20 km)\n", + "kmin_range = np.linspace(0., 0.3, nb)\n", + "kmax_range = kmin_range + (0.3/nb)\n", + "\n", + "for j in range(0,nb,1):\n", + " for l in range(0,nb,1):\n", + " kmin0 = kmin_range[j]\n", + " kmin1 = kmax_range[j]\n", + " kmax0 = kmin_range[l]\n", + " kmax1 = kmax_range[l]\n", + " [(Ztr,btr,dZtr), (Zor, bor, dZor)]=pycurious.tanaka1999(S, k, sigma2, (kmin0, kmin1), (kmax0, kmax1))\n", + " [Zb,eZb]=pycurious.ComputeTanaka(Ztr, dZtr, Zor, dZor)\n", + " hmap[j*nb+l,0]=(kmin0+kmin1)/2\n", + " hmap[j*nb+l,1]=(kmax0+kmax1)/2\n", + " hmap[j*nb+l,2]=Zb" + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.5,1,u'Heatmap of CPD')" + ] + }, + "execution_count": 70, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig2 = plt.figure(figsize=(16,16))\n", + "ax2 = fig2.add_subplot(111, xlabel=r'$\\nu$ window of $\\Phi/|k|$ (km$^{-1}$) (for Zo)', ylabel=r'$\\nu$ window of $\\Phi$ (for Zt)')\n", + "# SCATTER PLOT\n", + "im2 = ax2.scatter(hmap[:,1],hmap[:,0],2000,np.clip(hmap[:,2],10,20),marker='s')\n", + "fig2.colorbar(im2, label='CPD (km)')\n", + "plt.title('Heatmap of CPD')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Results of this test suggest that the precise $k$ location of $Z_t$ is significantly less influential than the $k$ location of $Z_o$. Furthermore, for this test case with a known $Z_b$ of 16 km, a spatial frequency $\\nu$ window of $0.125-0.2$ (i.e., $k\\in\\{0.8-1.25\\}$ gives estimates consistent with the true $Z_b$. For simplicity, based upon this test we see minimal reason to not use the same $\\nu/k$ window for each spectrum." + ] + }, + { + "cell_type": "code", + "execution_count": 101, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0,0.5,u'CPD depth (km)')" + ] + }, + "execution_count": 101, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# 2) How big a bandwidth in k-space do we want?\n", + "#ws=304e3\n", + "#subgrid = grid.subgrid(xpt, ypt, ws)\n", + "S, k, sigma2 = grid.radial_spectrum_log(subgrid, taper=None)\n", + "\n", + "# We are testing this by taking one central spatial frequency (k=1), and estimating Zb with increasing k-bandwidths.\n", + "# Recall k=2*pi*nu\n", + "nu=1/(2*np.pi)\n", + "\n", + "nbins=30\n", + "output=np.zeros((nbins,3))\n", + "nr = np.linspace(0., 0.3, nbins+1)\n", + "output[:,0]=nr[1:]\n", + "\n", + "for j in range(0,nbins,1):\n", + " \n", + " kmin=nu-output[j,0]/2\n", + " kmax=nu+output[j,0]/2\n", + " \n", + " [(Ztr,btr,dZtr), (Zor, bor, dZor)]=pycurious.tanaka1999(S, k, sigma2, (kmin, kmax), (kmin, kmax))\n", + " [Zb,eZb]=pycurious.ComputeTanaka(Ztr, dZtr, Zor, dZor)\n", + " output[j,1]=Zb\n", + " output[j,2]=eZb\n", + " \n", + "fig2 = plt.figure(figsize=(8,8))\n", + "ax2=plt.errorbar(output[:,0],output[:,1],yerr=output[:,2])\n", + "plt.gca().invert_yaxis()\n", + "plt.xlabel('$\\\\nu$-bandwidth')\n", + "plt.ylabel('CPD depth (km)')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The CPD estimates resulting from this test become consistent for $\\nu$-bandwidths greater than approximately 0.1. Statistics improve with larger bandwidths, however, it is worth remaining aware of the typically non-linear trend of the spectrum, as it may not be appropriate for a linear fit over a large domain of $\\nu$." + ] + }, + { + "cell_type": "code", + "execution_count": 134, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0,0.5,u'CPD misfit (km)')" + ] + }, + "execution_count": 134, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# 3) How large a window width of magnetic data is required?\n", + "grid = pycurious.CurieOptimise(d, xmin, xmax, ymin, ymax)\n", + "xpt = xmin + (xmax-xmin)/2\n", + "ypt = ymin + (ymax-ymin)/2\n", + "\n", + "nwin=50\n", + "baseW=10000\n", + "inc=2500\n", + "\n", + "output=np.zeros((nwin,3))\n", + "\n", + "# Define 'ws' as variable window size index\n", + "for i in range(0,nwin,1):\n", + " ws=baseW+i*inc\n", + " subgrid = grid.subgrid(xpt, ypt, ws)\n", + " S, k, sigma2 = grid.radial_spectrum_log(subgrid, taper=None)\n", + " [(Ztr,btr,dZtr), (Zor, bor, dZor)]=pycurious.tanaka1999(S, k, sigma2, (0.11, 0.21), (0.11, 0.21))\n", + " [Zb,eZb]=pycurious.ComputeTanaka(Ztr, dZtr, Zor, dZor)\n", + " output[i,0]=ws\n", + " output[i,1]=Zb\n", + " output[i,2]=eZb\n", + " #print('Zb estimate for '+str(ws)+' m: '+np.array2string(Zb)+', +/- '+np.array2string(eZb)+' km')\n", + "\n", + "fig, (ax1, ax2) = plt.subplots(1,2, figsize=(16,6),)\n", + "ax1.plot(output[:,0],output[:,1])\n", + "ax1.set_ylim(0,30)\n", + "ax1.invert_yaxis()\n", + "ax1.set_xlabel('Data window size (m)')\n", + "ax1.set_ylabel('CPD estimate (km)')\n", + "\n", + "ax2.plot(output[:,0],output[:,2])\n", + "ax2.set_xlabel('Data window size (m)')\n", + "ax2.set_ylabel('CPD misfit (km)')\n", + "#plt.gca().invert_yaxis()\n", + "#plt.xlabel('Data window size (km)')\n", + "#plt.ylabel('CPD depth (km)')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The results of this test highlight that there is a significant amount of variability in the CPD estimates at all window sizes, inferring that where possible, a range of window sizes should be tested for any data set. However, the righthand plot of propagated error in the CPD estimates clarifies that estimates from larger windows are more robust. In particular, with the prior knowledge that the CPD of the test data is 16 km, window sizes of greater than 80 km show a reduced improvement in statistics. " ] } ], From 2583ca7641998c09d6548eb679a86b83b5d0698d Mon Sep 17 00:00:00 2001 From: Robert Delhaye Date: Fri, 27 Jul 2018 13:48:39 +0100 Subject: [PATCH 020/170] BM added new method Compute Tanaka --- pycurious/__init__.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/pycurious/__init__.py b/pycurious/__init__.py index 31932e4..5241dd1 100644 --- a/pycurious/__init__.py +++ b/pycurious/__init__.py @@ -1,5 +1,5 @@ # -*- coding: utf-8 -*- -from .curie import CurieGrid, bouligand2009, tanaka1999, maus1995 +from .curie import CurieGrid, bouligand2009, tanaka1999, maus1995, ComputeTanaka from .optimise import CurieOptimise from .parallel import CurieParallel from .mapping import transform_coordinates, grid, trim \ No newline at end of file From 46ccca0d51c57ad601b13d4f4effda5eab96e594 Mon Sep 17 00:00:00 2001 From: Robert Delhaye Date: Fri, 27 Jul 2018 13:49:15 +0100 Subject: [PATCH 021/170] Tanaka method split to access Zt, Zo constituents --- pycurious/curie.py | 15 +++++++++++---- 1 file changed, 11 insertions(+), 4 deletions(-) diff --git a/pycurious/curie.py b/pycurious/curie.py index b2c988b..5c1d18b 100644 --- a/pycurious/curie.py +++ b/pycurious/curie.py @@ -546,12 +546,16 @@ def compute_coefficients(X, Y, E): X2E2sum = np.sum(X2/E2) Y2E2sum = np.sum(Y2/E2) - TL = XE2sum*YE2sum - np.sum(XY/E2*rE2sum) + #TL = XE2sum*YE2sum - np.sum(XY/E2*rE2sum) + # I think summation in second TL term needed to be split + TL = XE2sum*YE2sum - np.sum(XY/E2)*rE2sum BL = XE2sum**2 - X2E2sum*rE2sum Z = TL/BL b = (np.sum(XY/E2) - Z*X2E2sum)/XE2sum - dZ = np.sqrt( rE2sum/(X2E2sum*rE2sum - XE2sum) ) + #dZ = np.sqrt( rE2sum/(X2E2sum*rE2sum - XE2sum) ) + ## There was a missing **2 term at end of error term. + dZ = np.sqrt( rE2sum/(X2E2sum*rE2sum - XE2sum**2) ) return Z, b, dZ @@ -569,13 +573,16 @@ def compute_coefficients(X, Y, E): kmin, kmax = kmax_range mask2 = np.logical_and(sf >=kmin, sf <=kmax) X2 = sf[mask2] - Y2 = np.log(np.exp(S[mask2])/X2) - E2 = np.log(np.exp(sigma2[mask2])/X2) + Y2 = np.log(np.exp(S[mask2])/(X2*2*np.pi)) + E2 = np.log(np.exp(sigma2[mask2])/(X2*2*np.pi)) # compute top and bottom of magnetic layer Ztr, btr, dZtr = compute_coefficients(X1, Y1, E1) Zor, bor, dZor = compute_coefficients(X2, Y2, E2) + return (Ztr,btr,dZtr), (Zor, bor, dZor) + +def ComputeTanaka(Ztr, dZtr, Zor, dZor): Zb = 2.0*Zor - Ztr dZb = 2.0*dZor - dZtr return abs(Zb), dZb From b5384a5dfdacf57d80d8469ec3e33c31855ae2c1 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Sun, 26 Aug 2018 22:30:36 +0100 Subject: [PATCH 022/170] Changes to include sigma2 in misfit ... and a bunch of other modifications --- pycurious/curie.py | 18 +++-- pycurious/optimise.py | 152 ++++++++++++++++++++++++++++++++++++++++-- 2 files changed, 157 insertions(+), 13 deletions(-) diff --git a/pycurious/curie.py b/pycurious/curie.py index 10b7f02..cc7d023 100644 --- a/pycurious/curie.py +++ b/pycurious/curie.py @@ -39,7 +39,7 @@ def __init__(self, grid, xmin, xmax, ymin, ymax): warnings.warn("node spacing should be identical {}".format((dx,dy)), RuntimeWarning) - def subgrid(self, xc, yc, window): + def subgrid(self, window, xc, yc): """ Extract a subgrid from the data at a window around the point (xc,yc) @@ -212,7 +212,10 @@ def radial_spectrum(self, subgrid, taper=np.hanning, scale=0.001, **kwargs): k[i] = kk[mask].mean() sigma2[i] = np.std(rr)/np.sqrt(rr.size) - return S, k, sigma2 + + sigma_S = np.sqrt(sigma2) + + return k, S, sigma_S def radial_spectrum_log(self, subgrid, taper=np.hanning, scale=0.001, **kwargs): @@ -278,7 +281,9 @@ def radial_spectrum_log(self, subgrid, taper=np.hanning, scale=0.001, **kwargs): k[i] = kk[mask].mean() sigma2[i] = np.std(rr)/np.sqrt(rr.size) - return S, k, sigma2 + sigma_S = np.sqrt(sigma2) + + return k, S, sigma_S def azimuthal_spectrum(self, subgrid, taper=np.hanning, scale=0.001, theta=5.0, **kwargs): @@ -330,7 +335,8 @@ def azimuthal_spectrum(self, subgrid, taper=np.hanning, scale=0.001, theta=5.0, for i in range(0, dtheta.size): PSD = np.abs(np.fft.fft(vtaper*sinogram[:,i], n=nk)) S[i,:] = np.log( np.sqrt(PSD[1:kbins.size+1] )) - return S, kbins, dtheta + + return kbins, S, dtheta def reduce_to_pole(self, data, inc, dec, sinc=None, sdec=None): @@ -474,7 +480,7 @@ def upward_continuation(self, data, height): # Helper functions to calculate Curie depth -def bouligand2009(beta, zt, dz, kh, C=0.0): +def bouligand2009(kh, beta, zt, dz, C): """ Calculate the synthetic radial power spectrum of magnetic anomalies @@ -483,10 +489,10 @@ def bouligand2009(beta, zt, dz, kh, C=0.0): Parameters ---------- + kh : norm of the wave number in the horizontal plane beta : fractal parameter zt : top of magnetic sources dz : thickness of magnetic sources - kh : norm of the wave number in the horizontal plane C : field constant (Maus et al., 1997) Returns diff --git a/pycurious/optimise.py b/pycurious/optimise.py index 74152e0..ace5e2b 100644 --- a/pycurious/optimise.py +++ b/pycurious/optimise.py @@ -117,10 +117,10 @@ def objective_function(self, x, x0, sigma_x0, *args): ------- misfit : float """ - return np.linalg.norm((x - x0)/sigma_x0)**2 + return 0.5*np.linalg.norm((x - x0)/sigma_x0)**2 - def min_func(self, x, Phi_exp, kh): + def min_func(self, x, kh, Phi, sigma_Phi): """ Function to minimise @@ -144,9 +144,9 @@ def min_func(self, x, Phi_exp, kh): beta, zt, dz, C = x with warnings.catch_warnings() as w: warnings.simplefilter("ignore") - Phi_syn = bouligand2009(beta, zt, dz, kh, C) + Phi_syn = bouligand2009(kh, beta, zt, dz, C) - misfit = self.objective_function(Phi_syn, Phi_exp, 1.0) + misfit = self.objective_function(Phi_syn, Phi, sigma_Phi) if not np.isfinite(misfit): misfit = 1e99 else: @@ -188,14 +188,14 @@ def process_subgrid(subgrid): x0 = np.array([beta, zt, dz, C]) # get subgrid - subgrid = self.subgrid(xc, yc, window) + subgrid = self.subgrid(window, xc, yc) subgrid = process_subgrid(subgrid) # compute radial spectrum - S, k, sigma2 = self.radial_spectrum(subgrid, taper=taper, **kwargs) + k, Phi, sigma_Phi = self.radial_spectrum(subgrid, taper=taper, **kwargs) # minimise function - res = minimize(self.min_func, x0, args=(S, k), bounds=self.bounds) + res = minimize(self.min_func, x0, args=(k, Phi, sigma_Phi), bounds=self.bounds) return res.x @@ -262,6 +262,144 @@ def optimise_routine(self, window, xc_list, yc_list, beta=3.0, zt=1.0, dz=10.0, return Bopt, ztopt, dzopt, Copt + def metropolis_hastings(self, nsim, window, xc, yc, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs): + """ + MCMC algorithm using a Metropolis-Hastings sampler. + + Evaluates a Markov-Chain for starting values of beta, zt, dz, C + and returns the ensemble of model realisations. + + WARNING: Use starting values relatively close to the solution + - C can easily found from the mean of the radial power spectrum + + Parameters + ---------- + window : float - size of window in metres + xc : float - centroid x values + yc : float - centroid y values + beta : float - fractal parameter (starting value) + zt : float - top of magnetic layer (starting value) + dz : float - thickness of magnetic layer (starting value) + C : float - field constant (starting value) + + Returns + ------- + beta : ndarray shape(nsim,) - fractal parameters + zt : ndarray shape(nsim,) - top of magnetic layer + dz : ndarray shape(nsim,) - thickness of magnetic layer + C : ndarray shape(nsim,) - field constant + """ + if type(process_subgrid) == type(None): + # dummy function + def process_subgrid(subgrid): + return subgrid + + # get subgrid + subgrid = self.subgrid(window, xc, yc) + subgrid = process_subgrid(subgrid) + + # compute radial spectrum + k, Phi, sigma_Phi = self.radial_spectrum(subgrid, taper=taper, **kwargs) + + + samples = np.empty((nsim, 4)) + x0 = np.array([beta, zt, dz, C]) + + for i in range(nsim): + # add random perturbation + x1 = x0 + np.random.normal(size=4) + + # evaluate probability + P0 = np.exp(-self.min_func(x0, k, Phi, sigma_Phi)) + P1 = np.exp(-self.min_func(x1, k, Phi, sigma_Phi)) + + P = min(P1/P0, 1.0) + + # randomly accept probability + if np.random.rand() <= P: + x0 = x1 + + samples[i] = x0 + + return samples + + + def metropolis_hastings2(self, nsim, window, xc_list, yc_list, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs): + """ + MCMC algorithm using a Metropolis-Hastings sampler. + + Evaluates a Markov-Chain for starting values of beta, zt, dz, C + and returns the ensemble of model realisations. + + WARNING: Use starting values relatively close to the solution + - C can easily found from the mean of the radial power spectrum + + Parameters + ---------- + window : float - size of window in metres + xc : float - centroid x values + yc : float - centroid y values + beta : float - fractal parameter (starting value) + zt : float - top of magnetic layer (starting value) + dz : float - thickness of magnetic layer (starting value) + C : float - field constant (starting value) + + Returns + ------- + beta : ndarray shape(nsim,) - fractal parameters + zt : ndarray shape(nsim,) - top of magnetic layer + dz : ndarray shape(nsim,) - thickness of magnetic layer + C : ndarray shape(nsim,) - field constant + """ + if type(process_subgrid) == type(None): + # dummy function + def process_subgrid(subgrid): + return subgrid + + n = len(xc_list) + + if n != len(yc_list): + raise ValueError("xc_list and yc_list must be the same size") + + rbeta = np.random.uniform(0, 10, size=nsim) + samples = np.empty((n, nsim, 4)) + misfit = np.empty(n) + + for i in range(n): + xc = xc_list[i] + yc = yc_list[i] + + # get subgrid + subgrid = self.subgrid(xc, yc, window) + subgrid = process_subgrid(subgrid) + + # compute radial spectrum + S, k, sigma2 = self.radial_spectrum(subgrid, taper=taper, **kwargs) + + x0 = np.array([rbeta[0], 0.0, 20.0, S.mean()]) + + + for j in range(nsim): + # add random perturbation + x1 = x0 + np.random.normal(size=4) + x1[0] = rbeta[j] + + # evaluate probability + P0 = np.exp(-self.min_func(x0, S, k)) + P1 = np.exp(-self.min_func(x1, S, k)) + + P = min(P1/P0, 1.0) + + # randomly accept probability + if np.random.rand() <= P: + x0 = x1 + + samples[i,j] = x0 + # misfit[] + + return samples + + def sensitivity_routine(self, nsim, window, xc_list, yc_list, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs): """ Iterate through a list of centroids to compute the mean and From c392f1d545770ec2001de9aca73e283f81c9c1c9 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Sun, 26 Aug 2018 23:44:31 +0100 Subject: [PATCH 023/170] Moving Notebooks to resemble some form of structure --- .../Bouligand/Ex2-Compute-Curie-depth.ipynb | 250 ++++++++++++ ...-Compute-Curie-depth-Tanaka-approach.ipynb | 265 ------------ ...x2a-Compute-Curie-depth-Tanaka-approach.py | 35 -- Examples/Notebooks/Ex2a.py | 39 -- ...mpute-Curie-depth-Bouligand-approach.ipynb | 378 ------------------ .../Tanaka/Ex2-Compute-Curie-depth.ipynb | 272 +++++++++++++ 6 files changed, 522 insertions(+), 717 deletions(-) create mode 100644 Examples/Notebooks/Bouligand/Ex2-Compute-Curie-depth.ipynb delete mode 100644 Examples/Notebooks/Ex2a-Compute-Curie-depth-Tanaka-approach.ipynb delete mode 100644 Examples/Notebooks/Ex2a-Compute-Curie-depth-Tanaka-approach.py delete mode 100644 Examples/Notebooks/Ex2a.py delete mode 100644 Examples/Notebooks/Ex2b-Compute-Curie-depth-Bouligand-approach.ipynb create mode 100644 Examples/Notebooks/Tanaka/Ex2-Compute-Curie-depth.ipynb diff --git a/Examples/Notebooks/Bouligand/Ex2-Compute-Curie-depth.ipynb b/Examples/Notebooks/Bouligand/Ex2-Compute-Curie-depth.ipynb new file mode 100644 index 0000000..14290ae --- /dev/null +++ b/Examples/Notebooks/Bouligand/Ex2-Compute-Curie-depth.ipynb @@ -0,0 +1,250 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Example 2b - Compute Curie depth (Bouligand approach)\n", + "\n", + "Bouligand *et al.* (2009) formulated an expression for the radial power assuming a fractal model for crustal magnetisation (see [Ex1-Plot-power-spectra](./Ex1-Plot-power-spectrum.ipynb) for analytic solution), which depends on 4 parameters:\n", + "\n", + "- $\\beta$ - a fractal parameter\n", + "- $z_t$ - top of magnetic sources\n", + "- $\\Delta z$ - thickness of the magnetic layer\n", + "- $C$ - a field constant\n", + "\n", + "These parameters can be fitted to the radial power spectrum computed from FFT to determine Curie depth ($z_\\mathrm{curie} = z_t + \\Delta z$).\n", + "\n", + "### Contents\n", + "\n", + "- [Plot radial power spectrum](#Plot-radial-power-spectrum)\n", + "- [Optimise parameters](#Optimise-parameters)\n", + "- [Varying window sizes](#Varying-window-sizes)\n", + "- [Add prior constraints](#Add-prior-constraints)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "\n", + "import pycurious" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# load x,y,anomaly\n", + "mag_data = np.loadtxt(\"../data/test_mag_data.txt\")\n", + "\n", + "nx, ny = 305, 305\n", + "\n", + "x = mag_data[:,0]\n", + "y = mag_data[:,1]\n", + "d = mag_data[:,2].reshape(ny,nx)\n", + "\n", + "xmin, xmax = x.min(), x.max()\n", + "ymin, ymax = y.min(), y.max()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Plot radial power spectrum\n", + "\n", + "The radial power spectrum is computed from a square window of the magnetic anomaly. Methods to select window sizes and compute the Fast Fourier Transform (FFT) belong to the `CurieGrid` object. We apply the default `np.hanning` taper to the power spectrum as in [Ex1-Plot-power-spectrum](#./Ex1-Plot-power-spectrum.ipynb)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "grid = pycurious.CurieOptimise(d, xmin, xmax, ymin, ymax)\n", + "\n", + "# pick the centroid\n", + "xpt = 0.5*(xmin + xmax)\n", + "ypt = 0.5*(ymin + ymax)\n", + "\n", + "window_size = 200e3\n", + "subgrid = grid.subgrid(window_size, xpt, ypt)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "k, Phi, sigma_Phi = grid.radial_spectrum(subgrid)\n", + "\n", + "# plot radial power spectrum\n", + "plt.plot(k, Phi, '-o')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Optimise parameters\n", + "\n", + "The `optimise` routine determines the Curie parameters ($\\beta, z_t, \\Delta z, C$) by minimising the misfit between the analytic power spectum and the computed power spectrum. Optimisation is handles by the nonlinear least-squares algorithm implemented in `scipy.optimize.minimize`.\n", + "\n", + "```python\n", + "optimise(window, xc, yc, beta=3.0, zt=1.0, dz=10.0, C=5.0)\n", + "```\n", + "\n", + "These are sane defaults to initiate the optimisation, however, values close to the final solution will result in faster convergence and stability." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "beta, zt, dz, C = grid.optimise(window_size, xpt, ypt)\n", + "print(\"beta = {:.2f}\\n zt = {:.2f}\\n dz = {:.2f}\\n C = {:.2f}\".format(beta,zt,dz,C))\n", + "\n", + "Phi2 = pycurious.bouligand2009(k, beta, zt, dz, C)\n", + "\n", + "# plot radial power spectrum - compare analytic against computed\n", + "plt.plot(k, Phi, '-o')\n", + "plt.plot(k, Phi2, linewidth=2)\n", + "\n", + "print(\"\\nCurie depth is {:.2f} km\".format(zt + dz))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Varying window sizes\n", + "\n", + "Here, we observe the effect decreasing the window size has on the optimisation of Curie parameters. The number of points in the power spectrum decrease with smaller window sizes, particularly at low wavenumbers (long wavelengths). This significantly reduces the quality of Curie depth determinations for window sizes less than 200 km.\n", + "\n", + "As a rule of thumb, the window size should be > 4 times the maximum possible Curie depth that could be resolved from a study area." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "# window size in kilometres\n", + "window_size_range = [304e3, 200e3, 100e3, 50e3]\n", + "\n", + "\n", + "fig = plt.figure()\n", + "ax1 = fig.add_subplot(111)\n", + "\n", + "for i, window_size in enumerate(window_size_range):\n", + " \n", + " # compute radial power spectrum\n", + " subgrid = grid.subgrid(window_size, xpt, ypt)\n", + " k, Phi, sigma_Phi = grid.radial_spectrum(subgrid)\n", + " ax1.plot(k, Phi, '-o', color='C{}'.format(i))\n", + " \n", + " # optimise Curie variables\n", + " beta, zt, dz, C = grid.optimise(window_size, xpt, ypt)\n", + " print(\"beta = {:.2f}\\n zt = {:.2f}\\n dz = {:.2f}\\n C = {:.2f}\\n\".format(beta,zt,dz,C))\n", + " \n", + " Phi2 = pycurious.bouligand2009(k, beta, zt, dz, C)\n", + " ax1.plot(k, Phi2, color='C{}'.format(i), linewidth=2, label=\"window size = {}km\".format(window_size/1e3))\n", + "\n", + "ax1.legend()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Add prior constraints\n", + "\n", + "Spurious Curie depth values can often be obtained if windows of the magnetic anomaly do not contain long wavelengths. This often arises from selecting too small a small window size, but can also occur from uncorrected artefacts in the magnetic anomaly, or simply the absence of magnetic minerals close to the surface of the crust.\n", + "\n", + "Adding *a priori* information on $\\beta, z_t, \\Delta z, C$ can reduce the incidence of anomalous values. $\\beta$ and $C$ vary at long wavelengths, and $z_t + \\Delta z$ should be within the range of 10-40 km if we assume the Curie depth is equivalent to the 580$^\\circ$C isotherm. Adding prior information to any (or all) of these parameters penalises spurious values using a standard $\\ell_2$-norm misfit function.\n", + "\n", + "```python\n", + "from scipy import stats\n", + "\n", + "# define normal distributions\n", + "beta_p = stats.norm(3.0, 1.0)\n", + "zt_p = stats.norm(0.0, 1.0)\n", + "dz_p = stats.norm(10.0, 8.0)\n", + "C_p = stats.norm(10.0, 10.0)\n", + "\n", + "# add to grid object\n", + "grid.add_prior(beta=beta_p, zt=zt_p, dz=dz_p, C=C_p)\n", + "```\n", + "\n", + "A combination of priors can be added. `reset_priors()` removes all prior information." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "grid.reset_priors()\n", + "\n", + "from scipy import stats\n", + "beta_p = stats.norm(3.0, 0.01)\n", + "grid.add_prior(beta=beta_p)\n", + "\n", + "fig = plt.figure()\n", + "ax1 = fig.add_subplot(111, xlabel=\"wavenumber (rad/km)\", ylabel=\"radial power spectrum\")\n", + "\n", + "for i, window_size in enumerate(window_size_range):\n", + " \n", + " # compute radial power spectrum\n", + " subgrid = grid.subgrid(window_size, xpt, ypt)\n", + " k, Phi, sigma_Phi = grid.radial_spectrum(subgrid)\n", + " ax1.plot(k, Phi, '-o', color='C{}'.format(i), label='{} km window size'.format(window_size*1e-3))\n", + " \n", + " # optimise Curie variables\n", + " beta, zt, dz, C = grid.optimise(window_size, xpt, ypt)\n", + " print(\"beta = {:.2f}\\n zt = {:.2f}\\n dz = {:.2f}\\n C = {:.2f}\\n\".format(beta,zt,dz,C))\n", + " \n", + " Phi2 = pycurious.bouligand2009(k, beta, zt, dz, C)\n", + " ax1.plot(k, Phi2, color='C{}'.format(i), linewidth=2)\n", + " \n", + "ax1.legend()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.15" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Examples/Notebooks/Ex2a-Compute-Curie-depth-Tanaka-approach.ipynb b/Examples/Notebooks/Ex2a-Compute-Curie-depth-Tanaka-approach.ipynb deleted file mode 100644 index f94a1a1..0000000 --- a/Examples/Notebooks/Ex2a-Compute-Curie-depth-Tanaka-approach.ipynb +++ /dev/null @@ -1,265 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Example 2a - Compute Curie depth (Tanaka approach)\n", - "Tanaka *et al.* (1999) based their method upon an expression for the radial power spectrum that assumes random magnetisation of the crust, and a radially averaged power spectra $\\Phi_{\\Delta T}(|k|)$:\n", - "\n", - "$$(1) \\Phi_{\\Delta T}(|k|)=Ae^{-2|k|Z_t}(1-e^{-|k|(Z_b-Z_t)})^2$$\n", - "\n", - "where:\n", - " - $k$ - spatial wavenumber ($k=2\\pi/\\lambda$, where $\\lambda$ is wavelength).\n", - " - $Z_t$ - top of assumed magnetic source.\n", - " - $Z_b$ - bottom of assumed magnetic source.\n", - " - ($Z_b-Z_t$ is hence the thickness of the magnetic source)\n", - "\n", - "For wavelengths less than twice the source thickness, this simplifies to:\n", - "\n", - "$$(2) \\ln [\\Phi_{\\Delta T}(|k|)^{1/2}] = \\ln B-|k|Z_t $$\n", - "\n", - "where $B$ is another constant. Conversely, (1) can be rewritten, with $Z_o$ as the centroid depth of the magnetic source:\n", - "\n", - "$$(3) \\Phi_{\\Delta T}(|k|)^{1/2} = Ce^{-|k|Z_o}(e^{-|k|(Z_t-Z_o)}-e^{-|k|(Z_b-Z_o)}) $$\n", - "\n", - "For long wavelengths, where $2d$ is the magnetic source thickness:\n", - "$$(4) \\Phi_{\\Delta T}(|k|)^{1/2} = Ce^{-|k|Z_o}(e^{-|k|(-d)}-e^{-|k|(-d)})\\approx Ce^{-|k|Z_o}2|k|d $$\n", - "\n", - "$$ \\ln \\{\\Phi_{\\Delta T}(|k|)^{1/2}/|k|\\}=\\ln D-|k|Z_o $$\n", - "\n", - "\n", - "Estimates of $Z_t$ and $Z_o$ can be estimated from Equations (2) and (5), and hence the base of the magnetic source (assumed to be at the Curie point depth):\n", - "\n", - "$$(6) Z_b=Z_o-(Z_t-Z_o) = 2Z_o-Z_t $$\n", - "\n", - "### Contents\n", - "\n", - "- [Plot radial power spectrum](#Plot-radial-power-spectrum)\n", - "- [Compute CPD Estimate](#Compute-cpd-estimate)" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "%matplotlib inline\n", - "\n", - "import pycurious" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "# load x,y,anomaly\n", - "mag_data = np.loadtxt(\"../data/test_mag_data.txt\")\n", - "\n", - "nx, ny = 305, 305\n", - "\n", - "x = mag_data[:,0]\n", - "y = mag_data[:,1]\n", - "d = mag_data[:,2].reshape(ny,nx)\n", - "\n", - "xmin, xmax = x.min(), x.max()\n", - "ymin, ymax = y.min(), y.max()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Plot radial power spectrum\n", - "The radial power spectrum is computed from a square window of the magnetic anomaly. Methods to select window sizes and compute the Fast Fourier Transform (FFT) belong to the `CurieGrid` object. We apply the default `np.hanning` taper to the power spectrum as in [Ex1-Plot-power-spectrum](#./Ex1-Plot-power-spectrum.ipynb)." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [], - "source": [ - "# initialise CurieOptimise object\n", - "grid = pycurious.CurieOptimise(d, xmin, xmax, ymin, ymax)\n", - "#grid = pycurious.CurieGrid(d, xmin, xmax, ymin, ymax)\n", - "\n", - "# pick the centroid\n", - "xpt = 0.5*(xmin + xmax)\n", - "ypt = 0.5*(ymin + ymax)\n", - "\n", - "window_size = 304e3\n", - "subgrid = grid.subgrid(xpt, ypt, window_size)" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Text(0,0.5,u'$\\\\ln(\\\\Phi_{\\\\Delta T}(|k|)^{1/2})/(2\\\\pi)$')" - ] - }, - "execution_count": 5, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "S, k, sigma2 = grid.radial_spectrum_log(subgrid)\n", - "\n", - "# Plot of power spectrum, as function of spatial frequency\n", - "plt.plot(k/(2*np.pi), S/(2*np.pi), '-o')\n", - "plt.title('Power Spectrum')\n", - "plt.xlabel(r'$|k|/(2\\pi)$ [km$^{-1}$]')\n", - "plt.ylabel(r'$\\ln(\\Phi_{\\Delta T}(|k|)^{1/2})/(2\\pi)$')" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Text(0,0.5,u'$\\\\ln(\\\\Phi_{\\\\Delta T}(|k|)^{1/2}/|k|)/(2\\\\pi)$')" - ] - }, - "execution_count": 6, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "Sn=np.log(np.exp(S)/k)\n", - "plt.plot(k/(2*np.pi), Sn/(2*np.pi), '-o')\n", - "plt.title('Power Spectrum, weighted by k')\n", - "plt.xlabel(r'$|k|/(2\\pi)$ [km$^{-1}$]')\n", - "plt.ylabel(r'$\\ln(\\Phi_{\\Delta T}(|k|)^{1/2}/|k|)/(2\\pi)$')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Compute CPD Estimate\n", - "As described above, once the power spectrum (and weighted spectrum) are computed, then the gradient of linear fits of certain wavenumber/spatial frequency windows can be taken as estimates of $Z_t$ and $Z_o$. The weighted linear fitting of the respective spectral window is implemented in the `CurieGrid` parent class as `tanaka1999`, and takes the spectrum, wave number, and spectrum error as inputs. The function also has functionality to pass specific spectral windows for each spectra, however, the default is to consider spatial frequencies of 0.05 - 0.2 (recalling that $k$, the wavenumber, is proportional to the spatial frequency $\\nu$ by $k=2\\pi\\nu$).\n", - "\n", - "\n", - "The function has two tuple returns: the gradient estimate, intercept and errors of $Z_t$ and $Z_o$. The gradient and errors can then be passed into the `CurieGrid.ComputeTanaka` method to obtain estimates of $Zb$ and $\\varepsilon Zb$." - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Zb estimate: 17.80614059, +/- 2.02467493 km\n" - ] - } - ], - "source": [ - "[(Ztr,btr,dZtr), (Zor, bor, dZor)]=pycurious.tanaka1999(S, k, sigma2)\n", - "[Zb,eZb]=pycurious.ComputeTanaka(Ztr, dZtr, Zor, dZor)\n", - "print('Zb estimate: '+np.array2string(Zb)+', +/- '+np.array2string(eZb)+' km')" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Text(0,0.5,u'$\\\\ln(\\\\Phi_{\\\\Delta T}(|k|)^{1/2}/|k|)/(2\\\\pi)$')" - ] - }, - "execution_count": 9, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# make two plots with Z-lines overlain.\n", - "# Plot of power spectrum, as function of spatial frequency\n", - "fig, (ax1, ax2) = plt.subplots(1,2, figsize=(16,6),)\n", - "\n", - "ax1.plot(k/(2*np.pi), S/(2*np.pi), '-bo',k/(2*np.pi),(Ztr*k/(2*np.pi)+btr)/(2*np.pi),'r-')\n", - "#ax1.title('Power Spectrum')\n", - "ax1.set_xlabel(r'$|k|/(2\\pi)$ [km$^{-1}$]')\n", - "ax1.set_ylabel(r'$\\ln(\\Phi_{\\Delta T}(|k|)^{1/2})/(2\\pi)$')\n", - "\n", - "ax2.plot(k/(2*np.pi), Sn/(2*np.pi), '-o',k/(2*np.pi),(Zor*k/(2*np.pi)+bor)/(2*np.pi),'r-')\n", - "ax2.set_xlabel(r'$|k|/(2\\pi)$ [km$^{-1}$]')\n", - "ax2.set_ylabel(r'$\\ln(\\Phi_{\\Delta T}(|k|)^{1/2}/|k|)/(2\\pi)$')\n" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 2", - "language": "python", - "name": "python2" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 2 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython2", - "version": "2.7.15rc1" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/Examples/Notebooks/Ex2a-Compute-Curie-depth-Tanaka-approach.py b/Examples/Notebooks/Ex2a-Compute-Curie-depth-Tanaka-approach.py deleted file mode 100644 index 2b263c7..0000000 --- a/Examples/Notebooks/Ex2a-Compute-Curie-depth-Tanaka-approach.py +++ /dev/null @@ -1,35 +0,0 @@ -import numpy as np -import matplotlib.pyplot as plt -#matplotlib inline -import pycurious - - -# load x,y,anomaly -mag_data = np.loadtxt("../data/test_mag_data.txt") - -nx, ny = 305, 305 - -x = mag_data[:,0] -y = mag_data[:,1] -d = mag_data[:,2].reshape(ny,nx) - -xmin, xmax = x.min(), x.max() -ymin, ymax = y.min(), y.max() - -# initialise CurieOptimise object -#grid = pycurious.CurieOptimise(d, xmin, xmax, ymin, ymax) -grid = pycurious.CurieGrid(d, xmin, xmax, ymin, ymax) - -# pick the centroid -xpt = 0.5*(xmin + xmax) -ypt = 0.5*(ymin + ymax) - -window_size = 304e3 -subgrid = grid.subgrid(xpt, ypt, window_size) - -print(type(subgrid)) -print(type(grid)) -S, k, sigma2 = grid.radial_spectrum(subgrid) -print(np.size(S)) -S, k, sigma2 = grid.radial_spectrum_log(subgrid) -#S, k, sigma2 = grid.radial_spectrum_log(subgrid) diff --git a/Examples/Notebooks/Ex2a.py b/Examples/Notebooks/Ex2a.py deleted file mode 100644 index 416c4ed..0000000 --- a/Examples/Notebooks/Ex2a.py +++ /dev/null @@ -1,39 +0,0 @@ -import numpy as np -import matplotlib.pyplot as plt -#matplotlib inline -import pycurious - - -# load x,y,anomaly -mag_data = np.loadtxt("../data/test_mag_data.txt") - -nx, ny = 305, 305 - -x = mag_data[:,0] -y = mag_data[:,1] -d = mag_data[:,2].reshape(ny,nx) - -xmin, xmax = x.min(), x.max() -ymin, ymax = y.min(), y.max() - -# initialise CurieOptimise object -#grid = pycurious.CurieOptimise(d, xmin, xmax, ymin, ymax) -grid = pycurious.CurieGrid(d, xmin, xmax, ymin, ymax) - -# pick the centroid -xpt = 0.5*(xmin + xmax) -ypt = 0.5*(ymin + ymax) - -window_size = 304e3 -subgrid = grid.subgrid(xpt, ypt, window_size) - - -S, k, sigma2 = grid.radial_spectrum(subgrid) -#print(S) -S, k, sigma2 = grid.radial_spectrum_log(subgrid) -#print(S) -#S, k, sigma2 = grid.radial_spectrum_log(subgrid) - - -zb=pycurious.tanaka1999(S, k, sigma2) -print(zb) \ No newline at end of file diff --git a/Examples/Notebooks/Ex2b-Compute-Curie-depth-Bouligand-approach.ipynb b/Examples/Notebooks/Ex2b-Compute-Curie-depth-Bouligand-approach.ipynb deleted file mode 100644 index 38c6d92..0000000 --- a/Examples/Notebooks/Ex2b-Compute-Curie-depth-Bouligand-approach.ipynb +++ /dev/null @@ -1,378 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Example 2b - Compute Curie depth (Bouligand approach)\n", - "\n", - "Bouligand *et al.* (2009) formulated an expression for the radial power assuming a fractal model for crustal magnetisation (see [Ex1-Plot-power-spectra](./Ex1-Plot-power-spectrum.ipynb) for analytic solution), which depends on 4 parameters:\n", - "\n", - "- $\\beta$ - a fractal parameter\n", - "- $z_t$ - top of magnetic sources\n", - "- $\\Delta z$ - thickness of the magnetic layer\n", - "- $C$ - a field constant\n", - "\n", - "These parameters can be fitted to the radial power spectrum computed from FFT to determine Curie depth ($z_\\mathrm{curie} = z_t + \\Delta z$).\n", - "\n", - "### Contents\n", - "\n", - "- [Plot radial power spectrum](#Plot-radial-power-spectrum)\n", - "- [Optimise parameters](#Optimise-parameters)\n", - "- [Varying window sizes](#Varying-window-sizes)\n", - "- [Add prior constraints](#Add-prior-constraints)" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "%matplotlib inline\n", - "\n", - "import pycurious" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "# load x,y,anomaly\n", - "mag_data = np.loadtxt(\"../data/test_mag_data.txt\")\n", - "\n", - "nx, ny = 305, 305\n", - "\n", - "x = mag_data[:,0]\n", - "y = mag_data[:,1]\n", - "d = mag_data[:,2].reshape(ny,nx)\n", - "\n", - "xmin, xmax = x.min(), x.max()\n", - "ymin, ymax = y.min(), y.max()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Plot radial power spectrum\n", - "\n", - "The radial power spectrum is computed from a square window of the magnetic anomaly. Methods to select window sizes and compute the Fast Fourier Transform (FFT) belong to the `CurieGrid` object. We apply the default `np.hanning` taper to the power spectrum as in [Ex1-Plot-power-spectrum](#./Ex1-Plot-power-spectrum.ipynb)." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "grid = pycurious.CurieOptimise(d, xmin, xmax, ymin, ymax)\n", - "\n", - "# pick the centroid\n", - "xpt = 0.5*(xmin + xmax)\n", - "ypt = 0.5*(ymin + ymax)\n", - "\n", - "window_size = 304e3\n", - "subgrid = grid.subgrid(xpt, ypt, window_size)" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "[]" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "S, k, sigma2 = grid.radial_spectrum(subgrid)\n", - "\n", - "# plot radial power spectrum\n", - "plt.plot(k, S, '-o')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Optimise parameters\n", - "\n", - "The `optimise` routine determines the Curie parameters ($\\beta, z_t, \\Delta z, C$) by minimising the misfit between the analytic power spectum and the computed power spectrum. Optimisation is handles by the nonlinear least-squares algorithm implemented in `scipy.optimize.minimize`.\n", - "\n", - "```python\n", - "optimise(window, xc, yc, beta=3.0, zt=1.0, dz=10.0, C=5.0)\n", - "```\n", - "\n", - "These are sane defaults to initiate the optimisation, however, values close to the final solution will result in faster convergence and stability." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "beta = 0.00\n", - " zt = 1.31\n", - " dz = 107.74\n", - " C = 0.00\n", - "\n", - "Curie depth is 109.05 km\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "beta, zt, dz, C = grid.optimise(window_size, xpt, ypt)\n", - "print(\"beta = {:.2f}\\n zt = {:.2f}\\n dz = {:.2f}\\n C = {:.2f}\".format(beta,zt,dz,C))\n", - "\n", - "Sb = pycurious.bouligand2009(beta, zt, dz, k, C)\n", - "\n", - "# plot radial power spectrum - compare analytic against computed\n", - "plt.plot(k, S, '-o')\n", - "plt.plot(k, Sb, linewidth=2)\n", - "\n", - "print(\"\\nCurie depth is {:.2f} km\".format(zt + dz))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Varying window sizes\n", - "\n", - "Here, we observe the effect decreasing the window size has on the optimisation of Curie parameters. The number of points in the power spectrum decrease with smaller window sizes, particularly at low wavenumbers (long wavelengths). This significantly reduces the quality of Curie depth determinations for window sizes less than 200 km.\n", - "\n", - "As a rule of thumb, the window size should be > 4 times the maximum possible Curie depth that could be resolved from a study area." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "beta = 0.00\n", - " zt = 1.31\n", - " dz = 107.74\n", - " C = 0.00\n", - "\n", - "beta = 0.00\n", - " zt = 1.36\n", - " dz = 146.33\n", - " C = 0.00\n", - "\n", - "beta = 0.00\n", - " zt = 1.45\n", - " dz = 19.95\n", - " C = 0.00\n", - "\n", - "beta = 0.00\n", - " zt = 1.53\n", - " dz = 20.00\n", - " C = 0.00\n", - "\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "\n", - "# window size in kilometres\n", - "window_size_range = [304e3, 200e3, 100e3, 50e3]\n", - "\n", - "\n", - "fig = plt.figure()\n", - "ax1 = fig.add_subplot(111)\n", - "\n", - "for i, window_size in enumerate(window_size_range):\n", - " \n", - " # compute radial power spectrum\n", - " subgrid = grid.subgrid(xpt, ypt, window_size)\n", - " S, k, sigma2 = grid.radial_spectrum(subgrid)\n", - " ax1.plot(k, S, '-o', color='C{}'.format(i))\n", - " \n", - " # optimise Curie variables\n", - " beta, zt, dz, C = grid.optimise(window_size, xpt, ypt)\n", - " print(\"beta = {:.2f}\\n zt = {:.2f}\\n dz = {:.2f}\\n C = {:.2f}\\n\".format(beta,zt,dz,C))\n", - " \n", - " Sb = pycurious.bouligand2009(beta, zt, dz, k, C)\n", - " ax1.plot(k, Sb, color='C{}'.format(i), linewidth=2, label=\"window size = {}km\".format(window_size/1e3))\n", - "\n", - "ax1.legend()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Add prior constraints\n", - "\n", - "Spurious Curie depth values can often be obtained if windows of the magnetic anomaly do not contain long wavelengths. This often arises from selecting too small a small window size, but can also occur from uncorrected artefacts in the magnetic anomaly, or simply the absence of magnetic minerals close to the surface of the crust.\n", - "\n", - "Adding *a priori* information on $\\beta, z_t, \\Delta z, C$ can reduce the incidence of anomalous values. $\\beta$ and $C$ vary at long wavelengths, and $z_t + \\Delta z$ should be within the range of 10-40 km if we assume the Curie depth is equivalent to the 580$^\\circ$C isotherm. Adding prior information to any (or all) of these parameters penalises spurious values using a standard $\\ell_2$-norm misfit function.\n", - "\n", - "```python\n", - "from scipy import stats\n", - "\n", - "# define normal distributions\n", - "beta_p = stats.norm(3.0, 1.0)\n", - "zt_p = stats.norm(0.0, 1.0)\n", - "dz_p = stats.norm(10.0, 8.0)\n", - "C_p = stats.norm(10.0, 10.0)\n", - "\n", - "# add to grid object\n", - "grid.add_prior(beta=beta_p, zt=zt_p, dz=dz_p, C=C_p)\n", - "```\n", - "\n", - "A combination of priors can be added. `reset_priors()` removes all prior information." - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "beta = 3.01\n", - " zt = 0.50\n", - " dz = 0.65\n", - " C = 0.00\n", - "\n", - "beta = 2.99\n", - " zt = 0.76\n", - " dz = 0.54\n", - " C = 0.00\n", - "\n", - "beta = 3.00\n", - " zt = 0.62\n", - " dz = 0.34\n", - " C = 0.00\n", - "\n", - "beta = 3.00\n", - " zt = 0.86\n", - " dz = 20.00\n", - " C = 0.00\n", - "\n" - ] - }, - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 7, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "grid.reset_priors()\n", - "\n", - "from scipy import stats\n", - "beta_p = stats.norm(3.0, 0.01)\n", - "grid.add_prior(beta=beta_p)\n", - "\n", - "fig = plt.figure()\n", - "ax1 = fig.add_subplot(111, xlabel=\"wavenumber (rad/km)\", ylabel=\"radial power spectrum\")\n", - "\n", - "for i, window_size in enumerate(window_size_range):\n", - " \n", - " # compute radial power spectrum\n", - " subgrid = grid.subgrid(xpt, ypt, window_size)\n", - " S, k, sigma2 = grid.radial_spectrum(subgrid)\n", - " ax1.plot(k, S, '-o', color='C{}'.format(i), label='{} km window size'.format(window_size*1e-3))\n", - " \n", - " # optimise Curie variables\n", - " beta, zt, dz, C = grid.optimise(window_size, xpt, ypt)\n", - " print(\"beta = {:.2f}\\n zt = {:.2f}\\n dz = {:.2f}\\n C = {:.2f}\\n\".format(beta,zt,dz,C))\n", - " \n", - " Sb = pycurious.bouligand2009(beta, zt, dz, k, C)\n", - " ax1.plot(k, Sb, color='C{}'.format(i), linewidth=2)\n", - " \n", - "ax1.legend()" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 2", - "language": "python", - "name": "python2" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 2 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython2", - "version": "2.7.15rc1" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/Examples/Notebooks/Tanaka/Ex2-Compute-Curie-depth.ipynb b/Examples/Notebooks/Tanaka/Ex2-Compute-Curie-depth.ipynb new file mode 100644 index 0000000..0c2d823 --- /dev/null +++ b/Examples/Notebooks/Tanaka/Ex2-Compute-Curie-depth.ipynb @@ -0,0 +1,272 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Example 2a - Compute Curie depth (Tanaka approach)\n", + "Tanaka *et al.* (1999) based their method upon an expression for the radial power spectrum that assumes random magnetisation of the crust, and a radially averaged power spectra $\\Phi_{\\Delta T}(|k|)$:\n", + "\n", + "$$(1) \\Phi_{\\Delta T}(|k|)=Ae^{-2|k|Z_t}(1-e^{-|k|(Z_b-Z_t)})^2$$\n", + "\n", + "where:\n", + " - $k$ - spatial wavenumber ($k=2\\pi/\\lambda$, where $\\lambda$ is wavelength).\n", + " - $Z_t$ - top of assumed magnetic source.\n", + " - $Z_b$ - bottom of assumed magnetic source.\n", + " - ($Z_b-Z_t$ is hence the thickness of the magnetic source)\n", + "\n", + "For wavelengths less than twice the source thickness, this simplifies to:\n", + "\n", + "$$(2) \\ln [\\Phi_{\\Delta T}(|k|)^{1/2}] = \\ln B-|k|Z_t $$\n", + "\n", + "where $B$ is another constant. Conversely, (1) can be rewritten, with $Z_o$ as the centroid depth of the magnetic source:\n", + "\n", + "$$(3) \\Phi_{\\Delta T}(|k|)^{1/2} = Ce^{-|k|Z_o}(e^{-|k|(Z_t-Z_o)}-e^{-|k|(Z_b-Z_o)}) $$\n", + "\n", + "For long wavelengths, where $2d$ is the magnetic source thickness:\n", + "$$(4) \\Phi_{\\Delta T}(|k|)^{1/2} = Ce^{-|k|Z_o}(e^{-|k|(-d)}-e^{-|k|(-d)})\\approx Ce^{-|k|Z_o}2|k|d $$\n", + "\n", + "$$ \\ln \\{\\Phi_{\\Delta T}(|k|)^{1/2}/|k|\\}=\\ln D-|k|Z_o $$\n", + "\n", + "\n", + "Estimates of $Z_t$ and $Z_o$ can be estimated from Equations (2) and (5), and hence the base of the magnetic source (assumed to be at the Curie point depth):\n", + "\n", + "$$(6) Z_b=Z_o-(Z_t-Z_o) = 2Z_o-Z_t $$\n", + "\n", + "### Contents\n", + "\n", + "- [Plot radial power spectrum](#Plot-radial-power-spectrum)\n", + "- [Compute CPD Estimate](#Compute-cpd-estimate)" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "\n", + "import pycurious" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# load x,y,anomaly\n", + "mag_data = np.loadtxt(\"../data/test_mag_data.txt\")\n", + "\n", + "nx, ny = 305, 305\n", + "\n", + "x = mag_data[:,0]\n", + "y = mag_data[:,1]\n", + "d = mag_data[:,2].reshape(ny,nx)\n", + "\n", + "xmin, xmax = x.min(), x.max()\n", + "ymin, ymax = y.min(), y.max()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Plot radial power spectrum\n", + "The radial power spectrum is computed from a square window of the magnetic anomaly. Methods to select window sizes and compute the Fast Fourier Transform (FFT) belong to the `CurieGrid` object. We apply the default `np.hanning` taper to the power spectrum as in [Ex1-Plot-power-spectrum](#./Ex1-Plot-power-spectrum.ipynb)." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "# initialise CurieOptimise object\n", + "grid = pycurious.CurieOptimise(d, xmin, xmax, ymin, ymax)\n", + "#grid = pycurious.CurieGrid(d, xmin, xmax, ymin, ymax)\n", + "\n", + "# pick the centroid\n", + "xpt = 0.5*(xmin + xmax)\n", + "ypt = 0.5*(ymin + ymax)\n", + "\n", + "window_size = 200e3\n", + "subgrid = grid.subgrid(window_size, xpt, ypt)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "k, S, sigma2 = grid.radial_spectrum_log(subgrid, taper=None)\n", + "\n", + "# Plot of power spectrum, as function of spatial frequency\n", + "plt.plot(k/(2*np.pi), S/(2*np.pi), '-o')\n", + "plt.title('Power Spectrum')\n", + "plt.xlabel(r'$|k|/(2\\pi)$ [km$^{-1}$]')\n", + "plt.ylabel(r'$\\ln(\\Phi_{\\Delta T}(|k|)^{1/2})/(2\\pi)$')" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "Sn=np.log(np.exp(S)/k)\n", + "plt.plot(k/(2*np.pi), Sn/(2*np.pi), '-o')\n", + "plt.title('Power Spectrum, weighted by k')\n", + "plt.xlabel(r'$|k|/(2\\pi)$ [km$^{-1}$]')\n", + "plt.ylabel(r'$\\ln(\\Phi_{\\Delta T}(|k|)^{1/2}/|k|)/(2\\pi)$')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Compute CPD Estimate\n", + "As described above, once the power spectrum (and weighted spectrum) are computed, then the gradient of linear fits of certain wavenumber/spatial frequency windows can be taken as estimates of $Z_t$ and $Z_o$. The weighted linear fitting of the respective spectral window is implemented in the `CurieGrid` parent class as `tanaka1999`, and takes the spectrum, wave number, and spectrum error as inputs. The function also has functionality to pass specific spectral windows for each spectra, however, the default is to consider spatial frequencies of 0.05 - 0.2 (recalling that $k$, the wavenumber, is proportional to the spatial frequency $\\nu$ by $k=2\\pi\\nu$).\n", + "\n", + "\n", + "The function has two tuple returns: the gradient estimate, intercept and errors of $Z_t$ and $Z_o$. The gradient and errors can then be passed into the `CurieGrid.ComputeTanaka` method to obtain estimates of $Zb$ and $\\varepsilon Zb$." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Zb estimate: 6.64352756, +/- 2.42729754 km\n" + ] + } + ], + "source": [ + "(Ztr,btr,dZtr), (Zor, bor, dZor) = pycurious.tanaka1999(S, k, sigma2, (0,0.1), (0.2,0.3))\n", + "Zb, eZb = pycurious.ComputeTanaka(Ztr, dZtr, Zor, dZor)\n", + "print('Zb estimate: '+np.array2string(Zb)+', +/- '+np.array2string(eZb)+' km')" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# make two plots with Z-lines overlain.\n", + "# Plot of power spectrum, as function of spatial frequency\n", + "fig, (ax1, ax2) = plt.subplots(1,2, figsize=(16,6),)\n", + "\n", + "ax1.plot(k/(2*np.pi), S/(2*np.pi), '-bo',k/(2*np.pi),(Ztr*k/(2*np.pi)+btr)/(2*np.pi),'r-')\n", + "#ax1.title('Power Spectrum')\n", + "ax1.set_xlabel(r'$|k|/(2\\pi)$ [km$^{-1}$]')\n", + "ax1.set_ylabel(r'$\\ln(\\Phi_{\\Delta T}(|k|)^{1/2})/(2\\pi)$')\n", + "\n", + "ax2.plot(k/(2*np.pi), Sn/(2*np.pi), '-o',k/(2*np.pi),(Zor*k/(2*np.pi)+bor)/(2*np.pi),'r-')\n", + "ax2.set_xlabel(r'$|k|/(2\\pi)$ [km$^{-1}$]')\n", + "ax2.set_ylabel(r'$\\ln(\\Phi_{\\Delta T}(|k|)^{1/2}/|k|)/(2\\pi)$')\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.15" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From d8c2a2b5453ca13b8bde8067c0f895fe110bffb9 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Sun, 26 Aug 2018 23:57:06 +0100 Subject: [PATCH 024/170] More moving... --- .gitignore | 1 + .../Ex1-Plot-power-spectrum.ipynb | 0 .../Ex3-Optimisation-routine.ipynb | 0 .../Ex4-Mapping-Curie-depth-EMAG2.ipynb | 0 .../Notebooks/Ex5-parallel-processing.ipynb | 49 ------------------- 5 files changed, 1 insertion(+), 49 deletions(-) create mode 100644 .gitignore rename Examples/Notebooks/{ => Bouligand}/Ex1-Plot-power-spectrum.ipynb (100%) rename Examples/Notebooks/{ => Bouligand}/Ex3-Optimisation-routine.ipynb (100%) rename Examples/Notebooks/{ => Bouligand}/Ex4-Mapping-Curie-depth-EMAG2.ipynb (100%) delete mode 100644 Examples/Notebooks/Ex5-parallel-processing.ipynb diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..483e19a --- /dev/null +++ b/.gitignore @@ -0,0 +1 @@ +Examples/Notebooks/.ipynb_checkpoints/* diff --git a/Examples/Notebooks/Ex1-Plot-power-spectrum.ipynb b/Examples/Notebooks/Bouligand/Ex1-Plot-power-spectrum.ipynb similarity index 100% rename from Examples/Notebooks/Ex1-Plot-power-spectrum.ipynb rename to Examples/Notebooks/Bouligand/Ex1-Plot-power-spectrum.ipynb diff --git a/Examples/Notebooks/Ex3-Optimisation-routine.ipynb b/Examples/Notebooks/Bouligand/Ex3-Optimisation-routine.ipynb similarity index 100% rename from Examples/Notebooks/Ex3-Optimisation-routine.ipynb rename to Examples/Notebooks/Bouligand/Ex3-Optimisation-routine.ipynb diff --git a/Examples/Notebooks/Ex4-Mapping-Curie-depth-EMAG2.ipynb b/Examples/Notebooks/Bouligand/Ex4-Mapping-Curie-depth-EMAG2.ipynb similarity index 100% rename from Examples/Notebooks/Ex4-Mapping-Curie-depth-EMAG2.ipynb rename to Examples/Notebooks/Bouligand/Ex4-Mapping-Curie-depth-EMAG2.ipynb diff --git a/Examples/Notebooks/Ex5-parallel-processing.ipynb b/Examples/Notebooks/Ex5-parallel-processing.ipynb deleted file mode 100644 index ff77b96..0000000 --- a/Examples/Notebooks/Ex5-parallel-processing.ipynb +++ /dev/null @@ -1,49 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Example 5 - Parallel processing\n", - "\n", - "`CurieParallel` inherits from `CurieOptimise`, which, in turn, inherits from `CurieGrid`. Parallelism is handled by MPI via the Python interface, `mpi4py`.\n", - "\n", - "```bash\n", - "pip install [--user] mpi4py\n", - "```\n", - "\n", - "This requires an MPI implementation, such as [OpenMPI](https://www.open-mpi.org) or [MPICH](http://www.mpich.org/downloads), to be installed on the system.\n", - "\n", - "The parallel scheme operates by dividing a grid equally among processors with a shadow region equal to the maximum window size. This ensures that windows are not clipped close to the boundaries of the domain on any given processor." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 2", - "language": "python", - "name": "python2" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 2 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython2", - "version": "2.7.15" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} From a1b0449bd53332334809df6b516993063f9e0a89 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Tue, 28 Aug 2018 14:31:47 +0100 Subject: [PATCH 025/170] Notebooks complete! Now to merge with master branch --- .../Bouligand/Ex1-Plot-power-spectrum.ipynb | 53 +- .../Bouligand/Ex2-Compute-Curie-depth.ipynb | 15 +- .../Bouligand/Ex3-Optimisation-routine.ipynb | 468 - .../Ex3-Posing-the-inverse-problem.ipynb | 350 + ...Ex4-Spatial-variation-of-Curie-depth.ipynb | 306 + ...nb => Ex5-Mapping-Curie-depth-EMAG2.ipynb} | 34 +- .../Tanaka/Ex2-Compute-Curie-depth.ipynb | 121 +- .../Tanaka/Ex3-Parameter-exploration.ipynb | 264 + Examples/british_isles.py | 215 - Examples/british_isles_parallel.py | 171 - .../british_isles_parallel_sensitivity.py | 209 - Examples/british_isles_parallel_windows.py | 169 - Examples/data/test_mag_data.txt | 186050 +++++++-------- pycurious/curie.py | 6 +- pycurious/optimise.py | 187 +- 15 files changed, 94082 insertions(+), 94536 deletions(-) delete mode 100644 Examples/Notebooks/Bouligand/Ex3-Optimisation-routine.ipynb create mode 100644 Examples/Notebooks/Bouligand/Ex3-Posing-the-inverse-problem.ipynb create mode 100644 Examples/Notebooks/Bouligand/Ex4-Spatial-variation-of-Curie-depth.ipynb rename Examples/Notebooks/Bouligand/{Ex4-Mapping-Curie-depth-EMAG2.ipynb => Ex5-Mapping-Curie-depth-EMAG2.ipynb} (89%) create mode 100644 Examples/Notebooks/Tanaka/Ex3-Parameter-exploration.ipynb delete mode 100644 Examples/british_isles.py delete mode 100644 Examples/british_isles_parallel.py delete mode 100644 Examples/british_isles_parallel_sensitivity.py delete mode 100644 Examples/british_isles_parallel_windows.py diff --git a/Examples/Notebooks/Bouligand/Ex1-Plot-power-spectrum.ipynb b/Examples/Notebooks/Bouligand/Ex1-Plot-power-spectrum.ipynb index 1209b42..6647233 100644 --- a/Examples/Notebooks/Bouligand/Ex1-Plot-power-spectrum.ipynb +++ b/Examples/Notebooks/Bouligand/Ex1-Plot-power-spectrum.ipynb @@ -65,7 +65,8 @@ "# Bouligand 2009 test parameters\n", "beta = 3.0\n", "zt = 1.0\n", - "dz = 20.0" + "dz = 20.0\n", + "C = 0.0" ] }, { @@ -80,21 +81,21 @@ "\n", "# vary zt\n", "for zti in np.arange(0.0, 2.5, 0.5):\n", - " S = pycurious.bouligand2009(beta, zti, dz, k)\n", - " S -= S.max()\n", - " ax1.semilogx(k, S, label=r'$z_t$ = {} km'.format(zti))\n", + " Phi = pycurious.bouligand2009(k, beta, zti, dz, C)\n", + " Phi -= Phi.max()\n", + " ax1.semilogx(k, Phi, label=r'$z_t$ = {} km'.format(zti))\n", "\n", "# vary dz\n", "for dzi in [10., 20., 50., 100., 200.]:\n", - " S = pycurious.bouligand2009(beta, zt, dzi, k)\n", - " S -= S.min()\n", - " ax2.semilogx(k, S, label=r'$\\Delta z$ = {} km'.format(dzi))\n", + " Phi = pycurious.bouligand2009(k, beta, zt, dzi, C)\n", + " Phi -= Phi.min()\n", + " ax2.semilogx(k, Phi, label=r'$\\Delta z$ = {} km'.format(dzi))\n", "\n", "# vary beta\n", "for betai in np.arange(0, 5, 1):\n", - " S = pycurious.bouligand2009(betai, zt, dz, k)\n", - " S -= S[-1]\n", - " ax3.semilogx(k, S, label=r'$\\beta$ = {}'.format(betai))\n", + " Phi = pycurious.bouligand2009(k, betai, zt, dz, C)\n", + " Phi -= Phi[-1]\n", + " ax3.semilogx(k, Phi, label=r'$\\beta$ = {}'.format(betai))\n", "\n", "ax1.set_ylim(-20, 0)\n", "ax2.set_ylim(0, 20)\n", @@ -136,7 +137,7 @@ "outputs": [], "source": [ "# load magnetic anomaly - i.e. random fractal noise\n", - "mag_data = np.loadtxt(\"../data/test_mag_data.txt\")\n", + "mag_data = np.loadtxt(\"../../data/test_mag_data.txt\")\n", "\n", "nx, ny = 305, 305\n", "\n", @@ -176,7 +177,7 @@ "ypt = 0.5*(ymin + ymax)\n", "\n", "window_size = 304e3\n", - "subgrid = grid.subgrid(xpt, ypt, window_size)" + "subgrid = grid.subgrid(window_size, xpt, ypt)" ] }, { @@ -186,17 +187,17 @@ "outputs": [], "source": [ "# compute radial power spectrum\n", - "S, k, sigma2 = grid.radial_spectrum(subgrid)\n", + "k, Phi, sigma_Phi = grid.radial_spectrum(subgrid)\n", "\n", "# analytic formulation\n", - "Sb = pycurious.bouligand2009(3.0, 0.305, 10.0, k, -18)\n", + "Phi2 = pycurious.bouligand2009(k, 3.0, 0.305, 10.0, -18)\n", "\n", "\n", "# plot radial power spectrum\n", "fig = plt.figure()\n", "ax1 = fig.add_subplot(111, xlabel=\"wavenumber (rad/km)\", ylabel=\"radial power spectrum\")\n", - "ax1.plot(k, S, '-o')\n", - "ax1.plot(k, Sb)\n", + "ax1.plot(k, Phi, '-o')\n", + "ax1.plot(k, Phi2)\n", "plt.show()" ] }, @@ -216,16 +217,16 @@ "outputs": [], "source": [ "\n", - "S1, k1, sigma2 = grid.radial_spectrum(subgrid, taper=None)\n", - "S2, k2, sigma2 = grid.radial_spectrum(subgrid, taper=np.hanning)\n", - "S3, k3, sigma2 = grid.radial_spectrum(subgrid, taper=np.hamming)\n", + "k1, Phi1, sigma_Phi2 = grid.radial_spectrum(subgrid, taper=None)\n", + "k2, Phi2, sigma_Phi2 = grid.radial_spectrum(subgrid, taper=np.hanning)\n", + "k3, Phi3, sigma_Phi2 = grid.radial_spectrum(subgrid, taper=np.hamming)\n", "\n", "\n", "fig = plt.figure()\n", "ax1 = fig.add_subplot(111, xlabel=\"wavenumber (rad/km)\", ylabel=\"radial power spectrum\")\n", - "ax1.plot(k1, S1, '-o', label='none')\n", - "ax1.plot(k2, S2, '-o', label='hanning')\n", - "ax1.plot(k3, S3, '-o', label='hamming')\n", + "ax1.plot(k1, Phi1, '-o', label='none')\n", + "ax1.plot(k2, Phi2, '-o', label='hanning')\n", + "ax1.plot(k3, Phi3, '-o', label='hamming')\n", "ax1.legend()\n", "plt.show()" ] @@ -251,11 +252,11 @@ "metadata": {}, "outputs": [], "source": [ - "S, k, theta = grid.azimuthal_spectrum(subgrid, theta=20.0)\n", + "k, Phi, theta = grid.azimuthal_spectrum(subgrid, theta=20.0)\n", "\n", "fig = plt.figure()\n", "ax1 = fig.add_subplot(111, ylabel=r'azimuth $\\theta$', xlabel='wavenumber (rad/km)')\n", - "im1 = ax1.pcolor(k, theta, S)\n", + "im1 = ax1.pcolor(k, theta, Phi)\n", "fig.colorbar(im1, label='radial power spectrum')" ] }, @@ -276,7 +277,7 @@ "ax1 = fig.add_subplot(111, xlabel=\"wavenumber (rad/km)\", ylabel=\"radial power spectrum\")\n", "\n", "for i, angle in enumerate(theta):\n", - " ax1.plot(k, S[i], label=r'$\\theta = {}^\\circ$'.format(angle))\n", + " ax1.plot(k, Phi[i], label=r'$\\theta = {}^\\circ$'.format(angle))\n", "\n", "ax1.legend(bbox_to_anchor=(1,1))\n", "plt.show()" @@ -299,7 +300,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", - "version": "2.7.15rc1" + "version": "2.7.15" } }, "nbformat": 4, diff --git a/Examples/Notebooks/Bouligand/Ex2-Compute-Curie-depth.ipynb b/Examples/Notebooks/Bouligand/Ex2-Compute-Curie-depth.ipynb index 14290ae..416be32 100644 --- a/Examples/Notebooks/Bouligand/Ex2-Compute-Curie-depth.ipynb +++ b/Examples/Notebooks/Bouligand/Ex2-Compute-Curie-depth.ipynb @@ -4,7 +4,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Example 2b - Compute Curie depth (Bouligand approach)\n", + "# Example 2 - Compute Curie depth\n", "\n", "Bouligand *et al.* (2009) formulated an expression for the radial power assuming a fractal model for crustal magnetisation (see [Ex1-Plot-power-spectra](./Ex1-Plot-power-spectrum.ipynb) for analytic solution), which depends on 4 parameters:\n", "\n", @@ -43,7 +43,7 @@ "outputs": [], "source": [ "# load x,y,anomaly\n", - "mag_data = np.loadtxt(\"../data/test_mag_data.txt\")\n", + "mag_data = np.loadtxt(\"../../data/test_mag_data.txt\")\n", "\n", "nx, ny = 305, 305\n", "\n", @@ -173,9 +173,9 @@ "source": [ "## Add prior constraints\n", "\n", - "Spurious Curie depth values can often be obtained if windows of the magnetic anomaly do not contain long wavelengths. This often arises from selecting too small a small window size, but can also occur from uncorrected artefacts in the magnetic anomaly, or simply the absence of magnetic minerals close to the surface of the crust.\n", + "Spurious Curie depth values can often be obtained if windows of the magnetic anomaly do not contain long wavelengths. This often arises from selecting too small a small window size, but can also occur from uncorrected artefacts in the magnetic anomaly, or simply the absence of magnetic minerals close to the surface of the crust. Adding *a priori* information on $\\beta, z_t, \\Delta z, C$ can reduce the incidence of anomalous values if there is reasonable grounds to do so.\n", "\n", - "Adding *a priori* information on $\\beta, z_t, \\Delta z, C$ can reduce the incidence of anomalous values. $\\beta$ and $C$ vary at long wavelengths, and $z_t + \\Delta z$ should be within the range of 10-40 km if we assume the Curie depth is equivalent to the 580$^\\circ$C isotherm. Adding prior information to any (or all) of these parameters penalises spurious values using a standard $\\ell_2$-norm misfit function.\n", + "> **IMPORTANT:** strict priors can unfairly bias the results - *only* add priors if you have good reason to do so. (This is **not recommended** for most use cases.)\n", "\n", "```python\n", "from scipy import stats\n", @@ -190,6 +190,13 @@ "grid.add_prior(beta=beta_p, zt=zt_p, dz=dz_p, C=C_p)\n", "```\n", "\n", + "Priors can be accessed from a dictionary:\n", + "\n", + "```python\n", + "prior = grid.prior_pdf['beta'] # stats.norm object\n", + "prior = grid.prior['beta'] # stats.norm object arguments (3.0, 1.0)\n", + "```\n", + "\n", "A combination of priors can be added. `reset_priors()` removes all prior information." ] }, diff --git a/Examples/Notebooks/Bouligand/Ex3-Optimisation-routine.ipynb b/Examples/Notebooks/Bouligand/Ex3-Optimisation-routine.ipynb deleted file mode 100644 index 45c4e2d..0000000 --- a/Examples/Notebooks/Bouligand/Ex3-Optimisation-routine.ipynb +++ /dev/null @@ -1,468 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Example 3 - Optimisation routine\n", - "\n", - "In Examples 2a and 2b we computed the Curie depth for a single point using a fixed window. Here, we use `CurieOptimise` object to compute the Curie depth over an entire magnetic anomaly.\n", - "\n", - "`CurieOptimise` inherits all methods from `CurieGrid` in addition to:\n", - "\n", - "- iteratively evaluate the Curie depth across the magnetic anomaly\n", - "- add priors to limit spurious Curie depth determinations\n", - "- optimise Curie depth parameters using constraints from an objective function\n", - "\n", - "### Contents\n", - "\n", - "- [The inverse problem](#The-inverse-problem)\n", - "- [Sensitivity analysis](#Sensitivity analysis)\n", - "- [Compare Bouligand to Tanaka](#Compare-Bouligand-to-Tanaka)" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "%matplotlib inline\n", - "\n", - "import pycurious" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "# load x,y,anomaly\n", - "mag_data = np.loadtxt(\"../data/test_mag_data.txt\")\n", - "\n", - "nx, ny = 305, 305\n", - "\n", - "x = mag_data[:,0]\n", - "y = mag_data[:,1]\n", - "d = mag_data[:,2].reshape(ny,nx)\n", - "\n", - "xmin, xmax = x.min(), x.max()\n", - "ymin, ymax = y.min(), y.max()\n", - "\n", - "# initialise CurieOptimise object\n", - "grid = pycurious.CurieOptimise(d, xmin, xmax, ymin, ymax)" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "# get centroids\n", - "\n", - "window_size = 200e3\n", - "xc_list, yc_list = grid.create_centroid_list(window_size, spacingX=10e3, spacingY=10e3)\n", - "\n", - "print(\"number of centroids = {}\".format(len(xc_list)))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## The inverse problem\n", - "\n", - "It is notoriously difficult to estimate uncertainties from Curie depth determinations. Intuitively, the fewer points in the power spectrum should result in higher uncertainty, but it is difficult to quantify these uncertainties in practise. For [Bouligand *et al.*, 2009](http://doi.wiley.com/10.1029/2009JB006494) it is difficult to determine the values of $\\beta$ and $\\Delta z$ since both control the slope of the power spectrum at low wavenumbers. Similarly, for [Tanaka *et al.*, 1999](http://linkinghub.elsevier.com/retrieve/pii/S0040195199000724) the lower and upper ranges of the power spectrum used to compute $z_b$ and $z_t$ is highly subjective and can result in significantly different Curie depths.\n", - "\n", - "Here, we aim to assess the uncertainty of Curie depth determinations using a sensitivity analysis. The approach we outline here is not necessarily the most statistically robust methodology, but it is intended as a practical means to compute Curie depth whilst considering its uncertainty.\n", - "\n", - "First we find the best model with no priors to evaluate the heterogeneity in the signal we extract from the magnetic anomaly. We use the commonly used $\\ell_2$-norm objective function to calculate misfit. The objective function can be accessed (and modified) under `grid.objective_function`" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "# no priors\n", - "grid.reset_priors()\n", - "\n", - "beta, zt, dz, C = grid.optimise_routine(window_size, xc_list, yc_list)\n", - "\n", - "# plot results\n", - "fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2, 2, sharex=True, sharey=True, figsize=(10,10))\n", - "\n", - "sc1 = ax1.scatter(xc_list, yc_list, c=beta)\n", - "sc2 = ax2.scatter(xc_list, yc_list, c=zt)\n", - "sc3 = ax3.scatter(xc_list, yc_list, c=dz)\n", - "sc4 = ax4.scatter(xc_list, yc_list, c=C)\n", - "\n", - "fig.colorbar(sc1, ax=ax1, label=r\"$\\beta$\")\n", - "fig.colorbar(sc2, ax=ax2, label=r\"$z_t$\")\n", - "fig.colorbar(sc3, ax=ax3, label=r\"$\\Delta z$\")\n", - "fig.colorbar(sc4, ax=ax4, label=r\"$C$\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Sensitivity analysis\n", - "\n", - "The sensitivity analysis requires defining a prior distribution to sample from. The default is a Gaussian normal distribution,\n", - "\n", - "$$\n", - "P(\\mathbf{m}) = \\frac{1}{\\sqrt{2\\pi} \\sigma_p} \\exp \\left( \\frac{-\\mathbf{m}^2}{2 \\sigma_p^2} \\right)\n", - "$$\n", - "\n", - "but other distributions can be defined from the `scipy.stats` module. We repeat the inversion multiple times, sampling different values from $P(\\mathbf{m})$ to evaluate the uncertainty in each variable. Note: $\\mathbf{m}$ is the variables $\\beta, z_t, \\Delta z, C$ for the Bouligand approach or $z_t, z_b $ for the Tanaka approach.\n", - "\n", - "Prior distributions are added by\n", - "\n", - "```python\n", - "from scipy import stats\n", - "beta_p = stats.norm(3.0, 1.0)\n", - "grid.add_prior(beta=beta_p)\n", - "```\n", - "\n", - "and can be accessed from a dictionary:\n", - "\n", - "```python\n", - "prior = grid.prior_pdf['beta'] # stats.norm object\n", - "prior = grid.prior['beta'] # stats.norm object arguments (3.0, 1.0)\n", - "```" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "from scipy import stats\n", - "\n", - "beta_p = stats.norm(3.0, 1.0)\n", - "zt_p = stats.norm(0.0, 1.0)\n", - "dz_p = stats.norm(12.0, 8.0)\n", - "C_p = stats.norm(-17.0, 5.0)\n", - "\n", - "grid.add_prior(beta=beta_p, zt=zt_p, dz=dz_p, C=C_p)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "# number of simulations to run for each centroid\n", - "nsim = 10\n", - "\n", - "beta, zt, dz, C = grid.sensitivity_routine(nsim, window_size, xc_list, yc_list)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "fig = plt.figure(figsize=(16,4))\n", - "\n", - "\n", - "for i, (label, var) in enumerate([('beta', beta), ('zt', zt), ('dz', dz), ('C', C)]):\n", - " \n", - " # prior distribution\n", - " prior = grid.prior_pdf[label]\n", - " p, sigma_p = prior.mean(), prior.std()\n", - " \n", - " # posterior distribution\n", - " P, sigma_P = var[:,0].mean(), var[:,1].mean()\n", - " post = stats.norm(P, sigma_P)\n", - " \n", - " x_samples = np.linspace(p-2*sigma_p, p+2*sigma_p, 100)\n", - " \n", - " # plot pdf\n", - " ax = fig.add_subplot(1,4,i+1, xlabel=label)\n", - " ax.plot(x_samples, prior.pdf(x_samples), label=\"prior\")\n", - " ax.plot(x_samples, post.pdf(x_samples), label=\"posterior\")\n", - " ax.legend()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The precision of the values are properly resolved " - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Parameter Exploration of Spectral Analysis method (Tanaka)\n", - "\n", - "Due to the deterministic approach that [Tanaka *et al.*, 1999](http://linkinghub.elsevier.com/retrieve/pii/S0040195199000724) uses for estimating $Z_b$, the uncertainties returned by `CurieGrid.tanaka1999` are the simple results of error propagation from the initial spectra uncertainties. It should also be noted that the spectra uncertainties represent the variance within the sampled sector of the 2D FFT, and may comprise both noise and anisotropic signal.\n", - "\n", - "We present here several tests of the `CurieGrid.tanaka1999` function in order to explore how the input parameters affect the resulting Curie point depth estimates. In particular, we consider the following:\n", - "1. Effect of where in $k$-space is specific window used, separately for both the power and $k$-weighted power spectra (i.e., which $k$ do we consider?).\n", - "2. Effect of $k$-space window size (i.e., how much of the $k$-domain do we consider?). It is important to note that increasing the $k$-bandwidth also stabilises the estimation by increasing the statistics of the spectrum portion.\n", - "3. Effect of magnetic data window size (i.e., domain of magnetic data before computing FFT).\n" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [], - "source": [ - "#Default set up\n", - "grid = pycurious.CurieOptimise(d, xmin, xmax, ymin, ymax)\n", - "xpt = xmin + (xmax-xmin)/2\n", - "ypt = ymin + (ymax-ymin)/2" - ] - }, - { - "cell_type": "code", - "execution_count": 69, - "metadata": {}, - "outputs": [], - "source": [ - "# 1) Where in k-space do we locate window?\n", - "ws=304e3\n", - "subgrid = grid.subgrid(xpt, ypt, ws)\n", - "S, k, sigma2 = grid.radial_spectrum_log(subgrid, taper=None)\n", - "# Number of bins to divide k-range into\n", - "nb=10\n", - "hmap=np.zeros((nb*nb,3))\n", - "# k-range divided between 0 (i.e., DC), and 0.3 (i.e., spatial wavelengths of ~20 km)\n", - "kmin_range = np.linspace(0., 0.3, nb)\n", - "kmax_range = kmin_range + (0.3/nb)\n", - "\n", - "for j in range(0,nb,1):\n", - " for l in range(0,nb,1):\n", - " kmin0 = kmin_range[j]\n", - " kmin1 = kmax_range[j]\n", - " kmax0 = kmin_range[l]\n", - " kmax1 = kmax_range[l]\n", - " [(Ztr,btr,dZtr), (Zor, bor, dZor)]=pycurious.tanaka1999(S, k, sigma2, (kmin0, kmin1), (kmax0, kmax1))\n", - " [Zb,eZb]=pycurious.ComputeTanaka(Ztr, dZtr, Zor, dZor)\n", - " hmap[j*nb+l,0]=(kmin0+kmin1)/2\n", - " hmap[j*nb+l,1]=(kmax0+kmax1)/2\n", - " hmap[j*nb+l,2]=Zb" - ] - }, - { - "cell_type": "code", - "execution_count": 70, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Text(0.5,1,u'Heatmap of CPD')" - ] - }, - "execution_count": 70, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig2 = plt.figure(figsize=(16,16))\n", - "ax2 = fig2.add_subplot(111, xlabel=r'$\\nu$ window of $\\Phi/|k|$ (km$^{-1}$) (for Zo)', ylabel=r'$\\nu$ window of $\\Phi$ (for Zt)')\n", - "# SCATTER PLOT\n", - "im2 = ax2.scatter(hmap[:,1],hmap[:,0],2000,np.clip(hmap[:,2],10,20),marker='s')\n", - "fig2.colorbar(im2, label='CPD (km)')\n", - "plt.title('Heatmap of CPD')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Results of this test suggest that the precise $k$ location of $Z_t$ is significantly less influential than the $k$ location of $Z_o$. Furthermore, for this test case with a known $Z_b$ of 16 km, a spatial frequency $\\nu$ window of $0.125-0.2$ (i.e., $k\\in\\{0.8-1.25\\}$ gives estimates consistent with the true $Z_b$. For simplicity, based upon this test we see minimal reason to not use the same $\\nu/k$ window for each spectrum." - ] - }, - { - "cell_type": "code", - "execution_count": 101, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Text(0,0.5,u'CPD depth (km)')" - ] - }, - "execution_count": 101, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# 2) How big a bandwidth in k-space do we want?\n", - "#ws=304e3\n", - "#subgrid = grid.subgrid(xpt, ypt, ws)\n", - "S, k, sigma2 = grid.radial_spectrum_log(subgrid, taper=None)\n", - "\n", - "# We are testing this by taking one central spatial frequency (k=1), and estimating Zb with increasing k-bandwidths.\n", - "# Recall k=2*pi*nu\n", - "nu=1/(2*np.pi)\n", - "\n", - "nbins=30\n", - "output=np.zeros((nbins,3))\n", - "nr = np.linspace(0., 0.3, nbins+1)\n", - "output[:,0]=nr[1:]\n", - "\n", - "for j in range(0,nbins,1):\n", - " \n", - " kmin=nu-output[j,0]/2\n", - " kmax=nu+output[j,0]/2\n", - " \n", - " [(Ztr,btr,dZtr), (Zor, bor, dZor)]=pycurious.tanaka1999(S, k, sigma2, (kmin, kmax), (kmin, kmax))\n", - " [Zb,eZb]=pycurious.ComputeTanaka(Ztr, dZtr, Zor, dZor)\n", - " output[j,1]=Zb\n", - " output[j,2]=eZb\n", - " \n", - "fig2 = plt.figure(figsize=(8,8))\n", - "ax2=plt.errorbar(output[:,0],output[:,1],yerr=output[:,2])\n", - "plt.gca().invert_yaxis()\n", - "plt.xlabel('$\\\\nu$-bandwidth')\n", - "plt.ylabel('CPD depth (km)')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The CPD estimates resulting from this test become consistent for $\\nu$-bandwidths greater than approximately 0.1. Statistics improve with larger bandwidths, however, it is worth remaining aware of the typically non-linear trend of the spectrum, as it may not be appropriate for a linear fit over a large domain of $\\nu$." - ] - }, - { - "cell_type": "code", - "execution_count": 134, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Text(0,0.5,u'CPD misfit (km)')" - ] - }, - "execution_count": 134, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# 3) How large a window width of magnetic data is required?\n", - "grid = pycurious.CurieOptimise(d, xmin, xmax, ymin, ymax)\n", - "xpt = xmin + (xmax-xmin)/2\n", - "ypt = ymin + (ymax-ymin)/2\n", - "\n", - "nwin=50\n", - "baseW=10000\n", - "inc=2500\n", - "\n", - "output=np.zeros((nwin,3))\n", - "\n", - "# Define 'ws' as variable window size index\n", - "for i in range(0,nwin,1):\n", - " ws=baseW+i*inc\n", - " subgrid = grid.subgrid(xpt, ypt, ws)\n", - " S, k, sigma2 = grid.radial_spectrum_log(subgrid, taper=None)\n", - " [(Ztr,btr,dZtr), (Zor, bor, dZor)]=pycurious.tanaka1999(S, k, sigma2, (0.11, 0.21), (0.11, 0.21))\n", - " [Zb,eZb]=pycurious.ComputeTanaka(Ztr, dZtr, Zor, dZor)\n", - " output[i,0]=ws\n", - " output[i,1]=Zb\n", - " output[i,2]=eZb\n", - " #print('Zb estimate for '+str(ws)+' m: '+np.array2string(Zb)+', +/- '+np.array2string(eZb)+' km')\n", - "\n", - "fig, (ax1, ax2) = plt.subplots(1,2, figsize=(16,6),)\n", - "ax1.plot(output[:,0],output[:,1])\n", - "ax1.set_ylim(0,30)\n", - "ax1.invert_yaxis()\n", - "ax1.set_xlabel('Data window size (m)')\n", - "ax1.set_ylabel('CPD estimate (km)')\n", - "\n", - "ax2.plot(output[:,0],output[:,2])\n", - "ax2.set_xlabel('Data window size (m)')\n", - "ax2.set_ylabel('CPD misfit (km)')\n", - "#plt.gca().invert_yaxis()\n", - "#plt.xlabel('Data window size (km)')\n", - "#plt.ylabel('CPD depth (km)')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The results of this test highlight that there is a significant amount of variability in the CPD estimates at all window sizes, inferring that where possible, a range of window sizes should be tested for any data set. However, the righthand plot of propagated error in the CPD estimates clarifies that estimates from larger windows are more robust. In particular, with the prior knowledge that the CPD of the test data is 16 km, window sizes of greater than 80 km show a reduced improvement in statistics. " - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 2", - "language": "python", - "name": "python2" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 2 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython2", - "version": "2.7.15rc1" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/Examples/Notebooks/Bouligand/Ex3-Posing-the-inverse-problem.ipynb b/Examples/Notebooks/Bouligand/Ex3-Posing-the-inverse-problem.ipynb new file mode 100644 index 0000000..1aa42f2 --- /dev/null +++ b/Examples/Notebooks/Bouligand/Ex3-Posing-the-inverse-problem.ipynb @@ -0,0 +1,350 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Example 3 - Posing the Inverse Problem\n", + "\n", + "It is notoriously difficult to estimate uncertainties from Curie depth determinations. Intuitively, the fewer points in the power spectrum should result in higher uncertainty, but it is difficult to quantify these uncertainties in practise. For [Bouligand *et al.*, 2009](http://doi.wiley.com/10.1029/2009JB006494) it is difficult to determine the values of $\\beta$ and $\\Delta z$ since both control the slope of the power spectrum at low wavenumbers. Similarly, for [Tanaka *et al.*, 1999](http://linkinghub.elsevier.com/retrieve/pii/S0040195199000724) the lower and upper ranges of the power spectrum used to compute $z_b$ and $z_t$ is highly subjective and can result in significantly different Curie depths.\n", + "\n", + "Here, we pose the problem of finding the Curie depth from the radial power spectrum within a Bayesian framework. Thus, we can effectively estimate the uncertainty of our Curie depth estimates.\n", + "\n", + "### Contents\n", + "\n", + "- [Bayesian inverse framework](#Bayesian-inverse-framework)\n", + "- [Metropolis-Hastings algorithm](#Metropolis-Hastings-algorithm)\n", + "- [Appraising the ensemble](#Appraising-the-ensemble)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy import stats\n", + "%matplotlib inline\n", + "\n", + "import pycurious" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# load x,y,anomaly\n", + "mag_data = np.loadtxt(\"../../data/test_mag_data.txt\")\n", + "\n", + "nx, ny = 305, 305\n", + "\n", + "x = mag_data[:,0]\n", + "y = mag_data[:,1]\n", + "d = mag_data[:,2].reshape(ny,nx)\n", + "\n", + "xmin, xmax = x.min(), x.max()\n", + "ymin, ymax = y.min(), y.max()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "grid = pycurious.CurieOptimise(d, xmin, xmax, ymin, ymax)\n", + "\n", + "# pick the centroid\n", + "xpt = 0.5*(xmin + xmax)\n", + "ypt = 0.5*(ymin + ymax)\n", + "\n", + "window_size = 200e3\n", + "subgrid = grid.subgrid(window_size, xpt, ypt)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Bayesian inverse framwork\n", + "\n", + "Geophysical inversion often casts problems in a Bayesian framework, where information on input parameters are represented in probabilistic terms. The solution is given by _a posteriori_ probability, $P(\\mathbf{m}|\\mathbf{d})$, which is proportional to the product of the likelihood function $P(\\mathbf{d}|\\mathbf{m})$ and the _a priori_ probability $P(\\mathbf{m})$,\n", + "\n", + "$$\n", + "P(\\mathbf{m}|\\mathbf{d}) \\propto P(\\mathbf{d}|\\mathbf{m}) \\cdot P(\\mathbf{m})\n", + "$$\n", + "\n", + "The likelihood function is the probability of reproducing the data $\\mathbf{d}$ given a particular model $\\mathbf{m}$, and the _a priori_ model is what we know about the model before assimilating the data. The posterior probability can be evaluated through an objective function, $S(\\mathbf{m})$, which jointly compares the misfit between data and prior information, $\\mathbf{m}_p$,\n", + "\n", + "$$\n", + "P(\\mathbf{m}|\\mathbf{d}) = A \\, \\exp (-S(\\mathbf{m}))\n", + "$$\n", + "\n", + "where $A$ is a constant. We seek the maximum _a posteriori_ (MAP) estimate, which may be obtained by minimising the $\\ell_p$-norm objective function if data and prior information are both uncorrelated,\n", + "\n", + "$$\n", + "S(\\mathbf{m}) = \\frac{1}{s} \\sum_{i} \\frac{\\vert g^i(\\mathbf{m}) - d^i \\vert^s}{(\\sigma^i_d)^s} + \\frac{1}{r} \\sum_{j} \\frac{\\vert \\mathrm{m}^j - \\mathrm{m}^j_p \\vert^r}{(\\sigma^j_p)^r}\n", + "$$\n", + "\n", + "where $\\mathbf{g}(\\mathbf{m})$ is the forward operator that forms an explicit link with the data. In our case $\\mathbf{g}(\\mathbf{m}) = \\Phi$ and the objective function quantifies how well the analytic expression for the power spectrum, computed from model parameters $\\Phi(\\mathbf{m})$, fits the power spectrum computed from the magnetic anomaly, $\\Phi_d$,\n", + "\n", + "$$\n", + "S(\\mathbf{m}) = \\frac{1}{s} \\sum_i \\frac{\\lvert \\Phi^i(\\mathbf{m}) - \\Phi_d^i \\lvert^s}{(\\sigma_{\\Phi}^i)^s} + \\frac{1}{r} \\sum_{j} \\frac{\\vert \\mathrm{m}^j - \\mathrm{m}^j_p \\vert^r}{(\\sigma^j_p)^r}\n", + "$$\n", + "\n", + "By default, PyCurious assumes Gaussian uncertainties on $\\Phi$ ($s=2$), and a uniform prior over a large range ($r=\\infty$) for each model parameter where $-\\sigma_p^j \\leq \\mathrm{m}^j - \\mathrm{m}_p^j \\leq +\\sigma_p^j$. The prior can easily be defined by the user as we will demonstrate later. We have already covered the `optimise` method that uses gradient-based optimisation to quickly iterate to the MAP estimate in [Ex2-Compute-Curie-depth](./Ex2-Compute-Curie-depth.ipynb).\n", + "\n", + "\n", + "> **Note:** The objective function can be accessed (and modified) under `grid.objective_function`." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "beta_opt, zt_opt, dz_opt, C_opt = grid.optimise(window_size, xpt, ypt, taper=None)\n", + "\n", + "k, Phi, sigma_Phi = grid.radial_spectrum(subgrid, taper=None)\n", + "\n", + "# define a range of parameters over which to analyse the misfit\n", + "# use the optimum parameters to help constrain an appropriate range\n", + "nb = 50\n", + "beta_range = np.linspace(beta_opt - 0.5, beta_opt + 0.5,nb)\n", + "dz_range = np.linspace(dz_opt - 5.0, dz_opt + 5.0, nb)\n", + "\n", + "# constant values for zt and C\n", + "zt = zt_opt\n", + "C = C_opt\n", + "\n", + "# misfit matrix\n", + "misfit = np.zeros((nb,nb))\n", + "\n", + "for i, beta in enumerate(beta_range):\n", + " for j, dz in enumerate(dz_range):\n", + "\n", + " m = [beta, zt, dz, C]\n", + " \n", + " misfit[i,j] = grid.min_func(m, k, Phi, sigma_Phi)\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Plot joint probability\n", + "fig, (ax1,ax2) = plt.subplots(1,2, sharey=True, figsize=(12,4))\n", + "\n", + "X, Y = np.meshgrid(dz_range, beta_range)\n", + "\n", + "im1 = ax1.pcolormesh(X, Y, misfit)\n", + "im2 = ax2.pcolormesh(X, Y, np.exp(-misfit))\n", + "ax1.scatter(dz_opt, beta_opt, c='r')\n", + "ax2.scatter(dz_opt, beta_opt, c='r')\n", + "\n", + "ax1.set_ylabel(r\"$\\beta$\")\n", + "ax2.set_ylabel(r\"$\\beta$\")\n", + "ax1.set_xlabel(r\"$\\Delta z$\")\n", + "ax2.set_xlabel(r\"$\\Delta z$\")\n", + "ax1.set_title(r\"misfit $S(\\mathbf{m})$\")\n", + "ax2.set_title(r\"Posterior probability $P(\\mathbf{m}|\\mathbf{d})$\")\n", + "\n", + "fig.colorbar(im1, ax=ax1)\n", + "fig.colorbar(im2, ax=ax2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Metropolis-Hastings algorithm\n", + "\n", + "A practical approach to sample the posterior is to use MCMC methods such as the Metropolis-Hastings algorithm. This implements a random walk where $k=1,2,\\ldots,n$ for a Markov Chain $n$ samples long.\n", + "\n", + "1. Generate a candidate $\\mathbf{m}'$ for the next sample by picking from the prior distribution $P(\\mathbf{m})$.\n", + "2. Calculate the acceptance ratio between each sample of the posterior $\\alpha = P(\\mathbf{m}'|\\mathbf{d})/P(\\mathbf{m}_{k}|\\mathbf{d})$\n", + "3. Generate a random number $u: [0,1]$ which will be used to decide if a candidate is accepted or rejected.\n", + " - accept if $u \\leq \\alpha$ and set $\\mathbf{m}_{k+1} = \\mathbf{m}'$\n", + " - reject if $u > \\alpha$ and set $\\mathbf{m}_{k+1} = \\mathbf{m}_k$ instead\n", + "\n", + "The random walk should be initialised not too far from the MAP estimate. MCMC methods require tuning to adequately sample the posterior. Parameters to tweak include:\n", + "\n", + "- `burnin`: the number of burn-in simulations\n", + "- `nsim`: total simulation after burnin\n", + "- `x_scale`: scaling factor $\\gamma$ to generate a new candidate $\\mathbf{m}' = \\gamma \\mathbf{m}$.\n", + "\n", + "```python\n", + "posterior = metropolis_hastings(window_size, xpt, ypt, nsim, burnin, x_scale)\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "k, Phi, sigma_Phi = grid.radial_spectrum(subgrid, taper=None)\n", + "\n", + "x_scale = [0.25, 0.1, 1.0, 1.0]\n", + "\n", + "burnin = 1000\n", + "nsim = 100000\n", + "\n", + "# C can be initialised close to its MAP very easily\n", + "posterior = grid.metropolis_hastings(window_size, xpt, ypt, nsim, burnin, x_scale, C=Phi.mean(), taper=None)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Appraising the ensemble\n", + "\n", + "How best to visualise the ensemble after the MCMC simulation? We cover some of the following:\n", + "\n", + "- Histograms\n", + "- Scatter plots & joint probabilities\n", + "- Trajectory of the random walk\n", + "- MAP estimate" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "labels = [r'$\\beta$', r'$z_t$', r'$\\Delta z$', r'$C$']\n", + "\n", + "fig, axes = plt.subplots(1,4, figsize=(14,5))\n", + "for i, ax in enumerate(axes):\n", + " ax.hist(posterior[i], bins=20, normed=True)\n", + " ax.set_title(labels[i])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Below are some joint probabilities visualised with the trajectory of the random walk." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Plot joint probability and trajectory of random walk\n", + "fig, (ax1,ax2) = plt.subplots(1,2, figsize=(12,4))\n", + "\n", + "\n", + "H1, xedges, yedges = np.histogram2d(posterior[1], posterior[3], normed=True)\n", + "X1, Y1 = np.meshgrid(xedges, yedges)\n", + "\n", + "H2, xedges, yedges = np.histogram2d(posterior[2], posterior[0], normed=True)\n", + "X2, Y2 = np.meshgrid(xedges, yedges)\n", + "\n", + "\n", + "ax1.pcolormesh(X1, Y1, H1)\n", + "ax1.plot(posterior[1], posterior[3], c='w')\n", + "\n", + "ax2.pcolormesh(X2, Y2, H2)\n", + "ax2.plot(posterior[2], posterior[0], c='w')\n", + "\n", + "ax1.set_xlabel(r\"$z_t$\")\n", + "ax1.set_ylabel(r\"$C$\")\n", + "ax2.set_xlabel(r\"$\\Delta z$\")\n", + "ax2.set_ylabel(r\"$\\beta$\")\n", + "\n", + "fig.colorbar(im1, ax=ax1)\n", + "fig.colorbar(im2, ax=ax2)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "mode_result = stats.mode(np.vstack(posterior).T, axis=0)\n", + "\n", + "x_opt1 = grid.optimise(window_size, xpt, ypt, taper=None)\n", + "x_opt2 = mode_result.mode.ravel()\n", + "\n", + "str_fmt = \"beta = {:.2f} zt = {:.2f} dz = {:5.2f} C = {:.2f}\"\n", + "\n", + "print(str_fmt.format(*x_opt1))\n", + "print(str_fmt.format(*x_opt2))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig, (ax1, ax2) = plt.subplots(1,2,sharey=True,figsize=(12,4))\n", + "\n", + "Phi_opt1 = pycurious.bouligand2009(k, *x_opt1)\n", + "Phi_opt2 = pycurious.bouligand2009(k, *x_opt2)\n", + "\n", + "ax1.plot(k, Phi, 'o', c='0.5')\n", + "ax1.plot(k, Phi_opt1, linewidth=2, label='MAP (optimised)')\n", + "ax1.plot(k, Phi_opt2, linewidth=2, label='MAP (MCMC)')\n", + "ax2.semilogx(k, Phi, 'o', c='0.5')\n", + "ax2.semilogx(k, Phi_opt1, linewidth=2, label='MAP (optimised)')\n", + "ax2.semilogx(k, Phi_opt2, linewidth=2, label='MAP (MCMC)')\n", + "# ax2.semilogx(k, S2)\n", + "\n", + "ax1.set_ylabel('radial power spectrum')\n", + "ax1.set_xlabel('wavenumber (rad/km)')\n", + "ax2.set_xlabel('log wavenumber (rad/km)')\n", + "\n", + "ax1.legend()\n", + "ax2.legend()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The MAP estimate obtained from `grid.optimise` should be identical to that from `grid.metropolis_hastings`, but may in differ in practice if `nsim` is too few or `x_scale` is not properly tuned. Running multiple chains in parallel should alleviate most concerns. Otherwise parts of the probability space may be non-unique." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.15" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Examples/Notebooks/Bouligand/Ex4-Spatial-variation-of-Curie-depth.ipynb b/Examples/Notebooks/Bouligand/Ex4-Spatial-variation-of-Curie-depth.ipynb new file mode 100644 index 0000000..abbf3d1 --- /dev/null +++ b/Examples/Notebooks/Bouligand/Ex4-Spatial-variation-of-Curie-depth.ipynb @@ -0,0 +1,306 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Example 4 - Spatial variation of Curie depth\n", + "\n", + "In Example 2 and 3 we computed the Curie depth for a single point using a fixed window. Here, compute the Curie depth over a magnetic anomaly and estimate its uncertainty.\n", + "\n", + "### Contents\n", + "\n", + "- [Optimisation routine](#Optimisation-routine)\n", + "- [Uncertainty analysis](#Uncertainty-analysis)\n", + "- [Sensitivity analysis](#Sensitivity-analysis)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "\n", + "import pycurious" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# load x,y,anomaly\n", + "mag_data = np.loadtxt(\"../../data/test_mag_data.txt\")\n", + "\n", + "nx, ny = 305, 305\n", + "\n", + "x = mag_data[:,0]\n", + "y = mag_data[:,1]\n", + "d = mag_data[:,2].reshape(ny,nx)\n", + "\n", + "xmin, xmax = x.min(), x.max()\n", + "ymin, ymax = y.min(), y.max()\n", + "\n", + "# initialise CurieOptimise object\n", + "grid = pycurious.CurieOptimise(d, xmin, xmax, ymin, ymax)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Optimisation routine\n", + "\n", + "Here we iteratively evaluate the Curie depth across the magnetic anomaly. We use gradient-based inversion which is deterministic, because it doesn't include uncertainty, but a quick means to recover Curie depth from the magnetic anomaly." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# get centroids\n", + "\n", + "window_size = 200e3\n", + "xc_list, yc_list = grid.create_centroid_list(window_size, spacingX=10e3, spacingY=10e3)\n", + "\n", + "print(\"number of centroids = {}\".format(len(xc_list)))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# no priors\n", + "grid.reset_priors()\n", + "\n", + "beta, zt, dz, C = grid.optimise_routine(window_size, xc_list, yc_list)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# get dimensions of domain\n", + "xcoords = np.unique(xc_list)\n", + "ycoords = np.unique(yc_list)\n", + "nc, nr = xcoords.size, ycoords.size\n", + "\n", + "\n", + "# plot results\n", + "fig, (ax1, ax2, ax3, ax4) = plt.subplots(1, 4, sharex=True, sharey=True, figsize=(17,3.))\n", + "\n", + "im1 = ax1.imshow(beta.reshape(nr,nc))\n", + "im2 = ax2.imshow(zt.reshape(nr,nc))\n", + "im3 = ax3.imshow(dz.reshape(nr,nc))\n", + "im4 = ax4.imshow(C.reshape(nr,nc))\n", + "\n", + "fig.colorbar(im1, ax=ax1, label=r\"$\\beta$\")\n", + "fig.colorbar(im2, ax=ax2, label=r\"$z_t$\")\n", + "fig.colorbar(im3, ax=ax3, label=r\"$\\Delta z$\")\n", + "fig.colorbar(im4, ax=ax4, label=r\"$C$\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# plot Curie depth\n", + "\n", + "curie_depth = zt + dz\n", + "\n", + "fig = plt.figure()\n", + "ax1 = fig.add_subplot(111)\n", + "im1 = ax1.imshow(curie_depth.reshape(nr,nc), cmap=plt.cm.BrBG)\n", + "fig.colorbar(im1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Uncertainty analysis\n", + "\n", + "The variation of Curie depth is not particularly useful without any estimate of the uncertainty. We conduct the same MCMC simulation we performed in the previous example [Ex3-Posing-the-inverse-problem](./Ex3-Posing-the-inverse-problem.ipynb) to sample the posterior." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "x_scale = [0.25, 0.1, 1.0, 0.5]\n", + "\n", + "# run more simulations for production runs\n", + "burnin = 1000\n", + "nsim = 5000\n", + "\n", + "# mean across the domain\n", + "mu_beta, mu_zt, mu_dz, mu_C = beta.mean(), zt.mean(), dz.mean(), C.mean()\n", + "\n", + "pt_post = []\n", + "\n", + "# This will take some time\n", + "for xc, yc in zip(xc_list, yc_list):\n", + " posterior = grid.metropolis_hastings(window_size, xc, yc, nsim, burnin, x_scale,\\\n", + " mu_beta, mu_zt, mu_dz, mu_C, taper=None)\n", + " pt_post.append( posterior )" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "curie_depth = np.zeros_like(xc_list)\n", + "uncertainty = np.zeros_like(xc_list)\n", + "\n", + "for i, pt in enumerate(pt_post):\n", + " betaP, ztP, dzP, CP = pt\n", + " cpd = ztP + dzP\n", + " curie_depth[i] = np.mean(cpd)\n", + " uncertainty[i] = np.std(cpd)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# plot Curie depth\n", + "\n", + "curie_depth = zt + dz\n", + "\n", + "fig, (ax1,ax2) = plt.subplots(1,2, figsize=(11,4))\n", + "im1 = ax1.imshow(curie_depth.reshape(nr,nc), cmap=plt.cm.BrBG)\n", + "im2 = ax2.imshow(uncertainty.reshape(nr,nc), cmap=plt.cm.Blues)\n", + "fig.colorbar(im1, ax=ax1)\n", + "fig.colorbar(im2, ax=ax2)\n", + "\n", + "ax1.set_title(\"Curie depth (km)\")\n", + "ax2.set_title(\"Uncertainty (km)\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Sensitivity analysis\n", + "\n", + "The sensitivity analysis is a gradient-based solution to approximate the posterior distribution (read the motivation for this in Tarantola: *Inverse Problem Theory*). The radial power spectrum $\\Phi$ is randomly perturbed within its uncertainty $\\sigma_{\\Phi}$ to sample locally around the MAP estimate.\n", + "\n", + "$$\n", + "\\Phi_{d}^* = \\Phi_d + \\delta \\Phi_d\n", + "$$\n", + "\n", + "where $\\delta \\Phi_d$ is a random perturbation generated from the probability density of $\\Phi_d$. This is equivalent to pertubing the likelihood function,\n", + "\n", + "$$\n", + "P(\\Phi|\\mathbf{m}) = \\frac{1}{(\\sqrt{2\\pi} \\sigma_\\Phi)^n} \\exp \\left( - \\frac{\\lvert \\Phi(\\mathbf{m}) - \\Phi_d^* \\lvert^2}{2 \\sigma_\\Phi^2} \\right)\n", + "$$\n", + "\n", + "where $\\mathbf{m}^*$ is a perturbed prior distribution: $\\mathbf{m}_p^* = \\mathbf{m}_p + \\delta \\mathbf{m}_p$. If the prior is a Gaussian normal distribution, then the perturbed prior is\n", + "\n", + "$$\n", + "P(\\mathbf{m}) = \\frac{1}{\\sqrt{2\\pi} \\sigma_p} \\exp \\left( - \\frac{\\lvert \\mathbf{m} - \\mathbf{m}_p^* \\lvert^2}{2 \\sigma_p^2} \\right)\n", + "$$\n", + "\n", + "Prior distributions can be added by\n", + "\n", + "```python\n", + "from scipy import stats\n", + "beta_p = stats.norm(3.0, 1.0)\n", + "grid.add_prior(beta=beta_p)\n", + "```\n", + "\n", + "We repeat the inversion multiple times, sampling different values from $P(\\mathbf{m})$ and $P(\\Phi|\\mathbf{m})$ to evaluate the uncertainty in each variable." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "nsim = 100\n", + "pt_post = []\n", + "\n", + "for xc, yc in zip(xc_list, yc_list):\n", + " sensitivity = grid.sensitivity(window_size, xc, yc, nsim, mu_beta, mu_zt, mu_dz, mu_C, taper=None)\n", + " pt_post.append( sensitivity )" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "curie_depth = np.zeros_like(xc_list)\n", + "uncertainty = np.zeros_like(xc_list)\n", + "\n", + "for i, pt in enumerate(pt_post):\n", + " betaP, ztP, dzP, CP = pt\n", + " cpd = ztP + dzP\n", + " curie_depth[i] = np.mean(cpd)\n", + " uncertainty[i] = np.std(cpd)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# plot Curie depth\n", + "\n", + "curie_depth = zt + dz\n", + "\n", + "fig, (ax1,ax2) = plt.subplots(1,2, figsize=(11,4))\n", + "im1 = ax1.imshow(curie_depth.reshape(nr,nc), cmap=plt.cm.BrBG)\n", + "im2 = ax2.imshow(uncertainty.reshape(nr,nc), cmap=plt.cm.Blues)\n", + "fig.colorbar(im1, ax=ax1)\n", + "fig.colorbar(im2, ax=ax2)\n", + "\n", + "ax1.set_title(\"Curie depth (km)\")\n", + "ax2.set_title(\"Uncertainty (km)\")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.15" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Examples/Notebooks/Bouligand/Ex4-Mapping-Curie-depth-EMAG2.ipynb b/Examples/Notebooks/Bouligand/Ex5-Mapping-Curie-depth-EMAG2.ipynb similarity index 89% rename from Examples/Notebooks/Bouligand/Ex4-Mapping-Curie-depth-EMAG2.ipynb rename to Examples/Notebooks/Bouligand/Ex5-Mapping-Curie-depth-EMAG2.ipynb index a420a5a..034515f 100644 --- a/Examples/Notebooks/Bouligand/Ex4-Mapping-Curie-depth-EMAG2.ipynb +++ b/Examples/Notebooks/Bouligand/Ex5-Mapping-Curie-depth-EMAG2.ipynb @@ -4,7 +4,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Example 4 - Mapping Curie depth from EMAG2\n", + "# Example 5 - Mapping Curie depth from EMAG2\n", "\n", "Using global compilations of the magnetic anomaly, such as EMAG2, means there is no limitation on window sizes. The mapping module in *PyCurious* has several functions to simplify:\n", "\n", @@ -37,10 +37,8 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, + "execution_count": 2, + "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", @@ -48,6 +46,7 @@ "%matplotlib inline\n", "\n", "import pycurious\n", + "from pycurious import mapping\n", "\n", "import cartopy.crs as ccrs\n", "import cartopy.feature as cfeature\n", @@ -88,16 +87,17 @@ }, "outputs": [], "source": [ - "filedir = '/mnt/ben_raid/'\n", + "filedir = '/path/to/directory/'\n", + "emag2_name = 'EMAG2_V3_20170530'\n", "\n", "try:\n", - " with np.load(filedir+'EMAG2_V3_20170530.npz') as f:\n", + " with np.load(filedir+emag2_name+'.npz') as f:\n", " mag_data = f['data']\n", "except:\n", - " mag_data = np.loadtxt(filedir+'EMAG2_V3_20170530.csv', delimiter=',', usecols=(2,3,4,5,7))\n", + " mag_data = np.loadtxt(filedir+emag2_name+'.csv', delimiter=',', usecols=(2,3,4,5,7))\n", " lon_mask = mag_data[:,0] > 180.0\n", " mag_data[lon_mask,0] -= 360.0\n", - " np.savez_compressed(filedir+'EMAG2_V3_20170530.npz', data=mag_data.astype(np.float32))" + " np.savez_compressed(filedir+emag2_name+'.npz', data=mag_data.astype(np.float32))" ] }, { @@ -147,7 +147,7 @@ "extent_grid = [xmin, xmax, ymin, ymax]\n", "\n", "# extent on the sphere (WGS84)\n", - "extent_sphere = pycurious.mapping.convert_extent(extent_grid, epsg_in=2157, epsg_out=4326)\n", + "extent_sphere = mapping.convert_extent(extent_grid, epsg_in=2157, epsg_out=4326)\n", "\n", "# map extent - should be narrower than extent_sphere\n", "extent_map = [-10.8, 2, 49.5, 59]" @@ -165,10 +165,10 @@ "nx, ny = int(round((xmax-xmin)/dx)), int(round((ymax-ymin)/dy))\n", "\n", "# interpolate onto grid extent (for computation)\n", - "mag_grid = pycurious.mapping.grid(mag_data[:,:2], mag_data[:,3], extent_grid, shape=(ny,nx), epsg_in=4326, epsg_out=2157)\n", + "mag_grid = mapping.grid(mag_data[:,:2], mag_data[:,3], extent_grid, shape=(ny,nx), epsg_in=4326, epsg_out=2157)\n", "\n", "# interpolate onto extent on the sphere (for mapping)\n", - "mag_sphere = pycurious.mapping.grid(mag_data[:,:2], mag_data[:,3], extent_sphere, shape=(ny,nx))" + "mag_sphere = mapping.grid(mag_data[:,:2], mag_data[:,3], extent_sphere, shape=(ny,nx))" ] }, { @@ -229,7 +229,7 @@ "curie_depth = zt + dz\n", "centroids = np.column_stack([xc_list, yc_list])\n", "\n", - "curie_depth_sphere = pycurious.mapping.grid(centroids, curie_depth, extent_sphere, (ny,nx), epsg_in=2157, epsg_out=4326)" + "curie_depth_sphere = mapping.grid(centroids, curie_depth, extent_sphere, (ny,nx), epsg_in=2157, epsg_out=4326)" ] }, { @@ -274,7 +274,7 @@ "li_cpd = np.loadtxt(filedir + 'Li_2017_curiedepth.txt')\n", "li_cpd = li_cpd[~np.isnan(li_cpd[:,2])]\n", "\n", - "li_grid = pycurious.grid(li_cpd[:,:2], li_cpd[:,2], extent_sphere, shape=(ny,nx))" + "li_grid = mapping.grid(li_cpd[:,:2], li_cpd[:,2], extent_sphere, shape=(ny,nx))" ] }, { @@ -314,7 +314,7 @@ }, "outputs": [], "source": [ - "pycurious.mapping.export_geotiff(\"my-curie-depth.tiff\", curie_depth_sphere, extent_sphere, epsg=4326)" + "mapping.export_geotiff(\"my-curie-depth.tiff\", curie_depth_sphere, extent_sphere, epsg=4326)" ] }, { @@ -330,7 +330,7 @@ "metadata": {}, "outputs": [], "source": [ - "GTiff, GTextent = pycurious.mapping.import_geotiff(\"my-curie-depth.tiff\")\n", + "GTiff, GTextent = mapping.import_geotiff(\"my-curie-depth.tiff\")\n", "\n", "print(GTextent)\n", "print(GTiff.shape)" @@ -353,7 +353,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", - "version": "2.7.12" + "version": "2.7.15" } }, "nbformat": 4, diff --git a/Examples/Notebooks/Tanaka/Ex2-Compute-Curie-depth.ipynb b/Examples/Notebooks/Tanaka/Ex2-Compute-Curie-depth.ipynb index 0c2d823..d92e5ad 100644 --- a/Examples/Notebooks/Tanaka/Ex2-Compute-Curie-depth.ipynb +++ b/Examples/Notebooks/Tanaka/Ex2-Compute-Curie-depth.ipynb @@ -4,7 +4,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Example 2a - Compute Curie depth (Tanaka approach)\n", + "# Example 2 - Compute Curie depth\n", "Tanaka *et al.* (1999) based their method upon an expression for the radial power spectrum that assumes random magnetisation of the crust, and a radially averaged power spectra $\\Phi_{\\Delta T}(|k|)$:\n", "\n", "$$(1) \\Phi_{\\Delta T}(|k|)=Ae^{-2|k|Z_t}(1-e^{-|k|(Z_b-Z_t)})^2$$\n", @@ -41,7 +41,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -54,12 +54,12 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# load x,y,anomaly\n", - "mag_data = np.loadtxt(\"../data/test_mag_data.txt\")\n", + "mag_data = np.loadtxt(\"../../data/test_mag_data.txt\")\n", "\n", "nx, ny = 305, 305\n", "\n", @@ -81,7 +81,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -99,35 +99,14 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 13, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ - "k, S, sigma2 = grid.radial_spectrum_log(subgrid, taper=None)\n", + "k, Phi, sigma_Phi = grid.radial_spectrum_log(subgrid, taper=None)\n", "\n", "# Plot of power spectrum, as function of spatial frequency\n", - "plt.plot(k/(2*np.pi), S/(2*np.pi), '-o')\n", + "plt.plot(k/(2*np.pi), Phi/(2*np.pi), '-o')\n", "plt.title('Power Spectrum')\n", "plt.xlabel(r'$|k|/(2\\pi)$ [km$^{-1}$]')\n", "plt.ylabel(r'$\\ln(\\Phi_{\\Delta T}(|k|)^{1/2})/(2\\pi)$')" @@ -135,33 +114,12 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 14, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ - "Sn=np.log(np.exp(S)/k)\n", - "plt.plot(k/(2*np.pi), Sn/(2*np.pi), '-o')\n", + "Phi_n = np.log(np.exp(Phi)/k)\n", + "plt.plot(k/(2*np.pi), Phi_n/(2*np.pi), '-o')\n", "plt.title('Power Spectrum, weighted by k')\n", "plt.xlabel(r'$|k|/(2\\pi)$ [km$^{-1}$]')\n", "plt.ylabel(r'$\\ln(\\Phi_{\\Delta T}(|k|)^{1/2}/|k|)/(2\\pi)$')" @@ -180,72 +138,37 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": null, "metadata": { "scrolled": true }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Zb estimate: 6.64352756, +/- 2.42729754 km\n" - ] - } - ], + "outputs": [], "source": [ - "(Ztr,btr,dZtr), (Zor, bor, dZor) = pycurious.tanaka1999(S, k, sigma2, (0,0.1), (0.2,0.3))\n", + "(Ztr,btr,dZtr), (Zor, bor, dZor) = pycurious.tanaka1999(k, Phi, sigma_Phi, (0,0.1), (0.2,0.3))\n", "Zb, eZb = pycurious.ComputeTanaka(Ztr, dZtr, Zor, dZor)\n", - "print('Zb estimate: '+np.array2string(Zb)+', +/- '+np.array2string(eZb)+' km')" + "\n", + "print('Zb estimate: {:.2f} +/- {:.2f} km'.format(Zb, eZb))" ] }, { "cell_type": "code", - "execution_count": 20, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 20, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "# make two plots with Z-lines overlain.\n", "# Plot of power spectrum, as function of spatial frequency\n", "fig, (ax1, ax2) = plt.subplots(1,2, figsize=(16,6),)\n", "\n", - "ax1.plot(k/(2*np.pi), S/(2*np.pi), '-bo',k/(2*np.pi),(Ztr*k/(2*np.pi)+btr)/(2*np.pi),'r-')\n", + "ax1.plot(k/(2*np.pi), Phi/(2*np.pi), '-bo', k/(2*np.pi), (Ztr*k/(2*np.pi)+btr)/(2*np.pi),'r-')\n", "#ax1.title('Power Spectrum')\n", "ax1.set_xlabel(r'$|k|/(2\\pi)$ [km$^{-1}$]')\n", "ax1.set_ylabel(r'$\\ln(\\Phi_{\\Delta T}(|k|)^{1/2})/(2\\pi)$')\n", "\n", - "ax2.plot(k/(2*np.pi), Sn/(2*np.pi), '-o',k/(2*np.pi),(Zor*k/(2*np.pi)+bor)/(2*np.pi),'r-')\n", + "ax2.plot(k/(2*np.pi), Phi_n/(2*np.pi), '-o',k/(2*np.pi),(Zor*k/(2*np.pi)+bor)/(2*np.pi),'r-')\n", "ax2.set_xlabel(r'$|k|/(2\\pi)$ [km$^{-1}$]')\n", "ax2.set_ylabel(r'$\\ln(\\Phi_{\\Delta T}(|k|)^{1/2}/|k|)/(2\\pi)$')\n" ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] } ], "metadata": { diff --git a/Examples/Notebooks/Tanaka/Ex3-Parameter-exploration.ipynb b/Examples/Notebooks/Tanaka/Ex3-Parameter-exploration.ipynb new file mode 100644 index 0000000..d65f910 --- /dev/null +++ b/Examples/Notebooks/Tanaka/Ex3-Parameter-exploration.ipynb @@ -0,0 +1,264 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Example 3 - Parameter Exploration of Spectral Analysis method\n", + "\n", + "Due to the deterministic approach that [Tanaka *et al.*, 1999](http://linkinghub.elsevier.com/retrieve/pii/S0040195199000724) uses for estimating $Z_b$, the uncertainties returned by `CurieGrid.tanaka1999` are the simple results of error propagation from the initial spectra uncertainties. The spectra uncertainties represent the variance within the sampled sector of the 2D FFT, and may comprise both noise and anisotropic signal.\n", + "\n", + "We present here several tests of the `CurieGrid.tanaka1999` function in order to explore how the input parameters affect the resulting Curie point depth estimates. In particular, we consider the following:\n", + "\n", + "1. Effect of where in $k$-space is specific window used, separately for both the power and $k$-weighted power spectra (i.e., which $k$ do we consider?).\n", + "2. Effect of $k$-space window size (i.e., how much of the $k$-domain do we consider?). It is important to note that increasing the $k$-bandwidth also stabilises the estimation by increasing the statistics of the spectrum portion.\n", + "3. Effect of magnetic data window size (i.e., domain of magnetic data before computing FFT).\n", + "\n", + "### Contents\n", + "\n", + "- [Varying spatial frequency range](#Varying-spatial-frequency-range)\n", + "- [Varying spatial frequency size](#Varying-spatial-frequency-size)\n", + "- [Varying window size of magnetic anomaly](#Varying-window-size-of-magnetic-anomaly)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "\n", + "import pycurious" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# load x,y,anomaly\n", + "mag_data = np.loadtxt(\"../../data/test_mag_data.txt\")\n", + "\n", + "nx, ny = 305, 305\n", + "\n", + "x = mag_data[:,0]\n", + "y = mag_data[:,1]\n", + "d = mag_data[:,2].reshape(ny,nx)\n", + "\n", + "xmin, xmax = x.min(), x.max()\n", + "ymin, ymax = y.min(), y.max()\n", + "\n", + "# initialise CurieOptimise object\n", + "grid = pycurious.CurieOptimise(d, xmin, xmax, ymin, ymax)\n", + "\n", + "# pick centroid\n", + "xpt = xmin + (xmax-xmin)/2\n", + "ypt = ymin + (ymax-ymin)/2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Varying spatial frequency range\n", + "\n", + "This test explores where in $k$-space is specific window used, separately for both the power and $k$-weighted power." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# 1) Where in k-space do we locate window?\n", + "window_size = 304e3\n", + "subgrid = grid.subgrid(window_size, xpt, ypt)\n", + "k, Phi, sigma_Phi = grid.radial_spectrum_log(subgrid, taper=None)\n", + "\n", + "# Number of bins to divide k-range into\n", + "nbins = 10\n", + "hmap = np.zeros((nbins**2,3))\n", + "\n", + "# k-range divided between 0 (i.e., DC), and 0.3 (i.e., spatial wavelengths of ~20 km)\n", + "kmin_range = np.linspace(0., 0.3, nbins)\n", + "kmax_range = kmin_range + (0.3/nbins)\n", + "\n", + "for j in range(0,nbins):\n", + " for l in range(0,nbins):\n", + " kmin0 = kmin_range[j]\n", + " kmin1 = kmax_range[j]\n", + " kmax0 = kmin_range[l]\n", + " kmax1 = kmax_range[l]\n", + " \n", + " (Ztr,btr,dZtr), (Zor, bor, dZor) = pycurious.tanaka1999(k, Phi, sigma_Phi, (kmin0, kmin1), (kmax0, kmax1))\n", + " Zb,eZb = pycurious.ComputeTanaka(Ztr, dZtr, Zor, dZor)\n", + " \n", + " hmap[j*nbins+l,0] = (kmin0+kmin1)/2\n", + " hmap[j*nbins+l,1] = (kmax0+kmax1)/2\n", + " hmap[j*nbins+l,2] = Zb" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig2 = plt.figure(figsize=(16,16))\n", + "\n", + "ax2 = fig2.add_subplot(111)\n", + "ax2.set_xlabel(r'$\\nu$ window of $\\Phi/|k|$ (km$^{-1}$) (for Zo)')\n", + "ax2.set_ylabel(r'$\\nu$ window of $\\Phi$ (for Zt)')\n", + "\n", + "# SCATTER PLOT\n", + "im2 = ax2.scatter(hmap[:,1], hmap[:,0], 2000, np.clip(hmap[:,2],10,20), marker='s')\n", + "fig2.colorbar(im2, label='CPD (km)')\n", + "plt.title('Heatmap of CPD')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Results of this test suggest that the precise $k$ location of $Z_t$ is significantly less influential than the $k$ location of $Z_o$. Furthermore, for this test case with a known $Z_b$ of 16 km, a spatial frequency $\\nu$ window of $0.125-0.2$ (i.e., $k\\in\\{0.8-1.25\\}$ gives estimates consistent with the true $Z_b$. For simplicity, based upon this test we see minimal reason to not use the same $\\nu/k$ window for each spectrum." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Varying spatial frequency size\n", + "\n", + "Explore the effect of $k$-space window size (i.e., how much of the $k$-domain do we consider?). Increasing the $k$-bandwidth also stabilises the estimation by increasing the statistics of the spectrum portion." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# 2) How big a bandwidth in k-space do we want?\n", + "\n", + "k, Phi, sigma_Phi = grid.radial_spectrum_log(subgrid, taper=None)\n", + "\n", + "# We are testing this by taking one central spatial frequency (k=1), and estimating Zb with increasing k-bandwidths.\n", + "# Recall k=2*pi*nu\n", + "nu = 1.0/(2.0*np.pi)\n", + "\n", + "nbins = 30\n", + "output = np.zeros((nbins,3))\n", + "nr = np.linspace(0., 0.3, nbins+1)\n", + "output[:,0] = nr[1:]\n", + "\n", + "for j in range(0,nbins,1):\n", + " kmin = nu - 0.5*output[j,0]\n", + " kmax = nu + 0.5*output[j,0]\n", + " \n", + " (Ztr,btr,dZtr), (Zor, bor, dZor) = pycurious.tanaka1999(k, Phi, sigma_Phi, (kmin, kmax), (kmin, kmax))\n", + " Zb, eZb = pycurious.ComputeTanaka(Ztr, dZtr, Zor, dZor)\n", + " output[j,1] = Zb\n", + " output[j,2] = eZb\n", + " \n", + "fig2 = plt.figure(figsize=(8,8))\n", + "ax2 = fig2.add_subplot(111)\n", + "ax2.errorbar(output[:,0], output[:,1], yerr=output[:,2])\n", + "ax2.invert_yaxis()\n", + "ax2.set_xlabel('$\\\\nu$-bandwidth')\n", + "ax2.set_ylabel('CPD depth (km)')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The CPD estimates resulting from this test become consistent for $\\nu$-bandwidths greater than approximately 0.1. Statistics improve with larger bandwidths, however, it is worth remaining aware of the typically non-linear trend of the spectrum, as it may not be appropriate for a linear fit over a large domain of $\\nu$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Varying window size\n", + "\n", + "Effect of magnetic data window size - i.e., domain of magnetic data before computing the FFT." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# 3) How large a window width of magnetic data is required?\n", + "grid = pycurious.CurieOptimise(d, xmin, xmax, ymin, ymax)\n", + "xpt = xmin + (xmax-xmin)/2\n", + "ypt = ymin + (ymax-ymin)/2\n", + "\n", + "nwin = 50\n", + "baseW = 10000\n", + "inc = 2500\n", + "\n", + "output = np.zeros((nwin,3))\n", + "\n", + "# Define 'ws' as variable window size index\n", + "for i in range(0, nwin):\n", + " ws = baseW + i*inc\n", + " subgrid = grid.subgrid(ws, xpt, ypt)\n", + " k, Phi, sigma_Phi = grid.radial_spectrum_log(subgrid, taper=None)\n", + " (Ztr,btr,dZtr), (Zor, bor, dZor) = pycurious.tanaka1999(k, Phi, sigma_Phi, (0.11, 0.21), (0.11, 0.21))\n", + " Zb, eZb = pycurious.ComputeTanaka(Ztr, dZtr, Zor, dZor)\n", + " \n", + " output[i] = [ws, Zb, eZb]\n", + " #print('Zb estimate for '+str(ws)+' m: '+np.array2string(Zb)+', +/- '+np.array2string(eZb)+' km')\n", + "\n", + "fig, (ax1, ax2) = plt.subplots(1,2, figsize=(16,6),)\n", + "ax1.plot(output[:,0], output[:,1])\n", + "ax1.set_ylim(0,30)\n", + "ax1.invert_yaxis()\n", + "ax1.set_xlabel('Data window size (m)')\n", + "ax1.set_ylabel('CPD estimate (km)')\n", + "\n", + "ax2.plot(output[:,0], output[:,2])\n", + "ax2.set_xlabel('Data window size (m)')\n", + "ax2.set_ylabel('CPD misfit (km)')\n", + "#plt.gca().invert_yaxis()\n", + "#plt.xlabel('Data window size (km)')\n", + "#plt.ylabel('CPD depth (km)')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The results of this test highlight that there is a significant amount of variability in the CPD estimates at all window sizes, inferring that where possible, a range of window sizes should be tested for any data set. However, the righthand plot of propagated error in the CPD estimates clarifies that estimates from larger windows are more robust. In particular, with the prior knowledge that the CPD of the test data is 16 km, window sizes of greater than 80 km show a reduced improvement in statistics. " + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.15" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Examples/british_isles.py b/Examples/british_isles.py deleted file mode 100644 index c47966a..0000000 --- a/Examples/british_isles.py +++ /dev/null @@ -1,215 +0,0 @@ -# coding: utf-8 - -import numpy as np -import matplotlib.pyplot as plt -import pycurious - -""" -**EMAG2_V3_20170530.csv** - -- Column 1: i ; grid column/longitude index -- Column 2: j ; grid row/latitude index -- Column 3: LON ; Geographic Longitude WGS84 (decimal degrees) -- Column 4: LAT ; Geographic Latitude WGS84 (decimal degrees) -- Column 5: SeaLevel ; Magnetic Anomaly Value at Sea Level(nT) -- Column 6: UpCont ; Magnetic Anomaly Value at continuous 4km altitude (nT) -- Column 7: Code ; Data Source Code (see table below) -- Column 8: Error ; Error estimate (nT) - -Code 888 is assigned in certain cells on grid edges where the data source is ambiguous and assigned an error of -888 nT - -Code 999 is assigned in cells where no data is reported with the anomaly value assigned 99999 nT and an error of -999 nT -""" - -filedir = '/mnt/ben_raid/' - -try: - with np.load(filedir+'EMAG2_V3_20170530.npz') as f: - mag_data = f['data'] -except: - mag_data = np.loadtxt(filedir+'EMAG2_V3_20170530.csv', delimiter=',', usecols=(2,3,4,5,7)) - lon_mask = mag_data[:,0] > 180.0 - mag_data[lon_mask,0] -= 360.0 - np.savez_compressed(filedir+'EMAG2_V3_20170530.npz', data=mag_data.astype(np.float32)) - - -# filter NaNs -mag_data = mag_data[mag_data[:,3] != 99999.] -mag_data = mag_data[mag_data[:,4] != -888.] -mag_data = mag_data[mag_data[:,4] != -999.] - -# print min/max -mincols = mag_data.min(axis=0) -maxcols = mag_data.max(axis=0) - -fmt = "min/max {:.2f} -> {:.2f}" -for col in xrange(mag_data.shape[1]): - print(fmt.format(mincols[col], maxcols[col])) - - -# In[7]: - - -xmin = 250000.0 -xmax = 1400000.0 -ymin = 200000.0 -ymax = 1500000.0 -extent = [xmin, xmax, ymin, ymax] - -dx, dy = 1e3, 1e3 # 1km resolution -nx, ny = int(round((xmax-xmin)/dx)), int(round((ymax-ymin)/dy)) - -# also get WGS84 extent -tlon, tlat = pycurious.transform_coordinates([xmin,xmin,xmax,xmax], [ymin,ymax,ymin,ymax], 2157, 4326) -lonmin, lonmax = min(tlon), max(tlon) -latmin, latmax = min(tlat), max(tlat) -extent_sphere = [lonmin, lonmax, latmin, latmax] - -# grid data -mag_grid = pycurious.grid(mag_data[:,:2], mag_data[:,3], extent, shape=(ny,nx), epsg_in=4326, epsg_out=2157) -mag_sphere = pycurious.grid(mag_data[:,:2], mag_data[:,3], extent_sphere, shape=(ny,nx), epsg_in=4326, epsg_out=4326) - - - -# initialise CurieOptimise object -grd = pycurious.CurieOptimise(mag_grid, xmin, xmax, ymin, ymax) - -# let's pick a point in the centre of the study area -xpt = 0.5*(xmax + xmin) -ypt = 0.5*(ymax + ymin) - -# get a subsection of the grid -subgrd = grd.subgrid(xpt, ypt, 100000.) - -# compute radial spectrum -S, k, sigma2 = grd.radial_spectrum(subgrd, taper=None) - -""" -## Optimise - -We have 4 parameters we wish to optimise: -- beta : fractal parameter -- z_t : the top of magnetic sources -- dz : the thickness of magnetic sources -- C : a field constant - -We minimise this using `scipy.optimize.minimize` which defaults -to `L-BFGS-B` for constrained minimisation. - - -### Optimisation strategy - -The problem is that $dz$ in Bouligand *et al.* (2009) [eq. 4] is -least sensitive to the problem, but the most important parameter -for evaluating Curie depth. - -If we revisit the problem, however, we see that beta and C mostly -vary at long wavelengths, thus if we determine what their average -value is over the whole field then we can fix them as constants. -Our strategy is now a two-stage inversion method. - -**First pass** - -Ensure there is no *a priori* information and commence with -suitable starting values. -""" - -xc_list, yc_list = grd.create_centroid_list(100e3, spacingX=20e3, spacingY=20e3) -# xc_list, yc_list = grd.create_centroid_list(100e3) - -print("number of centroids = {}".format(len(xc_list))) - - - - -grd.reset_priors() -betaN, ztN, dzN, CN = grd.optimise_routine(100e3, xc_list, yc_list, 3.0, 1.0, 20.0, 5.0, taper=None) - - - - -xc = np.unique(xc_list) -yc = np.unique(yc_list) - -nr, nc = yc.size, xc.size - -plot_helper = [(betaN, 'beta'), (ztN, 'zt'), (dzN, 'dz'), (CN, 'C')] - -fig, (ax1,ax2,ax3,ax4) = plt.subplots(1, 4, sharey=True, figsize=(16,3.5)) -for i, ax in enumerate([ax1, ax2, ax3, ax4]): - title = plot_helper[i][1] - data = plot_helper[i][0] - mask = np.isfinite(data) - - ax.set_title(title) - sci = ax.scatter(xc_list[mask]/1e3, yc_list[mask]/1e3, c=data[mask]) - fig.colorbar(sci, ax=ax) - fig.savefig('CPD_initial.png', bbox_inches='tight') - - print("{:5} mean={:.2f} std={:.2f}".format(title, data.mean(), np.std(data))) - -""" -**Second pass** - -Take the mean and standard deviation of all parameters and add them -as priors within the misfit function, then run the optimisation again. - -beta, C, and z_t have the lowest standard deviation therefore the -effect of perturbing these greatly increases the misfit compared to dz. -""" - - -# these parameters did well based on previous experience... -# grd.add_prior(beta=(5.44,0.62), zt=(0.14,0.28), dz=(22.73,29.63), C=(11.88,1.38)) - -beta_mu, beta_std = np.mean(betaN), np.std(betaN) -zt_mu, zt_std = np.mean(ztN), np.std(ztN) -dz_mu, dz_std = np.mean(dzN), np.std(dzN) -C_mu, C_std = np.mean(CN), np.std(CN) - -grd.reset_priors() -grd.add_prior(beta=(beta_mu, beta_std)) -grd.add_prior(zt=(zt_mu, zt_std)) -grd.add_prior(dz=(20.0, 50.)) -grd.add_prior(C=(C_mu, C_std)) - -for p in ['beta', 'zt', 'dz', 'C']: - prior = grd.prior[p] - if type(prior) != type(None): - mu, sigma = prior - else: - mu, sigma = 0,0 - print("prior {:5} mean={:.2f} std={:.2f}".format(p, mu, sigma)) - -betaOpt, ztOpt, dzOpt, COpt = grd.optimise_routine(100e3, xc_list, yc_list, taper=None) - - - -plot_helper = [(betaOpt, 'beta'), (ztOpt, 'zt'), (dzOpt, 'dz'), (COpt, 'C')] - -fig, (ax1,ax2,ax3,ax4) = plt.subplots(1, 4, sharey=True, figsize=(16,3.5)) -for i, ax in enumerate([ax1, ax2, ax3, ax4]): - title = plot_helper[i][1] - data = plot_helper[i][0] - mask = np.isfinite(data) - - ax.set_title(title) - sci = ax.scatter(xc_list[mask]/1e3, yc_list[mask]/1e3, c=data[mask]) - fig.colorbar(sci, ax=ax) - fig.savefig('CPD_optimised.png', bbox_inches='tight') - - print("{:5} mean={:.2f} std={:.2f}".format(title, data.mean(), np.std(data))) - -""" -Not bad! -The Curie depth can be refined further if an average geotherm is assumed, -but then it is no longer an independent constraint on the temperature field. -""" - - -# Write to file -curie_depth = ztOpt + dzOpt - -lonc, latc = pycurious.transform_coordinates(xc_list, yc_list, epsg_in=2157, epsg_out=4326) -np.savetxt('british_isles_cpd.csv', np.column_stack([lonc, latc, curie_depth]),\ - fmt='%.6f', delimiter=',', header='lon, lat, curie_depth') diff --git a/Examples/british_isles_parallel.py b/Examples/british_isles_parallel.py deleted file mode 100644 index 87ca7e8..0000000 --- a/Examples/british_isles_parallel.py +++ /dev/null @@ -1,171 +0,0 @@ -# coding: utf-8 - -import numpy as np -import matplotlib.pyplot as plt -import pycurious - -from mpi4py import MPI - -""" -**EMAG2_V3_20170530.csv** - -- Column 1: i ; grid column/longitude index -- Column 2: j ; grid row/latitude index -- Column 3: LON ; Geographic Longitude WGS84 (decimal degrees) -- Column 4: LAT ; Geographic Latitude WGS84 (decimal degrees) -- Column 5: SeaLevel ; Magnetic Anomaly Value at Sea Level(nT) -- Column 6: UpCont ; Magnetic Anomaly Value at continuous 4km altitude (nT) -- Column 7: Code ; Data Source Code (see table below) -- Column 8: Error ; Error estimate (nT) - -Code 888 is assigned in certain cells on grid edges where the data source is ambiguous and assigned an error of -888 nT - -Code 999 is assigned in cells where no data is reported with the anomaly value assigned 99999 nT and an error of -999 nT - -## Optimise - -We have 4 parameters we wish to optimise: -- beta : fractal parameter -- z_t : the top of magnetic sources -- dz : the thickness of magnetic sources -- C : a field constant - -We minimise this using `scipy.optimize.minimize` which defaults -to `L-BFGS-B` for constrained minimisation. - - -### Optimisation strategy - -The problem is that $dz$ in Bouligand *et al.* (2009) [eq. 4] is -least sensitive to the problem, but the most important parameter -for evaluating Curie depth. - -If we revisit the problem, however, we see that beta and C mostly -vary at long wavelengths, thus if we determine what their average -value is over the whole field then we can fix them as constants. -Our strategy is now a two-stage inversion method. - -**First pass** - -Ensure there is no *a priori* information and commence with -suitable starting values. - -**Second pass** - -Take the mean and standard deviation of all parameters and add them -as priors within the misfit function, then run the optimisation again. - -beta, C, and z_t have the lowest standard deviation therefore the -effect of perturbing these greatly increases the misfit compared to dz. -""" - -filedir = '/mnt/ben_raid/' - -try: - with np.load(filedir+'EMAG2_V3_20170530.npz') as f: - mag_data = f['data'] -except: - mag_data = np.loadtxt(filedir+'EMAG2_V3_20170530.csv', delimiter=',', usecols=(2,3,4,5,7)) - lon_mask = mag_data[:,0] > 180.0 - mag_data[lon_mask,0] -= 360.0 - np.savez_compressed(filedir+'EMAG2_V3_20170530.npz', data=mag_data.astype(np.float32)) - - -# filter NaNs -mag_data = mag_data[mag_data[:,3] != 99999.] -mag_data = mag_data[mag_data[:,4] != -888.] -mag_data = mag_data[mag_data[:,4] != -999.] - -# print min/max -mincols = mag_data.min(axis=0) -maxcols = mag_data.max(axis=0) - -fmt = "min/max {:.2f} -> {:.2f}" -for col in xrange(mag_data.shape[1]): - print(fmt.format(mincols[col], maxcols[col])) - - -# In[7]: - - -xmin = 250000.0 -xmax = 1400000.0 -ymin = 200000.0 -ymax = 1500000.0 -extent = [xmin, xmax, ymin, ymax] - -dx, dy = 1e3, 1e3 # 1km resolution -nx, ny = int(round((xmax-xmin)/dx)), int(round((ymax-ymin)/dy)) - -# also get WGS84 extent -tlon, tlat = pycurious.transform_coordinates([xmin,xmin,xmax,xmax], [ymin,ymax,ymin,ymax], 2157, 4326) -lonmin, lonmax = min(tlon), max(tlon) -latmin, latmax = min(tlat), max(tlat) -extent_sphere = [lonmin, lonmax, latmin, latmax] - -# grid data -mag_grid = pycurious.grid(mag_data[:,:2], mag_data[:,3], extent, shape=(ny,nx), epsg_in=4326, epsg_out=2157) -mag_sphere = pycurious.grid(mag_data[:,:2], mag_data[:,3], extent_sphere, shape=(ny,nx), epsg_in=4326, epsg_out=4326) - - - -# initialise CurieOptimise object -max_window = 150e3 - -cpd = pycurious.CurieParallel(mag_grid, xmin, xmax, ymin, ymax, max_window) - -comm = cpd.comm -rank = comm.rank - - - -xc_list, yc_list = cpd.create_centroid_list(max_window, spacingX=4e3, spacingY=4e3) - -print("{} number of centroids = {}".format(rank, len(xc_list))) - - - - -cpd.reset_priors() -betaN, ztN, dzN, CN = cpd.optimise_routine(max_window, xc_list, yc_list, 3.0, 1.0, 20.0, 5.0) - - - - -xc = np.unique(xc_list) -yc = np.unique(yc_list) - -nr, nc = yc.size, xc.size - - - -# these parameters did well based on previous experience... -beta_mu, beta_std = np.mean(betaN), np.std(betaN) -zt_mu, zt_std = np.mean(ztN), np.std(ztN) -dz_mu, dz_std = np.mean(dzN), np.std(dzN) -C_mu, C_std = np.mean(CN), np.std(CN) - -cpd.reset_priors() -cpd.distribute_prior('mean', beta=(beta_mu, beta_std), zt=(zt_mu, zt_std), dz=(dz_mu, dz_std)) - - -for p in ['beta', 'zt', 'dz', 'C']: - prior = cpd.prior[p] - if type(prior) != type(None): - mu, sigma = prior # local - else: - mu, sigma = -1, -1 - print("{:3d} prior {:5} mean={:.2f} std={:.2f}".format(rank, p, mu, sigma)) - - -betaOpt, ztOpt, dzOpt, COpt = cpd.optimise_routine(max_window, xc_list, yc_list) - - - -# Write to file -lonc, latc = pycurious.transform_coordinates(xc_list, yc_list, epsg_in=2157, epsg_out=4326) - -out = np.column_stack([lonc, latc, betaOpt, ztOpt, dzOpt, COpt]) -np.savetxt('{}-british_isles_cpd.csv'.format(rank), out,\ - fmt='%.6f', delimiter=',', header='lon, lat, beta, zt, dz, C') - diff --git a/Examples/british_isles_parallel_sensitivity.py b/Examples/british_isles_parallel_sensitivity.py deleted file mode 100644 index 008e6ef..0000000 --- a/Examples/british_isles_parallel_sensitivity.py +++ /dev/null @@ -1,209 +0,0 @@ -# coding: utf-8 - -""" -**EMAG2_V3_20170530.csv** - -- Column 1: i ; grid column/longitude index -- Column 2: j ; grid row/latitude index -- Column 3: LON ; Geographic Longitude WGS84 (decimal degrees) -- Column 4: LAT ; Geographic Latitude WGS84 (decimal degrees) -- Column 5: SeaLevel ; Magnetic Anomaly Value at Sea Level(nT) -- Column 6: UpCont ; Magnetic Anomaly Value at continuous 4km altitude (nT) -- Column 7: Code ; Data Source Code (see table below) -- Column 8: Error ; Error estimate (nT) - -Code 888 is assigned in certain cells on grid edges where the data source is ambiguous and assigned an error of -888 nT - -Code 999 is assigned in cells where no data is reported with the anomaly value assigned 99999 nT and an error of -999 nT - - - -## Optimise - -We have 4 parameters we wish to optimise: -- beta : fractal parameter -- z_t : the top of magnetic sources -- dz : the thickness of magnetic sources -- C : a field constant - -We minimise this using `scipy.optimize.minimize` which defaults -to `L-BFGS-B` for constrained minimisation. - - -### Optimisation strategy - -The problem is that $dz$ in Bouligand *et al.* (2009) [eq. 4] is -least sensitive to the problem, but the most important parameter -for evaluating Curie depth. - -If we revisit the problem, however, we see that beta and C mostly -vary at long wavelengths, thus if we determine what their average -value is over the whole field then we can fix them as constants. -Our strategy is now a two-stage inversion method. - -**First pass** - -Ensure there is no *a priori* information and commence with -suitable starting values. - -**Second pass** - -Take the mean and standard deviation of all parameters and add them -as priors within the misfit function, then run the optimisation again. - -beta, C, and z_t have the lowest standard deviation therefore the -effect of perturbing these greatly increases the misfit compared to dz. -""" - -import numpy as np -import matplotlib.pyplot as plt -import pycurious - -from mpi4py import MPI -comm = MPI.COMM_WORLD -rank = comm.rank - - - -filedir = '/mnt/ben_raid/' -outputdir = filedir + 'pycurious-examples/' - -try: - with np.load(filedir+'EMAG2_V3_20170530.npz') as f: - mag_data = f['data'] -except: - mag_data = np.loadtxt(filedir+'EMAG2_V3_20170530.csv', delimiter=',', usecols=(2,3,4,5,7)) - lon_mask = mag_data[:,0] > 180.0 - mag_data[lon_mask,0] -= 360.0 - np.savez_compressed(filedir+'EMAG2_V3_20170530.npz', data=mag_data.astype(np.float32)) - - -# filter NaNs -mag_data = mag_data[mag_data[:,3] != 99999.] -mag_data = mag_data[mag_data[:,4] != -888.] -mag_data = mag_data[mag_data[:,4] != -999.] - -# print min/max -mincols = mag_data.min(axis=0) -maxcols = mag_data.max(axis=0) - - -if rank == 0: - fmt = "min/max {:.2f} -> {:.2f}" - for col in xrange(mag_data.shape[1]): - print(fmt.format(mincols[col], maxcols[col])) - - - - - -xmin = 200000.0 -xmax = 1450000.0 -ymin = 150000.0 -ymax = 1550000.0 -extent = [xmin, xmax, ymin, ymax] - -dx, dy = 1e3, 1e3 # 1km resolution -nx, ny = int(round((xmax-xmin)/dx)), int(round((ymax-ymin)/dy)) - - -# grid data -mag_grid = pycurious.grid(mag_data[:,:2], mag_data[:,3], extent, shape=(ny,nx), epsg_in=4326, epsg_out=2157) - - - -# initialise CurieOptimise object -max_window = 200e3 - -cpd = pycurious.CurieParallel(mag_grid, xmin, xmax, ymin, ymax, max_window) - -print("{:3d} old shape {} new shape {}".format(rank, mag_grid.shape, cpd.data.shape)) -print("{:3d} old extent {}".format(rank, (xmin, xmax, ymin, ymax))) -print("{:3d} new extent {}".format(rank, (cpd.xmin, cpd.xmax, cpd.ymin, cpd.ymax))) - - - -xc_list, yc_list = cpd.create_centroid_list(max_window, spacingX=10e3, spacingY=10e3) -print("{} number of centroids = {}".format(rank, len(xc_list))) - - - - -# first pass - no priors -betaN, ztN, dzN, CN = cpd.optimise_routine(max_window, xc_list, yc_list, taper=np.hanning) - - - -xc = np.unique(xc_list) -yc = np.unique(yc_list) - -nr, nc = yc.size, xc.size - - -# these parameters did well based on previous experience... -# cpd.add_prior(beta=(5.44,0.62), zt=(0.14,0.28), dz=(22.73,29.63), C=(11.88,1.38)) - -beta_mu, beta_std = np.mean(betaN), np.std(betaN) -zt_mu, zt_std = np.mean(ztN), np.std(ztN) -dz_mu, dz_std = np.mean(dzN), np.std(dzN) -C_mu, C_std = np.mean(CN), np.std(CN) - -cpd.reset_priors() -cpd.distribute_prior('mean', beta=(beta_mu, beta_std), zt=(zt_mu, zt_std), dz=(20.0, 80.), C=(C_mu,C_std)) - -beta_mu, beta_std = cpd.prior['beta'] -zt_mu, zt_std = cpd.prior['zt'] -dz_mu, dz_std = cpd.prior['dz'] -C_mu, C_std = cpd.prior['C'] - -for p in ['beta', 'zt', 'dz', 'C']: - prior = cpd.prior[p] - if type(prior) != type(None): - mu, sigma = prior # local - else: - mu, sigma = None, None - print("{:3d} prior {:5} mean={:.2f} std={:.2f}".format(rank, p, mu, sigma)) - - - -lonc, latc = pycurious.transform_coordinates(xc_list, yc_list, epsg_in=2157, epsg_out=4326) -posterior = np.empty((lonc.size, 6)) -posterior[:,0] = lonc -posterior[:,1] = latc - -# second pass - with distributed priors -nsim = 1000 - -prior = np.zeros((nsim,4)) -prior[:,0] = np.random.normal(beta_mu, beta_std, nsim) -prior[:,1] = np.random.normal(zt_mu, zt_std, nsim) -prior[:,2] = np.random.normal(dz_mu, dz_std, nsim) -prior[:,3] = np.random.normal(C_mu, C_std, nsim) - -# prior will be identical across all processors -comm.Bcast([prior, MPI.DOUBLE], root=0) - -if rank == 0: - np.savetxt(outputdir+'british_isles_cpd_sx.csv', prior, fmt='%.6f', delimiter=',', header='beta, zt, dz, C') - - -for i in xrange(0, nsim): - # random priors from root processor - beta, zt, dz, C = prior[i] - cpd.reset_priors() - cpd.add_prior(beta=(beta,beta_std), zt=(zt,zt_std), dz=(dz,dz_std)) - - betaOpt, ztOpt, dzOpt, COpt = cpd.optimise_routine(max_window, xc_list, yc_list, taper=np.hanning) - - - # Write to file - posterior[:,2] = betaOpt - posterior[:,3] = ztOpt - posterior[:,4] = dzOpt - posterior[:,5] = COpt - np.savetxt(outputdir+'{:03d}-british_isles_cpd_s{:06d}.csv'.format(rank, i), posterior,\ - fmt='%.6f', delimiter=',', header='lon, lat, beta, zt, dz, C') - - if i % 10 == 0 and i > 0: - print("{:3d} {:3d}/{} simulations complete".format(rank, i, nsim)) - diff --git a/Examples/british_isles_parallel_windows.py b/Examples/british_isles_parallel_windows.py deleted file mode 100644 index 2f1e6f4..0000000 --- a/Examples/british_isles_parallel_windows.py +++ /dev/null @@ -1,169 +0,0 @@ -# coding: utf-8 - -import numpy as np -import matplotlib.pyplot as plt -import pycurious - -from mpi4py import MPI -comm = MPI.COMM_WORLD -rank = comm.rank - -""" -**EMAG2_V3_20170530.csv** - -- Column 1: i ; grid column/longitude index -- Column 2: j ; grid row/latitude index -- Column 3: LON ; Geographic Longitude WGS84 (decimal degrees) -- Column 4: LAT ; Geographic Latitude WGS84 (decimal degrees) -- Column 5: SeaLevel ; Magnetic Anomaly Value at Sea Level(nT) -- Column 6: UpCont ; Magnetic Anomaly Value at continuous 4km altitude (nT) -- Column 7: Code ; Data Source Code (see table below) -- Column 8: Error ; Error estimate (nT) - -Code 888 is assigned in certain cells on grid edges where the data source is ambiguous and assigned an error of -888 nT - -Code 999 is assigned in cells where no data is reported with the anomaly value assigned 99999 nT and an error of -999 nT - -## Optimise - -We have 4 parameters we wish to optimise: -- beta : fractal parameter -- z_t : the top of magnetic sources -- dz : the thickness of magnetic sources -- C : a field constant - -We minimise this using `scipy.optimize.minimize` which defaults -to `L-BFGS-B` for constrained minimisation. - - -### Optimisation strategy - -The problem is that $dz$ in Bouligand *et al.* (2009) [eq. 4] is -least sensitive to the problem, but the most important parameter -for evaluating Curie depth. - -If we revisit the problem, however, we see that beta and C mostly -vary at long wavelengths, thus if we determine what their average -value is over the whole field then we can fix them as constants. -Our strategy is now a two-stage inversion method. - -**First pass** - -Ensure there is no *a priori* information and commence with -suitable starting values. - -**Second pass** - -Take the mean and standard deviation of all parameters and add them -as priors within the misfit function, then run the optimisation again. - -beta, C, and z_t have the lowest standard deviation therefore the -effect of perturbing these greatly increases the misfit compared to dz. -""" - -filedir = '/mnt/ben_raid/' - -try: - with np.load(filedir+'EMAG2_V3_20170530.npz') as f: - mag_data = f['data'] -except: - mag_data = np.loadtxt(filedir+'EMAG2_V3_20170530.csv', delimiter=',', usecols=(2,3,4,5,7)) - lon_mask = mag_data[:,0] > 180.0 - mag_data[lon_mask,0] -= 360.0 - np.savez_compressed(filedir+'EMAG2_V3_20170530.npz', data=mag_data.astype(np.float32)) - - -# filter NaNs -mag_data = mag_data[mag_data[:,3] != 99999.] -mag_data = mag_data[mag_data[:,4] != -888.] -mag_data = mag_data[mag_data[:,4] != -999.] - -# print min/max -mincols = mag_data.min(axis=0) -maxcols = mag_data.max(axis=0) - -fmt = "min/max {:.2f} -> {:.2f}" -if rank == 0: - for col in xrange(mag_data.shape[1]): - print(fmt.format(mincols[col], maxcols[col])) - - -# In[7]: - - -xmin = 250000.0 -xmax = 1400000.0 -ymin = 200000.0 -ymax = 1500000.0 -extent = [xmin, xmax, ymin, ymax] - -dx, dy = 1e3, 1e3 # 1km resolution -nx, ny = int(round((xmax-xmin)/dx)), int(round((ymax-ymin)/dy)) - -# also get WGS84 extent -tlon, tlat = pycurious.transform_coordinates([xmin,xmin,xmax,xmax], [ymin,ymax,ymin,ymax], 2157, 4326) -lonmin, lonmax = min(tlon), max(tlon) -latmin, latmax = min(tlat), max(tlat) -extent_sphere = [lonmin, lonmax, latmin, latmax] - -# grid data -mag_grid = pycurious.grid(mag_data[:,:2], mag_data[:,3], extent, shape=(ny,nx), epsg_in=4326, epsg_out=2157) -mag_sphere = pycurious.grid(mag_data[:,:2], mag_data[:,3], extent_sphere, shape=(ny,nx), epsg_in=4326, epsg_out=4326) - - - - - -# 2 arc minutes is approximately 4km -max_window = 350e3 -window_sizes = np.arange(100e3, max_window+50e3, 50e3) - - - -# first pass -# use the largest window size first to determine priors -window = window_sizes[-1] -cpd = pycurious.CurieParallel(mag_grid, xmin, xmax, ymin, ymax, window) -xc_list, yc_list = cpd.create_centroid_list(window, spacingX=10e3, spacingY=10e3) - - -betaN, ztN, dzN, CN = cpd.optimise_routine(window, xc_list, yc_list) - - -beta_mu, beta_std = np.mean(betaN), np.std(betaN) -zt_mu, zt_std = np.mean(ztN), np.std(ztN) -dz_mu, dz_std = np.mean(dzN), np.std(dzN) -C_mu, C_std = np.mean(CN), np.std(CN) - -cpd.reset_priors() -cpd.distribute_prior('mean', beta=(beta_mu, beta_std), zt=(zt_mu, zt_std), dz=(dz_mu, dz_std)) - - -for p in ['beta', 'zt', 'dz', 'C']: - prior = cpd.prior[p] - if type(prior) != type(None): - mu, sigma = prior # local - else: - mu, sigma = -1, -1 - print("{:3d} prior {:5} mean={:.2f} std={:.2f}".format(rank, p, mu, sigma)) - - - -# now priors will remain idential for all iterations -prior_dict = cpd.prior.copy() - -for window in window_sizes: - cpd = pycurious.CurieParallel(mag_grid, xmin, xmax, ymin, ymax, window) - cpd.prior = prior_dict - xc_list, yc_list = cpd.create_centroid_list(window, spacingX=4e3, spacingY=4e3) - print("{} window {:.1f} km, number of centroids = {}".format(rank, window/1e3, len(xc_list))) - - # second pass - betaOpt, ztOpt, dzOpt, COpt = cpd.optimise_routine(window, xc_list, yc_list) - - # Write to file - lonc, latc = pycurious.transform_coordinates(xc_list, yc_list, epsg_in=2157, epsg_out=4326) - out = np.column_stack([lonc, latc, betaOpt, ztOpt, dzOpt, COpt]) - np.savetxt('{}-british_isles_cpd_w{:06d}.csv'.format(rank, int(window/1e3)),\ - out, fmt='%.6f', delimiter=',', header='lon, lat, beta, zt, dz, C') - diff --git a/Examples/data/test_mag_data.txt b/Examples/data/test_mag_data.txt index 7f59a38..74c6097 100644 --- a/Examples/data/test_mag_data.txt +++ b/Examples/data/test_mag_data.txt @@ -1,93025 +1,93025 @@ -500.0 500.0 1.3829045815427966e-06 -500.0 1500.0 6.693675365186451e-07 -500.0 2500.0 6.659168246921286e-08 -500.0 3500.0 1.2567450678564302e-07 -500.0 4500.0 -2.7969574835422622e-08 -500.0 5500.0 5.8778198526398064e-08 -500.0 6500.0 1.389643281153164e-07 -500.0 7500.0 -4.343069444729531e-08 -500.0 8500.0 -3.922112066123098e-07 -500.0 9500.0 -1.049528502859961e-06 -500.0 10500.0 -1.481528577491253e-06 -500.0 11500.0 -1.3624871681887457e-06 -500.0 12500.0 -9.899344421816306e-07 -500.0 13500.0 -1.2298439748459228e-06 -500.0 14500.0 -1.7897975695072113e-06 -500.0 15500.0 -2.04795736747785e-06 -500.0 16500.0 -1.9008943947343503e-06 -500.0 17500.0 -1.292244935993277e-06 -500.0 18500.0 6.78236271117347e-08 -500.0 19500.0 1.008847387018908e-06 -500.0 20500.0 2.256432496885301e-06 -500.0 21500.0 2.564274394885848e-06 -500.0 22500.0 1.4342554286866581e-06 -500.0 23500.0 -3.798722136390692e-08 -500.0 24500.0 -1.3561718661133947e-06 -500.0 25500.0 -1.0571452221172988e-06 -500.0 26500.0 -7.585133329319716e-08 -500.0 27500.0 9.475731395728881e-07 -500.0 28500.0 2.15130993579387e-06 -500.0 29500.0 2.6716555560271846e-06 -500.0 30500.0 2.8681840707195413e-06 -500.0 31500.0 2.5580101171189803e-06 -500.0 32500.0 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a/pycurious/curie.py b/pycurious/curie.py index 0b155c2..cbe9de0 100644 --- a/pycurious/curie.py +++ b/pycurious/curie.py @@ -522,7 +522,7 @@ def bouligand2009(kh, beta, zt, dz, C): return Phi1d -def tanaka1999(S, k, sigma2, kmin_range=(0.05, 0.2), kmax_range=(0.05, 0.2)): +def tanaka1999(k, Phi, sigma_Phi, kmin_range=(0.05, 0.2), kmax_range=(0.05, 0.2)): """ Compute weighted linear fit of S over spatial frequency window kmin:kmax @@ -540,6 +540,10 @@ def tanaka1999(S, k, sigma2, kmin_range=(0.05, 0.2), kmax_range=(0.05, 0.2)): : No geothermal gradient, trivial to estimate. : Possible to extend, return fitted components? """ + # for now... + S = Phi + sigma2 = sigma_Phi**2 + def compute_coefficients(X, Y, E): X2 = X**2 Y2 = Y**2 diff --git a/pycurious/optimise.py b/pycurious/optimise.py index ace5e2b..8c41f37 100644 --- a/pycurious/optimise.py +++ b/pycurious/optimise.py @@ -244,25 +244,20 @@ def optimise_routine(self, window, xc_list, yc_list, beta=3.0, zt=1.0, dz=10.0, raise ValueError("xc_list and yc_list must be the same size") - # storage vectors - Bopt = np.empty(n) - ztopt = np.empty(n) - dzopt = np.empty(n) - Copt = np.empty(n) + # storage vector + xOpt = np.empty((n, 4)) for i in range(0, n): xc = xc_list[i] yc = yc_list[i] - Bopt[i], ztopt[i], dzopt[i], Copt[i] = self.optimise(window, xc, yc,\ - beta, zt, dz, C,\ - taper, process_subgrid,\ - **kwargs) + xOpt[i] = self.optimise(window, xc, yc, beta, zt, dz, C,\ + taper, process_subgrid, **kwargs) - return Bopt, ztopt, dzopt, Copt + return list(xOpt.T) - def metropolis_hastings(self, nsim, window, xc, yc, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs): + def metropolis_hastings(self, window, xc, yc, nsim, burnin, x_scale=None, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs): """ MCMC algorithm using a Metropolis-Hastings sampler. @@ -294,6 +289,14 @@ def metropolis_hastings(self, nsim, window, xc, yc, beta=3.0, zt=1.0, dz=10.0, C def process_subgrid(subgrid): return subgrid + + samples = np.empty((nsim, 4)) + x0 = np.array([beta, zt, dz, C]) + + if type(x_scale) == type(None): + x_scale = np.ones(4) + + # get subgrid subgrid = self.subgrid(window, xc, yc) subgrid = process_subgrid(subgrid) @@ -302,16 +305,29 @@ def process_subgrid(subgrid): k, Phi, sigma_Phi = self.radial_spectrum(subgrid, taper=taper, **kwargs) - samples = np.empty((nsim, 4)) - x0 = np.array([beta, zt, dz, C]) + # Burn-in phase + for i in range(burnin): + # add random perturbation + x1 = x0 + np.random.normal(size=4)*x_scale + + # evaluate probability + tempering + P0 = np.exp(-self.min_func(x0, k, Phi, sigma_Phi)/1000) + P1 = np.exp(-self.min_func(x1, k, Phi, sigma_Phi)/1000) + + # iterate towards MAP estimate + if P1 > P0: + x0 = x1 + + # Now sample posterior for i in range(nsim): # add random perturbation - x1 = x0 + np.random.normal(size=4) + x1 = x0 + np.random.normal(size=4)*x_scale # evaluate probability P0 = np.exp(-self.min_func(x0, k, Phi, sigma_Phi)) P1 = np.exp(-self.min_func(x1, k, Phi, sigma_Phi)) + P0 = max(P0, 1e-99) P = min(P1/P0, 1.0) @@ -321,86 +337,11 @@ def process_subgrid(subgrid): samples[i] = x0 - return samples - + return list(samples.T) - def metropolis_hastings2(self, nsim, window, xc_list, yc_list, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs): - """ - MCMC algorithm using a Metropolis-Hastings sampler. - Evaluates a Markov-Chain for starting values of beta, zt, dz, C - and returns the ensemble of model realisations. - - WARNING: Use starting values relatively close to the solution - - C can easily found from the mean of the radial power spectrum - - Parameters - ---------- - window : float - size of window in metres - xc : float - centroid x values - yc : float - centroid y values - beta : float - fractal parameter (starting value) - zt : float - top of magnetic layer (starting value) - dz : float - thickness of magnetic layer (starting value) - C : float - field constant (starting value) - Returns - ------- - beta : ndarray shape(nsim,) - fractal parameters - zt : ndarray shape(nsim,) - top of magnetic layer - dz : ndarray shape(nsim,) - thickness of magnetic layer - C : ndarray shape(nsim,) - field constant - """ - if type(process_subgrid) == type(None): - # dummy function - def process_subgrid(subgrid): - return subgrid - - n = len(xc_list) - - if n != len(yc_list): - raise ValueError("xc_list and yc_list must be the same size") - - rbeta = np.random.uniform(0, 10, size=nsim) - samples = np.empty((n, nsim, 4)) - misfit = np.empty(n) - - for i in range(n): - xc = xc_list[i] - yc = yc_list[i] - - # get subgrid - subgrid = self.subgrid(xc, yc, window) - subgrid = process_subgrid(subgrid) - - # compute radial spectrum - S, k, sigma2 = self.radial_spectrum(subgrid, taper=taper, **kwargs) - - x0 = np.array([rbeta[0], 0.0, 20.0, S.mean()]) - - - for j in range(nsim): - # add random perturbation - x1 = x0 + np.random.normal(size=4) - x1[0] = rbeta[j] - - # evaluate probability - P0 = np.exp(-self.min_func(x0, S, k)) - P1 = np.exp(-self.min_func(x1, S, k)) - - P = min(P1/P0, 1.0) - - # randomly accept probability - if np.random.rand() <= P: - x0 = x1 - - samples[i,j] = x0 - # misfit[] - - return samples - - - def sensitivity_routine(self, nsim, window, xc_list, yc_list, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs): + def sensitivity(self, window, xc, yc, nsim, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs): """ Iterate through a list of centroids to compute the mean and standard deviation of beta, zt, dz, C by perturbing their @@ -423,57 +364,39 @@ def sensitivity_routine(self, nsim, window, xc_list, yc_list, beta=3.0, zt=1.0, zt : ndarray shape(l,2) - top of magnetic layer (mean, stdev) dz : ndarray shape(l,2) - thickness of magnetic layer (mean, stdev) C : ndarray shape(l,2) - field constant (mean, stdev) - """ - - n = len(xc_list) - - if n != len(yc_list): - raise ValueError("xc_list and yc_list must be the same size") - - - # storage vectors for centroids (mean, std) - Bopt = np.empty((n,2)) - ztopt = np.empty((n,2)) - dzopt = np.empty((n,2)) - Copt = np.empty((n,2)) - - # storage vectors for nsim - Bsim = np.empty(nsim) - ztsim = np.empty(nsim) - dzsim = np.empty(nsim) - Csim = np.empty(nsim) + if type(process_subgrid) == type(None): + # dummy function + def process_subgrid(subgrid): + return subgrid + samples = np.empty((nsim, 4)) + x0 = np.array([beta, zt, dz, C]) + use_keys = [] for key in self.prior_pdf: prior_pdf = self.prior_pdf[key] if prior_pdf is not None: use_keys.append(key) + + # get subgrid + subgrid = self.subgrid(window, xc, yc) + subgrid = process_subgrid(subgrid) + # compute radial spectrum + k, Phi, sigma_Phi = self.radial_spectrum(subgrid, taper=taper, **kwargs) - for i in range(0, n): - xc = xc_list[i] - yc = yc_list[i] - - for sim in range(0, nsim): - - # randomly generate new prior values within PDF - for key in use_keys: - prior_pdf = self.prior_pdf[key] - self.prior[key][0] = prior_pdf.rvs() - - - # run the optimisation routine - Bsim[sim], ztsim[sim], dzsim[sim], Csim[sim] = self.optimise(window, xc, yc,\ - beta=beta, zt=zt, dz=dz, C=C,\ - taper=np.hanning, process_subgrid=None, **kwargs) + for sim in range(0, nsim): + # randomly generate new prior values within PDF + for key in use_keys: + prior_pdf = self.prior_pdf[key] + self.prior[key][0] = prior_pdf.rvs() - # store mean, stdev pairs - Bopt[i] = np.mean(Bsim), np.std(Bsim) - ztopt[i] = np.mean(ztsim), np.std(ztsim) - dzopt[i] = np.mean(dzsim), np.std(dzsim) - Copt[i] = np.mean(Csim), np.std(Csim) + # minimise function + rPhi = np.random.normal(Phi, sigma_Phi) + res = minimize(self.min_func, x0, args=(k, rPhi, sigma_Phi), bounds=self.bounds) + samples[sim] = res.x # restore priors @@ -481,4 +404,4 @@ def sensitivity_routine(self, nsim, window, xc_list, yc_list, beta=3.0, zt=1.0, prior_pdf = self.prior_pdf[key] self.prior[key] = list(prior_pdf.args) - return Bopt, ztopt, dzopt, Copt + return yc_list(samples.T) From 4d7446811a13dbed6b553181ceeea43eecf5e3b4 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Tue, 28 Aug 2018 18:19:43 +0100 Subject: [PATCH 026/170] Forgot Ex1 from Tanaka --- .../Tanaka/Ex1-Plot-power-spectrum.ipynb | 221 ++++++++++++++++++ 1 file changed, 221 insertions(+) create mode 100644 Examples/Notebooks/Tanaka/Ex1-Plot-power-spectrum.ipynb diff --git a/Examples/Notebooks/Tanaka/Ex1-Plot-power-spectrum.ipynb b/Examples/Notebooks/Tanaka/Ex1-Plot-power-spectrum.ipynb new file mode 100644 index 0000000..976bdb1 --- /dev/null +++ b/Examples/Notebooks/Tanaka/Ex1-Plot-power-spectrum.ipynb @@ -0,0 +1,221 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Example 1 - Plot power spectra\n", + "\n", + "`PyCurious` offers convenience functions to extract the radial power spectrum. This has been covered in the Bouligand folder of jupyter notebooks and is largely duplicated here.\n", + "\n", + "In this notebook we plot the radial power spectrum using the analytical expression, and the spectrum computed from a synthetic magnetic anomaly. (This can be generated from `Bouligand_forward.py` in the `tests` directory.)\n", + "\n", + "### Contents\n", + "\n", + "- [Radial power spectrum](#Power-spectrum-from-FFT)\n", + "- [Azimuthal power spectrum](#Azimuthal-power-spectrum)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "\n", + "import pycurious" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Radial power spectrum\n", + "\n", + "The radial power spectrum is computed from a square window of the magnetic anomaly. Methods to select window sizes and compute the Fast Fourier Transform (FFT) belong to the `CurieGrid` object.\n", + "\n", + "`CurieGrid` achieves the following purposes:\n", + "\n", + "- Upward continuation\n", + "- Reduction to the pole\n", + "- Compute the radial power spectrum using FFT\n", + "\n", + "The shape of the radial power spectrum is heavily dependent on window size. Resolution of long wavelength features require large windows.\n", + "\n", + "> Suggestion: use a window size **> 4 times** the maximum Curie depth.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# load magnetic anomaly - i.e. random fractal noise\n", + "mag_data = np.loadtxt(\"../../data/test_mag_data.txt\")\n", + "\n", + "nx, ny = 305, 305\n", + "\n", + "x = mag_data[:,0]\n", + "y = mag_data[:,1]\n", + "d = mag_data[:,2].reshape(ny,nx)\n", + "\n", + "xmin, xmax = x.min(), x.max()\n", + "ymin, ymax = y.min(), y.max()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "## Plot random fractal noise\n", + "\n", + "fig = plt.figure()\n", + "ax1 = fig.add_subplot(111)\n", + "im1 = ax1.imshow(d)\n", + "fig.colorbar(im1, label='nT')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# initialise CurieGrid object\n", + "grid = pycurious.CurieGrid(d, xmin, xmax, ymin, ymax)\n", + "\n", + "# pick the centroid\n", + "xpt = 0.5*(xmin + xmax)\n", + "ypt = 0.5*(ymin + ymax)\n", + "\n", + "window_size = 304e3\n", + "subgrid = grid.subgrid(window_size, xpt, ypt)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# compute radial power spectrum\n", + "k, Phi, sigma_Phi = grid.radial_spectrum(subgrid)\n", + "\n", + "# plot radial power spectrum\n", + "fig = plt.figure()\n", + "ax1 = fig.add_subplot(111, xlabel=\"wavenumber (rad/km)\", ylabel=\"radial power spectrum\")\n", + "ax1.plot(k, Phi, '-o')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Choice of taper**\n", + "\n", + "The default taper is the hanning filter (see [`numpy.hanning`](#hanning) for more details), but other functions can be passed to taper, or simply set it to `None`. There is a significant offset in the power spectrum with tapering functions, however, it is the *slope* of the spectrum with wavenumber that is most important when it comes to determining Curie depth." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "k1, Phi1, sigma_Phi2 = grid.radial_spectrum(subgrid, taper=None)\n", + "k2, Phi2, sigma_Phi2 = grid.radial_spectrum(subgrid, taper=np.hanning)\n", + "k3, Phi3, sigma_Phi2 = grid.radial_spectrum(subgrid, taper=np.hamming)\n", + "\n", + "\n", + "fig = plt.figure()\n", + "ax1 = fig.add_subplot(111, xlabel=\"wavenumber (rad/km)\", ylabel=\"radial power spectrum\")\n", + "ax1.plot(k1, Phi1, '-o', label='none')\n", + "ax1.plot(k2, Phi2, '-o', label='hanning')\n", + "ax1.plot(k3, Phi3, '-o', label='hamming')\n", + "ax1.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Azimuthal power spectrum\n", + "\n", + "The azimuthal spectrum computes the FFT on a square window that is polarised at a range of radii. This is useful to explore linear trends in the magnetic anomaly that may align with a particular foliation or strike orientation.\n", + "\n", + "```python\n", + "azimuthal_spectrum(subgrid, theta=5.0)\n", + "```\n", + "\n", + "`theta` controls the thickness of each azimuth (in degrees)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "k, Phi, theta = grid.azimuthal_spectrum(subgrid, theta=20.0)\n", + "\n", + "fig = plt.figure()\n", + "ax1 = fig.add_subplot(111, ylabel=r'azimuth $\\theta$', xlabel='wavenumber (rad/km)')\n", + "im1 = ax1.pcolor(k, theta, Phi)\n", + "fig.colorbar(im1, label='radial power spectrum')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plotting each azimuth on the power spectrum-wavenumber axis highlights the different in slope for different polarisations of the magnetic anomaly." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig = plt.figure()\n", + "ax1 = fig.add_subplot(111, xlabel=\"wavenumber (rad/km)\", ylabel=\"radial power spectrum\")\n", + "\n", + "for i, angle in enumerate(theta):\n", + " ax1.plot(k, Phi[i], label=r'$\\theta = {}^\\circ$'.format(angle))\n", + "\n", + "ax1.legend(bbox_to_anchor=(1,1))\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.15" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From fe5b6f94ee4975d0ec0e7d81810ba547d38b657a Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Tue, 28 Aug 2018 23:35:23 +0100 Subject: [PATCH 027/170] Directory restructuring Can also install documentation to another directory --- .gitignore | 4 ++- .../Ex1-Plot-power-spectrum-checkpoint.ipynb | 0 ...rie-depth-Tanaka-approach-checkpoint.ipynb | 0 ...-depth-Bouligand-approach-checkpoint.ipynb | 0 .../Ex3-Optimisation-routine-checkpoint.ipynb | 0 .../Bouligand/Ex1-Plot-power-spectrum.ipynb | 0 .../Bouligand/Ex2-Compute-Curie-depth.ipynb | 0 .../Ex3-Posing-the-inverse-problem.ipynb | 0 ...Ex4-Spatial-variation-of-Curie-depth.ipynb | 0 .../Ex5-Mapping-Curie-depth-EMAG2.ipynb | 0 .../Tanaka/Ex1-Plot-power-spectrum.ipynb | 0 .../Tanaka/Ex2-Compute-Curie-depth.ipynb | 0 .../Tanaka/Ex3-Parameter-exploration.ipynb | 0 .../Examples}/Scripts/BFwdTest.py | 0 .../Examples}/Scripts/CPD_Pts_find.sh | 0 .../Examples}/Scripts/IapetusCheck.py | 0 .../Examples}/Scripts/LinearFitScratch.py | 0 .../Examples}/Scripts/RobTest.py | 0 .../Examples}/Scripts/RosettePlot.sh | 0 .../Examples}/Scripts/mag_grid2.npz | Bin .../Examples}/Scripts/readme.txt | 0 .../Examples}/Scripts/tst_data.npz | Bin .../Examples}/data/test_mag_data.txt | 0 pycurious/__init__.py | 5 +-- pycurious/documentation.py | 34 ++++++++++++++++++ pycurious/grid/__init__.py | 2 ++ pycurious/{ => grid}/curie.py | 0 pycurious/mapping/__init__.py | 6 ++++ pycurious/{ => mapping}/mapping.py | 2 +- pycurious/optimise/__init__.py | 2 ++ pycurious/{ => optimise}/optimise.py | 2 +- pycurious/parallel/__init__.py | 2 ++ pycurious/{ => parallel}/parallel.py | 2 +- setup.py | 25 +++++++------ {pycurious => src}/cradon.c | 0 {pycurious => src}/cradon.h | 0 {pycurious => src}/cradon.pxd | 0 {pycurious => src}/radon.pyx | 0 38 files changed, 69 insertions(+), 17 deletions(-) rename {Examples => pycurious/Examples}/Notebooks/.ipynb_checkpoints/Ex1-Plot-power-spectrum-checkpoint.ipynb (100%) rename {Examples => pycurious/Examples}/Notebooks/.ipynb_checkpoints/Ex2a-Compute-Curie-depth-Tanaka-approach-checkpoint.ipynb (100%) rename {Examples => pycurious/Examples}/Notebooks/.ipynb_checkpoints/Ex2b-Compute-Curie-depth-Bouligand-approach-checkpoint.ipynb (100%) rename 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pycurious/{ => parallel}/parallel.py (99%) rename {pycurious => src}/cradon.c (100%) rename {pycurious => src}/cradon.h (100%) rename {pycurious => src}/cradon.pxd (100%) rename {pycurious => src}/radon.pyx (100%) diff --git a/.gitignore b/.gitignore index 483e19a..31b358a 100644 --- a/.gitignore +++ b/.gitignore @@ -1 +1,3 @@ -Examples/Notebooks/.ipynb_checkpoints/* +pycurious/Examples/Notebooks/Bouligand/.ipynb_checkpoints/* +pycurious/Examples/Notebooks/Tanaka/.ipynb_checkpoints/* +*.pyc diff --git a/Examples/Notebooks/.ipynb_checkpoints/Ex1-Plot-power-spectrum-checkpoint.ipynb b/pycurious/Examples/Notebooks/.ipynb_checkpoints/Ex1-Plot-power-spectrum-checkpoint.ipynb similarity index 100% rename from Examples/Notebooks/.ipynb_checkpoints/Ex1-Plot-power-spectrum-checkpoint.ipynb rename to pycurious/Examples/Notebooks/.ipynb_checkpoints/Ex1-Plot-power-spectrum-checkpoint.ipynb diff --git a/Examples/Notebooks/.ipynb_checkpoints/Ex2a-Compute-Curie-depth-Tanaka-approach-checkpoint.ipynb 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--git a/Examples/Scripts/BFwdTest.py b/pycurious/Examples/Scripts/BFwdTest.py similarity index 100% rename from Examples/Scripts/BFwdTest.py rename to pycurious/Examples/Scripts/BFwdTest.py diff --git a/Examples/Scripts/CPD_Pts_find.sh b/pycurious/Examples/Scripts/CPD_Pts_find.sh similarity index 100% rename from Examples/Scripts/CPD_Pts_find.sh rename to pycurious/Examples/Scripts/CPD_Pts_find.sh diff --git a/Examples/Scripts/IapetusCheck.py b/pycurious/Examples/Scripts/IapetusCheck.py similarity index 100% rename from Examples/Scripts/IapetusCheck.py rename to pycurious/Examples/Scripts/IapetusCheck.py diff --git a/Examples/Scripts/LinearFitScratch.py b/pycurious/Examples/Scripts/LinearFitScratch.py similarity index 100% rename from Examples/Scripts/LinearFitScratch.py rename to pycurious/Examples/Scripts/LinearFitScratch.py diff --git a/Examples/Scripts/RobTest.py b/pycurious/Examples/Scripts/RobTest.py similarity index 100% rename from Examples/Scripts/RobTest.py rename to pycurious/Examples/Scripts/RobTest.py diff --git a/Examples/Scripts/RosettePlot.sh b/pycurious/Examples/Scripts/RosettePlot.sh similarity index 100% rename from Examples/Scripts/RosettePlot.sh rename to pycurious/Examples/Scripts/RosettePlot.sh diff --git a/Examples/Scripts/mag_grid2.npz b/pycurious/Examples/Scripts/mag_grid2.npz similarity index 100% rename from Examples/Scripts/mag_grid2.npz rename to pycurious/Examples/Scripts/mag_grid2.npz diff --git a/Examples/Scripts/readme.txt b/pycurious/Examples/Scripts/readme.txt similarity index 100% rename from Examples/Scripts/readme.txt rename to pycurious/Examples/Scripts/readme.txt diff --git a/Examples/Scripts/tst_data.npz b/pycurious/Examples/Scripts/tst_data.npz similarity index 100% rename from Examples/Scripts/tst_data.npz rename to pycurious/Examples/Scripts/tst_data.npz diff --git a/Examples/data/test_mag_data.txt b/pycurious/Examples/data/test_mag_data.txt similarity index 100% rename from Examples/data/test_mag_data.txt rename to pycurious/Examples/data/test_mag_data.txt diff --git a/pycurious/__init__.py b/pycurious/__init__.py index 8710582..105b557 100644 --- a/pycurious/__init__.py +++ b/pycurious/__init__.py @@ -1,5 +1,6 @@ # -*- coding: utf-8 -*- -from .curie import CurieGrid, bouligand2009, tanaka1999, maus1995, ComputeTanaka +from .grid import CurieGrid, bouligand2009, tanaka1999, maus1995, ComputeTanaka from .optimise import CurieOptimise from .parallel import CurieParallel -from .mapping import * \ No newline at end of file +from . import mapping +from .documentation import install_documentation \ No newline at end of file diff --git a/pycurious/documentation.py b/pycurious/documentation.py new file mode 100644 index 0000000..5f1aa65 --- /dev/null +++ b/pycurious/documentation.py @@ -0,0 +1,34 @@ + +import pkg_resources as _pkg_resources +from distutils import dir_util as _dir_util +import os + + +def install_documentation(path="./PyCurious-Examples"): + """ + Install the examples for PyCurious in the given location. + + WARNING: If the path exists, the files will be written into the path + and will overwrite any existing files with which they collide. The default + path ("./PyCurious-Examples") is chosen to make collision less likely/problematic + + The documentation for PyCurious is in the form of jupyter notebooks. + + Some dependencies exist for the notebooks to be useful: + + - matplotlib: for some diagrams + - cartopy: for mapping and visualisation + - pyepsg: for converting between map projections + + PyCurious dependencies may be explicitly imported in the notebooks including: + + - numpy + - scipy + + """ + + Notebooks_Path = _pkg_resources.resource_filename("pycurious", os.path.join("Examples")) + + ct = _dir_util.copy_tree(Notebooks_Path, path, preserve_mode=1, preserve_times=1, preserve_symlinks=1, update=0, verbose=1, dry_run=0) + + return diff --git a/pycurious/grid/__init__.py b/pycurious/grid/__init__.py new file mode 100644 index 0000000..84bff0a --- /dev/null +++ b/pycurious/grid/__init__.py @@ -0,0 +1,2 @@ +# -*- coding: utf-8 -*- +from .curie import * \ No newline at end of file diff --git a/pycurious/curie.py b/pycurious/grid/curie.py similarity index 100% rename from pycurious/curie.py rename to pycurious/grid/curie.py diff --git a/pycurious/mapping/__init__.py b/pycurious/mapping/__init__.py new file mode 100644 index 0000000..fbd6bcd --- /dev/null +++ b/pycurious/mapping/__init__.py @@ -0,0 +1,6 @@ +# -*- coding: utf-8 -*- +from .mapping import transform_coordinates +from .mapping import convert_extent +from .mapping import trim +from .mapping import grid +from .mapping import import_geotiff \ No newline at end of file diff --git a/pycurious/mapping.py b/pycurious/mapping/mapping.py similarity index 99% rename from pycurious/mapping.py rename to pycurious/mapping/mapping.py index 6ade59a..1c2a31e 100644 --- a/pycurious/mapping.py +++ b/pycurious/mapping/mapping.py @@ -120,7 +120,7 @@ def grid(coords, data, extent, shape=None, epsg_in=None, epsg_out=None, **kwargs xtextent = [xtmin, xtmax, ytmin, ytmax] - # trim data - buffer = 1% + # trim data - buffer = 5% coords_trim, data_trim = trim(coords, data, xtextent, 0.05) diff --git a/pycurious/optimise/__init__.py b/pycurious/optimise/__init__.py new file mode 100644 index 0000000..833ac89 --- /dev/null +++ b/pycurious/optimise/__init__.py @@ -0,0 +1,2 @@ +# -*- coding: utf-8 -*- +from .optimise import * \ No newline at end of file diff --git a/pycurious/optimise.py b/pycurious/optimise/optimise.py similarity index 99% rename from pycurious/optimise.py rename to pycurious/optimise/optimise.py index 8c41f37..8539fd9 100644 --- a/pycurious/optimise.py +++ b/pycurious/optimise/optimise.py @@ -1,5 +1,5 @@ # -*- coding: utf-8 -*- -from .curie import * +from .. import CurieGrid, bouligand2009 import numpy as np from scipy.optimize import minimize from scipy.special import polygamma diff --git a/pycurious/parallel/__init__.py b/pycurious/parallel/__init__.py new file mode 100644 index 0000000..94ed2e5 --- /dev/null +++ b/pycurious/parallel/__init__.py @@ -0,0 +1,2 @@ +# -*- coding: utf-8 -*- +from .parallel import * \ No newline at end of file diff --git a/pycurious/parallel.py b/pycurious/parallel/parallel.py similarity index 99% rename from pycurious/parallel.py rename to pycurious/parallel/parallel.py index 5c4aa85..f902c2d 100644 --- a/pycurious/parallel.py +++ b/pycurious/parallel/parallel.py @@ -1,7 +1,7 @@ # -*- coding: utf-8 -*- import numpy as np import warnings -from .optimise import CurieOptimise +from ..optimise import CurieOptimise try: range=xrange except: pass diff --git a/setup.py b/setup.py index 754568c..3f3b8d2 100644 --- a/setup.py +++ b/setup.py @@ -7,8 +7,8 @@ from Cython.Build import cythonize ext = Extension(name = 'pycurious.radon', - sources = ['pycurious/radon.pyx','pycurious/cradon.c'], - include_dirs = [np.get_include(),'pycurious'], + sources = ['src/radon.pyx','src/cradon.c'], + include_dirs = [np.get_include(),'src'], library_dirs = ['pycurious'], extra_compile_args = ['-std=c99']) @@ -16,22 +16,25 @@ setup(name = 'pycurious', author = "Ben Mather", author_email = "brmather1@gmail.com", - url = "https://git.dias.ie/itherc/pycurious", + url = "https://github.com/brmather/pycurious", version = "0.1", description = "Python tool for computing the Curie depth from magnetic data", ext_modules = cythonize([ext]), - packages = ['pycurious'], + packages = ['pycurious', + 'pycurious.grid', + 'pycurious.optimise', + 'pycurious.mapping', + 'pycurious.parallel'], + package_data = {'pycurious': ['Examples/data/*', + 'Examples/Notebooks/Tanaka/*.ipynb', + 'Examples/Notebooks/Bouligand/*.ipynb', + 'Examples/Scripts/*.py']}, classifiers = ['Programming Language :: Python :: 2', - 'Programming Language :: Python :: 2.6', 'Programming Language :: Python :: 2.7', 'Programming Language :: Python :: 3', 'Programming Language :: Python :: 3.3', 'Programming Language :: Python :: 3.4', 'Programming Language :: Python :: 3.5', - 'Programming Language :: Python :: 3.6'] + 'Programming Language :: Python :: 3.6', + 'Programming Language :: Python :: 3.7'] ) - -# setup( -# name = 'radon', -# ext_modules = cythonize(extensions), -# ) diff --git a/pycurious/cradon.c b/src/cradon.c similarity index 100% rename from pycurious/cradon.c rename to src/cradon.c diff --git a/pycurious/cradon.h b/src/cradon.h similarity index 100% rename from pycurious/cradon.h rename to src/cradon.h diff --git a/pycurious/cradon.pxd b/src/cradon.pxd similarity index 100% rename from pycurious/cradon.pxd rename to src/cradon.pxd diff --git a/pycurious/radon.pyx b/src/radon.pyx similarity index 100% rename from pycurious/radon.pyx rename to src/radon.pyx From b0b888130d9e2b080e0f4d93dee97a9ce98860d2 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Wed, 29 Aug 2018 12:12:35 +0100 Subject: [PATCH 028/170] Added the GNU Lesser General Public License --- COPYING | 675 +++++++++++++++++++++++++++++++++ COPYING.LESSER | 166 ++++++++ MANIFEST.in | 12 + README.md | 39 +- docs/bouligand.md | 12 + pycurious/__init__.py | 18 + pycurious/documentation.py | 17 + pycurious/grid/__init__.py | 18 + pycurious/grid/curie.py | 18 + pycurious/mapping/__init__.py | 18 + pycurious/mapping/mapping.py | 18 + pycurious/optimise/__init__.py | 18 + pycurious/optimise/optimise.py | 18 + pycurious/parallel/__init__.py | 18 + pycurious/parallel/parallel.py | 20 +- 15 files changed, 1072 insertions(+), 13 deletions(-) create mode 100644 COPYING create mode 100644 COPYING.LESSER create mode 100644 MANIFEST.in create mode 100644 docs/bouligand.md diff --git a/COPYING b/COPYING new file mode 100644 index 0000000..10926e8 --- /dev/null +++ b/COPYING @@ -0,0 +1,675 @@ + GNU GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + Preamble + + The GNU General Public License is a free, copyleft license for +software and other kinds of works. + + The licenses for most software and other practical works are designed +to take away your freedom to share and change the works. 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If the Library as you +received it does not specify a version number of the GNU Lesser +General Public License, you may choose any version of the GNU Lesser +General Public License ever published by the Free Software Foundation. + + If the Library as you received it specifies that a proxy can decide +whether future versions of the GNU Lesser General Public License shall +apply, that proxy's public statement of acceptance of any version is +permanent authorization for you to choose that version for the +Library. + diff --git a/MANIFEST.in b/MANIFEST.in new file mode 100644 index 0000000..65cd352 --- /dev/null +++ b/MANIFEST.in @@ -0,0 +1,12 @@ +include README.md +include MANIFEST.in +include COPYING +include COPYING.LESSER +include setup.cfg +include src/* +include __init__.py +recursive-include pycurious/*.py +include docs/* +include tests/*.py + + diff --git a/README.md b/README.md index c9eadc2..3f64a57 100644 --- a/README.md +++ b/README.md @@ -2,16 +2,17 @@ Magnetic data is one of the most common geophysics datasets available on the surface of the Earth. Curie depth is the depth at which rocks lose their magnetism. This is most often interpreted as the 580C isotherm, which is the Curie point of magnetite - the most prevalent magnetic mineral. -All methods to derive Curie depth first compute the (fast) Fourier transform over a square window of a magnetic anomaly that has been reduced to the pole. Initial methods plotted the radial spectrum, obtained from FFT, against the wavenumber (rad/km) and used the gradient between two points to estimate the Curie depth ([Tanaka *et al.* 1999](http://linkinghub.elsevier.com/retrieve/pii/S0040195199000724)). The drawback here being that the choice of points is subjective and potentially meaningless if the window size is too small to capture long wavelength signals. Alternatively, [Bouligand *et al.* (2009)](http://doi.wiley.com/10.1029/2009JB006494) formulated an analytical expression for the radial power spectum using four parameters: +Current methods to derive Curie depth first compute the (fast) Fourier transform over a square window of a magnetic anomaly that has been reduced to the pole. The depth and thickness of magnetic sources is estimated from the slope of the radial power spectrum. *PyCurious* implements two common approaches: -- *beta* - a fractal parameter -- *zt* - the top of magnetic sources -- *dz* - the thickness of the magnetic layer -- *C* - a field constant +- [Tanaka *et al.* 1999](http://linkinghub.elsevier.com/retrieve/pii/S0040195199000724) +- [Bouligand *et al.* 2009](http://doi.wiley.com/10.1029/2009JB006494) -The Curie depth is determined by minimising the misfit between the analytical power spectrum and the power spectrum computed from FFT. +Both of these methods to compute Curie depth are covered extensively in the form of Jupyter notebooks. Copy these into your working directory by running, -This Python package implements the latter method for computing Curie depth. It was heavily inspired from the [pycpd](https://github.com/groupeLIAMG/pycpd) package which implements a user inferface. We have simplified the API and extended it for parallel computation. Significant effort has been made towards repurposing Curie depth determination within a Bayesian inverse framework. PyCurious implements an objective function that accepts *a priori* information, and quantifies the uncertainty of Curie depth from a sensitivity analysis. +```python +import pycurious +pycurious.install_documentation() +``` ## Usage @@ -21,9 +22,16 @@ PyCurious consists of 3 classes that inherit from each other: 2. **CurieOptimise**: optimisation module for fitting the synthetic power spectrum (inherits CurieGrid). 3. **CurieParallel**: parallel implementation based on the decomposition of subgrids (inherits CurieOptimise). -Also included is several functions for mapping, gridding scattered data points, and converting between coordinate reference systems (CRS). +Also included is a `mapping` module for gridding scattered data points, and converting between coordinate reference systems (CRS). -Two optimisation passes is generally required of a study area: in the first pass all parameters have no prior and are completely unconstrainted; in the second pass we obtain priors by taking the mean and standard deviation of the parameters after the first pass to obtain more precise Curie depth estimates. *beta* and *C* vary at long wavelengths, thus the objective function penalises these parameters more due to their low standard deviation. +Below is a simple workflow to calculate the radial power spectrum: + +```python +import pycurious +grid = pycurious.CurieOptimise(data2d, xmin, xmax, ymin, ymax) +subgrid = grid.subgrid(window_size, x, y) +k, Phi, sigma_Phi = grid.radial_power_spectrum(subgrid) +``` ## Dependencies @@ -47,8 +55,15 @@ Optional dependencies for parallel module: To install: -`python setup.py install --user` +```shell +python setup.py install --user +``` + +This will compile all C and Fortran sources and install them to the user directory (omit the `--user` flag to install to the system directory). Remember to delete the build folder if you are upgrading this package. + +Or install using pip: -This will compile all C and Fortran sources and install them to the user directory (omit the `--user` flag to install to the system directory). +```shell +pip install pycurious --user +``` -Remember to delete the build folder if you are upgrading this package. diff --git a/docs/bouligand.md b/docs/bouligand.md new file mode 100644 index 0000000..77874ba --- /dev/null +++ b/docs/bouligand.md @@ -0,0 +1,12 @@ +# Bouligand method + +All methods to derive Curie depth first compute the (fast) Fourier transform over a square window of a magnetic anomaly that has been reduced to the pole. Initial methods plotted the radial spectrum, obtained from FFT, against the wavenumber (rad/km) and used the gradient between two points to estimate the Curie depth ([Tanaka *et al.* 1999](http://linkinghub.elsevier.com/retrieve/pii/S0040195199000724)). The drawback here being that the choice of points is subjective and potentially meaningless if the window size is too small to capture long wavelength signals. Alternatively, [Bouligand *et al.* (2009)](http://doi.wiley.com/10.1029/2009JB006494) formulated an analytical expression for the radial power spectum using four parameters: + +- *beta* - a fractal parameter +- *zt* - the top of magnetic sources +- *dz* - the thickness of the magnetic layer +- *C* - a field constant + +The Curie depth is determined by minimising the misfit between the analytical power spectrum and the power spectrum computed from FFT. + +This module was heavily inspired from [pycpd](https://github.com/groupeLIAMG/pycpd). We have simplified the API and repurposed Curie depth determinations within a Bayesian inverse framework. PyCurious implements an objective function that accepts *a priori* information, and quantifies the uncertainty of Curie depth. diff --git a/pycurious/__init__.py b/pycurious/__init__.py index 105b557..609231f 100644 --- a/pycurious/__init__.py +++ b/pycurious/__init__.py @@ -1,3 +1,21 @@ +""" +Copyright 2018 Ben Mather, Robert Delhaye + +This file is part of PyCurious. + +PyCurious is free software: you can redistribute it and/or modify +it under the terms of the GNU Lesser General Public License as published by +the Free Software Foundation, either version 3 of the License, or any later version. + +PyCurious is distributed in the hope that it will be useful, +but WITHOUT ANY WARRANTY; without even the implied warranty of +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +GNU Lesser General Public License for more details. + +You should have received a copy of the GNU Lesser General Public License +along with PyCurious. If not, see . +""" + # -*- coding: utf-8 -*- from .grid import CurieGrid, bouligand2009, tanaka1999, maus1995, ComputeTanaka from .optimise import CurieOptimise diff --git a/pycurious/documentation.py b/pycurious/documentation.py index 5f1aa65..ff346ed 100644 --- a/pycurious/documentation.py +++ b/pycurious/documentation.py @@ -1,3 +1,20 @@ +""" +Copyright 2018 Ben Mather, Robert Delhaye + +This file is part of PyCurious. + +PyCurious is free software: you can redistribute it and/or modify +it under the terms of the GNU Lesser General Public License as published by +the Free Software Foundation, either version 3 of the License, or any later version. + +PyCurious is distributed in the hope that it will be useful, +but WITHOUT ANY WARRANTY; without even the implied warranty of +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +GNU Lesser General Public License for more details. + +You should have received a copy of the GNU Lesser General Public License +along with PyCurious. If not, see . +""" import pkg_resources as _pkg_resources from distutils import dir_util as _dir_util diff --git a/pycurious/grid/__init__.py b/pycurious/grid/__init__.py index 84bff0a..24d24b9 100644 --- a/pycurious/grid/__init__.py +++ b/pycurious/grid/__init__.py @@ -1,2 +1,20 @@ +""" +Copyright 2018 Ben Mather, Robert Delhaye + +This file is part of PyCurious. + +PyCurious is free software: you can redistribute it and/or modify +it under the terms of the GNU Lesser General Public License as published by +the Free Software Foundation, either version 3 of the License, or any later version. + +PyCurious is distributed in the hope that it will be useful, +but WITHOUT ANY WARRANTY; without even the implied warranty of +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +GNU Lesser General Public License for more details. + +You should have received a copy of the GNU Lesser General Public License +along with PyCurious. If not, see . +""" + # -*- coding: utf-8 -*- from .curie import * \ No newline at end of file diff --git a/pycurious/grid/curie.py b/pycurious/grid/curie.py index cbe9de0..d75a35d 100644 --- a/pycurious/grid/curie.py +++ b/pycurious/grid/curie.py @@ -1,3 +1,21 @@ +""" +Copyright 2018 Ben Mather, Robert Delhaye + +This file is part of PyCurious. + +PyCurious is free software: you can redistribute it and/or modify +it under the terms of the GNU Lesser General Public License as published by +the Free Software Foundation, either version 3 of the License, or any later version. + +PyCurious is distributed in the hope that it will be useful, +but WITHOUT ANY WARRANTY; without even the implied warranty of +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +GNU Lesser General Public License for more details. + +You should have received a copy of the GNU Lesser General Public License +along with PyCurious. If not, see . +""" + # -*- coding: utf-8 -*- import numpy as np from scipy.special import gamma, kv, lambertw diff --git a/pycurious/mapping/__init__.py b/pycurious/mapping/__init__.py index fbd6bcd..e3c0dc5 100644 --- a/pycurious/mapping/__init__.py +++ b/pycurious/mapping/__init__.py @@ -1,3 +1,21 @@ +""" +Copyright 2018 Ben Mather, Robert Delhaye + +This file is part of PyCurious. + +PyCurious is free software: you can redistribute it and/or modify +it under the terms of the GNU Lesser General Public License as published by +the Free Software Foundation, either version 3 of the License, or any later version. + +PyCurious is distributed in the hope that it will be useful, +but WITHOUT ANY WARRANTY; without even the implied warranty of +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +GNU Lesser General Public License for more details. + +You should have received a copy of the GNU Lesser General Public License +along with PyCurious. If not, see . +""" + # -*- coding: utf-8 -*- from .mapping import transform_coordinates from .mapping import convert_extent diff --git a/pycurious/mapping/mapping.py b/pycurious/mapping/mapping.py index 1c2a31e..a5f33bb 100644 --- a/pycurious/mapping/mapping.py +++ b/pycurious/mapping/mapping.py @@ -1,3 +1,21 @@ +""" +Copyright 2018 Ben Mather, Robert Delhaye + +This file is part of PyCurious. + +PyCurious is free software: you can redistribute it and/or modify +it under the terms of the GNU Lesser General Public License as published by +the Free Software Foundation, either version 3 of the License, or any later version. + +PyCurious is distributed in the hope that it will be useful, +but WITHOUT ANY WARRANTY; without even the implied warranty of +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +GNU Lesser General Public License for more details. + +You should have received a copy of the GNU Lesser General Public License +along with PyCurious. If not, see . +""" + # -*- coding: utf-8 -*- import numpy as np diff --git a/pycurious/optimise/__init__.py b/pycurious/optimise/__init__.py index 833ac89..79ef49b 100644 --- a/pycurious/optimise/__init__.py +++ b/pycurious/optimise/__init__.py @@ -1,2 +1,20 @@ +""" +Copyright 2018 Ben Mather, Robert Delhaye + +This file is part of PyCurious. + +PyCurious is free software: you can redistribute it and/or modify +it under the terms of the GNU Lesser General Public License as published by +the Free Software Foundation, either version 3 of the License, or any later version. + +PyCurious is distributed in the hope that it will be useful, +but WITHOUT ANY WARRANTY; without even the implied warranty of +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +GNU Lesser General Public License for more details. + +You should have received a copy of the GNU Lesser General Public License +along with PyCurious. If not, see . +""" + # -*- coding: utf-8 -*- from .optimise import * \ No newline at end of file diff --git a/pycurious/optimise/optimise.py b/pycurious/optimise/optimise.py index 8539fd9..9da13ab 100644 --- a/pycurious/optimise/optimise.py +++ b/pycurious/optimise/optimise.py @@ -1,3 +1,21 @@ +""" +Copyright 2018 Ben Mather, Robert Delhaye + +This file is part of PyCurious. + +PyCurious is free software: you can redistribute it and/or modify +it under the terms of the GNU Lesser General Public License as published by +the Free Software Foundation, either version 3 of the License, or any later version. + +PyCurious is distributed in the hope that it will be useful, +but WITHOUT ANY WARRANTY; without even the implied warranty of +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +GNU Lesser General Public License for more details. + +You should have received a copy of the GNU Lesser General Public License +along with PyCurious. If not, see . +""" + # -*- coding: utf-8 -*- from .. import CurieGrid, bouligand2009 import numpy as np diff --git a/pycurious/parallel/__init__.py b/pycurious/parallel/__init__.py index 94ed2e5..cfcac58 100644 --- a/pycurious/parallel/__init__.py +++ b/pycurious/parallel/__init__.py @@ -1,2 +1,20 @@ +""" +Copyright 2018 Ben Mather, Robert Delhaye + +This file is part of PyCurious. + +PyCurious is free software: you can redistribute it and/or modify +it under the terms of the GNU Lesser General Public License as published by +the Free Software Foundation, either version 3 of the License, or any later version. + +PyCurious is distributed in the hope that it will be useful, +but WITHOUT ANY WARRANTY; without even the implied warranty of +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +GNU Lesser General Public License for more details. + +You should have received a copy of the GNU Lesser General Public License +along with PyCurious. If not, see . +""" + # -*- coding: utf-8 -*- from .parallel import * \ No newline at end of file diff --git a/pycurious/parallel/parallel.py b/pycurious/parallel/parallel.py index f902c2d..caa4661 100644 --- a/pycurious/parallel/parallel.py +++ b/pycurious/parallel/parallel.py @@ -1,3 +1,21 @@ +""" +Copyright 2018 Ben Mather, Robert Delhaye + +This file is part of PyCurious. + +PyCurious is free software: you can redistribute it and/or modify +it under the terms of the GNU Lesser General Public License as published by +the Free Software Foundation, either version 3 of the License, or any later version. + +PyCurious is distributed in the hope that it will be useful, +but WITHOUT ANY WARRANTY; without even the implied warranty of +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +GNU Lesser General Public License for more details. + +You should have received a copy of the GNU Lesser General Public License +along with PyCurious. If not, see . +""" + # -*- coding: utf-8 -*- import numpy as np import warnings @@ -100,7 +118,7 @@ def subgrid(self, xc, yc, window): if window > self.max_window: raise ValueError("Max window size is {}".format(self.max_window)) - return super(CurieParallel, self).subgrid(xc, yc, window) + return super(CurieParallel, self).subgrid(window, xc, yc) def sync(self, vector): From 8818d72aca5fd92bcc283811d58f1e28ac1c5f13 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Wed, 29 Aug 2018 12:16:58 +0100 Subject: [PATCH 029/170] Set theme jekyll-theme-cayman --- docs/_config.yml | 1 + 1 file changed, 1 insertion(+) create mode 100644 docs/_config.yml diff --git a/docs/_config.yml b/docs/_config.yml new file mode 100644 index 0000000..c419263 --- /dev/null +++ b/docs/_config.yml @@ -0,0 +1 @@ +theme: jekyll-theme-cayman \ No newline at end of file From 56954c54884a980a5691f8167df3a5391c2d4bc3 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Wed, 29 Aug 2018 12:54:48 +0100 Subject: [PATCH 030/170] Final bugs before v0.1 --- README.md | 18 ++++++++++++------ .../Ex5-Mapping-Curie-depth-EMAG2.ipynb | 2 +- pycurious/optimise/optimise.py | 1 + 3 files changed, 14 insertions(+), 7 deletions(-) diff --git a/README.md b/README.md index 3f64a57..e9377a8 100644 --- a/README.md +++ b/README.md @@ -1,13 +1,13 @@ # PyCurious -Magnetic data is one of the most common geophysics datasets available on the surface of the Earth. Curie depth is the depth at which rocks lose their magnetism. This is most often interpreted as the 580C isotherm, which is the Curie point of magnetite - the most prevalent magnetic mineral. +Magnetic data is one of the most common geophysics datasets available on the surface of the Earth. Curie depth is the depth at which rocks lose their magnetism. This is most often interpreted as the 580C isotherm, which is the Curie point of magnetite and the most prevalent magnetic mineral. Current methods to derive Curie depth first compute the (fast) Fourier transform over a square window of a magnetic anomaly that has been reduced to the pole. The depth and thickness of magnetic sources is estimated from the slope of the radial power spectrum. *PyCurious* implements two common approaches: - [Tanaka *et al.* 1999](http://linkinghub.elsevier.com/retrieve/pii/S0040195199000724) - [Bouligand *et al.* 2009](http://doi.wiley.com/10.1029/2009JB006494) -Both of these methods to compute Curie depth are covered extensively in the form of Jupyter notebooks. Copy these into your working directory by running, +Both of these methods to compute Curie depth are covered in the form of Jupyter notebooks. Copy these into your working directory by running, ```python import pycurious @@ -28,8 +28,14 @@ Below is a simple workflow to calculate the radial power spectrum: ```python import pycurious -grid = pycurious.CurieOptimise(data2d, xmin, xmax, ymin, ymax) + +# initialise CurieOptimise object with 2D magnetic anomaly +grid = pycurious.CurieOptimise(mag_anomaly, xmin, xmax, ymin, ymax) + +# extract a square window of the magnetic anomaly subgrid = grid.subgrid(window_size, x, y) + +# compute the radial power spectrum k, Phi, sigma_Phi = grid.radial_power_spectrum(subgrid) ``` @@ -55,15 +61,15 @@ Optional dependencies for parallel module: To install: -```shell +``` python setup.py install --user ``` This will compile all C and Fortran sources and install them to the user directory (omit the `--user` flag to install to the system directory). Remember to delete the build folder if you are upgrading this package. -Or install using pip: +Alternatively, install using pip: -```shell +``` pip install pycurious --user ``` diff --git a/pycurious/Examples/Notebooks/Bouligand/Ex5-Mapping-Curie-depth-EMAG2.ipynb b/pycurious/Examples/Notebooks/Bouligand/Ex5-Mapping-Curie-depth-EMAG2.ipynb index 034515f..af8dec2 100644 --- a/pycurious/Examples/Notebooks/Bouligand/Ex5-Mapping-Curie-depth-EMAG2.ipynb +++ b/pycurious/Examples/Notebooks/Bouligand/Ex5-Mapping-Curie-depth-EMAG2.ipynb @@ -197,7 +197,7 @@ "source": [ "## Compute Curie depth\n", "\n", - "For this example we use the Bouligand *et al.*, 2009 approach we outlined in [Ex3-Optimisation-routine](#./Ex3-Optimisation-routine.ipynb)." + "For this example we use the Bouligand *et al.*, 2009 approach we outlined in previous notebooks." ] }, { diff --git a/pycurious/optimise/optimise.py b/pycurious/optimise/optimise.py index 9da13ab..9be0930 100644 --- a/pycurious/optimise/optimise.py +++ b/pycurious/optimise/optimise.py @@ -19,6 +19,7 @@ # -*- coding: utf-8 -*- from .. import CurieGrid, bouligand2009 import numpy as np +import warnings from scipy.optimize import minimize from scipy.special import polygamma from scipy import stats From b677b82964d72863cf2978e7676bd91b0a71b3ff Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Wed, 29 Aug 2018 17:15:20 +0100 Subject: [PATCH 031/170] version 0.1 release --- README.md | 2 +- pycurious/grid/curie.py | 148 ++++++++++++++++++--------------- pycurious/optimise/optimise.py | 74 ++++++++++------- setup.py | 15 +++- 4 files changed, 136 insertions(+), 103 deletions(-) diff --git a/README.md b/README.md index e9377a8..34e0e32 100644 --- a/README.md +++ b/README.md @@ -1,6 +1,6 @@ # PyCurious -Magnetic data is one of the most common geophysics datasets available on the surface of the Earth. Curie depth is the depth at which rocks lose their magnetism. This is most often interpreted as the 580C isotherm, which is the Curie point of magnetite and the most prevalent magnetic mineral. +Magnetic data is one of the most common geophysics datasets available on the surface of the Earth. Curie depth is the depth at which rocks lose their magnetism. The most prevalent magnetic mineral is magnetite, which has a Curie point of 580C, thus the Curie depth is often interpreted as the 580C isotherm. Current methods to derive Curie depth first compute the (fast) Fourier transform over a square window of a magnetic anomaly that has been reduced to the pole. The depth and thickness of magnetic sources is estimated from the slope of the radial power spectrum. *PyCurious* implements two common approaches: diff --git a/pycurious/grid/curie.py b/pycurious/grid/curie.py index d75a35d..44977f9 100644 --- a/pycurious/grid/curie.py +++ b/pycurious/grid/curie.py @@ -172,19 +172,19 @@ def radial_spectrum(self, subgrid, taper=np.hanning, scale=0.001, **kwargs): Parameters ---------- - subgrid : window of the original data - : (see subgrid method) - taper : taper function (np.hanning is default) - : set to None for no taper function - scale : scaling factor to get k into rad/km - : (0.001 by default) - args : keyword arguments to pass to taper + subgrid : window of the original data + : (see subgrid method) + taper : taper function (np.hanning is default) + : set to None for no taper function + scale : scaling factor to get k into rad/km + : (0.001 by default) + kwargs : keyword arguments to pass to taper Returns ------- - S : Radial spectrum - k : wavenumber in rad/km - sigma2 : variance of S + k : wavenumber in rad/km + Phi : Radial power spectrum + sigma_Phi : Standard deviation of Phi """ data = subgrid @@ -238,23 +238,23 @@ def radial_spectrum(self, subgrid, taper=np.hanning, scale=0.001, **kwargs): def radial_spectrum_log(self, subgrid, taper=np.hanning, scale=0.001, **kwargs): """ - Compute the radial spectrum for a square grid. + Compute the log of the radial spectrum for a square grid. Parameters ---------- - subgrid : window of the original data - : (see subgrid method) - taper : taper function (np.hanning is default) - : set to None for no taper function - scale : scaling factor to get k into rad/km - : (0.001 by default) - args : keyword arguments to pass to taper + subgrid : window of the original data + : (see subgrid method) + taper : taper function (np.hanning is default) + : set to None for no taper function + scale : scaling factor to get k into rad/km + : (0.001 by default) + kwargs : keyword arguments to pass to taper Returns ------- - S : Radial spectrum - k : wavenumber in rad/km - sigma2 : variance of S + k : wavenumber in rad/km + lnPhi : log of the radial power spectrum in ln(sqrt(S)) + lnsigma_Phi : standard deviation of lnPhi """ data = subgrid @@ -310,20 +310,20 @@ def azimuthal_spectrum(self, subgrid, taper=np.hanning, scale=0.001, theta=5.0, Parameters ---------- - subgrid : window of the original data - : (see subgrid method) - taper : taper function (np.hanning is default) - : set to None for no taper function - scale : scaling factor to get k into rad/km - : (0.001 by default) - theta : angle increment in degrees - args : arguments to pass to taper + subgrid : window of the original data + : (see subgrid method) + taper : taper function (np.hanning is default) + : set to None for no taper function + scale : scaling factor to get k into rad/km + : (0.001 by default) + theta : angle increment in degrees + args : arguments to pass to taper Returns ------- - S : Azimuthal spectrum - k : wavenumber [rad/km] - theta : angles + k : wavenumber in rad/km + Phi : Radial power spectrum + sigma_Phi : Standard deviation of Phi """ from pycurious import radon data = subgrid @@ -368,20 +368,18 @@ def reduce_to_pole(self, data, inc, dec, sinc=None, sdec=None): Parameters ---------- - data : 1d-array - The total field anomaly data at each point. - inc, dec : floats - The inclination and declination of the inducing Geomagnetic field - sinc, sdec : floats (optional) - The inclination and declination of the total magnetization of the - anomaly source. The total magnetization is the vector sum of the + data : 1d-array the total field anomaly data at each point. + inc : inclination of the inducing Geomagnetic field + dec : declination of the inducing Geomagnetic field + sinc : (optional) inclination of the total magnetization of the anomaly source + sdec : (optional) declination of the total magnetization of the anomaly source + The total magnetization is the vector sum of the induced and remanent magnetization. If there is only induced magnetization, use the *inc* and *dec* of the Geomagnetic field. Returns ------- - rtp : 2d-array - The data reduced to the pole. + rtp : 2d-array the data reduced to the pole. References ---------- @@ -454,27 +452,24 @@ def upward_continuation(self, data, height): Parameters ---------- - data : 2D grid - The potential field at the grid points - height : float - The height increase (delta z) in meters. + data : 2D grid - potential field at the grid points + height : float - height increase (delta z) in meters. Returns ------- - cont : array - The upward continued data + cont : array - upward continued data Notes ----- - It is not possible to get the FFT of a masked grid. The default - :func:`fatiando.gridder.interp` call using minimum curvature will - not be suitable. Use extrapolate=True or algorithm='nearest' to - get an unmasked grid. + It is not possible to get the FFT of a masked grid. The default + :func:`fatiando.gridder.interp` call using minimum curvature will + not be suitable. Use extrapolate=True or algorithm='nearest' to + get an unmasked grid. References ---------- - Blakely, R. J. (1996), Potential Theory in Gravity and Magnetic - Applications, Cambridge University Press. + Blakely, R. J. (1996), Potential Theory in Gravity and Magnetic + Applications, Cambridge University Press. """ nr, nc = data.shape @@ -507,16 +502,15 @@ def bouligand2009(kh, beta, zt, dz, C): Parameters ---------- - kh : norm of the wave number in the horizontal plane + kh : wavenumber in rad/km beta : fractal parameter zt : top of magnetic sources dz : thickness of magnetic sources - kh : norm of the wave number in the horizontal plane C : field constant (Maus et al., 1997) Returns ------- - Phi : radial power spectrum of magnetic anomalies + Phi : radial power spectrum of magnetic anomalies References ---------- @@ -540,27 +534,28 @@ def bouligand2009(kh, beta, zt, dz, C): return Phi1d -def tanaka1999(k, Phi, sigma_Phi, kmin_range=(0.05, 0.2), kmax_range=(0.05, 0.2)): +def tanaka1999(k, lnPhi, sigma_lnPhi, kmin_range=(0.05, 0.2), kmax_range=(0.05, 0.2)): """ - Compute weighted linear fit of S over spatial frequency window kmin:kmax + Compute weighted linear fit of Phi over spatial frequency window kmin:kmax Parameters ---------- - S : Power spectrum of signal (see radial spectrum), expected in ln(sqrt(S)) form - k : Wavenumber - sigma2 : Errors of S - kmin,kmax : Minimum and maximum spatial frequencies to fit. Ideally low frequency, straight-ish line + k : wavenumber in rad/km + lnPhi : log of the radial power spectrum (see power_spectrum_log) + expected in ln(sqrt(S)) form + sigma_lnPhi : standard deviation of lnPhi + kmin,kmax : minimum and maximum range of spatial frequencies to fit. + Ideally low frequency, straight-ish line Returns - ----------- - Zb : Estimated Curie point depth, as per Tanaka et al, 1999 - eZb : Error of Zb - : No geothermal gradient, trivial to estimate. - : Possible to extend, return fitted components? + ------- + (Ztr, btr, dZtr) : gradient, intercept, error for the top of magnetic sources + (Zor, bor, dZor) : gradient, intercept, error for the bottom of magnetic sources + """ # for now... - S = Phi - sigma2 = sigma_Phi**2 + S = lnPhi + sigma2 = sigma_lnPhi**2 def compute_coefficients(X, Y, E): X2 = X**2 @@ -611,6 +606,21 @@ def compute_coefficients(X, Y, E): def ComputeTanaka(Ztr, dZtr, Zor, dZor): + """ + Compute the Curie depth from the results of tanaka1999 + + Parameters + ---------- + Ztr : top of the magnetic source + dZtr : error of Ztr + Zor : bottom of the magnetic source + dZor : error of Zor + + Returns + ------- + Zb : estimated Curie point depth + eZb : error of Zb + """ Zb = 2.0*Zor - Ztr dZb = 2.0*dZor - dZtr return abs(Zb), dZb diff --git a/pycurious/optimise/optimise.py b/pycurious/optimise/optimise.py index 9be0930..09fd4c6 100644 --- a/pycurious/optimise/optimise.py +++ b/pycurious/optimise/optimise.py @@ -95,6 +95,9 @@ def add_prior(self, **kwargs): def reset_priors(self): + """ + Reset priors to uniform distribution + """ self.prior = {'beta':None, 'zt':None, 'dz':None, 'C':None} self.prior_pdf = {'beta':None, 'zt':None, 'dz':None, 'C':None} @@ -145,20 +148,21 @@ def min_func(self, x, kh, Phi, sigma_Phi): Parameters ---------- - x : array of variables [beta, zt, dz, C] - Phi_exp : radial spectrum - kh : wavenumbers [rad/km] + x : array of variables [beta, zt, dz, C] + kh : wavenumbers [rad/km] + Phi : radial power spectrum + sigma_Phi : standard deviation of Phi Returns ------- - misfit : sum of misfit (float) + misfit : sum of misfit (float) Notes ----- We purposely ignore all warnings raised by the bouligand2009 function because some combinations of input parameters will - trigger an out-of-range warning that will crash the minimiser - when this occurs we set the misfit to a very large number + trigger an out-of-range warning that will crash the minimiser. + Instead, the misfit is set to a very large number when this occurs. """ beta, zt, dz, C = x with warnings.catch_warnings() as w: @@ -187,6 +191,10 @@ def optimise(self, window, xc, yc, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.ha zt : float - top of magnetic layer (starting value) dz : float - thickness of magnetic layer (starting value) C : float - field constant (starting value) + taper : taper function (np.hanning is default) + : set to None for no taper function + process_subgrids : func - a custom function to process the subgrid + kwargs : keyword arguments to pass to radial_spectrum. Returns ------- @@ -222,9 +230,6 @@ def optimise_routine(self, window, xc_list, yc_list, beta=3.0, zt=1.0, dz=10.0, """ Iterate through a list of centroids to compute the optimal values of beta, zt, dz, C for a given window size. - - Use this routine to iteratively improve the precision of various - parameters (see notes) Parameters ---------- @@ -235,6 +240,10 @@ def optimise_routine(self, window, xc_list, yc_list, beta=3.0, zt=1.0, dz=10.0, zt : float - top of magnetic layer dz : float - thickness of magnetic layer C : float - field constant + taper : taper function (np.hanning is default) + : set to None for no taper function + process_subgrids : func - a custom function to process the subgrid + kwargs : keyword arguments to pass to radial_spectrum. Returns ------- @@ -243,18 +252,6 @@ def optimise_routine(self, window, xc_list, yc_list, beta=3.0, zt=1.0, dz=10.0, dz : ndarray shape(l,) - thickness of magnetic layer C : ndarray shape(l,) - field constant - Notes - ----- - Parameters such as beta and C vary over long wavelengths, - thus keeping these somewhat rigid can improve the precision - of zt and dz. - The mean and stdev of any vectors for beta, zt, dz, C can - be added as priors in the objective routine using add_prior - - Recommended usage is two passes: - 1. keep beta, zt, dz, C set to None with no prior - 2. add the mean and stdev of beta, zt, dz, C as priors - and run through a second pass """ n = len(xc_list) @@ -282,15 +279,16 @@ def metropolis_hastings(self, window, xc, yc, nsim, burnin, x_scale=None, beta=3 Evaluates a Markov-Chain for starting values of beta, zt, dz, C and returns the ensemble of model realisations. - - WARNING: Use starting values relatively close to the solution - - C can easily found from the mean of the radial power spectrum Parameters ---------- window : float - size of window in metres xc : float - centroid x values yc : float - centroid y values + nsim : int - number of simulations + burnin : int - number of burn-in simulations before to nsim + x_scale : float(4) (optional) - scaling factor for new proposals + default is [1,1,1,1] for [beta, zt, dz, C] - see notes beta : float - fractal parameter (starting value) zt : float - top of magnetic layer (starting value) dz : float - thickness of magnetic layer (starting value) @@ -298,10 +296,22 @@ def metropolis_hastings(self, window, xc, yc, nsim, burnin, x_scale=None, beta=3 Returns ------- - beta : ndarray shape(nsim,) - fractal parameters + beta : ndarray shape(nsim,) - fractal parameter zt : ndarray shape(nsim,) - top of magnetic layer dz : ndarray shape(nsim,) - thickness of magnetic layer C : ndarray shape(nsim,) - field constant + + Notes + ----- + nsim, burnin, and x_scale should be tweaked for optimal performance + Use starting values of beta, zt, dz, C relatively close to the solution + - C can easily found from the mean of the radial power spectrum. + + During the burn-in stage we apply tempering to the PDF to iterate closer + towards the solution. This has the effect of smoothing out the posterior + so that minima can be more easily found. This is necessary here because + large portions of the posterior probability are zero. + see see Sambridge 2013, DOI:10.1093/gji/ggt342 for more information. """ if type(process_subgrid) == type(None): # dummy function @@ -370,19 +380,21 @@ def sensitivity(self, window, xc, yc, nsim, beta=3.0, zt=1.0, dz=10.0, C=5.0, ta ---------- nsim : int - number of Monte Carlo simulations window : float - size of window in metres - xc_list : ndarray shape(l,) - centroid x values - yc_list : ndarray shape(l,) - centroid y values + xc : float - centroid x values + yc : float - centroid y values + nsim : int - number of simulations beta : float - starting fractal parameter zt : float - starting top of magnetic layer dz : float - starting thickness of magnetic layer C : float - starting field constant + Returns ------- - beta : ndarray shape(l,2) - fractal parameters (mean, stdev) - zt : ndarray shape(l,2) - top of magnetic layer (mean, stdev) - dz : ndarray shape(l,2) - thickness of magnetic layer (mean, stdev) - C : ndarray shape(l,2) - field constant (mean, stdev) + beta : ndarray shape(nsim,) - fractal parameters + zt : ndarray shape(nsim,) - top of magnetic layer + dz : ndarray shape(nsim,) - thickness of magnetic layer + C : ndarray shape(nsim,) - field constant """ if type(process_subgrid) == type(None): # dummy function diff --git a/setup.py b/setup.py index 3f3b8d2..40a8b36 100644 --- a/setup.py +++ b/setup.py @@ -2,9 +2,18 @@ # python3 setup.py build_ext --inplace import numpy as np -from distutils.core import setup -from distutils.extension import Extension +from setuptools import setup +from setuptools import Extension +# from distutils.core import setup +# from distutils.extension import Extension from Cython.Build import cythonize +from os import path + + +this_directory = path.abspath(path.dirname(__file__)) +with open(path.join(this_directory, 'README.md')) as f: + long_description = f.read() + ext = Extension(name = 'pycurious.radon', sources = ['src/radon.pyx','src/cradon.c'], @@ -14,6 +23,8 @@ if __name__ == "__main__": setup(name = 'pycurious', + long_description = long_description, + long_description_content_type = 'text/markdown', author = "Ben Mather", author_email = "brmather1@gmail.com", url = "https://github.com/brmather/pycurious", From b9f6d41e07e03847efa39d58a269191a8b01760e Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Thu, 30 Aug 2018 02:55:12 +0100 Subject: [PATCH 032/170] You always forget a few things... --- pycurious/optimise/optimise.py | 4 ++-- setup.py | 2 +- 2 files changed, 3 insertions(+), 3 deletions(-) diff --git a/pycurious/optimise/optimise.py b/pycurious/optimise/optimise.py index 09fd4c6..4f5597e 100644 --- a/pycurious/optimise/optimise.py +++ b/pycurious/optimise/optimise.py @@ -169,7 +169,7 @@ def min_func(self, x, kh, Phi, sigma_Phi): warnings.simplefilter("ignore") Phi_syn = bouligand2009(kh, beta, zt, dz, C) - misfit = self.objective_function(Phi_syn, Phi, sigma_Phi) + misfit = self.objective_function(Phi_syn, Phi, 1.0) if not np.isfinite(misfit): misfit = 1e99 else: @@ -435,4 +435,4 @@ def process_subgrid(subgrid): prior_pdf = self.prior_pdf[key] self.prior[key] = list(prior_pdf.args) - return yc_list(samples.T) + return list(samples.T) diff --git a/setup.py b/setup.py index 40a8b36..1f16716 100644 --- a/setup.py +++ b/setup.py @@ -28,7 +28,7 @@ author = "Ben Mather", author_email = "brmather1@gmail.com", url = "https://github.com/brmather/pycurious", - version = "0.1", + version = "0.1.1", description = "Python tool for computing the Curie depth from magnetic data", ext_modules = cythonize([ext]), packages = ['pycurious', From 53ca62fa00b7163721b420fb499d2ad22cba659d Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Mon, 3 Sep 2018 13:39:28 +0100 Subject: [PATCH 033/170] Simple parallelism using OpenMP --- pycurious/optimise/optimise.py | 117 ++++++++++++++++++++++++++++----- 1 file changed, 99 insertions(+), 18 deletions(-) diff --git a/pycurious/optimise/optimise.py b/pycurious/optimise/optimise.py index 4f5597e..d557b6d 100644 --- a/pycurious/optimise/optimise.py +++ b/pycurious/optimise/optimise.py @@ -23,10 +23,12 @@ from scipy.optimize import minimize from scipy.special import polygamma from scipy import stats +from multiprocessing import Pool, Process, Queue try: range=xrange except: pass + class CurieOptimise(CurieGrid): """ Extends the CurieGrid class to include optimisation routines @@ -226,6 +228,102 @@ def process_subgrid(subgrid): return res.x + def _func_queue(self, func, queue, pos, *args, **kwargs): + print args + res = func(*args, **kwargs) + queue.put((pos, res)) + return + + + def parallelise_routine(self, window, xc_list, yc_list, func, *args, **kwargs): + """ + Implements shared memory multiprocessing to split multiple + evaluations of a function centroids across processors. + + Supply the window size and lists of x,y coordinates to a function + along with any additional arguments or keyword arguments. + + Parameters + ---------- + window : float - size of window in metres + xc_list : array shape(l,) - centroid x values + yc_list : array shape(l,) - centroid y values + func : function to evaluate in parallel + args : additional arguments to pass to func + kwargs : additional keyword arguments to pass to func + + Returns + ------- + out : list (depends on output of func - see notes) + + Example usage + ------------- + An obvious use case is to compute the Curie depth for many + centroids in parallel. + + > self.parallelise_routine(window, xc_list, yc_list, self.optimise) + + Each centroid is assigned a new process and sent to a free processor + to compute. In this case, the output is separate lists of shape(l,) + for beta, zt, dz, and C. + + + Another example is to parallelise the sensitivity analysis: + + > self.parallelise_routine(window, xc_list, yc_list, self.sensitivity, nsim) + + This time the output will be a list of lists for beta, zt, dz, and C + i.e. if nc=2 is the number of centroids and nsim=4 is the number of + simulations then separatee lists [[k1, k2, k3, k4], [k1, k2, k3, k4]] + will be returned for beta, zt, dz, and C. + """ + + n = len(xc_list) + if n != len(yc_list): + raise ValueError("xc_list and yc_list must be the same size") + + xOpt = [[] for i in range(n)] + processes = [] + q = Queue() + + for i in range(n): + xc = xc_list[i] + yc = yc_list[i] + + pass_args = [func, q, i, window, xc, yc] + pass_args.extend(args) + + p = Process(target=self._func_queue,\ + args=tuple(pass_args),\ + kwargs=kwargs) + processes.append(p) + + [x.start() for x in processes] + [p.join() for p in processes] + + for i in range(n): + i, res = q.get() + xOpt[i] = res + + # process dimensions of output + ndim = np.array(res).ndim + + if ndim == 1: + # return separate lists of beta, zt, dz, C + xOpt = np.vstack(xOpt) + return list(xOpt.T) + elif ndim > 1: + # return lists of beta, zt, dz, C for each simulation + xOpt = np.hstack(xOpt) + out = list(xOpt) + for i in range(len(out)): + out[i] = np.split(out[i], n) + return out + else: + raise ValueError("Cannot determine shape of output") + + + def optimise_routine(self, window, xc_list, yc_list, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs): """ Iterate through a list of centroids to compute the optimal values @@ -253,24 +351,7 @@ def optimise_routine(self, window, xc_list, yc_list, beta=3.0, zt=1.0, dz=10.0, C : ndarray shape(l,) - field constant """ - - n = len(xc_list) - - if n != len(yc_list): - raise ValueError("xc_list and yc_list must be the same size") - - - # storage vector - xOpt = np.empty((n, 4)) - - for i in range(0, n): - xc = xc_list[i] - yc = yc_list[i] - - xOpt[i] = self.optimise(window, xc, yc, beta, zt, dz, C,\ - taper, process_subgrid, **kwargs) - - return list(xOpt.T) + return self.parallelise_routine(window, xc_list, yc_list, self.optimise, beta, zt, dz, C, taper, process_subgrid, **kwargs) def metropolis_hastings(self, window, xc, yc, nsim, burnin, x_scale=None, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs): From b0bec71cd2d2f35f74e8d7aa21037a356d352a42 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Mon, 3 Sep 2018 21:15:16 +0100 Subject: [PATCH 034/170] Only instantiate the available processors Old behaviour instantiated a new process for each job New behaviour instantiates a set number of processes and uses a queue-in queue-out to feed them new jobs. --- pycurious/optimise/optimise.py | 44 +++++++++++++++-------- tests/test_multiprocessing.py | 64 ++++++++++++++++++++++++++++++++++ 2 files changed, 94 insertions(+), 14 deletions(-) create mode 100644 tests/test_multiprocessing.py diff --git a/pycurious/optimise/optimise.py b/pycurious/optimise/optimise.py index d557b6d..b3fd0bb 100644 --- a/pycurious/optimise/optimise.py +++ b/pycurious/optimise/optimise.py @@ -23,7 +23,7 @@ from scipy.optimize import minimize from scipy.special import polygamma from scipy import stats -from multiprocessing import Pool, Process, Queue +from multiprocessing import Pool, Process, Queue, cpu_count try: range=xrange except: pass @@ -228,10 +228,17 @@ def process_subgrid(subgrid): return res.x - def _func_queue(self, func, queue, pos, *args, **kwargs): - print args - res = func(*args, **kwargs) - queue.put((pos, res)) + def _func_queue(self, func, q_in, q_out, window, *args, **kwargs): + while True: + pos, xc, yc = q_in.get() + if pos is None: + break + + pass_args = [window, xc, yc] + pass_args.extend(args) + + res = func(*pass_args, **kwargs) + q_out.put((pos, res)) return @@ -284,27 +291,36 @@ def parallelise_routine(self, window, xc_list, yc_list, func, *args, **kwargs): xOpt = [[] for i in range(n)] processes = [] - q = Queue() + q_in = Queue(1) + q_out = Queue() - for i in range(n): - xc = xc_list[i] - yc = yc_list[i] + nprocs = cpu_count() - pass_args = [func, q, i, window, xc, yc] + for i in range(nprocs): + pass_args = [func, q_in, q_out, window] pass_args.extend(args) p = Process(target=self._func_queue,\ args=tuple(pass_args),\ kwargs=kwargs) + processes.append(p) - [x.start() for x in processes] - [p.join() for p in processes] + for p in processes: + p.daemon = True + p.start() - for i in range(n): - i, res = q.get() + sent = [q_in.put((i, xc_list[i], yc_list[i])) for i in range(n)] + [q_in.put((None, None, None)) for _ in range(nprocs)] + + for i in range(len(sent)): + i, res = q_out.get() xOpt[i] = res + + [p.join() for p in processes] + + # process dimensions of output ndim = np.array(res).ndim diff --git a/tests/test_multiprocessing.py b/tests/test_multiprocessing.py new file mode 100644 index 0000000..3b98f89 --- /dev/null +++ b/tests/test_multiprocessing.py @@ -0,0 +1,64 @@ +import numpy as np +import pycurious + +# load x,y,anomaly +mag_data = np.loadtxt("../pycurious/Examples/data/test_mag_data.txt") + +nx, ny = 305, 305 + +x = mag_data[:,0] +y = mag_data[:,1] +d = mag_data[:,2].reshape(ny,nx) + +xmin, xmax = x.min(), x.max() +ymin, ymax = y.min(), y.max() + +# initialise CurieOptimise object +grid = pycurious.CurieOptimise(d, xmin, xmax, ymin, ymax) + + +# get centroids +window_size = 200e3 +xc_list, yc_list = grid.create_centroid_list(window_size, spacingX=10e3, spacingY=10e3) + +print("number of centroids = {}".format(len(xc_list))) + + +beta, zt, dz, C = grid.optimise_routine(window_size, xc_list, yc_list) +print "done with optimise_routine" + +result = grid.parallelise_routine(window_size, xc_list, yc_list, grid.sensitivity, 5) +print result +result1 = np.array(result) +print result1.shape +# print result1[:,0] +# print result1[:,1] +# print result1[:,:,0] + +# result2 = np.hstack(result) +# print result2.shape +# print result2[0] + +# print grid.sensitivity(window_size, xc_list[0], yc_list[0], 5) + + + +import matplotlib.pyplot as plt +# get dimensions of domain +xcoords = np.unique(xc_list) +ycoords = np.unique(yc_list) +nc, nr = xcoords.size, ycoords.size + +fig, (ax1, ax2, ax3, ax4) = plt.subplots(1, 4, sharex=True, sharey=True, figsize=(17,3.)) + +im1 = ax1.imshow(beta.reshape(nr,nc)) +im2 = ax2.imshow(zt.reshape(nr,nc)) +im3 = ax3.imshow(dz.reshape(nr,nc)) +im4 = ax4.imshow(C.reshape(nr,nc)) + +fig.colorbar(im1, ax=ax1, label=r"$\beta$") +fig.colorbar(im2, ax=ax2, label=r"$z_t$") +fig.colorbar(im3, ax=ax3, label=r"$\Delta z$") +fig.colorbar(im4, ax=ax4, label=r"$C$") + +fig.savefig("curie_depth.png") \ No newline at end of file From cd112b3b333bc6cca2e3754f11b5a654f4bb5c91 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Fri, 28 Sep 2018 13:55:53 +0100 Subject: [PATCH 035/170] No need to evaluate probability twice Metropolis-Hasings routine just needs to evaluate the proposal probability at each step in the random walk --- pycurious/optimise/optimise.py | 26 +++++++++++++++++--------- 1 file changed, 17 insertions(+), 9 deletions(-) diff --git a/pycurious/optimise/optimise.py b/pycurious/optimise/optimise.py index b3fd0bb..51e35f4 100644 --- a/pycurious/optimise/optimise.py +++ b/pycurious/optimise/optimise.py @@ -47,7 +47,7 @@ class CurieOptimise(CurieGrid): bounds : lower and upper bounds for beta, zt, dz, C prior : dictionary of priors for beta, zt, dz, C """ - def __init__(self, grid, xmin, xmax, ymin, ymax): + def __init__(self, grid, xmin, xmax, ymin, ymax, **kwargs): super(CurieOptimise, self).__init__(grid, xmin, xmax, ymin, ymax) @@ -61,6 +61,8 @@ def __init__(self, grid, xmin, xmax, ymin, ymax): bounds = list(zip(lb,ub)) self.bounds = bounds + self.max_processors = kwargs.pop("max_processors", cpu_count()) + return def add_prior(self, **kwargs): @@ -229,6 +231,7 @@ def process_subgrid(subgrid): def _func_queue(self, func, q_in, q_out, window, *args, **kwargs): + """ Retrive processes from the queue """ while True: pos, xc, yc = q_in.get() if pos is None: @@ -294,7 +297,7 @@ def parallelise_routine(self, window, xc_list, yc_list, func, *args, **kwargs): q_in = Queue(1) q_out = Queue() - nprocs = cpu_count() + nprocs = self.max_processors for i in range(nprocs): pass_args = [func, q_in, q_out, window] @@ -310,17 +313,19 @@ def parallelise_routine(self, window, xc_list, yc_list, func, *args, **kwargs): p.daemon = True p.start() + # put items in the queue sent = [q_in.put((i, xc_list[i], yc_list[i])) for i in range(n)] [q_in.put((None, None, None)) for _ in range(nprocs)] + # get the results for i in range(len(sent)): i, res = q_out.get() xOpt[i] = res + # wait until each processor has finished [p.join() for p in processes] - # process dimensions of output ndim = np.array(res).ndim @@ -329,7 +334,7 @@ def parallelise_routine(self, window, xc_list, yc_list, func, *args, **kwargs): xOpt = np.vstack(xOpt) return list(xOpt.T) elif ndim > 1: - # return lists of beta, zt, dz, C for each simulation + # return lists of beta, zt, dz, C for each centroid xOpt = np.hstack(xOpt) out = list(xOpt) for i in range(len(out)): @@ -430,36 +435,39 @@ def process_subgrid(subgrid): # compute radial spectrum k, Phi, sigma_Phi = self.radial_spectrum(subgrid, taper=taper, **kwargs) + P0 = np.exp(-self.min_func(x0, k, Phi, sigma_Phi)/1000) # Burn-in phase for i in range(burnin): # add random perturbation x1 = x0 + np.random.normal(size=4)*x_scale - # evaluate probability + tempering - P0 = np.exp(-self.min_func(x0, k, Phi, sigma_Phi)/1000) + # evaluate proposal probability + tempering P1 = np.exp(-self.min_func(x1, k, Phi, sigma_Phi)/1000) # iterate towards MAP estimate if P1 > P0: x0 = x1 + P0 = P1 + + P0 = np.exp(-self.min_func(x0, k, Phi, sigma_Phi)) # Now sample posterior for i in range(nsim): # add random perturbation x1 = x0 + np.random.normal(size=4)*x_scale - # evaluate probability - P0 = np.exp(-self.min_func(x0, k, Phi, sigma_Phi)) - P1 = np.exp(-self.min_func(x1, k, Phi, sigma_Phi)) + # evaluate proposal probability P0 = max(P0, 1e-99) + P1 = np.exp(-self.min_func(x1, k, Phi, sigma_Phi)) P = min(P1/P0, 1.0) # randomly accept probability if np.random.rand() <= P: x0 = x1 + P0 = P1 samples[i] = x0 From 22377f741402304c31c5508ac95a5d3ef25b0d83 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Tue, 2 Oct 2018 21:32:16 +0100 Subject: [PATCH 036/170] Initial commit of thermal solver --- pycurious/optimise/optimise.py | 2 - pycurious/therm/therm.py | 256 +++++++++++++++++++++++++++++++++ 2 files changed, 256 insertions(+), 2 deletions(-) create mode 100644 pycurious/therm/therm.py diff --git a/pycurious/optimise/optimise.py b/pycurious/optimise/optimise.py index 51e35f4..bcceb3e 100644 --- a/pycurious/optimise/optimise.py +++ b/pycurious/optimise/optimise.py @@ -451,8 +451,6 @@ def process_subgrid(subgrid): P0 = P1 - P0 = np.exp(-self.min_func(x0, k, Phi, sigma_Phi)) - # Now sample posterior for i in range(nsim): # add random perturbation diff --git a/pycurious/therm/therm.py b/pycurious/therm/therm.py new file mode 100644 index 0000000..e9329ef --- /dev/null +++ b/pycurious/therm/therm.py @@ -0,0 +1,256 @@ +""" +Copyright 2018 Ben Mather, Robert Delhaye + +This file is part of PyCurious. + +PyCurious is free software: you can redistribute it and/or modify +it under the terms of the GNU Lesser General Public License as published by +the Free Software Foundation, either version 3 of the License, or any later version. + +PyCurious is distributed in the hope that it will be useful, +but WITHOUT ANY WARRANTY; without even the implied warranty of +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +GNU Lesser General Public License for more details. + +You should have received a copy of the GNU Lesser General Public License +along with PyCurious. If not, see . +""" + +import numpy as np +from scipy import sparse +from sparse.linalg import spsolve + +try: range=xrange +except: pass + + +class CurieTherm(object): + + def __init__(self, minZ, maxZ, resZ, **kwargs): + + self.npoints = resZ + self.extent = (minZ, maxZ) + self.coords = np.linspace(minZ, maxZ, resZ) + self.nodes = np.arange(0, resZ, dtype=np.int) + self.sizes = (resZ, resZ) + + width = kwargs.pop('stencil_width', 1) + self.stencil_width = 2*width + 1 + + closure = [(0,-2),(2,0),(1,-1)] + self.closure = self._create_closure_object(closure) + + + self._initialise_COO_vectors() + self._initialise_boundary_dictionary() + + + def _initialise_COO_vectors(self): + + nn = self.npoints + + index = np.empty(nn + 2, dtype=np.int) + index.fill(-1) + self.index = index + + self.rows = np.empty((self.stencil_width, nn), dtype=np.int) + self.cols = np.empty((self.stencil_width, nn), dtype=np.int) + self.vals = np.empty((self.stencil_width, nn)) + + + def _initialise_boundary_dictionary(self): + + nn = self.npoints + coords = self.coords + minZ, maxZ = self.extent + + # Setup boundary dictionary + bc = dict() + + m0 = coords == minZ + m1 = coords == maxZ + d0 = abs(coords[1] - coords[0]) + d1 = abs(coords[-1] - coords[-2]) + + bc["minZ"] = {"val": 0.0, "delta": d0, "flux": True, "mask": m0} + bc["maxZ"] = {"val": 0.0, "delta": d1, "flux": True, "mask": m1} + + self.bc = bc + self.dirichlet_mask = np.zeros(nn, dtype=bool) + + + def _create_closure_object(self, closure): + + nn = self.npoints + obj = [[0] for i in range(self.stencil_width)] + + for i in range(0, self.stencil_width): + # construct slicing object + start, end = closure[i-j] + obj[i] = slice(start, nn+end+2) + + return obj + + + def update_properties(self, diffusivity, heat_sources): + """ + Update diffusivity and heat sources + """ + self.diffusivity = diffusivity + self.heat_sources = heat_sources + return + + + def boundary_condition(self, wall, val, flux=False): + """ + Set the boundary conditions on each wall of the domain. + By default each wall is a Neumann (flux) condition. + If flux=True, positive val indicates a flux vector towards the centre + of the domain. + + val can be a vector with the same number of elements as the wall + """ + wall = str(wall) + + if wall in self.bc: + self.bc[wall]["val"] = np.array(val, copy=True) + self.bc[wall]["flux"] = flux + d = self.bc[wall] + + mask = d['mask'] + + if flux: + self.dirichlet_mask[mask] = False + self.bc[wall]["val"] /= -d['delta'] + else: + self.dirichlet_mask[mask] = True + + else: + raise ValueError("Wall should be one of {}".format(self.bc.keys())) + + + def construct_matrix(self): + """ + Construct the coefficient matrix + i.e. matrix A in Ax = b + + We vectorise the 7-point stencil for fast matrix insertion. + An extra border of dummy values around the domain allows for automatic + Neumann (flux) boundary creation. + These are stomped on if there are any Dirichlet conditions. + + """ + + nodes = self.nodes + nn = self.npoints + + index = self.index + + rows = self.rows + cols = self.cols + vals = self.vals + + dirichlet_mask = self.dirichlet_mask + + u = self.diffusivity + + k = np.zeros(nn + 2) + k[1:-1] = u + + for i in range(0, self.stencil_width): + obj = self.closure[i] + + rows[i] = nodes + cols[i] = index[obj].ravel() + + distance = np.linalg.norm(self.coords[cols[i]] - self.coords, axis=1) + distance[distance==0] = 1e-12 # protect against dividing by zero + delta = 1.0/(2.0*distance**2) + + vals[i] = delta*(k[obj] + u).ravel() + + + # Dirichlet boundary conditions (duplicates are summed) + cols[:,dirichlet_mask] = nodes[dirichlet_mask] + vals[:,dirichlet_mask] = 0.0 + + # zero off-grid coordinates + vals[cols < 0] = 0.0 + + # centre point + vals[-1] = 0.0 + vals[-1][dirichlet_mask] = -1.0 + + + row = rows.ravel() + col = cols.ravel() + val = vals.ravel() + + + # mask off-grid entries and sum duplicates + mask = col >= 0 + row = row[mask] + col = col[mask] + val = val[mask] + + mat = sparse.coo_matrix((val, (row, col)), shape=self.sizes).tocsr() + mat.sum_duplicates() + diag = np.ravel(mat.sum(axis=1)) + diag *= -1 + mat.setdiag(diag) + + return mat + + + def construct_rhs(self): + """ + Construct the right-hand-side vector + i.e. vector b in Ax = b + + Boundary conditions are grabbed from the dictionary and + summed to the rhs. + Be careful of duplicate entries on the corners!! + """ + + rhs = -1.0*self.heat_sources + + for wall in self.bc: + val = self.bc[wall]['val'] + flux = self.bc[wall]['flux'] + mask = self.bc[wall]['mask'] + if flux: + rhs[mask] += val + else: + rhs[mask] = val + + return rhs + + + def solve(self, matrix=None, rhs=None): + """ + Construct the matrix A and vector b in Ax = b + and solve for x + """ + if matrix is None: + matrix = self.construct_matrix() + if rhs is None: + rhs = self.construct_rhs() + # res = self.temperature + + T = spsolve(matrix, rhs) + self.temperature = T + + return T + + + def gradient(self, vector, **kwargs): + + return np.gradient(vector, self.coords, **kwargs) + + + def heatflux(self): + + T = self.temperature + k = self.diffusivity + divT = self.gradient(T) + return -k*divT \ No newline at end of file From 4f15ba5d6838a45255a7ed326cf02a8eb4ac5c66 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Tue, 2 Oct 2018 23:37:09 +0100 Subject: [PATCH 037/170] Updated documentation for thermal solver --- pycurious/__init__.py | 1 + pycurious/therm/__init__.py | 20 +++++ pycurious/therm/therm.py | 173 ++++++++++++++++++++++++++++++------ 3 files changed, 168 insertions(+), 26 deletions(-) create mode 100644 pycurious/therm/__init__.py diff --git a/pycurious/__init__.py b/pycurious/__init__.py index 609231f..800680c 100644 --- a/pycurious/__init__.py +++ b/pycurious/__init__.py @@ -20,5 +20,6 @@ from .grid import CurieGrid, bouligand2009, tanaka1999, maus1995, ComputeTanaka from .optimise import CurieOptimise from .parallel import CurieParallel +from .therm import CurieTherm from . import mapping from .documentation import install_documentation \ No newline at end of file diff --git a/pycurious/therm/__init__.py b/pycurious/therm/__init__.py new file mode 100644 index 0000000..f5020cb --- /dev/null +++ b/pycurious/therm/__init__.py @@ -0,0 +1,20 @@ +""" +Copyright 2018 Ben Mather, Robert Delhaye + +This file is part of PyCurious. + +PyCurious is free software: you can redistribute it and/or modify +it under the terms of the GNU Lesser General Public License as published by +the Free Software Foundation, either version 3 of the License, or any later version. + +PyCurious is distributed in the hope that it will be useful, +but WITHOUT ANY WARRANTY; without even the implied warranty of +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +GNU Lesser General Public License for more details. + +You should have received a copy of the GNU Lesser General Public License +along with PyCurious. If not, see . +""" + +# -*- coding: utf-8 -*- +from .therm import * \ No newline at end of file diff --git a/pycurious/therm/therm.py b/pycurious/therm/therm.py index e9329ef..3e9eee5 100644 --- a/pycurious/therm/therm.py +++ b/pycurious/therm/therm.py @@ -19,12 +19,37 @@ import numpy as np from scipy import sparse from sparse.linalg import spsolve +from multiprocessing import Pool, Process, Queue, cpu_count try: range=xrange except: pass class CurieTherm(object): + """ + Implicit 1d solver for the steady-state heat equation + over a structured grid using sparse matrices. + + Parameters + ---------- + minZ : float, minimum Cartesian coordinate + maxZ : float, maximum Cartesian coordinate + resZ : int, resolution in the z direction + kwargs : dict, keyword arguments to pass to control + optional functionality e.g. + - stencil_width=int : number of node neighbours to + include in each matrix row + + Attributes + ---------- + diffusivity : float shape(n,) thermal conductivity field + heat_sources : float shape(n,) heat source field + temperature : float shape(n,) temperature field + + npoints : int, number of nodes in the mesh + sizes : (int,int) dimensions of the sparse matrix + + """ def __init__(self, minZ, maxZ, resZ, **kwargs): @@ -37,12 +62,15 @@ def __init__(self, minZ, maxZ, resZ, **kwargs): width = kwargs.pop('stencil_width', 1) self.stencil_width = 2*width + 1 - closure = [(0,-2),(2,0),(1,-1)] + closure = [(0,-2), (2,0), (1,-1)] self.closure = self._create_closure_object(closure) self._initialise_COO_vectors() self._initialise_boundary_dictionary() + self.diffusivity = np.zeros(resZ) + self.heat_sources = np.zeros(resZ) + self.temperature = np.zeros(resZ) def _initialise_COO_vectors(self): @@ -96,19 +124,30 @@ def update_properties(self, diffusivity, heat_sources): """ Update diffusivity and heat sources """ - self.diffusivity = diffusivity - self.heat_sources = heat_sources + self.diffusivity[:] = diffusivity + self.heat_sources[:] = heat_sources return def boundary_condition(self, wall, val, flux=False): """ Set the boundary conditions on each wall of the domain. - By default each wall is a Neumann (flux) condition. - If flux=True, positive val indicates a flux vector towards the centre - of the domain. - - val can be a vector with the same number of elements as the wall + By default each wall is a Dirichlet condition. + + Parameters + ---------- + wall : str, wall to assign bc - 'minZ' or 'maxZ' + val : float or array(n,) value(s) to assign to wall + flux : bool, toggle type of boundary condition + True = Neumann flux boundary condition + False = Dirichlet boundary condition (default) + + Notes + ----- + If flux=True, positive val indicates a flux vector towards the centre + of the domain. + + val can be a vector with the same number of elements as the wall """ wall = str(wall) @@ -131,14 +170,15 @@ def boundary_condition(self, wall, val, flux=False): def construct_matrix(self): """ - Construct the coefficient matrix - i.e. matrix A in Ax = b - - We vectorise the 7-point stencil for fast matrix insertion. - An extra border of dummy values around the domain allows for automatic - Neumann (flux) boundary creation. - These are stomped on if there are any Dirichlet conditions. - + Construct a sparse coefficient matrix + i.e. matrix A in AT = b + + Notes + ----- + We vectorise the 7-point stencil for fast matrix insertion. + An extra border of dummy values around the domain allows for automatic + Neumann (flux) boundary creation. + These are stomped on if there are any Dirichlet conditions. """ nodes = self.nodes @@ -151,6 +191,7 @@ def construct_matrix(self): vals = self.vals dirichlet_mask = self.dirichlet_mask + coords = self.coords.reshape(-1,1) u = self.diffusivity @@ -163,7 +204,7 @@ def construct_matrix(self): rows[i] = nodes cols[i] = index[obj].ravel() - distance = np.linalg.norm(self.coords[cols[i]] - self.coords, axis=1) + distance = np.linalg.norm(coords[cols[i]] - coords, axis=1) distance[distance==0] = 1e-12 # protect against dividing by zero delta = 1.0/(2.0*distance**2) @@ -205,11 +246,13 @@ def construct_matrix(self): def construct_rhs(self): """ Construct the right-hand-side vector - i.e. vector b in Ax = b + i.e. vector b in AT = b - Boundary conditions are grabbed from the dictionary and - summed to the rhs. - Be careful of duplicate entries on the corners!! + Notes + ----- + Boundary conditions are grabbed from the dictionary and + summed to the rhs. + Be careful of duplicate entries on the corners!! """ rhs = -1.0*self.heat_sources @@ -228,8 +271,24 @@ def construct_rhs(self): def solve(self, matrix=None, rhs=None): """ - Construct the matrix A and vector b in Ax = b - and solve for x + Construct the matrix A and vector b in AT = b and solve for T + (i.e. temperature field) + + Arguments + --------- + matrix : (optional) scipy sparse matrix object + build using construct_matrix() + rhs : (optional) numpy right-hand-side vector + build using construct_rhs() + + Returns + ------- + sol : 1d array shape(n,) temperature solution + + Notes + ----- + The solution to the system of linear equations AT = b is solved + with spsolve in the scipy.sparse.linalg module """ if matrix is None: matrix = self.construct_matrix() @@ -238,19 +297,81 @@ def solve(self, matrix=None, rhs=None): # res = self.temperature T = spsolve(matrix, rhs) - self.temperature = T + self.temperature[:] = T return T def gradient(self, vector, **kwargs): - + """ + Calculate gradient of a vector + + Arguments + --------- + vector : 1d array of shape(n,) + + Returns + ------- + dvdz : 1d array of shape(n,) + derivative of vector in z direction + """ return np.gradient(vector, self.coords, **kwargs) def heatflux(self): + """ + Calculate the heat flux from the conductivity field + and temperature solution + + Returns + ------- + qz : 1d array shape(n,) heat flux vector + """ T = self.temperature k = self.diffusivity divT = self.gradient(T) - return -k*divT \ No newline at end of file + return -k*divT + + + def isosurface(self, vector, isoval, interp='linear'): + """ + Calculate an isosurface along the z axis + + Parameters + ---------- + vector : array, the same size as the mesh (n,) + isoval : float, isosurface value + interp : str, interpolation method can be either + 'nearest' - nearest neighbour interpolation + 'linear' - linear interpolation + + Returns + ------- + z_interp : isosurface + """ + coords = self.coords + sort_idx = np.abs(vector - isoval).argsort() + i0 = sort_idx[0] + z0 = coords[i0] + + if interp == 'linear': + v0 = vector[i0] + + # identify next nearest node + i1 = sort_idx[1] + z1 = coords[i1] + v1 = vector[i1] + + vmin = min(v0,v1) + vmax = max(v0,v1) + + ratio = np.array([isoval, vmin, vmax]) + ratio -= ratio.min() + ratio /= ratio.max() + z_interp = ratio[0]*z1 + (1.0 - ratio[0])*z0 + return z_interp + elif interp == 'nearest': + return z0 + else: + raise ValueError("enter a valid interp method: 'linear' or 'nearest'") From 5e1ad77315f0ce2e406102e459400783a9209473 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Wed, 3 Oct 2018 11:51:49 +0100 Subject: [PATCH 038/170] Stupid mistake in metropolis_hastings routine --- pycurious/optimise/optimise.py | 1 + 1 file changed, 1 insertion(+) diff --git a/pycurious/optimise/optimise.py b/pycurious/optimise/optimise.py index bcceb3e..241a130 100644 --- a/pycurious/optimise/optimise.py +++ b/pycurious/optimise/optimise.py @@ -450,6 +450,7 @@ def process_subgrid(subgrid): x0 = x1 P0 = P1 + P0 = np.exp(-self.min_func(x0, k, Phi, sigma_Phi)) # Now sample posterior for i in range(nsim): From 8d4166b9a5b2f3331afd6e5407d07e0e7a1af8c9 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Tue, 9 Oct 2018 14:51:00 +0100 Subject: [PATCH 039/170] Bug fix to the standard deviation of Phi --- pycurious/grid/curie.py | 17 ++++++----------- pycurious/optimise/optimise.py | 1 + pycurious/therm/therm.py | 2 +- setup.py | 3 ++- 4 files changed, 10 insertions(+), 13 deletions(-) diff --git a/pycurious/grid/curie.py b/pycurious/grid/curie.py index 44977f9..3ad5af2 100644 --- a/pycurious/grid/curie.py +++ b/pycurious/grid/curie.py @@ -216,7 +216,7 @@ def radial_spectrum(self, subgrid, taper=np.hanning, scale=0.001, **kwargs): S = np.empty(nbins) k = np.empty(nbins) - sigma2 = np.empty(nbins) + sigma = np.empty(nbins) i0 = int((nw - 1)//2) nw_range = np.arange(0, nw) @@ -228,12 +228,9 @@ def radial_spectrum(self, subgrid, taper=np.hanning, scale=0.001, **kwargs): rr = 2.0*np.log(FT[mask]) S[i] = rr.mean() k[i] = kk[mask].mean() - sigma2[i] = np.std(rr)/np.sqrt(rr.size) + sigma[i] = np.std(rr) - - sigma_S = np.sqrt(sigma2) - - return k, S, sigma_S + return k, S, sigma def radial_spectrum_log(self, subgrid, taper=np.hanning, scale=0.001, **kwargs): @@ -286,7 +283,7 @@ def radial_spectrum_log(self, subgrid, taper=np.hanning, scale=0.001, **kwargs): S = np.empty(nbins) k = np.empty(nbins) - sigma2 = np.empty(nbins) + sigma = np.empty(nbins) i0 = int((nw - 1)//2) ix, iy = np.mgrid[0:nw,0:nw] @@ -297,11 +294,9 @@ def radial_spectrum_log(self, subgrid, taper=np.hanning, scale=0.001, **kwargs): rr = np.log(np.sqrt(FT[mask])) S[i] = rr.mean() k[i] = kk[mask].mean() - sigma2[i] = np.std(rr)/np.sqrt(rr.size) - - sigma_S = np.sqrt(sigma2) + sigma[i] = np.std(rr) - return k, S, sigma_S + return k, S, sigma def azimuthal_spectrum(self, subgrid, taper=np.hanning, scale=0.001, theta=5.0, **kwargs): diff --git a/pycurious/optimise/optimise.py b/pycurious/optimise/optimise.py index 241a130..6d6bb4e 100644 --- a/pycurious/optimise/optimise.py +++ b/pycurious/optimise/optimise.py @@ -132,6 +132,7 @@ def objective_routine(self, **kwargs): def objective_function(self, x, x0, sigma_x0, *args): """ Objective function used in objective_routine + Evaluates the l2-norm misfit Parameters --------- diff --git a/pycurious/therm/therm.py b/pycurious/therm/therm.py index 3e9eee5..ceba4d3 100644 --- a/pycurious/therm/therm.py +++ b/pycurious/therm/therm.py @@ -18,7 +18,7 @@ import numpy as np from scipy import sparse -from sparse.linalg import spsolve +from scipy.sparse.linalg import spsolve from multiprocessing import Pool, Process, Queue, cpu_count try: range=xrange diff --git a/setup.py b/setup.py index 1f16716..e2d17f4 100644 --- a/setup.py +++ b/setup.py @@ -35,7 +35,8 @@ 'pycurious.grid', 'pycurious.optimise', 'pycurious.mapping', - 'pycurious.parallel'], + 'pycurious.parallel', + 'pycurious.therm'], package_data = {'pycurious': ['Examples/data/*', 'Examples/Notebooks/Tanaka/*.ipynb', 'Examples/Notebooks/Bouligand/*.ipynb', From 90297d6aaaa8bdf8d49671644891226fd36f799c Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Tue, 23 Oct 2018 15:27:23 +0100 Subject: [PATCH 040/170] Include the uncertainty on the power spectrum --- pycurious/optimise/optimise.py | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/pycurious/optimise/optimise.py b/pycurious/optimise/optimise.py index 6d6bb4e..97b1d40 100644 --- a/pycurious/optimise/optimise.py +++ b/pycurious/optimise/optimise.py @@ -144,7 +144,7 @@ def objective_function(self, x, x0, sigma_x0, *args): ------- misfit : float """ - return 0.5*np.linalg.norm((x - x0)/sigma_x0)**2 + return 0.5*np.sum((x - x0)**2/sigma_x0**2) def min_func(self, x, kh, Phi, sigma_Phi): @@ -174,7 +174,7 @@ def min_func(self, x, kh, Phi, sigma_Phi): warnings.simplefilter("ignore") Phi_syn = bouligand2009(kh, beta, zt, dz, C) - misfit = self.objective_function(Phi_syn, Phi, 1.0) + misfit = self.objective_function(Phi_syn, Phi, sigma_Phi) if not np.isfinite(misfit): misfit = 1e99 else: From e2b9a6b9369462c03b9ff4361e55197f9eaeb9a4 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Tue, 23 Oct 2018 15:28:19 +0100 Subject: [PATCH 041/170] Slight efficiency improvement --- pycurious/grid/curie.py | 3 +-- 1 file changed, 1 insertion(+), 2 deletions(-) diff --git a/pycurious/grid/curie.py b/pycurious/grid/curie.py index 3ad5af2..f82150a 100644 --- a/pycurious/grid/curie.py +++ b/pycurious/grid/curie.py @@ -219,8 +219,7 @@ def radial_spectrum(self, subgrid, taper=np.hanning, scale=0.001, **kwargs): sigma = np.empty(nbins) i0 = int((nw - 1)//2) - nw_range = np.arange(0, nw) - iy, ix = np.meshgrid(nw_range, nw_range) + ix, iy = np.mgrid[0:nw,0:nw] kk = np.hypot((ix - i0)*dk, (iy - i0)*dk) for i in range(0, nbins): From 60c2ecc5d71cbf100162925aaacef39e745c882b Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Thu, 25 Oct 2018 15:26:05 +0100 Subject: [PATCH 042/170] Change back the weighting of the spectrum Since there are fewer points in the low wavenumbers, the weighting is already biased towards the high wavenumbers. Including sigma_Phi in the objective function biases these points even further. --- pycurious/optimise/optimise.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/pycurious/optimise/optimise.py b/pycurious/optimise/optimise.py index 97b1d40..4f80e48 100644 --- a/pycurious/optimise/optimise.py +++ b/pycurious/optimise/optimise.py @@ -174,7 +174,7 @@ def min_func(self, x, kh, Phi, sigma_Phi): warnings.simplefilter("ignore") Phi_syn = bouligand2009(kh, beta, zt, dz, C) - misfit = self.objective_function(Phi_syn, Phi, sigma_Phi) + misfit = self.objective_function(Phi_syn, Phi, 1.0) if not np.isfinite(misfit): misfit = 1e99 else: From db6ba97a8d05b5586eb4e7c4100b93b70613770c Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Thu, 10 Jan 2019 11:55:37 +1100 Subject: [PATCH 043/170] Add Dockerfile and update version --- README.md | 45 ++++++++++++++--------- docker/Dockerfile | 93 +++++++++++++++++++++++++++++++++++++++++++++++ setup.py | 2 +- 3 files changed, 122 insertions(+), 18 deletions(-) create mode 100644 docker/Dockerfile diff --git a/README.md b/README.md index 34e0e32..d65213f 100644 --- a/README.md +++ b/README.md @@ -1,5 +1,7 @@ # PyCurious +[![PyPI version](https://badge.fury.io/py/pycurious.svg)](https://badge.fury.io/py/pycurious) + Magnetic data is one of the most common geophysics datasets available on the surface of the Earth. Curie depth is the depth at which rocks lose their magnetism. The most prevalent magnetic mineral is magnetite, which has a Curie point of 580C, thus the Curie depth is often interpreted as the 580C isotherm. Current methods to derive Curie depth first compute the (fast) Fourier transform over a square window of a magnetic anomaly that has been reduced to the pole. The depth and thickness of magnetic sources is estimated from the slope of the radial power spectrum. *PyCurious* implements two common approaches: @@ -7,20 +9,27 @@ Current methods to derive Curie depth first compute the (fast) Fourier transform - [Tanaka *et al.* 1999](http://linkinghub.elsevier.com/retrieve/pii/S0040195199000724) - [Bouligand *et al.* 2009](http://doi.wiley.com/10.1029/2009JB006494) -Both of these methods to compute Curie depth are covered in the form of Jupyter notebooks. Copy these into your working directory by running, +Both of these methods to compute Curie depth are covered in the form of Jupyter notebooks. Copy these into your working directory by running: ```python import pycurious pycurious.install_documentation() ``` +| Features | Progress | +| ----------------------------------------------------- | ------------------ | +| Bayesian uncertainty analysis | :heavy_check_mark: | +| Conversion between coordinate reference systems | :heavy_check_mark: | +| Importing and exporting GeoTiffs | :heavy_check_mark: | +| Parallelisation using OpenMP implementation in Python | :heavy_check_mark: | +| Parallelisation using OpenMPI | 10% | + ## Usage -PyCurious consists of 3 classes that inherit from each other: +PyCurious consists of 2 classes: 1. **CurieGrid**: base class that computes radial power spectrum, centroids for processing, decomposition of subgrids. 2. **CurieOptimise**: optimisation module for fitting the synthetic power spectrum (inherits CurieGrid). -3. **CurieParallel**: parallel implementation based on the decomposition of subgrids (inherits CurieOptimise). Also included is a `mapping` module for gridding scattered data points, and converting between coordinate reference systems (CRS). @@ -36,14 +45,14 @@ grid = pycurious.CurieOptimise(mag_anomaly, xmin, xmax, ymin, ymax) subgrid = grid.subgrid(window_size, x, y) # compute the radial power spectrum -k, Phi, sigma_Phi = grid.radial_power_spectrum(subgrid) +k, Phi, sigma_Phi = grid.radial_spectrum(subgrid) ``` ## Dependencies -- Python 2.7 and above -- Numpy 1.9 and above -- Scipy 0.14 and above +- Python 2.7+ and 3.6+ +- Numpy 1.9+ +- Scipy 0.14+ - Cython Optional dependencies for mapping module: @@ -52,24 +61,26 @@ Optional dependencies for mapping module: - [pyproj](https://github.com/jswhit/pyproj) - [Cartopy](http://scitools.org.uk/cartopy/docs/latest/index.html) -Optional dependencies for parallel module: - -- [mpi4py](https://mpi4py.readthedocs.io/en/stable/) -- [petsc4py](http://www.mcs.anl.gov/petsc/petsc4py-current/docs/usrman/install.html) - ## Installation -To install: +To install with **setuptools**: -``` +```bash python setup.py install --user ``` -This will compile all C and Fortran sources and install them to the user directory (omit the `--user` flag to install to the system directory). Remember to delete the build folder if you are upgrading this package. +This will compile all C source code and install them to the user directory (omit the `--user` flag to install to the system directory). Remember to delete the build folder if you are upgrading this package. -Alternatively, install using pip: +Alternatively, install using **pip**: -``` +```bash pip install pycurious --user ``` +### Docker + +PyCurious and all of its dependencies are available for deployment with Docker: + +```bash +docker pull brmather/pycurious +``` diff --git a/docker/Dockerfile b/docker/Dockerfile new file mode 100644 index 0000000..875cda3 --- /dev/null +++ b/docker/Dockerfile @@ -0,0 +1,93 @@ +FROM alpine:latest +MAINTAINER https://github.com/brmather +ENV IMAGENAME=brmather/pycurious +ENV PROJ_NAME=pycurious-env + +# Install things +RUN echo "http://mirror.leaseweb.com/alpine/edge/testing" >> /etc/apk/repositories +RUN apk add --update --no-cache \ + gcc \ + g++ \ + gfortran \ + build-base \ + python3-dev \ + py3-pip \ + py3-numpy \ + py3-scipy \ + py3-zmq \ + cmake \ + curl \ + wget \ + libzmq \ + zlib-dev \ + musl-dev \ + freetype-dev \ + libpng-dev \ + libxml2-dev \ + openblas-dev \ + geos-dev \ + proj4-dev + +RUN echo "http://dl-cdn.alpinelinux.org/alpine/edge/main" >> /etc/apk/repositories +RUN apk add --update --no-cache \ + libressl2.7-libcrypto \ + gdal-dev + + +RUN ln -s /usr/include/locale.h /usr/include/xlocale.h +# RUN python3 -m pip install --no-cache-dir --upgrade numpy && \ +RUN python3 -m pip install --no-cache-dir --upgrade pip numpy && \ + python3 -m pip install --no-cache-dir setuptools wheel Cython && \ + python3 -m pip install --no-cache-dir \ + packaging \ + jupyter \ + pyepsg \ + cartopy && \ + python3 -m pip install --no-cache-dir matplotlib + + +# Install Tini.. this is required because CMD (below) doesn't play nice with notebooks for some reason: +# https://github.com/ipython/ipython/issues/7062, https://github.com/jupyter/notebook/issues/334 +RUN curl -L https://github.com/krallin/tini/releases/download/v0.10.0/tini > tini && \ + echo "1361527f39190a7338a0b434bd8c88ff7233ce7b9a4876f3315c22fce7eca1b0 *tini" | sha256sum -c - && \ + mv tini /usr/local/bin/tini && \ + chmod +x /usr/local/bin/tini + +# expose notebook port +EXPOSE 8888 + + +# add a notebook profile +RUN mkdir -p -m 700 /root/.jupyter/ && \ + echo "c.NotebookApp.ip = '0.0.0.0'" >> /root/.jupyter/jupyter_notebook_config.py + +# note we also use xvfb which is required for viz +ENTRYPOINT ["/usr/local/bin/tini", "--"] + + +# add pycurious +WORKDIR /work +ENV MODULE_DIR="pycurious-src" +RUN addgroup -S jovyan && \ + adduser -D -S jovyan -G jovyan + +ADD --chown=jovyan:jovyan . / pycurious-src/ +RUN cd pycurious-src && \ + python3 -m pip install --no-deps --upgrade . && \ + mv pycurious/Examples/data /home/jovyan/ && \ + mv pycurious/Examples/Notebooks /home/jovyan/ && \ + mv pycurious/Examples/Scripts /home/jovyan/ && \ + cd /work && \ + rm -rf /work/pycurious-src + + +# change ownership of everything +ENV NB_USER jovyan +RUN chown -R jovyan:jovyan /home/jovyan +USER jovyan +WORKDIR /home/jovyan/ +RUN find -name \*.ipynb -print0 | xargs -0 jupyter trust + + +# launch notebook +ENTRYPOINT ["jupyter", "notebook", "--ip='0.0.0.0'", "--no-browser"] \ No newline at end of file diff --git a/setup.py b/setup.py index e2d17f4..9b00ac3 100644 --- a/setup.py +++ b/setup.py @@ -28,7 +28,7 @@ author = "Ben Mather", author_email = "brmather1@gmail.com", url = "https://github.com/brmather/pycurious", - version = "0.1.1", + version = "0.2", description = "Python tool for computing the Curie depth from magnetic data", ext_modules = cythonize([ext]), packages = ['pycurious', From 7f291781da97f4f8fd0a1842b70988e01e77ff8e Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Thu, 10 Jan 2019 11:56:05 +1100 Subject: [PATCH 044/170] Convert Notebooks to Python 3 --- .../Notebooks/Bouligand/Ex1-Plot-power-spectrum.ipynb | 10 +++++----- .../Notebooks/Bouligand/Ex2-Compute-Curie-depth.ipynb | 10 +++++----- .../Bouligand/Ex3-Posing-the-inverse-problem.ipynb | 10 +++++----- .../Ex4-Spatial-variation-of-Curie-depth.ipynb | 10 +++++----- .../Bouligand/Ex5-Mapping-Curie-depth-EMAG2.ipynb | 10 +++++----- .../Notebooks/Tanaka/Ex1-Plot-power-spectrum.ipynb | 10 +++++----- .../Notebooks/Tanaka/Ex2-Compute-Curie-depth.ipynb | 10 +++++----- .../Notebooks/Tanaka/Ex3-Parameter-exploration.ipynb | 10 +++++----- 8 files changed, 40 insertions(+), 40 deletions(-) diff --git a/pycurious/Examples/Notebooks/Bouligand/Ex1-Plot-power-spectrum.ipynb b/pycurious/Examples/Notebooks/Bouligand/Ex1-Plot-power-spectrum.ipynb index 6647233..671aea3 100644 --- a/pycurious/Examples/Notebooks/Bouligand/Ex1-Plot-power-spectrum.ipynb +++ b/pycurious/Examples/Notebooks/Bouligand/Ex1-Plot-power-spectrum.ipynb @@ -286,21 +286,21 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 2", + "display_name": "Python 3", "language": "python", - "name": "python2" + "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", - "version": 2 + "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", - "pygments_lexer": "ipython2", - "version": "2.7.15" + "pygments_lexer": "ipython3", + "version": "3.6.8" } }, "nbformat": 4, diff --git a/pycurious/Examples/Notebooks/Bouligand/Ex2-Compute-Curie-depth.ipynb b/pycurious/Examples/Notebooks/Bouligand/Ex2-Compute-Curie-depth.ipynb index 416be32..d3386be 100644 --- a/pycurious/Examples/Notebooks/Bouligand/Ex2-Compute-Curie-depth.ipynb +++ b/pycurious/Examples/Notebooks/Bouligand/Ex2-Compute-Curie-depth.ipynb @@ -235,21 +235,21 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 2", + "display_name": "Python 3", "language": "python", - "name": "python2" + "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", - "version": 2 + "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", - "pygments_lexer": "ipython2", - "version": "2.7.15" + "pygments_lexer": "ipython3", + "version": "3.6.8" } }, "nbformat": 4, diff --git a/pycurious/Examples/Notebooks/Bouligand/Ex3-Posing-the-inverse-problem.ipynb b/pycurious/Examples/Notebooks/Bouligand/Ex3-Posing-the-inverse-problem.ipynb index 1aa42f2..b11dcca 100644 --- a/pycurious/Examples/Notebooks/Bouligand/Ex3-Posing-the-inverse-problem.ipynb +++ b/pycurious/Examples/Notebooks/Bouligand/Ex3-Posing-the-inverse-problem.ipynb @@ -328,21 +328,21 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 2", + "display_name": "Python 3", "language": "python", - "name": "python2" + "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", - "version": 2 + "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", - "pygments_lexer": "ipython2", - "version": "2.7.15" + "pygments_lexer": "ipython3", + "version": "3.6.8" } }, "nbformat": 4, diff --git a/pycurious/Examples/Notebooks/Bouligand/Ex4-Spatial-variation-of-Curie-depth.ipynb b/pycurious/Examples/Notebooks/Bouligand/Ex4-Spatial-variation-of-Curie-depth.ipynb index abbf3d1..aed8b01 100644 --- a/pycurious/Examples/Notebooks/Bouligand/Ex4-Spatial-variation-of-Curie-depth.ipynb +++ b/pycurious/Examples/Notebooks/Bouligand/Ex4-Spatial-variation-of-Curie-depth.ipynb @@ -284,21 +284,21 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 2", + "display_name": "Python 3", "language": "python", - "name": "python2" + "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", - "version": 2 + "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", - "pygments_lexer": "ipython2", - "version": "2.7.15" + "pygments_lexer": "ipython3", + "version": "3.6.8" } }, "nbformat": 4, diff --git a/pycurious/Examples/Notebooks/Bouligand/Ex5-Mapping-Curie-depth-EMAG2.ipynb b/pycurious/Examples/Notebooks/Bouligand/Ex5-Mapping-Curie-depth-EMAG2.ipynb index af8dec2..9a4604e 100644 --- a/pycurious/Examples/Notebooks/Bouligand/Ex5-Mapping-Curie-depth-EMAG2.ipynb +++ b/pycurious/Examples/Notebooks/Bouligand/Ex5-Mapping-Curie-depth-EMAG2.ipynb @@ -339,21 +339,21 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 2", + "display_name": "Python 3", "language": "python", - "name": "python2" + "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", - "version": 2 + "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", - "pygments_lexer": "ipython2", - "version": "2.7.15" + "pygments_lexer": "ipython3", + "version": "3.6.8" } }, "nbformat": 4, diff --git a/pycurious/Examples/Notebooks/Tanaka/Ex1-Plot-power-spectrum.ipynb b/pycurious/Examples/Notebooks/Tanaka/Ex1-Plot-power-spectrum.ipynb index 976bdb1..8676c09 100644 --- a/pycurious/Examples/Notebooks/Tanaka/Ex1-Plot-power-spectrum.ipynb +++ b/pycurious/Examples/Notebooks/Tanaka/Ex1-Plot-power-spectrum.ipynb @@ -199,21 +199,21 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 2", + "display_name": "Python 3", "language": "python", - "name": "python2" + "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", - "version": 2 + "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", - "pygments_lexer": "ipython2", - "version": "2.7.15" + "pygments_lexer": "ipython3", + "version": "3.6.8" } }, "nbformat": 4, diff --git a/pycurious/Examples/Notebooks/Tanaka/Ex2-Compute-Curie-depth.ipynb b/pycurious/Examples/Notebooks/Tanaka/Ex2-Compute-Curie-depth.ipynb index d92e5ad..e2df8b5 100644 --- a/pycurious/Examples/Notebooks/Tanaka/Ex2-Compute-Curie-depth.ipynb +++ b/pycurious/Examples/Notebooks/Tanaka/Ex2-Compute-Curie-depth.ipynb @@ -173,21 +173,21 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 2", + "display_name": "Python 3", "language": "python", - "name": "python2" + "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", - "version": 2 + "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", - "pygments_lexer": "ipython2", - "version": "2.7.15" + "pygments_lexer": "ipython3", + "version": "3.6.8" } }, "nbformat": 4, diff --git a/pycurious/Examples/Notebooks/Tanaka/Ex3-Parameter-exploration.ipynb b/pycurious/Examples/Notebooks/Tanaka/Ex3-Parameter-exploration.ipynb index d65f910..717a8f2 100644 --- a/pycurious/Examples/Notebooks/Tanaka/Ex3-Parameter-exploration.ipynb +++ b/pycurious/Examples/Notebooks/Tanaka/Ex3-Parameter-exploration.ipynb @@ -242,21 +242,21 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 2", + "display_name": "Python 3", "language": "python", - "name": "python2" + "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", - "version": 2 + "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", - "pygments_lexer": "ipython2", - "version": "2.7.15" + "pygments_lexer": "ipython3", + "version": "3.6.8" } }, "nbformat": 4, From efbe3c27c1fc20bda022eb70ac4e10a2638d277a Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Thu, 10 Jan 2019 12:59:19 +1100 Subject: [PATCH 045/170] build off base image --- docker/Dockerfile | 67 +---------------------------------------------- 1 file changed, 1 insertion(+), 66 deletions(-) diff --git a/docker/Dockerfile b/docker/Dockerfile index 875cda3..c54da49 100644 --- a/docker/Dockerfile +++ b/docker/Dockerfile @@ -1,69 +1,4 @@ -FROM alpine:latest -MAINTAINER https://github.com/brmather -ENV IMAGENAME=brmather/pycurious -ENV PROJ_NAME=pycurious-env - -# Install things -RUN echo "http://mirror.leaseweb.com/alpine/edge/testing" >> /etc/apk/repositories -RUN apk add --update --no-cache \ - gcc \ - g++ \ - gfortran \ - build-base \ - python3-dev \ - py3-pip \ - py3-numpy \ - py3-scipy \ - py3-zmq \ - cmake \ - curl \ - wget \ - libzmq \ - zlib-dev \ - musl-dev \ - freetype-dev \ - libpng-dev \ - libxml2-dev \ - openblas-dev \ - geos-dev \ - proj4-dev - -RUN echo "http://dl-cdn.alpinelinux.org/alpine/edge/main" >> /etc/apk/repositories -RUN apk add --update --no-cache \ - libressl2.7-libcrypto \ - gdal-dev - - -RUN ln -s /usr/include/locale.h /usr/include/xlocale.h -# RUN python3 -m pip install --no-cache-dir --upgrade numpy && \ -RUN python3 -m pip install --no-cache-dir --upgrade pip numpy && \ - python3 -m pip install --no-cache-dir setuptools wheel Cython && \ - python3 -m pip install --no-cache-dir \ - packaging \ - jupyter \ - pyepsg \ - cartopy && \ - python3 -m pip install --no-cache-dir matplotlib - - -# Install Tini.. this is required because CMD (below) doesn't play nice with notebooks for some reason: -# https://github.com/ipython/ipython/issues/7062, https://github.com/jupyter/notebook/issues/334 -RUN curl -L https://github.com/krallin/tini/releases/download/v0.10.0/tini > tini && \ - echo "1361527f39190a7338a0b434bd8c88ff7233ce7b9a4876f3315c22fce7eca1b0 *tini" | sha256sum -c - && \ - mv tini /usr/local/bin/tini && \ - chmod +x /usr/local/bin/tini - -# expose notebook port -EXPOSE 8888 - - -# add a notebook profile -RUN mkdir -p -m 700 /root/.jupyter/ && \ - echo "c.NotebookApp.ip = '0.0.0.0'" >> /root/.jupyter/jupyter_notebook_config.py - -# note we also use xvfb which is required for viz -ENTRYPOINT ["/usr/local/bin/tini", "--"] - +FROM brmather/pycurious-base:latest # add pycurious WORKDIR /work From 4f3bc2ced38bd0accf6984ee0607ac31f74533e9 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Thu, 10 Jan 2019 21:33:20 +1100 Subject: [PATCH 046/170] Move dockerfile to top level directory --- docker/Dockerfile => Dockerfile | 0 docker/Dockerfile-base | 62 +++++++++++++++++++++++++++++++++ 2 files changed, 62 insertions(+) rename docker/Dockerfile => Dockerfile (100%) create mode 100644 docker/Dockerfile-base diff --git a/docker/Dockerfile b/Dockerfile similarity index 100% rename from docker/Dockerfile rename to Dockerfile diff --git a/docker/Dockerfile-base b/docker/Dockerfile-base new file mode 100644 index 0000000..6cac64f --- /dev/null +++ b/docker/Dockerfile-base @@ -0,0 +1,62 @@ +FROM alpine:latest + +# Install things +RUN echo "http://mirror.leaseweb.com/alpine/edge/testing" >> /etc/apk/repositories +RUN apk add --update --no-cache \ + gcc \ + g++ \ + gfortran \ + build-base \ + python3-dev \ + py3-pip \ + py3-numpy \ + py3-scipy \ + py3-zmq \ + cmake \ + curl \ + wget \ + libzmq \ + zlib-dev \ + musl-dev \ + freetype-dev \ + libpng-dev \ + libxml2-dev \ + openblas-dev \ + geos-dev \ + proj4-dev + +RUN echo "http://dl-cdn.alpinelinux.org/alpine/edge/main" >> /etc/apk/repositories +RUN apk add --update --no-cache \ + libressl2.7-libcrypto \ + gdal-dev + + +RUN ln -s /usr/include/locale.h /usr/include/xlocale.h +# RUN python3 -m pip install --no-cache-dir --upgrade numpy && \ +RUN python3 -m pip install --no-cache-dir --upgrade pip numpy && \ + python3 -m pip install --no-cache-dir setuptools wheel Cython && \ + python3 -m pip install --no-cache-dir \ + packaging \ + jupyter \ + pyepsg \ + cartopy && \ + python3 -m pip install --no-cache-dir matplotlib + + +# Install Tini.. this is required because CMD (below) doesn't play nice with notebooks for some reason: +# https://github.com/ipython/ipython/issues/7062, https://github.com/jupyter/notebook/issues/334 +RUN curl -L https://github.com/krallin/tini/releases/download/v0.10.0/tini > tini && \ + echo "1361527f39190a7338a0b434bd8c88ff7233ce7b9a4876f3315c22fce7eca1b0 *tini" | sha256sum -c - && \ + mv tini /usr/local/bin/tini && \ + chmod +x /usr/local/bin/tini + +# expose notebook port +EXPOSE 8888 + + +# add a notebook profile +RUN mkdir -p -m 700 /root/.jupyter/ && \ + echo "c.NotebookApp.ip = '0.0.0.0'" >> /root/.jupyter/jupyter_notebook_config.py + +# note we also use xvfb which is required for viz +ENTRYPOINT ["/usr/local/bin/tini", "--"] \ No newline at end of file From 99fb6bcf18e822ca8654d90aab32c5ae507cf2c5 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Tue, 19 Mar 2019 15:24:59 +1100 Subject: [PATCH 047/170] Reorganising directory structure --- {docker => Docker}/Dockerfile-base | 0 README.md | 87 +----------------- docs/_config.yml | 1 - docs/bouligand.md | 12 --- COPYING => pycurious-src/COPYING | 0 .../COPYING.LESSER | 0 MANIFEST.in => pycurious-src/MANIFEST.in | 0 pycurious-src/README.md | 86 +++++++++++++++++ .../Ex1-Plot-power-spectrum-checkpoint.ipynb | 0 ...rie-depth-Tanaka-approach-checkpoint.ipynb | 0 ...-depth-Bouligand-approach-checkpoint.ipynb | 0 .../Ex3-Optimisation-routine-checkpoint.ipynb | 0 .../Bouligand/Ex1-Plot-power-spectrum.ipynb | 0 .../Bouligand/Ex2-Compute-Curie-depth.ipynb | 0 .../Ex3-Posing-the-inverse-problem.ipynb | 0 ...Ex4-Spatial-variation-of-Curie-depth.ipynb | 0 .../Ex5-Mapping-Curie-depth-EMAG2.ipynb | 0 .../Tanaka/Ex1-Plot-power-spectrum.ipynb | 0 .../Tanaka/Ex2-Compute-Curie-depth.ipynb | 0 .../Tanaka/Ex3-Parameter-exploration.ipynb | 0 .../pycurious}/Examples/Scripts/BFwdTest.py | 0 .../Examples/Scripts/CPD_Pts_find.sh | 0 .../Examples/Scripts/IapetusCheck.py | 0 .../Examples/Scripts/LinearFitScratch.py | 0 .../pycurious}/Examples/Scripts/RobTest.py | 0 .../Examples/Scripts/RosettePlot.sh | 0 .../pycurious}/Examples/Scripts/mag_grid2.npz | Bin .../pycurious}/Examples/Scripts/readme.txt | 0 .../pycurious}/Examples/Scripts/tst_data.npz | Bin .../Examples/data/test_mag_data.txt | 0 .../pycurious}/__init__.py | 0 .../pycurious}/documentation.py | 0 .../pycurious}/grid/__init__.py | 0 .../pycurious}/grid/curie.py | 0 .../pycurious}/mapping/__init__.py | 0 .../pycurious}/mapping/mapping.py | 0 .../pycurious}/optimise/__init__.py | 0 .../pycurious}/optimise/optimise.py | 0 .../pycurious}/parallel/__init__.py | 0 .../pycurious}/parallel/parallel.py | 0 .../pycurious}/therm/__init__.py | 0 .../pycurious}/therm/therm.py | 0 setup.cfg => pycurious-src/setup.cfg | 0 setup.py => pycurious-src/setup.py | 0 {src => pycurious-src/src}/cradon.c | 0 {src => pycurious-src/src}/cradon.h | 0 {src => pycurious-src/src}/cradon.pxd | 0 {src => pycurious-src/src}/radon.pyx | 0 .../tests}/Bouligand_forward.py | 0 .../tests}/optimise_test.py | 0 .../tests}/parallel_test.py | 0 .../tests}/test_multiprocessing.py | 0 .../tests}/valid_numbers.py | 0 53 files changed, 87 insertions(+), 99 deletions(-) rename {docker => Docker}/Dockerfile-base (100%) mode change 100644 => 120000 README.md delete mode 100644 docs/_config.yml delete mode 100644 docs/bouligand.md rename COPYING => pycurious-src/COPYING (100%) rename COPYING.LESSER => pycurious-src/COPYING.LESSER (100%) rename MANIFEST.in => pycurious-src/MANIFEST.in (100%) create mode 100644 pycurious-src/README.md rename {pycurious => pycurious-src/pycurious}/Examples/Notebooks/.ipynb_checkpoints/Ex1-Plot-power-spectrum-checkpoint.ipynb (100%) rename {pycurious => pycurious-src/pycurious}/Examples/Notebooks/.ipynb_checkpoints/Ex2a-Compute-Curie-depth-Tanaka-approach-checkpoint.ipynb (100%) rename {pycurious => pycurious-src/pycurious}/Examples/Notebooks/.ipynb_checkpoints/Ex2b-Compute-Curie-depth-Bouligand-approach-checkpoint.ipynb (100%) rename {pycurious => pycurious-src/pycurious}/Examples/Notebooks/.ipynb_checkpoints/Ex3-Optimisation-routine-checkpoint.ipynb (100%) rename {pycurious => pycurious-src/pycurious}/Examples/Notebooks/Bouligand/Ex1-Plot-power-spectrum.ipynb (100%) rename {pycurious => pycurious-src/pycurious}/Examples/Notebooks/Bouligand/Ex2-Compute-Curie-depth.ipynb (100%) rename {pycurious => pycurious-src/pycurious}/Examples/Notebooks/Bouligand/Ex3-Posing-the-inverse-problem.ipynb (100%) rename {pycurious => pycurious-src/pycurious}/Examples/Notebooks/Bouligand/Ex4-Spatial-variation-of-Curie-depth.ipynb (100%) rename {pycurious => pycurious-src/pycurious}/Examples/Notebooks/Bouligand/Ex5-Mapping-Curie-depth-EMAG2.ipynb (100%) 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pycurious-src/pycurious}/therm/therm.py (100%) rename setup.cfg => pycurious-src/setup.cfg (100%) rename setup.py => pycurious-src/setup.py (100%) rename {src => pycurious-src/src}/cradon.c (100%) rename {src => pycurious-src/src}/cradon.h (100%) rename {src => pycurious-src/src}/cradon.pxd (100%) rename {src => pycurious-src/src}/radon.pyx (100%) rename {tests => pycurious-src/tests}/Bouligand_forward.py (100%) rename {tests => pycurious-src/tests}/optimise_test.py (100%) rename {tests => pycurious-src/tests}/parallel_test.py (100%) rename {tests => pycurious-src/tests}/test_multiprocessing.py (100%) rename {tests => pycurious-src/tests}/valid_numbers.py (100%) diff --git a/docker/Dockerfile-base b/Docker/Dockerfile-base similarity index 100% rename from docker/Dockerfile-base rename to Docker/Dockerfile-base diff --git a/README.md b/README.md deleted file mode 100644 index d65213f..0000000 --- a/README.md +++ /dev/null @@ -1,86 +0,0 @@ -# PyCurious - -[![PyPI version](https://badge.fury.io/py/pycurious.svg)](https://badge.fury.io/py/pycurious) - -Magnetic data is one of the most common geophysics datasets available on the surface of the Earth. Curie depth is the depth at which rocks lose their magnetism. The most prevalent magnetic mineral is magnetite, which has a Curie point of 580C, thus the Curie depth is often interpreted as the 580C isotherm. - -Current methods to derive Curie depth first compute the (fast) Fourier transform over a square window of a magnetic anomaly that has been reduced to the pole. The depth and thickness of magnetic sources is estimated from the slope of the radial power spectrum. *PyCurious* implements two common approaches: - -- [Tanaka *et al.* 1999](http://linkinghub.elsevier.com/retrieve/pii/S0040195199000724) -- [Bouligand *et al.* 2009](http://doi.wiley.com/10.1029/2009JB006494) - -Both of these methods to compute Curie depth are covered in the form of Jupyter notebooks. Copy these into your working directory by running: - -```python -import pycurious -pycurious.install_documentation() -``` - -| Features | Progress | -| ----------------------------------------------------- | ------------------ | -| Bayesian uncertainty analysis | :heavy_check_mark: | -| Conversion between coordinate reference systems | :heavy_check_mark: | -| Importing and exporting GeoTiffs | :heavy_check_mark: | -| Parallelisation using OpenMP implementation in Python | :heavy_check_mark: | -| Parallelisation using OpenMPI | 10% | - -## Usage - -PyCurious consists of 2 classes: - -1. **CurieGrid**: base class that computes radial power spectrum, centroids for processing, decomposition of subgrids. -2. **CurieOptimise**: optimisation module for fitting the synthetic power spectrum (inherits CurieGrid). - -Also included is a `mapping` module for gridding scattered data points, and converting between coordinate reference systems (CRS). - -Below is a simple workflow to calculate the radial power spectrum: - -```python -import pycurious - -# initialise CurieOptimise object with 2D magnetic anomaly -grid = pycurious.CurieOptimise(mag_anomaly, xmin, xmax, ymin, ymax) - -# extract a square window of the magnetic anomaly -subgrid = grid.subgrid(window_size, x, y) - -# compute the radial power spectrum -k, Phi, sigma_Phi = grid.radial_spectrum(subgrid) -``` - -## Dependencies - -- Python 2.7+ and 3.6+ -- Numpy 1.9+ -- Scipy 0.14+ -- Cython - -Optional dependencies for mapping module: - -- Matplotlib -- [pyproj](https://github.com/jswhit/pyproj) -- [Cartopy](http://scitools.org.uk/cartopy/docs/latest/index.html) - -## Installation - -To install with **setuptools**: - -```bash -python setup.py install --user -``` - -This will compile all C source code and install them to the user directory (omit the `--user` flag to install to the system directory). Remember to delete the build folder if you are upgrading this package. - -Alternatively, install using **pip**: - -```bash -pip install pycurious --user -``` - -### Docker - -PyCurious and all of its dependencies are available for deployment with Docker: - -```bash -docker pull brmather/pycurious -``` diff --git a/README.md b/README.md new file mode 120000 index 0000000..48c8f82 --- /dev/null +++ b/README.md @@ -0,0 +1 @@ +pycurious-src/README.md \ No newline at end of file diff --git a/docs/_config.yml b/docs/_config.yml deleted file mode 100644 index c419263..0000000 --- a/docs/_config.yml +++ /dev/null @@ -1 +0,0 @@ -theme: jekyll-theme-cayman \ No newline at end of file diff --git a/docs/bouligand.md b/docs/bouligand.md deleted file mode 100644 index 77874ba..0000000 --- a/docs/bouligand.md +++ /dev/null @@ -1,12 +0,0 @@ -# Bouligand method - -All methods to derive Curie depth first compute the (fast) Fourier transform over a square window of a magnetic anomaly that has been reduced to the pole. Initial methods plotted the radial spectrum, obtained from FFT, against the wavenumber (rad/km) and used the gradient between two points to estimate the Curie depth ([Tanaka *et al.* 1999](http://linkinghub.elsevier.com/retrieve/pii/S0040195199000724)). The drawback here being that the choice of points is subjective and potentially meaningless if the window size is too small to capture long wavelength signals. Alternatively, [Bouligand *et al.* (2009)](http://doi.wiley.com/10.1029/2009JB006494) formulated an analytical expression for the radial power spectum using four parameters: - -- *beta* - a fractal parameter -- *zt* - the top of magnetic sources -- *dz* - the thickness of the magnetic layer -- *C* - a field constant - -The Curie depth is determined by minimising the misfit between the analytical power spectrum and the power spectrum computed from FFT. - -This module was heavily inspired from [pycpd](https://github.com/groupeLIAMG/pycpd). We have simplified the API and repurposed Curie depth determinations within a Bayesian inverse framework. PyCurious implements an objective function that accepts *a priori* information, and quantifies the uncertainty of Curie depth. diff --git a/COPYING b/pycurious-src/COPYING similarity index 100% rename from COPYING rename to pycurious-src/COPYING diff --git a/COPYING.LESSER b/pycurious-src/COPYING.LESSER similarity index 100% rename from COPYING.LESSER rename to pycurious-src/COPYING.LESSER diff --git a/MANIFEST.in b/pycurious-src/MANIFEST.in similarity index 100% rename from MANIFEST.in rename to pycurious-src/MANIFEST.in diff --git a/pycurious-src/README.md b/pycurious-src/README.md new file mode 100644 index 0000000..d65213f --- /dev/null +++ b/pycurious-src/README.md @@ -0,0 +1,86 @@ +# PyCurious + +[![PyPI version](https://badge.fury.io/py/pycurious.svg)](https://badge.fury.io/py/pycurious) + +Magnetic data is one of the most common geophysics datasets available on the surface of the Earth. Curie depth is the depth at which rocks lose their magnetism. The most prevalent magnetic mineral is magnetite, which has a Curie point of 580C, thus the Curie depth is often interpreted as the 580C isotherm. + +Current methods to derive Curie depth first compute the (fast) Fourier transform over a square window of a magnetic anomaly that has been reduced to the pole. The depth and thickness of magnetic sources is estimated from the slope of the radial power spectrum. *PyCurious* implements two common approaches: + +- [Tanaka *et al.* 1999](http://linkinghub.elsevier.com/retrieve/pii/S0040195199000724) +- [Bouligand *et al.* 2009](http://doi.wiley.com/10.1029/2009JB006494) + +Both of these methods to compute Curie depth are covered in the form of Jupyter notebooks. Copy these into your working directory by running: + +```python +import pycurious +pycurious.install_documentation() +``` + +| Features | Progress | +| ----------------------------------------------------- | ------------------ | +| Bayesian uncertainty analysis | :heavy_check_mark: | +| Conversion between coordinate reference systems | :heavy_check_mark: | +| Importing and exporting GeoTiffs | :heavy_check_mark: | +| Parallelisation using OpenMP implementation in Python | :heavy_check_mark: | +| Parallelisation using OpenMPI | 10% | + +## Usage + +PyCurious consists of 2 classes: + +1. **CurieGrid**: base class that computes radial power spectrum, centroids for processing, decomposition of subgrids. +2. **CurieOptimise**: optimisation module for fitting the synthetic power spectrum (inherits CurieGrid). + +Also included is a `mapping` module for gridding scattered data points, and converting between coordinate reference systems (CRS). + +Below is a simple workflow to calculate the radial power spectrum: + +```python +import pycurious + +# initialise CurieOptimise object with 2D magnetic anomaly +grid = pycurious.CurieOptimise(mag_anomaly, xmin, xmax, ymin, ymax) + +# extract a square window of the magnetic anomaly +subgrid = grid.subgrid(window_size, x, y) + +# compute the radial power spectrum +k, Phi, sigma_Phi = grid.radial_spectrum(subgrid) +``` + +## Dependencies + +- Python 2.7+ and 3.6+ +- Numpy 1.9+ +- Scipy 0.14+ +- Cython + +Optional dependencies for mapping module: + +- Matplotlib +- [pyproj](https://github.com/jswhit/pyproj) +- [Cartopy](http://scitools.org.uk/cartopy/docs/latest/index.html) + +## Installation + +To install with **setuptools**: + +```bash +python setup.py install --user +``` + +This will compile all C source code and install them to the user directory (omit the `--user` flag to install to the system directory). Remember to delete the build folder if you are upgrading this package. + +Alternatively, install using **pip**: + +```bash +pip install pycurious --user +``` + +### Docker + +PyCurious and all of its dependencies are available for deployment with Docker: + +```bash +docker pull brmather/pycurious +``` diff --git a/pycurious/Examples/Notebooks/.ipynb_checkpoints/Ex1-Plot-power-spectrum-checkpoint.ipynb b/pycurious-src/pycurious/Examples/Notebooks/.ipynb_checkpoints/Ex1-Plot-power-spectrum-checkpoint.ipynb similarity index 100% rename from pycurious/Examples/Notebooks/.ipynb_checkpoints/Ex1-Plot-power-spectrum-checkpoint.ipynb rename to pycurious-src/pycurious/Examples/Notebooks/.ipynb_checkpoints/Ex1-Plot-power-spectrum-checkpoint.ipynb diff --git a/pycurious/Examples/Notebooks/.ipynb_checkpoints/Ex2a-Compute-Curie-depth-Tanaka-approach-checkpoint.ipynb b/pycurious-src/pycurious/Examples/Notebooks/.ipynb_checkpoints/Ex2a-Compute-Curie-depth-Tanaka-approach-checkpoint.ipynb similarity 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b/pycurious-src/src/radon.pyx similarity index 100% rename from src/radon.pyx rename to pycurious-src/src/radon.pyx diff --git a/tests/Bouligand_forward.py b/pycurious-src/tests/Bouligand_forward.py similarity index 100% rename from tests/Bouligand_forward.py rename to pycurious-src/tests/Bouligand_forward.py diff --git a/tests/optimise_test.py b/pycurious-src/tests/optimise_test.py similarity index 100% rename from tests/optimise_test.py rename to pycurious-src/tests/optimise_test.py diff --git a/tests/parallel_test.py b/pycurious-src/tests/parallel_test.py similarity index 100% rename from tests/parallel_test.py rename to pycurious-src/tests/parallel_test.py diff --git a/tests/test_multiprocessing.py b/pycurious-src/tests/test_multiprocessing.py similarity index 100% rename from tests/test_multiprocessing.py rename to pycurious-src/tests/test_multiprocessing.py diff --git a/tests/valid_numbers.py b/pycurious-src/tests/valid_numbers.py similarity index 100% rename from tests/valid_numbers.py rename to pycurious-src/tests/valid_numbers.py From 6cdc13f6c35d3211f12b74a20407adfee82a5973 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Wed, 20 Mar 2019 15:03:12 +1100 Subject: [PATCH 048/170] Updated README.md and directory structure for docker --- .gitignore | 5 +- Docker/Dockerfile | 64 +++++++++ Docker/Dockerfile-base | 52 ++++--- Docker/scripts/run-jupyter.sh | 16 +++ Dockerfile | 28 ---- pycurious-src/MANIFEST.in | 1 + pycurious-src/README.md | 84 +++++++---- .../pycurious/Examples/0-StartHere.ipynb | 134 ++++++++++++++++++ pycurious-src/setup.py | 3 +- 9 files changed, 308 insertions(+), 79 deletions(-) create mode 100644 Docker/Dockerfile create mode 100755 Docker/scripts/run-jupyter.sh delete mode 100644 Dockerfile create mode 100644 pycurious-src/pycurious/Examples/0-StartHere.ipynb diff --git a/.gitignore b/.gitignore index 31b358a..7166ecd 100644 --- a/.gitignore +++ b/.gitignore @@ -1,3 +1,4 @@ -pycurious/Examples/Notebooks/Bouligand/.ipynb_checkpoints/* -pycurious/Examples/Notebooks/Tanaka/.ipynb_checkpoints/* +pycurious-src/pycurious/Examples/Notebooks/Bouligand/.ipynb_checkpoints/* +pycurious-src/pycurious/Examples/Notebooks/Tanaka/.ipynb_checkpoints/* +pycurious-src/pycurious/Examples/.ipynb_checkpoints/* *.pyc diff --git a/Docker/Dockerfile b/Docker/Dockerfile new file mode 100644 index 0000000..f899d9b --- /dev/null +++ b/Docker/Dockerfile @@ -0,0 +1,64 @@ +################################################# +# Short docker file to distribute some notebooks +################################################# + +ARG FROMIMG_ARG=brmather/pycurious-base:0.9.1 +FROM ${FROMIMG_ARG} + +################################################## +# Non standard as the files come from the packages + +USER root +WORKDIR /home/jovyan/ + +### PyCurious - Notebooks + +ENV MODULE_DIR="pycurious-src" +ADD --chown=jovyan:jovyan $MODULE_DIR $MODULE_DIR +RUN cd $MODULE_DIR && python3 -m pip install --no-cache-dir --upgrade --no-deps . + +RUN ipython3 -c 'import pycurious; pycurious.documentation.install_documentation(path="Notebooks")' + + +# change ownership of everything +ENV NB_USER jovyan +RUN chown -R jovyan:jovyan /home/jovyan +USER jovyan + + +## These are supplied by the build script +## build-dockerfile.sh + +ARG IMAGENAME_ARG +ARG PROJ_NAME_ARG=pycurious +ARG NB_PORT_ARG=8888 +ARG NB_PASSWD_ARG="" +ARG NB_DIR_ARG="Notebooks" +ARG START_NB_ARG="0-StartHere.ipynb" + +# The args need to go into the environment so they +# can be picked up by commands/templates (defined previously) +# when the container runs + +ENV IMAGENAME=$IMAGENAME_ARG +ENV PROJ_NAME=$PROJ_NAME_ARG +ENV NB_PORT=$NB_PORT_ARG +ENV NB_PASSWD=$NB_PASSWD_ARG +ENV NB_DIR=$NB_DIR_ARG +ENV START_NB=$START_NB_ARG + + +# Trust all notebooks +RUN find -name \*.ipynb -print0 | xargs -0 jupyter trust + +# expose notebook port server port +EXPOSE $NB_PORT + +VOLUME /home/jovyan/$NB_DIR/user_data + + +ENTRYPOINT ["/sbin/tini", "--"] + +# launch notebook +ADD --chown=jovyan:jovyan Docker/scripts/run-jupyter.sh scripts/run-jupyter.sh +CMD scripts/run-jupyter.sh \ No newline at end of file diff --git a/Docker/Dockerfile-base b/Docker/Dockerfile-base index 6cac64f..261a846 100644 --- a/Docker/Dockerfile-base +++ b/Docker/Dockerfile-base @@ -1,12 +1,15 @@ -FROM alpine:latest +FROM alpine:edge + +LABEL maintainer="brmather1@gmail.com" +LABEL repo="https://github.com/brmather/pycurious" # Install things -RUN echo "http://mirror.leaseweb.com/alpine/edge/testing" >> /etc/apk/repositories RUN apk add --update --no-cache \ gcc \ g++ \ gfortran \ build-base \ + linux-headers \ python3-dev \ py3-pip \ py3-numpy \ @@ -15,13 +18,17 @@ RUN apk add --update --no-cache \ cmake \ curl \ wget \ + tini \ libzmq \ zlib-dev \ musl-dev \ freetype-dev \ libpng-dev \ libxml2-dev \ - openblas-dev \ + openblas-dev + +RUN echo "http://mirror.leaseweb.com/alpine/edge/testing" >> /etc/apk/repositories +RUN apk add --update --no-cache \ geos-dev \ proj4-dev @@ -32,23 +39,18 @@ RUN apk add --update --no-cache \ RUN ln -s /usr/include/locale.h /usr/include/xlocale.h -# RUN python3 -m pip install --no-cache-dir --upgrade numpy && \ -RUN python3 -m pip install --no-cache-dir --upgrade pip numpy && \ +RUN python3 -m pip install --no-cache-dir --upgrade pip && \ + python3 -m pip install --no-cache-dir --upgrade --force-reinstall numpy scipy && \ python3 -m pip install --no-cache-dir setuptools wheel Cython && \ python3 -m pip install --no-cache-dir \ packaging \ + gdal \ jupyter \ + tornado \ pyepsg \ cartopy && \ - python3 -m pip install --no-cache-dir matplotlib - - -# Install Tini.. this is required because CMD (below) doesn't play nice with notebooks for some reason: -# https://github.com/ipython/ipython/issues/7062, https://github.com/jupyter/notebook/issues/334 -RUN curl -L https://github.com/krallin/tini/releases/download/v0.10.0/tini > tini && \ - echo "1361527f39190a7338a0b434bd8c88ff7233ce7b9a4876f3315c22fce7eca1b0 *tini" | sha256sum -c - && \ - mv tini /usr/local/bin/tini && \ - chmod +x /usr/local/bin/tini + python3 -m pip install --no-cache-dir matplotlib && \ + python3 -m pip install --no-cache-dir --upgrade --ignore-installed pyzmq # expose notebook port EXPOSE 8888 @@ -56,7 +58,23 @@ EXPOSE 8888 # add a notebook profile RUN mkdir -p -m 700 /root/.jupyter/ && \ - echo "c.NotebookApp.ip = '0.0.0.0'" >> /root/.jupyter/jupyter_notebook_config.py + echo "c.NotebookApp.ip = '0.0.0.0'" >> /root/.jupyter/jupyter_notebook_config.py && \ + echo "c.NotebookApp.token = ''" >> /root/.jupyter/jupyter_notebook_config.py + + +RUN addgroup jovyan && \ + adduser -D jovyan -G jovyan + +WORKDIR /home/jovyan +RUN chown -R jovyan:jovyan /home/jovyan +USER jovyan + + +VOLUME /home/jovyan/$NB_DIR/user_data + + +ENTRYPOINT ["/sbin/tini", "--"] -# note we also use xvfb which is required for viz -ENTRYPOINT ["/usr/local/bin/tini", "--"] \ No newline at end of file +# launch notebook +# CMD scripts/run-jupyter.sh +CMD ["jupyter", "notebook", "--ip='0.0.0.0'", "--NotebookApp.token='' ", "--no-browser"] \ No newline at end of file diff --git a/Docker/scripts/run-jupyter.sh b/Docker/scripts/run-jupyter.sh new file mode 100755 index 0000000..7443d1b --- /dev/null +++ b/Docker/scripts/run-jupyter.sh @@ -0,0 +1,16 @@ +#!/usr/bin/env sh + +PASS=${NB_PASSWD:-""} +OPEN=${START_NB:-""} +PORT=${NB_PORT:-8888} + +cd /home/jovyan/Notebooks + +jupyter-notebook --port=$NB_PORT --ip='0.0.0.0' --no-browser --allow-root \ + --NotebookApp.token=$NB_PASSWD --NotebookApp.default_url=/tree/$OPEN + +# Don't exit + +while true; do + sleep 600 +done diff --git a/Dockerfile b/Dockerfile deleted file mode 100644 index c54da49..0000000 --- a/Dockerfile +++ /dev/null @@ -1,28 +0,0 @@ -FROM brmather/pycurious-base:latest - -# add pycurious -WORKDIR /work -ENV MODULE_DIR="pycurious-src" -RUN addgroup -S jovyan && \ - adduser -D -S jovyan -G jovyan - -ADD --chown=jovyan:jovyan . / pycurious-src/ -RUN cd pycurious-src && \ - python3 -m pip install --no-deps --upgrade . && \ - mv pycurious/Examples/data /home/jovyan/ && \ - mv pycurious/Examples/Notebooks /home/jovyan/ && \ - mv pycurious/Examples/Scripts /home/jovyan/ && \ - cd /work && \ - rm -rf /work/pycurious-src - - -# change ownership of everything -ENV NB_USER jovyan -RUN chown -R jovyan:jovyan /home/jovyan -USER jovyan -WORKDIR /home/jovyan/ -RUN find -name \*.ipynb -print0 | xargs -0 jupyter trust - - -# launch notebook -ENTRYPOINT ["jupyter", "notebook", "--ip='0.0.0.0'", "--no-browser"] \ No newline at end of file diff --git a/pycurious-src/MANIFEST.in b/pycurious-src/MANIFEST.in index 65cd352..1e73e56 100644 --- a/pycurious-src/MANIFEST.in +++ b/pycurious-src/MANIFEST.in @@ -6,6 +6,7 @@ include setup.cfg include src/* include __init__.py recursive-include pycurious/*.py +recursive-include pycurious/*.ipynb include docs/* include tests/*.py diff --git a/pycurious-src/README.md b/pycurious-src/README.md index d65213f..390cb00 100644 --- a/pycurious-src/README.md +++ b/pycurious-src/README.md @@ -1,35 +1,51 @@ # PyCurious -[![PyPI version](https://badge.fury.io/py/pycurious.svg)](https://badge.fury.io/py/pycurious) +[![Docker Cloud Automated build](https://img.shields.io/docker/cloud/automated/brmather/pycurious.svg)](https://hub.docker.com/r/brmather/pycurious) +[![PyPI](https://img.shields.io/pypi/v/pycurious.svg)](https://pypi.org/project/pycurious/) Magnetic data is one of the most common geophysics datasets available on the surface of the Earth. Curie depth is the depth at which rocks lose their magnetism. The most prevalent magnetic mineral is magnetite, which has a Curie point of 580C, thus the Curie depth is often interpreted as the 580C isotherm. -Current methods to derive Curie depth first compute the (fast) Fourier transform over a square window of a magnetic anomaly that has been reduced to the pole. The depth and thickness of magnetic sources is estimated from the slope of the radial power spectrum. *PyCurious* implements two common approaches: +Current methods to derive Curie depth first compute the (fast) Fourier transform over a square window of a magnetic anomaly that has been reduced to the pole. The depth and thickness of magnetic sources is estimated from the slope of the radial power spectrum. `pycurious` implements the Tanaka *et al.* (1999) and Bouligand *et al.* (2009) methods for computing the thickness of a buried magnetic source, which are covered within Jupyter notebooks. -- [Tanaka *et al.* 1999](http://linkinghub.elsevier.com/retrieve/pii/S0040195199000724) -- [Bouligand *et al.* 2009](http://doi.wiley.com/10.1029/2009JB006494) +#### Binder -Both of these methods to compute Curie depth are covered in the form of Jupyter notebooks. Copy these into your working directory by running: +Launch the demonstration at [mybinder.org](https://mybinder.org/v2/gh/brmather/pycurious/binder?filepath=Notebooks%2F0-StartHere.ipynb) + +[![badge](https://img.shields.io/badge/launch-pycurious-E66581.svg?logo=data:image/png;base64,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)](https://mybinder.org/v2/gh/brmather/pycurious/binder?filepath=Notebooks%2F0-StartHere.ipynb) + +## Navigation / Notebooks + +There are two matching sets of `pycurious` notebooks - one set for the [Tanaka](#Tanaka) and one for [Bouligand](#Bouligand) implementations. The Bouligand set of noteboks are a natural choice for Bayesian inference applications. + +### Tanaka + +- [Ex1-Plot-power-spectrum.ipynb](pycurious-src/pycurious/Examples/Notebooks/Tanaka/Ex1-Plot-power-spectrum.ipynb) +- [Ex2-Compute-Curie-depth.ipynb](pycurious-src/pycurious/Examples/Notebooks/Tanaka/Ex2-Compute-Curie-depth.ipynb) +- [Ex3-Parameter-exploration.ipynb](pycurious-src/pycurious/Examples/Notebooks/Tanaka/Ex3-Parameter-exploration.ipynb) + +### Bouligand + +- [Ex1-Plot-power-spectrum.ipynb](pycurious-src/pycurious/Examples/Notebooks/Bouligand/Ex1-Plot-power-spectrum.ipynb) +- [Ex2-Compute-Curie-depth.ipynb](pycurious-src/pycurious/Examples/Notebooks/Bouligand/Ex2-Compute-Curie-depth.ipynb) +- [Ex3-Posing-the-inverse-problem.ipynb](pycurious-src/pycurious/Examples/Notebooks/Bouligand/Ex3-Posing-the-inverse-problem.ipynb) +- [Ex4-Spatial-variation-of-Curie-depth.ipynb](pycurious-src/pycurious/Examples/Notebooks/Bouligand/Ex4-Spatial-variation-of-Curie-depth.ipynb) +- [Ex5-Mapping-Curie-depth-EMAG2.ipynb](pycurious-src/pycurious/Examples/Notebooks/Bouligand/Ex5-Mapping-Curie-depth-EMAG2.ipynb) + +## Examples + +Note, these examples can be installed from the package itself by running: ```python import pycurious -pycurious.install_documentation() +pycurious.install_documentation(path="Notebooks") ``` -| Features | Progress | -| ----------------------------------------------------- | ------------------ | -| Bayesian uncertainty analysis | :heavy_check_mark: | -| Conversion between coordinate reference systems | :heavy_check_mark: | -| Importing and exporting GeoTiffs | :heavy_check_mark: | -| Parallelisation using OpenMP implementation in Python | :heavy_check_mark: | -| Parallelisation using OpenMPI | 10% | - ## Usage PyCurious consists of 2 classes: -1. **CurieGrid**: base class that computes radial power spectrum, centroids for processing, decomposition of subgrids. -2. **CurieOptimise**: optimisation module for fitting the synthetic power spectrum (inherits CurieGrid). +- `CurieGrid`: base class that computes radial power spectrum, centroids for processing, decomposition of subgrids. +- `CurieOptimise`: optimisation module for fitting the synthetic power spectrum (inherits CurieGrid). Also included is a `mapping` module for gridding scattered data points, and converting between coordinate reference systems (CRS). @@ -48,19 +64,6 @@ subgrid = grid.subgrid(window_size, x, y) k, Phi, sigma_Phi = grid.radial_spectrum(subgrid) ``` -## Dependencies - -- Python 2.7+ and 3.6+ -- Numpy 1.9+ -- Scipy 0.14+ -- Cython - -Optional dependencies for mapping module: - -- Matplotlib -- [pyproj](https://github.com/jswhit/pyproj) -- [Cartopy](http://scitools.org.uk/cartopy/docs/latest/index.html) - ## Installation To install with **setuptools**: @@ -77,10 +80,29 @@ Alternatively, install using **pip**: pip install pycurious --user ``` +### Dependencies + +- Python 2.7+ and 3.6+ +- Numpy 1.9+ +- Scipy 0.14+ +- Cython + +Optional dependencies for mapping module: + +- Matplotlib +- [pyproj](https://github.com/jswhit/pyproj) +- [Cartopy](http://scitools.org.uk/cartopy/docs/latest/index.html) + ### Docker -PyCurious and all of its dependencies are available for deployment with Docker: +A more straightforward installation for `pycurious` and all of its dependencies may be deployed with [Docker](https://www.docker.com). To install the docker image and test it is working: ```bash -docker pull brmather/pycurious +docker pull brmather/pycurious:latest +docker run --rm brmather/pycurious:latest help ``` + +## References + +1. Bouligand, C., Glen, J. M. G., & Blakely, R. J. (2009). Mapping Curie temperature depth in the western United States with a fractal model for crustal magnetization. Journal of Geophysical Research, 114(B11104), 1–25. https://doi.org/10.1029/2009JB006494 +2. Tanaka, A., Okubo, Y., & Matsubayashi, O. (1999). Curie point depth based on spectrum analysis of the magnetic anomaly data in East and Southeast Asia. Tectonophysics, 306(3–4), 461–470. https://doi.org/10.1016/S0040-1951(99)00072-4 diff --git a/pycurious-src/pycurious/Examples/0-StartHere.ipynb b/pycurious-src/pycurious/Examples/0-StartHere.ipynb new file mode 100644 index 0000000..d1df166 --- /dev/null +++ b/pycurious-src/pycurious/Examples/0-StartHere.ipynb @@ -0,0 +1,134 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# PyCurious\n", + "\n", + "Magnetic data is one of the most common geophysics datasets available on the surface of the Earth. Curie depth is the depth at which rocks lose their magnetism. The most prevalent magnetic mineral is magnetite, which has a Curie point of 580C, thus the Curie depth is often interpreted as the 580C isotherm.\n", + "\n", + "Current methods to derive Curie depth first compute the (fast) Fourier transform over a square window of a magnetic anomaly that has been reduced to the pole. The depth and thickness of magnetic sources is estimated from the slope of the radial power spectrum. `pycurious` implements the Tanaka *et al.* (1999) and Bouligand *et al.* (2009) methods for computing the thickness of a buried magnetic source, which are covered within Jupyter notebooks.\n", + "\n", + "#### Binder\n", + "\n", + "Launch the demonstration at [mybinder.org](https://mybinder.org/v2/gh/brmather/pycurious/binder?filepath=Notebooks%2F0-StartHere.ipynb)\n", + "\n", + "## Navigation / Notebooks\n", + "\n", + "There are two matching sets of `pycurious` notebooks - one set for the [Tanaka](#Tanaka) and one for [Bouligand](#Bouligand) implementations. The Bouligand set of noteboks are a natural choice for Bayesian inference applications.\n", + "\n", + "### Tanaka\n", + "\n", + "- [Ex1-Plot-power-spectrum.ipynb](./Notebooks/Tanaka/Ex1-Plot-power-spectrum.ipynb)\n", + "- [Ex2-Compute-Curie-depth.ipynb](./Notebooks/Tanaka/Ex2-Compute-Curie-depth.ipynb)\n", + "- [Ex3-Parameter-exploration.ipynb](./Notebooks/Tanaka/Ex3-Parameter-exploration.ipynb)\n", + "\n", + "### Bouligand\n", + "\n", + "- [Ex1-Plot-power-spectrum.ipynb](./Notebooks/Bouligand/Ex1-Plot-power-spectrum.ipynb)\n", + "- [Ex2-Compute-Curie-depth.ipynb](./Notebooks/Bouligand/Ex2-Compute-Curie-depth.ipynb)\n", + "- [Ex3-Posing-the-inverse-problem.ipynb](./Notebooks/Bouligand/Ex3-Posing-the-inverse-problem.ipynb)\n", + "- [Ex4-Spatial-variation-of-Curie-depth.ipynb](./Notebooks/Bouligand/Ex4-Spatial-variation-of-Curie-depth.ipynb)\n", + "- [Ex5-Mapping-Curie-depth-EMAG2.ipynb](./Notebooks/Bouligand/Ex5-Mapping-Curie-depth-EMAG2.ipynb)\n", + "\n", + "### Examples\n", + "\n", + "Note, these examples can be installed from the package itself by running:\n", + "\n", + "```python\n", + "import pycurious\n", + "pycurious.install_documentation(path=\"Notebooks\")\n", + "```\n", + "\n", + "## Usage\n", + "\n", + "PyCurious consists of 2 classes:\n", + "\n", + "- `CurieGrid`: base class that computes radial power spectrum, centroids for processing, decomposition of subgrids.\n", + "- `CurieOptimise`: optimisation module for fitting the synthetic power spectrum (inherits CurieGrid).\n", + "\n", + "Also included is a `mapping` module for gridding scattered data points, and converting between coordinate reference systems (CRS).\n", + "\n", + "Below is a simple workflow to calculate the radial power spectrum:\n", + "\n", + "```python\n", + "import pycurious\n", + "\n", + "# initialise CurieOptimise object with 2D magnetic anomaly\n", + "grid = pycurious.CurieOptimise(mag_anomaly, xmin, xmax, ymin, ymax)\n", + "\n", + "# extract a square window of the magnetic anomaly\n", + "subgrid = grid.subgrid(window_size, x, y)\n", + "\n", + "# compute the radial power spectrum\n", + "k, Phi, sigma_Phi = grid.radial_spectrum(subgrid)\n", + "```\n", + "\n", + "## Installation\n", + "\n", + "To install with **setuptools**:\n", + "\n", + "```bash\n", + "python setup.py install --user\n", + "```\n", + "\n", + "This will compile all C source code and install them to the user directory (omit the `--user` flag to install to the system directory). Remember to delete the build folder if you are upgrading this package.\n", + "\n", + "Alternatively, install using **pip**:\n", + "\n", + "```bash\n", + "pip install pycurious --user\n", + "```\n", + "\n", + "### Dependencies\n", + "\n", + "- Python 2.7+ and 3.6+\n", + "- Numpy 1.9+\n", + "- Scipy 0.14+\n", + "- Cython\n", + "\n", + "Optional dependencies for mapping module:\n", + "\n", + "- Matplotlib\n", + "- [pyproj](https://github.com/jswhit/pyproj)\n", + "- [Cartopy](http://scitools.org.uk/cartopy/docs/latest/index.html)\n", + "\n", + "### Docker\n", + "\n", + "A more straightforward installation for `pycurious` and all of its dependencies may be deployed with [Docker](https://www.docker.com). To install the docker image and test it is working:\n", + "\n", + "```bash\n", + "docker pull brmather/pycurious:latest\n", + "docker run --rm brmather/pycurious:latest help\n", + "```\n", + "\n", + "## References\n", + "\n", + "1. Bouligand, C., Glen, J. M. G., & Blakely, R. J. (2009). Mapping Curie temperature depth in the western United States with a fractal model for crustal magnetization. Journal of Geophysical Research, 114(B11104), 1–25. https://doi.org/10.1029/2009JB006494\n", + "2. Tanaka, A., Okubo, Y., & Matsubayashi, O. (1999). Curie point depth based on spectrum analysis of the magnetic anomaly data in East and Southeast Asia. Tectonophysics, 306(3–4), 461–470. https://doi.org/10.1016/S0040-1951(99)00072-4\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.8" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/pycurious-src/setup.py b/pycurious-src/setup.py index 9b00ac3..0f266bb 100644 --- a/pycurious-src/setup.py +++ b/pycurious-src/setup.py @@ -28,7 +28,7 @@ author = "Ben Mather", author_email = "brmather1@gmail.com", url = "https://github.com/brmather/pycurious", - version = "0.2", + version = "0.3", description = "Python tool for computing the Curie depth from magnetic data", ext_modules = cythonize([ext]), packages = ['pycurious', @@ -38,6 +38,7 @@ 'pycurious.parallel', 'pycurious.therm'], package_data = {'pycurious': ['Examples/data/*', + 'Examples/*.ipynb', 'Examples/Notebooks/Tanaka/*.ipynb', 'Examples/Notebooks/Bouligand/*.ipynb', 'Examples/Scripts/*.py']}, From 74c1837a4123d2421b558f0240ff2c4e6151d7e9 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Mon, 3 Jun 2019 22:34:34 +1000 Subject: [PATCH 049/170] Restructure directory --- pycurious-src/COPYING => COPYING | 0 .../COPYING.LESSER => COPYING.LESSER | 0 pycurious-src/MANIFEST.in => MANIFEST.in | 0 README.md | 109 +++++++++++++++++- pycurious-src/README.md | 108 ----------------- .../Examples/0-StartHere.ipynb | 0 .../Ex1-Plot-power-spectrum-checkpoint.ipynb | 0 ...rie-depth-Tanaka-approach-checkpoint.ipynb | 0 ...-depth-Bouligand-approach-checkpoint.ipynb | 0 .../Ex3-Optimisation-routine-checkpoint.ipynb | 0 .../Bouligand/Ex1-Plot-power-spectrum.ipynb | 0 .../Bouligand/Ex2-Compute-Curie-depth.ipynb | 0 .../Ex3-Posing-the-inverse-problem.ipynb | 0 ...Ex4-Spatial-variation-of-Curie-depth.ipynb | 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100% rename from pycurious-src/COPYING.LESSER rename to COPYING.LESSER diff --git a/pycurious-src/MANIFEST.in b/MANIFEST.in similarity index 100% rename from pycurious-src/MANIFEST.in rename to MANIFEST.in diff --git a/README.md b/README.md deleted file mode 120000 index 48c8f82..0000000 --- a/README.md +++ /dev/null @@ -1 +0,0 @@ -pycurious-src/README.md \ No newline at end of file diff --git a/README.md b/README.md new file mode 100644 index 0000000..390cb00 --- /dev/null +++ b/README.md @@ -0,0 +1,108 @@ +# PyCurious + +[![Docker Cloud Automated build](https://img.shields.io/docker/cloud/automated/brmather/pycurious.svg)](https://hub.docker.com/r/brmather/pycurious) +[![PyPI](https://img.shields.io/pypi/v/pycurious.svg)](https://pypi.org/project/pycurious/) + +Magnetic data is one of the most common geophysics datasets available on the surface of the Earth. Curie depth is the depth at which rocks lose their magnetism. The most prevalent magnetic mineral is magnetite, which has a Curie point of 580C, thus the Curie depth is often interpreted as the 580C isotherm. + +Current methods to derive Curie depth first compute the (fast) Fourier transform over a square window of a magnetic anomaly that has been reduced to the pole. The depth and thickness of magnetic sources is estimated from the slope of the radial power spectrum. `pycurious` implements the Tanaka *et al.* (1999) and Bouligand *et al.* (2009) methods for computing the thickness of a buried magnetic source, which are covered within Jupyter notebooks. + +#### Binder + +Launch the demonstration at [mybinder.org](https://mybinder.org/v2/gh/brmather/pycurious/binder?filepath=Notebooks%2F0-StartHere.ipynb) + +[![badge](https://img.shields.io/badge/launch-pycurious-E66581.svg?logo=data:image/png;base64,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)](https://mybinder.org/v2/gh/brmather/pycurious/binder?filepath=Notebooks%2F0-StartHere.ipynb) + +## Navigation / Notebooks + +There are two matching sets of `pycurious` notebooks - one set for the [Tanaka](#Tanaka) and one for [Bouligand](#Bouligand) implementations. The Bouligand set of noteboks are a natural choice for Bayesian inference applications. + +### Tanaka + +- [Ex1-Plot-power-spectrum.ipynb](pycurious-src/pycurious/Examples/Notebooks/Tanaka/Ex1-Plot-power-spectrum.ipynb) +- [Ex2-Compute-Curie-depth.ipynb](pycurious-src/pycurious/Examples/Notebooks/Tanaka/Ex2-Compute-Curie-depth.ipynb) +- [Ex3-Parameter-exploration.ipynb](pycurious-src/pycurious/Examples/Notebooks/Tanaka/Ex3-Parameter-exploration.ipynb) + +### Bouligand + +- [Ex1-Plot-power-spectrum.ipynb](pycurious-src/pycurious/Examples/Notebooks/Bouligand/Ex1-Plot-power-spectrum.ipynb) +- [Ex2-Compute-Curie-depth.ipynb](pycurious-src/pycurious/Examples/Notebooks/Bouligand/Ex2-Compute-Curie-depth.ipynb) +- [Ex3-Posing-the-inverse-problem.ipynb](pycurious-src/pycurious/Examples/Notebooks/Bouligand/Ex3-Posing-the-inverse-problem.ipynb) +- [Ex4-Spatial-variation-of-Curie-depth.ipynb](pycurious-src/pycurious/Examples/Notebooks/Bouligand/Ex4-Spatial-variation-of-Curie-depth.ipynb) +- [Ex5-Mapping-Curie-depth-EMAG2.ipynb](pycurious-src/pycurious/Examples/Notebooks/Bouligand/Ex5-Mapping-Curie-depth-EMAG2.ipynb) + +## Examples + +Note, these examples can be installed from the package itself by running: + +```python +import pycurious +pycurious.install_documentation(path="Notebooks") +``` + +## Usage + +PyCurious consists of 2 classes: + +- `CurieGrid`: base class that computes radial power spectrum, centroids for processing, decomposition of subgrids. +- `CurieOptimise`: optimisation module for fitting the synthetic power spectrum (inherits CurieGrid). + +Also included is a `mapping` module for gridding scattered data points, and converting between coordinate reference systems (CRS). + +Below is a simple workflow to calculate the radial power spectrum: + +```python +import pycurious + +# initialise CurieOptimise object with 2D magnetic anomaly +grid = pycurious.CurieOptimise(mag_anomaly, xmin, xmax, ymin, ymax) + +# extract a square window of the magnetic anomaly +subgrid = grid.subgrid(window_size, x, y) + +# compute the radial power spectrum +k, Phi, sigma_Phi = grid.radial_spectrum(subgrid) +``` + +## Installation + +To install with **setuptools**: + +```bash +python setup.py install --user +``` + +This will compile all C source code and install them to the user directory (omit the `--user` flag to install to the system directory). Remember to delete the build folder if you are upgrading this package. + +Alternatively, install using **pip**: + +```bash +pip install pycurious --user +``` + +### Dependencies + +- Python 2.7+ and 3.6+ +- Numpy 1.9+ +- Scipy 0.14+ +- Cython + +Optional dependencies for mapping module: + +- Matplotlib +- [pyproj](https://github.com/jswhit/pyproj) +- [Cartopy](http://scitools.org.uk/cartopy/docs/latest/index.html) + +### Docker + +A more straightforward installation for `pycurious` and all of its dependencies may be deployed with [Docker](https://www.docker.com). To install the docker image and test it is working: + +```bash +docker pull brmather/pycurious:latest +docker run --rm brmather/pycurious:latest help +``` + +## References + +1. Bouligand, C., Glen, J. M. G., & Blakely, R. J. (2009). Mapping Curie temperature depth in the western United States with a fractal model for crustal magnetization. Journal of Geophysical Research, 114(B11104), 1–25. https://doi.org/10.1029/2009JB006494 +2. Tanaka, A., Okubo, Y., & Matsubayashi, O. (1999). Curie point depth based on spectrum analysis of the magnetic anomaly data in East and Southeast Asia. Tectonophysics, 306(3–4), 461–470. https://doi.org/10.1016/S0040-1951(99)00072-4 diff --git a/pycurious-src/README.md b/pycurious-src/README.md deleted file mode 100644 index 390cb00..0000000 --- a/pycurious-src/README.md +++ /dev/null @@ -1,108 +0,0 @@ -# PyCurious - -[![Docker Cloud Automated build](https://img.shields.io/docker/cloud/automated/brmather/pycurious.svg)](https://hub.docker.com/r/brmather/pycurious) -[![PyPI](https://img.shields.io/pypi/v/pycurious.svg)](https://pypi.org/project/pycurious/) - -Magnetic data is one of the most common geophysics datasets available on the surface of the Earth. Curie depth is the depth at which rocks lose their magnetism. The most prevalent magnetic mineral is magnetite, which has a Curie point of 580C, thus the Curie depth is often interpreted as the 580C isotherm. - -Current methods to derive Curie depth first compute the (fast) Fourier transform over a square window of a magnetic anomaly that has been reduced to the pole. The depth and thickness of magnetic sources is estimated from the slope of the radial power spectrum. `pycurious` implements the Tanaka *et al.* (1999) and Bouligand *et al.* (2009) methods for computing the thickness of a buried magnetic source, which are covered within Jupyter notebooks. - -#### Binder - -Launch the demonstration at [mybinder.org](https://mybinder.org/v2/gh/brmather/pycurious/binder?filepath=Notebooks%2F0-StartHere.ipynb) - -[![badge](https://img.shields.io/badge/launch-pycurious-E66581.svg?logo=data:image/png;base64,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)](https://mybinder.org/v2/gh/brmather/pycurious/binder?filepath=Notebooks%2F0-StartHere.ipynb) - -## Navigation / Notebooks - -There are two matching sets of `pycurious` notebooks - one set for the [Tanaka](#Tanaka) and one for [Bouligand](#Bouligand) implementations. The Bouligand set of noteboks are a natural choice for Bayesian inference applications. - -### Tanaka - -- [Ex1-Plot-power-spectrum.ipynb](pycurious-src/pycurious/Examples/Notebooks/Tanaka/Ex1-Plot-power-spectrum.ipynb) -- [Ex2-Compute-Curie-depth.ipynb](pycurious-src/pycurious/Examples/Notebooks/Tanaka/Ex2-Compute-Curie-depth.ipynb) -- [Ex3-Parameter-exploration.ipynb](pycurious-src/pycurious/Examples/Notebooks/Tanaka/Ex3-Parameter-exploration.ipynb) - -### Bouligand - -- [Ex1-Plot-power-spectrum.ipynb](pycurious-src/pycurious/Examples/Notebooks/Bouligand/Ex1-Plot-power-spectrum.ipynb) -- [Ex2-Compute-Curie-depth.ipynb](pycurious-src/pycurious/Examples/Notebooks/Bouligand/Ex2-Compute-Curie-depth.ipynb) -- [Ex3-Posing-the-inverse-problem.ipynb](pycurious-src/pycurious/Examples/Notebooks/Bouligand/Ex3-Posing-the-inverse-problem.ipynb) -- [Ex4-Spatial-variation-of-Curie-depth.ipynb](pycurious-src/pycurious/Examples/Notebooks/Bouligand/Ex4-Spatial-variation-of-Curie-depth.ipynb) -- [Ex5-Mapping-Curie-depth-EMAG2.ipynb](pycurious-src/pycurious/Examples/Notebooks/Bouligand/Ex5-Mapping-Curie-depth-EMAG2.ipynb) - -## Examples - -Note, these examples can be installed from the package itself by running: - -```python -import pycurious -pycurious.install_documentation(path="Notebooks") -``` - -## Usage - -PyCurious consists of 2 classes: - -- `CurieGrid`: base class that computes radial power spectrum, centroids for processing, decomposition of subgrids. -- `CurieOptimise`: optimisation module for fitting the synthetic power spectrum (inherits CurieGrid). - -Also included is a `mapping` module for gridding scattered data points, and converting between coordinate reference systems (CRS). - -Below is a simple workflow to calculate the radial power spectrum: - -```python -import pycurious - -# initialise CurieOptimise object with 2D magnetic anomaly -grid = pycurious.CurieOptimise(mag_anomaly, xmin, xmax, ymin, ymax) - -# extract a square window of the magnetic anomaly -subgrid = grid.subgrid(window_size, x, y) - -# compute the radial power spectrum -k, Phi, sigma_Phi = grid.radial_spectrum(subgrid) -``` - -## Installation - -To install with **setuptools**: - -```bash -python setup.py install --user -``` - -This will compile all C source code and install them to the user directory (omit the `--user` flag to install to the system directory). Remember to delete the build folder if you are upgrading this package. - -Alternatively, install using **pip**: - -```bash -pip install pycurious --user -``` - -### Dependencies - -- Python 2.7+ and 3.6+ -- Numpy 1.9+ -- Scipy 0.14+ -- Cython - -Optional dependencies for mapping module: - -- Matplotlib -- [pyproj](https://github.com/jswhit/pyproj) -- [Cartopy](http://scitools.org.uk/cartopy/docs/latest/index.html) - -### Docker - -A more straightforward installation for `pycurious` and all of its dependencies may be deployed with [Docker](https://www.docker.com). To install the docker image and test it is working: - -```bash -docker pull brmather/pycurious:latest -docker run --rm brmather/pycurious:latest help -``` - -## References - -1. Bouligand, C., Glen, J. M. G., & Blakely, R. J. (2009). Mapping Curie temperature depth in the western United States with a fractal model for crustal magnetization. Journal of Geophysical Research, 114(B11104), 1–25. https://doi.org/10.1029/2009JB006494 -2. Tanaka, A., Okubo, Y., & Matsubayashi, O. (1999). Curie point depth based on spectrum analysis of the magnetic anomaly data in East and Southeast Asia. Tectonophysics, 306(3–4), 461–470. https://doi.org/10.1016/S0040-1951(99)00072-4 diff --git a/pycurious-src/pycurious/Examples/0-StartHere.ipynb b/pycurious/Examples/0-StartHere.ipynb similarity index 100% rename from pycurious-src/pycurious/Examples/0-StartHere.ipynb rename to pycurious/Examples/0-StartHere.ipynb diff --git a/pycurious-src/pycurious/Examples/Notebooks/.ipynb_checkpoints/Ex1-Plot-power-spectrum-checkpoint.ipynb b/pycurious/Examples/Notebooks/.ipynb_checkpoints/Ex1-Plot-power-spectrum-checkpoint.ipynb similarity index 100% rename from pycurious-src/pycurious/Examples/Notebooks/.ipynb_checkpoints/Ex1-Plot-power-spectrum-checkpoint.ipynb rename to pycurious/Examples/Notebooks/.ipynb_checkpoints/Ex1-Plot-power-spectrum-checkpoint.ipynb diff --git a/pycurious-src/pycurious/Examples/Notebooks/.ipynb_checkpoints/Ex2a-Compute-Curie-depth-Tanaka-approach-checkpoint.ipynb b/pycurious/Examples/Notebooks/.ipynb_checkpoints/Ex2a-Compute-Curie-depth-Tanaka-approach-checkpoint.ipynb 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pycurious-src/pycurious/__init__.py rename to pycurious/__init__.py diff --git a/pycurious-src/pycurious/documentation.py b/pycurious/documentation.py similarity index 100% rename from pycurious-src/pycurious/documentation.py rename to pycurious/documentation.py diff --git a/pycurious-src/pycurious/grid/__init__.py b/pycurious/grid/__init__.py similarity index 100% rename from pycurious-src/pycurious/grid/__init__.py rename to pycurious/grid/__init__.py diff --git a/pycurious-src/pycurious/grid/curie.py b/pycurious/grid/curie.py similarity index 100% rename from pycurious-src/pycurious/grid/curie.py rename to pycurious/grid/curie.py diff --git a/pycurious-src/pycurious/mapping/__init__.py b/pycurious/mapping/__init__.py similarity index 100% rename from pycurious-src/pycurious/mapping/__init__.py rename to pycurious/mapping/__init__.py diff --git a/pycurious-src/pycurious/mapping/mapping.py b/pycurious/mapping/mapping.py similarity index 100% rename from pycurious-src/pycurious/mapping/mapping.py rename to pycurious/mapping/mapping.py diff --git a/pycurious-src/pycurious/optimise/__init__.py b/pycurious/optimise/__init__.py similarity index 100% rename from pycurious-src/pycurious/optimise/__init__.py rename to pycurious/optimise/__init__.py diff --git a/pycurious-src/pycurious/optimise/optimise.py b/pycurious/optimise/optimise.py similarity index 100% rename from pycurious-src/pycurious/optimise/optimise.py rename to pycurious/optimise/optimise.py diff --git a/pycurious-src/pycurious/parallel/__init__.py b/pycurious/parallel/__init__.py similarity index 100% rename from pycurious-src/pycurious/parallel/__init__.py rename to pycurious/parallel/__init__.py diff --git a/pycurious-src/pycurious/parallel/parallel.py b/pycurious/parallel/parallel.py similarity index 100% rename from pycurious-src/pycurious/parallel/parallel.py rename to pycurious/parallel/parallel.py diff --git a/pycurious-src/pycurious/therm/__init__.py b/pycurious/therm/__init__.py similarity index 100% rename from pycurious-src/pycurious/therm/__init__.py rename to pycurious/therm/__init__.py diff --git a/pycurious-src/pycurious/therm/therm.py b/pycurious/therm/therm.py similarity index 100% rename from pycurious-src/pycurious/therm/therm.py rename to pycurious/therm/therm.py diff --git a/pycurious-src/setup.cfg b/setup.cfg similarity index 100% rename from pycurious-src/setup.cfg rename to setup.cfg diff --git a/pycurious-src/setup.py b/setup.py similarity index 100% rename from pycurious-src/setup.py rename to setup.py diff --git a/pycurious-src/src/cradon.c b/src/src/cradon.c similarity index 100% rename from pycurious-src/src/cradon.c rename to src/src/cradon.c diff --git a/pycurious-src/src/cradon.h b/src/src/cradon.h similarity index 100% rename from pycurious-src/src/cradon.h rename to src/src/cradon.h diff --git a/pycurious-src/src/cradon.pxd b/src/src/cradon.pxd similarity index 100% rename from pycurious-src/src/cradon.pxd rename to src/src/cradon.pxd diff --git a/pycurious-src/src/radon.pyx b/src/src/radon.pyx similarity index 100% rename from pycurious-src/src/radon.pyx rename to src/src/radon.pyx diff --git a/pycurious-src/tests/Bouligand_forward.py b/tests/Bouligand_forward.py similarity index 100% rename from pycurious-src/tests/Bouligand_forward.py rename to tests/Bouligand_forward.py diff --git a/pycurious-src/tests/optimise_test.py b/tests/optimise_test.py similarity index 100% rename from pycurious-src/tests/optimise_test.py rename to tests/optimise_test.py diff --git a/pycurious-src/tests/parallel_test.py b/tests/parallel_test.py similarity index 100% rename from pycurious-src/tests/parallel_test.py rename to tests/parallel_test.py diff --git a/pycurious-src/tests/test_multiprocessing.py b/tests/test_multiprocessing.py similarity index 100% rename from pycurious-src/tests/test_multiprocessing.py rename to tests/test_multiprocessing.py diff --git a/pycurious-src/tests/valid_numbers.py b/tests/valid_numbers.py similarity index 100% rename from pycurious-src/tests/valid_numbers.py rename to tests/valid_numbers.py From ccc75c2e279983d77b2c1aa98f26d4210b4534b4 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Mon, 3 Jun 2019 22:39:04 +1000 Subject: [PATCH 050/170] Forgot a few files... --- src/{src => }/cradon.c | 0 src/{src => }/cradon.h | 0 src/{src => }/cradon.pxd | 0 src/radon.c | 10736 +++++++++++++++++++++++++++++++++++++ src/{src => }/radon.pyx | 0 5 files changed, 10736 insertions(+) rename src/{src => }/cradon.c (100%) rename src/{src => }/cradon.h (100%) rename src/{src => }/cradon.pxd (100%) create mode 100644 src/radon.c rename src/{src => }/radon.pyx (100%) diff --git a/src/src/cradon.c b/src/cradon.c similarity index 100% rename from src/src/cradon.c rename to src/cradon.c diff --git a/src/src/cradon.h b/src/cradon.h similarity index 100% rename from src/src/cradon.h rename to src/cradon.h diff --git a/src/src/cradon.pxd b/src/cradon.pxd similarity index 100% rename from src/src/cradon.pxd rename to src/cradon.pxd diff --git a/src/radon.c b/src/radon.c new file mode 100644 index 0000000..cf725a6 --- /dev/null +++ b/src/radon.c @@ -0,0 +1,10736 @@ +/* Generated by Cython 0.29.1 */ + +/* BEGIN: Cython Metadata +{ + "distutils": { + "depends": [ + "/usr/lib/python2.7/site-packages/numpy/core/include/numpy/arrayobject.h", + "/usr/lib/python2.7/site-packages/numpy/core/include/numpy/ufuncobject.h" + ], + "extra_compile_args": [ + "-std=c99" + ], + "include_dirs": [ + "/usr/lib/python2.7/site-packages/numpy/core/include", + "src" + ], + "library_dirs": [ + "pycurious" + ], + "name": "pycurious.radon", + "sources": [ + "src/radon.pyx", + "src/cradon.c" + ] + }, + "module_name": "pycurious.radon" +} +END: Cython Metadata */ + +#define PY_SSIZE_T_CLEAN +#include "Python.h" +#ifndef Py_PYTHON_H + #error Python headers needed to compile C extensions, please install development version of Python. +#elif PY_VERSION_HEX < 0x02060000 || (0x03000000 <= PY_VERSION_HEX && PY_VERSION_HEX < 0x03030000) + #error Cython requires Python 2.6+ or Python 3.3+. +#else +#define CYTHON_ABI "0_29_1" +#define CYTHON_HEX_VERSION 0x001D01F0 +#define CYTHON_FUTURE_DIVISION 0 +#include +#ifndef offsetof + #define offsetof(type, member) ( (size_t) & ((type*)0) -> member ) +#endif +#if !defined(WIN32) && !defined(MS_WINDOWS) + #ifndef __stdcall + #define __stdcall + #endif + #ifndef __cdecl + #define __cdecl + #endif + #ifndef __fastcall + #define __fastcall + #endif +#endif +#ifndef DL_IMPORT + #define DL_IMPORT(t) t +#endif +#ifndef DL_EXPORT + #define DL_EXPORT(t) t +#endif +#define __PYX_COMMA , +#ifndef HAVE_LONG_LONG + #if PY_VERSION_HEX >= 0x02070000 + #define HAVE_LONG_LONG + #endif +#endif +#ifndef PY_LONG_LONG + #define PY_LONG_LONG LONG_LONG +#endif +#ifndef Py_HUGE_VAL + #define Py_HUGE_VAL HUGE_VAL +#endif +#ifdef PYPY_VERSION + #define CYTHON_COMPILING_IN_PYPY 1 + #define CYTHON_COMPILING_IN_PYSTON 0 + #define CYTHON_COMPILING_IN_CPYTHON 0 + #undef CYTHON_USE_TYPE_SLOTS + #define CYTHON_USE_TYPE_SLOTS 0 + #undef CYTHON_USE_PYTYPE_LOOKUP + #define CYTHON_USE_PYTYPE_LOOKUP 0 + #if PY_VERSION_HEX < 0x03050000 + #undef CYTHON_USE_ASYNC_SLOTS + #define CYTHON_USE_ASYNC_SLOTS 0 + #elif !defined(CYTHON_USE_ASYNC_SLOTS) + #define CYTHON_USE_ASYNC_SLOTS 1 + #endif + #undef CYTHON_USE_PYLIST_INTERNALS + #define CYTHON_USE_PYLIST_INTERNALS 0 + #undef CYTHON_USE_UNICODE_INTERNALS + #define CYTHON_USE_UNICODE_INTERNALS 0 + #undef CYTHON_USE_UNICODE_WRITER + #define CYTHON_USE_UNICODE_WRITER 0 + #undef CYTHON_USE_PYLONG_INTERNALS + #define CYTHON_USE_PYLONG_INTERNALS 0 + #undef CYTHON_AVOID_BORROWED_REFS + #define CYTHON_AVOID_BORROWED_REFS 1 + #undef CYTHON_ASSUME_SAFE_MACROS + #define CYTHON_ASSUME_SAFE_MACROS 0 + #undef CYTHON_UNPACK_METHODS + #define CYTHON_UNPACK_METHODS 0 + #undef CYTHON_FAST_THREAD_STATE + #define CYTHON_FAST_THREAD_STATE 0 + #undef CYTHON_FAST_PYCALL + #define CYTHON_FAST_PYCALL 0 + #undef CYTHON_PEP489_MULTI_PHASE_INIT + #define CYTHON_PEP489_MULTI_PHASE_INIT 0 + #undef CYTHON_USE_TP_FINALIZE + #define CYTHON_USE_TP_FINALIZE 0 + #undef CYTHON_USE_DICT_VERSIONS + #define CYTHON_USE_DICT_VERSIONS 0 + #undef CYTHON_USE_EXC_INFO_STACK + #define CYTHON_USE_EXC_INFO_STACK 0 +#elif defined(PYSTON_VERSION) + #define CYTHON_COMPILING_IN_PYPY 0 + #define CYTHON_COMPILING_IN_PYSTON 1 + #define CYTHON_COMPILING_IN_CPYTHON 0 + #ifndef CYTHON_USE_TYPE_SLOTS + #define CYTHON_USE_TYPE_SLOTS 1 + #endif + #undef CYTHON_USE_PYTYPE_LOOKUP + #define CYTHON_USE_PYTYPE_LOOKUP 0 + #undef CYTHON_USE_ASYNC_SLOTS + #define CYTHON_USE_ASYNC_SLOTS 0 + #undef CYTHON_USE_PYLIST_INTERNALS + #define CYTHON_USE_PYLIST_INTERNALS 0 + #ifndef CYTHON_USE_UNICODE_INTERNALS + #define CYTHON_USE_UNICODE_INTERNALS 1 + #endif + #undef CYTHON_USE_UNICODE_WRITER + #define CYTHON_USE_UNICODE_WRITER 0 + #undef CYTHON_USE_PYLONG_INTERNALS + #define CYTHON_USE_PYLONG_INTERNALS 0 + #ifndef CYTHON_AVOID_BORROWED_REFS + #define CYTHON_AVOID_BORROWED_REFS 0 + #endif + #ifndef CYTHON_ASSUME_SAFE_MACROS + #define CYTHON_ASSUME_SAFE_MACROS 1 + #endif + #ifndef CYTHON_UNPACK_METHODS + #define CYTHON_UNPACK_METHODS 1 + #endif + #undef CYTHON_FAST_THREAD_STATE + #define CYTHON_FAST_THREAD_STATE 0 + #undef CYTHON_FAST_PYCALL + #define CYTHON_FAST_PYCALL 0 + #undef CYTHON_PEP489_MULTI_PHASE_INIT + #define CYTHON_PEP489_MULTI_PHASE_INIT 0 + #undef CYTHON_USE_TP_FINALIZE + #define CYTHON_USE_TP_FINALIZE 0 + #undef CYTHON_USE_DICT_VERSIONS + #define CYTHON_USE_DICT_VERSIONS 0 + #undef CYTHON_USE_EXC_INFO_STACK + #define CYTHON_USE_EXC_INFO_STACK 0 +#else + #define CYTHON_COMPILING_IN_PYPY 0 + #define CYTHON_COMPILING_IN_PYSTON 0 + #define CYTHON_COMPILING_IN_CPYTHON 1 + #ifndef CYTHON_USE_TYPE_SLOTS + #define CYTHON_USE_TYPE_SLOTS 1 + #endif + #if PY_VERSION_HEX < 0x02070000 + #undef CYTHON_USE_PYTYPE_LOOKUP + #define CYTHON_USE_PYTYPE_LOOKUP 0 + #elif !defined(CYTHON_USE_PYTYPE_LOOKUP) + #define CYTHON_USE_PYTYPE_LOOKUP 1 + #endif + #if PY_MAJOR_VERSION < 3 + #undef CYTHON_USE_ASYNC_SLOTS + #define CYTHON_USE_ASYNC_SLOTS 0 + #elif !defined(CYTHON_USE_ASYNC_SLOTS) + #define CYTHON_USE_ASYNC_SLOTS 1 + #endif + #if PY_VERSION_HEX < 0x02070000 + #undef CYTHON_USE_PYLONG_INTERNALS + #define CYTHON_USE_PYLONG_INTERNALS 0 + #elif !defined(CYTHON_USE_PYLONG_INTERNALS) + #define CYTHON_USE_PYLONG_INTERNALS 1 + #endif + #ifndef CYTHON_USE_PYLIST_INTERNALS + #define CYTHON_USE_PYLIST_INTERNALS 1 + #endif + #ifndef CYTHON_USE_UNICODE_INTERNALS + #define CYTHON_USE_UNICODE_INTERNALS 1 + #endif + #if PY_VERSION_HEX < 0x030300F0 + #undef CYTHON_USE_UNICODE_WRITER + #define CYTHON_USE_UNICODE_WRITER 0 + #elif !defined(CYTHON_USE_UNICODE_WRITER) + #define CYTHON_USE_UNICODE_WRITER 1 + #endif + #ifndef CYTHON_AVOID_BORROWED_REFS + #define CYTHON_AVOID_BORROWED_REFS 0 + #endif + #ifndef CYTHON_ASSUME_SAFE_MACROS + #define CYTHON_ASSUME_SAFE_MACROS 1 + #endif + #ifndef CYTHON_UNPACK_METHODS + #define CYTHON_UNPACK_METHODS 1 + #endif + #ifndef CYTHON_FAST_THREAD_STATE + #define CYTHON_FAST_THREAD_STATE 1 + #endif + #ifndef CYTHON_FAST_PYCALL + #define CYTHON_FAST_PYCALL 1 + #endif + #ifndef CYTHON_PEP489_MULTI_PHASE_INIT + #define CYTHON_PEP489_MULTI_PHASE_INIT (PY_VERSION_HEX >= 0x03050000) + #endif + #ifndef CYTHON_USE_TP_FINALIZE + #define CYTHON_USE_TP_FINALIZE (PY_VERSION_HEX >= 0x030400a1) + #endif + #ifndef CYTHON_USE_DICT_VERSIONS + #define CYTHON_USE_DICT_VERSIONS (PY_VERSION_HEX >= 0x030600B1) + #endif + #ifndef CYTHON_USE_EXC_INFO_STACK + #define CYTHON_USE_EXC_INFO_STACK (PY_VERSION_HEX >= 0x030700A3) + #endif +#endif +#if !defined(CYTHON_FAST_PYCCALL) +#define CYTHON_FAST_PYCCALL (CYTHON_FAST_PYCALL && PY_VERSION_HEX >= 0x030600B1) +#endif +#if CYTHON_USE_PYLONG_INTERNALS + #include "longintrepr.h" + #undef SHIFT + #undef BASE + #undef MASK + #ifdef SIZEOF_VOID_P + enum { __pyx_check_sizeof_voidp = 1/(SIZEOF_VOID_P == sizeof(void*)) }; + #endif +#endif +#ifndef __has_attribute + #define __has_attribute(x) 0 +#endif +#ifndef __has_cpp_attribute + #define __has_cpp_attribute(x) 0 +#endif +#ifndef CYTHON_RESTRICT + #if defined(__GNUC__) + #define CYTHON_RESTRICT __restrict__ + #elif defined(_MSC_VER) && _MSC_VER >= 1400 + #define CYTHON_RESTRICT __restrict + #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L + #define CYTHON_RESTRICT restrict + #else + #define CYTHON_RESTRICT + #endif +#endif +#ifndef CYTHON_UNUSED +# if defined(__GNUC__) +# if !(defined(__cplusplus)) || (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 4)) +# define CYTHON_UNUSED __attribute__ ((__unused__)) +# else +# define CYTHON_UNUSED +# endif +# elif defined(__ICC) || (defined(__INTEL_COMPILER) && !defined(_MSC_VER)) +# define CYTHON_UNUSED __attribute__ ((__unused__)) +# else +# define CYTHON_UNUSED +# endif +#endif +#ifndef CYTHON_MAYBE_UNUSED_VAR +# if defined(__cplusplus) + template void CYTHON_MAYBE_UNUSED_VAR( const T& ) { } +# else +# define CYTHON_MAYBE_UNUSED_VAR(x) (void)(x) +# endif +#endif +#ifndef CYTHON_NCP_UNUSED +# if CYTHON_COMPILING_IN_CPYTHON +# define CYTHON_NCP_UNUSED +# else +# define CYTHON_NCP_UNUSED CYTHON_UNUSED +# endif +#endif +#define __Pyx_void_to_None(void_result) ((void)(void_result), Py_INCREF(Py_None), Py_None) +#ifdef _MSC_VER + #ifndef _MSC_STDINT_H_ + #if _MSC_VER < 1300 + typedef unsigned char uint8_t; + typedef unsigned int uint32_t; + #else + typedef unsigned __int8 uint8_t; + typedef unsigned __int32 uint32_t; + #endif + #endif +#else + #include +#endif +#ifndef CYTHON_FALLTHROUGH + #if defined(__cplusplus) && __cplusplus >= 201103L + #if __has_cpp_attribute(fallthrough) + #define CYTHON_FALLTHROUGH [[fallthrough]] + #elif __has_cpp_attribute(clang::fallthrough) + #define CYTHON_FALLTHROUGH [[clang::fallthrough]] + #elif __has_cpp_attribute(gnu::fallthrough) + #define CYTHON_FALLTHROUGH [[gnu::fallthrough]] + #endif + #endif + #ifndef CYTHON_FALLTHROUGH + #if __has_attribute(fallthrough) + #define CYTHON_FALLTHROUGH __attribute__((fallthrough)) + #else + #define CYTHON_FALLTHROUGH + #endif + #endif + #if defined(__clang__ ) && defined(__apple_build_version__) + #if __apple_build_version__ < 7000000 + #undef CYTHON_FALLTHROUGH + #define CYTHON_FALLTHROUGH + #endif + #endif +#endif + +#ifndef CYTHON_INLINE + #if defined(__clang__) + #define CYTHON_INLINE __inline__ __attribute__ ((__unused__)) + #elif defined(__GNUC__) + #define CYTHON_INLINE __inline__ + #elif defined(_MSC_VER) + #define CYTHON_INLINE __inline + #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L + #define CYTHON_INLINE inline + #else + #define CYTHON_INLINE + #endif +#endif + +#if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x02070600 && !defined(Py_OptimizeFlag) + #define Py_OptimizeFlag 0 +#endif +#define __PYX_BUILD_PY_SSIZE_T "n" +#define CYTHON_FORMAT_SSIZE_T "z" +#if PY_MAJOR_VERSION < 3 + #define __Pyx_BUILTIN_MODULE_NAME "__builtin__" + #define __Pyx_PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\ + PyCode_New(a+k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos) + #define __Pyx_DefaultClassType PyClass_Type +#else + #define __Pyx_BUILTIN_MODULE_NAME "builtins" + #define __Pyx_PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\ + PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos) + #define __Pyx_DefaultClassType PyType_Type +#endif +#ifndef Py_TPFLAGS_CHECKTYPES + #define Py_TPFLAGS_CHECKTYPES 0 +#endif +#ifndef Py_TPFLAGS_HAVE_INDEX + #define Py_TPFLAGS_HAVE_INDEX 0 +#endif +#ifndef Py_TPFLAGS_HAVE_NEWBUFFER + #define Py_TPFLAGS_HAVE_NEWBUFFER 0 +#endif +#ifndef Py_TPFLAGS_HAVE_FINALIZE + #define Py_TPFLAGS_HAVE_FINALIZE 0 +#endif +#ifndef METH_STACKLESS + #define METH_STACKLESS 0 +#endif +#if PY_VERSION_HEX <= 0x030700A3 || !defined(METH_FASTCALL) + #ifndef METH_FASTCALL + #define METH_FASTCALL 0x80 + #endif + typedef PyObject *(*__Pyx_PyCFunctionFast) (PyObject *self, PyObject *const *args, Py_ssize_t nargs); + typedef PyObject *(*__Pyx_PyCFunctionFastWithKeywords) (PyObject *self, PyObject *const *args, + Py_ssize_t nargs, PyObject *kwnames); +#else + #define __Pyx_PyCFunctionFast _PyCFunctionFast + #define __Pyx_PyCFunctionFastWithKeywords _PyCFunctionFastWithKeywords +#endif +#if CYTHON_FAST_PYCCALL +#define __Pyx_PyFastCFunction_Check(func)\ + ((PyCFunction_Check(func) && (METH_FASTCALL == (PyCFunction_GET_FLAGS(func) & ~(METH_CLASS | METH_STATIC | METH_COEXIST | METH_KEYWORDS | METH_STACKLESS))))) +#else +#define __Pyx_PyFastCFunction_Check(func) 0 +#endif +#if CYTHON_USE_DICT_VERSIONS +#define __PYX_GET_DICT_VERSION(dict) (((PyDictObject*)(dict))->ma_version_tag) +#define __PYX_UPDATE_DICT_CACHE(dict, value, cache_var, version_var)\ + (version_var) = __PYX_GET_DICT_VERSION(dict);\ + (cache_var) = (value); +#define __PYX_PY_DICT_LOOKUP_IF_MODIFIED(VAR, DICT, LOOKUP) {\ + static PY_UINT64_T __pyx_dict_version = 0;\ + static PyObject *__pyx_dict_cached_value = NULL;\ + if (likely(__PYX_GET_DICT_VERSION(DICT) == __pyx_dict_version)) {\ + (VAR) = __pyx_dict_cached_value;\ + } else {\ + (VAR) = __pyx_dict_cached_value = (LOOKUP);\ + __pyx_dict_version = __PYX_GET_DICT_VERSION(DICT);\ + }\ + } +#else +#define __PYX_GET_DICT_VERSION(dict) (0) +#define __PYX_UPDATE_DICT_CACHE(dict, value, cache_var, version_var) +#define __PYX_PY_DICT_LOOKUP_IF_MODIFIED(VAR, DICT, LOOKUP) (VAR) = (LOOKUP); +#endif +#if CYTHON_COMPILING_IN_PYPY && !defined(PyObject_Malloc) + #define PyObject_Malloc(s) PyMem_Malloc(s) + #define PyObject_Free(p) PyMem_Free(p) + #define PyObject_Realloc(p) PyMem_Realloc(p) +#endif +#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX < 0x030400A1 + #define PyMem_RawMalloc(n) PyMem_Malloc(n) + #define PyMem_RawRealloc(p, n) PyMem_Realloc(p, n) + #define PyMem_RawFree(p) PyMem_Free(p) +#endif +#if CYTHON_COMPILING_IN_PYSTON + #define __Pyx_PyCode_HasFreeVars(co) PyCode_HasFreeVars(co) + #define __Pyx_PyFrame_SetLineNumber(frame, lineno) PyFrame_SetLineNumber(frame, lineno) +#else + #define __Pyx_PyCode_HasFreeVars(co) (PyCode_GetNumFree(co) > 0) + #define __Pyx_PyFrame_SetLineNumber(frame, lineno) (frame)->f_lineno = (lineno) +#endif +#if !CYTHON_FAST_THREAD_STATE || PY_VERSION_HEX < 0x02070000 + #define __Pyx_PyThreadState_Current PyThreadState_GET() +#elif PY_VERSION_HEX >= 0x03060000 + #define __Pyx_PyThreadState_Current _PyThreadState_UncheckedGet() +#elif PY_VERSION_HEX >= 0x03000000 + #define __Pyx_PyThreadState_Current PyThreadState_GET() +#else + #define __Pyx_PyThreadState_Current _PyThreadState_Current +#endif +#if PY_VERSION_HEX < 0x030700A2 && !defined(PyThread_tss_create) && !defined(Py_tss_NEEDS_INIT) +#include "pythread.h" +#define Py_tss_NEEDS_INIT 0 +typedef int Py_tss_t; +static CYTHON_INLINE int PyThread_tss_create(Py_tss_t *key) { + *key = PyThread_create_key(); + return 0; // PyThread_create_key reports success always +} +static CYTHON_INLINE Py_tss_t * PyThread_tss_alloc(void) { + Py_tss_t *key = (Py_tss_t *)PyObject_Malloc(sizeof(Py_tss_t)); + *key = Py_tss_NEEDS_INIT; + return key; +} +static CYTHON_INLINE void PyThread_tss_free(Py_tss_t *key) { + PyObject_Free(key); +} +static CYTHON_INLINE int PyThread_tss_is_created(Py_tss_t *key) { + return *key != Py_tss_NEEDS_INIT; +} +static CYTHON_INLINE void PyThread_tss_delete(Py_tss_t *key) { + PyThread_delete_key(*key); + *key = Py_tss_NEEDS_INIT; +} +static CYTHON_INLINE int PyThread_tss_set(Py_tss_t *key, void *value) { + return PyThread_set_key_value(*key, value); +} +static CYTHON_INLINE void * PyThread_tss_get(Py_tss_t *key) { + return PyThread_get_key_value(*key); +} +#endif // TSS (Thread Specific Storage) API +#if CYTHON_COMPILING_IN_CPYTHON || defined(_PyDict_NewPresized) +#define __Pyx_PyDict_NewPresized(n) ((n <= 8) ? PyDict_New() : _PyDict_NewPresized(n)) +#else +#define __Pyx_PyDict_NewPresized(n) PyDict_New() +#endif +#if PY_MAJOR_VERSION >= 3 || CYTHON_FUTURE_DIVISION + #define __Pyx_PyNumber_Divide(x,y) PyNumber_TrueDivide(x,y) + #define __Pyx_PyNumber_InPlaceDivide(x,y) PyNumber_InPlaceTrueDivide(x,y) +#else + #define __Pyx_PyNumber_Divide(x,y) PyNumber_Divide(x,y) + #define __Pyx_PyNumber_InPlaceDivide(x,y) PyNumber_InPlaceDivide(x,y) +#endif +#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030500A1 && CYTHON_USE_UNICODE_INTERNALS +#define __Pyx_PyDict_GetItemStr(dict, name) _PyDict_GetItem_KnownHash(dict, name, ((PyASCIIObject *) name)->hash) +#else +#define __Pyx_PyDict_GetItemStr(dict, name) PyDict_GetItem(dict, name) +#endif +#if PY_VERSION_HEX > 0x03030000 && defined(PyUnicode_KIND) + #define CYTHON_PEP393_ENABLED 1 + #define __Pyx_PyUnicode_READY(op) (likely(PyUnicode_IS_READY(op)) ?\ + 0 : _PyUnicode_Ready((PyObject *)(op))) + #define __Pyx_PyUnicode_GET_LENGTH(u) PyUnicode_GET_LENGTH(u) + #define __Pyx_PyUnicode_READ_CHAR(u, i) PyUnicode_READ_CHAR(u, i) + #define __Pyx_PyUnicode_MAX_CHAR_VALUE(u) PyUnicode_MAX_CHAR_VALUE(u) + #define __Pyx_PyUnicode_KIND(u) PyUnicode_KIND(u) + #define __Pyx_PyUnicode_DATA(u) PyUnicode_DATA(u) + #define __Pyx_PyUnicode_READ(k, d, i) PyUnicode_READ(k, d, i) + #define __Pyx_PyUnicode_WRITE(k, d, i, ch) PyUnicode_WRITE(k, d, i, ch) + #define __Pyx_PyUnicode_IS_TRUE(u) (0 != (likely(PyUnicode_IS_READY(u)) ? PyUnicode_GET_LENGTH(u) : PyUnicode_GET_SIZE(u))) +#else + #define CYTHON_PEP393_ENABLED 0 + #define PyUnicode_1BYTE_KIND 1 + #define PyUnicode_2BYTE_KIND 2 + #define PyUnicode_4BYTE_KIND 4 + #define __Pyx_PyUnicode_READY(op) (0) + #define __Pyx_PyUnicode_GET_LENGTH(u) PyUnicode_GET_SIZE(u) + #define __Pyx_PyUnicode_READ_CHAR(u, i) ((Py_UCS4)(PyUnicode_AS_UNICODE(u)[i])) + #define __Pyx_PyUnicode_MAX_CHAR_VALUE(u) ((sizeof(Py_UNICODE) == 2) ? 65535 : 1114111) + #define __Pyx_PyUnicode_KIND(u) (sizeof(Py_UNICODE)) + #define __Pyx_PyUnicode_DATA(u) ((void*)PyUnicode_AS_UNICODE(u)) + #define __Pyx_PyUnicode_READ(k, d, i) ((void)(k), (Py_UCS4)(((Py_UNICODE*)d)[i])) + #define __Pyx_PyUnicode_WRITE(k, d, i, ch) (((void)(k)), ((Py_UNICODE*)d)[i] = ch) + #define __Pyx_PyUnicode_IS_TRUE(u) (0 != PyUnicode_GET_SIZE(u)) +#endif +#if CYTHON_COMPILING_IN_PYPY + #define __Pyx_PyUnicode_Concat(a, b) PyNumber_Add(a, b) + #define __Pyx_PyUnicode_ConcatSafe(a, b) PyNumber_Add(a, b) +#else + #define __Pyx_PyUnicode_Concat(a, b) PyUnicode_Concat(a, b) + #define __Pyx_PyUnicode_ConcatSafe(a, b) ((unlikely((a) == Py_None) || unlikely((b) == Py_None)) ?\ + PyNumber_Add(a, b) : __Pyx_PyUnicode_Concat(a, b)) +#endif +#if CYTHON_COMPILING_IN_PYPY && !defined(PyUnicode_Contains) + #define PyUnicode_Contains(u, s) PySequence_Contains(u, s) +#endif +#if CYTHON_COMPILING_IN_PYPY && !defined(PyByteArray_Check) + #define PyByteArray_Check(obj) PyObject_TypeCheck(obj, &PyByteArray_Type) +#endif +#if CYTHON_COMPILING_IN_PYPY && !defined(PyObject_Format) + #define PyObject_Format(obj, fmt) PyObject_CallMethod(obj, "__format__", "O", fmt) +#endif +#define __Pyx_PyString_FormatSafe(a, b) ((unlikely((a) == Py_None || (PyString_Check(b) && !PyString_CheckExact(b)))) ? PyNumber_Remainder(a, b) : __Pyx_PyString_Format(a, b)) +#define __Pyx_PyUnicode_FormatSafe(a, b) ((unlikely((a) == Py_None || (PyUnicode_Check(b) && !PyUnicode_CheckExact(b)))) ? PyNumber_Remainder(a, b) : PyUnicode_Format(a, b)) +#if PY_MAJOR_VERSION >= 3 + #define __Pyx_PyString_Format(a, b) PyUnicode_Format(a, b) +#else + #define __Pyx_PyString_Format(a, b) PyString_Format(a, b) +#endif +#if PY_MAJOR_VERSION < 3 && !defined(PyObject_ASCII) + #define PyObject_ASCII(o) PyObject_Repr(o) +#endif +#if PY_MAJOR_VERSION >= 3 + #define PyBaseString_Type PyUnicode_Type + #define PyStringObject PyUnicodeObject + #define PyString_Type PyUnicode_Type + #define PyString_Check PyUnicode_Check + #define PyString_CheckExact PyUnicode_CheckExact + #define PyObject_Unicode PyObject_Str +#endif +#if PY_MAJOR_VERSION >= 3 + #define __Pyx_PyBaseString_Check(obj) PyUnicode_Check(obj) + #define __Pyx_PyBaseString_CheckExact(obj) PyUnicode_CheckExact(obj) +#else + #define __Pyx_PyBaseString_Check(obj) (PyString_Check(obj) || PyUnicode_Check(obj)) + #define __Pyx_PyBaseString_CheckExact(obj) (PyString_CheckExact(obj) || PyUnicode_CheckExact(obj)) +#endif +#ifndef PySet_CheckExact + #define PySet_CheckExact(obj) (Py_TYPE(obj) == &PySet_Type) +#endif +#if CYTHON_ASSUME_SAFE_MACROS + #define __Pyx_PySequence_SIZE(seq) Py_SIZE(seq) +#else + #define __Pyx_PySequence_SIZE(seq) PySequence_Size(seq) +#endif +#if PY_MAJOR_VERSION >= 3 + #define PyIntObject PyLongObject + #define PyInt_Type PyLong_Type + #define PyInt_Check(op) PyLong_Check(op) + #define PyInt_CheckExact(op) PyLong_CheckExact(op) + #define PyInt_FromString PyLong_FromString + #define PyInt_FromUnicode PyLong_FromUnicode + #define PyInt_FromLong PyLong_FromLong + #define PyInt_FromSize_t PyLong_FromSize_t + #define PyInt_FromSsize_t PyLong_FromSsize_t + #define PyInt_AsLong PyLong_AsLong + #define PyInt_AS_LONG PyLong_AS_LONG + #define PyInt_AsSsize_t PyLong_AsSsize_t + #define PyInt_AsUnsignedLongMask PyLong_AsUnsignedLongMask + #define PyInt_AsUnsignedLongLongMask PyLong_AsUnsignedLongLongMask + #define PyNumber_Int PyNumber_Long +#endif +#if PY_MAJOR_VERSION >= 3 + #define PyBoolObject PyLongObject +#endif +#if PY_MAJOR_VERSION >= 3 && CYTHON_COMPILING_IN_PYPY + #ifndef PyUnicode_InternFromString + #define PyUnicode_InternFromString(s) PyUnicode_FromString(s) + #endif +#endif +#if PY_VERSION_HEX < 0x030200A4 + typedef long Py_hash_t; + #define __Pyx_PyInt_FromHash_t PyInt_FromLong + #define __Pyx_PyInt_AsHash_t PyInt_AsLong +#else + #define __Pyx_PyInt_FromHash_t PyInt_FromSsize_t + #define __Pyx_PyInt_AsHash_t PyInt_AsSsize_t +#endif +#if PY_MAJOR_VERSION >= 3 + #define __Pyx_PyMethod_New(func, self, klass) ((self) ? PyMethod_New(func, self) : (Py_INCREF(func), func)) +#else + #define __Pyx_PyMethod_New(func, self, klass) PyMethod_New(func, self, klass) +#endif +#if CYTHON_USE_ASYNC_SLOTS + #if PY_VERSION_HEX >= 0x030500B1 + #define __Pyx_PyAsyncMethodsStruct PyAsyncMethods + #define __Pyx_PyType_AsAsync(obj) (Py_TYPE(obj)->tp_as_async) + #else + #define __Pyx_PyType_AsAsync(obj) ((__Pyx_PyAsyncMethodsStruct*) (Py_TYPE(obj)->tp_reserved)) + #endif +#else + #define __Pyx_PyType_AsAsync(obj) NULL +#endif +#ifndef __Pyx_PyAsyncMethodsStruct + typedef struct { + unaryfunc am_await; + unaryfunc am_aiter; + unaryfunc am_anext; + } __Pyx_PyAsyncMethodsStruct; +#endif + +#if defined(WIN32) || defined(MS_WINDOWS) + #define _USE_MATH_DEFINES +#endif +#include +#ifdef NAN +#define __PYX_NAN() ((float) NAN) +#else +static CYTHON_INLINE float __PYX_NAN() { + float value; + memset(&value, 0xFF, sizeof(value)); + return value; +} +#endif +#if defined(__CYGWIN__) && defined(_LDBL_EQ_DBL) +#define __Pyx_truncl trunc +#else +#define __Pyx_truncl truncl +#endif + + +#define __PYX_ERR(f_index, lineno, Ln_error) \ +{ \ + __pyx_filename = __pyx_f[f_index]; __pyx_lineno = lineno; __pyx_clineno = __LINE__; goto Ln_error; \ +} + +#ifndef __PYX_EXTERN_C + #ifdef __cplusplus + #define __PYX_EXTERN_C extern "C" + #else + #define __PYX_EXTERN_C extern + #endif +#endif + +#define __PYX_HAVE__pycurious__radon +#define __PYX_HAVE_API__pycurious__radon +/* Early includes */ +#include +#include +#include "numpy/arrayobject.h" +#include "numpy/ufuncobject.h" +#include "cradon.h" +#ifdef _OPENMP +#include +#endif /* _OPENMP */ + +#if defined(PYREX_WITHOUT_ASSERTIONS) && !defined(CYTHON_WITHOUT_ASSERTIONS) +#define CYTHON_WITHOUT_ASSERTIONS +#endif + +typedef struct {PyObject **p; const char *s; const Py_ssize_t n; const char* encoding; + const char is_unicode; const char is_str; const char intern; } __Pyx_StringTabEntry; + +#define __PYX_DEFAULT_STRING_ENCODING_IS_ASCII 0 +#define __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT 0 +#define __PYX_DEFAULT_STRING_ENCODING "" +#define __Pyx_PyObject_FromString __Pyx_PyBytes_FromString +#define __Pyx_PyObject_FromStringAndSize __Pyx_PyBytes_FromStringAndSize +#define __Pyx_uchar_cast(c) ((unsigned char)c) +#define __Pyx_long_cast(x) ((long)x) +#define __Pyx_fits_Py_ssize_t(v, type, is_signed) (\ + (sizeof(type) < sizeof(Py_ssize_t)) ||\ + (sizeof(type) > sizeof(Py_ssize_t) &&\ + likely(v < (type)PY_SSIZE_T_MAX ||\ + v == (type)PY_SSIZE_T_MAX) &&\ + (!is_signed || likely(v > (type)PY_SSIZE_T_MIN ||\ + v == (type)PY_SSIZE_T_MIN))) ||\ + (sizeof(type) == sizeof(Py_ssize_t) &&\ + (is_signed || likely(v < (type)PY_SSIZE_T_MAX ||\ + v == (type)PY_SSIZE_T_MAX))) ) +static CYTHON_INLINE int __Pyx_is_valid_index(Py_ssize_t i, Py_ssize_t limit) { + return (size_t) i < (size_t) limit; +} +#if defined (__cplusplus) && __cplusplus >= 201103L + #include + #define __Pyx_sst_abs(value) std::abs(value) +#elif SIZEOF_INT >= SIZEOF_SIZE_T + #define __Pyx_sst_abs(value) abs(value) +#elif SIZEOF_LONG >= SIZEOF_SIZE_T + #define __Pyx_sst_abs(value) labs(value) +#elif defined (_MSC_VER) + #define __Pyx_sst_abs(value) ((Py_ssize_t)_abs64(value)) +#elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L + #define __Pyx_sst_abs(value) llabs(value) +#elif defined (__GNUC__) + #define __Pyx_sst_abs(value) __builtin_llabs(value) +#else + #define __Pyx_sst_abs(value) ((value<0) ? -value : value) +#endif +static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject*); +static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject*, Py_ssize_t* length); +#define __Pyx_PyByteArray_FromString(s) PyByteArray_FromStringAndSize((const char*)s, strlen((const char*)s)) +#define __Pyx_PyByteArray_FromStringAndSize(s, l) PyByteArray_FromStringAndSize((const char*)s, l) +#define __Pyx_PyBytes_FromString PyBytes_FromString +#define __Pyx_PyBytes_FromStringAndSize PyBytes_FromStringAndSize +static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char*); +#if PY_MAJOR_VERSION < 3 + #define __Pyx_PyStr_FromString __Pyx_PyBytes_FromString + #define __Pyx_PyStr_FromStringAndSize __Pyx_PyBytes_FromStringAndSize +#else + #define __Pyx_PyStr_FromString __Pyx_PyUnicode_FromString + #define __Pyx_PyStr_FromStringAndSize __Pyx_PyUnicode_FromStringAndSize +#endif +#define __Pyx_PyBytes_AsWritableString(s) ((char*) PyBytes_AS_STRING(s)) +#define __Pyx_PyBytes_AsWritableSString(s) ((signed char*) PyBytes_AS_STRING(s)) +#define __Pyx_PyBytes_AsWritableUString(s) ((unsigned char*) PyBytes_AS_STRING(s)) +#define __Pyx_PyBytes_AsString(s) ((const char*) PyBytes_AS_STRING(s)) +#define __Pyx_PyBytes_AsSString(s) ((const signed char*) PyBytes_AS_STRING(s)) +#define __Pyx_PyBytes_AsUString(s) ((const unsigned char*) PyBytes_AS_STRING(s)) +#define __Pyx_PyObject_AsWritableString(s) ((char*) __Pyx_PyObject_AsString(s)) +#define __Pyx_PyObject_AsWritableSString(s) ((signed char*) __Pyx_PyObject_AsString(s)) +#define __Pyx_PyObject_AsWritableUString(s) ((unsigned char*) __Pyx_PyObject_AsString(s)) +#define __Pyx_PyObject_AsSString(s) ((const signed char*) __Pyx_PyObject_AsString(s)) +#define __Pyx_PyObject_AsUString(s) ((const unsigned char*) __Pyx_PyObject_AsString(s)) +#define __Pyx_PyObject_FromCString(s) __Pyx_PyObject_FromString((const char*)s) +#define __Pyx_PyBytes_FromCString(s) __Pyx_PyBytes_FromString((const char*)s) +#define __Pyx_PyByteArray_FromCString(s) __Pyx_PyByteArray_FromString((const char*)s) +#define __Pyx_PyStr_FromCString(s) __Pyx_PyStr_FromString((const char*)s) +#define __Pyx_PyUnicode_FromCString(s) __Pyx_PyUnicode_FromString((const char*)s) +static CYTHON_INLINE size_t __Pyx_Py_UNICODE_strlen(const Py_UNICODE *u) { + const Py_UNICODE *u_end = u; + while (*u_end++) ; + return (size_t)(u_end - u - 1); +} +#define __Pyx_PyUnicode_FromUnicode(u) PyUnicode_FromUnicode(u, __Pyx_Py_UNICODE_strlen(u)) +#define __Pyx_PyUnicode_FromUnicodeAndLength PyUnicode_FromUnicode +#define __Pyx_PyUnicode_AsUnicode PyUnicode_AsUnicode +#define __Pyx_NewRef(obj) (Py_INCREF(obj), obj) +#define __Pyx_Owned_Py_None(b) __Pyx_NewRef(Py_None) +static CYTHON_INLINE PyObject * __Pyx_PyBool_FromLong(long b); +static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject*); +static CYTHON_INLINE int __Pyx_PyObject_IsTrueAndDecref(PyObject*); +static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x); +#define __Pyx_PySequence_Tuple(obj)\ + (likely(PyTuple_CheckExact(obj)) ? __Pyx_NewRef(obj) : PySequence_Tuple(obj)) +static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject*); +static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t); +#if CYTHON_ASSUME_SAFE_MACROS +#define __pyx_PyFloat_AsDouble(x) (PyFloat_CheckExact(x) ? PyFloat_AS_DOUBLE(x) : PyFloat_AsDouble(x)) +#else +#define __pyx_PyFloat_AsDouble(x) PyFloat_AsDouble(x) +#endif +#define __pyx_PyFloat_AsFloat(x) ((float) __pyx_PyFloat_AsDouble(x)) +#if PY_MAJOR_VERSION >= 3 +#define __Pyx_PyNumber_Int(x) (PyLong_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Long(x)) +#else +#define __Pyx_PyNumber_Int(x) (PyInt_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Int(x)) +#endif +#define __Pyx_PyNumber_Float(x) (PyFloat_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Float(x)) +#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII +static int __Pyx_sys_getdefaultencoding_not_ascii; +static int __Pyx_init_sys_getdefaultencoding_params(void) { + PyObject* sys; + PyObject* default_encoding = NULL; + PyObject* ascii_chars_u = NULL; + PyObject* ascii_chars_b = NULL; + const char* default_encoding_c; + sys = PyImport_ImportModule("sys"); + if (!sys) goto bad; + default_encoding = PyObject_CallMethod(sys, (char*) "getdefaultencoding", NULL); + Py_DECREF(sys); + if (!default_encoding) goto bad; + default_encoding_c = PyBytes_AsString(default_encoding); + if (!default_encoding_c) goto bad; + if (strcmp(default_encoding_c, "ascii") == 0) { + __Pyx_sys_getdefaultencoding_not_ascii = 0; + } else { + char ascii_chars[128]; + int c; + for (c = 0; c < 128; c++) { + ascii_chars[c] = c; + } + __Pyx_sys_getdefaultencoding_not_ascii = 1; + ascii_chars_u = PyUnicode_DecodeASCII(ascii_chars, 128, NULL); + if (!ascii_chars_u) goto bad; + ascii_chars_b = PyUnicode_AsEncodedString(ascii_chars_u, default_encoding_c, NULL); + if (!ascii_chars_b || !PyBytes_Check(ascii_chars_b) || memcmp(ascii_chars, PyBytes_AS_STRING(ascii_chars_b), 128) != 0) { + PyErr_Format( + PyExc_ValueError, + "This module compiled with c_string_encoding=ascii, but default encoding '%.200s' is not a superset of ascii.", + default_encoding_c); + goto bad; + } + Py_DECREF(ascii_chars_u); + Py_DECREF(ascii_chars_b); + } + Py_DECREF(default_encoding); + return 0; +bad: + Py_XDECREF(default_encoding); + Py_XDECREF(ascii_chars_u); + Py_XDECREF(ascii_chars_b); + return -1; +} +#endif +#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT && PY_MAJOR_VERSION >= 3 +#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_DecodeUTF8(c_str, size, NULL) +#else +#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_Decode(c_str, size, __PYX_DEFAULT_STRING_ENCODING, NULL) +#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT +static char* __PYX_DEFAULT_STRING_ENCODING; +static int __Pyx_init_sys_getdefaultencoding_params(void) { + PyObject* sys; + PyObject* default_encoding = NULL; + char* default_encoding_c; + sys = PyImport_ImportModule("sys"); + if (!sys) goto bad; + default_encoding = PyObject_CallMethod(sys, (char*) (const char*) "getdefaultencoding", NULL); + Py_DECREF(sys); + if (!default_encoding) goto bad; + default_encoding_c = PyBytes_AsString(default_encoding); + if (!default_encoding_c) goto bad; + __PYX_DEFAULT_STRING_ENCODING = (char*) malloc(strlen(default_encoding_c) + 1); + if (!__PYX_DEFAULT_STRING_ENCODING) goto bad; + strcpy(__PYX_DEFAULT_STRING_ENCODING, default_encoding_c); + Py_DECREF(default_encoding); + return 0; +bad: + Py_XDECREF(default_encoding); + return -1; +} +#endif +#endif + + +/* Test for GCC > 2.95 */ +#if defined(__GNUC__) && (__GNUC__ > 2 || (__GNUC__ == 2 && (__GNUC_MINOR__ > 95))) + #define likely(x) __builtin_expect(!!(x), 1) + #define unlikely(x) __builtin_expect(!!(x), 0) +#else /* !__GNUC__ or GCC < 2.95 */ + #define likely(x) (x) + #define unlikely(x) (x) +#endif /* __GNUC__ */ +static CYTHON_INLINE void __Pyx_pretend_to_initialize(void* ptr) { (void)ptr; } + +static PyObject *__pyx_m = NULL; +static PyObject *__pyx_d; +static PyObject *__pyx_b; +static PyObject *__pyx_cython_runtime = NULL; +static PyObject *__pyx_empty_tuple; +static PyObject *__pyx_empty_bytes; +static PyObject *__pyx_empty_unicode; +static int __pyx_lineno; +static int __pyx_clineno = 0; +static const char * __pyx_cfilenm= __FILE__; +static const char *__pyx_filename; + +/* Header.proto */ +#if !defined(CYTHON_CCOMPLEX) + #if defined(__cplusplus) + #define CYTHON_CCOMPLEX 1 + #elif defined(_Complex_I) + #define CYTHON_CCOMPLEX 1 + #else + #define CYTHON_CCOMPLEX 0 + #endif +#endif +#if CYTHON_CCOMPLEX + #ifdef __cplusplus + #include + #else + #include + #endif +#endif +#if CYTHON_CCOMPLEX && !defined(__cplusplus) && defined(__sun__) && defined(__GNUC__) + #undef _Complex_I + #define _Complex_I 1.0fj +#endif + + +static const char *__pyx_f[] = { + "src/radon.pyx", + "__init__.pxd", + "type.pxd", +}; + +/* "../../../../usr/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":776 + * # in Cython to enable them only on the right systems. + * + * ctypedef npy_int8 int8_t # <<<<<<<<<<<<<< + * ctypedef npy_int16 int16_t + * ctypedef npy_int32 int32_t + */ +typedef npy_int8 __pyx_t_5numpy_int8_t; + +/* "../../../../usr/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":777 + * + * ctypedef npy_int8 int8_t + * ctypedef npy_int16 int16_t # <<<<<<<<<<<<<< + * ctypedef npy_int32 int32_t + * ctypedef npy_int64 int64_t + */ +typedef npy_int16 __pyx_t_5numpy_int16_t; + +/* "../../../../usr/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":778 + * ctypedef npy_int8 int8_t + * ctypedef npy_int16 int16_t + * ctypedef npy_int32 int32_t # <<<<<<<<<<<<<< + * ctypedef npy_int64 int64_t + * #ctypedef npy_int96 int96_t + */ +typedef npy_int32 __pyx_t_5numpy_int32_t; + +/* "../../../../usr/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":779 + * ctypedef npy_int16 int16_t + * ctypedef npy_int32 int32_t + * ctypedef npy_int64 int64_t # <<<<<<<<<<<<<< + * #ctypedef npy_int96 int96_t + * #ctypedef npy_int128 int128_t + */ +typedef npy_int64 __pyx_t_5numpy_int64_t; + +/* "../../../../usr/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":783 + * #ctypedef npy_int128 int128_t + * + * ctypedef npy_uint8 uint8_t # <<<<<<<<<<<<<< + * ctypedef npy_uint16 uint16_t + * ctypedef npy_uint32 uint32_t + */ +typedef npy_uint8 __pyx_t_5numpy_uint8_t; + +/* "../../../../usr/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":784 + * + * ctypedef npy_uint8 uint8_t + * ctypedef npy_uint16 uint16_t # <<<<<<<<<<<<<< + * ctypedef npy_uint32 uint32_t + * ctypedef npy_uint64 uint64_t + */ +typedef npy_uint16 __pyx_t_5numpy_uint16_t; + +/* "../../../../usr/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":785 + * ctypedef npy_uint8 uint8_t + * ctypedef npy_uint16 uint16_t + * ctypedef npy_uint32 uint32_t # <<<<<<<<<<<<<< + * ctypedef npy_uint64 uint64_t + * #ctypedef npy_uint96 uint96_t + */ +typedef npy_uint32 __pyx_t_5numpy_uint32_t; + +/* "../../../../usr/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":786 + * ctypedef npy_uint16 uint16_t + * ctypedef npy_uint32 uint32_t + * ctypedef npy_uint64 uint64_t # <<<<<<<<<<<<<< + * #ctypedef npy_uint96 uint96_t + * #ctypedef npy_uint128 uint128_t + */ +typedef npy_uint64 __pyx_t_5numpy_uint64_t; 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+ +/* "../../../../usr/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":808 + * ctypedef npy_ulonglong ulonglong_t + * + * ctypedef npy_intp intp_t # <<<<<<<<<<<<<< + * ctypedef npy_uintp uintp_t + * + */ +typedef npy_intp __pyx_t_5numpy_intp_t; + +/* "../../../../usr/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":809 + * + * ctypedef npy_intp intp_t + * ctypedef npy_uintp uintp_t # <<<<<<<<<<<<<< + * + * ctypedef npy_double float_t + */ +typedef npy_uintp __pyx_t_5numpy_uintp_t; + +/* "../../../../usr/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":811 + * ctypedef npy_uintp uintp_t + * + * ctypedef npy_double float_t # <<<<<<<<<<<<<< + * ctypedef npy_double double_t + * ctypedef npy_longdouble longdouble_t + */ +typedef npy_double __pyx_t_5numpy_float_t; + +/* "../../../../usr/lib/python2.7/site-packages/Cython/Includes/numpy/__init__.pxd":812 + * + * ctypedef npy_double float_t + * ctypedef npy_double double_t # <<<<<<<<<<<<<< + * ctypedef npy_longdouble longdouble_t + * + */ +typedef npy_double __pyx_t_5numpy_double_t; 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+static CYTHON_INLINE void __Pyx_ErrFetchInState(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb); +#if CYTHON_COMPILING_IN_CPYTHON +#define __Pyx_PyErr_SetNone(exc) (Py_INCREF(exc), __Pyx_ErrRestore((exc), NULL, NULL)) +#else +#define __Pyx_PyErr_SetNone(exc) PyErr_SetNone(exc) +#endif +#else +#define __Pyx_PyErr_Clear() PyErr_Clear() +#define __Pyx_PyErr_SetNone(exc) PyErr_SetNone(exc) +#define __Pyx_ErrRestoreWithState(type, value, tb) PyErr_Restore(type, value, tb) +#define __Pyx_ErrFetchWithState(type, value, tb) PyErr_Fetch(type, value, tb) +#define __Pyx_ErrRestoreInState(tstate, type, value, tb) PyErr_Restore(type, value, tb) +#define __Pyx_ErrFetchInState(tstate, type, value, tb) PyErr_Fetch(type, value, tb) +#define __Pyx_ErrRestore(type, value, tb) PyErr_Restore(type, value, tb) +#define __Pyx_ErrFetch(type, value, tb) PyErr_Fetch(type, value, tb) +#endif + +/* RaiseException.proto */ +static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause); + +/* RaiseTooManyValuesToUnpack.proto */ +static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(Py_ssize_t expected); + +/* RaiseNeedMoreValuesToUnpack.proto */ +static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index); + +/* IterFinish.proto */ +static CYTHON_INLINE int __Pyx_IterFinish(void); + +/* UnpackItemEndCheck.proto */ +static int __Pyx_IternextUnpackEndCheck(PyObject *retval, Py_ssize_t expected); + +/* GetItemInt.proto */ +#define __Pyx_GetItemInt(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\ + (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\ + __Pyx_GetItemInt_Fast(o, (Py_ssize_t)i, is_list, wraparound, boundscheck) :\ + (is_list ? (PyErr_SetString(PyExc_IndexError, "list index out of range"), (PyObject*)NULL) :\ + __Pyx_GetItemInt_Generic(o, to_py_func(i)))) +#define __Pyx_GetItemInt_List(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\ + (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\ + __Pyx_GetItemInt_List_Fast(o, (Py_ssize_t)i, wraparound, boundscheck) :\ + (PyErr_SetString(PyExc_IndexError, "list index out of range"), (PyObject*)NULL)) +static CYTHON_INLINE PyObject *__Pyx_GetItemInt_List_Fast(PyObject *o, Py_ssize_t i, + int wraparound, int boundscheck); +#define __Pyx_GetItemInt_Tuple(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\ + (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\ + __Pyx_GetItemInt_Tuple_Fast(o, (Py_ssize_t)i, wraparound, boundscheck) :\ + (PyErr_SetString(PyExc_IndexError, "tuple index out of range"), (PyObject*)NULL)) +static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Tuple_Fast(PyObject *o, Py_ssize_t i, + int wraparound, int boundscheck); +static PyObject *__Pyx_GetItemInt_Generic(PyObject *o, PyObject* j); +static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Fast(PyObject *o, Py_ssize_t i, + int is_list, int wraparound, int boundscheck); + +/* PyFloatBinop.proto */ +#if !CYTHON_COMPILING_IN_PYPY +static PyObject* __Pyx_PyFloat_EqObjC(PyObject *op1, PyObject *op2, double floatval, int inplace); +#else +#define __Pyx_PyFloat_EqObjC(op1, op2, floatval, inplace)\ + (PyObject_RichCompare(op1, op2, Py_EQ)) + #endif + +/* ObjectGetItem.proto */ +#if CYTHON_USE_TYPE_SLOTS +static CYTHON_INLINE PyObject *__Pyx_PyObject_GetItem(PyObject *obj, PyObject* key); +#else +#define __Pyx_PyObject_GetItem(obj, key) PyObject_GetItem(obj, key) +#endif + +/* PyIntBinop.proto */ +#if !CYTHON_COMPILING_IN_PYPY +static PyObject* __Pyx_PyInt_SubtractObjC(PyObject *op1, PyObject *op2, long intval, int inplace); +#else +#define __Pyx_PyInt_SubtractObjC(op1, op2, intval, inplace)\ + (inplace ? PyNumber_InPlaceSubtract(op1, op2) : PyNumber_Subtract(op1, op2)) +#endif + +/* PyFloatBinop.proto */ +#if !CYTHON_COMPILING_IN_PYPY +static PyObject* __Pyx_PyFloat_SubtractCObj(PyObject *op1, PyObject *op2, double floatval, int inplace); +#else +#define __Pyx_PyFloat_SubtractCObj(op1, op2, floatval, inplace)\ + (inplace ? PyNumber_InPlaceSubtract(op1, op2) : PyNumber_Subtract(op1, op2)) +#endif + +/* PyFloatBinop.proto */ +#if !CYTHON_COMPILING_IN_PYPY +static PyObject* __Pyx_PyFloat_DivideObjC(PyObject *op1, PyObject *op2, double floatval, int inplace); +#else +#define __Pyx_PyFloat_DivideObjC(op1, op2, floatval, inplace)\ + ((inplace ? __Pyx_PyNumber_InPlaceDivide(op1, op2) : __Pyx_PyNumber_Divide(op1, op2))) + #endif + +/* None.proto */ +static CYTHON_INLINE void __Pyx_RaiseUnboundLocalError(const char *varname); + +/* ExtTypeTest.proto */ +static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type); + +/* PyObjectCallNoArg.proto */ +#if CYTHON_COMPILING_IN_CPYTHON +static CYTHON_INLINE PyObject* __Pyx_PyObject_CallNoArg(PyObject *func); +#else +#define __Pyx_PyObject_CallNoArg(func) __Pyx_PyObject_Call(func, __pyx_empty_tuple, NULL) +#endif + +/* DictGetItem.proto */ +#if PY_MAJOR_VERSION >= 3 && !CYTHON_COMPILING_IN_PYPY +static PyObject *__Pyx_PyDict_GetItem(PyObject *d, PyObject* key); +#define __Pyx_PyObject_Dict_GetItem(obj, name)\ + (likely(PyDict_CheckExact(obj)) ?\ + __Pyx_PyDict_GetItem(obj, name) : PyObject_GetItem(obj, name)) +#else +#define __Pyx_PyDict_GetItem(d, key) PyObject_GetItem(d, key) +#define __Pyx_PyObject_Dict_GetItem(obj, name) PyObject_GetItem(obj, name) +#endif + +/* RaiseNoneIterError.proto */ +static CYTHON_INLINE void __Pyx_RaiseNoneNotIterableError(void); + +/* GetTopmostException.proto */ +#if CYTHON_USE_EXC_INFO_STACK +static _PyErr_StackItem * __Pyx_PyErr_GetTopmostException(PyThreadState *tstate); +#endif + +/* SaveResetException.proto */ +#if CYTHON_FAST_THREAD_STATE +#define __Pyx_ExceptionSave(type, value, tb) __Pyx__ExceptionSave(__pyx_tstate, type, value, tb) +static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb); +#define __Pyx_ExceptionReset(type, value, tb) __Pyx__ExceptionReset(__pyx_tstate, type, value, tb) +static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb); +#else +#define __Pyx_ExceptionSave(type, value, tb) PyErr_GetExcInfo(type, value, tb) +#define __Pyx_ExceptionReset(type, value, tb) PyErr_SetExcInfo(type, value, tb) +#endif + +/* PyErrExceptionMatches.proto */ +#if CYTHON_FAST_THREAD_STATE +#define __Pyx_PyErr_ExceptionMatches(err) __Pyx_PyErr_ExceptionMatchesInState(__pyx_tstate, err) +static CYTHON_INLINE int __Pyx_PyErr_ExceptionMatchesInState(PyThreadState* tstate, PyObject* err); +#else +#define __Pyx_PyErr_ExceptionMatches(err) PyErr_ExceptionMatches(err) +#endif + +/* GetException.proto */ +#if CYTHON_FAST_THREAD_STATE +#define __Pyx_GetException(type, value, tb) __Pyx__GetException(__pyx_tstate, type, value, tb) +static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb); +#else +static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb); +#endif + +/* TypeImport.proto */ +#ifndef __PYX_HAVE_RT_ImportType_proto +#define __PYX_HAVE_RT_ImportType_proto +enum __Pyx_ImportType_CheckSize { + __Pyx_ImportType_CheckSize_Error = 0, + __Pyx_ImportType_CheckSize_Warn = 1, + __Pyx_ImportType_CheckSize_Ignore = 2 +}; +static PyTypeObject *__Pyx_ImportType(PyObject* module, const char *module_name, const char *class_name, size_t size, enum __Pyx_ImportType_CheckSize check_size); +#endif + +/* Import.proto */ +static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level); + +/* ImportFrom.proto */ +static PyObject* __Pyx_ImportFrom(PyObject* module, PyObject* name); + +/* CLineInTraceback.proto */ +#ifdef CYTHON_CLINE_IN_TRACEBACK +#define __Pyx_CLineForTraceback(tstate, c_line) (((CYTHON_CLINE_IN_TRACEBACK)) ? c_line : 0) +#else +static int __Pyx_CLineForTraceback(PyThreadState *tstate, int c_line); +#endif + +/* CodeObjectCache.proto */ +typedef struct { + PyCodeObject* code_object; + int code_line; +} __Pyx_CodeObjectCacheEntry; +struct __Pyx_CodeObjectCache { + int count; + int max_count; + __Pyx_CodeObjectCacheEntry* entries; +}; +static struct __Pyx_CodeObjectCache __pyx_code_cache = {0,0,NULL}; +static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line); +static PyCodeObject *__pyx_find_code_object(int code_line); +static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object); + +/* AddTraceback.proto */ +static void __Pyx_AddTraceback(const char *funcname, int c_line, + int py_line, const char *filename); + +/* CIntToPy.proto */ +static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value); + +/* Print.proto */ +static int __Pyx_Print(PyObject*, PyObject *, int); +#if CYTHON_COMPILING_IN_PYPY || PY_MAJOR_VERSION >= 3 +static PyObject* __pyx_print = 0; +static PyObject* __pyx_print_kwargs = 0; +#endif + +/* RealImag.proto */ +#if CYTHON_CCOMPLEX + #ifdef __cplusplus + #define __Pyx_CREAL(z) ((z).real()) + #define __Pyx_CIMAG(z) ((z).imag()) + #else + #define __Pyx_CREAL(z) (__real__(z)) + #define __Pyx_CIMAG(z) (__imag__(z)) + #endif +#else + #define __Pyx_CREAL(z) ((z).real) + #define __Pyx_CIMAG(z) ((z).imag) +#endif +#if defined(__cplusplus) && CYTHON_CCOMPLEX\ + && (defined(_WIN32) || defined(__clang__) || (defined(__GNUC__) && (__GNUC__ >= 5 || __GNUC__ == 4 && __GNUC_MINOR__ >= 4 )) || __cplusplus >= 201103) + #define __Pyx_SET_CREAL(z,x) ((z).real(x)) + #define __Pyx_SET_CIMAG(z,y) ((z).imag(y)) +#else + #define __Pyx_SET_CREAL(z,x) __Pyx_CREAL(z) = (x) + #define __Pyx_SET_CIMAG(z,y) __Pyx_CIMAG(z) = (y) +#endif + +/* Arithmetic.proto */ +#if CYTHON_CCOMPLEX + #define __Pyx_c_eq_float(a, b) ((a)==(b)) + #define __Pyx_c_sum_float(a, b) ((a)+(b)) + #define __Pyx_c_diff_float(a, b) ((a)-(b)) + #define __Pyx_c_prod_float(a, b) ((a)*(b)) + #define __Pyx_c_quot_float(a, b) ((a)/(b)) + #define __Pyx_c_neg_float(a) (-(a)) + #ifdef __cplusplus + #define __Pyx_c_is_zero_float(z) ((z)==(float)0) + #define __Pyx_c_conj_float(z) (::std::conj(z)) + #if 1 + #define __Pyx_c_abs_float(z) (::std::abs(z)) + #define __Pyx_c_pow_float(a, b) (::std::pow(a, b)) + #endif + #else + #define __Pyx_c_is_zero_float(z) ((z)==0) + #define __Pyx_c_conj_float(z) (conjf(z)) + #if 1 + #define __Pyx_c_abs_float(z) (cabsf(z)) + #define __Pyx_c_pow_float(a, b) (cpowf(a, b)) + #endif + #endif +#else + static CYTHON_INLINE int __Pyx_c_eq_float(__pyx_t_float_complex, __pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sum_float(__pyx_t_float_complex, __pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_diff_float(__pyx_t_float_complex, __pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prod_float(__pyx_t_float_complex, __pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex, __pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_neg_float(__pyx_t_float_complex); + static CYTHON_INLINE int __Pyx_c_is_zero_float(__pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conj_float(__pyx_t_float_complex); + #if 1 + static CYTHON_INLINE float __Pyx_c_abs_float(__pyx_t_float_complex); + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_pow_float(__pyx_t_float_complex, __pyx_t_float_complex); + #endif +#endif + +/* Arithmetic.proto */ +#if CYTHON_CCOMPLEX + #define __Pyx_c_eq_double(a, b) ((a)==(b)) + #define __Pyx_c_sum_double(a, b) ((a)+(b)) + #define __Pyx_c_diff_double(a, b) ((a)-(b)) + #define __Pyx_c_prod_double(a, b) ((a)*(b)) + #define __Pyx_c_quot_double(a, b) ((a)/(b)) + #define __Pyx_c_neg_double(a) (-(a)) + #ifdef __cplusplus + #define __Pyx_c_is_zero_double(z) ((z)==(double)0) + #define __Pyx_c_conj_double(z) (::std::conj(z)) + #if 1 + #define __Pyx_c_abs_double(z) (::std::abs(z)) + #define __Pyx_c_pow_double(a, b) (::std::pow(a, b)) + #endif + #else + #define __Pyx_c_is_zero_double(z) ((z)==0) + #define __Pyx_c_conj_double(z) (conj(z)) + #if 1 + #define __Pyx_c_abs_double(z) (cabs(z)) + #define __Pyx_c_pow_double(a, b) (cpow(a, b)) + #endif + #endif +#else + static CYTHON_INLINE int __Pyx_c_eq_double(__pyx_t_double_complex, __pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum_double(__pyx_t_double_complex, __pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff_double(__pyx_t_double_complex, __pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod_double(__pyx_t_double_complex, __pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex, __pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg_double(__pyx_t_double_complex); + static CYTHON_INLINE int __Pyx_c_is_zero_double(__pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj_double(__pyx_t_double_complex); + #if 1 + static CYTHON_INLINE double __Pyx_c_abs_double(__pyx_t_double_complex); + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow_double(__pyx_t_double_complex, __pyx_t_double_complex); + #endif +#endif + +/* CIntToPy.proto */ +static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value); + +/* CIntToPy.proto */ +static CYTHON_INLINE PyObject* __Pyx_PyInt_From_enum__NPY_TYPES(enum NPY_TYPES value); + +/* CIntFromPy.proto */ +static CYTHON_INLINE size_t __Pyx_PyInt_As_size_t(PyObject *); + +/* PrintOne.proto */ +static int __Pyx_PrintOne(PyObject* stream, PyObject *o); + +/* CIntFromPy.proto */ +static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *); + +/* CIntFromPy.proto */ +static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *); + +/* FastTypeChecks.proto */ +#if CYTHON_COMPILING_IN_CPYTHON +#define __Pyx_TypeCheck(obj, type) __Pyx_IsSubtype(Py_TYPE(obj), (PyTypeObject *)type) +static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b); +static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches(PyObject *err, PyObject *type); +static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObject *type1, PyObject *type2); +#else +#define __Pyx_TypeCheck(obj, type) PyObject_TypeCheck(obj, (PyTypeObject *)type) +#define __Pyx_PyErr_GivenExceptionMatches(err, type) PyErr_GivenExceptionMatches(err, type) +#define __Pyx_PyErr_GivenExceptionMatches2(err, type1, type2) (PyErr_GivenExceptionMatches(err, type1) || PyErr_GivenExceptionMatches(err, type2)) +#endif +#define __Pyx_PyException_Check(obj) __Pyx_TypeCheck(obj, PyExc_Exception) + +/* CheckBinaryVersion.proto */ +static int __Pyx_check_binary_version(void); + +/* InitStrings.proto */ +static int __Pyx_InitStrings(__Pyx_StringTabEntry *t); + + +/* Module declarations from 'cpython.buffer' */ + +/* Module declarations from 'libc.string' */ + +/* Module declarations from 'libc.stdio' */ + +/* Module declarations from '__builtin__' */ + +/* Module declarations from 'cpython.type' */ +static PyTypeObject *__pyx_ptype_7cpython_4type_type = 0; + +/* Module declarations from 'cpython' */ + +/* Module declarations from 'cpython.object' */ + +/* Module declarations from 'cpython.ref' */ + +/* Module declarations from 'cpython.mem' */ + +/* Module declarations from 'numpy' */ + +/* Module declarations from 'numpy' */ +static PyTypeObject *__pyx_ptype_5numpy_dtype = 0; +static PyTypeObject *__pyx_ptype_5numpy_flatiter = 0; +static PyTypeObject *__pyx_ptype_5numpy_broadcast = 0; +static PyTypeObject *__pyx_ptype_5numpy_ndarray = 0; +static PyTypeObject *__pyx_ptype_5numpy_ufunc = 0; +static CYTHON_INLINE char *__pyx_f_5numpy__util_dtypestring(PyArray_Descr *, char *, char *, int *); /*proto*/ + +/* Module declarations from 'cradon' */ + +/* Module declarations from 'pycurious.radon' */ +#define __Pyx_MODULE_NAME "pycurious.radon" +extern int __pyx_module_is_main_pycurious__radon; +int __pyx_module_is_main_pycurious__radon = 0; + +/* Implementation of 'pycurious.radon' */ +static PyObject *__pyx_builtin_xrange; +static PyObject *__pyx_builtin_ValueError; +static PyObject *__pyx_builtin_RuntimeError; +static PyObject *__pyx_builtin_range; +static PyObject *__pyx_builtin_ImportError; +static const char __pyx_k_L[] = "L"; +static const char __pyx_k_M[] = "M"; +static const char __pyx_k_N[] = "N"; +static const char __pyx_k_n[] = "n"; +static const char __pyx_k_p[] = "p"; +static const char __pyx_k_Rx[] = "Rx "; +static const char __pyx_k_Tx[] = "Tx "; +static const char __pyx_k_np[] = "np"; +static const char __pyx_k_nt[] = "nt"; +static const char __pyx_k_nw[] = "nw"; +static const char __pyx_k_nx[] = "nx"; +static const char __pyx_k_ny[] = "ny"; +static const char __pyx_k_pi[] = "pi"; +static const char __pyx_k_x0[] = "x0"; +static const char __pyx_k_x1[] = "x1"; +static const char __pyx_k_xk[] = "xk"; +static const char __pyx_k_xs[] = "xs"; +static const char __pyx_k_y0[] = "y0"; +static const char __pyx_k_y1[] = "y1"; +static const char __pyx_k_yk[] = "yk"; +static const char __pyx_k_ys[] = "ys"; +static const char __pyx_k_abs[] = "abs"; +static const char __pyx_k_cos[] = "cos"; +static const char __pyx_k_dot[] = "dot"; +static const char __pyx_k_end[] = "end"; +static const char __pyx_k_max[] = "max"; +static const char __pyx_k_min[] = "min"; +static const char __pyx_k_nTx[] = "nTx"; +static const char __pyx_k_sin[] = "sin"; +static const char __pyx_k_tan[] = "tan"; +static const char __pyx_k_Rx_2[] = "Rx"; +static const char __pyx_k_Tx_2[] = "Tx"; +static const char __pyx_k_data[] = "data"; +static const char __pyx_k_file[] = "file"; +static const char __pyx_k_main[] = "__main__"; +static const char __pyx_k_name[] = "__name__"; +static const char __pyx_k_size[] = "size"; +static const char __pyx_k_test[] = "__test__"; +static const char __pyx_k_Ldata[] = "Ldata"; +static const char __pyx_k_numpy[] = "numpy"; +static const char __pyx_k_print[] = "print"; +static const char __pyx_k_range[] = "range"; +static const char __pyx_k_shape[] = "shape"; +static const char __pyx_k_theta[] = "theta"; +static const char __pyx_k_zeros[] = "zeros"; +static const char __pyx_k_import[] = "__import__"; +static const char __pyx_k_xrange[] = "xrange"; +static const char __pyx_k_flatten[] = "flatten"; +static const char __pyx_k_radon2d[] = "radon2d"; +static const char __pyx_k_sinogram[] = "sinogram"; +static const char __pyx_k_ValueError[] = "ValueError"; +static const char __pyx_k_csr_matrix[] = "csr_matrix"; +static const char __pyx_k_ImportError[] = "ImportError"; +static const char __pyx_k_RuntimeError[] = "RuntimeError"; +static const char __pyx_k_scipy_sparse[] = "scipy.sparse"; +static const char __pyx_k_src_radon_pyx[] = "src/radon.pyx"; +static const char __pyx_k_pycurious_radon[] = "pycurious.radon"; +static const char __pyx_k_cline_in_traceback[] = "cline_in_traceback"; +static const char __pyx_k_ndarray_is_not_C_contiguous[] = "ndarray is not C contiguous"; +static const char __pyx_k_theta_should_be_within_0_pi[] = "theta should be within [0 pi)"; +static const char __pyx_k_data_should_be_a_square_array[] = "data should be a square array"; +static const char __pyx_k_numpy_core_multiarray_failed_to[] = "numpy.core.multiarray failed to import"; +static const char __pyx_k_unknown_dtype_code_in_numpy_pxd[] = "unknown dtype code in numpy.pxd (%d)"; +static const char __pyx_k_Format_string_allocated_too_shor[] = "Format string allocated too short, see comment in numpy.pxd"; +static const char __pyx_k_Non_native_byte_order_not_suppor[] = "Non-native byte order not supported"; +static const char __pyx_k_ndarray_is_not_Fortran_contiguou[] = "ndarray is not Fortran contiguous"; +static const char __pyx_k_numpy_core_umath_failed_to_impor[] = "numpy.core.umath failed to import"; +static const char __pyx_k_Format_string_allocated_too_shor_2[] = "Format string allocated too short."; 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+ void *r = NULL; + m = PyImport_ImportModule(modname); + if (!m) goto end; + p = PyObject_GetAttrString(m, "RefNannyAPI"); + if (!p) goto end; + r = PyLong_AsVoidPtr(p); +end: + Py_XDECREF(p); + Py_XDECREF(m); + return (__Pyx_RefNannyAPIStruct *)r; +} +#endif + +/* PyObjectGetAttrStr */ +#if CYTHON_USE_TYPE_SLOTS +static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStr(PyObject* obj, PyObject* attr_name) { + PyTypeObject* tp = Py_TYPE(obj); + if (likely(tp->tp_getattro)) + return tp->tp_getattro(obj, attr_name); +#if PY_MAJOR_VERSION < 3 + if (likely(tp->tp_getattr)) + return tp->tp_getattr(obj, PyString_AS_STRING(attr_name)); +#endif + return PyObject_GetAttr(obj, attr_name); +} +#endif + +/* GetBuiltinName */ +static PyObject *__Pyx_GetBuiltinName(PyObject *name) { + PyObject* result = __Pyx_PyObject_GetAttrStr(__pyx_b, name); + if (unlikely(!result)) { + PyErr_Format(PyExc_NameError, +#if PY_MAJOR_VERSION >= 3 + "name '%U' is not defined", name); +#else + "name '%.200s' is not defined", PyString_AS_STRING(name)); +#endif + } + return result; +} + +/* RaiseArgTupleInvalid */ +static void __Pyx_RaiseArgtupleInvalid( + const char* func_name, + int exact, + Py_ssize_t num_min, + Py_ssize_t num_max, + Py_ssize_t num_found) +{ + Py_ssize_t num_expected; + const char *more_or_less; + if (num_found < num_min) { + num_expected = num_min; + more_or_less = "at least"; + } else { + num_expected = num_max; + more_or_less = "at most"; + } + if (exact) { + more_or_less = "exactly"; + } + PyErr_Format(PyExc_TypeError, + "%.200s() takes %.8s %" CYTHON_FORMAT_SSIZE_T "d positional argument%.1s (%" CYTHON_FORMAT_SSIZE_T "d given)", + func_name, more_or_less, num_expected, + (num_expected == 1) ? "" : "s", num_found); +} + +/* RaiseDoubleKeywords */ +static void __Pyx_RaiseDoubleKeywordsError( + const char* func_name, + PyObject* kw_name) +{ + PyErr_Format(PyExc_TypeError, + #if PY_MAJOR_VERSION >= 3 + "%s() got multiple values for keyword argument '%U'", func_name, kw_name); + #else + "%s() got multiple values for keyword argument '%s'", func_name, + PyString_AsString(kw_name)); + #endif +} + +/* ParseKeywords */ +static int __Pyx_ParseOptionalKeywords( + PyObject *kwds, + PyObject **argnames[], + PyObject *kwds2, + PyObject *values[], + Py_ssize_t num_pos_args, + const char* function_name) +{ + PyObject *key = 0, *value = 0; + Py_ssize_t pos = 0; + PyObject*** name; + PyObject*** first_kw_arg = argnames + num_pos_args; + while (PyDict_Next(kwds, &pos, &key, &value)) { + name = first_kw_arg; + while (*name && (**name != key)) name++; + if (*name) { + values[name-argnames] = value; + continue; + } + name = first_kw_arg; + #if PY_MAJOR_VERSION < 3 + if (likely(PyString_CheckExact(key)) || likely(PyString_Check(key))) { + while (*name) { + if ((CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**name) == PyString_GET_SIZE(key)) + && _PyString_Eq(**name, key)) { + values[name-argnames] = value; + break; + } + name++; + } + if (*name) continue; + else { + PyObject*** argname = argnames; + while (argname != first_kw_arg) { + if ((**argname == key) || ( + (CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**argname) == PyString_GET_SIZE(key)) + && _PyString_Eq(**argname, key))) { + goto arg_passed_twice; + } + argname++; + } + } + } else + #endif + if (likely(PyUnicode_Check(key))) { + while (*name) { + int cmp = (**name == key) ? 0 : + #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3 + (PyUnicode_GET_SIZE(**name) != PyUnicode_GET_SIZE(key)) ? 1 : + #endif + PyUnicode_Compare(**name, key); + if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad; + if (cmp == 0) { + values[name-argnames] = value; + break; + } + name++; + } + if (*name) continue; + else { + PyObject*** argname = argnames; + while (argname != first_kw_arg) { + int cmp = (**argname == key) ? 0 : + #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3 + (PyUnicode_GET_SIZE(**argname) != PyUnicode_GET_SIZE(key)) ? 1 : + #endif + PyUnicode_Compare(**argname, key); + if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad; + if (cmp == 0) goto arg_passed_twice; + argname++; + } + } + } else + goto invalid_keyword_type; + if (kwds2) { + if (unlikely(PyDict_SetItem(kwds2, key, value))) goto bad; + } else { + goto invalid_keyword; + } + } + return 0; +arg_passed_twice: + __Pyx_RaiseDoubleKeywordsError(function_name, key); + goto bad; +invalid_keyword_type: + PyErr_Format(PyExc_TypeError, + "%.200s() keywords must be strings", function_name); + goto bad; +invalid_keyword: + PyErr_Format(PyExc_TypeError, + #if PY_MAJOR_VERSION < 3 + "%.200s() got an unexpected keyword argument '%.200s'", + function_name, PyString_AsString(key)); + #else + "%s() got an unexpected keyword argument '%U'", + function_name, key); + #endif +bad: + return -1; +} + +/* GetModuleGlobalName */ +#if CYTHON_USE_DICT_VERSIONS +static PyObject *__Pyx__GetModuleGlobalName(PyObject *name, PY_UINT64_T *dict_version, PyObject **dict_cached_value) +#else +static CYTHON_INLINE PyObject *__Pyx__GetModuleGlobalName(PyObject *name) +#endif +{ + PyObject *result; +#if !CYTHON_AVOID_BORROWED_REFS +#if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x030500A1 + result = _PyDict_GetItem_KnownHash(__pyx_d, name, ((PyASCIIObject *) name)->hash); + __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version) + if (likely(result)) { + return __Pyx_NewRef(result); + } else if (unlikely(PyErr_Occurred())) { + return NULL; + } +#else + result = PyDict_GetItem(__pyx_d, name); + __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version) + if (likely(result)) { + return __Pyx_NewRef(result); + } +#endif +#else + result = PyObject_GetItem(__pyx_d, name); + __PYX_UPDATE_DICT_CACHE(__pyx_d, result, *dict_cached_value, *dict_version) + if (likely(result)) { + return __Pyx_NewRef(result); + } + PyErr_Clear(); +#endif + return __Pyx_GetBuiltinName(name); +} + +/* PyCFunctionFastCall */ +#if CYTHON_FAST_PYCCALL +static CYTHON_INLINE PyObject * __Pyx_PyCFunction_FastCall(PyObject *func_obj, PyObject **args, Py_ssize_t nargs) { + PyCFunctionObject *func = (PyCFunctionObject*)func_obj; + PyCFunction meth = PyCFunction_GET_FUNCTION(func); + PyObject *self = PyCFunction_GET_SELF(func); + int flags = PyCFunction_GET_FLAGS(func); + assert(PyCFunction_Check(func)); + assert(METH_FASTCALL == (flags & ~(METH_CLASS | METH_STATIC | METH_COEXIST | METH_KEYWORDS | METH_STACKLESS))); + assert(nargs >= 0); + assert(nargs == 0 || args != NULL); + /* _PyCFunction_FastCallDict() must not be called with an exception set, + because it may clear it (directly or indirectly) and so the + caller loses its exception */ + assert(!PyErr_Occurred()); + if ((PY_VERSION_HEX < 0x030700A0) || unlikely(flags & METH_KEYWORDS)) { + return (*((__Pyx_PyCFunctionFastWithKeywords)(void*)meth)) (self, args, nargs, NULL); + } else { + return (*((__Pyx_PyCFunctionFast)(void*)meth)) (self, args, nargs); + } +} +#endif + +/* PyFunctionFastCall */ +#if CYTHON_FAST_PYCALL +static PyObject* __Pyx_PyFunction_FastCallNoKw(PyCodeObject *co, PyObject **args, Py_ssize_t na, + PyObject *globals) { + PyFrameObject *f; + PyThreadState *tstate = __Pyx_PyThreadState_Current; + PyObject **fastlocals; + Py_ssize_t i; + PyObject *result; + assert(globals != NULL); + /* XXX Perhaps we should create a specialized + PyFrame_New() that doesn't take locals, but does + take builtins without sanity checking them. + */ + assert(tstate != NULL); + f = PyFrame_New(tstate, co, globals, NULL); + if (f == NULL) { + return NULL; + } + fastlocals = __Pyx_PyFrame_GetLocalsplus(f); + for (i = 0; i < na; i++) { + Py_INCREF(*args); + fastlocals[i] = *args++; + } + result = PyEval_EvalFrameEx(f,0); + ++tstate->recursion_depth; + Py_DECREF(f); + --tstate->recursion_depth; + return result; +} +#if 1 || PY_VERSION_HEX < 0x030600B1 +static PyObject *__Pyx_PyFunction_FastCallDict(PyObject *func, PyObject **args, int nargs, PyObject *kwargs) { + PyCodeObject *co = (PyCodeObject *)PyFunction_GET_CODE(func); + PyObject *globals = PyFunction_GET_GLOBALS(func); + PyObject *argdefs = PyFunction_GET_DEFAULTS(func); + PyObject *closure; +#if PY_MAJOR_VERSION >= 3 + PyObject *kwdefs; +#endif + PyObject *kwtuple, **k; + PyObject **d; + Py_ssize_t nd; + Py_ssize_t nk; + PyObject *result; + assert(kwargs == NULL || PyDict_Check(kwargs)); + nk = kwargs ? PyDict_Size(kwargs) : 0; + if (Py_EnterRecursiveCall((char*)" while calling a Python object")) { + return NULL; + } + if ( +#if PY_MAJOR_VERSION >= 3 + co->co_kwonlyargcount == 0 && +#endif + likely(kwargs == NULL || nk == 0) && + co->co_flags == (CO_OPTIMIZED | CO_NEWLOCALS | CO_NOFREE)) { + if (argdefs == NULL && co->co_argcount == nargs) { + result = __Pyx_PyFunction_FastCallNoKw(co, args, nargs, globals); + goto done; + } + else if (nargs == 0 && argdefs != NULL + && co->co_argcount == Py_SIZE(argdefs)) { + /* function called with no arguments, but all parameters have + a default value: use default values as arguments .*/ + args = &PyTuple_GET_ITEM(argdefs, 0); + result =__Pyx_PyFunction_FastCallNoKw(co, args, Py_SIZE(argdefs), globals); + goto done; + } + } + if (kwargs != NULL) { + Py_ssize_t pos, i; + kwtuple = PyTuple_New(2 * nk); + if (kwtuple == NULL) { + result = NULL; + goto done; + } + k = &PyTuple_GET_ITEM(kwtuple, 0); + pos = i = 0; + while (PyDict_Next(kwargs, &pos, &k[i], &k[i+1])) { + Py_INCREF(k[i]); + Py_INCREF(k[i+1]); + i += 2; + } + nk = i / 2; + } + else { + kwtuple = NULL; + k = NULL; + } + closure = PyFunction_GET_CLOSURE(func); +#if PY_MAJOR_VERSION >= 3 + kwdefs = PyFunction_GET_KW_DEFAULTS(func); +#endif + if (argdefs != NULL) { + d = &PyTuple_GET_ITEM(argdefs, 0); + nd = Py_SIZE(argdefs); + } + else { + d = NULL; + nd = 0; + } +#if PY_MAJOR_VERSION >= 3 + result = PyEval_EvalCodeEx((PyObject*)co, globals, (PyObject *)NULL, + args, nargs, + k, (int)nk, + d, (int)nd, kwdefs, closure); +#else + result = PyEval_EvalCodeEx(co, globals, (PyObject *)NULL, + args, nargs, + k, (int)nk, + d, (int)nd, closure); +#endif + Py_XDECREF(kwtuple); +done: + Py_LeaveRecursiveCall(); + return result; +} +#endif +#endif + +/* PyObjectCall */ +#if CYTHON_COMPILING_IN_CPYTHON +static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw) { + PyObject *result; + ternaryfunc call = func->ob_type->tp_call; + if (unlikely(!call)) + return PyObject_Call(func, arg, kw); + if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object"))) + return NULL; + result = (*call)(func, arg, kw); + Py_LeaveRecursiveCall(); + if (unlikely(!result) && unlikely(!PyErr_Occurred())) { + PyErr_SetString( + PyExc_SystemError, + "NULL result without error in PyObject_Call"); + } + return result; +} +#endif + +/* PyObjectCall2Args */ +static CYTHON_UNUSED PyObject* __Pyx_PyObject_Call2Args(PyObject* function, PyObject* arg1, PyObject* arg2) { + PyObject *args, *result = NULL; + #if CYTHON_FAST_PYCALL + if (PyFunction_Check(function)) { + PyObject *args[2] = {arg1, arg2}; + return __Pyx_PyFunction_FastCall(function, args, 2); + } + #endif + #if CYTHON_FAST_PYCCALL + if (__Pyx_PyFastCFunction_Check(function)) { + PyObject *args[2] = {arg1, arg2}; + return __Pyx_PyCFunction_FastCall(function, args, 2); + } + #endif + args = PyTuple_New(2); + if (unlikely(!args)) goto done; + Py_INCREF(arg1); + PyTuple_SET_ITEM(args, 0, arg1); + Py_INCREF(arg2); + PyTuple_SET_ITEM(args, 1, arg2); + Py_INCREF(function); + result = __Pyx_PyObject_Call(function, args, NULL); + Py_DECREF(args); + Py_DECREF(function); +done: + return result; +} + +/* PyObjectCallMethO */ +#if CYTHON_COMPILING_IN_CPYTHON +static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg) { + PyObject *self, *result; + PyCFunction cfunc; + cfunc = PyCFunction_GET_FUNCTION(func); + self = PyCFunction_GET_SELF(func); + if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object"))) + return NULL; + result = cfunc(self, arg); + Py_LeaveRecursiveCall(); + if (unlikely(!result) && unlikely(!PyErr_Occurred())) { + PyErr_SetString( + PyExc_SystemError, + "NULL result without error in PyObject_Call"); + } + return result; +} +#endif + +/* PyObjectCallOneArg */ +#if CYTHON_COMPILING_IN_CPYTHON +static PyObject* __Pyx__PyObject_CallOneArg(PyObject *func, PyObject *arg) { + PyObject *result; + PyObject *args = PyTuple_New(1); + if (unlikely(!args)) return NULL; + Py_INCREF(arg); + PyTuple_SET_ITEM(args, 0, arg); + result = __Pyx_PyObject_Call(func, args, NULL); + Py_DECREF(args); + return result; +} +static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) { +#if CYTHON_FAST_PYCALL + if (PyFunction_Check(func)) { + return __Pyx_PyFunction_FastCall(func, &arg, 1); + } +#endif + if (likely(PyCFunction_Check(func))) { + if (likely(PyCFunction_GET_FLAGS(func) & METH_O)) { + return __Pyx_PyObject_CallMethO(func, arg); +#if CYTHON_FAST_PYCCALL + } else if (PyCFunction_GET_FLAGS(func) & METH_FASTCALL) { + return __Pyx_PyCFunction_FastCall(func, &arg, 1); +#endif + } + } + return __Pyx__PyObject_CallOneArg(func, arg); +} +#else +static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) { + PyObject *result; + PyObject *args = PyTuple_Pack(1, arg); + if (unlikely(!args)) return NULL; + result = __Pyx_PyObject_Call(func, args, NULL); + Py_DECREF(args); + return result; +} +#endif + +/* PyErrFetchRestore */ +#if CYTHON_FAST_THREAD_STATE +static CYTHON_INLINE void __Pyx_ErrRestoreInState(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) { + PyObject *tmp_type, *tmp_value, *tmp_tb; + tmp_type = tstate->curexc_type; + tmp_value = tstate->curexc_value; + tmp_tb = tstate->curexc_traceback; + tstate->curexc_type = type; + tstate->curexc_value = value; + tstate->curexc_traceback = tb; + Py_XDECREF(tmp_type); + Py_XDECREF(tmp_value); + Py_XDECREF(tmp_tb); +} +static CYTHON_INLINE void __Pyx_ErrFetchInState(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) { + *type = tstate->curexc_type; + *value = tstate->curexc_value; + *tb = tstate->curexc_traceback; + tstate->curexc_type = 0; + tstate->curexc_value = 0; + tstate->curexc_traceback = 0; +} +#endif + +/* RaiseException */ +#if PY_MAJOR_VERSION < 3 +static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, + CYTHON_UNUSED PyObject *cause) { + __Pyx_PyThreadState_declare + Py_XINCREF(type); + if (!value || value == Py_None) + value = NULL; + else + Py_INCREF(value); + if (!tb || tb == Py_None) + tb = NULL; + else { + Py_INCREF(tb); + if (!PyTraceBack_Check(tb)) { + PyErr_SetString(PyExc_TypeError, + "raise: arg 3 must be a traceback or None"); + goto raise_error; + } + } + if (PyType_Check(type)) { +#if CYTHON_COMPILING_IN_PYPY + if (!value) { + Py_INCREF(Py_None); + value = Py_None; + } +#endif + PyErr_NormalizeException(&type, &value, &tb); + } else { + if (value) { + PyErr_SetString(PyExc_TypeError, + "instance exception may not have a separate value"); + goto raise_error; + } + value = type; + type = (PyObject*) Py_TYPE(type); + Py_INCREF(type); + if (!PyType_IsSubtype((PyTypeObject *)type, (PyTypeObject *)PyExc_BaseException)) { + PyErr_SetString(PyExc_TypeError, + "raise: exception class must be a subclass of BaseException"); + goto raise_error; + } + } + __Pyx_PyThreadState_assign + __Pyx_ErrRestore(type, value, tb); + return; +raise_error: + Py_XDECREF(value); + Py_XDECREF(type); + Py_XDECREF(tb); + return; +} +#else +static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause) { + PyObject* owned_instance = NULL; + if (tb == Py_None) { + tb = 0; + } else if (tb && !PyTraceBack_Check(tb)) { + PyErr_SetString(PyExc_TypeError, + "raise: arg 3 must be a traceback or None"); + goto bad; + } + if (value == Py_None) + value = 0; + if (PyExceptionInstance_Check(type)) { + if (value) { + PyErr_SetString(PyExc_TypeError, + "instance exception may not have a separate value"); + goto bad; + } + value = type; + type = (PyObject*) Py_TYPE(value); + } else if (PyExceptionClass_Check(type)) { + PyObject *instance_class = NULL; + if (value && PyExceptionInstance_Check(value)) { + instance_class = (PyObject*) Py_TYPE(value); + if (instance_class != type) { + int is_subclass = PyObject_IsSubclass(instance_class, type); + if (!is_subclass) { + instance_class = NULL; + } else if (unlikely(is_subclass == -1)) { + goto bad; + } else { + type = instance_class; + } + } + } + if (!instance_class) { + PyObject *args; + if (!value) + args = PyTuple_New(0); + else if (PyTuple_Check(value)) { + Py_INCREF(value); + args = value; + } else + args = PyTuple_Pack(1, value); + if (!args) + goto bad; + owned_instance = PyObject_Call(type, args, NULL); + Py_DECREF(args); + if (!owned_instance) + goto bad; + value = owned_instance; + if (!PyExceptionInstance_Check(value)) { + PyErr_Format(PyExc_TypeError, + "calling %R should have returned an instance of " + "BaseException, not %R", + type, Py_TYPE(value)); + goto bad; + } + } + } else { + PyErr_SetString(PyExc_TypeError, + "raise: exception class must be a subclass of BaseException"); + goto bad; + } + if (cause) { + PyObject *fixed_cause; + if (cause == Py_None) { + fixed_cause = NULL; + } else if (PyExceptionClass_Check(cause)) { + fixed_cause = PyObject_CallObject(cause, NULL); + if (fixed_cause == NULL) + goto bad; + } else if (PyExceptionInstance_Check(cause)) { + fixed_cause = cause; + Py_INCREF(fixed_cause); + } else { + PyErr_SetString(PyExc_TypeError, + "exception causes must derive from " + "BaseException"); + goto bad; + } + PyException_SetCause(value, fixed_cause); + } + PyErr_SetObject(type, value); + if (tb) { +#if CYTHON_COMPILING_IN_PYPY + PyObject *tmp_type, *tmp_value, *tmp_tb; + PyErr_Fetch(&tmp_type, &tmp_value, &tmp_tb); + Py_INCREF(tb); + PyErr_Restore(tmp_type, tmp_value, tb); + Py_XDECREF(tmp_tb); +#else + PyThreadState *tstate = __Pyx_PyThreadState_Current; + PyObject* tmp_tb = tstate->curexc_traceback; + if (tb != tmp_tb) { + Py_INCREF(tb); + tstate->curexc_traceback = tb; + Py_XDECREF(tmp_tb); + } +#endif + } +bad: + Py_XDECREF(owned_instance); + return; +} +#endif + +/* RaiseTooManyValuesToUnpack */ +static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(Py_ssize_t expected) { + PyErr_Format(PyExc_ValueError, + "too many values to unpack (expected %" CYTHON_FORMAT_SSIZE_T "d)", expected); +} + +/* RaiseNeedMoreValuesToUnpack */ +static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index) { + PyErr_Format(PyExc_ValueError, + "need more than %" CYTHON_FORMAT_SSIZE_T "d value%.1s to unpack", + index, (index == 1) ? "" : "s"); +} + +/* IterFinish */ +static CYTHON_INLINE int __Pyx_IterFinish(void) { +#if CYTHON_FAST_THREAD_STATE + PyThreadState *tstate = __Pyx_PyThreadState_Current; + PyObject* exc_type = tstate->curexc_type; + if (unlikely(exc_type)) { + if (likely(__Pyx_PyErr_GivenExceptionMatches(exc_type, PyExc_StopIteration))) { + PyObject *exc_value, *exc_tb; + exc_value = tstate->curexc_value; + exc_tb = tstate->curexc_traceback; + tstate->curexc_type = 0; + tstate->curexc_value = 0; + tstate->curexc_traceback = 0; + Py_DECREF(exc_type); + Py_XDECREF(exc_value); + Py_XDECREF(exc_tb); + return 0; + } else { + return -1; + } + } + return 0; +#else + if (unlikely(PyErr_Occurred())) { + if (likely(PyErr_ExceptionMatches(PyExc_StopIteration))) { + PyErr_Clear(); + return 0; + } else { + return -1; + } + } + return 0; +#endif +} + +/* UnpackItemEndCheck */ +static int __Pyx_IternextUnpackEndCheck(PyObject *retval, Py_ssize_t expected) { + if (unlikely(retval)) { + Py_DECREF(retval); + __Pyx_RaiseTooManyValuesError(expected); + return -1; + } else { + return __Pyx_IterFinish(); + } + return 0; +} + +/* GetItemInt */ +static PyObject *__Pyx_GetItemInt_Generic(PyObject *o, PyObject* j) { + PyObject *r; + if (!j) return NULL; + r = PyObject_GetItem(o, j); + Py_DECREF(j); + return r; +} +static CYTHON_INLINE PyObject *__Pyx_GetItemInt_List_Fast(PyObject *o, Py_ssize_t i, + CYTHON_NCP_UNUSED int wraparound, + CYTHON_NCP_UNUSED int boundscheck) { +#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS + Py_ssize_t wrapped_i = i; + if (wraparound & unlikely(i < 0)) { + wrapped_i += PyList_GET_SIZE(o); + } + if ((!boundscheck) || likely(__Pyx_is_valid_index(wrapped_i, PyList_GET_SIZE(o)))) { + PyObject *r = PyList_GET_ITEM(o, wrapped_i); + Py_INCREF(r); + return r; + } + return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i)); +#else + return PySequence_GetItem(o, i); +#endif +} +static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Tuple_Fast(PyObject *o, Py_ssize_t i, + CYTHON_NCP_UNUSED int wraparound, + CYTHON_NCP_UNUSED int boundscheck) { +#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS + Py_ssize_t wrapped_i = i; + if (wraparound & unlikely(i < 0)) { + wrapped_i += PyTuple_GET_SIZE(o); + } + if ((!boundscheck) || likely(__Pyx_is_valid_index(wrapped_i, PyTuple_GET_SIZE(o)))) { + PyObject *r = PyTuple_GET_ITEM(o, wrapped_i); + Py_INCREF(r); + return r; + } + return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i)); +#else + return PySequence_GetItem(o, i); +#endif +} +static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Fast(PyObject *o, Py_ssize_t i, int is_list, + CYTHON_NCP_UNUSED int wraparound, + CYTHON_NCP_UNUSED int boundscheck) { +#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS && CYTHON_USE_TYPE_SLOTS + if (is_list || PyList_CheckExact(o)) { + Py_ssize_t n = ((!wraparound) | likely(i >= 0)) ? i : i + PyList_GET_SIZE(o); + if ((!boundscheck) || (likely(__Pyx_is_valid_index(n, PyList_GET_SIZE(o))))) { + PyObject *r = PyList_GET_ITEM(o, n); + Py_INCREF(r); + return r; + } + } + else if (PyTuple_CheckExact(o)) { + Py_ssize_t n = ((!wraparound) | likely(i >= 0)) ? i : i + PyTuple_GET_SIZE(o); + if ((!boundscheck) || likely(__Pyx_is_valid_index(n, PyTuple_GET_SIZE(o)))) { + PyObject *r = PyTuple_GET_ITEM(o, n); + Py_INCREF(r); + return r; + } + } else { + PySequenceMethods *m = Py_TYPE(o)->tp_as_sequence; + if (likely(m && m->sq_item)) { + if (wraparound && unlikely(i < 0) && likely(m->sq_length)) { + Py_ssize_t l = m->sq_length(o); + if (likely(l >= 0)) { + i += l; + } else { + if (!PyErr_ExceptionMatches(PyExc_OverflowError)) + return NULL; + PyErr_Clear(); + } + } + return m->sq_item(o, i); + } + } +#else + if (is_list || PySequence_Check(o)) { + return PySequence_GetItem(o, i); + } +#endif + return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i)); +} + +/* PyFloatBinop */ +#if !CYTHON_COMPILING_IN_PYPY +static PyObject* __Pyx_PyFloat_EqObjC(PyObject *op1, PyObject *op2, double floatval, CYTHON_UNUSED int inplace) { + const double b = floatval; + double a; + if (op1 == op2) { + Py_RETURN_TRUE; + } + if (likely(PyFloat_CheckExact(op1))) { + a = PyFloat_AS_DOUBLE(op1); + } else + #if PY_MAJOR_VERSION < 3 + if (likely(PyInt_CheckExact(op1))) { + a = (double) PyInt_AS_LONG(op1); + } else + #endif + if (likely(PyLong_CheckExact(op1))) { + #if CYTHON_USE_PYLONG_INTERNALS + const digit* digits = ((PyLongObject*)op1)->ob_digit; + const Py_ssize_t size = Py_SIZE(op1); + switch (size) { + case 0: a = 0.0; break; + case -1: a = -(double) digits[0]; break; + case 1: a = (double) digits[0]; break; + case -2: + case 2: + if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT && ((8 * sizeof(unsigned long) < 53) || (1 * PyLong_SHIFT < 53))) { + a = (double) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])); + if ((8 * sizeof(unsigned long) < 53) || (2 * PyLong_SHIFT < 53) || (a < (double) ((PY_LONG_LONG)1 << 53))) { + if (size == -2) + a = -a; + break; + } + } + CYTHON_FALLTHROUGH; + case -3: + case 3: + if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT && ((8 * sizeof(unsigned long) < 53) || (2 * PyLong_SHIFT < 53))) { + a = (double) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])); + if ((8 * sizeof(unsigned long) < 53) || (3 * PyLong_SHIFT < 53) || (a < (double) ((PY_LONG_LONG)1 << 53))) { + if (size == -3) + a = -a; + break; + } + } + CYTHON_FALLTHROUGH; + case -4: + case 4: + if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT && ((8 * sizeof(unsigned long) < 53) || (3 * PyLong_SHIFT < 53))) { + a = (double) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])); + if ((8 * sizeof(unsigned long) < 53) || (4 * PyLong_SHIFT < 53) || (a < (double) ((PY_LONG_LONG)1 << 53))) { + if (size == -4) + a = -a; + break; + } + } + CYTHON_FALLTHROUGH; + default: + #else + { + #endif + return ( + PyFloat_Type.tp_richcompare(op2, op1, Py_EQ)); + } + } else { + return ( + PyObject_RichCompare(op1, op2, Py_EQ)); + } + if (a == b) { + Py_RETURN_TRUE; + } else { + Py_RETURN_FALSE; + } +} +#endif + +/* ObjectGetItem */ + #if CYTHON_USE_TYPE_SLOTS +static PyObject *__Pyx_PyObject_GetIndex(PyObject *obj, PyObject* index) { + PyObject *runerr; + Py_ssize_t key_value; + PySequenceMethods *m = Py_TYPE(obj)->tp_as_sequence; + if (unlikely(!(m && m->sq_item))) { + PyErr_Format(PyExc_TypeError, "'%.200s' object is not subscriptable", Py_TYPE(obj)->tp_name); + return NULL; + } + key_value = __Pyx_PyIndex_AsSsize_t(index); + if (likely(key_value != -1 || !(runerr = PyErr_Occurred()))) { + return __Pyx_GetItemInt_Fast(obj, key_value, 0, 1, 1); + } + if (PyErr_GivenExceptionMatches(runerr, PyExc_OverflowError)) { + PyErr_Clear(); + PyErr_Format(PyExc_IndexError, "cannot fit '%.200s' into an index-sized integer", Py_TYPE(index)->tp_name); + } + return NULL; +} +static PyObject *__Pyx_PyObject_GetItem(PyObject *obj, PyObject* key) { + PyMappingMethods *m = Py_TYPE(obj)->tp_as_mapping; + if (likely(m && m->mp_subscript)) { + return m->mp_subscript(obj, key); + } + return __Pyx_PyObject_GetIndex(obj, key); +} +#endif + +/* PyIntBinop */ + #if !CYTHON_COMPILING_IN_PYPY +static PyObject* __Pyx_PyInt_SubtractObjC(PyObject *op1, PyObject *op2, CYTHON_UNUSED long intval, CYTHON_UNUSED int inplace) { + #if PY_MAJOR_VERSION < 3 + if (likely(PyInt_CheckExact(op1))) { + const long b = intval; + long x; + long a = PyInt_AS_LONG(op1); + x = (long)((unsigned long)a - b); + if (likely((x^a) >= 0 || (x^~b) >= 0)) + return PyInt_FromLong(x); + return PyLong_Type.tp_as_number->nb_subtract(op1, op2); + } + #endif + #if CYTHON_USE_PYLONG_INTERNALS + if (likely(PyLong_CheckExact(op1))) { + const long b = intval; + long a, x; +#ifdef HAVE_LONG_LONG + const PY_LONG_LONG llb = intval; + PY_LONG_LONG lla, llx; +#endif + const digit* digits = ((PyLongObject*)op1)->ob_digit; + const Py_ssize_t size = Py_SIZE(op1); + if (likely(__Pyx_sst_abs(size) <= 1)) { + a = likely(size) ? digits[0] : 0; + if (size == -1) a = -a; + } else { + switch (size) { + case -2: + if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) { + a = -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])); + break; +#ifdef HAVE_LONG_LONG + } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) { + lla = -(PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0])); + goto long_long; +#endif + } + CYTHON_FALLTHROUGH; + case 2: + if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) { + a = (long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])); + break; +#ifdef HAVE_LONG_LONG + } else if (8 * sizeof(PY_LONG_LONG) - 1 > 2 * PyLong_SHIFT) { + lla = (PY_LONG_LONG) (((((unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0])); + goto long_long; +#endif + } + CYTHON_FALLTHROUGH; + case -3: + if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) { + a = -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])); + break; +#ifdef HAVE_LONG_LONG + } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) { + lla = -(PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0])); + goto long_long; +#endif + } + CYTHON_FALLTHROUGH; + case 3: + if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) { + a = (long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])); + break; +#ifdef HAVE_LONG_LONG + } else if (8 * sizeof(PY_LONG_LONG) - 1 > 3 * PyLong_SHIFT) { + lla = (PY_LONG_LONG) (((((((unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0])); + goto long_long; +#endif + } + CYTHON_FALLTHROUGH; + case -4: + if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) { + a = -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])); + break; +#ifdef HAVE_LONG_LONG + } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) { + lla = -(PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0])); + goto long_long; +#endif + } + CYTHON_FALLTHROUGH; + case 4: + if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) { + a = (long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])); + break; +#ifdef HAVE_LONG_LONG + } else if (8 * sizeof(PY_LONG_LONG) - 1 > 4 * PyLong_SHIFT) { + lla = (PY_LONG_LONG) (((((((((unsigned PY_LONG_LONG)digits[3]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[2]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[1]) << PyLong_SHIFT) | (unsigned PY_LONG_LONG)digits[0])); + goto long_long; +#endif + } + CYTHON_FALLTHROUGH; + default: return PyLong_Type.tp_as_number->nb_subtract(op1, op2); + } + } + x = a - b; + return PyLong_FromLong(x); +#ifdef HAVE_LONG_LONG + long_long: + llx = lla - llb; + return PyLong_FromLongLong(llx); +#endif + + + } + #endif + if (PyFloat_CheckExact(op1)) { + const long b = intval; + double a = PyFloat_AS_DOUBLE(op1); + double result; + PyFPE_START_PROTECT("subtract", return NULL) + result = ((double)a) - (double)b; + PyFPE_END_PROTECT(result) + return PyFloat_FromDouble(result); + } + return (inplace ? PyNumber_InPlaceSubtract : PyNumber_Subtract)(op1, op2); +} +#endif + +/* PyFloatBinop */ + #if !CYTHON_COMPILING_IN_PYPY +static PyObject* __Pyx_PyFloat_SubtractCObj(PyObject *op1, PyObject *op2, double floatval, CYTHON_UNUSED int inplace) { + const double a = floatval; + double b, result; + if (likely(PyFloat_CheckExact(op2))) { + b = PyFloat_AS_DOUBLE(op2); + } else + #if PY_MAJOR_VERSION < 3 + if (likely(PyInt_CheckExact(op2))) { + b = (double) PyInt_AS_LONG(op2); + } else + #endif + if (likely(PyLong_CheckExact(op2))) { + #if CYTHON_USE_PYLONG_INTERNALS + const digit* digits = ((PyLongObject*)op2)->ob_digit; + const Py_ssize_t size = Py_SIZE(op2); + switch (size) { + case 0: b = 0.0; break; + case -1: b = -(double) digits[0]; break; + case 1: b = (double) digits[0]; break; + case -2: + case 2: + if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT && ((8 * sizeof(unsigned long) < 53) || (1 * PyLong_SHIFT < 53))) { + b = (double) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])); + if ((8 * sizeof(unsigned long) < 53) || (2 * PyLong_SHIFT < 53) || (b < (double) ((PY_LONG_LONG)1 << 53))) { + if (size == -2) + b = -b; + break; + } + } + CYTHON_FALLTHROUGH; + case -3: + case 3: + if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT && ((8 * sizeof(unsigned long) < 53) || (2 * PyLong_SHIFT < 53))) { + b = (double) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])); + if ((8 * sizeof(unsigned long) < 53) || (3 * PyLong_SHIFT < 53) || (b < (double) ((PY_LONG_LONG)1 << 53))) { + if (size == -3) + b = -b; + break; + } + } + CYTHON_FALLTHROUGH; + case -4: + case 4: + if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT && ((8 * sizeof(unsigned long) < 53) || (3 * PyLong_SHIFT < 53))) { + b = (double) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])); + if ((8 * sizeof(unsigned long) < 53) || (4 * PyLong_SHIFT < 53) || (b < (double) ((PY_LONG_LONG)1 << 53))) { + if (size == -4) + b = -b; + break; + } + } + CYTHON_FALLTHROUGH; + default: + #else + { + #endif + b = PyLong_AsDouble(op2); + if (unlikely(b == -1.0 && PyErr_Occurred())) return NULL; + } + } else { + return (inplace ? PyNumber_InPlaceSubtract : PyNumber_Subtract)(op1, op2); + } + PyFPE_START_PROTECT("subtract", return NULL) + result = a - b; + PyFPE_END_PROTECT(result) + return PyFloat_FromDouble(result); +} +#endif + +/* PyFloatBinop */ + #if !CYTHON_COMPILING_IN_PYPY +static PyObject* __Pyx_PyFloat_DivideObjC(PyObject *op1, PyObject *op2, double floatval, CYTHON_UNUSED int inplace) { + const double b = floatval; + double a, result; + if (likely(PyFloat_CheckExact(op1))) { + a = PyFloat_AS_DOUBLE(op1); + } else + #if PY_MAJOR_VERSION < 3 + if (likely(PyInt_CheckExact(op1))) { + a = (double) PyInt_AS_LONG(op1); + } else + #endif + if (likely(PyLong_CheckExact(op1))) { + #if CYTHON_USE_PYLONG_INTERNALS + const digit* digits = ((PyLongObject*)op1)->ob_digit; + const Py_ssize_t size = Py_SIZE(op1); + switch (size) { + case 0: a = 0.0; break; + case -1: a = -(double) digits[0]; break; + case 1: a = (double) digits[0]; break; + case -2: + case 2: + if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT && ((8 * sizeof(unsigned long) < 53) || (1 * PyLong_SHIFT < 53))) { + a = (double) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])); + if ((8 * sizeof(unsigned long) < 53) || (2 * PyLong_SHIFT < 53) || (a < (double) ((PY_LONG_LONG)1 << 53))) { + if (size == -2) + a = -a; + break; + } + } + CYTHON_FALLTHROUGH; + case -3: + case 3: + if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT && ((8 * sizeof(unsigned long) < 53) || (2 * PyLong_SHIFT < 53))) { + a = (double) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])); + if ((8 * sizeof(unsigned long) < 53) || (3 * PyLong_SHIFT < 53) || (a < (double) ((PY_LONG_LONG)1 << 53))) { + if (size == -3) + a = -a; + break; + } + } + CYTHON_FALLTHROUGH; + case -4: + case 4: + if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT && ((8 * sizeof(unsigned long) < 53) || (3 * PyLong_SHIFT < 53))) { + a = (double) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])); + if ((8 * sizeof(unsigned long) < 53) || (4 * PyLong_SHIFT < 53) || (a < (double) ((PY_LONG_LONG)1 << 53))) { + if (size == -4) + a = -a; + break; + } + } + CYTHON_FALLTHROUGH; + default: + #else + { + #endif + a = PyLong_AsDouble(op1); + if (unlikely(a == -1.0 && PyErr_Occurred())) return NULL; + } + } else { + return (inplace ? __Pyx_PyNumber_InPlaceDivide(op1, op2) : __Pyx_PyNumber_Divide(op1, op2)); + } + PyFPE_START_PROTECT("divide", return NULL) + result = a / b; + PyFPE_END_PROTECT(result) + return PyFloat_FromDouble(result); +} +#endif + +/* None */ + static CYTHON_INLINE void __Pyx_RaiseUnboundLocalError(const char *varname) { + PyErr_Format(PyExc_UnboundLocalError, "local variable '%s' referenced before assignment", varname); +} + +/* ExtTypeTest */ + static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type) { + if (unlikely(!type)) { + PyErr_SetString(PyExc_SystemError, "Missing type object"); + return 0; + } + if (likely(__Pyx_TypeCheck(obj, type))) + return 1; + PyErr_Format(PyExc_TypeError, "Cannot convert %.200s to %.200s", + Py_TYPE(obj)->tp_name, type->tp_name); + return 0; +} + +/* PyObjectCallNoArg */ + #if CYTHON_COMPILING_IN_CPYTHON +static CYTHON_INLINE PyObject* __Pyx_PyObject_CallNoArg(PyObject *func) { +#if CYTHON_FAST_PYCALL + if (PyFunction_Check(func)) { + return __Pyx_PyFunction_FastCall(func, NULL, 0); + } +#endif +#ifdef __Pyx_CyFunction_USED + if (likely(PyCFunction_Check(func) || __Pyx_CyFunction_Check(func))) +#else + if (likely(PyCFunction_Check(func))) +#endif + { + if (likely(PyCFunction_GET_FLAGS(func) & METH_NOARGS)) { + return __Pyx_PyObject_CallMethO(func, NULL); + } + } + return __Pyx_PyObject_Call(func, __pyx_empty_tuple, NULL); +} +#endif + +/* DictGetItem */ + #if PY_MAJOR_VERSION >= 3 && !CYTHON_COMPILING_IN_PYPY +static PyObject *__Pyx_PyDict_GetItem(PyObject *d, PyObject* key) { + PyObject *value; + value = PyDict_GetItemWithError(d, key); + if (unlikely(!value)) { + if (!PyErr_Occurred()) { + if (unlikely(PyTuple_Check(key))) { + PyObject* args = PyTuple_Pack(1, key); + if (likely(args)) { + PyErr_SetObject(PyExc_KeyError, args); + Py_DECREF(args); + } + } else { + PyErr_SetObject(PyExc_KeyError, key); + } + } + return NULL; + } + Py_INCREF(value); + return value; +} +#endif + +/* RaiseNoneIterError */ + static CYTHON_INLINE void __Pyx_RaiseNoneNotIterableError(void) { + PyErr_SetString(PyExc_TypeError, "'NoneType' object is not iterable"); +} + +/* GetTopmostException */ + #if CYTHON_USE_EXC_INFO_STACK +static _PyErr_StackItem * +__Pyx_PyErr_GetTopmostException(PyThreadState *tstate) +{ + _PyErr_StackItem *exc_info = tstate->exc_info; + while ((exc_info->exc_type == NULL || exc_info->exc_type == Py_None) && + exc_info->previous_item != NULL) + { + exc_info = exc_info->previous_item; + } + return exc_info; +} +#endif + +/* SaveResetException */ + #if CYTHON_FAST_THREAD_STATE +static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) { + #if CYTHON_USE_EXC_INFO_STACK + _PyErr_StackItem *exc_info = __Pyx_PyErr_GetTopmostException(tstate); + *type = exc_info->exc_type; + *value = exc_info->exc_value; + *tb = exc_info->exc_traceback; + #else + *type = tstate->exc_type; + *value = tstate->exc_value; + *tb = tstate->exc_traceback; + #endif + Py_XINCREF(*type); + Py_XINCREF(*value); + Py_XINCREF(*tb); +} +static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) { + PyObject *tmp_type, *tmp_value, *tmp_tb; + #if CYTHON_USE_EXC_INFO_STACK + _PyErr_StackItem *exc_info = tstate->exc_info; + tmp_type = exc_info->exc_type; + tmp_value = exc_info->exc_value; + tmp_tb = exc_info->exc_traceback; + exc_info->exc_type = type; + exc_info->exc_value = value; + exc_info->exc_traceback = tb; + #else + tmp_type = tstate->exc_type; + tmp_value = tstate->exc_value; + tmp_tb = tstate->exc_traceback; + tstate->exc_type = type; + tstate->exc_value = value; + tstate->exc_traceback = tb; + #endif + Py_XDECREF(tmp_type); + Py_XDECREF(tmp_value); + Py_XDECREF(tmp_tb); +} +#endif + +/* PyErrExceptionMatches */ + #if CYTHON_FAST_THREAD_STATE +static int __Pyx_PyErr_ExceptionMatchesTuple(PyObject *exc_type, PyObject *tuple) { + Py_ssize_t i, n; + n = PyTuple_GET_SIZE(tuple); +#if PY_MAJOR_VERSION >= 3 + for (i=0; icurexc_type; + if (exc_type == err) return 1; + if (unlikely(!exc_type)) return 0; + if (unlikely(PyTuple_Check(err))) + return __Pyx_PyErr_ExceptionMatchesTuple(exc_type, err); + return __Pyx_PyErr_GivenExceptionMatches(exc_type, err); +} +#endif + +/* GetException */ + #if CYTHON_FAST_THREAD_STATE +static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) +#else +static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb) +#endif +{ + PyObject *local_type, *local_value, *local_tb; +#if CYTHON_FAST_THREAD_STATE + PyObject *tmp_type, *tmp_value, *tmp_tb; + local_type = tstate->curexc_type; + local_value = tstate->curexc_value; + local_tb = tstate->curexc_traceback; + tstate->curexc_type = 0; + tstate->curexc_value = 0; + tstate->curexc_traceback = 0; +#else + PyErr_Fetch(&local_type, &local_value, &local_tb); +#endif + PyErr_NormalizeException(&local_type, &local_value, &local_tb); +#if CYTHON_FAST_THREAD_STATE + if (unlikely(tstate->curexc_type)) +#else + if (unlikely(PyErr_Occurred())) +#endif + goto bad; + #if PY_MAJOR_VERSION >= 3 + if (local_tb) { + if (unlikely(PyException_SetTraceback(local_value, local_tb) < 0)) + goto bad; + } + #endif + Py_XINCREF(local_tb); + Py_XINCREF(local_type); + Py_XINCREF(local_value); + *type = local_type; + *value = local_value; + *tb = local_tb; +#if CYTHON_FAST_THREAD_STATE + #if CYTHON_USE_EXC_INFO_STACK + { + _PyErr_StackItem *exc_info = tstate->exc_info; + tmp_type = exc_info->exc_type; + tmp_value = exc_info->exc_value; + tmp_tb = exc_info->exc_traceback; + exc_info->exc_type = local_type; + exc_info->exc_value = local_value; + exc_info->exc_traceback = local_tb; + } + #else + tmp_type = tstate->exc_type; + tmp_value = tstate->exc_value; + tmp_tb = tstate->exc_traceback; + tstate->exc_type = local_type; + tstate->exc_value = local_value; + tstate->exc_traceback = local_tb; + #endif + Py_XDECREF(tmp_type); + Py_XDECREF(tmp_value); + Py_XDECREF(tmp_tb); +#else + PyErr_SetExcInfo(local_type, local_value, local_tb); +#endif + return 0; +bad: + *type = 0; + *value = 0; + *tb = 0; + Py_XDECREF(local_type); + Py_XDECREF(local_value); + Py_XDECREF(local_tb); + return -1; +} + +/* TypeImport */ + #ifndef __PYX_HAVE_RT_ImportType +#define __PYX_HAVE_RT_ImportType +static PyTypeObject *__Pyx_ImportType(PyObject *module, const char *module_name, const char *class_name, + size_t size, enum __Pyx_ImportType_CheckSize check_size) +{ + PyObject *result = 0; + char warning[200]; + Py_ssize_t basicsize; +#ifdef Py_LIMITED_API + PyObject *py_basicsize; +#endif + result = PyObject_GetAttrString(module, class_name); + if (!result) + goto bad; + if (!PyType_Check(result)) { + PyErr_Format(PyExc_TypeError, + "%.200s.%.200s is not a type object", + module_name, class_name); + goto bad; + } +#ifndef Py_LIMITED_API + basicsize = ((PyTypeObject *)result)->tp_basicsize; +#else + py_basicsize = PyObject_GetAttrString(result, "__basicsize__"); + if (!py_basicsize) + goto bad; + basicsize = PyLong_AsSsize_t(py_basicsize); + Py_DECREF(py_basicsize); + py_basicsize = 0; + if (basicsize == (Py_ssize_t)-1 && PyErr_Occurred()) + goto bad; +#endif + if ((size_t)basicsize < size) { + PyErr_Format(PyExc_ValueError, + "%.200s.%.200s size changed, may indicate binary incompatibility. " + "Expected %zd from C header, got %zd from PyObject", + module_name, class_name, size, basicsize); + goto bad; + } + if (check_size == __Pyx_ImportType_CheckSize_Error && (size_t)basicsize != size) { + PyErr_Format(PyExc_ValueError, + "%.200s.%.200s size changed, may indicate binary incompatibility. " + "Expected %zd from C header, got %zd from PyObject", + module_name, class_name, size, basicsize); + goto bad; + } + else if (check_size == __Pyx_ImportType_CheckSize_Warn && (size_t)basicsize > size) { + PyOS_snprintf(warning, sizeof(warning), + "%s.%s size changed, may indicate binary incompatibility. " + "Expected %zd from C header, got %zd from PyObject", + module_name, class_name, size, basicsize); + if (PyErr_WarnEx(NULL, warning, 0) < 0) goto bad; + } + return (PyTypeObject *)result; +bad: + Py_XDECREF(result); + return NULL; +} +#endif + +/* Import */ + static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level) { + PyObject *empty_list = 0; + PyObject *module = 0; + PyObject *global_dict = 0; + PyObject *empty_dict = 0; + PyObject *list; + #if PY_MAJOR_VERSION < 3 + PyObject *py_import; + py_import = __Pyx_PyObject_GetAttrStr(__pyx_b, __pyx_n_s_import); + if (!py_import) + goto bad; + #endif + if (from_list) + list = from_list; + else { + empty_list = PyList_New(0); + if (!empty_list) + goto bad; + list = empty_list; + } + global_dict = PyModule_GetDict(__pyx_m); + if (!global_dict) + goto bad; + empty_dict = PyDict_New(); + if (!empty_dict) + goto bad; + { + #if PY_MAJOR_VERSION >= 3 + if (level == -1) { + if (strchr(__Pyx_MODULE_NAME, '.')) { + module = PyImport_ImportModuleLevelObject( + name, global_dict, empty_dict, list, 1); + if (!module) { + if (!PyErr_ExceptionMatches(PyExc_ImportError)) + goto bad; + PyErr_Clear(); + } + } + level = 0; + } + #endif + if (!module) { + #if PY_MAJOR_VERSION < 3 + PyObject *py_level = PyInt_FromLong(level); + if (!py_level) + goto bad; + module = PyObject_CallFunctionObjArgs(py_import, + name, global_dict, empty_dict, list, py_level, (PyObject *)NULL); + Py_DECREF(py_level); + #else + module = PyImport_ImportModuleLevelObject( + name, global_dict, empty_dict, list, level); + #endif + } + } +bad: + #if PY_MAJOR_VERSION < 3 + Py_XDECREF(py_import); + #endif + Py_XDECREF(empty_list); + Py_XDECREF(empty_dict); + return module; +} + +/* ImportFrom */ + static PyObject* __Pyx_ImportFrom(PyObject* module, PyObject* name) { + PyObject* value = __Pyx_PyObject_GetAttrStr(module, name); + if (unlikely(!value) && PyErr_ExceptionMatches(PyExc_AttributeError)) { + PyErr_Format(PyExc_ImportError, + #if PY_MAJOR_VERSION < 3 + "cannot import name %.230s", PyString_AS_STRING(name)); + #else + "cannot import name %S", name); + #endif + } + return value; +} + +/* CLineInTraceback */ + #ifndef CYTHON_CLINE_IN_TRACEBACK +static int __Pyx_CLineForTraceback(PyThreadState *tstate, int c_line) { + PyObject *use_cline; + PyObject *ptype, *pvalue, *ptraceback; +#if CYTHON_COMPILING_IN_CPYTHON + PyObject **cython_runtime_dict; +#endif + if (unlikely(!__pyx_cython_runtime)) { + return c_line; + } + __Pyx_ErrFetchInState(tstate, &ptype, &pvalue, &ptraceback); +#if CYTHON_COMPILING_IN_CPYTHON + cython_runtime_dict = _PyObject_GetDictPtr(__pyx_cython_runtime); + if (likely(cython_runtime_dict)) { + __PYX_PY_DICT_LOOKUP_IF_MODIFIED( + use_cline, *cython_runtime_dict, + __Pyx_PyDict_GetItemStr(*cython_runtime_dict, __pyx_n_s_cline_in_traceback)) + } else +#endif + { + PyObject *use_cline_obj = __Pyx_PyObject_GetAttrStr(__pyx_cython_runtime, __pyx_n_s_cline_in_traceback); + if (use_cline_obj) { + use_cline = PyObject_Not(use_cline_obj) ? Py_False : Py_True; + Py_DECREF(use_cline_obj); + } else { + PyErr_Clear(); + use_cline = NULL; + } + } + if (!use_cline) { + c_line = 0; + PyObject_SetAttr(__pyx_cython_runtime, __pyx_n_s_cline_in_traceback, Py_False); + } + else if (use_cline == Py_False || (use_cline != Py_True && PyObject_Not(use_cline) != 0)) { + c_line = 0; + } + __Pyx_ErrRestoreInState(tstate, ptype, pvalue, ptraceback); + return c_line; +} +#endif + +/* CodeObjectCache */ + static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line) { + int start = 0, mid = 0, end = count - 1; + if (end >= 0 && code_line > entries[end].code_line) { + return count; + } + while (start < end) { + mid = start + (end - start) / 2; + if (code_line < entries[mid].code_line) { + end = mid; + } else if (code_line > entries[mid].code_line) { + start = mid + 1; + } else { + return mid; + } + } + if (code_line <= entries[mid].code_line) { + return mid; + } else { + return mid + 1; + } +} +static PyCodeObject *__pyx_find_code_object(int code_line) { + PyCodeObject* code_object; + int pos; + if (unlikely(!code_line) || unlikely(!__pyx_code_cache.entries)) { + return NULL; + } + pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line); + if (unlikely(pos >= __pyx_code_cache.count) || unlikely(__pyx_code_cache.entries[pos].code_line != code_line)) { + return NULL; + } + code_object = __pyx_code_cache.entries[pos].code_object; + Py_INCREF(code_object); + return code_object; +} +static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object) { + int pos, i; + __Pyx_CodeObjectCacheEntry* entries = __pyx_code_cache.entries; + if (unlikely(!code_line)) { + return; + } + if (unlikely(!entries)) { + entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Malloc(64*sizeof(__Pyx_CodeObjectCacheEntry)); + if (likely(entries)) { + __pyx_code_cache.entries = entries; + __pyx_code_cache.max_count = 64; + __pyx_code_cache.count = 1; + entries[0].code_line = code_line; + entries[0].code_object = code_object; + Py_INCREF(code_object); + } + return; + } + pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line); + if ((pos < __pyx_code_cache.count) && unlikely(__pyx_code_cache.entries[pos].code_line == code_line)) { + PyCodeObject* tmp = entries[pos].code_object; + entries[pos].code_object = code_object; + Py_DECREF(tmp); + return; + } + if (__pyx_code_cache.count == __pyx_code_cache.max_count) { + int new_max = __pyx_code_cache.max_count + 64; + entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Realloc( + __pyx_code_cache.entries, (size_t)new_max*sizeof(__Pyx_CodeObjectCacheEntry)); + if (unlikely(!entries)) { + return; + } + __pyx_code_cache.entries = entries; + __pyx_code_cache.max_count = new_max; + } + for (i=__pyx_code_cache.count; i>pos; i--) { + entries[i] = entries[i-1]; + } + entries[pos].code_line = code_line; + entries[pos].code_object = code_object; + __pyx_code_cache.count++; + Py_INCREF(code_object); +} + +/* AddTraceback */ + #include "compile.h" +#include "frameobject.h" +#include "traceback.h" +static PyCodeObject* __Pyx_CreateCodeObjectForTraceback( + const char *funcname, int c_line, + int py_line, const char *filename) { + PyCodeObject *py_code = 0; + PyObject *py_srcfile = 0; + PyObject *py_funcname = 0; + #if PY_MAJOR_VERSION < 3 + py_srcfile = PyString_FromString(filename); + #else + py_srcfile = PyUnicode_FromString(filename); + #endif + if (!py_srcfile) goto bad; + if (c_line) { + #if PY_MAJOR_VERSION < 3 + py_funcname = PyString_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line); + #else + py_funcname = PyUnicode_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line); + #endif + } + else { + #if PY_MAJOR_VERSION < 3 + py_funcname = PyString_FromString(funcname); + #else + py_funcname = PyUnicode_FromString(funcname); + #endif + } + if (!py_funcname) goto bad; + py_code = __Pyx_PyCode_New( + 0, + 0, + 0, + 0, + 0, + __pyx_empty_bytes, /*PyObject *code,*/ + __pyx_empty_tuple, /*PyObject *consts,*/ + __pyx_empty_tuple, /*PyObject *names,*/ + __pyx_empty_tuple, /*PyObject *varnames,*/ + __pyx_empty_tuple, /*PyObject *freevars,*/ + __pyx_empty_tuple, /*PyObject *cellvars,*/ + py_srcfile, /*PyObject *filename,*/ + py_funcname, /*PyObject *name,*/ + py_line, + __pyx_empty_bytes /*PyObject *lnotab*/ + ); + Py_DECREF(py_srcfile); + Py_DECREF(py_funcname); + return py_code; +bad: + Py_XDECREF(py_srcfile); + Py_XDECREF(py_funcname); + return NULL; +} +static void __Pyx_AddTraceback(const char *funcname, int c_line, + int py_line, const char *filename) { + PyCodeObject *py_code = 0; + PyFrameObject *py_frame = 0; + PyThreadState *tstate = __Pyx_PyThreadState_Current; + if (c_line) { + c_line = __Pyx_CLineForTraceback(tstate, c_line); + } + py_code = __pyx_find_code_object(c_line ? -c_line : py_line); + if (!py_code) { + py_code = __Pyx_CreateCodeObjectForTraceback( + funcname, c_line, py_line, filename); + if (!py_code) goto bad; + __pyx_insert_code_object(c_line ? -c_line : py_line, py_code); + } + py_frame = PyFrame_New( + tstate, /*PyThreadState *tstate,*/ + py_code, /*PyCodeObject *code,*/ + __pyx_d, /*PyObject *globals,*/ + 0 /*PyObject *locals*/ + ); + if (!py_frame) goto bad; + __Pyx_PyFrame_SetLineNumber(py_frame, py_line); + PyTraceBack_Here(py_frame); +bad: + Py_XDECREF(py_code); + Py_XDECREF(py_frame); +} + +/* CIntToPy */ + static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value) { + const long neg_one = (long) ((long) 0 - (long) 1), const_zero = (long) 0; + const int is_unsigned = neg_one > const_zero; + if (is_unsigned) { + if (sizeof(long) < sizeof(long)) { + return PyInt_FromLong((long) value); + } else if (sizeof(long) <= sizeof(unsigned long)) { + return PyLong_FromUnsignedLong((unsigned long) value); +#ifdef HAVE_LONG_LONG + } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) { + return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value); +#endif + } + } else { + if (sizeof(long) <= sizeof(long)) { + return PyInt_FromLong((long) value); +#ifdef HAVE_LONG_LONG + } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) { + return PyLong_FromLongLong((PY_LONG_LONG) value); +#endif + } + } + { + int one = 1; int little = (int)*(unsigned char *)&one; + unsigned char *bytes = (unsigned char *)&value; + return _PyLong_FromByteArray(bytes, sizeof(long), + little, !is_unsigned); + } +} + +/* CIntFromPyVerify */ + #define __PYX_VERIFY_RETURN_INT(target_type, func_type, func_value)\ + __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 0) +#define __PYX_VERIFY_RETURN_INT_EXC(target_type, func_type, func_value)\ + __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 1) +#define __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, exc)\ + {\ + func_type value = func_value;\ + if (sizeof(target_type) < sizeof(func_type)) {\ + if (unlikely(value != (func_type) (target_type) value)) {\ + func_type zero = 0;\ + if (exc && unlikely(value == (func_type)-1 && PyErr_Occurred()))\ + return (target_type) -1;\ + if (is_unsigned && unlikely(value < zero))\ + goto raise_neg_overflow;\ + else\ + goto raise_overflow;\ + }\ + }\ + return (target_type) value;\ + } + +/* Print */ + #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION < 3 +static PyObject *__Pyx_GetStdout(void) { + PyObject *f = PySys_GetObject((char *)"stdout"); + if (!f) { + PyErr_SetString(PyExc_RuntimeError, "lost sys.stdout"); + } + return f; +} +static int __Pyx_Print(PyObject* f, PyObject *arg_tuple, int newline) { + int i; + if (!f) { + if (!(f = __Pyx_GetStdout())) + return -1; + } + Py_INCREF(f); + for (i=0; i < PyTuple_GET_SIZE(arg_tuple); i++) { + PyObject* v; + if (PyFile_SoftSpace(f, 1)) { + if (PyFile_WriteString(" ", f) < 0) + goto error; + } + v = PyTuple_GET_ITEM(arg_tuple, i); + if (PyFile_WriteObject(v, f, Py_PRINT_RAW) < 0) + goto error; + if (PyString_Check(v)) { + char *s = PyString_AsString(v); + Py_ssize_t len = PyString_Size(v); + if (len > 0) { + switch (s[len-1]) { + case ' ': break; + case '\f': case '\r': case '\n': case '\t': case '\v': + PyFile_SoftSpace(f, 0); + break; + default: break; + } + } + } + } + if (newline) { + if (PyFile_WriteString("\n", f) < 0) + goto error; + PyFile_SoftSpace(f, 0); + } + Py_DECREF(f); + return 0; +error: + Py_DECREF(f); + return -1; +} +#else +static int __Pyx_Print(PyObject* stream, PyObject *arg_tuple, int newline) { + PyObject* kwargs = 0; + PyObject* result = 0; + PyObject* end_string; + if (unlikely(!__pyx_print)) { + __pyx_print = PyObject_GetAttr(__pyx_b, __pyx_n_s_print); + if (!__pyx_print) + return -1; + } + if (stream) { + kwargs = PyDict_New(); + if (unlikely(!kwargs)) + return -1; + if (unlikely(PyDict_SetItem(kwargs, __pyx_n_s_file, stream) < 0)) + goto bad; + if (!newline) { + end_string = PyUnicode_FromStringAndSize(" ", 1); + if (unlikely(!end_string)) + goto bad; + if (PyDict_SetItem(kwargs, __pyx_n_s_end, end_string) < 0) { + Py_DECREF(end_string); + goto bad; + } + Py_DECREF(end_string); + } + } else if (!newline) { + if (unlikely(!__pyx_print_kwargs)) { + __pyx_print_kwargs = PyDict_New(); + if (unlikely(!__pyx_print_kwargs)) + return -1; + end_string = PyUnicode_FromStringAndSize(" ", 1); + if (unlikely(!end_string)) + return -1; + if (PyDict_SetItem(__pyx_print_kwargs, __pyx_n_s_end, end_string) < 0) { + Py_DECREF(end_string); + return -1; + } + Py_DECREF(end_string); + } + kwargs = __pyx_print_kwargs; + } + result = PyObject_Call(__pyx_print, arg_tuple, kwargs); + if (unlikely(kwargs) && (kwargs != __pyx_print_kwargs)) + Py_DECREF(kwargs); + if (!result) + return -1; + Py_DECREF(result); + return 0; +bad: + if (kwargs != __pyx_print_kwargs) + Py_XDECREF(kwargs); + return -1; +} +#endif + +/* Declarations */ + #if CYTHON_CCOMPLEX + #ifdef __cplusplus + static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) { + return ::std::complex< float >(x, y); + } + #else + static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) { + return x + y*(__pyx_t_float_complex)_Complex_I; + } + #endif +#else + static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) { + __pyx_t_float_complex z; + z.real = x; + z.imag = y; + return z; + } +#endif + +/* Arithmetic */ + #if CYTHON_CCOMPLEX +#else + static CYTHON_INLINE int __Pyx_c_eq_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { + return (a.real == b.real) && (a.imag == b.imag); + } + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sum_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { + __pyx_t_float_complex z; + z.real = a.real + b.real; + z.imag = a.imag + b.imag; + return z; + } + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_diff_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { + __pyx_t_float_complex z; + z.real = a.real - b.real; + z.imag = a.imag - b.imag; + return z; + } + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prod_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { + __pyx_t_float_complex z; + z.real = a.real * b.real - a.imag * b.imag; + z.imag = a.real * b.imag + a.imag * b.real; + return z; + } + #if 1 + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { + if (b.imag == 0) { + return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.real); + } else if (fabsf(b.real) >= fabsf(b.imag)) { + if (b.real == 0 && b.imag == 0) { + return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.imag); + } else { + float r = b.imag / b.real; + float s = 1.0 / (b.real + b.imag * r); + return __pyx_t_float_complex_from_parts( + (a.real + a.imag * r) * s, (a.imag - a.real * r) * s); + } + } else { + float r = b.real / b.imag; + float s = 1.0 / (b.imag + b.real * r); + return __pyx_t_float_complex_from_parts( + (a.real * r + a.imag) * s, (a.imag * r - a.real) * s); + } + } + #else + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { + if (b.imag == 0) { + return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.real); + } else { + float denom = b.real * b.real + b.imag * b.imag; + return __pyx_t_float_complex_from_parts( + (a.real * b.real + a.imag * b.imag) / denom, + (a.imag * b.real - a.real * b.imag) / denom); + } + } + #endif + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_neg_float(__pyx_t_float_complex a) { + __pyx_t_float_complex z; + z.real = -a.real; + z.imag = -a.imag; + return z; + } + static CYTHON_INLINE int __Pyx_c_is_zero_float(__pyx_t_float_complex a) { + return (a.real == 0) && (a.imag == 0); + } + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conj_float(__pyx_t_float_complex a) { + __pyx_t_float_complex z; + z.real = a.real; + z.imag = -a.imag; + return z; + } + #if 1 + static CYTHON_INLINE float __Pyx_c_abs_float(__pyx_t_float_complex z) { + #if !defined(HAVE_HYPOT) || defined(_MSC_VER) + return sqrtf(z.real*z.real + z.imag*z.imag); + #else + return hypotf(z.real, z.imag); + #endif + } + static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_pow_float(__pyx_t_float_complex a, __pyx_t_float_complex b) { + __pyx_t_float_complex z; + float r, lnr, theta, z_r, z_theta; + if (b.imag == 0 && b.real == (int)b.real) { + if (b.real < 0) { + float denom = a.real * a.real + a.imag * a.imag; + a.real = a.real / denom; + a.imag = -a.imag / denom; + b.real = -b.real; + } + switch ((int)b.real) { + case 0: + z.real = 1; + z.imag = 0; + return z; + case 1: + return a; + case 2: + z = __Pyx_c_prod_float(a, a); + return __Pyx_c_prod_float(a, a); + case 3: + z = __Pyx_c_prod_float(a, a); + return __Pyx_c_prod_float(z, a); + case 4: + z = __Pyx_c_prod_float(a, a); + return __Pyx_c_prod_float(z, z); + } + } + if (a.imag == 0) { + if (a.real == 0) { + return a; + } else if (b.imag == 0) { + z.real = powf(a.real, b.real); + z.imag = 0; + return z; + } else if (a.real > 0) { + r = a.real; + theta = 0; + } else { + r = -a.real; + theta = atan2f(0, -1); + } + } else { + r = __Pyx_c_abs_float(a); + theta = atan2f(a.imag, a.real); + } + lnr = logf(r); + z_r = expf(lnr * b.real - theta * b.imag); + z_theta = theta * b.real + lnr * b.imag; + z.real = z_r * cosf(z_theta); + z.imag = z_r * sinf(z_theta); + return z; + } + #endif +#endif + +/* Declarations */ + #if CYTHON_CCOMPLEX + #ifdef __cplusplus + static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) { + return ::std::complex< double >(x, y); + } + #else + static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) { + return x + y*(__pyx_t_double_complex)_Complex_I; + } + #endif +#else + static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) { + __pyx_t_double_complex z; + z.real = x; + z.imag = y; + return z; + } +#endif + +/* Arithmetic */ + #if CYTHON_CCOMPLEX +#else + static CYTHON_INLINE int __Pyx_c_eq_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { + return (a.real == b.real) && (a.imag == b.imag); + } + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { + __pyx_t_double_complex z; + z.real = a.real + b.real; + z.imag = a.imag + b.imag; + return z; + } + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { + __pyx_t_double_complex z; + z.real = a.real - b.real; + z.imag = a.imag - b.imag; + return z; + } + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { + __pyx_t_double_complex z; + z.real = a.real * b.real - a.imag * b.imag; + z.imag = a.real * b.imag + a.imag * b.real; + return z; + } + #if 1 + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { + if (b.imag == 0) { + return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.real); + } else if (fabs(b.real) >= fabs(b.imag)) { + if (b.real == 0 && b.imag == 0) { + return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.imag); + } else { + double r = b.imag / b.real; + double s = 1.0 / (b.real + b.imag * r); + return __pyx_t_double_complex_from_parts( + (a.real + a.imag * r) * s, (a.imag - a.real * r) * s); + } + } else { + double r = b.real / b.imag; + double s = 1.0 / (b.imag + b.real * r); + return __pyx_t_double_complex_from_parts( + (a.real * r + a.imag) * s, (a.imag * r - a.real) * s); + } + } + #else + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { + if (b.imag == 0) { + return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.real); + } else { + double denom = b.real * b.real + b.imag * b.imag; + return __pyx_t_double_complex_from_parts( + (a.real * b.real + a.imag * b.imag) / denom, + (a.imag * b.real - a.real * b.imag) / denom); + } + } + #endif + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg_double(__pyx_t_double_complex a) { + __pyx_t_double_complex z; + z.real = -a.real; + z.imag = -a.imag; + return z; + } + static CYTHON_INLINE int __Pyx_c_is_zero_double(__pyx_t_double_complex a) { + return (a.real == 0) && (a.imag == 0); + } + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj_double(__pyx_t_double_complex a) { + __pyx_t_double_complex z; + z.real = a.real; + z.imag = -a.imag; + return z; + } + #if 1 + static CYTHON_INLINE double __Pyx_c_abs_double(__pyx_t_double_complex z) { + #if !defined(HAVE_HYPOT) || defined(_MSC_VER) + return sqrt(z.real*z.real + z.imag*z.imag); + #else + return hypot(z.real, z.imag); + #endif + } + static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow_double(__pyx_t_double_complex a, __pyx_t_double_complex b) { + __pyx_t_double_complex z; + double r, lnr, theta, z_r, z_theta; + if (b.imag == 0 && b.real == (int)b.real) { + if (b.real < 0) { + double denom = a.real * a.real + a.imag * a.imag; + a.real = a.real / denom; + a.imag = -a.imag / denom; + b.real = -b.real; + } + switch ((int)b.real) { + case 0: + z.real = 1; + z.imag = 0; + return z; + case 1: + return a; + case 2: + z = __Pyx_c_prod_double(a, a); + return __Pyx_c_prod_double(a, a); + case 3: + z = __Pyx_c_prod_double(a, a); + return __Pyx_c_prod_double(z, a); + case 4: + z = __Pyx_c_prod_double(a, a); + return __Pyx_c_prod_double(z, z); + } + } + if (a.imag == 0) { + if (a.real == 0) { + return a; + } else if (b.imag == 0) { + z.real = pow(a.real, b.real); + z.imag = 0; + return z; + } else if (a.real > 0) { + r = a.real; + theta = 0; + } else { + r = -a.real; + theta = atan2(0, -1); + } + } else { + r = __Pyx_c_abs_double(a); + theta = atan2(a.imag, a.real); + } + lnr = log(r); + z_r = exp(lnr * b.real - theta * b.imag); + z_theta = theta * b.real + lnr * b.imag; + z.real = z_r * cos(z_theta); + z.imag = z_r * sin(z_theta); + return z; + } + #endif +#endif + +/* CIntToPy */ + static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value) { + const int neg_one = (int) ((int) 0 - (int) 1), const_zero = (int) 0; + const int is_unsigned = neg_one > const_zero; + if (is_unsigned) { + if (sizeof(int) < sizeof(long)) { + return PyInt_FromLong((long) value); + } else if (sizeof(int) <= sizeof(unsigned long)) { + return PyLong_FromUnsignedLong((unsigned long) value); +#ifdef HAVE_LONG_LONG + } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) { + return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value); +#endif + } + } else { + if (sizeof(int) <= sizeof(long)) { + return PyInt_FromLong((long) value); +#ifdef HAVE_LONG_LONG + } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) { + return PyLong_FromLongLong((PY_LONG_LONG) value); +#endif + } + } + { + int one = 1; int little = (int)*(unsigned char *)&one; + unsigned char *bytes = (unsigned char *)&value; + return _PyLong_FromByteArray(bytes, sizeof(int), + little, !is_unsigned); + } +} + +/* CIntToPy */ + static CYTHON_INLINE PyObject* __Pyx_PyInt_From_enum__NPY_TYPES(enum NPY_TYPES value) { + const enum NPY_TYPES neg_one = (enum NPY_TYPES) ((enum NPY_TYPES) 0 - (enum NPY_TYPES) 1), const_zero = (enum NPY_TYPES) 0; + const int is_unsigned = neg_one > const_zero; + if (is_unsigned) { + if (sizeof(enum NPY_TYPES) < sizeof(long)) { + return PyInt_FromLong((long) value); + } else if (sizeof(enum NPY_TYPES) <= sizeof(unsigned long)) { + return PyLong_FromUnsignedLong((unsigned long) value); +#ifdef HAVE_LONG_LONG + } else if (sizeof(enum NPY_TYPES) <= sizeof(unsigned PY_LONG_LONG)) { + return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value); +#endif + } + } else { + if (sizeof(enum NPY_TYPES) <= sizeof(long)) { + return PyInt_FromLong((long) value); +#ifdef HAVE_LONG_LONG + } else if (sizeof(enum NPY_TYPES) <= sizeof(PY_LONG_LONG)) { + return PyLong_FromLongLong((PY_LONG_LONG) value); +#endif + } + } + { + int one = 1; int little = (int)*(unsigned char *)&one; + unsigned char *bytes = (unsigned char *)&value; + return _PyLong_FromByteArray(bytes, sizeof(enum NPY_TYPES), + little, !is_unsigned); + } +} + +/* CIntFromPy */ + static CYTHON_INLINE size_t __Pyx_PyInt_As_size_t(PyObject *x) { + const size_t neg_one = (size_t) ((size_t) 0 - (size_t) 1), const_zero = (size_t) 0; + const int is_unsigned = neg_one > const_zero; +#if PY_MAJOR_VERSION < 3 + if (likely(PyInt_Check(x))) { + if (sizeof(size_t) < sizeof(long)) { + __PYX_VERIFY_RETURN_INT(size_t, long, PyInt_AS_LONG(x)) + } else { + long val = PyInt_AS_LONG(x); + if (is_unsigned && unlikely(val < 0)) { + goto raise_neg_overflow; + } + return (size_t) val; + } + } else +#endif + if (likely(PyLong_Check(x))) { + if (is_unsigned) { +#if CYTHON_USE_PYLONG_INTERNALS + const digit* digits = ((PyLongObject*)x)->ob_digit; + switch (Py_SIZE(x)) { + case 0: return (size_t) 0; + case 1: __PYX_VERIFY_RETURN_INT(size_t, digit, digits[0]) + case 2: + if (8 * sizeof(size_t) > 1 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(size_t, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(size_t) >= 2 * PyLong_SHIFT) { + return (size_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); + } + } + break; + case 3: + if (8 * sizeof(size_t) > 2 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(size_t, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(size_t) >= 3 * PyLong_SHIFT) { + return (size_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); + } + } + break; + case 4: + if (8 * sizeof(size_t) > 3 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(size_t, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(size_t) >= 4 * PyLong_SHIFT) { + return (size_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); + } + } + break; + } +#endif +#if CYTHON_COMPILING_IN_CPYTHON + if (unlikely(Py_SIZE(x) < 0)) { + goto raise_neg_overflow; + } +#else + { + int result = PyObject_RichCompareBool(x, Py_False, Py_LT); + if (unlikely(result < 0)) + return (size_t) -1; + if (unlikely(result == 1)) + goto raise_neg_overflow; + } +#endif + if (sizeof(size_t) <= sizeof(unsigned long)) { + __PYX_VERIFY_RETURN_INT_EXC(size_t, unsigned long, PyLong_AsUnsignedLong(x)) +#ifdef HAVE_LONG_LONG + } else if (sizeof(size_t) <= sizeof(unsigned PY_LONG_LONG)) { + __PYX_VERIFY_RETURN_INT_EXC(size_t, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x)) +#endif + } + } else { +#if CYTHON_USE_PYLONG_INTERNALS + const digit* digits = ((PyLongObject*)x)->ob_digit; + switch (Py_SIZE(x)) { + case 0: return (size_t) 0; + case -1: __PYX_VERIFY_RETURN_INT(size_t, sdigit, (sdigit) (-(sdigit)digits[0])) + case 1: __PYX_VERIFY_RETURN_INT(size_t, digit, +digits[0]) + case -2: + if (8 * sizeof(size_t) - 1 > 1 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(size_t, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(size_t) - 1 > 2 * PyLong_SHIFT) { + return (size_t) (((size_t)-1)*(((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]))); + } + } + break; + case 2: + if (8 * sizeof(size_t) > 1 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(size_t, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(size_t) - 1 > 2 * PyLong_SHIFT) { + return (size_t) ((((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]))); + } + } + break; + case -3: + if (8 * sizeof(size_t) - 1 > 2 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(size_t, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(size_t) - 1 > 3 * PyLong_SHIFT) { + return (size_t) (((size_t)-1)*(((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]))); + } + } + break; + case 3: + if (8 * sizeof(size_t) > 2 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(size_t, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(size_t) - 1 > 3 * PyLong_SHIFT) { + return (size_t) ((((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]))); + } + } + break; + case -4: + if (8 * sizeof(size_t) - 1 > 3 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(size_t, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(size_t) - 1 > 4 * PyLong_SHIFT) { + return (size_t) (((size_t)-1)*(((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]))); + } + } + break; + case 4: + if (8 * sizeof(size_t) > 3 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(size_t, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(size_t) - 1 > 4 * PyLong_SHIFT) { + return (size_t) ((((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]))); + } + } + break; + } +#endif + if (sizeof(size_t) <= sizeof(long)) { + __PYX_VERIFY_RETURN_INT_EXC(size_t, long, PyLong_AsLong(x)) +#ifdef HAVE_LONG_LONG + } else if (sizeof(size_t) <= sizeof(PY_LONG_LONG)) { + __PYX_VERIFY_RETURN_INT_EXC(size_t, PY_LONG_LONG, PyLong_AsLongLong(x)) +#endif + } + } + { +#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray) + PyErr_SetString(PyExc_RuntimeError, + "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers"); +#else + size_t val; + PyObject *v = __Pyx_PyNumber_IntOrLong(x); + #if PY_MAJOR_VERSION < 3 + if (likely(v) && !PyLong_Check(v)) { + PyObject *tmp = v; + v = PyNumber_Long(tmp); + Py_DECREF(tmp); + } + #endif + if (likely(v)) { + int one = 1; int is_little = (int)*(unsigned char *)&one; + unsigned char *bytes = (unsigned char *)&val; + int ret = _PyLong_AsByteArray((PyLongObject *)v, + bytes, sizeof(val), + is_little, !is_unsigned); + Py_DECREF(v); + if (likely(!ret)) + return val; + } +#endif + return (size_t) -1; + } + } else { + size_t val; + PyObject *tmp = __Pyx_PyNumber_IntOrLong(x); + if (!tmp) return (size_t) -1; + val = __Pyx_PyInt_As_size_t(tmp); + Py_DECREF(tmp); + return val; + } +raise_overflow: + PyErr_SetString(PyExc_OverflowError, + "value too large to convert to size_t"); + return (size_t) -1; +raise_neg_overflow: + PyErr_SetString(PyExc_OverflowError, + "can't convert negative value to size_t"); + return (size_t) -1; +} + +/* PrintOne */ + #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION < 3 +static int __Pyx_PrintOne(PyObject* f, PyObject *o) { + if (!f) { + if (!(f = __Pyx_GetStdout())) + return -1; + } + Py_INCREF(f); + if (PyFile_SoftSpace(f, 0)) { + if (PyFile_WriteString(" ", f) < 0) + goto error; + } + if (PyFile_WriteObject(o, f, Py_PRINT_RAW) < 0) + goto error; + if (PyFile_WriteString("\n", f) < 0) + goto error; + Py_DECREF(f); + return 0; +error: + Py_DECREF(f); + return -1; + /* the line below is just to avoid C compiler + * warnings about unused functions */ + return __Pyx_Print(f, NULL, 0); +} +#else +static int __Pyx_PrintOne(PyObject* stream, PyObject *o) { + int res; + PyObject* arg_tuple = PyTuple_Pack(1, o); + if (unlikely(!arg_tuple)) + return -1; + res = __Pyx_Print(stream, arg_tuple, 1); + Py_DECREF(arg_tuple); + return res; +} +#endif + +/* CIntFromPy */ + static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *x) { + const int neg_one = (int) ((int) 0 - (int) 1), const_zero = (int) 0; + const int is_unsigned = neg_one > const_zero; +#if PY_MAJOR_VERSION < 3 + if (likely(PyInt_Check(x))) { + if (sizeof(int) < sizeof(long)) { + __PYX_VERIFY_RETURN_INT(int, long, PyInt_AS_LONG(x)) + } else { + long val = PyInt_AS_LONG(x); + if (is_unsigned && unlikely(val < 0)) { + goto raise_neg_overflow; + } + return (int) val; + } + } else +#endif + if (likely(PyLong_Check(x))) { + if (is_unsigned) { +#if CYTHON_USE_PYLONG_INTERNALS + const digit* digits = ((PyLongObject*)x)->ob_digit; + switch (Py_SIZE(x)) { + case 0: return (int) 0; + case 1: __PYX_VERIFY_RETURN_INT(int, digit, digits[0]) + case 2: + if (8 * sizeof(int) > 1 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) >= 2 * PyLong_SHIFT) { + return (int) (((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])); + } + } + break; + case 3: + if (8 * sizeof(int) > 2 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) >= 3 * PyLong_SHIFT) { + return (int) (((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])); + } + } + break; + case 4: + if (8 * sizeof(int) > 3 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) >= 4 * PyLong_SHIFT) { + return (int) (((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])); + } + } + break; + } +#endif +#if CYTHON_COMPILING_IN_CPYTHON + if (unlikely(Py_SIZE(x) < 0)) { + goto raise_neg_overflow; + } +#else + { + int result = PyObject_RichCompareBool(x, Py_False, Py_LT); + if (unlikely(result < 0)) + return (int) -1; + if (unlikely(result == 1)) + goto raise_neg_overflow; + } +#endif + if (sizeof(int) <= sizeof(unsigned long)) { + __PYX_VERIFY_RETURN_INT_EXC(int, unsigned long, PyLong_AsUnsignedLong(x)) +#ifdef HAVE_LONG_LONG + } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) { + __PYX_VERIFY_RETURN_INT_EXC(int, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x)) +#endif + } + } else { +#if CYTHON_USE_PYLONG_INTERNALS + const digit* digits = ((PyLongObject*)x)->ob_digit; + switch (Py_SIZE(x)) { + case 0: return (int) 0; + case -1: __PYX_VERIFY_RETURN_INT(int, sdigit, (sdigit) (-(sdigit)digits[0])) + case 1: __PYX_VERIFY_RETURN_INT(int, digit, +digits[0]) + case -2: + if (8 * sizeof(int) - 1 > 1 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) { + return (int) (((int)-1)*(((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); + } + } + break; + case 2: + if (8 * sizeof(int) > 1 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) { + return (int) ((((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); + } + } + break; + case -3: + if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) { + return (int) (((int)-1)*(((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); + } + } + break; + case 3: + if (8 * sizeof(int) > 2 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) { + return (int) ((((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); + } + } + break; + case -4: + if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) { + return (int) (((int)-1)*(((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); + } + } + break; + case 4: + if (8 * sizeof(int) > 3 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) { + return (int) ((((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]))); + } + } + break; + } +#endif + if (sizeof(int) <= sizeof(long)) { + __PYX_VERIFY_RETURN_INT_EXC(int, long, PyLong_AsLong(x)) +#ifdef HAVE_LONG_LONG + } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) { + __PYX_VERIFY_RETURN_INT_EXC(int, PY_LONG_LONG, PyLong_AsLongLong(x)) +#endif + } + } + { +#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray) + PyErr_SetString(PyExc_RuntimeError, + "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers"); +#else + int val; + PyObject *v = __Pyx_PyNumber_IntOrLong(x); + #if PY_MAJOR_VERSION < 3 + if (likely(v) && !PyLong_Check(v)) { + PyObject *tmp = v; + v = PyNumber_Long(tmp); + Py_DECREF(tmp); + } + #endif + if (likely(v)) { + int one = 1; int is_little = (int)*(unsigned char *)&one; + unsigned char *bytes = (unsigned char *)&val; + int ret = _PyLong_AsByteArray((PyLongObject *)v, + bytes, sizeof(val), + is_little, !is_unsigned); + Py_DECREF(v); + if (likely(!ret)) + return val; + } +#endif + return (int) -1; + } + } else { + int val; + PyObject *tmp = __Pyx_PyNumber_IntOrLong(x); + if (!tmp) return (int) -1; + val = __Pyx_PyInt_As_int(tmp); + Py_DECREF(tmp); + return val; + } +raise_overflow: + PyErr_SetString(PyExc_OverflowError, + "value too large to convert to int"); + return (int) -1; +raise_neg_overflow: + PyErr_SetString(PyExc_OverflowError, + "can't convert negative value to int"); + return (int) -1; +} + +/* CIntFromPy */ + static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *x) { + const long neg_one = (long) ((long) 0 - (long) 1), const_zero = (long) 0; + const int is_unsigned = neg_one > const_zero; +#if PY_MAJOR_VERSION < 3 + if (likely(PyInt_Check(x))) { + if (sizeof(long) < sizeof(long)) { + __PYX_VERIFY_RETURN_INT(long, long, PyInt_AS_LONG(x)) + } else { + long val = PyInt_AS_LONG(x); + if (is_unsigned && unlikely(val < 0)) { + goto raise_neg_overflow; + } + return (long) val; + } + } else +#endif + if (likely(PyLong_Check(x))) { + if (is_unsigned) { +#if CYTHON_USE_PYLONG_INTERNALS + const digit* digits = ((PyLongObject*)x)->ob_digit; + switch (Py_SIZE(x)) { + case 0: return (long) 0; + case 1: __PYX_VERIFY_RETURN_INT(long, digit, digits[0]) + case 2: + if (8 * sizeof(long) > 1 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) >= 2 * PyLong_SHIFT) { + return (long) (((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])); + } + } + break; + case 3: + if (8 * sizeof(long) > 2 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) >= 3 * PyLong_SHIFT) { + return (long) (((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])); + } + } + break; + case 4: + if (8 * sizeof(long) > 3 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) >= 4 * PyLong_SHIFT) { + return (long) (((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])); + } + } + break; + } +#endif +#if CYTHON_COMPILING_IN_CPYTHON + if (unlikely(Py_SIZE(x) < 0)) { + goto raise_neg_overflow; + } +#else + { + int result = PyObject_RichCompareBool(x, Py_False, Py_LT); + if (unlikely(result < 0)) + return (long) -1; + if (unlikely(result == 1)) + goto raise_neg_overflow; + } +#endif + if (sizeof(long) <= sizeof(unsigned long)) { + __PYX_VERIFY_RETURN_INT_EXC(long, unsigned long, PyLong_AsUnsignedLong(x)) +#ifdef HAVE_LONG_LONG + } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) { + __PYX_VERIFY_RETURN_INT_EXC(long, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x)) +#endif + } + } else { +#if CYTHON_USE_PYLONG_INTERNALS + const digit* digits = ((PyLongObject*)x)->ob_digit; + switch (Py_SIZE(x)) { + case 0: return (long) 0; + case -1: __PYX_VERIFY_RETURN_INT(long, sdigit, (sdigit) (-(sdigit)digits[0])) + case 1: __PYX_VERIFY_RETURN_INT(long, digit, +digits[0]) + case -2: + if (8 * sizeof(long) - 1 > 1 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) { + return (long) (((long)-1)*(((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); + } + } + break; + case 2: + if (8 * sizeof(long) > 1 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) { + return (long) ((((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); + } + } + break; + case -3: + if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) { + return (long) (((long)-1)*(((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); + } + } + break; + case 3: + if (8 * sizeof(long) > 2 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) { + return (long) ((((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); + } + } + break; + case -4: + if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) { + return (long) (((long)-1)*(((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); + } + } + break; + case 4: + if (8 * sizeof(long) > 3 * PyLong_SHIFT) { + if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) { + __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0]))) + } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) { + return (long) ((((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]))); + } + } + break; + } +#endif + if (sizeof(long) <= sizeof(long)) { + __PYX_VERIFY_RETURN_INT_EXC(long, long, PyLong_AsLong(x)) +#ifdef HAVE_LONG_LONG + } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) { + __PYX_VERIFY_RETURN_INT_EXC(long, PY_LONG_LONG, PyLong_AsLongLong(x)) +#endif + } + } + { +#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray) + PyErr_SetString(PyExc_RuntimeError, + "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers"); +#else + long val; + PyObject *v = __Pyx_PyNumber_IntOrLong(x); + #if PY_MAJOR_VERSION < 3 + if (likely(v) && !PyLong_Check(v)) { + PyObject *tmp = v; + v = PyNumber_Long(tmp); + Py_DECREF(tmp); + } + #endif + if (likely(v)) { + int one = 1; int is_little = (int)*(unsigned char *)&one; + unsigned char *bytes = (unsigned char *)&val; + int ret = _PyLong_AsByteArray((PyLongObject *)v, + bytes, sizeof(val), + is_little, !is_unsigned); + Py_DECREF(v); + if (likely(!ret)) + return val; + } +#endif + return (long) -1; + } + } else { + long val; + PyObject *tmp = __Pyx_PyNumber_IntOrLong(x); + if (!tmp) return (long) -1; + val = __Pyx_PyInt_As_long(tmp); + Py_DECREF(tmp); + return val; + } +raise_overflow: + PyErr_SetString(PyExc_OverflowError, + "value too large to convert to long"); + return (long) -1; +raise_neg_overflow: + PyErr_SetString(PyExc_OverflowError, + "can't convert negative value to long"); + return (long) -1; +} + +/* FastTypeChecks */ + #if CYTHON_COMPILING_IN_CPYTHON +static int __Pyx_InBases(PyTypeObject *a, PyTypeObject *b) { + while (a) { + a = a->tp_base; + if (a == b) + return 1; + } + return b == &PyBaseObject_Type; +} +static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b) { + PyObject *mro; + if (a == b) return 1; + mro = a->tp_mro; + if (likely(mro)) { + Py_ssize_t i, n; + n = PyTuple_GET_SIZE(mro); + for (i = 0; i < n; i++) { + if (PyTuple_GET_ITEM(mro, i) == (PyObject *)b) + return 1; + } + return 0; + } + return __Pyx_InBases(a, b); +} +#if PY_MAJOR_VERSION == 2 +static int __Pyx_inner_PyErr_GivenExceptionMatches2(PyObject *err, PyObject* exc_type1, PyObject* exc_type2) { + PyObject *exception, *value, *tb; + int res; + __Pyx_PyThreadState_declare + __Pyx_PyThreadState_assign + __Pyx_ErrFetch(&exception, &value, &tb); + res = exc_type1 ? PyObject_IsSubclass(err, exc_type1) : 0; + if (unlikely(res == -1)) { + PyErr_WriteUnraisable(err); + res = 0; + } + if (!res) { + res = PyObject_IsSubclass(err, exc_type2); + if (unlikely(res == -1)) { + PyErr_WriteUnraisable(err); + res = 0; + } + } + __Pyx_ErrRestore(exception, value, tb); + return res; +} +#else +static CYTHON_INLINE int __Pyx_inner_PyErr_GivenExceptionMatches2(PyObject *err, PyObject* exc_type1, PyObject *exc_type2) { + int res = exc_type1 ? __Pyx_IsSubtype((PyTypeObject*)err, (PyTypeObject*)exc_type1) : 0; + if (!res) { + res = __Pyx_IsSubtype((PyTypeObject*)err, (PyTypeObject*)exc_type2); + } + return res; +} +#endif +static int __Pyx_PyErr_GivenExceptionMatchesTuple(PyObject *exc_type, PyObject *tuple) { + Py_ssize_t i, n; + assert(PyExceptionClass_Check(exc_type)); + n = PyTuple_GET_SIZE(tuple); +#if PY_MAJOR_VERSION >= 3 + for (i=0; ip) { + #if PY_MAJOR_VERSION < 3 + if (t->is_unicode) { + *t->p = PyUnicode_DecodeUTF8(t->s, t->n - 1, NULL); + } else if (t->intern) { + *t->p = PyString_InternFromString(t->s); + } else { + *t->p = PyString_FromStringAndSize(t->s, t->n - 1); + } + #else + if (t->is_unicode | t->is_str) { + if (t->intern) { + *t->p = PyUnicode_InternFromString(t->s); + } else if (t->encoding) { + *t->p = PyUnicode_Decode(t->s, t->n - 1, t->encoding, NULL); + } else { + *t->p = PyUnicode_FromStringAndSize(t->s, t->n - 1); + } + } else { + *t->p = PyBytes_FromStringAndSize(t->s, t->n - 1); + } + #endif + if (!*t->p) + return -1; + if (PyObject_Hash(*t->p) == -1) + return -1; + ++t; + } + return 0; +} + +static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char* c_str) { + return __Pyx_PyUnicode_FromStringAndSize(c_str, (Py_ssize_t)strlen(c_str)); +} +static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject* o) { + Py_ssize_t ignore; + return __Pyx_PyObject_AsStringAndSize(o, &ignore); +} +#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT +#if !CYTHON_PEP393_ENABLED +static const char* __Pyx_PyUnicode_AsStringAndSize(PyObject* o, Py_ssize_t *length) { + char* defenc_c; + PyObject* defenc = _PyUnicode_AsDefaultEncodedString(o, NULL); + if (!defenc) return NULL; + defenc_c = PyBytes_AS_STRING(defenc); +#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII + { + char* end = defenc_c + PyBytes_GET_SIZE(defenc); + char* c; + for (c = defenc_c; c < end; c++) { + if ((unsigned char) (*c) >= 128) { + PyUnicode_AsASCIIString(o); + return NULL; + } + } + } +#endif + *length = PyBytes_GET_SIZE(defenc); + return defenc_c; +} +#else +static CYTHON_INLINE const char* __Pyx_PyUnicode_AsStringAndSize(PyObject* o, Py_ssize_t *length) { + if (unlikely(__Pyx_PyUnicode_READY(o) == -1)) return NULL; +#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII + if (likely(PyUnicode_IS_ASCII(o))) { + *length = PyUnicode_GET_LENGTH(o); + return PyUnicode_AsUTF8(o); + } else { + PyUnicode_AsASCIIString(o); + return NULL; + } +#else + return PyUnicode_AsUTF8AndSize(o, length); +#endif +} +#endif +#endif +static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject* o, Py_ssize_t *length) { +#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT + if ( +#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII + __Pyx_sys_getdefaultencoding_not_ascii && +#endif + PyUnicode_Check(o)) { + return __Pyx_PyUnicode_AsStringAndSize(o, length); + } else +#endif +#if (!CYTHON_COMPILING_IN_PYPY) || (defined(PyByteArray_AS_STRING) && defined(PyByteArray_GET_SIZE)) + if (PyByteArray_Check(o)) { + *length = PyByteArray_GET_SIZE(o); + return PyByteArray_AS_STRING(o); + } else +#endif + { + char* result; + int r = PyBytes_AsStringAndSize(o, &result, length); + if (unlikely(r < 0)) { + return NULL; + } else { + return result; + } + } +} +static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject* x) { + int is_true = x == Py_True; + if (is_true | (x == Py_False) | (x == Py_None)) return is_true; + else return PyObject_IsTrue(x); +} +static CYTHON_INLINE int __Pyx_PyObject_IsTrueAndDecref(PyObject* x) { + int retval; + if (unlikely(!x)) return -1; + retval = __Pyx_PyObject_IsTrue(x); + Py_DECREF(x); + return retval; +} +static PyObject* __Pyx_PyNumber_IntOrLongWrongResultType(PyObject* result, const char* type_name) { +#if PY_MAJOR_VERSION >= 3 + if (PyLong_Check(result)) { + if (PyErr_WarnFormat(PyExc_DeprecationWarning, 1, + "__int__ returned non-int (type %.200s). " + "The ability to return an instance of a strict subclass of int " + "is deprecated, and may be removed in a future version of Python.", + Py_TYPE(result)->tp_name)) { + Py_DECREF(result); + return NULL; + } + return result; + } +#endif + PyErr_Format(PyExc_TypeError, + "__%.4s__ returned non-%.4s (type %.200s)", + type_name, type_name, Py_TYPE(result)->tp_name); + Py_DECREF(result); + return NULL; +} +static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x) { +#if CYTHON_USE_TYPE_SLOTS + PyNumberMethods *m; +#endif + const char *name = NULL; + PyObject *res = NULL; +#if PY_MAJOR_VERSION < 3 + if (likely(PyInt_Check(x) || PyLong_Check(x))) +#else + if (likely(PyLong_Check(x))) +#endif + return __Pyx_NewRef(x); +#if CYTHON_USE_TYPE_SLOTS + m = Py_TYPE(x)->tp_as_number; + #if PY_MAJOR_VERSION < 3 + if (m && m->nb_int) { + name = "int"; + res = m->nb_int(x); + } + else if (m && m->nb_long) { + name = "long"; + res = m->nb_long(x); + } + #else + if (likely(m && m->nb_int)) { + name = "int"; + res = m->nb_int(x); + } + #endif +#else + if (!PyBytes_CheckExact(x) && !PyUnicode_CheckExact(x)) { + res = PyNumber_Int(x); + } +#endif + if (likely(res)) { +#if PY_MAJOR_VERSION < 3 + if (unlikely(!PyInt_Check(res) && !PyLong_Check(res))) { +#else + if (unlikely(!PyLong_CheckExact(res))) { +#endif + return __Pyx_PyNumber_IntOrLongWrongResultType(res, name); + } + } + else if (!PyErr_Occurred()) { + PyErr_SetString(PyExc_TypeError, + "an integer is required"); + } + return res; +} +static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject* b) { + Py_ssize_t ival; + PyObject *x; +#if PY_MAJOR_VERSION < 3 + if (likely(PyInt_CheckExact(b))) { + if (sizeof(Py_ssize_t) >= sizeof(long)) + return PyInt_AS_LONG(b); + else + return PyInt_AsSsize_t(b); + } +#endif + if (likely(PyLong_CheckExact(b))) { + #if CYTHON_USE_PYLONG_INTERNALS + const digit* digits = ((PyLongObject*)b)->ob_digit; + const Py_ssize_t size = Py_SIZE(b); + if (likely(__Pyx_sst_abs(size) <= 1)) { + ival = likely(size) ? digits[0] : 0; + if (size == -1) ival = -ival; + return ival; + } else { + switch (size) { + case 2: + if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) { + return (Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); + } + break; + case -2: + if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) { + return -(Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); + } + break; + case 3: + if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) { + return (Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); + } + break; + case -3: + if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) { + return -(Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); + } + break; + case 4: + if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) { + return (Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); + } + break; + case -4: + if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) { + return -(Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0])); + } + break; + } + } + #endif + return PyLong_AsSsize_t(b); + } + x = PyNumber_Index(b); + if (!x) return -1; + ival = PyInt_AsSsize_t(x); + Py_DECREF(x); + return ival; +} +static CYTHON_INLINE PyObject * __Pyx_PyBool_FromLong(long b) { + return b ? __Pyx_NewRef(Py_True) : __Pyx_NewRef(Py_False); +} +static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t ival) { + return PyInt_FromSize_t(ival); +} + + +#endif /* Py_PYTHON_H */ diff --git a/src/src/radon.pyx b/src/radon.pyx similarity index 100% rename from src/src/radon.pyx rename to src/radon.pyx From 9b42487d8780c9896acaf95339b6f40de4d3a181 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Tue, 4 Jun 2019 00:30:48 +1000 Subject: [PATCH 051/170] Deleted lots of broken tests and fixed docstrings --- pycurious/Examples/Scripts/BFwdTest.py | 154 ------ pycurious/Examples/Scripts/CPD_Pts_find.sh | 6 - pycurious/Examples/Scripts/IapetusCheck.py | 138 ----- .../Examples/Scripts/LinearFitScratch.py | 182 ------- pycurious/Examples/Scripts/RobTest.py | 122 ----- pycurious/Examples/Scripts/RosettePlot.sh | 20 - pycurious/Examples/Scripts/mag_grid2.npz | Bin 3931407 -> 0 bytes pycurious/Examples/Scripts/readme.txt | 1 - pycurious/Examples/Scripts/tst_data.npz | Bin 343823 -> 0 bytes pycurious/__init__.py | 10 +- pycurious/{grid/curie.py => grid.py} | 506 +++++++++--------- pycurious/grid/__init__.py | 20 - pycurious/{mapping => }/mapping.py | 118 ++-- pycurious/mapping/__init__.py | 24 - pycurious/{optimise => }/optimise.py | 388 ++++++++------ pycurious/optimise/__init__.py | 20 - pycurious/{parallel => }/parallel.py | 2 +- pycurious/parallel/__init__.py | 20 - pycurious/{therm => }/therm.py | 0 pycurious/therm/__init__.py | 20 - setup.py | 11 +- 21 files changed, 558 insertions(+), 1204 deletions(-) delete mode 100644 pycurious/Examples/Scripts/BFwdTest.py delete mode 100644 pycurious/Examples/Scripts/CPD_Pts_find.sh delete mode 100644 pycurious/Examples/Scripts/IapetusCheck.py delete mode 100644 pycurious/Examples/Scripts/LinearFitScratch.py delete mode 100644 pycurious/Examples/Scripts/RobTest.py delete mode 100644 pycurious/Examples/Scripts/RosettePlot.sh delete mode 100644 pycurious/Examples/Scripts/mag_grid2.npz delete mode 100644 pycurious/Examples/Scripts/readme.txt delete mode 100644 pycurious/Examples/Scripts/tst_data.npz rename pycurious/{grid/curie.py => grid.py} (58%) delete mode 100644 pycurious/grid/__init__.py rename pycurious/{mapping => }/mapping.py (72%) delete mode 100644 pycurious/mapping/__init__.py rename pycurious/{optimise => }/optimise.py (58%) delete mode 100644 pycurious/optimise/__init__.py rename pycurious/{parallel => }/parallel.py (99%) delete mode 100644 pycurious/parallel/__init__.py rename pycurious/{therm => }/therm.py (100%) delete mode 100644 pycurious/therm/__init__.py diff --git a/pycurious/Examples/Scripts/BFwdTest.py b/pycurious/Examples/Scripts/BFwdTest.py deleted file mode 100644 index 8ae3dfd..0000000 --- a/pycurious/Examples/Scripts/BFwdTest.py +++ /dev/null @@ -1,154 +0,0 @@ -import numpy as np -import matplotlib.pyplot as plt -import pycurious -# %matplotlib inline - -#xmin = 600000. -#xmax = 660000. -#ymin = 780000. -#ymax = 835000. - -#nx = int((xmax - xmin)/200.) -#ny = int((ymax - ymin)/200.) -#xcoords, dx = np.linspace(xmin, xmax, nx, retstep=True) -#ycoords, dy = np.linspace(ymin, ymax, ny, retstep=True) -#xq, yq = np.meshgrid(xcoords, ycoords) -# importing the data and gridding is time consuming -# see if the grid exists first, otherwise proceed gridding -# ORIGINAL -# try: - # with np.load('mag_grid.npz') as f: - # mag_grid = f['data'] -# except: - # from scipy.interpolate import griddata - # # import data X | Y | Z | nT - # xc, yc, zc, mag = np.loadtxt('./mag2.xyz', dtype=np.float32, unpack=True) - # mag_grid = griddata(np.column_stack([xc, yc]), mag, (xq, yq)) - # # save grid - # np.savez_compressed('mag_grid.npz', data=mag_grid) - -# NEW -try: - # with np.load('mag_grid.npz') as f: - # with np.load('mag2.npz') as f: - with np.load('tst_data.npz') as f: - print('tst_data.npz found...') - mag_grid = f['data'] - xmin = f['xm'] - xmin = xmin[()] - xmax = f['xM'] - xmax = xmax[()] - ymin = f['ym'] - ymin = ymin[()] - ymax = f['yM'] - ymax = ymax[()] - - # print(mag2[:,0]) - # xc, yc, zc, mag = mag2 - # mag_grid = griddata(np.column_stack([mag2[:,0], mag2[:,1]]), mag2[:,3], (xq, yq)) -except: - print('making tst_data.npz...') - from scipy.interpolate import griddata - # import data X | Y | Z | nT - xc, yc, mag = np.loadtxt('./test_mag_data.txt', dtype=np.float32, unpack=True) - xmin = np.nanmin(xc[0]) - xmax = np.nanmax(xc[-1]) - ymin = np.nanmin(yc[0]) - ymax = np.nanmax(yc[-1]) - - nx = int((xmax - xmin)/1000.) - ny = int((ymax - ymin)/1000.) - #print(xmin,xmax,ymin,ymax,nx,ny) - xcoords, dx = np.linspace(xmin, xmax, nx, retstep=True) - ycoords, dy = np.linspace(ymin, ymax, ny, retstep=True) - xq, yq = np.meshgrid(xcoords, ycoords) - mag_grid = griddata(np.column_stack([xc, yc]), mag, (xq, yq),method='nearest') - #mag_grid = griddata(np.column_stack([mag2[:,0], mag2[:,1]]), mag2[:,3], (xq, yq),method='nearest') - # save grid - np.savez_compressed('tst_data.npz', data=mag_grid,xm=xmin,xM=xmax,ym=ymin,yM=ymax) - -#print(mag_grid.shape,xmin,xmax,ymin,ymax) -#plt.imshow(mag_grid, extent=(xmin, xmax, ymin, ymax), origin='lower') -#plt.show() -#exit() - - -## plt.imshow(mag_grid, extent=(xmin, xmax, ymin, ymax), origin='lower') -## initialise CurieGrid object -grid = pycurious.CurieGrid(mag_grid, xmin, xmax, ymin, ymax) - - -## Let's not!' -## let's pick a point in the centre of the study area -xpt = xmin + (xmax-xmin)/2 -ypt = ymin + (ymax-ymin)/2 - -subgrid = grid.subgrid(xpt, ypt, 125000.) -S, k, sigma2 = grid.radial_spectrum(subgrid, taper=None) - -DK=0.025 -nb=20 -hmap=np.zeros((nb,nb)) -ZT=np.zeros((nb,1)) -ZO=np.zeros((nb,1)) -for j in range(1,nb,1): - for l in range(1,nb,1): - print((j-1)*0.05, (j)*0.05,(l-1)*0.05, (l)*0.05) - Zb,eZb, Ztr, Zor = grid.Tanakac(S, k, sigma2,(j-1)*DK, (j)*DK,(l-1)*DK, (l)*DK) - hmap[j,l]=Zb - ZO[l]=Zor - ZT[j]=Ztr - -fig2 = plt.figure(figsize=(8,8)) -ax2 = fig2.add_subplot(111, xlabel=r'$\nu$ window of $\Phi/|k|$ (km$^{-1}$)', ylabel=r'$\nu$ window of $\Phi$') -#im2 = ax2.imshow(np.clip(hmap,-30,-10), extent=[0., (nb+1)*DK, 0., (nb+1)*DK], aspect=1) -im2 = ax2.imshow(np.clip(hmap,-30,-10), extent=[0., 0.5, 0., 0.5], aspect=1) -fig2.colorbar(im2, label='CPD') -plt.title('Heatmap of CPD') -plt.savefig('Heatmap.jpg') -plt.show() - - - - -#f.write(str(xpt)) -# compute radial spectrum - -Zb,eZb = grid.Tanaka(S, k, sigma2,kmin=0.05, kmax=0.25) - -print(Zb,eZb) -#exit() - -#print(xpt,ypt) -## get a subsection of the grid -#subgrid = grid.subgrid(xpt, ypt, 50000.) -#print(subgrid.shape) -## compute radial spectrum -#S, k, sigma2 = grid.radial_spectrum(subgrid, taper=None) -## fig, (ax1, ax2) = plt.subplots(1,2,figsize=(12,4)) -## ax1.plot(k, abs(S)) -##ax2.plot(sf, abs(S)) -#Zb,eZb = grid.Tanaka(S, k, sigma2,kmin=0.05, kmax=0.2) -#print(Zb,eZb) - -## INSTEAD -## Let's read a central point from file pts.xy -#cx,cy=np.loadtxt('pts.xy',unpack=True) -#f=open("CPD_pts.txt","w+") -#for xpt, ypt in zip(cx,cy): - ### get a subsection of the grid - #subgrid = grid.subgrid(xpt, ypt, 75000.) - #if subgrid.shape[0] != subgrid.shape[1]: - #continue - ##f.write(str(xpt)) - ## compute radial spectrum - #try: - #S, k, sigma2 = grid.radial_spectrum(subgrid, taper=None) - #Zb,eZb = grid.Tanaka(S, k, sigma2,kmin=0.05, kmax=0.2) - ##print(xpt,ypt,Zb,eZb) - #f.write(' '.join([str(xpt),str(ypt),str(Zb),str(eZb),"\n"])) - #except: - #print('Error for ',xpt,ypt) - ##break - -#f.close() diff --git a/pycurious/Examples/Scripts/CPD_Pts_find.sh b/pycurious/Examples/Scripts/CPD_Pts_find.sh deleted file mode 100644 index c21b3c7..0000000 --- a/pycurious/Examples/Scripts/CPD_Pts_find.sh +++ /dev/null @@ -1,6 +0,0 @@ -#!/bin/bash -gmtset PROJ_SCALE_FACTOR 0.999820 -x0= -y0= - -# Find SW point that's on land \ No newline at end of file diff --git a/pycurious/Examples/Scripts/IapetusCheck.py b/pycurious/Examples/Scripts/IapetusCheck.py deleted file mode 100644 index 61ad335..0000000 --- a/pycurious/Examples/Scripts/IapetusCheck.py +++ /dev/null @@ -1,138 +0,0 @@ -import numpy as np -import matplotlib.pyplot as plt -import pycurious -# %matplotlib inline - - -#nx = int((xmax - xmin)/200.) -#ny = int((ymax - ymin)/200.) -#xcoords, dx = np.linspace(xmin, xmax, nx, retstep=True) -#ycoords, dy = np.linspace(ymin, ymax, ny, retstep=True) -#xq, yq = np.meshgrid(xcoords, ycoords) -# importing the data and gridding is time consuming -# see if the grid exists first, otherwise proceed gridding -# ORIGINAL -# try: - # with np.load('mag_grid.npz') as f: - # mag_grid = f['data'] -# except: - # from scipy.interpolate import griddata - # # import data X | Y | Z | nT - # xc, yc, zc, mag = np.loadtxt('./mag2.xyz', dtype=np.float32, unpack=True) - # mag_grid = griddata(np.column_stack([xc, yc]), mag, (xq, yq)) - # # save grid - # np.savez_compressed('mag_grid.npz', data=mag_grid) - -# NEW -try: - # with np.load('mag_grid.npz') as f: - # with np.load('mag2.npz') as f: - with np.load('mag_grid2.npz') as f: - print('mag_grid2.npz found...') - mag_grid = f['data'] - xmin = f['xm'] - xmin = xmin[()] - xmax = f['xM'] - xmax = xmax[()] - ymin = f['ym'] - ymin = ymin[()] - ymax = f['yM'] - ymax = ymax[()] - - # print(mag2[:,0]) - # xc, yc, zc, mag = mag2 - # mag_grid = griddata(np.column_stack([mag2[:,0], mag2[:,1]]), mag2[:,3], (xq, yq)) -except: - print('making mag_grid2.npz...') - from scipy.interpolate import griddata - # import data X | Y | Z | nT - with np.load('mag2.npz') as f: - print('mag2.npz found...') - mag2 = f['mag2'] - # xc, yc, zc, mag = np.loadtxt('./mag2.xyz', dtype=np.float32, unpack=True) - print(mag2[0,]) - xmin = np.nanmin(mag2[:,0],axis=0) - xmax = np.nanmax(mag2[:,0],axis=0) - ymin = np.nanmin(mag2[:,1],axis=0) - ymax = np.nanmax(mag2[:,1],axis=0) - - nx = int((xmax - xmin)/200.) - ny = int((ymax - ymin)/200.) - print(xmin,xmax,ymin,ymax,nx,ny) - xcoords, dx = np.linspace(xmin, xmax, nx, retstep=True) - ycoords, dy = np.linspace(ymin, ymax, ny, retstep=True) - xq, yq = np.meshgrid(xcoords, ycoords) - mag_grid = griddata(np.column_stack([mag2[:,0], mag2[:,1]]), mag2[:,3], (xq, yq),method='nearest') - # save grid - np.savez_compressed('mag_grid2.npz', data=mag_grid,xm=xmin,xM=xmax,ym=ymin,yM=ymax) - -#print(mag_grid.shape,xmin,xmax,ymin,ymax) -#plt.imshow(mag_grid, extent=(xmin, xmax, ymin, ymax), origin='lower') -#plt.show() -#exit() - - - - -## plt.imshow(mag_grid, extent=(xmin, xmax, ymin, ymax), origin='lower') -## initialise CurieGrid object -grid = pycurious.CurieGrid(mag_grid, xmin, xmax, ymin, ymax) - - -## Let's not!' -## let's pick a point in the centre of the study area -#xpt = xmin + (xmax-xmin)/2 -#ypt = ymin + (ymax-ymin)/2 -#print(xpt,ypt) -## get a subsection of the grid -#subgrid = grid.subgrid(xpt, ypt, 50000.) -#print(subgrid.shape) -## compute radial spectrum -#S, k, sigma2 = grid.radial_spectrum(subgrid, taper=None) -## fig, (ax1, ax2) = plt.subplots(1,2,figsize=(12,4)) -## ax1.plot(k, abs(S)) -##ax2.plot(sf, abs(S)) -#Zb,eZb = grid.Tanaka(S, k, sigma2,kmin=0.05, kmax=0.2) -#print(Zb,eZb) - -f=open("iap_rosette.txt","w+") -xpt=632781 -ypt=805755 - ## get a subsection of the grid -subgrid = grid.subgrid(xpt, ypt, 75000.) -#if subgrid.shape[0] != subgrid.shape[1]: -# continue - #f.write(str(xpt)) - # compute radial spectrum -#try: -S, k, dtheta = grid.azimuthal_spectrum(subgrid, taper=None, scale=0.001, theta=5.0) - -# plot -#fig = plt.figure(figsize=(12,3)) -#ax1 = fig.add_subplot(111, xlabel='wavenumber (rad/km)', ylabel='theta ($^{\circ}$)') -#im1 = ax1.imshow(S, extent=[k.min(), k.max(), dtheta.min(), dtheta.max()], aspect=0.025) -#fig.colorbar(im1, label='Azimuthal spectrum') -#plt.show() - -for t in range(dtheta.size): - Zb= grid.Tanakab(S[t,:], k, kmin=0.05, kmax=0.2) - f.write(' '.join([str(dtheta[t]),str(Zb),"\n"])) -#print(Zb) - -#S, k, sigma2 = grid.radial_spectrum(subgrid, taper=None) - #Zb,eZb = grid.Tanaka(S, k, sigma2,kmin=0.05, kmax=0.2) - #print(xpt,ypt,Zb,eZb) - #f.write(' '.join([str(xpt),str(ypt),str(Zb),str(eZb),"\n"])) -#except: -# print('Error for ',xpt,ypt) - - - - -#cx,cy=np.loadtxt('pts.xy',unpack=True) - - - - - -f.close() diff --git a/pycurious/Examples/Scripts/LinearFitScratch.py b/pycurious/Examples/Scripts/LinearFitScratch.py deleted file mode 100644 index ebcd90c..0000000 --- a/pycurious/Examples/Scripts/LinearFitScratch.py +++ /dev/null @@ -1,182 +0,0 @@ -import numpy as np -import matplotlib.pyplot as plt -import pycurious -try: - # with np.load('mag_grid.npz') as f: - # with np.load('mag2.npz') as f: - with np.load('mag_grid2.npz') as f: - print('mag_grid2.npz found...') - mag_grid = f['data'] - xmin = f['xm'] - xmin = xmin[()] - xmax = f['xM'] - xmax = xmax[()] - ymin = f['ym'] - ymin = ymin[()] - ymax = f['yM'] - ymax = ymax[()] -except: - print('making mag_grid2.npz...') - from scipy.interpolate import griddata - # import data X | Y | Z | nT - with np.load('mag2.npz') as f: - print('mag2.npz found...') - mag2 = f['mag2'] - print(mag2[0,]) - xmin = np.nanmin(mag2[:,0],axis=0) - xmax = np.nanmax(mag2[:,0],axis=0) - ymin = np.nanmin(mag2[:,1],axis=0) - ymax = np.nanmax(mag2[:,1],axis=0) - - nx = int((xmax - xmin)/200.) - ny = int((ymax - ymin)/200.) - print(xmin,xmax,ymin,ymax,nx,ny) - xcoords, dx = np.linspace(xmin, xmax, nx, retstep=True) - ycoords, dy = np.linspace(ymin, ymax, ny, retstep=True) - xq, yq = np.meshgrid(xcoords, ycoords) - mag_grid = griddata(np.column_stack([mag2[:,0], mag2[:,1]]), mag2[:,3], (xq, yq),method='nearest') - # save grid - np.savez_compressed('mag_grid2.npz', data=mag_grid,xm=xmin,xM=xmax,ym=ymin,yM=ymax) - -grid = pycurious.CurieGrid(mag_grid, xmin, xmax, ymin, ymax) - - - - -xpt=632781 -ypt=805755 - ## get a subsection of the grid -subgrid = grid.subgrid(xpt, ypt, 75000.) - -S, k, sigma2 = grid.radial_spectrum(subgrid, taper=None) - - -#ax1.plot(k, abs(S)) -# ok, let's plot the interval derivatives of dS/dk -Sn=np.log(np.exp(S)/(k/(2.0*np.pi))) -dS = np.zeros((S.size-1, 1)) -dSn = np.zeros((S.size-1, 1)) -dk = np.zeros((S.size-1, 1)) -#print(S.size,dS.size) -def running_mean(x, N): - cumsum = np.cumsum(np.insert(x, 0, 0)) - return (cumsum[N:] - cumsum[:-N]) / float(N) -for x in range(dS.size): - dS[x]=(abs(S[x+1])-abs(S[x]))/(k[x+1]-k[x]) - dSn[x]=(abs(Sn[x+1])-abs(Sn[x]))/(k[x+1]-k[x]) - dk[x]=(k[x+1]+k[x])/2 - #print(dS) - #break - #print(str((S(x+1)-S(x))/(k(x+1)-k(1)))) -# let's compute variance over the same 5 pts... -dSm=running_mean(dS,5) -dSnm=running_mean(dSn,5) -var=np.zeros(dSm.size) -varn=np.zeros(dSm.size) -for x in range(var.size): - var[x]=np.var(dS[x:x+5]) - varn[x]=np.var(dSn[x:x+5]) -#print(var) -#ax2.plot(dk,dS,dk[2:-2],dSm) -plt.figure(figsize=(20,12)) -plt.subplot(2,3,1) -plt.plot(k/(2.0*np.pi),S/(2.0*np.pi)) -plt.title('$\Phi$') -plt.subplot(2,3,2) -plt.plot(dk/(2.0*np.pi),dS/(2.0*np.pi),dk[2:-2]/(2.0*np.pi),dSm/(2.0*np.pi)) -plt.title('$\partial\Phi/\partial k$') -plt.legend(['Original','5pt mean']) -plt.subplot(2,3,3) -plt.plot(dk[2:-2]/(2.0*np.pi),var) -plt.title('$\sigma^2(\partial\Phi/\partial k($') -plt.subplot(2,3,4) -plt.plot(k/(2.0*np.pi),Sn/(2.0*np.pi)) -plt.title('$\Phi/|k|$') -plt.xlabel('Spatial Frequency') -plt.subplot(2,3,5) -plt.plot(dk/(2.0*np.pi),dSn/(2.0*np.pi),dk[2:-2]/(2.0*np.pi),dSnm/(2.0*np.pi)) -plt.title('$\partial(\Phi/|k|)/\partial k$') -plt.legend(['Original','5pt mean']) -plt.xlabel('Spatial Frequency') -plt.subplot(2,3,6) -plt.plot(dk[2:-2]/(2.0*np.pi),varn) -plt.title('$\sigma^2(\partial(\Phi/|k|)/\partial k($') -plt.xlabel('Spatial Frequency') -plt.savefig('dSpectra.jpg') - -f2, ax2 = plt.subplots(1,1,figsize=(12,4)) -ax2.plot(k/(2.0*np.pi),S/(2.0*np.pi),k/(2.0*np.pi),np.log(np.exp(S)/(k/(2.0*np.pi)))/(2.0*np.pi)) -plt.xlabel('Spatial Frequency$') -plt.legend(['$\Phi$','$\Phi/|k|$']) -plt.title('Spectra') -plt.savefig('Spectra.jpg') -#plt.show() -#exit() -#ax4.plot(k/(2.0*np.pi),np.log(np.exp(S)/(k/(2.0*np.pi)))/(2.0*np.pi)) - - -#print(k/(2.0*np.pi)) -DK=0.05 -nb=48 -hmap=np.zeros((nb,nb)) -ZT=np.zeros((nb,1)) -ZO=np.zeros((nb,1)) -for j in range(1,nb,1): - for l in range(1,nb,1): - #print((j-1)*0.05, (j)*0.05) - Zb,eZb, Ztr, Zor = grid.Tanakac(S, k, sigma2,(j-1)*DK, (j)*DK,(l-1)*DK, (l)*DK) - hmap[j,l]=Zb - ZO[l]=Zor - ZT[j]=Ztr - -fig2 = plt.figure(figsize=(8,8)) -ax2 = fig2.add_subplot(111, xlabel='$k$ window of $\Phi/|k|$', ylabel='$k$ window of $\Phi$') -#im2 = ax2.imshow(np.clip(hmap,-30,-10), extent=[0., (nb+1)*DK, 0., (nb+1)*DK], aspect=1) -im2 = ax2.imshow(np.clip(hmap,-30,-10), extent=[0., 0.5, 0., 0.5], aspect=1) -fig2.colorbar(im2, label='CPD') -plt.title('Heatmap of CPD') -plt.savefig('Heatmap.jpg') - -fig4 = plt.figure(figsize=(12,6)) -ax5 = fig4.add_subplot(111,xlabel='k', ylabel='Z (km)') -nk=np.linspace(0, nb*DK, nb) -ax5.plot(nk,ZT,nk,ZO) -plt.legend(['Z_t','Z_o']) -plt.ylim(-40,0) -plt.savefig('Z_dist.jpg') - -plt.show() -#plt.clim(-50,0) -#exit() - - - - - - - - - - - -### INSTEAD -### Let's read a central point from file pts.xy -#cx,cy=np.loadtxt('pts.xy',unpack=True) -#f=open("CPD_pts.txt","w+") -#for xpt, ypt in zip(cx,cy): - ### get a subsection of the grid - #subgrid = grid.subgrid(xpt, ypt, 75000.) - #if subgrid.shape[0] != subgrid.shape[1]: - #continue - ##f.write(str(xpt)) - ## compute radial spectrum - #try: - #S, k, sigma2 = grid.radial_spectrum(subgrid, taper=None) - #Zb,eZb = grid.Tanaka(S, k, sigma2,kmin=0.05, kmax=0.2) - ##print(xpt,ypt,Zb,eZb) - #f.write(' '.join([str(xpt),str(ypt),str(Zb),str(eZb),"\n"])) - #except: - #print('Error for ',xpt,ypt) - ##break - -#f.close() diff --git a/pycurious/Examples/Scripts/RobTest.py b/pycurious/Examples/Scripts/RobTest.py deleted file mode 100644 index 416c906..0000000 --- a/pycurious/Examples/Scripts/RobTest.py +++ /dev/null @@ -1,122 +0,0 @@ -import numpy as np -import matplotlib.pyplot as plt -import pycurious -# %matplotlib inline - -#xmin = 600000. -#xmax = 660000. -#ymin = 780000. -#ymax = 835000. - -#nx = int((xmax - xmin)/200.) -#ny = int((ymax - ymin)/200.) -#xcoords, dx = np.linspace(xmin, xmax, nx, retstep=True) -#ycoords, dy = np.linspace(ymin, ymax, ny, retstep=True) -#xq, yq = np.meshgrid(xcoords, ycoords) -# importing the data and gridding is time consuming -# see if the grid exists first, otherwise proceed gridding -# ORIGINAL -# try: - # with np.load('mag_grid.npz') as f: - # mag_grid = f['data'] -# except: - # from scipy.interpolate import griddata - # # import data X | Y | Z | nT - # xc, yc, zc, mag = np.loadtxt('./mag2.xyz', dtype=np.float32, unpack=True) - # mag_grid = griddata(np.column_stack([xc, yc]), mag, (xq, yq)) - # # save grid - # np.savez_compressed('mag_grid.npz', data=mag_grid) - -# NEW -try: - # with np.load('mag_grid.npz') as f: - # with np.load('mag2.npz') as f: - with np.load('mag_grid2.npz') as f: - print('mag_grid2.npz found...') - mag_grid = f['data'] - xmin = f['xm'] - xmin = xmin[()] - xmax = f['xM'] - xmax = xmax[()] - ymin = f['ym'] - ymin = ymin[()] - ymax = f['yM'] - ymax = ymax[()] - - # print(mag2[:,0]) - # xc, yc, zc, mag = mag2 - # mag_grid = griddata(np.column_stack([mag2[:,0], mag2[:,1]]), mag2[:,3], (xq, yq)) -except: - print('making mag_grid2.npz...') - from scipy.interpolate import griddata - # import data X | Y | Z | nT - with np.load('mag2.npz') as f: - print('mag2.npz found...') - mag2 = f['mag2'] - # xc, yc, zc, mag = np.loadtxt('./mag2.xyz', dtype=np.float32, unpack=True) - print(mag2[0,]) - xmin = np.nanmin(mag2[:,0],axis=0) - xmax = np.nanmax(mag2[:,0],axis=0) - ymin = np.nanmin(mag2[:,1],axis=0) - ymax = np.nanmax(mag2[:,1],axis=0) - - nx = int((xmax - xmin)/200.) - ny = int((ymax - ymin)/200.) - print(xmin,xmax,ymin,ymax,nx,ny) - xcoords, dx = np.linspace(xmin, xmax, nx, retstep=True) - ycoords, dy = np.linspace(ymin, ymax, ny, retstep=True) - xq, yq = np.meshgrid(xcoords, ycoords) - mag_grid = griddata(np.column_stack([mag2[:,0], mag2[:,1]]), mag2[:,3], (xq, yq),method='nearest') - # save grid - np.savez_compressed('mag_grid2.npz', data=mag_grid,xm=xmin,xM=xmax,ym=ymin,yM=ymax) - -#print(mag_grid.shape,xmin,xmax,ymin,ymax) -#plt.imshow(mag_grid, extent=(xmin, xmax, ymin, ymax), origin='lower') -#plt.show() -#exit() - - - - -## plt.imshow(mag_grid, extent=(xmin, xmax, ymin, ymax), origin='lower') -## initialise CurieGrid object -grid = pycurious.CurieGrid(mag_grid, xmin, xmax, ymin, ymax) - - -## Let's not!' -## let's pick a point in the centre of the study area -#xpt = xmin + (xmax-xmin)/2 -#ypt = ymin + (ymax-ymin)/2 -#print(xpt,ypt) -## get a subsection of the grid -#subgrid = grid.subgrid(xpt, ypt, 50000.) -#print(subgrid.shape) -## compute radial spectrum -#S, k, sigma2 = grid.radial_spectrum(subgrid, taper=None) -## fig, (ax1, ax2) = plt.subplots(1,2,figsize=(12,4)) -## ax1.plot(k, abs(S)) -##ax2.plot(sf, abs(S)) -#Zb,eZb = grid.Tanaka(S, k, sigma2,kmin=0.05, kmax=0.2) -#print(Zb,eZb) - -## INSTEAD -## Let's read a central point from file pts.xy -cx,cy=np.loadtxt('pts.xy',unpack=True) -f=open("CPD_pts.txt","w+") -for xpt, ypt in zip(cx,cy): - ## get a subsection of the grid - subgrid = grid.subgrid(xpt, ypt, 75000.) - if subgrid.shape[0] != subgrid.shape[1]: - continue - #f.write(str(xpt)) - # compute radial spectrum - try: - S, k, sigma2 = grid.radial_spectrum(subgrid, taper=None) - Zb,eZb = grid.Tanaka(S, k, sigma2,kmin=0.05, kmax=0.2) - #print(xpt,ypt,Zb,eZb) - f.write(' '.join([str(xpt),str(ypt),str(Zb),str(eZb),"\n"])) - except: - print('Error for ',xpt,ypt) - #break - -f.close() diff --git a/pycurious/Examples/Scripts/RosettePlot.sh b/pycurious/Examples/Scripts/RosettePlot.sh deleted file mode 100644 index 64d5fc7..0000000 --- a/pycurious/Examples/Scripts/RosettePlot.sh +++ /dev/null @@ -1,20 +0,0 @@ -#!/bin/bash - -oFile='RosetteTest.ps' - -# Several plots... -# plot of theta vs CPD - -J=' -JX8c/6c' -R=' -R0/180/-35/-15' -psbasemap $J $R -Ba30/a10g5::neWS -K > $oFile -cat iap_rosette.txt | psxy -R -J -O -K -W2p,blue>> $oFile -echo '90 -35 Azimuth (@+o@+)' | pstext -R -J -O -K -N -Ya-1.25c >> $oFile -echo '0 -25 CPD (km)' | pstext -R -J -O -K -N -F+a90 -Xa-1.25c >> $oFile - -psbasemap $J -R0/2/-35/-15 -B/a10g5::neWS -O -K -Y10c >> $oFile -echo '1 -23.7 -19.7 -22.3 -24.48 -29.09' | psxy -R -J -EY -G127 -O -K >> $oFile -echo '1 -23.7 -19.7 -22.3 -24.48 -29.09' | psxy -R -J -Sc0.2c -G127 -O -K >> $oFile - -# box & whisker -# fancy rosette...? \ No newline at end of file diff --git a/pycurious/Examples/Scripts/mag_grid2.npz 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z4S?bE)}+RGhg1$k-8H8*y(Pqn=7aCtr*uo+3jCd!&uB!Wv&|xAzpQ+}pcOjBEktff z%Y!0))Vf#XM`VGWHe7?8H`?27HPhrnxYx(8wOZ^9)j=c)S8LYlNbql@u}^Ktwi57j zd23~osETj=fl>`H14ndytx8C<&V@k5rgt-S)O>P@7D)!L)Mk6(tvb6FPQ0NJME1m^ZcD2{fqbzQxJ;P)8{?4#2HVO9q!BV>`aOJM3x z|G}1*Gw6GRGqt?r^`So}G`zc_zE)tSuTM56;xeR@gS&b!dppOR*T0KCRrNJPhh?dk z5r{lL52A5&n4@!C<^=>qodq6GyEuti5LoU^g$?f?&XRgyj;Hd6C^%?{?qkV0KJ`Kc z+)}dMeJIt9y&>-}cpIuX;VdpQ_w{+z^V}&inw!4uvJ{1sDJ%A?<@HQROwt?2HoD<8 z1(=?7TP%b{-%{ciDg*_6P>SSbxKGHJJw=0C0la26uO@3&Cgy5ibSxJ>5F2tDLoTbG ziMXx<`9C7b{lAD*6Yi$M z{~wY5GbgYA-*WQ$f0`3G1SaJFuGHCz85$KoG+5wY=>M+WSF!$k3k3hKgQ=0L(SJQp zMVbE-^`Fn;e=uNRf#5P<_xhh||0m`@EA_uI&Hsh@?;QUV^M8*+A^;8cKNa{-%>O-3 bNorth, y->East, z->Down. - Inclination is positive down and declination is measured with respect - to x (North). - - Examples - -------- + Args: + intensity : float or 1D array + The intensity (norm) of the vector + inc : float + The inclination of the vector (in degrees) + dec : float + The declination of the vector (in degrees) + + Returns: + vec : array = [x, y, z] + 3-component vector + + Notes: + Coordinate system is assumed to be x->North, y->East, z->Down. + Inclination is positive down and declination is measured with respect + to x (North). + + Examples: >>> import numpy >>> print ang2vec(3, 45, 45) [ 1.5 1.5 2.12132034] @@ -705,23 +728,20 @@ def dircos(inc, dec): Returns the 3 coordinates of a unit vector given its inclination and declination. - Parameters - ---------- - inc : float - The inclination of the vector (in degrees) - dec : float - The declination of the vector (in degrees) - - Returns - ------- - vect : list = [x, y, z] - The unit vector - - Notes - ----- - Coordinate system is assumed to be x->North, y->East, z->Down. - Inclination is positive down and declination is measured with respect - to x (North). + Args: + inc : float + The inclination of the vector (in degrees) + dec : float + The declination of the vector (in degrees) + + Returns: + vect : list + The unit vector = [x, y, z] + + Notes: + Coordinate system is assumed to be x->North, y->East, z->Down. + Inclination is positive down and declination is measured with respect + to x (North). """ d2r = np.pi/180.0 vect = [np.cos(d2r * inc) * np.cos(d2r * dec), \ diff --git a/pycurious/grid/__init__.py b/pycurious/grid/__init__.py deleted file mode 100644 index 24d24b9..0000000 --- a/pycurious/grid/__init__.py +++ /dev/null @@ -1,20 +0,0 @@ -""" -Copyright 2018 Ben Mather, Robert Delhaye - -This file is part of PyCurious. - -PyCurious is free software: you can redistribute it and/or modify -it under the terms of the GNU Lesser General Public License as published by -the Free Software Foundation, either version 3 of the License, or any later version. - -PyCurious is distributed in the hope that it will be useful, -but WITHOUT ANY WARRANTY; without even the implied warranty of -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -GNU Lesser General Public License for more details. - -You should have received a copy of the GNU Lesser General Public License -along with PyCurious. If not, see . -""" - -# -*- coding: utf-8 -*- -from .curie import * \ No newline at end of file diff --git a/pycurious/mapping/mapping.py b/pycurious/mapping.py similarity index 72% rename from pycurious/mapping/mapping.py rename to pycurious/mapping.py index a5f33bb..6513265 100644 --- a/pycurious/mapping/mapping.py +++ b/pycurious/mapping.py @@ -26,7 +26,7 @@ def transform_coordinates(x, y, epsg_in, epsg_out): """ Transform between any coordinate system. - Requires pyproj + Requires `pyproj` """ import pyproj proj_in = pyproj.Proj("+init=EPSG:"+str(epsg_in)) @@ -38,15 +38,17 @@ def convert_extent(extent_in, epsg_in, epsg_out): """ Transform extent from epsg_in to epsg_out - Parameters - ---------- - extent_in : bounding box [minX, maxX, minY, maxY] - epsg_in : CRS of extent - epsg_out : CRS of output - - Returns - ------- - extent_out : bounding box in new CRS + Args: + extent_in : tuple + bounding box [minX, maxX, minY, maxY] + epsg_in : int + CRS of extent + epsg_out : int + CRS of output + + Returns: + extent_out : tuple + bounding box in new CRS """ xmin, xmax, ymin, ymax = extent_in xi = [xmin, xmin, xmax, xmax] @@ -58,21 +60,25 @@ def convert_extent(extent_in, epsg_in, epsg_out): def trim(coords, data, extent, buffer_amount=0.0): """ - Grid a smaller section of a large dataset taking into + Trim a smaller section of a large dataset taking into consideration transformations into various coordinate reference systems (CRS) - Parameters - ---------- - coords : geographical / projected coordinates - data : values corresponding to coordinates - extent : box contained within the data - buffer : amount of buffer to include (default=0.0) - - Returns - ------- - coords_trim : trimmed coordinates - data_trim : trimmed data array + Args: + coords : array shape (n,2) + geographical / projected coordinates + data : array shape (n,) + values corresponding to coordinates + extent : tuple + bounding box to trim data + buffer : float + amount of buffer to include (default=0.0) + + Returns: + coords_trim : array shape (l,2) + trimmed coordinates + data_trim : array shape (l,2) + trimmed data array """ xmin, xmax, ymin, ymax = extent @@ -104,22 +110,26 @@ def grid(coords, data, extent, shape=None, epsg_in=None, epsg_out=None, **kwargs consideration transformations into various coordinate reference systems (CRS) - Parameters - ---------- - coords : geographical coordinates - data : values corresponding to coordinates - extent : box contained within the data in espg_out - coordinates - shape : size of the box (nrows,ncols) - : if None, shape is estimated from coords spacing - epsg_in : CRS of data (if transformation is required) - epsg_out : CRS of grid (if transformation is required) - kwargs : keyword arguments to pass to griddata from - : scipy.interpolate.griddata + Args: + coords : array shape (n,2) + geographical coordinates + data : array shape (n,) + values corresponding to coordinates + extent : tuple + box contained within the data in espg_out coordinates + shape : tuple (nrows,ncols) + size of the box, if None, shape is estimated from coords spacing + epsg_in : int + CRS of data (if transformation is required) + epsg_out : int + CRS of grid (if transformation is required) + kwargs : keyword arguments + keyword arguments to pass to griddata from + `scipy.interpolate.griddata` - Returns - ------- - grid : rectangular section of data bounded by extent + Returns: + grid : array shape (nrows, ncols) + rectangular section of data bounded by extent """ from scipy.interpolate import griddata xmin, xmax, ymin, ymax = extent @@ -177,15 +187,15 @@ def import_geotiff(file_path): Import a GeoTIFF to a numpy array and prints information of the Coordinate Reference System (CRS) - Parameters - ---------- - file_path : path to the GeoTIFF + Args: + file_path : str + path to the GeoTIFF - Returns - ------- - data : 2D numpy array - extent : extent in the projection of the GeoTIFF - e.g. [xmin, xmax, ymin, ymax] + Returns: + data : 2D array + extent : tuple + extent in the projection of the GeoTIFF + e.g. [xmin, xmax, ymin, ymax] """ from osgeo import gdal, osr @@ -214,13 +224,17 @@ def export_geotiff(file_path, array, extent, epsg): Export a GeoTIFF from a numpy array projected in a predefined Coordinate Reference System (CRS) - Parameters - ---------- - file_path : str, path to write the GeoTIFF - array : 2D numpy array - extent : extent in the projection of the GeoTIFF - e.g. [xmin, xmax, ymin, ymax] - epsg : int, CRS of the GeoTIFF + Args: + file_path : str + path to write the GeoTIFF + array: 2D array + array to save to GeoTiff + extent : tuple + extent in the projection of the GeoTIFF + e.g. [xmin, xmax, ymin, ymax] + epsg : int + CRS of the GeoTIFF + e.g. 4326 for WGS84 """ from osgeo import gdal, osr diff --git a/pycurious/mapping/__init__.py b/pycurious/mapping/__init__.py deleted file mode 100644 index e3c0dc5..0000000 --- a/pycurious/mapping/__init__.py +++ /dev/null @@ -1,24 +0,0 @@ -""" -Copyright 2018 Ben Mather, Robert Delhaye - -This file is part of PyCurious. - -PyCurious is free software: you can redistribute it and/or modify -it under the terms of the GNU Lesser General Public License as published by -the Free Software Foundation, either version 3 of the License, or any later version. - -PyCurious is distributed in the hope that it will be useful, -but WITHOUT ANY WARRANTY; without even the implied warranty of -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -GNU Lesser General Public License for more details. - -You should have received a copy of the GNU Lesser General Public License -along with PyCurious. If not, see . -""" - -# -*- coding: utf-8 -*- -from .mapping import transform_coordinates -from .mapping import convert_extent -from .mapping import trim -from .mapping import grid -from .mapping import import_geotiff \ No newline at end of file diff --git a/pycurious/optimise/optimise.py b/pycurious/optimise.py similarity index 58% rename from pycurious/optimise/optimise.py rename to pycurious/optimise.py index 4f80e48..6de0f10 100644 --- a/pycurious/optimise/optimise.py +++ b/pycurious/optimise.py @@ -17,7 +17,7 @@ """ # -*- coding: utf-8 -*- -from .. import CurieGrid, bouligand2009 +from .grid import CurieGrid, bouligand2009 import numpy as np import warnings from scipy.optimize import minimize @@ -34,18 +34,23 @@ class CurieOptimise(CurieGrid): Extends the CurieGrid class to include optimisation routines see scipy.optimize.minimize for a description of the algorithm - Parameters - ---------- - grid : 2D array of magnetic data - xmin : minimum x bound in metres - xmax : maximum x bound in metres - ymin : minimum y bound in metres - ymax : maximum y bound in metres + Args: + grid : 2D numpy array + 2D array of magnetic data + xmin : float + minimum x bound in metres + xmax : float + maximum x bound in metres + ymin : float + minimum y bound in metres + ymax : float + maximum y bound in metres - Attributes - ---------- - bounds : lower and upper bounds for beta, zt, dz, C - prior : dictionary of priors for beta, zt, dz, C + Attributes: + bounds : list of tuples + lower and upper bounds for beta, zt, dz, C + prior : dict + dictionary of priors for beta, zt, dz, C """ def __init__(self, grid, xmin, xmax, ymin, ymax, **kwargs): @@ -73,10 +78,10 @@ def add_prior(self, **kwargs): Assumes a normal distribution or define another distribution from scipy.stats - Usage - ----- - add_prior(beta=(p, sigma_p)) - add_prior(beta=scipy.stats.norm(p, sigma_p)) + Usage: + >>> add_prior(beta=(p, sigma_p)) + + >>> add_prior(beta=scipy.stats.norm(p, sigma_p)) """ for key in kwargs: @@ -111,13 +116,12 @@ def objective_routine(self, **kwargs): Evaluate the objective routine to find the misfit with priors Only keys stored in self.prior will be added to the total misfit - Example Usage - ------------- - objective_routine(beta=2.5) + Usage: + >>> objective_routine(beta=2.5) - Returns - ------- - misfit : sum of misfit (float) + Returns: + misfit : float + misfit integrated over all observations and priors """ c = 0.0 @@ -131,18 +135,16 @@ def objective_routine(self, **kwargs): def objective_function(self, x, x0, sigma_x0, *args): """ - Objective function used in objective_routine + Objective function used in `objective_routine` Evaluates the l2-norm misfit - Parameters - --------- - x : float, ndarray - x0 : float, ndarray - sigma_x0 : float, ndarray + Args: + x : float, ndarray + x0 : float, ndarray + sigma_x0 : float, ndarray - Returns - ------- - misfit : float + Returns: + misfit : float """ return 0.5*np.sum((x - x0)**2/sigma_x0**2) @@ -151,23 +153,25 @@ def min_func(self, x, kh, Phi, sigma_Phi): """ Function to minimise - Parameters - ---------- - x : array of variables [beta, zt, dz, C] - kh : wavenumbers [rad/km] - Phi : radial power spectrum - sigma_Phi : standard deviation of Phi - - Returns - ------- - misfit : sum of misfit (float) - - Notes - ----- - We purposely ignore all warnings raised by the bouligand2009 - function because some combinations of input parameters will - trigger an out-of-range warning that will crash the minimiser. - Instead, the misfit is set to a very large number when this occurs. + Args: + x : array shape (n,) + array of variables [beta, zt, dz, C] + kh : array shape (n,) + wavenumbers (rad/km) + Phi : array shape (n,) + radial power spectrum + sigma_Phi : array shape (n,) + standard deviation of Phi + + Returns: + misfit : float + sum of misfit (float) + + Notes: + We purposely ignore all warnings raised by the bouligand2009 + function because some combinations of input parameters will + trigger an out-of-range warning that will crash the minimiser. + Instead, the misfit is set to a very large number when this occurs. """ beta, zt, dz, C = x with warnings.catch_warnings() as w: @@ -187,26 +191,37 @@ def optimise(self, window, xc, yc, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.ha Find the optimal parameters of beta, zt, dz, C for a given centroid (xc,yc) and window size. - Parameters - ---------- - window : float - size of window in metres - xc : float - centroid x values - yc : float - centroid y values - beta : float - fractal parameter (starting value) - zt : float - top of magnetic layer (starting value) - dz : float - thickness of magnetic layer (starting value) - C : float - field constant (starting value) - taper : taper function (np.hanning is default) - : set to None for no taper function - process_subgrids : func - a custom function to process the subgrid - kwargs : keyword arguments to pass to radial_spectrum. - - Returns - ------- - beta : float - fractal parameters - zt : float - top of magnetic layer - dz : float - thickness of magnetic layer - C : float - field constant + Args: + window : float + size of window in metres + xc : float + centroid x values + yc : float + centroid y values + beta : float + fractal parameter (starting value) + zt : float + top of magnetic layer (starting value) + dz : float + thickness of magnetic layer (starting value) + C : float + field constant (starting value) + taper : taper (default=np.hanning) + taper function, set to None for no taper function + process_subgrids : function + a custom function to process the subgrid + kwargs : keyword arguments + to pass to radial_spectrum. + + Returns: + beta : float + fractal parameters + zt : float + top of magnetic layer + dz : float + thickness of magnetic layer + C : float + field constant """ if type(process_subgrid) == type(None): @@ -254,39 +269,42 @@ def parallelise_routine(self, window, xc_list, yc_list, func, *args, **kwargs): Supply the window size and lists of x,y coordinates to a function along with any additional arguments or keyword arguments. - Parameters - ---------- - window : float - size of window in metres - xc_list : array shape(l,) - centroid x values - yc_list : array shape(l,) - centroid y values - func : function to evaluate in parallel - args : additional arguments to pass to func - kwargs : additional keyword arguments to pass to func - - Returns - ------- - out : list (depends on output of func - see notes) - - Example usage - ------------- - An obvious use case is to compute the Curie depth for many - centroids in parallel. - - > self.parallelise_routine(window, xc_list, yc_list, self.optimise) + Args: + window : float + size of window in metres + xc_list : array shape (l,) + centroid x values + yc_list : array shape (l,) + centroid y values + func : function + Python function to evaluate in parallel + args : arguments + additional arguments to pass to func + kwargs : keyword arguments + additional keyword arguments to pass to func + + Returns: + out : list + (depends on output of func - see notes) + + Usage: + An obvious use case is to compute the Curie depth for many + centroids in parallel. + + >>> self.parallelise_routine(window, xc_list, yc_list, self.optimise) - Each centroid is assigned a new process and sent to a free processor - to compute. In this case, the output is separate lists of shape(l,) - for beta, zt, dz, and C. - + Each centroid is assigned a new process and sent to a free processor + to compute. In this case, the output is separate lists of shape(l,) + for beta, zt, dz, and C. - Another example is to parallelise the sensitivity analysis: + Another example is to parallelise the sensitivity analysis: - > self.parallelise_routine(window, xc_list, yc_list, self.sensitivity, nsim) + >>> self.parallelise_routine(window, xc_list, yc_list, self.sensitivity, nsim) - This time the output will be a list of lists for beta, zt, dz, and C - i.e. if nc=2 is the number of centroids and nsim=4 is the number of - simulations then separatee lists [[k1, k2, k3, k4], [k1, k2, k3, k4]] - will be returned for beta, zt, dz, and C. + This time the output will be a list of lists for beta, zt, dz, and C + i.e. if nc=2 is the number of centroids and nsim=4 is the number of + simulations then separatee lists [[k1, k2, k3, k4], [k1, k2, k3, k4]] + will be returned for beta, zt, dz, and C. """ n = len(xc_list) @@ -351,26 +369,38 @@ def optimise_routine(self, window, xc_list, yc_list, beta=3.0, zt=1.0, dz=10.0, Iterate through a list of centroids to compute the optimal values of beta, zt, dz, C for a given window size. - Parameters - ---------- - window : float - size of window in metres - xc_list : ndarray shape(l,) - centroid x values - yc_list : ndarray shape(l,) - centroid y values - beta : float - fractal parameter - zt : float - top of magnetic layer - dz : float - thickness of magnetic layer - C : float - field constant - taper : taper function (np.hanning is default) - : set to None for no taper function - process_subgrids : func - a custom function to process the subgrid - kwargs : keyword arguments to pass to radial_spectrum. - - Returns - ------- - beta : ndarray shape(l,) - fractal parameters - zt : ndarray shape(l,) - top of magnetic layer - dz : ndarray shape(l,) - thickness of magnetic layer - C : ndarray shape(l,) - field constant + Args: + window : float + size of window in metres + xc_list : ndarray shape (l,) + centroid x values + yc_list : ndarray shape (l,) + centroid y values + beta : float + fractal parameter + zt : float + top of magnetic layer + dz : float + thickness of magnetic layer + C : float + field constant + taper : function + taper function (default=np.hanning) + set to None for no taper function + process_subgrids : func + a custom function to process the subgrid + kwargs : keyword arguments + to pass to radial_spectrum. + + Returns: + beta : ndarray shape (l,) + fractal parameters + zt : ndarray shape (l,) + top of magnetic layer + dz : ndarray shape (l,) + thickness of magnetic layer + C : ndarray shape (l,) + field constant """ return self.parallelise_routine(window, xc_list, yc_list, self.optimise, beta, zt, dz, C, taper, process_subgrid, **kwargs) @@ -383,38 +413,49 @@ def metropolis_hastings(self, window, xc, yc, nsim, burnin, x_scale=None, beta=3 Evaluates a Markov-Chain for starting values of beta, zt, dz, C and returns the ensemble of model realisations. - Parameters - ---------- - window : float - size of window in metres - xc : float - centroid x values - yc : float - centroid y values - nsim : int - number of simulations - burnin : int - number of burn-in simulations before to nsim - x_scale : float(4) (optional) - scaling factor for new proposals - default is [1,1,1,1] for [beta, zt, dz, C] - see notes - beta : float - fractal parameter (starting value) - zt : float - top of magnetic layer (starting value) - dz : float - thickness of magnetic layer (starting value) - C : float - field constant (starting value) - - Returns - ------- - beta : ndarray shape(nsim,) - fractal parameter - zt : ndarray shape(nsim,) - top of magnetic layer - dz : ndarray shape(nsim,) - thickness of magnetic layer - C : ndarray shape(nsim,) - field constant - - Notes - ----- - nsim, burnin, and x_scale should be tweaked for optimal performance - Use starting values of beta, zt, dz, C relatively close to the solution - - C can easily found from the mean of the radial power spectrum. - - During the burn-in stage we apply tempering to the PDF to iterate closer - towards the solution. This has the effect of smoothing out the posterior - so that minima can be more easily found. This is necessary here because - large portions of the posterior probability are zero. - see see Sambridge 2013, DOI:10.1093/gji/ggt342 for more information. + Args: + window : float + size of window in metres + xc : float + centroid x values + yc : float + centroid y values + nsim : int + number of simulations + burnin : int + number of burn-in simulations before to nsim + x_scale: float(4) (optional) + scaling factor for new proposals + default is [1,1,1,1] for [beta, zt, dz, C] - see notes + beta : float + fractal parameter (starting value) + zt : float + top of magnetic layer (starting value) + dz : float + thickness of magnetic layer (starting value) + C : float + field constant (starting value) + + Returns: + beta : ndarray shape (nsim,) + fractal parameter + zt : ndarray shape (nsim,) + top of magnetic layer + dz : ndarray shape (nsim,) + thickness of magnetic layer + C : ndarray shape (nsim,) + field constant + + Notes: + nsim, burnin, and x_scale should be tweaked for optimal performance + Use starting values of beta, zt, dz, C relatively close to the solution + - C can easily found from the mean of the radial power spectrum. + + During the burn-in stage we apply tempering to the PDF to iterate closer + towards the solution. This has the effect of smoothing out the posterior + so that minima can be more easily found. This is necessary here because + large portions of the posterior probability are zero. + see see Sambridge 2013, DOI:10.1093/gji/ggt342 for more information. """ if type(process_subgrid) == type(None): # dummy function @@ -481,25 +522,36 @@ def sensitivity(self, window, xc, yc, nsim, beta=3.0, zt=1.0, dz=10.0, C=5.0, ta standard deviation of beta, zt, dz, C by perturbing their prior distributions (if provided by the user - see add_prior). - Parameters - ---------- - nsim : int - number of Monte Carlo simulations - window : float - size of window in metres - xc : float - centroid x values - yc : float - centroid y values - nsim : int - number of simulations - beta : float - starting fractal parameter - zt : float - starting top of magnetic layer - dz : float - starting thickness of magnetic layer - C : float - starting field constant - - - Returns - ------- - beta : ndarray shape(nsim,) - fractal parameters - zt : ndarray shape(nsim,) - top of magnetic layer - dz : ndarray shape(nsim,) - thickness of magnetic layer - C : ndarray shape(nsim,) - field constant + Args: + nsim : int + number of Monte Carlo simulations + window : float + size of window in metres + xc : float + centroid x values + yc : float + centroid y values + nsim : int + - number of simulations + beta : float + starting fractal parameter + zt : float + starting top of magnetic layer + dz : float + starting thickness of magnetic layer + C : float + starting field constant + + + Returns: + beta : ndarray shape (nsim,) + fractal parameters + zt : ndarray shape (nsim,) + top of magnetic layer + dz : ndarray shape (nsim,) + thickness of magnetic layer + C : ndarray shape (nsim,) + field constant """ if type(process_subgrid) == type(None): # dummy function diff --git a/pycurious/optimise/__init__.py b/pycurious/optimise/__init__.py deleted file mode 100644 index 79ef49b..0000000 --- a/pycurious/optimise/__init__.py +++ /dev/null @@ -1,20 +0,0 @@ -""" -Copyright 2018 Ben Mather, Robert Delhaye - -This file is part of PyCurious. - -PyCurious is free software: you can redistribute it and/or modify -it under the terms of the GNU Lesser General Public License as published by -the Free Software Foundation, either version 3 of the License, or any later version. - -PyCurious is distributed in the hope that it will be useful, -but WITHOUT ANY WARRANTY; without even the implied warranty of -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -GNU Lesser General Public License for more details. - -You should have received a copy of the GNU Lesser General Public License -along with PyCurious. If not, see . -""" - -# -*- coding: utf-8 -*- -from .optimise import * \ No newline at end of file diff --git a/pycurious/parallel/parallel.py b/pycurious/parallel.py similarity index 99% rename from pycurious/parallel/parallel.py rename to pycurious/parallel.py index caa4661..cb75af7 100644 --- a/pycurious/parallel/parallel.py +++ b/pycurious/parallel.py @@ -19,7 +19,7 @@ # -*- coding: utf-8 -*- import numpy as np import warnings -from ..optimise import CurieOptimise +from .optimise import CurieOptimise try: range=xrange except: pass diff --git a/pycurious/parallel/__init__.py b/pycurious/parallel/__init__.py deleted file mode 100644 index cfcac58..0000000 --- a/pycurious/parallel/__init__.py +++ /dev/null @@ -1,20 +0,0 @@ -""" -Copyright 2018 Ben Mather, Robert Delhaye - -This file is part of PyCurious. - -PyCurious is free software: you can redistribute it and/or modify -it under the terms of the GNU Lesser General Public License as published by -the Free Software Foundation, either version 3 of the License, or any later version. - -PyCurious is distributed in the hope that it will be useful, -but WITHOUT ANY WARRANTY; without even the implied warranty of -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -GNU Lesser General Public License for more details. - -You should have received a copy of the GNU Lesser General Public License -along with PyCurious. If not, see . -""" - -# -*- coding: utf-8 -*- -from .parallel import * \ No newline at end of file diff --git a/pycurious/therm/therm.py b/pycurious/therm.py similarity index 100% rename from pycurious/therm/therm.py rename to pycurious/therm.py diff --git a/pycurious/therm/__init__.py b/pycurious/therm/__init__.py deleted file mode 100644 index f5020cb..0000000 --- a/pycurious/therm/__init__.py +++ /dev/null @@ -1,20 +0,0 @@ -""" -Copyright 2018 Ben Mather, Robert Delhaye - -This file is part of PyCurious. - -PyCurious is free software: you can redistribute it and/or modify -it under the terms of the GNU Lesser General Public License as published by -the Free Software Foundation, either version 3 of the License, or any later version. - -PyCurious is distributed in the hope that it will be useful, -but WITHOUT ANY WARRANTY; without even the implied warranty of -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -GNU Lesser General Public License for more details. - -You should have received a copy of the GNU Lesser General Public License -along with PyCurious. If not, see . -""" - -# -*- coding: utf-8 -*- -from .therm import * \ No newline at end of file diff --git a/setup.py b/setup.py index 0f266bb..da6e6cd 100644 --- a/setup.py +++ b/setup.py @@ -28,15 +28,10 @@ author = "Ben Mather", author_email = "brmather1@gmail.com", url = "https://github.com/brmather/pycurious", - version = "0.3", + version = "0.4", description = "Python tool for computing the Curie depth from magnetic data", ext_modules = cythonize([ext]), - packages = ['pycurious', - 'pycurious.grid', - 'pycurious.optimise', - 'pycurious.mapping', - 'pycurious.parallel', - 'pycurious.therm'], + packages = ['pycurious'], package_data = {'pycurious': ['Examples/data/*', 'Examples/*.ipynb', 'Examples/Notebooks/Tanaka/*.ipynb', @@ -45,8 +40,6 @@ classifiers = ['Programming Language :: Python :: 2', 'Programming Language :: Python :: 2.7', 'Programming Language :: Python :: 3', - 'Programming Language :: Python :: 3.3', - 'Programming Language :: Python :: 3.4', 'Programming Language :: Python :: 3.5', 'Programming Language :: Python :: 3.6', 'Programming Language :: Python :: 3.7'] From 24704c922fa6121c34e5133553f803e224d53a6f Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Tue, 4 Jun 2019 00:32:11 +1000 Subject: [PATCH 052/170] Added HtML documentation for deployment on GitHub pages --- docs/documentation.html | 180 +++ docs/grid.html | 2452 +++++++++++++++++++++++++++++++++++++++ docs/index.html | 128 ++ docs/mapping.html | 714 ++++++++++++ docs/optimise.html | 2141 ++++++++++++++++++++++++++++++++++ docs/parallel.html | 689 +++++++++++ docs/therm.html | 1216 +++++++++++++++++++ 7 files changed, 7520 insertions(+) create mode 100644 docs/documentation.html create mode 100644 docs/grid.html create mode 100644 docs/index.html create mode 100644 docs/mapping.html create mode 100644 docs/optimise.html create mode 100644 docs/parallel.html create mode 100644 docs/therm.html diff --git a/docs/documentation.html b/docs/documentation.html new file mode 100644 index 0000000..b33100b --- /dev/null +++ b/docs/documentation.html @@ -0,0 +1,180 @@ + + + + + + +pycurious.documentation API documentation + + + + + + + + + +

          +
          +
          +

          Module pycurious.documentation

          +
          +
          +

          Copyright 2018 Ben Mather, Robert Delhaye

          +

          This file is part of PyCurious.

          +

          PyCurious is free software: you can redistribute it and/or modify +it under the terms of the GNU Lesser General Public License as published by +the Free Software Foundation, either version 3 of the License, or any later version.

          +

          PyCurious is distributed in the hope that it will be useful, +but WITHOUT ANY WARRANTY; without even the implied warranty of +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. +See the +GNU Lesser General Public License for more details.

          +

          You should have received a copy of the GNU Lesser General Public License +along with PyCurious. +If not, see http://www.gnu.org/licenses/.

          +
          +Source code +
          """
          +Copyright 2018 Ben Mather, Robert Delhaye
          +
          +This file is part of PyCurious.
          +
          +PyCurious is free software: you can redistribute it and/or modify
          +it under the terms of the GNU Lesser General Public License as published by
          +the Free Software Foundation, either version 3 of the License, or any later version.
          +
          +PyCurious is distributed in the hope that it will be useful,
          +but WITHOUT ANY WARRANTY; without even the implied warranty of
          +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
          +GNU Lesser General Public License for more details.
          +
          +You should have received a copy of the GNU Lesser General Public License
          +along with PyCurious.  If not, see <http://www.gnu.org/licenses/>.
          +"""
          +
          +import pkg_resources as _pkg_resources
          +from distutils import dir_util as _dir_util
          +import os
          +
          +
          +def install_documentation(path="./PyCurious-Examples"):
          +    """
          +    Install the examples for PyCurious in the given location.
          +
          +    WARNING: If the path exists, the files will be written into the path
          +    and will overwrite any existing files with which they collide. The default
          +    path ("./PyCurious-Examples") is chosen to make collision less likely/problematic
          +
          +    The documentation for PyCurious is in the form of jupyter notebooks.
          +
          +    Some dependencies exist for the notebooks to be useful:
          +
          +       - matplotlib: for some diagrams
          +       - cartopy: for mapping and visualisation
          +       - pyepsg: for converting between map projections
          +
          +    PyCurious dependencies may be explicitly imported in the notebooks including:
          +
          +       - numpy
          +       - scipy
          +
          +    """
          +
          +    Notebooks_Path = _pkg_resources.resource_filename("pycurious", os.path.join("Examples"))
          +
          +    ct = _dir_util.copy_tree(Notebooks_Path, path, preserve_mode=1, preserve_times=1, preserve_symlinks=1, update=0, verbose=1, dry_run=0)
          +
          +    return
          +
          +
          +
          +
          +
          +
          +
          +

          Functions

          +
          +
          +def install_documentation(path='./PyCurious-Examples') +
          +
          +

          Install the examples for PyCurious in the given location.

          +

          WARNING: If the path exists, the files will be written into the path +and will overwrite any existing files with which they collide. The default +path ("./PyCurious-Examples") is chosen to make collision less likely/problematic

          +

          The documentation for PyCurious is in the form of jupyter notebooks.

          +

          Some dependencies exist for the notebooks to be useful:

          +
            +
          • matplotlib: for some diagrams
          • +
          • cartopy: for mapping and visualisation
          • +
          • pyepsg: for converting between map projections
          • +
          +

          PyCurious dependencies may be explicitly imported in the notebooks including:

          +
            +
          • numpy
          • +
          • scipy
          • +
          +
          +Source code +
          def install_documentation(path="./PyCurious-Examples"):
          +    """
          +    Install the examples for PyCurious in the given location.
          +
          +    WARNING: If the path exists, the files will be written into the path
          +    and will overwrite any existing files with which they collide. The default
          +    path ("./PyCurious-Examples") is chosen to make collision less likely/problematic
          +
          +    The documentation for PyCurious is in the form of jupyter notebooks.
          +
          +    Some dependencies exist for the notebooks to be useful:
          +
          +       - matplotlib: for some diagrams
          +       - cartopy: for mapping and visualisation
          +       - pyepsg: for converting between map projections
          +
          +    PyCurious dependencies may be explicitly imported in the notebooks including:
          +
          +       - numpy
          +       - scipy
          +
          +    """
          +
          +    Notebooks_Path = _pkg_resources.resource_filename("pycurious", os.path.join("Examples"))
          +
          +    ct = _dir_util.copy_tree(Notebooks_Path, path, preserve_mode=1, preserve_times=1, preserve_symlinks=1, update=0, verbose=1, dry_run=0)
          +
          +    return
          +
          +
          +
          +
          +
          +
          +
          + +
          + + + + + \ No newline at end of file diff --git a/docs/grid.html b/docs/grid.html new file mode 100644 index 0000000..2dba02d --- /dev/null +++ b/docs/grid.html @@ -0,0 +1,2452 @@ + + + + + + +pycurious.grid API documentation + + + + + + + + + +
          +
          +
          +

          Module pycurious.grid

          +
          +
          +

          Copyright 2018 Ben Mather, Robert Delhaye

          +

          This file is part of PyCurious.

          +

          PyCurious is free software: you can redistribute it and/or modify +it under the terms of the GNU Lesser General Public License as published by +the Free Software Foundation, either version 3 of the License, or any later version.

          +

          PyCurious is distributed in the hope that it will be useful, +but WITHOUT ANY WARRANTY; without even the implied warranty of +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. +See the +GNU Lesser General Public License for more details.

          +

          You should have received a copy of the GNU Lesser General Public License +along with PyCurious. +If not, see http://www.gnu.org/licenses/.

          +
          +Source code +
          """
          +Copyright 2018 Ben Mather, Robert Delhaye
          +
          +This file is part of PyCurious.
          +
          +PyCurious is free software: you can redistribute it and/or modify
          +it under the terms of the GNU Lesser General Public License as published by
          +the Free Software Foundation, either version 3 of the License, or any later version.
          +
          +PyCurious is distributed in the hope that it will be useful,
          +but WITHOUT ANY WARRANTY; without even the implied warranty of
          +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
          +GNU Lesser General Public License for more details.
          +
          +You should have received a copy of the GNU Lesser General Public License
          +along with PyCurious.  If not, see <http://www.gnu.org/licenses/>.
          +"""
          +
          +# -*- coding: utf-8 -*-
          +import numpy as np
          +from scipy.special import gamma, kv, lambertw
          +from scipy.optimize import minimize
          +from scipy.signal import tukey
          +import warnings
          +
          +try: range = xrange
          +except: pass
          +
          +
          +class CurieGrid(object):
          +    """
          +    Accepts a 2D array and Cartesian coordinates specifying the
          +    bounding box of the array
          +
          +    Grid must be projected in metres
          +
          +    Args:
          +     grid : 2D array of magnetic data
          +     xmin : minimum x bound in metres
          +     xmax : maximum x bound in metres
          +     ymin : minimum y bound in metres
          +     ymax : maximum y bound in metres
          +    """
          +    def __init__(self, grid, xmin, xmax, ymin, ymax):
          +        
          +        self.data = np.array(grid)
          +        ny, nx = self.data.shape
          +        self.xmin, self.xmax = xmin, xmax
          +        self.ymin, self.ymax = ymin, ymax
          +        self.xcoords, dx = np.linspace(xmin, xmax, nx, retstep=True)
          +        self.ycoords, dy = np.linspace(ymin, ymax, ny, retstep=True)
          +        self.nx, self.ny = nx, ny
          +        self.dx, self.dy = dx, dy
          +
          +        if abs(dx - dy) > 1.0:
          +            warnings.warn("node spacing should be identical {}".format((dx,dy)), RuntimeWarning)
          +
          +
          +    def subgrid(self, window, xc, yc):
          +        """
          +        Extract a subgrid from the data at a window around
          +        the point (xc,yc)
          +        
          +        Args:
          +            xc : float
          +                x coordinate
          +            yc : float
          +                y coordinate
          +            window : float
          +                size of window in metres
          +
          +        Returns:
          +            data : 2D array
          +                subgrid encompassing window size
          +        """
          +
          +        # check in coordinate in grid
          +        if xc < self.xmin or xc > self.xmax or yc < self.ymin or yc > self.ymax:
          +            raise ValueError("Point ({},{}) outside data range".format(xc,yc))
          +
          +        # find nearest index to xc,yc
          +        ix = np.abs(self.xcoords - xc).argmin()
          +        iy = np.abs(self.ycoords - yc).argmin()
          +
          +        nw = int(round(window/self.dx))
          +        n2w = nw//2
          +
          +        # extract a square window from the data
          +        imin = ix - n2w
          +        imax = ix + n2w + 1
          +        jmin = iy - n2w
          +        jmax = iy + n2w + 1
          +
          +        # safeguard if window size is larger than grid
          +        imin = max(imin, 0)
          +        imax = min(imax, self.nx)
          +        jmin = max(jmin, 0)
          +        jmax = min(jmax, self.ny)
          +        
          +        data = self.data[jmin:jmax, imin:imax]
          +
          +        return data
          +
          +
          +    def create_centroid_list(self, window, spacingX=None, spacingY=None):
          +        """
          +        Create a list of xc,yc values to extract subgrids.
          +
          +        Args:
          +            window : float
          +                size of the windows in metres
          +            spacingX : float (optional)
          +                specify spacing in metres in the X direction
          +                will default to maximum X resolution
          +            spacingY : float (optional)
          +                specify spacing in metres in the Y direction
          +                will default to maximum Y resolution
          +
          +        Returns:
          +            xc_list : 1D array
          +                array of x coordinates
          +            yc_list : 1D array
          +                array of y coordinates
          +        """
          +        
          +        nx, ny = self.nx, self.ny
          +        xcoords = self.xcoords
          +        ycoords = self.ycoords
          +        
          +        nw = int(round(window/self.dx))
          +        n2w = nw//2
          +        
          +        # this is the densest spacing possible given the data
          +        xc = xcoords[n2w:-n2w]
          +        yc = ycoords[n2w:-n2w]
          +        
          +        # but we can alter it if required
          +        if type(spacingX) != type(None):
          +            xc = np.arange(xc.min(), xc.max(), spacingX)
          +        if type(spacingY) != type(None):
          +            yc = np.arange(yc.min(), yc.max(), spacingY)
          +
          +        xq, yq = np.meshgrid(xc, yc)
          +            
          +        return xq.ravel(), yq.ravel()
          +
          +
          +    def remove_trend_linear(self, data):
          +        """
          +        Remove the best-fitting linear trend from the data
          +
          +        This may come in handy if the magnetic data has not been
          +        reduced to the pole.
          +
          +        Args:
          +            data : 2D numpy array
          +
          +        Returns:
          +         data : 2D numpy array
          +        """
          +        data = data.copy()
          +        nr, nc = data.shape
          +        xq, yq = np.meshgrid(np.arange(0, nc), np.arange(0, nr))
          +
          +        A = np.column_stack((x.flatten(), y.flatten(), np.ones(x.size)))
          +        c, resid, rank, sigma = np.linalg.lstsq(A, data.flatten())
          +
          +        data.flat[:] -= np.dot(A, c)
          +        return data
          +
          +    def radial_spectrum(self, subgrid, taper=np.hanning, scale=0.001, **kwargs):
          +        """
          +        Compute the radial spectrum for a square grid.
          +
          +        Args:
          +            subgrid : 2D array
          +                window of the original data (see subgrid method)
          +            taper : function (default=np.hanning)
          +                taper function, set to None for no taper function
          +            scale : float (default: 0.001)
          +                scaling factor to get k into rad/km
          +            kwargs : keyword arguments
          +                keyword arguments to pass to `taper`
          +
          +        Returns:
          +            k : 1D array shape (n,)
          +                wavenumber in rad/km
          +            Phi : 1D array shape (n,)
          +                Radial power spectrum
          +            sigma_Phi : 1D array shape (n,)
          +                Standard deviation of Phi
          +        """
          +
          +        data = subgrid
          +        nr, nc = data.shape
          +        nw = nr
          +
          +        if nr != nc:
          +            warnings.warn("subgrid is not square {}".format((nr,nc)), RuntimeWarning)
          +
          +
          +        # control taper
          +        if type(taper) == type(None):
          +            vtaper = 1.0
          +        else:
          +            rt = taper(nr, **kwargs)
          +            ct = taper(nc, **kwargs)
          +            xq, yq = np.meshgrid(ct, rt)
          +            vtaper = xq*yq
          +
          +        dx_scale = self.dx*scale
          +        dk = 2.0*np.pi/(nw - 1)/dx_scale
          +
          +        # fast Fourier transform and shift
          +        FT = np.abs(np.fft.fft2(data*vtaper))
          +        FT = np.fft.fftshift(FT)
          +
          +        kbins = np.arange(dk, dk*nw/2, dk)
          +        nbins = kbins.size - 1
          +
          +        S = np.empty(nbins)
          +        k = np.empty(nbins)
          +        sigma = np.empty(nbins)
          +
          +        i0 = int((nw - 1)//2)
          +        ix, iy = np.mgrid[0:nw,0:nw]
          +        kk = np.hypot((ix - i0)*dk, (iy - i0)*dk)
          +
          +        for i in range(0, nbins):
          +            mask = np.logical_and(kk >= kbins[i], kk <= kbins[i+1])
          +            rr = 2.0*np.log(FT[mask])
          +            S[i] = rr.mean()
          +            k[i] = kk[mask].mean()
          +            sigma[i] = np.std(rr)
          +
          +        return k, S, sigma
          +
          +
          +    def radial_spectrum_log(self, subgrid, taper=np.hanning, scale=0.001, **kwargs):
          +        """
          +        Compute the log of the radial spectrum for a square grid.
          +
          +        Args:
          +         subgrid : 2D array
          +            window of the original data (see subgrid method)
          +         taper : function (default=np.hanning)
          +            taper function, set to None for no taper function
          +         scale : float (detault=0.001)
          +            scaling factor to get k into rad/km
          +         kwargs : keyword arguments
          +            keyword arguments to pass to `taper`
          +
          +        Returns:
          +            k : 1D array shape (n,)
          +                wavenumber in rad/km
          +            lnPhi : 1D array
          +                log of the radial power spectrum in ln(sqrt(S))
          +            lnsigma_Phi : 1D array
          +                standard deviation of lnPhi
          +        """
          +
          +        data = subgrid
          +        nr, nc = data.shape
          +        nw = nr
          +
          +        if nr != nc:
          +            warnings.warn("subgrid is not square {}".format((nr,nc)), RuntimeWarning)
          +
          +
          +        # control taper
          +        if type(taper) == type(None):
          +            vtaper = 1.0
          +        else:
          +            rt = taper(nr, **kwargs)
          +            ct = taper(nc, **kwargs)
          +            xq, yq = np.meshgrid(ct, rt)
          +            vtaper = xq*yq
          +
          +        dx_scale = self.dx*scale
          +        dk = 2.0*np.pi/(nw - 1)/dx_scale
          +
          +        # fast Fourier transform and shift
          +        FT = np.abs(np.fft.fft2(data*vtaper))
          +        FT = np.fft.fftshift(FT)
          +
          +        kbins = np.arange(dk, dk*nw/2, dk)
          +        nbins = kbins.size - 1
          +
          +        S = np.empty(nbins)
          +        k = np.empty(nbins)
          +        sigma = np.empty(nbins)
          +
          +        i0 = int((nw - 1)//2)
          +        ix, iy = np.mgrid[0:nw,0:nw]
          +        kk = np.hypot((ix - i0)*dk, (iy - i0)*dk)
          +
          +        for i in range(0, nbins):
          +            mask = np.logical_and(kk >= kbins[i], kk <= kbins[i+1])
          +            rr = np.log(np.sqrt(FT[mask]))
          +            S[i] = rr.mean()
          +            k[i] = kk[mask].mean()
          +            sigma[i] = np.std(rr)
          +
          +        return k, S, sigma
          +        
          +        
          +    def azimuthal_spectrum(self, subgrid, taper=np.hanning, scale=0.001, theta=5.0, **kwargs):
          +        """
          +        Compute azimuthal spectrum for a square grid.
          +
          +        Args:
          +            subgrid : 2D array
          +                window of the original data (see subgrid method)
          +            taper : function (default=np.hanning)
          +                taper function, set to None for no taper function
          +            scale : float (default=0.001)
          +                scaling factor to get k into rad/km
          +            theta : float
          +                angle increment in degrees
          +            args : arguments
          +                arguments o pass to taper
          +
          +        Returns:
          +            k : 1D array shape (n,)
          +                wavenumber in rad/km
          +            Phi : 1D array shape (n,)
          +                Radial power spectrum
          +            sigma_Phi : 1D array shape (n,)
          +                Standard deviation of Phi
          +        """
          +        from pycurious import radon
          +        data = subgrid
          +        nr, nc = data.shape
          +        nw = nr
          +
          +        if nr != nc:
          +            raise RuntimeWarning("subgrid is not square {}".format((nr,nc)))
          +
          +        dx_scale = self.dx*scale
          +        dk = 2.0*np.pi/(nw - 1)/dx_scale
          +
          +        kbins = np.arange(dk, dk*nw/2, dk)
          +
          +        dtheta = np.arange(0.0, 180.0, theta)
          +        sinogram = radon.radon2d(data, np.pi*dtheta/180.0)
          +        S = np.zeros((dtheta.size, kbins.size))
          +        sigma2 = np.zeros((dtheta.size, kbins.size))
          +
          +        # control taper
          +        if taper is None:
          +            vtaper = 1.0
          +        else:
          +            vtaper = taper(sinogram.shape[0], **kwargs)
          +
          +        nk = 1 + 2*kbins.size
          +        for i in range(0, dtheta.size):
          +            PSD = np.abs(np.fft.fft(vtaper*sinogram[:,i], n=nk))
          +            S[i,:] = np.log( np.sqrt(PSD[1:kbins.size+1] ))
          +        
          +        return kbins, S, dtheta
          +
          +
          +    def reduce_to_pole(self, data, inc, dec, sinc=None, sdec=None):
          +        r"""
          +        Reduce total field magnetic anomaly data to the pole.
          +
          +        The reduction to the pole if a phase transformation that can be
          +        applied to total field magnetic anomaly data. It simulates how
          +        the data would be if both the Geomagnetic field and the
          +        magnetization of the source were vertical (Blakely, 1996).
          +
          +        Args:
          +            data : 1D array
          +                the total field anomaly data at each point.
          +            inc : float / 1D array
          +                inclination of the inducing Geomagnetic field
          +            dec : float / 1D array
          +                declination of the inducing Geomagnetic field
          +            sinc : float / 1D array (optional)
          +                inclination of the total magnetization of the anomaly source
          +            sdec : float / 1D array (optional)
          +                declination of the total magnetization of the anomaly source
          +                The total magnetization is the vector sum of the
          +                induced and remanent magnetization. If there is only induced
          +                magnetization, use the *inc* and *dec* of the Geomagnetic field.
          +
          +        Returns:
          +            rtp : 2D array
          +                the data reduced to the pole.
          +        
          +        References:
          +            Blakely, R. J. (1996), Potential Theory in Gravity and Magnetic
          +            Applications, Cambridge University Press.
          +
          +        Notes:
          +            This functions performs the reduction in the frequency domain
          +            (using the FFT). The transform filter is (in the freq domain):
          +                RTP(k_x, k_y) = \frac{|k|}{
          +                    a_1 k_x^2 + a_2 k_y^2 + a_3 k_x k_y +
          +                    i|k|(b_1 k_x + b_2 k_y)}
          +            in which k_x and k_y are the wave-numbers in the x and y
          +            directions and
          +                |k| = \sqrt{k_x^2 + k_y^2} \\
          +                a_1 = m_z f_z - m_x f_x \\
          +                a_2 = m_z f_z - m_y f_y \\
          +                a_3 = -m_y f_x - m_x f_y \\
          +                b_1 = m_x f_z + m_z f_x \\
          +                b_2 = m_y f_z + m_z f_y
          +            \mathbf{m} = (m_x, m_y, m_z)` is the unit-vector of the total
          +            magnetization of the source and
          +            \mathbf{f} = (f_x, f_y, f_z)` is the unit-vector of the
          +            Geomagnetic field.
          +        """
          +        nr, nc = data.shape
          +
          +        if nr != nc:
          +            warnings.warn("subgrid is not square {}".format((nr,nc)), RuntimeWarning)
          +
          +        fx, fy, fz = ang2vec(1.0, inc, dec)
          +        if sinc is None or sdec is None:
          +            mx, my, mz = fx, fy, fz
          +        else:
          +            mx, my, mz = ang2vec(1.0, sinc, sdec)
          +
          +        kx, ky = [k for k in _fftfreqs(self.dx, self.dy, data.shape)]
          +        kz = np.hypot(kx, ky)
          +
          +        a1 = mz*fz - mx*fx
          +        a2 = mz*fz - my*fy
          +        a3 = -my*fx - mx*fy
          +        b1 = mx*fz + mz*fx
          +        b2 = my*fz + mz*fy
          +
          +        # The division gives a RuntimeWarning because of the zero frequency term.
          +        # This suppresses the warning.
          +        with np.errstate(divide='ignore', invalid='ignore'):
          +            rtp = (kz)/(a1*kx**2 + a2*ky**2 + a3*kx*ky + \
          +                            1j*np.sqrt(kz)*(b1*kx + b2*ky))
          +        
          +        rtp[0, 0] = 0
          +        ft_pole = rtp*np.fft.fft2(data)
          +        return np.real(np.fft.ifft2(ft_pole))
          +
          +
          +    def upward_continuation(self, data, height):
          +        r"""
          +        Upward continuation of potential field data.
          +
          +        Calculates the continuation through the Fast Fourier Transform in
          +        the wavenumber domain (Blakely, 1996):
          +
          +            F\{h_{up}\} = F\{h\} e^{-\Delta z |k|}
          +
          +        and then transformed back to the space domain. :math:`h_{up}` is the
          +        upward continue data, \Delta z is the height increase, F denotes
          +        the Fourier Transform, |k| is the wavenumber modulus.
          +
          +        Args:
          +            data   : 2D array
          +                potential field at the grid points
          +            height : float
          +                height increase (delta z) in meters.
          +        
          +        Returns:
          +            cont : array
          +                upward continued data
          +
          +        Notes:
          +            It is not possible to get the FFT of a masked grid. The default
          +            :func:`fatiando.gridder.interp` call using minimum curvature will
          +            not be suitable.  Use extrapolate=True or algorithm='nearest' to
          +            get an unmasked grid.
          +
          +        References:
          +            Blakely, R. J. (1996), Potential Theory in Gravity and Magnetic
          +            Applications, Cambridge University Press.
          +        """
          +        nr, nc = data.shape
          +
          +        if nr != nc:
          +            warnings.warn("subgrid is not square {}".format((nr,nc)), RuntimeWarning)
          +
          +        if height <= 0:
          +            warnings.warn("Using 'height' <= 0 means downward continuation, " +
          +                          "which is known to be unstable.")
          +
          +        fx = 2.0*np.pi*np.fft.fftfreq(nr, self.dx)
          +        fy = 2.0*np.pi*np.fft.fftfreq(nc, self.dy)
          +
          +        kx, ky = np.meshgrid(fy, fx)[::-1]
          +        kz = np.hypot(kx, ky)
          +
          +        upcont_ft = np.fft.fft2(data)*np.exp(-height*kz)
          +        cont = np.real(np.fft.ifft2(upcont_ft))
          +        return cont
          +
          +
          +# Helper functions to calculate Curie depth
          +
          +def bouligand2009(kh, beta, zt, dz, C):
          +    """
          +    Calculate the synthetic radial power spectrum of
          +    magnetic anomalies
          +
          +    Equation (4) of Bouligand et al. (2009)
          +
          +    Args:
          +        kh : float / 1D array
          +            wavenumber in rad/km
          +        beta : float / 1D array
          +            fractal parameter
          +        zt : float / 1D array
          +            top of magnetic sources
          +        dz : float / 1D array
          +            thickness of magnetic sources
          +        C : float 1D array
          +            field constant (Maus et al., 1997)
          +
          +    Returns:
          +        Phi : float / 1D array
          +            radial power spectrum of magnetic anomalies
          +
          +    References:
          +        Bouligand, C., J. M. G. Glen, and R. J. Blakely (2009), Mapping Curie
          +        temperature depth in the western United States with a fractal model for
          +        crustal magnetization, J. Geophys. Res., 114, B11104,
          +        doi:10.1029/2009JB006494
          +
          +        Maus, S., D. Gordon, and D. Fairhead (1997), Curie temperature depth
          +        estimation using a self-similar magnetization model, Geophys. J. Int.,
          +        129, 163-168, doi:10.1111/j.1365-246X.1997.tb00945.x
          +    """
          +    # from scipy.special import kv
          +    khdz = kh*dz
          +    coshkhdz = np.cosh(khdz)
          +
          +    Phi1d = C - 2.0*kh*zt - (beta-1.0)*np.log(kh) - khdz
          +    A = np.sqrt(np.pi)/gamma(1.0+0.5*beta) * \
          +        (0.5*coshkhdz*gamma(0.5*(1.0+beta)) - \
          +        kv((-0.5*(1.0+beta)), khdz) * np.power(0.5*khdz,(0.5*(1.0+beta)) ))
          +    Phi1d += np.log(A)
          +    return Phi1d
          +
          +
          +def tanaka1999(k, lnPhi, sigma_lnPhi, kmin_range=(0.05, 0.2), kmax_range=(0.05, 0.2)):
          +    """
          +    Compute weighted linear fit of Phi over spatial frequency window kmin:kmax
          +
          +    Args:
          +        k : float / 1D-array
          +            wavenumber in rad/km
          +        lnPhi : float / 1D array
          +            log of the radial power spectrum (see power_spectrum_log)
          +            expected in ln(sqrt(S)) form
          +        sigma_lnPhi : standard deviation of lnPhi
          +        kmin_range : tuple (default:(0.05, 0.2))
          +            minimum and maximum range of spatial frequencies to fit for the 
          +            top of magnetic sources - ideally low frequency, straight line
          +        kmax_range : tuple (default:(0.05, 0.2))
          +            minimum and maximum range of spatial frequencies to fit for the
          +            bottom of magnetic source - ideally low frequency, straight line
          +
          +    Returns:
          +        upper_source : tuple
          +            (Ztr,btr,dZtr) gradient, intercept, error for the top of magnetic sources
          +        lower_source : tuple
          +            (Zor,bor,dZor) gradient, intercept, error for the bottom of magnetic sources
          +
          +    """
          +    # for now...
          +    S = lnPhi
          +    sigma2 = sigma_lnPhi**2
          +
          +    def compute_coefficients(X, Y, E):
          +        X2 = X**2
          +        Y2 = Y**2
          +        E2 = E**2
          +
          +        XY = np.multiply(X, Y)
          +        XE2sum = np.sum(X/E2)
          +        YE2sum = np.sum(Y/E2)
          +        rE2sum = np.sum(1.0/E2)
          +        X2E2sum = np.sum(X2/E2)
          +        Y2E2sum = np.sum(Y2/E2)
          +
          +        #TL = XE2sum*YE2sum - np.sum(XY/E2*rE2sum)
          +        # I think summation in second TL term needed to be split
          +        TL = XE2sum*YE2sum - np.sum(XY/E2)*rE2sum
          +        BL = XE2sum**2 - X2E2sum*rE2sum
          +
          +        Z  = TL/BL
          +        b  = (np.sum(XY/E2) - Z*X2E2sum)/XE2sum
          +        #dZ = np.sqrt( rE2sum/(X2E2sum*rE2sum - XE2sum) )
          +        ## There was a missing **2 term at end of error term.
          +        dZ = np.sqrt( rE2sum/(X2E2sum*rE2sum - XE2sum**2) )
          +        return Z, b, dZ
          +
          +
          +    sf=k/(2.0*np.pi)
          +    S2=np.log(np.exp(S)/sf)
          +
          +    # mask low wavenumbers
          +    kmin, kmax = kmin_range
          +    mask1 = np.logical_and(sf >=kmin, sf <=kmax)
          +    X1 = sf[mask1]
          +    Y1 = S[mask1]
          +    E1 = sigma2[mask1]
          +    
          +    # mask high wavenumbers
          +    kmin, kmax = kmax_range
          +    mask2 = np.logical_and(sf >=kmin, sf <=kmax)
          +    X2 = sf[mask2]
          +    Y2 = np.log(np.exp(S[mask2])/(X2*2*np.pi))
          +    E2 = np.log(np.exp(sigma2[mask2])/(X2*2*np.pi))
          +
          +    # compute top and bottom of magnetic layer
          +    Ztr, btr, dZtr = compute_coefficients(X1, Y1, E1)
          +    Zor, bor, dZor = compute_coefficients(X2, Y2, E2)
          +    return (Ztr,btr,dZtr), (Zor, bor, dZor)
          +    
          +    
          +def ComputeTanaka(Ztr, dZtr, Zor, dZor):
          +    """
          +    Compute the Curie depth from the results of tanaka1999
          +
          +    Args:
          +        Ztr : float / 1D array
          +            top of the magnetic source
          +        dZtr : float / 1D array
          +            error of Ztr
          +        Zor : float / 1D array 
          +            bottom of the magnetic source
          +        dZor : float / 1D array
          +            error of Zor
          +
          +    Returns:
          +        Zb : float / 1D array
          +            estimated Curie point depth
          +        eZb : float / 1D array
          +            error of `Zb`
          +    """
          +    Zb = 2.0*Zor - Ztr
          +    dZb  = 2.0*dZor - dZtr
          +    return abs(Zb), dZb
          +
          +
          +def maus1995(beta, zt, kh, C=0.0):
          +    """
          +    Calculate the synthetic radial power spectrum of
          +    magnetic anomalies (Maus and Dimri; 1995)
          +
          +    This is not all that useful except when testing
          +    overflow errors which occur for the second term
          +    in Bouligand et al. (2009).
          +
          +    Args:
          +        beta : float / 1D array
          +            fractal parameter
          +        zt : float / 1D array
          +            top of magnetic sources
          +        kh : float / 1D array
          +            norm of the wave number in the horizontal plane
          +        C : float / 1D array
          +            field constant (Maus et al., 1997)
          +
          +    Returns:
          +        Phi : float / 1D array
          +            radial power spectrum of magnetic anomalies
          +
          +    References:
          +        Bouligand, C., J. M. G. Glen, and R. J. Blakely (2009), Mapping Curie
          +        temperature depth in the western United States with a fractal model for
          +        crustal magnetization, J. Geophys. Res., 114, B11104,
          +        doi:10.1029/2009JB006494
          +
          +        Maus, S., D. Gordon, and D. Fairhead (1997), Curie temperature depth
          +        estimation using a self-similar magnetization model, Geophys. J. Int.,
          +        129, 163-168, doi:10.1111/j.1365-246X.1997.tb00945.x
          +    """
          +    return C - 2.0*kh*zt - (beta-1.0)*np.log(kh)
          +
          +
          +def _fftfreqs(dx, dy, shape):
          +    """
          +    Get two 2D-arrays with the wave numbers in the x and y directions.
          +    """
          +    fx = 2.0*np.pi*np.fft.fftfreq(shape[0], dx)
          +    fy = 2.0*np.pi*np.fft.fftfreq(shape[1], dy)
          +    return np.meshgrid(fy, fx)[::-1]
          +
          +def ang2vec(intensity, inc, dec):
          +    """
          +    Convert intensity, inclination and  declination to a 3-component vector
          +
          +    Args:
          +        intensity : float or 1D array
          +            The intensity (norm) of the vector
          +        inc : float
          +            The inclination of the vector (in degrees)
          +        dec : float
          +            The declination of the vector (in degrees)
          +
          +    Returns:
          +        vec : array = [x, y, z]
          +            3-component vector
          +
          +    Notes:
          +        Coordinate system is assumed to be x->North, y->East, z->Down.
          +        Inclination is positive down and declination is measured with respect
          +        to x (North).
          +
          +    Examples:
          +        >>> import numpy
          +        >>> print ang2vec(3, 45, 45)
          +        [ 1.5         1.5         2.12132034]
          +        >>> print ang2vec(numpy.arange(4), 45, 45)
          +        [[ 0.          0.          0.        ]
          +         [ 0.5         0.5         0.70710678]
          +         [ 1.          1.          1.41421356]
          +         [ 1.5         1.5         2.12132034]]
          +
          +    """
          +    return np.transpose([intensity * i for i in dircos(inc, dec)])
          +
          +
          +def dircos(inc, dec):
          +    """
          +    Returns the 3 coordinates of a unit vector given its inclination and
          +    declination.
          +
          +    Args:
          +        inc : float
          +            The inclination of the vector (in degrees)
          +        dec : float
          +            The declination of the vector (in degrees)
          +
          +    Returns:
          +        vect : list
          +            The unit vector = [x, y, z]
          +
          +    Notes:
          +        Coordinate system is assumed to be x->North, y->East, z->Down.
          +        Inclination is positive down and declination is measured with respect
          +        to x (North).
          +    """
          +    d2r = np.pi/180.0
          +    vect = [np.cos(d2r * inc) * np.cos(d2r * dec), \
          +            np.cos(d2r * inc) * np.sin(d2r * dec), \
          +            np.sin(d2r * inc)]
          +    return vect
          +
          +
          +
          +
          +
          +
          +
          +

          Functions

          +
          +
          +def ComputeTanaka(Ztr, dZtr, Zor, dZor) +
          +
          +

          Compute the Curie depth from the results of tanaka1999

          +

          Args

          +
          +
          Ztr : float / 1D array
          +
          top of the magnetic source
          +
          dZtr : float / 1D array
          +
          error of Ztr
          +
          Zor : float / 1D array
          +
          bottom of the magnetic source
          +
          dZor : float / 1D array
          +
          error of Zor
          +
          +

          Returns

          +
          +
          Zb : float / 1D array
          +
          estimated Curie point depth
          +
          eZb : float / 1D array
          +
          error of Zb
          +
          +
          +Source code +
          def ComputeTanaka(Ztr, dZtr, Zor, dZor):
          +    """
          +    Compute the Curie depth from the results of tanaka1999
          +
          +    Args:
          +        Ztr : float / 1D array
          +            top of the magnetic source
          +        dZtr : float / 1D array
          +            error of Ztr
          +        Zor : float / 1D array 
          +            bottom of the magnetic source
          +        dZor : float / 1D array
          +            error of Zor
          +
          +    Returns:
          +        Zb : float / 1D array
          +            estimated Curie point depth
          +        eZb : float / 1D array
          +            error of `Zb`
          +    """
          +    Zb = 2.0*Zor - Ztr
          +    dZb  = 2.0*dZor - dZtr
          +    return abs(Zb), dZb
          +
          +
          +
          +def ang2vec(intensity, inc, dec) +
          +
          +

          Convert intensity, inclination and +declination to a 3-component vector

          +

          Args

          +
          +
          intensity : float or 1D array
          +
          The intensity (norm) of the vector
          +
          inc : float
          +
          The inclination of the vector (in degrees)
          +
          dec : float
          +
          The declination of the vector (in degrees)
          +
          +

          Returns

          +
          +
          vec : array = [x, y, z]
          +
          3-component vector
          +
          +

          Notes

          +

          Coordinate system is assumed to be x->North, y->East, z->Down. +Inclination is positive down and declination is measured with respect +to x (North).

          +

          Examples

          +
          >>> import numpy
          +>>> print ang2vec(3, 45, 45)
          +[ 1.5         1.5         2.12132034]
          +>>> print ang2vec(numpy.arange(4), 45, 45)
          +[[ 0.          0.          0.        ]
          +
          +

          [ 0.5 +0.5 +0.70710678] +[ 1. +1. +1.41421356] +[ 1.5 +1.5 +2.12132034]]

          +
          +Source code +
          def ang2vec(intensity, inc, dec):
          +    """
          +    Convert intensity, inclination and  declination to a 3-component vector
          +
          +    Args:
          +        intensity : float or 1D array
          +            The intensity (norm) of the vector
          +        inc : float
          +            The inclination of the vector (in degrees)
          +        dec : float
          +            The declination of the vector (in degrees)
          +
          +    Returns:
          +        vec : array = [x, y, z]
          +            3-component vector
          +
          +    Notes:
          +        Coordinate system is assumed to be x->North, y->East, z->Down.
          +        Inclination is positive down and declination is measured with respect
          +        to x (North).
          +
          +    Examples:
          +        >>> import numpy
          +        >>> print ang2vec(3, 45, 45)
          +        [ 1.5         1.5         2.12132034]
          +        >>> print ang2vec(numpy.arange(4), 45, 45)
          +        [[ 0.          0.          0.        ]
          +         [ 0.5         0.5         0.70710678]
          +         [ 1.          1.          1.41421356]
          +         [ 1.5         1.5         2.12132034]]
          +
          +    """
          +    return np.transpose([intensity * i for i in dircos(inc, dec)])
          +
          +
          +
          +def bouligand2009(kh, beta, zt, dz, C) +
          +
          +

          Calculate the synthetic radial power spectrum of +magnetic anomalies

          +

          Equation (4) of Bouligand et al. (2009)

          +

          Args

          +
          +
          kh : float / 1D array
          +
          wavenumber in rad/km
          +
          beta : float / 1D array
          +
          fractal parameter
          +
          zt : float / 1D array
          +
          top of magnetic sources
          +
          dz : float / 1D array
          +
          thickness of magnetic sources
          +
          C : float 1D array
          +
          field constant (Maus et al., 1997)
          +
          +

          Returns

          +
          +
          Phi : float / 1D array
          +
          radial power spectrum of magnetic anomalies
          +
          +

          References

          +

          Bouligand, C., J. M. G. Glen, and R. J. Blakely (2009), Mapping Curie +temperature depth in the western United States with a fractal model for +crustal magnetization, J. Geophys. Res., 114, B11104, +doi:10.1029/2009JB006494

          +

          Maus, S., D. Gordon, and D. Fairhead (1997), Curie temperature depth +estimation using a self-similar magnetization model, Geophys. J. Int., +129, 163-168, doi:10.1111/j.1365-246X.1997.tb00945.x

          +
          +Source code +
          def bouligand2009(kh, beta, zt, dz, C):
          +    """
          +    Calculate the synthetic radial power spectrum of
          +    magnetic anomalies
          +
          +    Equation (4) of Bouligand et al. (2009)
          +
          +    Args:
          +        kh : float / 1D array
          +            wavenumber in rad/km
          +        beta : float / 1D array
          +            fractal parameter
          +        zt : float / 1D array
          +            top of magnetic sources
          +        dz : float / 1D array
          +            thickness of magnetic sources
          +        C : float 1D array
          +            field constant (Maus et al., 1997)
          +
          +    Returns:
          +        Phi : float / 1D array
          +            radial power spectrum of magnetic anomalies
          +
          +    References:
          +        Bouligand, C., J. M. G. Glen, and R. J. Blakely (2009), Mapping Curie
          +        temperature depth in the western United States with a fractal model for
          +        crustal magnetization, J. Geophys. Res., 114, B11104,
          +        doi:10.1029/2009JB006494
          +
          +        Maus, S., D. Gordon, and D. Fairhead (1997), Curie temperature depth
          +        estimation using a self-similar magnetization model, Geophys. J. Int.,
          +        129, 163-168, doi:10.1111/j.1365-246X.1997.tb00945.x
          +    """
          +    # from scipy.special import kv
          +    khdz = kh*dz
          +    coshkhdz = np.cosh(khdz)
          +
          +    Phi1d = C - 2.0*kh*zt - (beta-1.0)*np.log(kh) - khdz
          +    A = np.sqrt(np.pi)/gamma(1.0+0.5*beta) * \
          +        (0.5*coshkhdz*gamma(0.5*(1.0+beta)) - \
          +        kv((-0.5*(1.0+beta)), khdz) * np.power(0.5*khdz,(0.5*(1.0+beta)) ))
          +    Phi1d += np.log(A)
          +    return Phi1d
          +
          +
          +
          +def dircos(inc, dec) +
          +
          +

          Returns the 3 coordinates of a unit vector given its inclination and +declination.

          +

          Args

          +
          +
          inc : float
          +
          The inclination of the vector (in degrees)
          +
          dec : float
          +
          The declination of the vector (in degrees)
          +
          +

          Returns

          +
          +
          vect : list
          +
          The unit vector = [x, y, z]
          +
          +

          Notes

          +

          Coordinate system is assumed to be x->North, y->East, z->Down. +Inclination is positive down and declination is measured with respect +to x (North).

          +
          +Source code +
          def dircos(inc, dec):
          +    """
          +    Returns the 3 coordinates of a unit vector given its inclination and
          +    declination.
          +
          +    Args:
          +        inc : float
          +            The inclination of the vector (in degrees)
          +        dec : float
          +            The declination of the vector (in degrees)
          +
          +    Returns:
          +        vect : list
          +            The unit vector = [x, y, z]
          +
          +    Notes:
          +        Coordinate system is assumed to be x->North, y->East, z->Down.
          +        Inclination is positive down and declination is measured with respect
          +        to x (North).
          +    """
          +    d2r = np.pi/180.0
          +    vect = [np.cos(d2r * inc) * np.cos(d2r * dec), \
          +            np.cos(d2r * inc) * np.sin(d2r * dec), \
          +            np.sin(d2r * inc)]
          +    return vect
          +
          +
          +
          +def maus1995(beta, zt, kh, C=0.0) +
          +
          +

          Calculate the synthetic radial power spectrum of +magnetic anomalies (Maus and Dimri; 1995)

          +

          This is not all that useful except when testing +overflow errors which occur for the second term +in Bouligand et al. (2009).

          +

          Args

          +
          +
          beta : float / 1D array
          +
          fractal parameter
          +
          zt : float / 1D array
          +
          top of magnetic sources
          +
          kh : float / 1D array
          +
          norm of the wave number in the horizontal plane
          +
          C : float / 1D array
          +
          field constant (Maus et al., 1997)
          +
          +

          Returns

          +
          +
          Phi : float / 1D array
          +
          radial power spectrum of magnetic anomalies
          +
          +

          References

          +

          Bouligand, C., J. M. G. Glen, and R. J. Blakely (2009), Mapping Curie +temperature depth in the western United States with a fractal model for +crustal magnetization, J. Geophys. Res., 114, B11104, +doi:10.1029/2009JB006494

          +

          Maus, S., D. Gordon, and D. Fairhead (1997), Curie temperature depth +estimation using a self-similar magnetization model, Geophys. J. Int., +129, 163-168, doi:10.1111/j.1365-246X.1997.tb00945.x

          +
          +Source code +
          def maus1995(beta, zt, kh, C=0.0):
          +    """
          +    Calculate the synthetic radial power spectrum of
          +    magnetic anomalies (Maus and Dimri; 1995)
          +
          +    This is not all that useful except when testing
          +    overflow errors which occur for the second term
          +    in Bouligand et al. (2009).
          +
          +    Args:
          +        beta : float / 1D array
          +            fractal parameter
          +        zt : float / 1D array
          +            top of magnetic sources
          +        kh : float / 1D array
          +            norm of the wave number in the horizontal plane
          +        C : float / 1D array
          +            field constant (Maus et al., 1997)
          +
          +    Returns:
          +        Phi : float / 1D array
          +            radial power spectrum of magnetic anomalies
          +
          +    References:
          +        Bouligand, C., J. M. G. Glen, and R. J. Blakely (2009), Mapping Curie
          +        temperature depth in the western United States with a fractal model for
          +        crustal magnetization, J. Geophys. Res., 114, B11104,
          +        doi:10.1029/2009JB006494
          +
          +        Maus, S., D. Gordon, and D. Fairhead (1997), Curie temperature depth
          +        estimation using a self-similar magnetization model, Geophys. J. Int.,
          +        129, 163-168, doi:10.1111/j.1365-246X.1997.tb00945.x
          +    """
          +    return C - 2.0*kh*zt - (beta-1.0)*np.log(kh)
          +
          +
          +
          +def tanaka1999(k, lnPhi, sigma_lnPhi, kmin_range=(0.05, 0.2), kmax_range=(0.05, 0.2)) +
          +
          +

          Compute weighted linear fit of Phi over spatial frequency window kmin:kmax

          +

          Args

          +
          +
          k : float / 1D-array
          +
          wavenumber in rad/km
          +
          lnPhi : float / 1D array
          +
          log of the radial power spectrum (see power_spectrum_log) +expected in ln(sqrt(S)) form
          +
          sigma_lnPhi : standard deviation of lnPhi
          +
           
          +
          kmin_range : tuple (default:(0.05, 0.2))
          +
          minimum and maximum range of spatial frequencies to fit for the +top of magnetic sources - ideally low frequency, straight line
          +
          kmax_range : tuple (default:(0.05, 0.2))
          +
          minimum and maximum range of spatial frequencies to fit for the +bottom of magnetic source - ideally low frequency, straight line
          +
          +

          Returns

          +
          +
          upper_source : tuple
          +
          (Ztr,btr,dZtr) gradient, intercept, error for the top of magnetic sources
          +
          lower_source : tuple
          +
          (Zor,bor,dZor) gradient, intercept, error for the bottom of magnetic sources
          +
          +
          +Source code +
          def tanaka1999(k, lnPhi, sigma_lnPhi, kmin_range=(0.05, 0.2), kmax_range=(0.05, 0.2)):
          +    """
          +    Compute weighted linear fit of Phi over spatial frequency window kmin:kmax
          +
          +    Args:
          +        k : float / 1D-array
          +            wavenumber in rad/km
          +        lnPhi : float / 1D array
          +            log of the radial power spectrum (see power_spectrum_log)
          +            expected in ln(sqrt(S)) form
          +        sigma_lnPhi : standard deviation of lnPhi
          +        kmin_range : tuple (default:(0.05, 0.2))
          +            minimum and maximum range of spatial frequencies to fit for the 
          +            top of magnetic sources - ideally low frequency, straight line
          +        kmax_range : tuple (default:(0.05, 0.2))
          +            minimum and maximum range of spatial frequencies to fit for the
          +            bottom of magnetic source - ideally low frequency, straight line
          +
          +    Returns:
          +        upper_source : tuple
          +            (Ztr,btr,dZtr) gradient, intercept, error for the top of magnetic sources
          +        lower_source : tuple
          +            (Zor,bor,dZor) gradient, intercept, error for the bottom of magnetic sources
          +
          +    """
          +    # for now...
          +    S = lnPhi
          +    sigma2 = sigma_lnPhi**2
          +
          +    def compute_coefficients(X, Y, E):
          +        X2 = X**2
          +        Y2 = Y**2
          +        E2 = E**2
          +
          +        XY = np.multiply(X, Y)
          +        XE2sum = np.sum(X/E2)
          +        YE2sum = np.sum(Y/E2)
          +        rE2sum = np.sum(1.0/E2)
          +        X2E2sum = np.sum(X2/E2)
          +        Y2E2sum = np.sum(Y2/E2)
          +
          +        #TL = XE2sum*YE2sum - np.sum(XY/E2*rE2sum)
          +        # I think summation in second TL term needed to be split
          +        TL = XE2sum*YE2sum - np.sum(XY/E2)*rE2sum
          +        BL = XE2sum**2 - X2E2sum*rE2sum
          +
          +        Z  = TL/BL
          +        b  = (np.sum(XY/E2) - Z*X2E2sum)/XE2sum
          +        #dZ = np.sqrt( rE2sum/(X2E2sum*rE2sum - XE2sum) )
          +        ## There was a missing **2 term at end of error term.
          +        dZ = np.sqrt( rE2sum/(X2E2sum*rE2sum - XE2sum**2) )
          +        return Z, b, dZ
          +
          +
          +    sf=k/(2.0*np.pi)
          +    S2=np.log(np.exp(S)/sf)
          +
          +    # mask low wavenumbers
          +    kmin, kmax = kmin_range
          +    mask1 = np.logical_and(sf >=kmin, sf <=kmax)
          +    X1 = sf[mask1]
          +    Y1 = S[mask1]
          +    E1 = sigma2[mask1]
          +    
          +    # mask high wavenumbers
          +    kmin, kmax = kmax_range
          +    mask2 = np.logical_and(sf >=kmin, sf <=kmax)
          +    X2 = sf[mask2]
          +    Y2 = np.log(np.exp(S[mask2])/(X2*2*np.pi))
          +    E2 = np.log(np.exp(sigma2[mask2])/(X2*2*np.pi))
          +
          +    # compute top and bottom of magnetic layer
          +    Ztr, btr, dZtr = compute_coefficients(X1, Y1, E1)
          +    Zor, bor, dZor = compute_coefficients(X2, Y2, E2)
          +    return (Ztr,btr,dZtr), (Zor, bor, dZor)
          +
          +
          +
          +
          +
          +

          Classes

          +
          +
          +class CurieGrid +(grid, xmin, xmax, ymin, ymax) +
          +
          +

          Accepts a 2D array and Cartesian coordinates specifying the +bounding box of the array

          +

          Grid must be projected in metres

          +

          Args: +grid : 2D array of magnetic data +xmin : minimum x bound in metres +xmax : maximum x bound in metres +ymin : minimum y bound in metres +ymax : maximum y bound in metres

          +
          +Source code +
          class CurieGrid(object):
          +    """
          +    Accepts a 2D array and Cartesian coordinates specifying the
          +    bounding box of the array
          +
          +    Grid must be projected in metres
          +
          +    Args:
          +     grid : 2D array of magnetic data
          +     xmin : minimum x bound in metres
          +     xmax : maximum x bound in metres
          +     ymin : minimum y bound in metres
          +     ymax : maximum y bound in metres
          +    """
          +    def __init__(self, grid, xmin, xmax, ymin, ymax):
          +        
          +        self.data = np.array(grid)
          +        ny, nx = self.data.shape
          +        self.xmin, self.xmax = xmin, xmax
          +        self.ymin, self.ymax = ymin, ymax
          +        self.xcoords, dx = np.linspace(xmin, xmax, nx, retstep=True)
          +        self.ycoords, dy = np.linspace(ymin, ymax, ny, retstep=True)
          +        self.nx, self.ny = nx, ny
          +        self.dx, self.dy = dx, dy
          +
          +        if abs(dx - dy) > 1.0:
          +            warnings.warn("node spacing should be identical {}".format((dx,dy)), RuntimeWarning)
          +
          +
          +    def subgrid(self, window, xc, yc):
          +        """
          +        Extract a subgrid from the data at a window around
          +        the point (xc,yc)
          +        
          +        Args:
          +            xc : float
          +                x coordinate
          +            yc : float
          +                y coordinate
          +            window : float
          +                size of window in metres
          +
          +        Returns:
          +            data : 2D array
          +                subgrid encompassing window size
          +        """
          +
          +        # check in coordinate in grid
          +        if xc < self.xmin or xc > self.xmax or yc < self.ymin or yc > self.ymax:
          +            raise ValueError("Point ({},{}) outside data range".format(xc,yc))
          +
          +        # find nearest index to xc,yc
          +        ix = np.abs(self.xcoords - xc).argmin()
          +        iy = np.abs(self.ycoords - yc).argmin()
          +
          +        nw = int(round(window/self.dx))
          +        n2w = nw//2
          +
          +        # extract a square window from the data
          +        imin = ix - n2w
          +        imax = ix + n2w + 1
          +        jmin = iy - n2w
          +        jmax = iy + n2w + 1
          +
          +        # safeguard if window size is larger than grid
          +        imin = max(imin, 0)
          +        imax = min(imax, self.nx)
          +        jmin = max(jmin, 0)
          +        jmax = min(jmax, self.ny)
          +        
          +        data = self.data[jmin:jmax, imin:imax]
          +
          +        return data
          +
          +
          +    def create_centroid_list(self, window, spacingX=None, spacingY=None):
          +        """
          +        Create a list of xc,yc values to extract subgrids.
          +
          +        Args:
          +            window : float
          +                size of the windows in metres
          +            spacingX : float (optional)
          +                specify spacing in metres in the X direction
          +                will default to maximum X resolution
          +            spacingY : float (optional)
          +                specify spacing in metres in the Y direction
          +                will default to maximum Y resolution
          +
          +        Returns:
          +            xc_list : 1D array
          +                array of x coordinates
          +            yc_list : 1D array
          +                array of y coordinates
          +        """
          +        
          +        nx, ny = self.nx, self.ny
          +        xcoords = self.xcoords
          +        ycoords = self.ycoords
          +        
          +        nw = int(round(window/self.dx))
          +        n2w = nw//2
          +        
          +        # this is the densest spacing possible given the data
          +        xc = xcoords[n2w:-n2w]
          +        yc = ycoords[n2w:-n2w]
          +        
          +        # but we can alter it if required
          +        if type(spacingX) != type(None):
          +            xc = np.arange(xc.min(), xc.max(), spacingX)
          +        if type(spacingY) != type(None):
          +            yc = np.arange(yc.min(), yc.max(), spacingY)
          +
          +        xq, yq = np.meshgrid(xc, yc)
          +            
          +        return xq.ravel(), yq.ravel()
          +
          +
          +    def remove_trend_linear(self, data):
          +        """
          +        Remove the best-fitting linear trend from the data
          +
          +        This may come in handy if the magnetic data has not been
          +        reduced to the pole.
          +
          +        Args:
          +            data : 2D numpy array
          +
          +        Returns:
          +         data : 2D numpy array
          +        """
          +        data = data.copy()
          +        nr, nc = data.shape
          +        xq, yq = np.meshgrid(np.arange(0, nc), np.arange(0, nr))
          +
          +        A = np.column_stack((x.flatten(), y.flatten(), np.ones(x.size)))
          +        c, resid, rank, sigma = np.linalg.lstsq(A, data.flatten())
          +
          +        data.flat[:] -= np.dot(A, c)
          +        return data
          +
          +    def radial_spectrum(self, subgrid, taper=np.hanning, scale=0.001, **kwargs):
          +        """
          +        Compute the radial spectrum for a square grid.
          +
          +        Args:
          +            subgrid : 2D array
          +                window of the original data (see subgrid method)
          +            taper : function (default=np.hanning)
          +                taper function, set to None for no taper function
          +            scale : float (default: 0.001)
          +                scaling factor to get k into rad/km
          +            kwargs : keyword arguments
          +                keyword arguments to pass to `taper`
          +
          +        Returns:
          +            k : 1D array shape (n,)
          +                wavenumber in rad/km
          +            Phi : 1D array shape (n,)
          +                Radial power spectrum
          +            sigma_Phi : 1D array shape (n,)
          +                Standard deviation of Phi
          +        """
          +
          +        data = subgrid
          +        nr, nc = data.shape
          +        nw = nr
          +
          +        if nr != nc:
          +            warnings.warn("subgrid is not square {}".format((nr,nc)), RuntimeWarning)
          +
          +
          +        # control taper
          +        if type(taper) == type(None):
          +            vtaper = 1.0
          +        else:
          +            rt = taper(nr, **kwargs)
          +            ct = taper(nc, **kwargs)
          +            xq, yq = np.meshgrid(ct, rt)
          +            vtaper = xq*yq
          +
          +        dx_scale = self.dx*scale
          +        dk = 2.0*np.pi/(nw - 1)/dx_scale
          +
          +        # fast Fourier transform and shift
          +        FT = np.abs(np.fft.fft2(data*vtaper))
          +        FT = np.fft.fftshift(FT)
          +
          +        kbins = np.arange(dk, dk*nw/2, dk)
          +        nbins = kbins.size - 1
          +
          +        S = np.empty(nbins)
          +        k = np.empty(nbins)
          +        sigma = np.empty(nbins)
          +
          +        i0 = int((nw - 1)//2)
          +        ix, iy = np.mgrid[0:nw,0:nw]
          +        kk = np.hypot((ix - i0)*dk, (iy - i0)*dk)
          +
          +        for i in range(0, nbins):
          +            mask = np.logical_and(kk >= kbins[i], kk <= kbins[i+1])
          +            rr = 2.0*np.log(FT[mask])
          +            S[i] = rr.mean()
          +            k[i] = kk[mask].mean()
          +            sigma[i] = np.std(rr)
          +
          +        return k, S, sigma
          +
          +
          +    def radial_spectrum_log(self, subgrid, taper=np.hanning, scale=0.001, **kwargs):
          +        """
          +        Compute the log of the radial spectrum for a square grid.
          +
          +        Args:
          +         subgrid : 2D array
          +            window of the original data (see subgrid method)
          +         taper : function (default=np.hanning)
          +            taper function, set to None for no taper function
          +         scale : float (detault=0.001)
          +            scaling factor to get k into rad/km
          +         kwargs : keyword arguments
          +            keyword arguments to pass to `taper`
          +
          +        Returns:
          +            k : 1D array shape (n,)
          +                wavenumber in rad/km
          +            lnPhi : 1D array
          +                log of the radial power spectrum in ln(sqrt(S))
          +            lnsigma_Phi : 1D array
          +                standard deviation of lnPhi
          +        """
          +
          +        data = subgrid
          +        nr, nc = data.shape
          +        nw = nr
          +
          +        if nr != nc:
          +            warnings.warn("subgrid is not square {}".format((nr,nc)), RuntimeWarning)
          +
          +
          +        # control taper
          +        if type(taper) == type(None):
          +            vtaper = 1.0
          +        else:
          +            rt = taper(nr, **kwargs)
          +            ct = taper(nc, **kwargs)
          +            xq, yq = np.meshgrid(ct, rt)
          +            vtaper = xq*yq
          +
          +        dx_scale = self.dx*scale
          +        dk = 2.0*np.pi/(nw - 1)/dx_scale
          +
          +        # fast Fourier transform and shift
          +        FT = np.abs(np.fft.fft2(data*vtaper))
          +        FT = np.fft.fftshift(FT)
          +
          +        kbins = np.arange(dk, dk*nw/2, dk)
          +        nbins = kbins.size - 1
          +
          +        S = np.empty(nbins)
          +        k = np.empty(nbins)
          +        sigma = np.empty(nbins)
          +
          +        i0 = int((nw - 1)//2)
          +        ix, iy = np.mgrid[0:nw,0:nw]
          +        kk = np.hypot((ix - i0)*dk, (iy - i0)*dk)
          +
          +        for i in range(0, nbins):
          +            mask = np.logical_and(kk >= kbins[i], kk <= kbins[i+1])
          +            rr = np.log(np.sqrt(FT[mask]))
          +            S[i] = rr.mean()
          +            k[i] = kk[mask].mean()
          +            sigma[i] = np.std(rr)
          +
          +        return k, S, sigma
          +        
          +        
          +    def azimuthal_spectrum(self, subgrid, taper=np.hanning, scale=0.001, theta=5.0, **kwargs):
          +        """
          +        Compute azimuthal spectrum for a square grid.
          +
          +        Args:
          +            subgrid : 2D array
          +                window of the original data (see subgrid method)
          +            taper : function (default=np.hanning)
          +                taper function, set to None for no taper function
          +            scale : float (default=0.001)
          +                scaling factor to get k into rad/km
          +            theta : float
          +                angle increment in degrees
          +            args : arguments
          +                arguments o pass to taper
          +
          +        Returns:
          +            k : 1D array shape (n,)
          +                wavenumber in rad/km
          +            Phi : 1D array shape (n,)
          +                Radial power spectrum
          +            sigma_Phi : 1D array shape (n,)
          +                Standard deviation of Phi
          +        """
          +        from pycurious import radon
          +        data = subgrid
          +        nr, nc = data.shape
          +        nw = nr
          +
          +        if nr != nc:
          +            raise RuntimeWarning("subgrid is not square {}".format((nr,nc)))
          +
          +        dx_scale = self.dx*scale
          +        dk = 2.0*np.pi/(nw - 1)/dx_scale
          +
          +        kbins = np.arange(dk, dk*nw/2, dk)
          +
          +        dtheta = np.arange(0.0, 180.0, theta)
          +        sinogram = radon.radon2d(data, np.pi*dtheta/180.0)
          +        S = np.zeros((dtheta.size, kbins.size))
          +        sigma2 = np.zeros((dtheta.size, kbins.size))
          +
          +        # control taper
          +        if taper is None:
          +            vtaper = 1.0
          +        else:
          +            vtaper = taper(sinogram.shape[0], **kwargs)
          +
          +        nk = 1 + 2*kbins.size
          +        for i in range(0, dtheta.size):
          +            PSD = np.abs(np.fft.fft(vtaper*sinogram[:,i], n=nk))
          +            S[i,:] = np.log( np.sqrt(PSD[1:kbins.size+1] ))
          +        
          +        return kbins, S, dtheta
          +
          +
          +    def reduce_to_pole(self, data, inc, dec, sinc=None, sdec=None):
          +        r"""
          +        Reduce total field magnetic anomaly data to the pole.
          +
          +        The reduction to the pole if a phase transformation that can be
          +        applied to total field magnetic anomaly data. It simulates how
          +        the data would be if both the Geomagnetic field and the
          +        magnetization of the source were vertical (Blakely, 1996).
          +
          +        Args:
          +            data : 1D array
          +                the total field anomaly data at each point.
          +            inc : float / 1D array
          +                inclination of the inducing Geomagnetic field
          +            dec : float / 1D array
          +                declination of the inducing Geomagnetic field
          +            sinc : float / 1D array (optional)
          +                inclination of the total magnetization of the anomaly source
          +            sdec : float / 1D array (optional)
          +                declination of the total magnetization of the anomaly source
          +                The total magnetization is the vector sum of the
          +                induced and remanent magnetization. If there is only induced
          +                magnetization, use the *inc* and *dec* of the Geomagnetic field.
          +
          +        Returns:
          +            rtp : 2D array
          +                the data reduced to the pole.
          +        
          +        References:
          +            Blakely, R. J. (1996), Potential Theory in Gravity and Magnetic
          +            Applications, Cambridge University Press.
          +
          +        Notes:
          +            This functions performs the reduction in the frequency domain
          +            (using the FFT). The transform filter is (in the freq domain):
          +                RTP(k_x, k_y) = \frac{|k|}{
          +                    a_1 k_x^2 + a_2 k_y^2 + a_3 k_x k_y +
          +                    i|k|(b_1 k_x + b_2 k_y)}
          +            in which k_x and k_y are the wave-numbers in the x and y
          +            directions and
          +                |k| = \sqrt{k_x^2 + k_y^2} \\
          +                a_1 = m_z f_z - m_x f_x \\
          +                a_2 = m_z f_z - m_y f_y \\
          +                a_3 = -m_y f_x - m_x f_y \\
          +                b_1 = m_x f_z + m_z f_x \\
          +                b_2 = m_y f_z + m_z f_y
          +            \mathbf{m} = (m_x, m_y, m_z)` is the unit-vector of the total
          +            magnetization of the source and
          +            \mathbf{f} = (f_x, f_y, f_z)` is the unit-vector of the
          +            Geomagnetic field.
          +        """
          +        nr, nc = data.shape
          +
          +        if nr != nc:
          +            warnings.warn("subgrid is not square {}".format((nr,nc)), RuntimeWarning)
          +
          +        fx, fy, fz = ang2vec(1.0, inc, dec)
          +        if sinc is None or sdec is None:
          +            mx, my, mz = fx, fy, fz
          +        else:
          +            mx, my, mz = ang2vec(1.0, sinc, sdec)
          +
          +        kx, ky = [k for k in _fftfreqs(self.dx, self.dy, data.shape)]
          +        kz = np.hypot(kx, ky)
          +
          +        a1 = mz*fz - mx*fx
          +        a2 = mz*fz - my*fy
          +        a3 = -my*fx - mx*fy
          +        b1 = mx*fz + mz*fx
          +        b2 = my*fz + mz*fy
          +
          +        # The division gives a RuntimeWarning because of the zero frequency term.
          +        # This suppresses the warning.
          +        with np.errstate(divide='ignore', invalid='ignore'):
          +            rtp = (kz)/(a1*kx**2 + a2*ky**2 + a3*kx*ky + \
          +                            1j*np.sqrt(kz)*(b1*kx + b2*ky))
          +        
          +        rtp[0, 0] = 0
          +        ft_pole = rtp*np.fft.fft2(data)
          +        return np.real(np.fft.ifft2(ft_pole))
          +
          +
          +    def upward_continuation(self, data, height):
          +        r"""
          +        Upward continuation of potential field data.
          +
          +        Calculates the continuation through the Fast Fourier Transform in
          +        the wavenumber domain (Blakely, 1996):
          +
          +            F\{h_{up}\} = F\{h\} e^{-\Delta z |k|}
          +
          +        and then transformed back to the space domain. :math:`h_{up}` is the
          +        upward continue data, \Delta z is the height increase, F denotes
          +        the Fourier Transform, |k| is the wavenumber modulus.
          +
          +        Args:
          +            data   : 2D array
          +                potential field at the grid points
          +            height : float
          +                height increase (delta z) in meters.
          +        
          +        Returns:
          +            cont : array
          +                upward continued data
          +
          +        Notes:
          +            It is not possible to get the FFT of a masked grid. The default
          +            :func:`fatiando.gridder.interp` call using minimum curvature will
          +            not be suitable.  Use extrapolate=True or algorithm='nearest' to
          +            get an unmasked grid.
          +
          +        References:
          +            Blakely, R. J. (1996), Potential Theory in Gravity and Magnetic
          +            Applications, Cambridge University Press.
          +        """
          +        nr, nc = data.shape
          +
          +        if nr != nc:
          +            warnings.warn("subgrid is not square {}".format((nr,nc)), RuntimeWarning)
          +
          +        if height <= 0:
          +            warnings.warn("Using 'height' <= 0 means downward continuation, " +
          +                          "which is known to be unstable.")
          +
          +        fx = 2.0*np.pi*np.fft.fftfreq(nr, self.dx)
          +        fy = 2.0*np.pi*np.fft.fftfreq(nc, self.dy)
          +
          +        kx, ky = np.meshgrid(fy, fx)[::-1]
          +        kz = np.hypot(kx, ky)
          +
          +        upcont_ft = np.fft.fft2(data)*np.exp(-height*kz)
          +        cont = np.real(np.fft.ifft2(upcont_ft))
          +        return cont
          +
          +

          Subclasses

          + +

          Methods

          +
          +
          +def azimuthal_spectrum(self, subgrid, taper=, scale=0.001, theta=5.0, **kwargs) +
          +
          +

          Compute azimuthal spectrum for a square grid.

          +

          Args

          +
          +
          subgrid : 2D array
          +
          window of the original data (see subgrid method)
          +
          taper : function (default=np.hanning)
          +
          taper function, set to None for no taper function
          +
          scale : float (default=0.001)
          +
          scaling factor to get k into rad/km
          +
          theta : float
          +
          angle increment in degrees
          +
          args : arguments
          +
          arguments o pass to taper
          +
          +

          Returns

          +
          +
          k : 1D array shape (n,)
          +
          wavenumber in rad/km
          +
          Phi : 1D array shape (n,)
          +
          Radial power spectrum
          +
          sigma_Phi : 1D array shape (n,)
          +
          Standard deviation of Phi
          +
          +
          +Source code +
          def azimuthal_spectrum(self, subgrid, taper=np.hanning, scale=0.001, theta=5.0, **kwargs):
          +    """
          +    Compute azimuthal spectrum for a square grid.
          +
          +    Args:
          +        subgrid : 2D array
          +            window of the original data (see subgrid method)
          +        taper : function (default=np.hanning)
          +            taper function, set to None for no taper function
          +        scale : float (default=0.001)
          +            scaling factor to get k into rad/km
          +        theta : float
          +            angle increment in degrees
          +        args : arguments
          +            arguments o pass to taper
          +
          +    Returns:
          +        k : 1D array shape (n,)
          +            wavenumber in rad/km
          +        Phi : 1D array shape (n,)
          +            Radial power spectrum
          +        sigma_Phi : 1D array shape (n,)
          +            Standard deviation of Phi
          +    """
          +    from pycurious import radon
          +    data = subgrid
          +    nr, nc = data.shape
          +    nw = nr
          +
          +    if nr != nc:
          +        raise RuntimeWarning("subgrid is not square {}".format((nr,nc)))
          +
          +    dx_scale = self.dx*scale
          +    dk = 2.0*np.pi/(nw - 1)/dx_scale
          +
          +    kbins = np.arange(dk, dk*nw/2, dk)
          +
          +    dtheta = np.arange(0.0, 180.0, theta)
          +    sinogram = radon.radon2d(data, np.pi*dtheta/180.0)
          +    S = np.zeros((dtheta.size, kbins.size))
          +    sigma2 = np.zeros((dtheta.size, kbins.size))
          +
          +    # control taper
          +    if taper is None:
          +        vtaper = 1.0
          +    else:
          +        vtaper = taper(sinogram.shape[0], **kwargs)
          +
          +    nk = 1 + 2*kbins.size
          +    for i in range(0, dtheta.size):
          +        PSD = np.abs(np.fft.fft(vtaper*sinogram[:,i], n=nk))
          +        S[i,:] = np.log( np.sqrt(PSD[1:kbins.size+1] ))
          +    
          +    return kbins, S, dtheta
          +
          +
          +
          +def create_centroid_list(self, window, spacingX=None, spacingY=None) +
          +
          +

          Create a list of xc,yc values to extract subgrids.

          +

          Args

          +
          +
          window : float
          +
          size of the windows in metres
          +
          spacingX : float (optional)
          +
          specify spacing in metres in the X direction +will default to maximum X resolution
          +
          spacingY : float (optional)
          +
          specify spacing in metres in the Y direction +will default to maximum Y resolution
          +
          +

          Returns

          +
          +
          xc_list : 1D array
          +
          array of x coordinates
          +
          yc_list : 1D array
          +
          array of y coordinates
          +
          +
          +Source code +
          def create_centroid_list(self, window, spacingX=None, spacingY=None):
          +    """
          +    Create a list of xc,yc values to extract subgrids.
          +
          +    Args:
          +        window : float
          +            size of the windows in metres
          +        spacingX : float (optional)
          +            specify spacing in metres in the X direction
          +            will default to maximum X resolution
          +        spacingY : float (optional)
          +            specify spacing in metres in the Y direction
          +            will default to maximum Y resolution
          +
          +    Returns:
          +        xc_list : 1D array
          +            array of x coordinates
          +        yc_list : 1D array
          +            array of y coordinates
          +    """
          +    
          +    nx, ny = self.nx, self.ny
          +    xcoords = self.xcoords
          +    ycoords = self.ycoords
          +    
          +    nw = int(round(window/self.dx))
          +    n2w = nw//2
          +    
          +    # this is the densest spacing possible given the data
          +    xc = xcoords[n2w:-n2w]
          +    yc = ycoords[n2w:-n2w]
          +    
          +    # but we can alter it if required
          +    if type(spacingX) != type(None):
          +        xc = np.arange(xc.min(), xc.max(), spacingX)
          +    if type(spacingY) != type(None):
          +        yc = np.arange(yc.min(), yc.max(), spacingY)
          +
          +    xq, yq = np.meshgrid(xc, yc)
          +        
          +    return xq.ravel(), yq.ravel()
          +
          +
          +
          +def radial_spectrum(self, subgrid, taper=, scale=0.001, **kwargs) +
          +
          +

          Compute the radial spectrum for a square grid.

          +

          Args

          +
          +
          subgrid : 2D array
          +
          window of the original data (see subgrid method)
          +
          taper : function (default=np.hanning)
          +
          taper function, set to None for no taper function
          +
          scale : float (default: 0.001)
          +
          scaling factor to get k into rad/km
          +
          kwargs : keyword arguments
          +
          keyword arguments to pass to taper
          +
          +

          Returns

          +
          +
          k : 1D array shape (n,)
          +
          wavenumber in rad/km
          +
          Phi : 1D array shape (n,)
          +
          Radial power spectrum
          +
          sigma_Phi : 1D array shape (n,)
          +
          Standard deviation of Phi
          +
          +
          +Source code +
          def radial_spectrum(self, subgrid, taper=np.hanning, scale=0.001, **kwargs):
          +    """
          +    Compute the radial spectrum for a square grid.
          +
          +    Args:
          +        subgrid : 2D array
          +            window of the original data (see subgrid method)
          +        taper : function (default=np.hanning)
          +            taper function, set to None for no taper function
          +        scale : float (default: 0.001)
          +            scaling factor to get k into rad/km
          +        kwargs : keyword arguments
          +            keyword arguments to pass to `taper`
          +
          +    Returns:
          +        k : 1D array shape (n,)
          +            wavenumber in rad/km
          +        Phi : 1D array shape (n,)
          +            Radial power spectrum
          +        sigma_Phi : 1D array shape (n,)
          +            Standard deviation of Phi
          +    """
          +
          +    data = subgrid
          +    nr, nc = data.shape
          +    nw = nr
          +
          +    if nr != nc:
          +        warnings.warn("subgrid is not square {}".format((nr,nc)), RuntimeWarning)
          +
          +
          +    # control taper
          +    if type(taper) == type(None):
          +        vtaper = 1.0
          +    else:
          +        rt = taper(nr, **kwargs)
          +        ct = taper(nc, **kwargs)
          +        xq, yq = np.meshgrid(ct, rt)
          +        vtaper = xq*yq
          +
          +    dx_scale = self.dx*scale
          +    dk = 2.0*np.pi/(nw - 1)/dx_scale
          +
          +    # fast Fourier transform and shift
          +    FT = np.abs(np.fft.fft2(data*vtaper))
          +    FT = np.fft.fftshift(FT)
          +
          +    kbins = np.arange(dk, dk*nw/2, dk)
          +    nbins = kbins.size - 1
          +
          +    S = np.empty(nbins)
          +    k = np.empty(nbins)
          +    sigma = np.empty(nbins)
          +
          +    i0 = int((nw - 1)//2)
          +    ix, iy = np.mgrid[0:nw,0:nw]
          +    kk = np.hypot((ix - i0)*dk, (iy - i0)*dk)
          +
          +    for i in range(0, nbins):
          +        mask = np.logical_and(kk >= kbins[i], kk <= kbins[i+1])
          +        rr = 2.0*np.log(FT[mask])
          +        S[i] = rr.mean()
          +        k[i] = kk[mask].mean()
          +        sigma[i] = np.std(rr)
          +
          +    return k, S, sigma
          +
          +
          +
          +def radial_spectrum_log(self, subgrid, taper=, scale=0.001, **kwargs) +
          +
          +

          Compute the log of the radial spectrum for a square grid.

          +

          Args: +subgrid : 2D array +window of the original data (see subgrid method) +taper : function (default=np.hanning) +taper function, set to None for no taper function +scale : float (detault=0.001) +scaling factor to get k into rad/km +kwargs : keyword arguments +keyword arguments to pass to taper

          +

          Returns

          +
          +
          k : 1D array shape (n,)
          +
          wavenumber in rad/km
          +
          lnPhi : 1D array
          +
          log of the radial power spectrum in ln(sqrt(S))
          +
          lnsigma_Phi : 1D array
          +
          standard deviation of lnPhi
          +
          +
          +Source code +
          def radial_spectrum_log(self, subgrid, taper=np.hanning, scale=0.001, **kwargs):
          +    """
          +    Compute the log of the radial spectrum for a square grid.
          +
          +    Args:
          +     subgrid : 2D array
          +        window of the original data (see subgrid method)
          +     taper : function (default=np.hanning)
          +        taper function, set to None for no taper function
          +     scale : float (detault=0.001)
          +        scaling factor to get k into rad/km
          +     kwargs : keyword arguments
          +        keyword arguments to pass to `taper`
          +
          +    Returns:
          +        k : 1D array shape (n,)
          +            wavenumber in rad/km
          +        lnPhi : 1D array
          +            log of the radial power spectrum in ln(sqrt(S))
          +        lnsigma_Phi : 1D array
          +            standard deviation of lnPhi
          +    """
          +
          +    data = subgrid
          +    nr, nc = data.shape
          +    nw = nr
          +
          +    if nr != nc:
          +        warnings.warn("subgrid is not square {}".format((nr,nc)), RuntimeWarning)
          +
          +
          +    # control taper
          +    if type(taper) == type(None):
          +        vtaper = 1.0
          +    else:
          +        rt = taper(nr, **kwargs)
          +        ct = taper(nc, **kwargs)
          +        xq, yq = np.meshgrid(ct, rt)
          +        vtaper = xq*yq
          +
          +    dx_scale = self.dx*scale
          +    dk = 2.0*np.pi/(nw - 1)/dx_scale
          +
          +    # fast Fourier transform and shift
          +    FT = np.abs(np.fft.fft2(data*vtaper))
          +    FT = np.fft.fftshift(FT)
          +
          +    kbins = np.arange(dk, dk*nw/2, dk)
          +    nbins = kbins.size - 1
          +
          +    S = np.empty(nbins)
          +    k = np.empty(nbins)
          +    sigma = np.empty(nbins)
          +
          +    i0 = int((nw - 1)//2)
          +    ix, iy = np.mgrid[0:nw,0:nw]
          +    kk = np.hypot((ix - i0)*dk, (iy - i0)*dk)
          +
          +    for i in range(0, nbins):
          +        mask = np.logical_and(kk >= kbins[i], kk <= kbins[i+1])
          +        rr = np.log(np.sqrt(FT[mask]))
          +        S[i] = rr.mean()
          +        k[i] = kk[mask].mean()
          +        sigma[i] = np.std(rr)
          +
          +    return k, S, sigma
          +
          +
          +
          +def reduce_to_pole(self, data, inc, dec, sinc=None, sdec=None) +
          +
          +

          Reduce total field magnetic anomaly data to the pole.

          +

          The reduction to the pole if a phase transformation that can be +applied to total field magnetic anomaly data. It simulates how +the data would be if both the Geomagnetic field and the +magnetization of the source were vertical (Blakely, 1996).

          +

          Args

          +
          +
          data : 1D array
          +
          the total field anomaly data at each point.
          +
          inc : float / 1D array
          +
          inclination of the inducing Geomagnetic field
          +
          dec : float / 1D array
          +
          declination of the inducing Geomagnetic field
          +
          sinc : float / 1D array (optional)
          +
          inclination of the total magnetization of the anomaly source
          +
          sdec : float / 1D array (optional)
          +
          declination of the total magnetization of the anomaly source +The total magnetization is the vector sum of the +induced and remanent magnetization. If there is only induced +magnetization, use the inc and dec of the Geomagnetic field.
          +
          +

          Returns

          +
          +
          rtp : 2D array
          +
          the data reduced to the pole.
          +
          +

          References

          +

          Blakely, R. J. (1996), Potential Theory in Gravity and Magnetic +Applications, Cambridge University Press.

          +

          Notes

          +

          This functions performs the reduction in the frequency domain +(using the FFT). The transform filter is (in the freq domain): +RTP(k_x, k_y) = \frac{|k|}{ +a_1 k_x^2 + a_2 k_y^2 + a_3 k_x k_y + +i|k|(b_1 k_x + b_2 k_y)} +in which k_x and k_y are the wave-numbers in the x and y +directions and +|k| = \sqrt{k_x^2 + k_y^2} \ +a_1 = m_z f_z - m_x f_x \ +a_2 = m_z f_z - m_y f_y \ +a_3 = -m_y f_x - m_x f_y \ +b_1 = m_x f_z + m_z f_x \ +b_2 = m_y f_z + m_z f_y +\mathbf{m} = (m_x, m_y, m_z)is the unit-vector of the total +magnetization of the source and +\mathbf{f} = (f_x, f_y, f_z) is the unit-vector of the +Geomagnetic field.

          +
          +Source code +
          def reduce_to_pole(self, data, inc, dec, sinc=None, sdec=None):
          +    r"""
          +    Reduce total field magnetic anomaly data to the pole.
          +
          +    The reduction to the pole if a phase transformation that can be
          +    applied to total field magnetic anomaly data. It simulates how
          +    the data would be if both the Geomagnetic field and the
          +    magnetization of the source were vertical (Blakely, 1996).
          +
          +    Args:
          +        data : 1D array
          +            the total field anomaly data at each point.
          +        inc : float / 1D array
          +            inclination of the inducing Geomagnetic field
          +        dec : float / 1D array
          +            declination of the inducing Geomagnetic field
          +        sinc : float / 1D array (optional)
          +            inclination of the total magnetization of the anomaly source
          +        sdec : float / 1D array (optional)
          +            declination of the total magnetization of the anomaly source
          +            The total magnetization is the vector sum of the
          +            induced and remanent magnetization. If there is only induced
          +            magnetization, use the *inc* and *dec* of the Geomagnetic field.
          +
          +    Returns:
          +        rtp : 2D array
          +            the data reduced to the pole.
          +    
          +    References:
          +        Blakely, R. J. (1996), Potential Theory in Gravity and Magnetic
          +        Applications, Cambridge University Press.
          +
          +    Notes:
          +        This functions performs the reduction in the frequency domain
          +        (using the FFT). The transform filter is (in the freq domain):
          +            RTP(k_x, k_y) = \frac{|k|}{
          +                a_1 k_x^2 + a_2 k_y^2 + a_3 k_x k_y +
          +                i|k|(b_1 k_x + b_2 k_y)}
          +        in which k_x and k_y are the wave-numbers in the x and y
          +        directions and
          +            |k| = \sqrt{k_x^2 + k_y^2} \\
          +            a_1 = m_z f_z - m_x f_x \\
          +            a_2 = m_z f_z - m_y f_y \\
          +            a_3 = -m_y f_x - m_x f_y \\
          +            b_1 = m_x f_z + m_z f_x \\
          +            b_2 = m_y f_z + m_z f_y
          +        \mathbf{m} = (m_x, m_y, m_z)` is the unit-vector of the total
          +        magnetization of the source and
          +        \mathbf{f} = (f_x, f_y, f_z)` is the unit-vector of the
          +        Geomagnetic field.
          +    """
          +    nr, nc = data.shape
          +
          +    if nr != nc:
          +        warnings.warn("subgrid is not square {}".format((nr,nc)), RuntimeWarning)
          +
          +    fx, fy, fz = ang2vec(1.0, inc, dec)
          +    if sinc is None or sdec is None:
          +        mx, my, mz = fx, fy, fz
          +    else:
          +        mx, my, mz = ang2vec(1.0, sinc, sdec)
          +
          +    kx, ky = [k for k in _fftfreqs(self.dx, self.dy, data.shape)]
          +    kz = np.hypot(kx, ky)
          +
          +    a1 = mz*fz - mx*fx
          +    a2 = mz*fz - my*fy
          +    a3 = -my*fx - mx*fy
          +    b1 = mx*fz + mz*fx
          +    b2 = my*fz + mz*fy
          +
          +    # The division gives a RuntimeWarning because of the zero frequency term.
          +    # This suppresses the warning.
          +    with np.errstate(divide='ignore', invalid='ignore'):
          +        rtp = (kz)/(a1*kx**2 + a2*ky**2 + a3*kx*ky + \
          +                        1j*np.sqrt(kz)*(b1*kx + b2*ky))
          +    
          +    rtp[0, 0] = 0
          +    ft_pole = rtp*np.fft.fft2(data)
          +    return np.real(np.fft.ifft2(ft_pole))
          +
          +
          +
          +def remove_trend_linear(self, data) +
          +
          +

          Remove the best-fitting linear trend from the data

          +

          This may come in handy if the magnetic data has not been +reduced to the pole.

          +

          Args

          +
          +
          data : 2D numpy array
          +
           
          +
          +

          Returns: +data : 2D numpy array

          +
          +Source code +
          def remove_trend_linear(self, data):
          +    """
          +    Remove the best-fitting linear trend from the data
          +
          +    This may come in handy if the magnetic data has not been
          +    reduced to the pole.
          +
          +    Args:
          +        data : 2D numpy array
          +
          +    Returns:
          +     data : 2D numpy array
          +    """
          +    data = data.copy()
          +    nr, nc = data.shape
          +    xq, yq = np.meshgrid(np.arange(0, nc), np.arange(0, nr))
          +
          +    A = np.column_stack((x.flatten(), y.flatten(), np.ones(x.size)))
          +    c, resid, rank, sigma = np.linalg.lstsq(A, data.flatten())
          +
          +    data.flat[:] -= np.dot(A, c)
          +    return data
          +
          +
          +
          +def subgrid(self, window, xc, yc) +
          +
          +

          Extract a subgrid from the data at a window around +the point (xc,yc)

          +

          Args

          +
          +
          xc : float
          +
          x coordinate
          +
          yc : float
          +
          y coordinate
          +
          window : float
          +
          size of window in metres
          +
          +

          Returns

          +
          +
          data : 2D array
          +
          subgrid encompassing window size
          +
          +
          +Source code +
          def subgrid(self, window, xc, yc):
          +    """
          +    Extract a subgrid from the data at a window around
          +    the point (xc,yc)
          +    
          +    Args:
          +        xc : float
          +            x coordinate
          +        yc : float
          +            y coordinate
          +        window : float
          +            size of window in metres
          +
          +    Returns:
          +        data : 2D array
          +            subgrid encompassing window size
          +    """
          +
          +    # check in coordinate in grid
          +    if xc < self.xmin or xc > self.xmax or yc < self.ymin or yc > self.ymax:
          +        raise ValueError("Point ({},{}) outside data range".format(xc,yc))
          +
          +    # find nearest index to xc,yc
          +    ix = np.abs(self.xcoords - xc).argmin()
          +    iy = np.abs(self.ycoords - yc).argmin()
          +
          +    nw = int(round(window/self.dx))
          +    n2w = nw//2
          +
          +    # extract a square window from the data
          +    imin = ix - n2w
          +    imax = ix + n2w + 1
          +    jmin = iy - n2w
          +    jmax = iy + n2w + 1
          +
          +    # safeguard if window size is larger than grid
          +    imin = max(imin, 0)
          +    imax = min(imax, self.nx)
          +    jmin = max(jmin, 0)
          +    jmax = min(jmax, self.ny)
          +    
          +    data = self.data[jmin:jmax, imin:imax]
          +
          +    return data
          +
          +
          +
          +def upward_continuation(self, data, height) +
          +
          +

          Upward continuation of potential field data.

          +

          Calculates the continuation through the Fast Fourier Transform in +the wavenumber domain (Blakely, 1996):

          +
          F\{h_{up}\} = F\{h\} e^{-\Delta z |k|}
          +
          +

          and then transformed back to the space domain. :math:h_{up} is the +upward continue data, \Delta z is the height increase, F denotes +the Fourier Transform, |k| is the wavenumber modulus.

          +

          Args

          +
          +
          data +: 2D array
          +
          potential field at the grid points
          +
          height : float
          +
          height increase (delta z) in meters.
          +
          +

          Returns

          +
          +
          cont : array
          +
          upward continued data
          +
          +

          Notes

          +

          It is not possible to get the FFT of a masked grid. The default +:func:fatiando.gridder.interp call using minimum curvature will +not be suitable. +Use extrapolate=True or algorithm='nearest' to +get an unmasked grid.

          +

          References

          +

          Blakely, R. J. (1996), Potential Theory in Gravity and Magnetic +Applications, Cambridge University Press.

          +
          +Source code +
          def upward_continuation(self, data, height):
          +    r"""
          +    Upward continuation of potential field data.
          +
          +    Calculates the continuation through the Fast Fourier Transform in
          +    the wavenumber domain (Blakely, 1996):
          +
          +        F\{h_{up}\} = F\{h\} e^{-\Delta z |k|}
          +
          +    and then transformed back to the space domain. :math:`h_{up}` is the
          +    upward continue data, \Delta z is the height increase, F denotes
          +    the Fourier Transform, |k| is the wavenumber modulus.
          +
          +    Args:
          +        data   : 2D array
          +            potential field at the grid points
          +        height : float
          +            height increase (delta z) in meters.
          +    
          +    Returns:
          +        cont : array
          +            upward continued data
          +
          +    Notes:
          +        It is not possible to get the FFT of a masked grid. The default
          +        :func:`fatiando.gridder.interp` call using minimum curvature will
          +        not be suitable.  Use extrapolate=True or algorithm='nearest' to
          +        get an unmasked grid.
          +
          +    References:
          +        Blakely, R. J. (1996), Potential Theory in Gravity and Magnetic
          +        Applications, Cambridge University Press.
          +    """
          +    nr, nc = data.shape
          +
          +    if nr != nc:
          +        warnings.warn("subgrid is not square {}".format((nr,nc)), RuntimeWarning)
          +
          +    if height <= 0:
          +        warnings.warn("Using 'height' <= 0 means downward continuation, " +
          +                      "which is known to be unstable.")
          +
          +    fx = 2.0*np.pi*np.fft.fftfreq(nr, self.dx)
          +    fy = 2.0*np.pi*np.fft.fftfreq(nc, self.dy)
          +
          +    kx, ky = np.meshgrid(fy, fx)[::-1]
          +    kz = np.hypot(kx, ky)
          +
          +    upcont_ft = np.fft.fft2(data)*np.exp(-height*kz)
          +    cont = np.real(np.fft.ifft2(upcont_ft))
          +    return cont
          +
          +
          +
          +
          +
          +
          +
          + +
          + + + + + \ No newline at end of file diff --git a/docs/index.html b/docs/index.html new file mode 100644 index 0000000..fae4ccf --- /dev/null +++ b/docs/index.html @@ -0,0 +1,128 @@ + + + + + + +pycurious API documentation + + + + + + + + + +
          +
          +
          +

          Module pycurious

          +
          +
          +

          Copyright 2018 Ben Mather, Robert Delhaye

          +

          This file is part of PyCurious.

          +

          PyCurious is free software: you can redistribute it and/or modify +it under the terms of the GNU Lesser General Public License as published by +the Free Software Foundation, either version 3 of the License, or any later version.

          +

          PyCurious is distributed in the hope that it will be useful, +but WITHOUT ANY WARRANTY; without even the implied warranty of +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. +See the +GNU Lesser General Public License for more details.

          +

          You should have received a copy of the GNU Lesser General Public License +along with PyCurious. +If not, see http://www.gnu.org/licenses/.

          +
          +Source code +
          """
          +Copyright 2018 Ben Mather, Robert Delhaye
          +
          +This file is part of PyCurious.
          +
          +PyCurious is free software: you can redistribute it and/or modify
          +it under the terms of the GNU Lesser General Public License as published by
          +the Free Software Foundation, either version 3 of the License, or any later version.
          +
          +PyCurious is distributed in the hope that it will be useful,
          +but WITHOUT ANY WARRANTY; without even the implied warranty of
          +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
          +GNU Lesser General Public License for more details.
          +
          +You should have received a copy of the GNU Lesser General Public License
          +along with PyCurious.  If not, see <http://www.gnu.org/licenses/>.
          +"""
          +
          +# -*- coding: utf-8 -*-
          +from .documentation import install_documentation
          +from .grid import CurieGrid, bouligand2009, tanaka1999, maus1995, ComputeTanaka
          +from .optimise import CurieOptimise
          +from .mapping import transform_coordinates
          +from .mapping import convert_extent
          +from .mapping import trim
          +from .mapping import grid
          +from .mapping import import_geotiff
          +
          +
          +
          +

          Sub-modules

          +
          +
          pycurious.documentation
          +
          +

          Copyright 2018 Ben Mather, Robert Delhaye …

          +
          +
          pycurious.grid
          +
          +

          Copyright 2018 Ben Mather, Robert Delhaye …

          +
          +
          pycurious.mapping
          +
          +

          Copyright 2018 Ben Mather, Robert Delhaye …

          +
          +
          pycurious.optimise
          +
          +

          Copyright 2018 Ben Mather, Robert Delhaye …

          +
          +
          pycurious.parallel
          +
          +

          Copyright 2018 Ben Mather, Robert Delhaye …

          +
          +
          pycurious.therm
          +
          +

          Copyright 2018 Ben Mather, Robert Delhaye …

          +
          +
          +
          +
          +
          +
          +
          +
          +
          +
          + +
          + + + + + \ No newline at end of file diff --git a/docs/mapping.html b/docs/mapping.html new file mode 100644 index 0000000..c476d4e --- /dev/null +++ b/docs/mapping.html @@ -0,0 +1,714 @@ + + + + + + +pycurious.mapping API documentation + + + + + + + + + +
          +
          +
          +

          Module pycurious.mapping

          +
          +
          +

          Copyright 2018 Ben Mather, Robert Delhaye

          +

          This file is part of PyCurious.

          +

          PyCurious is free software: you can redistribute it and/or modify +it under the terms of the GNU Lesser General Public License as published by +the Free Software Foundation, either version 3 of the License, or any later version.

          +

          PyCurious is distributed in the hope that it will be useful, +but WITHOUT ANY WARRANTY; without even the implied warranty of +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. +See the +GNU Lesser General Public License for more details.

          +

          You should have received a copy of the GNU Lesser General Public License +along with PyCurious. +If not, see http://www.gnu.org/licenses/.

          +
          +Source code +
          """
          +Copyright 2018 Ben Mather, Robert Delhaye
          +
          +This file is part of PyCurious.
          +
          +PyCurious is free software: you can redistribute it and/or modify
          +it under the terms of the GNU Lesser General Public License as published by
          +the Free Software Foundation, either version 3 of the License, or any later version.
          +
          +PyCurious is distributed in the hope that it will be useful,
          +but WITHOUT ANY WARRANTY; without even the implied warranty of
          +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
          +GNU Lesser General Public License for more details.
          +
          +You should have received a copy of the GNU Lesser General Public License
          +along with PyCurious.  If not, see <http://www.gnu.org/licenses/>.
          +"""
          +
          +# -*- coding: utf-8 -*-
          +import numpy as np
          +
          +try: range=xrange
          +except: pass
          +
          +def transform_coordinates(x, y, epsg_in, epsg_out):
          +    """
          +    Transform between any coordinate system.
          +
          +    Requires `pyproj`
          +    """
          +    import pyproj
          +    proj_in  = pyproj.Proj("+init=EPSG:"+str(epsg_in))
          +    proj_out = pyproj.Proj("+init=EPSG:"+str(epsg_out))
          +    return pyproj.transform(proj_in, proj_out, x, y)
          +
          +
          +def convert_extent(extent_in, epsg_in, epsg_out):
          +    """
          +    Transform extent from epsg_in to epsg_out
          +
          +    Args:
          +        extent_in : tuple
          +            bounding box [minX, maxX, minY, maxY]
          +        epsg_in : int
          +            CRS of extent
          +        epsg_out : int
          +            CRS of output
          +
          +    Returns:
          +        extent_out : tuple
          +            bounding box in new CRS
          +    """
          +    xmin, xmax, ymin, ymax = extent_in
          +    xi = [xmin, xmin, xmax, xmax]
          +    yi = [ymin, ymax, ymin, ymax]
          +    xo, yo = transform_coordinates(xi, yi, epsg_in, epsg_out)
          +    extent_out = [min(xo), max(xo), min(yo), max(yo)]
          +    return extent_out
          +
          +
          +def trim(coords, data, extent, buffer_amount=0.0):
          +    """
          +    Trim a smaller section of a large dataset taking into
          +    consideration transformations into various coordinate
          +    reference systems (CRS)
          +    
          +    Args:
          +        coords : array shape (n,2)
          +            geographical / projected coordinates
          +        data : array shape (n,)
          +            values corresponding to coordinates
          +        extent : tuple
          +            bounding box to trim data
          +        buffer : float
          +            amount of buffer to include (default=0.0)
          +
          +    Returns:
          +        coords_trim : array shape (l,2)
          +            trimmed coordinates
          +        data_trim : array shape (l,2)
          +            trimmed data array
          +    """
          +    xmin, xmax, ymin, ymax = extent
          +
          +    # Extract only the data within the extent
          +    data_mask = np.ones(data.shape[0], dtype=bool)
          +
          +    # Add a 1 percent buffer zone
          +    x_buffer = buffer_amount*(xmax - xmin)
          +    y_buffer = buffer_amount*(ymax - ymin)
          +
          +    mask_e = coords[:,0] < xmin - x_buffer
          +    mask_w = coords[:,0] > xmax + x_buffer
          +    mask_n = coords[:,1] < ymin - y_buffer
          +    mask_s = coords[:,1] > ymax + y_buffer
          +    data_mask[mask_n] = False
          +    data_mask[mask_s] = False
          +    data_mask[mask_e] = False
          +    data_mask[mask_w] = False
          +    
          +    data_trim = data[data_mask]
          +    coords_trim = coords[data_mask]
          +
          +    return coords_trim, data_trim
          +
          +
          +def grid(coords, data, extent, shape=None, epsg_in=None, epsg_out=None, **kwargs):
          +    """
          +    Grid a smaller section of a large dataset taking into
          +    consideration transformations into various coordinate
          +    reference systems (CRS)
          +    
          +    Args:
          +        coords : array shape (n,2)
          +            geographical coordinates
          +        data : array shape (n,) 
          +            values corresponding to coordinates
          +        extent : tuple
          +           box contained within the data in espg_out coordinates
          +        shape : tuple (nrows,ncols)
          +           size of the box, if None, shape is estimated from coords spacing
          +        epsg_in : int
          +           CRS of data (if transformation is required)
          +        epsg_out : int
          +           CRS of grid (if transformation is required)
          +        kwargs : keyword arguments
          +           keyword arguments to pass to griddata from
          +           `scipy.interpolate.griddata`
          +    
          +    Returns:
          +        grid : array shape (nrows, ncols)
          +            rectangular section of data bounded by extent
          +    """
          +    from scipy.interpolate import griddata
          +    xmin, xmax, ymin, ymax = extent
          +    
          +    if type(epsg_in) != type(None):
          +        xt, yt = transform_coordinates(np.array([xmin, xmin, xmax, xmax]),\
          +                                       np.array([ymin, ymax, ymin, ymax]),\
          +                                       epsg_out, epsg_in)
          +        # find the coordinates that will completely
          +        # engulf the extent
          +        xtmin, xtmax = min(xt), max(xt)
          +        ytmin, ytmax = min(yt), max(yt)
          +    else:
          +        xtmin, xtmax = xmin, xmax
          +        ytmin, ytmax = ymin, ymax
          +
          +    xtextent = [xtmin, xtmax, ytmin, ytmax]
          +
          +    # trim data - buffer = 5%
          +    coords_trim, data_trim = trim(coords, data, xtextent, 0.05)
          +
          +
          +    if type(epsg_in) != type(None):
          +        # convert back to output CRS
          +        xtrim, ytrim = transform_coordinates(coords_trim[:,0],\
          +                                             coords_trim[:,1],\
          +                                             epsg_in, epsg_out)
          +        coords_trim = np.column_stack([xtrim, ytrim])
          +
          +
          +    if shape == None:
          +        # estimate based on the data spacing
          +        xunique = np.unique(coords_trim[:,0])
          +        yunique = np.unique(coords_trim[:,1])
          +        dx = np.diff(xunique).mean()
          +        dy = np.diff(yunique).mean()
          +        nc = int((xtmax - xtmin)/dx)
          +        nr = int((ytmax - ytmin)/dy)
          +        print("using nrows={}, ncols={} with cell spacing of {}".format(nr,nc,(dy,dx)))
          +    else:
          +        nr, nc = shape
          +
          +    # interpolate
          +
          +    xcoords = np.linspace(xmin, xmax, nc)
          +    ycoords = np.linspace(ymin, ymax, nr)
          +    xq, yq = np.meshgrid(xcoords, ycoords)
          +
          +    vq = griddata(coords_trim, data_trim, (xq, yq), **kwargs)
          +    return vq
          +
          +
          +def import_geotiff(file_path):
          +    """
          +    Import a GeoTIFF to a numpy array and prints
          +    information of the Coordinate Reference System (CRS)
          +
          +    Args:
          +        file_path : str
          +            path to the GeoTIFF
          +
          +    Returns:
          +        data : 2D array
          +        extent : tuple
          +            extent in the projection of the GeoTIFF
          +            e.g. [xmin, xmax, ymin, ymax]
          +    """
          +    from osgeo import gdal, osr
          +    
          +    gtiff = gdal.Open(file_path)
          +    data = gtiff.ReadAsArray()
          +    gt = gtiff.GetGeoTransform()
          +    gtproj = gtiff.GetProjection()
          +
          +    inproj = osr.SpatialReference()
          +    inproj.ImportFromWkt(gtproj)
          +
          +    gtextent = (gt[0], gt[0] + gtiff.RasterXSize*gt[1],\
          +                gt[3], gt[3] + gtiff.RasterYSize*gt[5])
          +
          +    # print projection information
          +    print(inproj)
          +
          +    # this closes the geotiff
          +    gtiff = None
          +
          +    return data, gtextent
          +
          +
          +def export_geotiff(file_path, array, extent, epsg):
          +    """
          +    Export a GeoTIFF from a numpy array projected in a
          +    predefined Coordinate Reference System (CRS)
          +
          +    Args:
          +        file_path : str
          +            path to write the GeoTIFF
          +        array: 2D array
          +            array to save to GeoTiff
          +        extent : tuple
          +            extent in the projection of the GeoTIFF
          +            e.g. [xmin, xmax, ymin, ymax]
          +        epsg : int
          +            CRS of the GeoTIFF
          +            e.g. 4326 for WGS84
          +
          +    """
          +    from osgeo import gdal, osr
          +    # import ogr, gdal, osr, os
          +
          +    cols = array.shape[1]
          +    rows = array.shape[0]
          +
          +    xmin, xmax, ymin, ymax = extent
          +    spacingX = (xmax - xmin)/cols
          +    spacingY = (ymax - ymin)/rows
          +
          +    driver = gdal.GetDriverByName('GTiff')
          +    outRaster = driver.Create(file_path, cols, rows, 1, gdal.GDT_Float64)
          +    outRaster.SetGeoTransform((xmin, spacingX, 0, ymin, 0, spacingY))
          +    outband = outRaster.GetRasterBand(1)
          +    outband.WriteArray(array)
          +    outRasterSRS = osr.SpatialReference()
          +    outRasterSRS.ImportFromEPSG(epsg)
          +    outRaster.SetProjection(outRasterSRS.ExportToWkt())
          +    outband.FlushCache()
          +    return
          +
          +
          +
          +
          +
          +
          +
          +

          Functions

          +
          +
          +def convert_extent(extent_in, epsg_in, epsg_out) +
          +
          +

          Transform extent from epsg_in to epsg_out

          +

          Args

          +
          +
          extent_in : tuple
          +
          bounding box [minX, maxX, minY, maxY]
          +
          epsg_in : int
          +
          CRS of extent
          +
          epsg_out : int
          +
          CRS of output
          +
          +

          Returns

          +
          +
          extent_out : tuple
          +
          bounding box in new CRS
          +
          +
          +Source code +
          def convert_extent(extent_in, epsg_in, epsg_out):
          +    """
          +    Transform extent from epsg_in to epsg_out
          +
          +    Args:
          +        extent_in : tuple
          +            bounding box [minX, maxX, minY, maxY]
          +        epsg_in : int
          +            CRS of extent
          +        epsg_out : int
          +            CRS of output
          +
          +    Returns:
          +        extent_out : tuple
          +            bounding box in new CRS
          +    """
          +    xmin, xmax, ymin, ymax = extent_in
          +    xi = [xmin, xmin, xmax, xmax]
          +    yi = [ymin, ymax, ymin, ymax]
          +    xo, yo = transform_coordinates(xi, yi, epsg_in, epsg_out)
          +    extent_out = [min(xo), max(xo), min(yo), max(yo)]
          +    return extent_out
          +
          +
          +
          +def export_geotiff(file_path, array, extent, epsg) +
          +
          +

          Export a GeoTIFF from a numpy array projected in a +predefined Coordinate Reference System (CRS)

          +

          Args

          +
          +
          file_path : str
          +
          path to write the GeoTIFF
          +
          array
          +
          2D array +array to save to GeoTiff
          +
          extent : tuple
          +
          extent in the projection of the GeoTIFF +e.g. [xmin, xmax, ymin, ymax]
          +
          epsg : int
          +
          CRS of the GeoTIFF +e.g. 4326 for WGS84
          +
          +
          +Source code +
          def export_geotiff(file_path, array, extent, epsg):
          +    """
          +    Export a GeoTIFF from a numpy array projected in a
          +    predefined Coordinate Reference System (CRS)
          +
          +    Args:
          +        file_path : str
          +            path to write the GeoTIFF
          +        array: 2D array
          +            array to save to GeoTiff
          +        extent : tuple
          +            extent in the projection of the GeoTIFF
          +            e.g. [xmin, xmax, ymin, ymax]
          +        epsg : int
          +            CRS of the GeoTIFF
          +            e.g. 4326 for WGS84
          +
          +    """
          +    from osgeo import gdal, osr
          +    # import ogr, gdal, osr, os
          +
          +    cols = array.shape[1]
          +    rows = array.shape[0]
          +
          +    xmin, xmax, ymin, ymax = extent
          +    spacingX = (xmax - xmin)/cols
          +    spacingY = (ymax - ymin)/rows
          +
          +    driver = gdal.GetDriverByName('GTiff')
          +    outRaster = driver.Create(file_path, cols, rows, 1, gdal.GDT_Float64)
          +    outRaster.SetGeoTransform((xmin, spacingX, 0, ymin, 0, spacingY))
          +    outband = outRaster.GetRasterBand(1)
          +    outband.WriteArray(array)
          +    outRasterSRS = osr.SpatialReference()
          +    outRasterSRS.ImportFromEPSG(epsg)
          +    outRaster.SetProjection(outRasterSRS.ExportToWkt())
          +    outband.FlushCache()
          +    return
          +
          +
          +
          +def grid(coords, data, extent, shape=None, epsg_in=None, epsg_out=None, **kwargs) +
          +
          +

          Grid a smaller section of a large dataset taking into +consideration transformations into various coordinate +reference systems (CRS)

          +

          Args

          +
          +
          coords : array shape (n,2)
          +
          geographical coordinates
          +
          data : array shape (n,)
          +
          values corresponding to coordinates
          +
          extent : tuple
          +
           
          +
          box contained within the data in espg_out coordinates
          +
          shape : tuple (nrows,ncols)
          +
           
          +
          size of the box, if None, shape is estimated from coords spacing
          +
          epsg_in : int
          +
           
          +
          CRS of data (if transformation is required)
          +
          epsg_out : int
          +
           
          +
          CRS of grid (if transformation is required)
          +
          kwargs : keyword arguments
          +
           
          +
          +

          keyword arguments to pass to griddata from +scipy.interpolate.griddata

          +

          Returns

          +
          +
          grid() : array shape (nrows, ncols)
          +
          rectangular section of data bounded by extent
          +
          +
          +Source code +
          def grid(coords, data, extent, shape=None, epsg_in=None, epsg_out=None, **kwargs):
          +    """
          +    Grid a smaller section of a large dataset taking into
          +    consideration transformations into various coordinate
          +    reference systems (CRS)
          +    
          +    Args:
          +        coords : array shape (n,2)
          +            geographical coordinates
          +        data : array shape (n,) 
          +            values corresponding to coordinates
          +        extent : tuple
          +           box contained within the data in espg_out coordinates
          +        shape : tuple (nrows,ncols)
          +           size of the box, if None, shape is estimated from coords spacing
          +        epsg_in : int
          +           CRS of data (if transformation is required)
          +        epsg_out : int
          +           CRS of grid (if transformation is required)
          +        kwargs : keyword arguments
          +           keyword arguments to pass to griddata from
          +           `scipy.interpolate.griddata`
          +    
          +    Returns:
          +        grid : array shape (nrows, ncols)
          +            rectangular section of data bounded by extent
          +    """
          +    from scipy.interpolate import griddata
          +    xmin, xmax, ymin, ymax = extent
          +    
          +    if type(epsg_in) != type(None):
          +        xt, yt = transform_coordinates(np.array([xmin, xmin, xmax, xmax]),\
          +                                       np.array([ymin, ymax, ymin, ymax]),\
          +                                       epsg_out, epsg_in)
          +        # find the coordinates that will completely
          +        # engulf the extent
          +        xtmin, xtmax = min(xt), max(xt)
          +        ytmin, ytmax = min(yt), max(yt)
          +    else:
          +        xtmin, xtmax = xmin, xmax
          +        ytmin, ytmax = ymin, ymax
          +
          +    xtextent = [xtmin, xtmax, ytmin, ytmax]
          +
          +    # trim data - buffer = 5%
          +    coords_trim, data_trim = trim(coords, data, xtextent, 0.05)
          +
          +
          +    if type(epsg_in) != type(None):
          +        # convert back to output CRS
          +        xtrim, ytrim = transform_coordinates(coords_trim[:,0],\
          +                                             coords_trim[:,1],\
          +                                             epsg_in, epsg_out)
          +        coords_trim = np.column_stack([xtrim, ytrim])
          +
          +
          +    if shape == None:
          +        # estimate based on the data spacing
          +        xunique = np.unique(coords_trim[:,0])
          +        yunique = np.unique(coords_trim[:,1])
          +        dx = np.diff(xunique).mean()
          +        dy = np.diff(yunique).mean()
          +        nc = int((xtmax - xtmin)/dx)
          +        nr = int((ytmax - ytmin)/dy)
          +        print("using nrows={}, ncols={} with cell spacing of {}".format(nr,nc,(dy,dx)))
          +    else:
          +        nr, nc = shape
          +
          +    # interpolate
          +
          +    xcoords = np.linspace(xmin, xmax, nc)
          +    ycoords = np.linspace(ymin, ymax, nr)
          +    xq, yq = np.meshgrid(xcoords, ycoords)
          +
          +    vq = griddata(coords_trim, data_trim, (xq, yq), **kwargs)
          +    return vq
          +
          +
          +
          +def import_geotiff(file_path) +
          +
          +

          Import a GeoTIFF to a numpy array and prints +information of the Coordinate Reference System (CRS)

          +

          Args

          +
          +
          file_path : str
          +
          path to the GeoTIFF
          +
          +

          Returns

          +
          +
          data : 2D array
          +
           
          +
          extent : tuple
          +
          extent in the projection of the GeoTIFF +e.g. [xmin, xmax, ymin, ymax]
          +
          +
          +Source code +
          def import_geotiff(file_path):
          +    """
          +    Import a GeoTIFF to a numpy array and prints
          +    information of the Coordinate Reference System (CRS)
          +
          +    Args:
          +        file_path : str
          +            path to the GeoTIFF
          +
          +    Returns:
          +        data : 2D array
          +        extent : tuple
          +            extent in the projection of the GeoTIFF
          +            e.g. [xmin, xmax, ymin, ymax]
          +    """
          +    from osgeo import gdal, osr
          +    
          +    gtiff = gdal.Open(file_path)
          +    data = gtiff.ReadAsArray()
          +    gt = gtiff.GetGeoTransform()
          +    gtproj = gtiff.GetProjection()
          +
          +    inproj = osr.SpatialReference()
          +    inproj.ImportFromWkt(gtproj)
          +
          +    gtextent = (gt[0], gt[0] + gtiff.RasterXSize*gt[1],\
          +                gt[3], gt[3] + gtiff.RasterYSize*gt[5])
          +
          +    # print projection information
          +    print(inproj)
          +
          +    # this closes the geotiff
          +    gtiff = None
          +
          +    return data, gtextent
          +
          +
          +
          +def transform_coordinates(x, y, epsg_in, epsg_out) +
          +
          +

          Transform between any coordinate system.

          +

          Requires pyproj

          +
          +Source code +
          def transform_coordinates(x, y, epsg_in, epsg_out):
          +    """
          +    Transform between any coordinate system.
          +
          +    Requires `pyproj`
          +    """
          +    import pyproj
          +    proj_in  = pyproj.Proj("+init=EPSG:"+str(epsg_in))
          +    proj_out = pyproj.Proj("+init=EPSG:"+str(epsg_out))
          +    return pyproj.transform(proj_in, proj_out, x, y)
          +
          +
          +
          +def trim(coords, data, extent, buffer_amount=0.0) +
          +
          +

          Trim a smaller section of a large dataset taking into +consideration transformations into various coordinate +reference systems (CRS)

          +

          Args

          +
          +
          coords : array shape (n,2)
          +
          geographical / projected coordinates
          +
          data : array shape (n,)
          +
          values corresponding to coordinates
          +
          extent : tuple
          +
          bounding box to trim data
          +
          buffer : float
          +
          amount of buffer to include (default=0.0)
          +
          +

          Returns

          +
          +
          coords_trim : array shape (l,2)
          +
          trimmed coordinates
          +
          data_trim : array shape (l,2)
          +
          trimmed data array
          +
          +
          +Source code +
          def trim(coords, data, extent, buffer_amount=0.0):
          +    """
          +    Trim a smaller section of a large dataset taking into
          +    consideration transformations into various coordinate
          +    reference systems (CRS)
          +    
          +    Args:
          +        coords : array shape (n,2)
          +            geographical / projected coordinates
          +        data : array shape (n,)
          +            values corresponding to coordinates
          +        extent : tuple
          +            bounding box to trim data
          +        buffer : float
          +            amount of buffer to include (default=0.0)
          +
          +    Returns:
          +        coords_trim : array shape (l,2)
          +            trimmed coordinates
          +        data_trim : array shape (l,2)
          +            trimmed data array
          +    """
          +    xmin, xmax, ymin, ymax = extent
          +
          +    # Extract only the data within the extent
          +    data_mask = np.ones(data.shape[0], dtype=bool)
          +
          +    # Add a 1 percent buffer zone
          +    x_buffer = buffer_amount*(xmax - xmin)
          +    y_buffer = buffer_amount*(ymax - ymin)
          +
          +    mask_e = coords[:,0] < xmin - x_buffer
          +    mask_w = coords[:,0] > xmax + x_buffer
          +    mask_n = coords[:,1] < ymin - y_buffer
          +    mask_s = coords[:,1] > ymax + y_buffer
          +    data_mask[mask_n] = False
          +    data_mask[mask_s] = False
          +    data_mask[mask_e] = False
          +    data_mask[mask_w] = False
          +    
          +    data_trim = data[data_mask]
          +    coords_trim = coords[data_mask]
          +
          +    return coords_trim, data_trim
          +
          +
          +
          +
          +
          +
          +
          + +
          + + + + + \ No newline at end of file diff --git a/docs/optimise.html b/docs/optimise.html new file mode 100644 index 0000000..b600418 --- /dev/null +++ b/docs/optimise.html @@ -0,0 +1,2141 @@ + + + + + + +pycurious.optimise API documentation + + + + + + + + + +
          +
          +
          +

          Module pycurious.optimise

          +
          +
          +

          Copyright 2018 Ben Mather, Robert Delhaye

          +

          This file is part of PyCurious.

          +

          PyCurious is free software: you can redistribute it and/or modify +it under the terms of the GNU Lesser General Public License as published by +the Free Software Foundation, either version 3 of the License, or any later version.

          +

          PyCurious is distributed in the hope that it will be useful, +but WITHOUT ANY WARRANTY; without even the implied warranty of +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. +See the +GNU Lesser General Public License for more details.

          +

          You should have received a copy of the GNU Lesser General Public License +along with PyCurious. +If not, see http://www.gnu.org/licenses/.

          +
          +Source code +
          """
          +Copyright 2018 Ben Mather, Robert Delhaye
          +
          +This file is part of PyCurious.
          +
          +PyCurious is free software: you can redistribute it and/or modify
          +it under the terms of the GNU Lesser General Public License as published by
          +the Free Software Foundation, either version 3 of the License, or any later version.
          +
          +PyCurious is distributed in the hope that it will be useful,
          +but WITHOUT ANY WARRANTY; without even the implied warranty of
          +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
          +GNU Lesser General Public License for more details.
          +
          +You should have received a copy of the GNU Lesser General Public License
          +along with PyCurious.  If not, see <http://www.gnu.org/licenses/>.
          +"""
          +
          +# -*- coding: utf-8 -*-
          +from .grid import CurieGrid, bouligand2009
          +import numpy as np
          +import warnings
          +from scipy.optimize import minimize
          +from scipy.special import polygamma
          +from scipy import stats
          +from multiprocessing import Pool, Process, Queue, cpu_count
          +
          +try: range=xrange
          +except: pass
          +
          +
          +class CurieOptimise(CurieGrid):
          +    """
          +    Extends the CurieGrid class to include optimisation routines
          +    see scipy.optimize.minimize for a description of the algorithm
          +
          +    Args:
          +        grid : 2D numpy array
          +            2D array of magnetic data
          +        xmin : float
          +            minimum x bound in metres
          +        xmax : float
          +            maximum x bound in metres
          +        ymin : float
          +            minimum y bound in metres
          +        ymax : float
          +            maximum y bound in metres
          +    
          +    Attributes:
          +        bounds : list of tuples
          +            lower and upper bounds for beta, zt, dz, C
          +        prior  : dict
          +            dictionary of priors for beta, zt, dz, C
          +    """
          +    def __init__(self, grid, xmin, xmax, ymin, ymax, **kwargs):
          +
          +        super(CurieOptimise, self).__init__(grid, xmin, xmax, ymin, ymax)
          +
          +        # initialise prior dictionary
          +        self.reset_priors()
          +
          +        # lower / upper bounds
          +        # [beta, zt, dz, C]
          +        lb = [0.0, 0.0, 0.0, None]
          +        ub = [None]*len(lb)
          +        bounds = list(zip(lb,ub))
          +        self.bounds = bounds
          +
          +        self.max_processors = kwargs.pop("max_processors", cpu_count())
          +
          +        return
          +
          +    def add_prior(self, **kwargs):
          +        """
          +        Add a prior to the dictionary (tuple)
          +        Available priors are beta, zt, dz, C
          +
          +        Assumes a normal distribution or
          +        define another distribution from scipy.stats
          +
          +        Usage:
          +            >>> add_prior(beta=(p, sigma_p))
          +
          +            >>> add_prior(beta=scipy.stats.norm(p, sigma_p))
          +        """
          +
          +        for key in kwargs:
          +            if key in self.prior:
          +                prior = kwargs[key]
          +                if type(prior) == tuple:
          +                    p, sigma_p = prior
          +                    pdf = stats.norm(p, sigma_p)
          +                elif type(prior) == stats._distn_infrastructure.rv_frozen:
          +                    pdf = prior
          +                else:
          +                    raise ValueError("Use a distribution from scipy.stats module")
          +
          +                # add prior PDF to dictionary
          +                self.prior_pdf[key] = pdf
          +                self.prior[key] = list(pdf.args)
          +
          +            else:
          +                raise ValueError("prior must be one of {}".format(self.prior.keys()))
          +
          +
          +    def reset_priors(self):
          +        """
          +        Reset priors to uniform distribution
          +        """
          +        self.prior = {'beta':None, 'zt':None, 'dz':None, 'C':None}
          +        self.prior_pdf = {'beta':None, 'zt':None, 'dz':None, 'C':None}
          +
          +
          +    def objective_routine(self, **kwargs):
          +        """
          +        Evaluate the objective routine to find the misfit with priors
          +        Only keys stored in self.prior will be added to the total misfit
          +
          +        Usage:
          +            >>> objective_routine(beta=2.5)
          +
          +        Returns:
          +            misfit  : float
          +                misfit integrated over all observations and priors
          +        """
          +        c = 0.0
          +
          +        for key in kwargs:
          +            val = kwargs[key]
          +            if key in self.prior:
          +                prior_args = self.prior[key]
          +                if prior_args is not None:
          +                    c += self.objective_function(val, *prior_args)
          +        return c
          +
          +    def objective_function(self, x, x0, sigma_x0, *args):
          +        """
          +        Objective function used in `objective_routine`
          +        Evaluates the l2-norm misfit
          +
          +        Args:
          +            x : float, ndarray
          +            x0 : float, ndarray
          +            sigma_x0 : float, ndarray
          +
          +        Returns:
          +            misfit   : float
          +        """
          +        return 0.5*np.sum((x - x0)**2/sigma_x0**2)
          +
          +
          +    def min_func(self, x, kh, Phi, sigma_Phi):
          +        """
          +        Function to minimise
          +
          +        Args:
          +            x : array shape (n,)
          +                array of variables [beta, zt, dz, C]
          +            kh : array shape (n,)
          +                wavenumbers (rad/km)
          +            Phi : array shape (n,)
          +                radial power spectrum
          +            sigma_Phi : array shape (n,)
          +                standard deviation of Phi
          +
          +        Returns:
          +            misfit    : float
          +                sum of misfit (float)
          +
          +        Notes:
          +            We purposely ignore all warnings raised by the bouligand2009
          +            function because some combinations of input parameters will
          +            trigger an out-of-range warning that will crash the minimiser.
          +            Instead, the misfit is set to a very large number when this occurs.
          +        """
          +        beta, zt, dz, C = x
          +        with warnings.catch_warnings() as w:
          +            warnings.simplefilter("ignore")
          +            Phi_syn = bouligand2009(kh, beta, zt, dz, C)
          +
          +        misfit = self.objective_function(Phi_syn, Phi, 1.0)
          +        if not np.isfinite(misfit):
          +            misfit = 1e99
          +        else:
          +            misfit += self.objective_routine(beta=beta, zt=zt, dz=dz, C=C)
          +        return misfit
          +
          +
          +    def optimise(self, window, xc, yc, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs):
          +        """
          +        Find the optimal parameters of beta, zt, dz, C for a given
          +        centroid (xc,yc) and window size.
          +
          +        Args:
          +            window  : float
          +                size of window in metres
          +            xc : float
          +                centroid x values
          +            yc : float
          +                centroid y values
          +            beta : float
          +                fractal parameter (starting value)
          +            zt : float
          +                top of magnetic layer (starting value)
          +            dz : float
          +                thickness of magnetic layer (starting value)
          +            C : float
          +                field constant (starting value)
          +            taper : taper (default=np.hanning)
          +                taper function, set to None for no taper function
          +            process_subgrids : function
          +                a custom function to process the subgrid
          +            kwargs : keyword arguments
          +                to pass to radial_spectrum.
          +
          +        Returns:
          +            beta : float
          +                fractal parameters
          +            zt : float
          +                top of magnetic layer
          +            dz : float
          +                thickness of magnetic layer
          +            C : float
          +                field constant
          +        """
          +
          +        if type(process_subgrid) == type(None):
          +            # dummy function
          +            def process_subgrid(subgrid):
          +                return subgrid
          +
          +        # initial constants for minimisation
          +        # w = 1.0 # weight low frequency?
          +
          +        x0 = np.array([beta, zt, dz, C])
          +
          +        # get subgrid
          +        subgrid = self.subgrid(window, xc, yc)
          +        subgrid = process_subgrid(subgrid)
          +
          +        # compute radial spectrum
          +        k, Phi, sigma_Phi = self.radial_spectrum(subgrid, taper=taper, **kwargs)
          +
          +        # minimise function
          +        res = minimize(self.min_func, x0, args=(k, Phi, sigma_Phi), bounds=self.bounds)
          +        return res.x
          +
          +
          +    def _func_queue(self, func, q_in, q_out, window, *args, **kwargs):
          +        """ Retrive processes from the queue """
          +        while True:
          +            pos, xc, yc = q_in.get()
          +            if pos is None:
          +                break
          +
          +            pass_args = [window, xc, yc]
          +            pass_args.extend(args)
          +
          +            res = func(*pass_args, **kwargs)
          +            q_out.put((pos, res))
          +        return
          +
          +
          +    def parallelise_routine(self, window, xc_list, yc_list, func, *args, **kwargs):
          +        """
          +        Implements shared memory multiprocessing to split multiple
          +        evaluations of a function centroids across processors.
          +
          +        Supply the window size and lists of x,y coordinates to a function
          +        along with any additional arguments or keyword arguments.
          +
          +        Args:
          +         window : float
          +            size of window in metres
          +         xc_list : array shape (l,)
          +            centroid x values
          +         yc_list : array shape (l,)
          +            centroid y values
          +         func : function
          +            Python function to evaluate in parallel
          +         args : arguments
          +            additional arguments to pass to func
          +         kwargs : keyword arguments
          +            additional keyword arguments to pass to func
          +
          +        Returns:
          +            out : list
          +                (depends on output of func - see notes)
          +
          +        Usage:
          +            An obvious use case is to compute the Curie depth for many
          +            centroids in parallel.
          +
          +            >>> self.parallelise_routine(window, xc_list, yc_list, self.optimise)
          +        
          +            Each centroid is assigned a new process and sent to a free processor
          +            to compute. In this case, the output is separate lists of shape(l,)
          +            for beta, zt, dz, and C.
          +
          +            Another example is to parallelise the sensitivity analysis:
          +
          +            >>> self.parallelise_routine(window, xc_list, yc_list, self.sensitivity, nsim)
          +
          +            This time the output will be a list of lists for beta, zt, dz, and C
          +            i.e. if nc=2 is the number of centroids and nsim=4 is the number of
          +            simulations then separatee lists [[k1, k2, k3, k4], [k1, k2, k3, k4]]
          +            will be returned for beta, zt, dz, and C.
          +        """
          +
          +        n = len(xc_list)
          +        if n != len(yc_list):
          +            raise ValueError("xc_list and yc_list must be the same size")
          +
          +        xOpt = [[] for i in range(n)]
          +        processes = []
          +        q_in = Queue(1)
          +        q_out = Queue()
          +
          +        nprocs = self.max_processors
          +
          +        for i in range(nprocs):
          +            pass_args = [func, q_in, q_out, window]
          +            pass_args.extend(args)
          +
          +            p = Process(target=self._func_queue,\
          +                        args=tuple(pass_args),\
          +                        kwargs=kwargs)
          +
          +            processes.append(p)
          +
          +        for p in processes:
          +            p.daemon = True
          +            p.start()
          +
          +        # put items in the queue
          +        sent = [q_in.put((i, xc_list[i], yc_list[i])) for i in range(n)]
          +        [q_in.put((None, None, None)) for _ in range(nprocs)]
          +
          +        # get the results
          +        for i in range(len(sent)):
          +            i, res = q_out.get()
          +            xOpt[i] = res
          +
          +
          +        # wait until each processor has finished
          +        [p.join() for p in processes]
          +
          +        # process dimensions of output
          +        ndim = np.array(res).ndim
          +
          +        if ndim == 1:
          +            # return separate lists of beta, zt, dz, C
          +            xOpt = np.vstack(xOpt)
          +            return list(xOpt.T)
          +        elif ndim > 1:
          +            # return lists of beta, zt, dz, C for each centroid
          +            xOpt = np.hstack(xOpt)
          +            out = list(xOpt)
          +            for i in range(len(out)):
          +                out[i] = np.split(out[i], n)
          +            return out
          +        else:
          +            raise ValueError("Cannot determine shape of output")
          +
          +
          +
          +    def optimise_routine(self, window, xc_list, yc_list, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs):
          +        """
          +        Iterate through a list of centroids to compute the optimal values
          +        of beta, zt, dz, C for a given window size.
          +        
          +        Args:
          +            window : float
          +                size of window in metres
          +            xc_list : ndarray shape (l,)
          +                centroid x values 
          +            yc_list : ndarray shape (l,)
          +                centroid y values 
          +            beta : float
          +                fractal parameter 
          +            zt : float
          +                top of magnetic layer
          +            dz : float
          +                thickness of magnetic layer
          +            C : float
          +                field constant
          +            taper : function
          +                taper function (default=np.hanning)
          +                set to None for no taper function
          +         process_subgrids : func
          +            a custom function to process the subgrid
          +         kwargs : keyword arguments
          +            to pass to radial_spectrum.
          +
          +        Returns:
          +            beta : ndarray shape (l,)
          +                fractal parameters
          +            zt : ndarray shape (l,)
          +                top of magnetic layer
          +            dz : ndarray shape (l,)
          +                thickness of magnetic layer
          +            C : ndarray shape (l,)
          +                field constant
          +
          +        """
          +        return self.parallelise_routine(window, xc_list, yc_list, self.optimise, beta, zt, dz, C, taper, process_subgrid, **kwargs)
          +
          +
          +    def metropolis_hastings(self, window, xc, yc, nsim, burnin, x_scale=None, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs):
          +        """
          +        MCMC algorithm using a Metropolis-Hastings sampler.
          +
          +        Evaluates a Markov-Chain for starting values of beta, zt, dz, C
          +        and returns the ensemble of model realisations.
          +        
          +        Args:
          +            window : float
          +                size of window in metres
          +            xc : float
          +                centroid x values
          +            yc : float
          +                centroid y values
          +            nsim : int
          +                number of simulations
          +            burnin : int
          +                number of burn-in simulations before to nsim
          +            x_scale: float(4) (optional)
          +                scaling factor for new proposals
          +                default is [1,1,1,1] for [beta, zt, dz, C] - see notes
          +            beta : float
          +                fractal parameter (starting value)
          +            zt : float
          +                top of magnetic layer (starting value)
          +            dz : float
          +                thickness of magnetic layer (starting value)
          +            C : float
          +                field constant (starting value)
          +
          +        Returns:
          +            beta : ndarray shape (nsim,)
          +                fractal parameter
          +            zt : ndarray shape (nsim,)
          +                top of magnetic layer
          +            dz : ndarray shape (nsim,)
          +                thickness of magnetic layer
          +            C : ndarray shape (nsim,)
          +                field constant
          +
          +        Notes:
          +            nsim, burnin, and x_scale should be tweaked for optimal performance
          +            Use starting values of beta, zt, dz, C relatively close to the solution
          +            - C can easily found from the mean of the radial power spectrum.
          +
          +            During the burn-in stage we apply tempering to the PDF to iterate closer
          +            towards the solution. This has the effect of smoothing out the posterior
          +            so that minima can be more easily found. This is necessary here because
          +            large portions of the posterior probability are zero.
          +            see see Sambridge 2013, DOI:10.1093/gji/ggt342 for more information.
          +        """
          +        if type(process_subgrid) == type(None):
          +            # dummy function
          +            def process_subgrid(subgrid):
          +                return subgrid
          +
          +
          +        samples = np.empty((nsim, 4))
          +        x0 = np.array([beta, zt, dz, C])
          +
          +        if type(x_scale) == type(None):
          +            x_scale = np.ones(4)
          +
          +
          +        # get subgrid
          +        subgrid = self.subgrid(window, xc, yc)
          +        subgrid = process_subgrid(subgrid)
          +
          +        # compute radial spectrum
          +        k, Phi, sigma_Phi = self.radial_spectrum(subgrid, taper=taper, **kwargs)
          +
          +        P0 = np.exp(-self.min_func(x0, k, Phi, sigma_Phi)/1000)
          +
          +        # Burn-in phase
          +        for i in range(burnin):
          +            # add random perturbation
          +            x1 = x0 + np.random.normal(size=4)*x_scale
          +
          +            # evaluate proposal probability + tempering
          +            P1 = np.exp(-self.min_func(x1, k, Phi, sigma_Phi)/1000)
          +
          +            # iterate towards MAP estimate
          +            if P1 > P0:
          +                x0 = x1
          +                P0 = P1
          +
          +        P0 = np.exp(-self.min_func(x0, k, Phi, sigma_Phi))
          +
          +        # Now sample posterior
          +        for i in range(nsim):
          +            # add random perturbation
          +            x1 = x0 + np.random.normal(size=4)*x_scale
          +
          +            # evaluate proposal probability
          +            P0 = max(P0, 1e-99)
          +            P1 = np.exp(-self.min_func(x1, k, Phi, sigma_Phi))
          +
          +            P = min(P1/P0, 1.0)
          +
          +            # randomly accept probability
          +            if np.random.rand() <= P:
          +                x0 = x1
          +                P0 = P1
          +
          +            samples[i] = x0
          +
          +        return list(samples.T)
          +
          +
          +
          +    def sensitivity(self, window, xc, yc, nsim, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs):
          +        """
          +        Iterate through a list of centroids to compute the mean and
          +        standard deviation of beta, zt, dz, C by perturbing their
          +        prior distributions (if provided by the user - see add_prior).
          +        
          +        Args:
          +            nsim : int
          +                number of Monte Carlo simulations
          +            window : float
          +                size of window in metres
          +            xc : float
          +                centroid x values
          +            yc : float
          +                centroid y values
          +            nsim : int
          +                - number of simulations
          +            beta : float
          +                starting fractal parameter 
          +            zt : float
          +                starting top of magnetic layer
          +            dz : float
          +                starting thickness of magnetic layer
          +            C : float
          +                starting field constant
          +
          +
          +        Returns:
          +            beta : ndarray shape (nsim,)
          +                fractal parameters
          +            zt : ndarray shape (nsim,)
          +                top of magnetic layer
          +            dz : ndarray shape (nsim,)
          +                thickness of magnetic layer
          +            C : ndarray shape (nsim,)
          +                field constant
          +        """
          +        if type(process_subgrid) == type(None):
          +            # dummy function
          +            def process_subgrid(subgrid):
          +                return subgrid
          +
          +
          +        samples = np.empty((nsim, 4))
          +        x0 = np.array([beta, zt, dz, C])
          +        
          +        use_keys = []
          +        for key in self.prior_pdf:
          +            prior_pdf = self.prior_pdf[key]
          +            if prior_pdf is not None:
          +                use_keys.append(key)
          +        
          +        # get subgrid
          +        subgrid = self.subgrid(window, xc, yc)
          +        subgrid = process_subgrid(subgrid)
          +
          +        # compute radial spectrum
          +        k, Phi, sigma_Phi = self.radial_spectrum(subgrid, taper=taper, **kwargs)
          +
          +        for sim in range(0, nsim):
          +            # randomly generate new prior values within PDF
          +            for key in use_keys:
          +                prior_pdf = self.prior_pdf[key]
          +                self.prior[key][0] = prior_pdf.rvs()
          +
          +            # minimise function
          +            rPhi = np.random.normal(Phi, sigma_Phi)
          +            res = minimize(self.min_func, x0, args=(k, rPhi, sigma_Phi), bounds=self.bounds)
          +            samples[sim] = res.x
          +
          +
          +        # restore priors
          +        for key in use_keys:
          +            prior_pdf = self.prior_pdf[key]
          +            self.prior[key] = list(prior_pdf.args)
          +
          +        return list(samples.T)
          +
          +
          +
          +
          +
          +
          +
          +
          +
          +

          Classes

          +
          +
          +class CurieOptimise +(grid, xmin, xmax, ymin, ymax, **kwargs) +
          +
          +

          Extends the CurieGrid class to include optimisation routines +see scipy.optimize.minimize for a description of the algorithm

          +

          Args

          +
          +
          grid : 2D numpy array
          +
          2D array of magnetic data
          +
          xmin : float
          +
          minimum x bound in metres
          +
          xmax : float
          +
          maximum x bound in metres
          +
          ymin : float
          +
          minimum y bound in metres
          +
          ymax : float
          +
          maximum y bound in metres
          +
          +

          Attributes

          +
          +
          bounds : list of tuples
          +
          lower and upper bounds for beta, zt, dz, C
          +
          +

          prior +: dict +dictionary of priors for beta, zt, dz, C

          +
          +Source code +
          class CurieOptimise(CurieGrid):
          +    """
          +    Extends the CurieGrid class to include optimisation routines
          +    see scipy.optimize.minimize for a description of the algorithm
          +
          +    Args:
          +        grid : 2D numpy array
          +            2D array of magnetic data
          +        xmin : float
          +            minimum x bound in metres
          +        xmax : float
          +            maximum x bound in metres
          +        ymin : float
          +            minimum y bound in metres
          +        ymax : float
          +            maximum y bound in metres
          +    
          +    Attributes:
          +        bounds : list of tuples
          +            lower and upper bounds for beta, zt, dz, C
          +        prior  : dict
          +            dictionary of priors for beta, zt, dz, C
          +    """
          +    def __init__(self, grid, xmin, xmax, ymin, ymax, **kwargs):
          +
          +        super(CurieOptimise, self).__init__(grid, xmin, xmax, ymin, ymax)
          +
          +        # initialise prior dictionary
          +        self.reset_priors()
          +
          +        # lower / upper bounds
          +        # [beta, zt, dz, C]
          +        lb = [0.0, 0.0, 0.0, None]
          +        ub = [None]*len(lb)
          +        bounds = list(zip(lb,ub))
          +        self.bounds = bounds
          +
          +        self.max_processors = kwargs.pop("max_processors", cpu_count())
          +
          +        return
          +
          +    def add_prior(self, **kwargs):
          +        """
          +        Add a prior to the dictionary (tuple)
          +        Available priors are beta, zt, dz, C
          +
          +        Assumes a normal distribution or
          +        define another distribution from scipy.stats
          +
          +        Usage:
          +            >>> add_prior(beta=(p, sigma_p))
          +
          +            >>> add_prior(beta=scipy.stats.norm(p, sigma_p))
          +        """
          +
          +        for key in kwargs:
          +            if key in self.prior:
          +                prior = kwargs[key]
          +                if type(prior) == tuple:
          +                    p, sigma_p = prior
          +                    pdf = stats.norm(p, sigma_p)
          +                elif type(prior) == stats._distn_infrastructure.rv_frozen:
          +                    pdf = prior
          +                else:
          +                    raise ValueError("Use a distribution from scipy.stats module")
          +
          +                # add prior PDF to dictionary
          +                self.prior_pdf[key] = pdf
          +                self.prior[key] = list(pdf.args)
          +
          +            else:
          +                raise ValueError("prior must be one of {}".format(self.prior.keys()))
          +
          +
          +    def reset_priors(self):
          +        """
          +        Reset priors to uniform distribution
          +        """
          +        self.prior = {'beta':None, 'zt':None, 'dz':None, 'C':None}
          +        self.prior_pdf = {'beta':None, 'zt':None, 'dz':None, 'C':None}
          +
          +
          +    def objective_routine(self, **kwargs):
          +        """
          +        Evaluate the objective routine to find the misfit with priors
          +        Only keys stored in self.prior will be added to the total misfit
          +
          +        Usage:
          +            >>> objective_routine(beta=2.5)
          +
          +        Returns:
          +            misfit  : float
          +                misfit integrated over all observations and priors
          +        """
          +        c = 0.0
          +
          +        for key in kwargs:
          +            val = kwargs[key]
          +            if key in self.prior:
          +                prior_args = self.prior[key]
          +                if prior_args is not None:
          +                    c += self.objective_function(val, *prior_args)
          +        return c
          +
          +    def objective_function(self, x, x0, sigma_x0, *args):
          +        """
          +        Objective function used in `objective_routine`
          +        Evaluates the l2-norm misfit
          +
          +        Args:
          +            x : float, ndarray
          +            x0 : float, ndarray
          +            sigma_x0 : float, ndarray
          +
          +        Returns:
          +            misfit   : float
          +        """
          +        return 0.5*np.sum((x - x0)**2/sigma_x0**2)
          +
          +
          +    def min_func(self, x, kh, Phi, sigma_Phi):
          +        """
          +        Function to minimise
          +
          +        Args:
          +            x : array shape (n,)
          +                array of variables [beta, zt, dz, C]
          +            kh : array shape (n,)
          +                wavenumbers (rad/km)
          +            Phi : array shape (n,)
          +                radial power spectrum
          +            sigma_Phi : array shape (n,)
          +                standard deviation of Phi
          +
          +        Returns:
          +            misfit    : float
          +                sum of misfit (float)
          +
          +        Notes:
          +            We purposely ignore all warnings raised by the bouligand2009
          +            function because some combinations of input parameters will
          +            trigger an out-of-range warning that will crash the minimiser.
          +            Instead, the misfit is set to a very large number when this occurs.
          +        """
          +        beta, zt, dz, C = x
          +        with warnings.catch_warnings() as w:
          +            warnings.simplefilter("ignore")
          +            Phi_syn = bouligand2009(kh, beta, zt, dz, C)
          +
          +        misfit = self.objective_function(Phi_syn, Phi, 1.0)
          +        if not np.isfinite(misfit):
          +            misfit = 1e99
          +        else:
          +            misfit += self.objective_routine(beta=beta, zt=zt, dz=dz, C=C)
          +        return misfit
          +
          +
          +    def optimise(self, window, xc, yc, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs):
          +        """
          +        Find the optimal parameters of beta, zt, dz, C for a given
          +        centroid (xc,yc) and window size.
          +
          +        Args:
          +            window  : float
          +                size of window in metres
          +            xc : float
          +                centroid x values
          +            yc : float
          +                centroid y values
          +            beta : float
          +                fractal parameter (starting value)
          +            zt : float
          +                top of magnetic layer (starting value)
          +            dz : float
          +                thickness of magnetic layer (starting value)
          +            C : float
          +                field constant (starting value)
          +            taper : taper (default=np.hanning)
          +                taper function, set to None for no taper function
          +            process_subgrids : function
          +                a custom function to process the subgrid
          +            kwargs : keyword arguments
          +                to pass to radial_spectrum.
          +
          +        Returns:
          +            beta : float
          +                fractal parameters
          +            zt : float
          +                top of magnetic layer
          +            dz : float
          +                thickness of magnetic layer
          +            C : float
          +                field constant
          +        """
          +
          +        if type(process_subgrid) == type(None):
          +            # dummy function
          +            def process_subgrid(subgrid):
          +                return subgrid
          +
          +        # initial constants for minimisation
          +        # w = 1.0 # weight low frequency?
          +
          +        x0 = np.array([beta, zt, dz, C])
          +
          +        # get subgrid
          +        subgrid = self.subgrid(window, xc, yc)
          +        subgrid = process_subgrid(subgrid)
          +
          +        # compute radial spectrum
          +        k, Phi, sigma_Phi = self.radial_spectrum(subgrid, taper=taper, **kwargs)
          +
          +        # minimise function
          +        res = minimize(self.min_func, x0, args=(k, Phi, sigma_Phi), bounds=self.bounds)
          +        return res.x
          +
          +
          +    def _func_queue(self, func, q_in, q_out, window, *args, **kwargs):
          +        """ Retrive processes from the queue """
          +        while True:
          +            pos, xc, yc = q_in.get()
          +            if pos is None:
          +                break
          +
          +            pass_args = [window, xc, yc]
          +            pass_args.extend(args)
          +
          +            res = func(*pass_args, **kwargs)
          +            q_out.put((pos, res))
          +        return
          +
          +
          +    def parallelise_routine(self, window, xc_list, yc_list, func, *args, **kwargs):
          +        """
          +        Implements shared memory multiprocessing to split multiple
          +        evaluations of a function centroids across processors.
          +
          +        Supply the window size and lists of x,y coordinates to a function
          +        along with any additional arguments or keyword arguments.
          +
          +        Args:
          +         window : float
          +            size of window in metres
          +         xc_list : array shape (l,)
          +            centroid x values
          +         yc_list : array shape (l,)
          +            centroid y values
          +         func : function
          +            Python function to evaluate in parallel
          +         args : arguments
          +            additional arguments to pass to func
          +         kwargs : keyword arguments
          +            additional keyword arguments to pass to func
          +
          +        Returns:
          +            out : list
          +                (depends on output of func - see notes)
          +
          +        Usage:
          +            An obvious use case is to compute the Curie depth for many
          +            centroids in parallel.
          +
          +            >>> self.parallelise_routine(window, xc_list, yc_list, self.optimise)
          +        
          +            Each centroid is assigned a new process and sent to a free processor
          +            to compute. In this case, the output is separate lists of shape(l,)
          +            for beta, zt, dz, and C.
          +
          +            Another example is to parallelise the sensitivity analysis:
          +
          +            >>> self.parallelise_routine(window, xc_list, yc_list, self.sensitivity, nsim)
          +
          +            This time the output will be a list of lists for beta, zt, dz, and C
          +            i.e. if nc=2 is the number of centroids and nsim=4 is the number of
          +            simulations then separatee lists [[k1, k2, k3, k4], [k1, k2, k3, k4]]
          +            will be returned for beta, zt, dz, and C.
          +        """
          +
          +        n = len(xc_list)
          +        if n != len(yc_list):
          +            raise ValueError("xc_list and yc_list must be the same size")
          +
          +        xOpt = [[] for i in range(n)]
          +        processes = []
          +        q_in = Queue(1)
          +        q_out = Queue()
          +
          +        nprocs = self.max_processors
          +
          +        for i in range(nprocs):
          +            pass_args = [func, q_in, q_out, window]
          +            pass_args.extend(args)
          +
          +            p = Process(target=self._func_queue,\
          +                        args=tuple(pass_args),\
          +                        kwargs=kwargs)
          +
          +            processes.append(p)
          +
          +        for p in processes:
          +            p.daemon = True
          +            p.start()
          +
          +        # put items in the queue
          +        sent = [q_in.put((i, xc_list[i], yc_list[i])) for i in range(n)]
          +        [q_in.put((None, None, None)) for _ in range(nprocs)]
          +
          +        # get the results
          +        for i in range(len(sent)):
          +            i, res = q_out.get()
          +            xOpt[i] = res
          +
          +
          +        # wait until each processor has finished
          +        [p.join() for p in processes]
          +
          +        # process dimensions of output
          +        ndim = np.array(res).ndim
          +
          +        if ndim == 1:
          +            # return separate lists of beta, zt, dz, C
          +            xOpt = np.vstack(xOpt)
          +            return list(xOpt.T)
          +        elif ndim > 1:
          +            # return lists of beta, zt, dz, C for each centroid
          +            xOpt = np.hstack(xOpt)
          +            out = list(xOpt)
          +            for i in range(len(out)):
          +                out[i] = np.split(out[i], n)
          +            return out
          +        else:
          +            raise ValueError("Cannot determine shape of output")
          +
          +
          +
          +    def optimise_routine(self, window, xc_list, yc_list, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs):
          +        """
          +        Iterate through a list of centroids to compute the optimal values
          +        of beta, zt, dz, C for a given window size.
          +        
          +        Args:
          +            window : float
          +                size of window in metres
          +            xc_list : ndarray shape (l,)
          +                centroid x values 
          +            yc_list : ndarray shape (l,)
          +                centroid y values 
          +            beta : float
          +                fractal parameter 
          +            zt : float
          +                top of magnetic layer
          +            dz : float
          +                thickness of magnetic layer
          +            C : float
          +                field constant
          +            taper : function
          +                taper function (default=np.hanning)
          +                set to None for no taper function
          +         process_subgrids : func
          +            a custom function to process the subgrid
          +         kwargs : keyword arguments
          +            to pass to radial_spectrum.
          +
          +        Returns:
          +            beta : ndarray shape (l,)
          +                fractal parameters
          +            zt : ndarray shape (l,)
          +                top of magnetic layer
          +            dz : ndarray shape (l,)
          +                thickness of magnetic layer
          +            C : ndarray shape (l,)
          +                field constant
          +
          +        """
          +        return self.parallelise_routine(window, xc_list, yc_list, self.optimise, beta, zt, dz, C, taper, process_subgrid, **kwargs)
          +
          +
          +    def metropolis_hastings(self, window, xc, yc, nsim, burnin, x_scale=None, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs):
          +        """
          +        MCMC algorithm using a Metropolis-Hastings sampler.
          +
          +        Evaluates a Markov-Chain for starting values of beta, zt, dz, C
          +        and returns the ensemble of model realisations.
          +        
          +        Args:
          +            window : float
          +                size of window in metres
          +            xc : float
          +                centroid x values
          +            yc : float
          +                centroid y values
          +            nsim : int
          +                number of simulations
          +            burnin : int
          +                number of burn-in simulations before to nsim
          +            x_scale: float(4) (optional)
          +                scaling factor for new proposals
          +                default is [1,1,1,1] for [beta, zt, dz, C] - see notes
          +            beta : float
          +                fractal parameter (starting value)
          +            zt : float
          +                top of magnetic layer (starting value)
          +            dz : float
          +                thickness of magnetic layer (starting value)
          +            C : float
          +                field constant (starting value)
          +
          +        Returns:
          +            beta : ndarray shape (nsim,)
          +                fractal parameter
          +            zt : ndarray shape (nsim,)
          +                top of magnetic layer
          +            dz : ndarray shape (nsim,)
          +                thickness of magnetic layer
          +            C : ndarray shape (nsim,)
          +                field constant
          +
          +        Notes:
          +            nsim, burnin, and x_scale should be tweaked for optimal performance
          +            Use starting values of beta, zt, dz, C relatively close to the solution
          +            - C can easily found from the mean of the radial power spectrum.
          +
          +            During the burn-in stage we apply tempering to the PDF to iterate closer
          +            towards the solution. This has the effect of smoothing out the posterior
          +            so that minima can be more easily found. This is necessary here because
          +            large portions of the posterior probability are zero.
          +            see see Sambridge 2013, DOI:10.1093/gji/ggt342 for more information.
          +        """
          +        if type(process_subgrid) == type(None):
          +            # dummy function
          +            def process_subgrid(subgrid):
          +                return subgrid
          +
          +
          +        samples = np.empty((nsim, 4))
          +        x0 = np.array([beta, zt, dz, C])
          +
          +        if type(x_scale) == type(None):
          +            x_scale = np.ones(4)
          +
          +
          +        # get subgrid
          +        subgrid = self.subgrid(window, xc, yc)
          +        subgrid = process_subgrid(subgrid)
          +
          +        # compute radial spectrum
          +        k, Phi, sigma_Phi = self.radial_spectrum(subgrid, taper=taper, **kwargs)
          +
          +        P0 = np.exp(-self.min_func(x0, k, Phi, sigma_Phi)/1000)
          +
          +        # Burn-in phase
          +        for i in range(burnin):
          +            # add random perturbation
          +            x1 = x0 + np.random.normal(size=4)*x_scale
          +
          +            # evaluate proposal probability + tempering
          +            P1 = np.exp(-self.min_func(x1, k, Phi, sigma_Phi)/1000)
          +
          +            # iterate towards MAP estimate
          +            if P1 > P0:
          +                x0 = x1
          +                P0 = P1
          +
          +        P0 = np.exp(-self.min_func(x0, k, Phi, sigma_Phi))
          +
          +        # Now sample posterior
          +        for i in range(nsim):
          +            # add random perturbation
          +            x1 = x0 + np.random.normal(size=4)*x_scale
          +
          +            # evaluate proposal probability
          +            P0 = max(P0, 1e-99)
          +            P1 = np.exp(-self.min_func(x1, k, Phi, sigma_Phi))
          +
          +            P = min(P1/P0, 1.0)
          +
          +            # randomly accept probability
          +            if np.random.rand() <= P:
          +                x0 = x1
          +                P0 = P1
          +
          +            samples[i] = x0
          +
          +        return list(samples.T)
          +
          +
          +
          +    def sensitivity(self, window, xc, yc, nsim, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs):
          +        """
          +        Iterate through a list of centroids to compute the mean and
          +        standard deviation of beta, zt, dz, C by perturbing their
          +        prior distributions (if provided by the user - see add_prior).
          +        
          +        Args:
          +            nsim : int
          +                number of Monte Carlo simulations
          +            window : float
          +                size of window in metres
          +            xc : float
          +                centroid x values
          +            yc : float
          +                centroid y values
          +            nsim : int
          +                - number of simulations
          +            beta : float
          +                starting fractal parameter 
          +            zt : float
          +                starting top of magnetic layer
          +            dz : float
          +                starting thickness of magnetic layer
          +            C : float
          +                starting field constant
          +
          +
          +        Returns:
          +            beta : ndarray shape (nsim,)
          +                fractal parameters
          +            zt : ndarray shape (nsim,)
          +                top of magnetic layer
          +            dz : ndarray shape (nsim,)
          +                thickness of magnetic layer
          +            C : ndarray shape (nsim,)
          +                field constant
          +        """
          +        if type(process_subgrid) == type(None):
          +            # dummy function
          +            def process_subgrid(subgrid):
          +                return subgrid
          +
          +
          +        samples = np.empty((nsim, 4))
          +        x0 = np.array([beta, zt, dz, C])
          +        
          +        use_keys = []
          +        for key in self.prior_pdf:
          +            prior_pdf = self.prior_pdf[key]
          +            if prior_pdf is not None:
          +                use_keys.append(key)
          +        
          +        # get subgrid
          +        subgrid = self.subgrid(window, xc, yc)
          +        subgrid = process_subgrid(subgrid)
          +
          +        # compute radial spectrum
          +        k, Phi, sigma_Phi = self.radial_spectrum(subgrid, taper=taper, **kwargs)
          +
          +        for sim in range(0, nsim):
          +            # randomly generate new prior values within PDF
          +            for key in use_keys:
          +                prior_pdf = self.prior_pdf[key]
          +                self.prior[key][0] = prior_pdf.rvs()
          +
          +            # minimise function
          +            rPhi = np.random.normal(Phi, sigma_Phi)
          +            res = minimize(self.min_func, x0, args=(k, rPhi, sigma_Phi), bounds=self.bounds)
          +            samples[sim] = res.x
          +
          +
          +        # restore priors
          +        for key in use_keys:
          +            prior_pdf = self.prior_pdf[key]
          +            self.prior[key] = list(prior_pdf.args)
          +
          +        return list(samples.T)
          +
          +

          Ancestors

          + +

          Subclasses

          + +

          Methods

          +
          +
          +def add_prior(self, **kwargs) +
          +
          +

          Add a prior to the dictionary (tuple) +Available priors are beta, zt, dz, C

          +

          Assumes a normal distribution or +define another distribution from scipy.stats

          +

          Usage

          +
          >>> add_prior(beta=(p, sigma_p))
          +
          +
          +
          +
          +

          add_prior(beta=scipy.stats.norm(p, sigma_p))

          +
          +
          +
          +
          +Source code +
          def add_prior(self, **kwargs):
          +    """
          +    Add a prior to the dictionary (tuple)
          +    Available priors are beta, zt, dz, C
          +
          +    Assumes a normal distribution or
          +    define another distribution from scipy.stats
          +
          +    Usage:
          +        >>> add_prior(beta=(p, sigma_p))
          +
          +        >>> add_prior(beta=scipy.stats.norm(p, sigma_p))
          +    """
          +
          +    for key in kwargs:
          +        if key in self.prior:
          +            prior = kwargs[key]
          +            if type(prior) == tuple:
          +                p, sigma_p = prior
          +                pdf = stats.norm(p, sigma_p)
          +            elif type(prior) == stats._distn_infrastructure.rv_frozen:
          +                pdf = prior
          +            else:
          +                raise ValueError("Use a distribution from scipy.stats module")
          +
          +            # add prior PDF to dictionary
          +            self.prior_pdf[key] = pdf
          +            self.prior[key] = list(pdf.args)
          +
          +        else:
          +            raise ValueError("prior must be one of {}".format(self.prior.keys()))
          +
          +
          +
          +def metropolis_hastings(self, window, xc, yc, nsim, burnin, x_scale=None, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=, process_subgrid=None, **kwargs) +
          +
          +

          MCMC algorithm using a Metropolis-Hastings sampler.

          +

          Evaluates a Markov-Chain for starting values of beta, zt, dz, C +and returns the ensemble of model realisations.

          +

          Args

          +
          +
          window : float
          +
          size of window in metres
          +
          xc : float
          +
          centroid x values
          +
          yc : float
          +
          centroid y values
          +
          nsim : int
          +
          number of simulations
          +
          burnin : int
          +
          number of burn-in simulations before to nsim
          +
          x_scale
          +
          float(4) (optional) +scaling factor for new proposals +default is [1,1,1,1] for [beta, zt, dz, C] - see notes
          +
          beta : float
          +
          fractal parameter (starting value)
          +
          zt : float
          +
          top of magnetic layer (starting value)
          +
          dz : float
          +
          thickness of magnetic layer (starting value)
          +
          C : float
          +
          field constant (starting value)
          +
          +

          Returns

          +
          +
          beta : ndarray shape (nsim,)
          +
          fractal parameter
          +
          zt : ndarray shape (nsim,)
          +
          top of magnetic layer
          +
          dz : ndarray shape (nsim,)
          +
          thickness of magnetic layer
          +
          C : ndarray shape (nsim,)
          +
          field constant
          +
          +

          Notes

          +

          nsim, burnin, and x_scale should be tweaked for optimal performance +Use starting values of beta, zt, dz, C relatively close to the solution +- C can easily found from the mean of the radial power spectrum.

          +

          During the burn-in stage we apply tempering to the PDF to iterate closer +towards the solution. This has the effect of smoothing out the posterior +so that minima can be more easily found. This is necessary here because +large portions of the posterior probability are zero. +see see Sambridge 2013, DOI:10.1093/gji/ggt342 for more information.

          +
          +Source code +
          def metropolis_hastings(self, window, xc, yc, nsim, burnin, x_scale=None, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs):
          +    """
          +    MCMC algorithm using a Metropolis-Hastings sampler.
          +
          +    Evaluates a Markov-Chain for starting values of beta, zt, dz, C
          +    and returns the ensemble of model realisations.
          +    
          +    Args:
          +        window : float
          +            size of window in metres
          +        xc : float
          +            centroid x values
          +        yc : float
          +            centroid y values
          +        nsim : int
          +            number of simulations
          +        burnin : int
          +            number of burn-in simulations before to nsim
          +        x_scale: float(4) (optional)
          +            scaling factor for new proposals
          +            default is [1,1,1,1] for [beta, zt, dz, C] - see notes
          +        beta : float
          +            fractal parameter (starting value)
          +        zt : float
          +            top of magnetic layer (starting value)
          +        dz : float
          +            thickness of magnetic layer (starting value)
          +        C : float
          +            field constant (starting value)
          +
          +    Returns:
          +        beta : ndarray shape (nsim,)
          +            fractal parameter
          +        zt : ndarray shape (nsim,)
          +            top of magnetic layer
          +        dz : ndarray shape (nsim,)
          +            thickness of magnetic layer
          +        C : ndarray shape (nsim,)
          +            field constant
          +
          +    Notes:
          +        nsim, burnin, and x_scale should be tweaked for optimal performance
          +        Use starting values of beta, zt, dz, C relatively close to the solution
          +        - C can easily found from the mean of the radial power spectrum.
          +
          +        During the burn-in stage we apply tempering to the PDF to iterate closer
          +        towards the solution. This has the effect of smoothing out the posterior
          +        so that minima can be more easily found. This is necessary here because
          +        large portions of the posterior probability are zero.
          +        see see Sambridge 2013, DOI:10.1093/gji/ggt342 for more information.
          +    """
          +    if type(process_subgrid) == type(None):
          +        # dummy function
          +        def process_subgrid(subgrid):
          +            return subgrid
          +
          +
          +    samples = np.empty((nsim, 4))
          +    x0 = np.array([beta, zt, dz, C])
          +
          +    if type(x_scale) == type(None):
          +        x_scale = np.ones(4)
          +
          +
          +    # get subgrid
          +    subgrid = self.subgrid(window, xc, yc)
          +    subgrid = process_subgrid(subgrid)
          +
          +    # compute radial spectrum
          +    k, Phi, sigma_Phi = self.radial_spectrum(subgrid, taper=taper, **kwargs)
          +
          +    P0 = np.exp(-self.min_func(x0, k, Phi, sigma_Phi)/1000)
          +
          +    # Burn-in phase
          +    for i in range(burnin):
          +        # add random perturbation
          +        x1 = x0 + np.random.normal(size=4)*x_scale
          +
          +        # evaluate proposal probability + tempering
          +        P1 = np.exp(-self.min_func(x1, k, Phi, sigma_Phi)/1000)
          +
          +        # iterate towards MAP estimate
          +        if P1 > P0:
          +            x0 = x1
          +            P0 = P1
          +
          +    P0 = np.exp(-self.min_func(x0, k, Phi, sigma_Phi))
          +
          +    # Now sample posterior
          +    for i in range(nsim):
          +        # add random perturbation
          +        x1 = x0 + np.random.normal(size=4)*x_scale
          +
          +        # evaluate proposal probability
          +        P0 = max(P0, 1e-99)
          +        P1 = np.exp(-self.min_func(x1, k, Phi, sigma_Phi))
          +
          +        P = min(P1/P0, 1.0)
          +
          +        # randomly accept probability
          +        if np.random.rand() <= P:
          +            x0 = x1
          +            P0 = P1
          +
          +        samples[i] = x0
          +
          +    return list(samples.T)
          +
          +
          +
          +def min_func(self, x, kh, Phi, sigma_Phi) +
          +
          +

          Function to minimise

          +

          Args

          +
          +
          x : array shape (n,)
          +
          array of variables [beta, zt, dz, C]
          +
          kh : array shape (n,)
          +
          wavenumbers (rad/km)
          +
          Phi : array shape (n,)
          +
          radial power spectrum
          +
          sigma_Phi : array shape (n,)
          +
          standard deviation of Phi
          +
          +

          Returns

          +
          +
          misfit +: float
          +
          sum of misfit (float)
          +
          +

          Notes

          +

          We purposely ignore all warnings raised by the bouligand2009 +function because some combinations of input parameters will +trigger an out-of-range warning that will crash the minimiser. +Instead, the misfit is set to a very large number when this occurs.

          +
          +Source code +
          def min_func(self, x, kh, Phi, sigma_Phi):
          +    """
          +    Function to minimise
          +
          +    Args:
          +        x : array shape (n,)
          +            array of variables [beta, zt, dz, C]
          +        kh : array shape (n,)
          +            wavenumbers (rad/km)
          +        Phi : array shape (n,)
          +            radial power spectrum
          +        sigma_Phi : array shape (n,)
          +            standard deviation of Phi
          +
          +    Returns:
          +        misfit    : float
          +            sum of misfit (float)
          +
          +    Notes:
          +        We purposely ignore all warnings raised by the bouligand2009
          +        function because some combinations of input parameters will
          +        trigger an out-of-range warning that will crash the minimiser.
          +        Instead, the misfit is set to a very large number when this occurs.
          +    """
          +    beta, zt, dz, C = x
          +    with warnings.catch_warnings() as w:
          +        warnings.simplefilter("ignore")
          +        Phi_syn = bouligand2009(kh, beta, zt, dz, C)
          +
          +    misfit = self.objective_function(Phi_syn, Phi, 1.0)
          +    if not np.isfinite(misfit):
          +        misfit = 1e99
          +    else:
          +        misfit += self.objective_routine(beta=beta, zt=zt, dz=dz, C=C)
          +    return misfit
          +
          +
          +
          +def objective_function(self, x, x0, sigma_x0, *args) +
          +
          +

          Objective function used in objective_routine +Evaluates the l2-norm misfit

          +

          Args

          +
          +
          x : float, ndarray
          +
           
          +
          x0 : float, ndarray
          +
           
          +
          sigma_x0 : float, ndarray
          +
           
          +
          +

          Returns

          +
          +
          misfit +: float
          +
           
          +
          +
          +Source code +
          def objective_function(self, x, x0, sigma_x0, *args):
          +    """
          +    Objective function used in `objective_routine`
          +    Evaluates the l2-norm misfit
          +
          +    Args:
          +        x : float, ndarray
          +        x0 : float, ndarray
          +        sigma_x0 : float, ndarray
          +
          +    Returns:
          +        misfit   : float
          +    """
          +    return 0.5*np.sum((x - x0)**2/sigma_x0**2)
          +
          +
          +
          +def objective_routine(self, **kwargs) +
          +
          +

          Evaluate the objective routine to find the misfit with priors +Only keys stored in self.prior will be added to the total misfit

          +

          Usage

          +
          >>> objective_routine(beta=2.5)
          +
          +

          Returns

          +
          +
          misfit +: float
          +
          misfit integrated over all observations and priors
          +
          +
          +Source code +
          def objective_routine(self, **kwargs):
          +    """
          +    Evaluate the objective routine to find the misfit with priors
          +    Only keys stored in self.prior will be added to the total misfit
          +
          +    Usage:
          +        >>> objective_routine(beta=2.5)
          +
          +    Returns:
          +        misfit  : float
          +            misfit integrated over all observations and priors
          +    """
          +    c = 0.0
          +
          +    for key in kwargs:
          +        val = kwargs[key]
          +        if key in self.prior:
          +            prior_args = self.prior[key]
          +            if prior_args is not None:
          +                c += self.objective_function(val, *prior_args)
          +    return c
          +
          +
          +
          +def optimise(self, window, xc, yc, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=, process_subgrid=None, **kwargs) +
          +
          +

          Find the optimal parameters of beta, zt, dz, C for a given +centroid (xc,yc) and window size.

          +

          Args

          +
          +
          window +: float
          +
          size of window in metres
          +
          xc : float
          +
          centroid x values
          +
          yc : float
          +
          centroid y values
          +
          beta : float
          +
          fractal parameter (starting value)
          +
          zt : float
          +
          top of magnetic layer (starting value)
          +
          dz : float
          +
          thickness of magnetic layer (starting value)
          +
          C : float
          +
          field constant (starting value)
          +
          taper : taper (default=np.hanning)
          +
          taper function, set to None for no taper function
          +
          process_subgrids : function
          +
          a custom function to process the subgrid
          +
          kwargs : keyword arguments
          +
          to pass to radial_spectrum.
          +
          +

          Returns

          +
          +
          beta : float
          +
          fractal parameters
          +
          zt : float
          +
          top of magnetic layer
          +
          dz : float
          +
          thickness of magnetic layer
          +
          C : float
          +
          field constant
          +
          +
          +Source code +
          def optimise(self, window, xc, yc, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs):
          +    """
          +    Find the optimal parameters of beta, zt, dz, C for a given
          +    centroid (xc,yc) and window size.
          +
          +    Args:
          +        window  : float
          +            size of window in metres
          +        xc : float
          +            centroid x values
          +        yc : float
          +            centroid y values
          +        beta : float
          +            fractal parameter (starting value)
          +        zt : float
          +            top of magnetic layer (starting value)
          +        dz : float
          +            thickness of magnetic layer (starting value)
          +        C : float
          +            field constant (starting value)
          +        taper : taper (default=np.hanning)
          +            taper function, set to None for no taper function
          +        process_subgrids : function
          +            a custom function to process the subgrid
          +        kwargs : keyword arguments
          +            to pass to radial_spectrum.
          +
          +    Returns:
          +        beta : float
          +            fractal parameters
          +        zt : float
          +            top of magnetic layer
          +        dz : float
          +            thickness of magnetic layer
          +        C : float
          +            field constant
          +    """
          +
          +    if type(process_subgrid) == type(None):
          +        # dummy function
          +        def process_subgrid(subgrid):
          +            return subgrid
          +
          +    # initial constants for minimisation
          +    # w = 1.0 # weight low frequency?
          +
          +    x0 = np.array([beta, zt, dz, C])
          +
          +    # get subgrid
          +    subgrid = self.subgrid(window, xc, yc)
          +    subgrid = process_subgrid(subgrid)
          +
          +    # compute radial spectrum
          +    k, Phi, sigma_Phi = self.radial_spectrum(subgrid, taper=taper, **kwargs)
          +
          +    # minimise function
          +    res = minimize(self.min_func, x0, args=(k, Phi, sigma_Phi), bounds=self.bounds)
          +    return res.x
          +
          +
          +
          +def optimise_routine(self, window, xc_list, yc_list, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=, process_subgrid=None, **kwargs) +
          +
          +

          Iterate through a list of centroids to compute the optimal values +of beta, zt, dz, C for a given window size.

          +

          Args

          +
          +
          window : float
          +
          size of window in metres
          +
          xc_list : ndarray shape (l,)
          +
          centroid x values
          +
          yc_list : ndarray shape (l,)
          +
          centroid y values
          +
          beta : float
          +
          fractal parameter
          +
          zt : float
          +
          top of magnetic layer
          +
          dz : float
          +
          thickness of magnetic layer
          +
          C : float
          +
          field constant
          +
          taper : function
          +
          taper function (default=np.hanning) +set to None for no taper function
          +
          +

          process_subgrids : func +a custom function to process the subgrid +kwargs : keyword arguments +to pass to radial_spectrum.

          +

          Returns

          +
          +
          beta : ndarray shape (l,)
          +
          fractal parameters
          +
          zt : ndarray shape (l,)
          +
          top of magnetic layer
          +
          dz : ndarray shape (l,)
          +
          thickness of magnetic layer
          +
          C : ndarray shape (l,)
          +
          field constant
          +
          +
          +Source code +
          def optimise_routine(self, window, xc_list, yc_list, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs):
          +    """
          +    Iterate through a list of centroids to compute the optimal values
          +    of beta, zt, dz, C for a given window size.
          +    
          +    Args:
          +        window : float
          +            size of window in metres
          +        xc_list : ndarray shape (l,)
          +            centroid x values 
          +        yc_list : ndarray shape (l,)
          +            centroid y values 
          +        beta : float
          +            fractal parameter 
          +        zt : float
          +            top of magnetic layer
          +        dz : float
          +            thickness of magnetic layer
          +        C : float
          +            field constant
          +        taper : function
          +            taper function (default=np.hanning)
          +            set to None for no taper function
          +     process_subgrids : func
          +        a custom function to process the subgrid
          +     kwargs : keyword arguments
          +        to pass to radial_spectrum.
          +
          +    Returns:
          +        beta : ndarray shape (l,)
          +            fractal parameters
          +        zt : ndarray shape (l,)
          +            top of magnetic layer
          +        dz : ndarray shape (l,)
          +            thickness of magnetic layer
          +        C : ndarray shape (l,)
          +            field constant
          +
          +    """
          +    return self.parallelise_routine(window, xc_list, yc_list, self.optimise, beta, zt, dz, C, taper, process_subgrid, **kwargs)
          +
          +
          +
          +def parallelise_routine(self, window, xc_list, yc_list, func, *args, **kwargs) +
          +
          +

          Implements shared memory multiprocessing to split multiple +evaluations of a function centroids across processors.

          +

          Supply the window size and lists of x,y coordinates to a function +along with any additional arguments or keyword arguments.

          +

          Args: +window : float +size of window in metres +xc_list : array shape (l,) +centroid x values +yc_list : array shape (l,) +centroid y values +func : function +Python function to evaluate in parallel +args : arguments +additional arguments to pass to func +kwargs : keyword arguments +additional keyword arguments to pass to func

          +

          Returns

          +
          +
          out : list
          +
          (depends on output of func - see notes)
          +
          +

          Usage

          +

          An obvious use case is to compute the Curie depth for many +centroids in parallel.

          +
          >>> self.parallelise_routine(window, xc_list, yc_list, self.optimise)
          +
          +

          Each centroid is assigned a new process and sent to a free processor +to compute. In this case, the output is separate lists of shape(l,) +for beta, zt, dz, and C.

          +

          Another example is to parallelise the sensitivity analysis:

          +
          >>> self.parallelise_routine(window, xc_list, yc_list, self.sensitivity, nsim)
          +
          +

          This time the output will be a list of lists for beta, zt, dz, and C +i.e. if nc=2 is the number of centroids and nsim=4 is the number of +simulations then separatee lists [[k1, k2, k3, k4], [k1, k2, k3, k4]] +will be returned for beta, zt, dz, and C.

          +
          +Source code +
          def parallelise_routine(self, window, xc_list, yc_list, func, *args, **kwargs):
          +    """
          +    Implements shared memory multiprocessing to split multiple
          +    evaluations of a function centroids across processors.
          +
          +    Supply the window size and lists of x,y coordinates to a function
          +    along with any additional arguments or keyword arguments.
          +
          +    Args:
          +     window : float
          +        size of window in metres
          +     xc_list : array shape (l,)
          +        centroid x values
          +     yc_list : array shape (l,)
          +        centroid y values
          +     func : function
          +        Python function to evaluate in parallel
          +     args : arguments
          +        additional arguments to pass to func
          +     kwargs : keyword arguments
          +        additional keyword arguments to pass to func
          +
          +    Returns:
          +        out : list
          +            (depends on output of func - see notes)
          +
          +    Usage:
          +        An obvious use case is to compute the Curie depth for many
          +        centroids in parallel.
          +
          +        >>> self.parallelise_routine(window, xc_list, yc_list, self.optimise)
          +    
          +        Each centroid is assigned a new process and sent to a free processor
          +        to compute. In this case, the output is separate lists of shape(l,)
          +        for beta, zt, dz, and C.
          +
          +        Another example is to parallelise the sensitivity analysis:
          +
          +        >>> self.parallelise_routine(window, xc_list, yc_list, self.sensitivity, nsim)
          +
          +        This time the output will be a list of lists for beta, zt, dz, and C
          +        i.e. if nc=2 is the number of centroids and nsim=4 is the number of
          +        simulations then separatee lists [[k1, k2, k3, k4], [k1, k2, k3, k4]]
          +        will be returned for beta, zt, dz, and C.
          +    """
          +
          +    n = len(xc_list)
          +    if n != len(yc_list):
          +        raise ValueError("xc_list and yc_list must be the same size")
          +
          +    xOpt = [[] for i in range(n)]
          +    processes = []
          +    q_in = Queue(1)
          +    q_out = Queue()
          +
          +    nprocs = self.max_processors
          +
          +    for i in range(nprocs):
          +        pass_args = [func, q_in, q_out, window]
          +        pass_args.extend(args)
          +
          +        p = Process(target=self._func_queue,\
          +                    args=tuple(pass_args),\
          +                    kwargs=kwargs)
          +
          +        processes.append(p)
          +
          +    for p in processes:
          +        p.daemon = True
          +        p.start()
          +
          +    # put items in the queue
          +    sent = [q_in.put((i, xc_list[i], yc_list[i])) for i in range(n)]
          +    [q_in.put((None, None, None)) for _ in range(nprocs)]
          +
          +    # get the results
          +    for i in range(len(sent)):
          +        i, res = q_out.get()
          +        xOpt[i] = res
          +
          +
          +    # wait until each processor has finished
          +    [p.join() for p in processes]
          +
          +    # process dimensions of output
          +    ndim = np.array(res).ndim
          +
          +    if ndim == 1:
          +        # return separate lists of beta, zt, dz, C
          +        xOpt = np.vstack(xOpt)
          +        return list(xOpt.T)
          +    elif ndim > 1:
          +        # return lists of beta, zt, dz, C for each centroid
          +        xOpt = np.hstack(xOpt)
          +        out = list(xOpt)
          +        for i in range(len(out)):
          +            out[i] = np.split(out[i], n)
          +        return out
          +    else:
          +        raise ValueError("Cannot determine shape of output")
          +
          +
          +
          +def reset_priors(self) +
          +
          +

          Reset priors to uniform distribution

          +
          +Source code +
          def reset_priors(self):
          +    """
          +    Reset priors to uniform distribution
          +    """
          +    self.prior = {'beta':None, 'zt':None, 'dz':None, 'C':None}
          +    self.prior_pdf = {'beta':None, 'zt':None, 'dz':None, 'C':None}
          +
          +
          +
          +def sensitivity(self, window, xc, yc, nsim, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=, process_subgrid=None, **kwargs) +
          +
          +

          Iterate through a list of centroids to compute the mean and +standard deviation of beta, zt, dz, C by perturbing their +prior distributions (if provided by the user - see add_prior).

          +

          Args

          +
          +
          nsim : int
          +
          number of Monte Carlo simulations
          +
          window : float
          +
          size of window in metres
          +
          xc : float
          +
          centroid x values
          +
          yc : float
          +
          centroid y values
          +
          nsim : int
          +
          +
            +
          • number of simulations
          • +
          +
          +
          beta : float
          +
          starting fractal parameter
          +
          zt : float
          +
          starting top of magnetic layer
          +
          dz : float
          +
          starting thickness of magnetic layer
          +
          C : float
          +
          starting field constant
          +
          +

          Returns

          +
          +
          beta : ndarray shape (nsim,)
          +
          fractal parameters
          +
          zt : ndarray shape (nsim,)
          +
          top of magnetic layer
          +
          dz : ndarray shape (nsim,)
          +
          thickness of magnetic layer
          +
          C : ndarray shape (nsim,)
          +
          field constant
          +
          +
          +Source code +
          def sensitivity(self, window, xc, yc, nsim, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs):
          +    """
          +    Iterate through a list of centroids to compute the mean and
          +    standard deviation of beta, zt, dz, C by perturbing their
          +    prior distributions (if provided by the user - see add_prior).
          +    
          +    Args:
          +        nsim : int
          +            number of Monte Carlo simulations
          +        window : float
          +            size of window in metres
          +        xc : float
          +            centroid x values
          +        yc : float
          +            centroid y values
          +        nsim : int
          +            - number of simulations
          +        beta : float
          +            starting fractal parameter 
          +        zt : float
          +            starting top of magnetic layer
          +        dz : float
          +            starting thickness of magnetic layer
          +        C : float
          +            starting field constant
          +
          +
          +    Returns:
          +        beta : ndarray shape (nsim,)
          +            fractal parameters
          +        zt : ndarray shape (nsim,)
          +            top of magnetic layer
          +        dz : ndarray shape (nsim,)
          +            thickness of magnetic layer
          +        C : ndarray shape (nsim,)
          +            field constant
          +    """
          +    if type(process_subgrid) == type(None):
          +        # dummy function
          +        def process_subgrid(subgrid):
          +            return subgrid
          +
          +
          +    samples = np.empty((nsim, 4))
          +    x0 = np.array([beta, zt, dz, C])
          +    
          +    use_keys = []
          +    for key in self.prior_pdf:
          +        prior_pdf = self.prior_pdf[key]
          +        if prior_pdf is not None:
          +            use_keys.append(key)
          +    
          +    # get subgrid
          +    subgrid = self.subgrid(window, xc, yc)
          +    subgrid = process_subgrid(subgrid)
          +
          +    # compute radial spectrum
          +    k, Phi, sigma_Phi = self.radial_spectrum(subgrid, taper=taper, **kwargs)
          +
          +    for sim in range(0, nsim):
          +        # randomly generate new prior values within PDF
          +        for key in use_keys:
          +            prior_pdf = self.prior_pdf[key]
          +            self.prior[key][0] = prior_pdf.rvs()
          +
          +        # minimise function
          +        rPhi = np.random.normal(Phi, sigma_Phi)
          +        res = minimize(self.min_func, x0, args=(k, rPhi, sigma_Phi), bounds=self.bounds)
          +        samples[sim] = res.x
          +
          +
          +    # restore priors
          +    for key in use_keys:
          +        prior_pdf = self.prior_pdf[key]
          +        self.prior[key] = list(prior_pdf.args)
          +
          +    return list(samples.T)
          +
          +
          +
          +

          Inherited members

          + +
          +
          +
          +
          + +
          + + + + + \ No newline at end of file diff --git a/docs/parallel.html b/docs/parallel.html new file mode 100644 index 0000000..c8b6e69 --- /dev/null +++ b/docs/parallel.html @@ -0,0 +1,689 @@ + + + + + + +pycurious.parallel API documentation + + + + + + + + + +
          +
          +
          +

          Module pycurious.parallel

          +
          +
          +

          Copyright 2018 Ben Mather, Robert Delhaye

          +

          This file is part of PyCurious.

          +

          PyCurious is free software: you can redistribute it and/or modify +it under the terms of the GNU Lesser General Public License as published by +the Free Software Foundation, either version 3 of the License, or any later version.

          +

          PyCurious is distributed in the hope that it will be useful, +but WITHOUT ANY WARRANTY; without even the implied warranty of +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. +See the +GNU Lesser General Public License for more details.

          +

          You should have received a copy of the GNU Lesser General Public License +along with PyCurious. +If not, see http://www.gnu.org/licenses/.

          +
          +Source code +
          """
          +Copyright 2018 Ben Mather, Robert Delhaye
          +
          +This file is part of PyCurious.
          +
          +PyCurious is free software: you can redistribute it and/or modify
          +it under the terms of the GNU Lesser General Public License as published by
          +the Free Software Foundation, either version 3 of the License, or any later version.
          +
          +PyCurious is distributed in the hope that it will be useful,
          +but WITHOUT ANY WARRANTY; without even the implied warranty of
          +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
          +GNU Lesser General Public License for more details.
          +
          +You should have received a copy of the GNU Lesser General Public License
          +along with PyCurious.  If not, see <http://www.gnu.org/licenses/>.
          +"""
          +
          +# -*- coding: utf-8 -*-
          +import numpy as np
          +import warnings
          +from .optimise import CurieOptimise
          +
          +try: range=xrange
          +except: pass
          +
          +
          +class CurieParallel(CurieOptimise):
          +    """
          +    A parallel implementation built on the PETSc DMDA mesh structure
          +    Almost a trivially parallel problem: each processor works locally
          +    on their portion of the grid. A stipulation being that the window
          +    size must not exceed the thickness of shadow zones or else the
          +    subgrid will be truncated.
          +
          +    This inherits from CurieOptimise and CurieGrid classes.
          +
          +
          +    Parameters
          +    ----------
          +     grid       : 2D array of magnetic data
          +     xmin       : minimum x bound in metres
          +     xmax       : maximum x bound in metres
          +     ymin       : minimum y bound in metres
          +     ymax       : maximum y bound in metres
          +     max_window : maximum size of the windows
          +                : this will be enforced for all methods
          +    
          +    Attributes
          +    ----------
          +     bounds     : lower and upper bounds for beta, zt, dz, C
          +     prior      : dictionary of priors for beta, zt, dz, C
          +     coords     : local xy coordinates
          +    """
          +
          +    def __init__(self, grid, xmin, xmax, ymin, ymax, max_window):
          +
          +        from petsc4py import PETSc
          +        from mpi4py import MPI
          +        comm = MPI.COMM_WORLD
          +        self.comm = comm
          +        self.MPI = MPI
          +
          +        # super(CurieParallel, self).__init__(grid, xmin, xmax, ymin, ymax)
          +
          +        # determine stencil width (should be window size/2)
          +        ny, nx = grid.shape
          +        dx = (xmax - xmin)/nx
          +        dy = (ymax - ymin)/ny
          +        nw = max_window/dx
          +        n2w = int(nw/2) + 1 # add some buffer
          +
          +        if abs(dx - dy) > 1.0:
          +            warnings.warn("node spacing should be identical {}".format((dx,dy)), RuntimeWarning)
          +
          +
          +        dm = PETSc.DMDA().create(dim=2, sizes=(nx,ny), stencil_width=n2w, comm=comm)
          +        dm.setUniformCoordinates(xmin, xmax, ymin, ymax)
          +
          +        self.dm = dm
          +        self.lgmap = dm.getLGMap()
          +        self.lvec = dm.createLocalVector()
          +        self.gvec = dm.createGlobalVector()
          +
          +        coords = dm.getCoordinatesLocal().array.reshape(-1, 2)
          +        xmin, ymin = coords.min(axis=0)
          +        xmax, ymax = coords.max(axis=0)
          +        self.coords = coords
          +        self.max_window = max_window
          +
          +        (imin, imax), (jmin, jmax) = dm.getGhostRanges()
          +
          +        # now decompose grid for each processor
          +
          +        grid_chunk = grid[jmin:jmax, imin:imax]
          +
          +        super(CurieParallel, self).__init__(grid_chunk, xmin, xmax, ymin, ymax)
          +
          +        reduce_methods = {'sum': MPI.SUM, 'max': MPI.MAX, 'min': MPI.MIN, 'mean': MPI.SUM}
          +        self._reduce_methods = reduce_methods
          +
          +
          +    def subgrid(self, xc, yc, window):
          +        """
          +        Extract a subgrid from the data at a window around
          +        the point (xc,yc)
          +        
          +        Parameters
          +        ----------
          +         xc      : x coordinate
          +         yc      : y coordinate
          +         window  : size of window in metres
          +
          +        Returns
          +        -------
          +         data    : subgrid
          +        """
          +        if window > self.max_window:
          +            raise ValueError("Max window size is {}".format(self.max_window))
          +
          +        return super(CurieParallel, self).subgrid(window, xc, yc)
          +
          +    
          +    def sync(self, vector):
          +        """
          +        Synchronise a local vector across all processors
          +        """
          +        self.lvec.setArray(vector)
          +        self.dm.localToGlobal(self.lvec, self.gvec)
          +        self.dm.globalToLocal(self.gvec, self.lvec)
          +        return self.lvec.array.copy()
          +
          +
          +    def add_parallel_prior(self, **kwargs):
          +        """
          +        Add a prior to the dictionary (tuple)
          +        This version broadcasts just the values from the root processor
          +
          +        Available priors are beta, zt, dz, C
          +
          +        Usage
          +        -----
          +         add_parallel_prior(beta=(p, sigma_p))
          +        """
          +
          +        comm = self.comm
          +        MPI = self.MPI
          +
          +        for key in kwargs:
          +            if key in self.prior:
          +                prior = kwargs[key]
          +                p  = np.array(prior[0]) # prior
          +                dp = np.array(prior[1]) # uncertainty
          +
          +                comm.Bcast([p, MPI.DOUBLE], root=0)
          +                comm.Bcast([dp,MPI.DOUBLE], root=0)
          +
          +                self.prior[key] = (float(p), float(dp))
          +            else:
          +                raise ValueError("prior must be one of {}".format(self.prior.keys()))
          +
          +
          +    def distribute_prior(self, method, **kwargs):
          +        """
          +        Distribute priors across all processors using a specific method.
          +
          +        Parameters
          +        ----------
          +         method  : operation to reduce the local priors to a single value
          +                 : choose from one of 'sum', 'mean', 'min', 'max'
          +         kwargs  : (prior, sigma_prior) tuple
          +
          +        Notes
          +        -----
          +         add_prior will broadcast the prior on the root processor (rank=0)
          +         distribute_prior enacts a MPI Allreduce operation.
          +        """
          +
          +        comm = self.comm
          +        MPI = self.MPI
          +
          +        if method in self._reduce_methods:
          +            op = self._reduce_methods[method]
          +        else:
          +            raise ValueError("choose one of the following methods {}".format(self._reduce_methods.keys()))
          +
          +        for key in kwargs:
          +            if key in self.prior:
          +                prior = kwargs[key]
          +                local_p  = np.array(prior[0]) # prior
          +                local_dp = np.array(prior[1]) # uncertainty
          +
          +                global_p = np.array(0.0)
          +                global_dp = np.array(0.0)
          +
          +                comm.Allreduce([local_p, MPI.DOUBLE], [global_p, MPI.DOUBLE], op=op)
          +                comm.Allreduce([local_dp, MPI.DOUBLE], [global_dp, MPI.DOUBLE], op=op)
          +                if method == 'mean':
          +                    global_p  /= comm.size
          +                    global_dp /= comm.size
          +
          +                self.prior[key] = (float(global_p), float(global_dp))
          +            else:
          +                raise ValueError("prior must be one of {}".format(self.prior.keys()))
          +
          +
          +
          +
          +
          +
          +
          +
          +
          +

          Classes

          +
          +
          +class CurieParallel +(grid, xmin, xmax, ymin, ymax, max_window) +
          +
          +

          A parallel implementation built on the PETSc DMDA mesh structure +Almost a trivially parallel problem: each processor works locally +on their portion of the grid. A stipulation being that the window +size must not exceed the thickness of shadow zones or else the +subgrid will be truncated.

          +

          This inherits from CurieOptimise and CurieGrid classes.

          +

          Parameters

          +

          grid +: 2D array of magnetic data +xmin +: minimum x bound in metres +xmax +: maximum x bound in metres +ymin +: minimum y bound in metres +ymax +: maximum y bound in metres +max_window : maximum size of the windows +: this will be enforced for all methods

          +

          Attributes

          +

          bounds +: lower and upper bounds for beta, zt, dz, C +prior +: dictionary of priors for beta, zt, dz, C +coords +: local xy coordinates

          +
          +Source code +
          class CurieParallel(CurieOptimise):
          +    """
          +    A parallel implementation built on the PETSc DMDA mesh structure
          +    Almost a trivially parallel problem: each processor works locally
          +    on their portion of the grid. A stipulation being that the window
          +    size must not exceed the thickness of shadow zones or else the
          +    subgrid will be truncated.
          +
          +    This inherits from CurieOptimise and CurieGrid classes.
          +
          +
          +    Parameters
          +    ----------
          +     grid       : 2D array of magnetic data
          +     xmin       : minimum x bound in metres
          +     xmax       : maximum x bound in metres
          +     ymin       : minimum y bound in metres
          +     ymax       : maximum y bound in metres
          +     max_window : maximum size of the windows
          +                : this will be enforced for all methods
          +    
          +    Attributes
          +    ----------
          +     bounds     : lower and upper bounds for beta, zt, dz, C
          +     prior      : dictionary of priors for beta, zt, dz, C
          +     coords     : local xy coordinates
          +    """
          +
          +    def __init__(self, grid, xmin, xmax, ymin, ymax, max_window):
          +
          +        from petsc4py import PETSc
          +        from mpi4py import MPI
          +        comm = MPI.COMM_WORLD
          +        self.comm = comm
          +        self.MPI = MPI
          +
          +        # super(CurieParallel, self).__init__(grid, xmin, xmax, ymin, ymax)
          +
          +        # determine stencil width (should be window size/2)
          +        ny, nx = grid.shape
          +        dx = (xmax - xmin)/nx
          +        dy = (ymax - ymin)/ny
          +        nw = max_window/dx
          +        n2w = int(nw/2) + 1 # add some buffer
          +
          +        if abs(dx - dy) > 1.0:
          +            warnings.warn("node spacing should be identical {}".format((dx,dy)), RuntimeWarning)
          +
          +
          +        dm = PETSc.DMDA().create(dim=2, sizes=(nx,ny), stencil_width=n2w, comm=comm)
          +        dm.setUniformCoordinates(xmin, xmax, ymin, ymax)
          +
          +        self.dm = dm
          +        self.lgmap = dm.getLGMap()
          +        self.lvec = dm.createLocalVector()
          +        self.gvec = dm.createGlobalVector()
          +
          +        coords = dm.getCoordinatesLocal().array.reshape(-1, 2)
          +        xmin, ymin = coords.min(axis=0)
          +        xmax, ymax = coords.max(axis=0)
          +        self.coords = coords
          +        self.max_window = max_window
          +
          +        (imin, imax), (jmin, jmax) = dm.getGhostRanges()
          +
          +        # now decompose grid for each processor
          +
          +        grid_chunk = grid[jmin:jmax, imin:imax]
          +
          +        super(CurieParallel, self).__init__(grid_chunk, xmin, xmax, ymin, ymax)
          +
          +        reduce_methods = {'sum': MPI.SUM, 'max': MPI.MAX, 'min': MPI.MIN, 'mean': MPI.SUM}
          +        self._reduce_methods = reduce_methods
          +
          +
          +    def subgrid(self, xc, yc, window):
          +        """
          +        Extract a subgrid from the data at a window around
          +        the point (xc,yc)
          +        
          +        Parameters
          +        ----------
          +         xc      : x coordinate
          +         yc      : y coordinate
          +         window  : size of window in metres
          +
          +        Returns
          +        -------
          +         data    : subgrid
          +        """
          +        if window > self.max_window:
          +            raise ValueError("Max window size is {}".format(self.max_window))
          +
          +        return super(CurieParallel, self).subgrid(window, xc, yc)
          +
          +    
          +    def sync(self, vector):
          +        """
          +        Synchronise a local vector across all processors
          +        """
          +        self.lvec.setArray(vector)
          +        self.dm.localToGlobal(self.lvec, self.gvec)
          +        self.dm.globalToLocal(self.gvec, self.lvec)
          +        return self.lvec.array.copy()
          +
          +
          +    def add_parallel_prior(self, **kwargs):
          +        """
          +        Add a prior to the dictionary (tuple)
          +        This version broadcasts just the values from the root processor
          +
          +        Available priors are beta, zt, dz, C
          +
          +        Usage
          +        -----
          +         add_parallel_prior(beta=(p, sigma_p))
          +        """
          +
          +        comm = self.comm
          +        MPI = self.MPI
          +
          +        for key in kwargs:
          +            if key in self.prior:
          +                prior = kwargs[key]
          +                p  = np.array(prior[0]) # prior
          +                dp = np.array(prior[1]) # uncertainty
          +
          +                comm.Bcast([p, MPI.DOUBLE], root=0)
          +                comm.Bcast([dp,MPI.DOUBLE], root=0)
          +
          +                self.prior[key] = (float(p), float(dp))
          +            else:
          +                raise ValueError("prior must be one of {}".format(self.prior.keys()))
          +
          +
          +    def distribute_prior(self, method, **kwargs):
          +        """
          +        Distribute priors across all processors using a specific method.
          +
          +        Parameters
          +        ----------
          +         method  : operation to reduce the local priors to a single value
          +                 : choose from one of 'sum', 'mean', 'min', 'max'
          +         kwargs  : (prior, sigma_prior) tuple
          +
          +        Notes
          +        -----
          +         add_prior will broadcast the prior on the root processor (rank=0)
          +         distribute_prior enacts a MPI Allreduce operation.
          +        """
          +
          +        comm = self.comm
          +        MPI = self.MPI
          +
          +        if method in self._reduce_methods:
          +            op = self._reduce_methods[method]
          +        else:
          +            raise ValueError("choose one of the following methods {}".format(self._reduce_methods.keys()))
          +
          +        for key in kwargs:
          +            if key in self.prior:
          +                prior = kwargs[key]
          +                local_p  = np.array(prior[0]) # prior
          +                local_dp = np.array(prior[1]) # uncertainty
          +
          +                global_p = np.array(0.0)
          +                global_dp = np.array(0.0)
          +
          +                comm.Allreduce([local_p, MPI.DOUBLE], [global_p, MPI.DOUBLE], op=op)
          +                comm.Allreduce([local_dp, MPI.DOUBLE], [global_dp, MPI.DOUBLE], op=op)
          +                if method == 'mean':
          +                    global_p  /= comm.size
          +                    global_dp /= comm.size
          +
          +                self.prior[key] = (float(global_p), float(global_dp))
          +            else:
          +                raise ValueError("prior must be one of {}".format(self.prior.keys()))
          +
          +

          Ancestors

          + +

          Methods

          +
          +
          +def add_parallel_prior(self, **kwargs) +
          +
          +

          Add a prior to the dictionary (tuple) +This version broadcasts just the values from the root processor

          +

          Available priors are beta, zt, dz, C

          +

          Usage

          +

          add_parallel_prior(beta=(p, sigma_p))

          +
          +Source code +
          def add_parallel_prior(self, **kwargs):
          +    """
          +    Add a prior to the dictionary (tuple)
          +    This version broadcasts just the values from the root processor
          +
          +    Available priors are beta, zt, dz, C
          +
          +    Usage
          +    -----
          +     add_parallel_prior(beta=(p, sigma_p))
          +    """
          +
          +    comm = self.comm
          +    MPI = self.MPI
          +
          +    for key in kwargs:
          +        if key in self.prior:
          +            prior = kwargs[key]
          +            p  = np.array(prior[0]) # prior
          +            dp = np.array(prior[1]) # uncertainty
          +
          +            comm.Bcast([p, MPI.DOUBLE], root=0)
          +            comm.Bcast([dp,MPI.DOUBLE], root=0)
          +
          +            self.prior[key] = (float(p), float(dp))
          +        else:
          +            raise ValueError("prior must be one of {}".format(self.prior.keys()))
          +
          +
          +
          +def distribute_prior(self, method, **kwargs) +
          +
          +

          Distribute priors across all processors using a specific method.

          +

          Parameters

          +

          method +: operation to reduce the local priors to a single value +: choose from one of 'sum', 'mean', 'min', 'max' +kwargs +: (prior, sigma_prior) tuple

          +

          Notes

          +

          add_prior will broadcast the prior on the root processor (rank=0) +distribute_prior enacts a MPI Allreduce operation.

          +
          +Source code +
          def distribute_prior(self, method, **kwargs):
          +    """
          +    Distribute priors across all processors using a specific method.
          +
          +    Parameters
          +    ----------
          +     method  : operation to reduce the local priors to a single value
          +             : choose from one of 'sum', 'mean', 'min', 'max'
          +     kwargs  : (prior, sigma_prior) tuple
          +
          +    Notes
          +    -----
          +     add_prior will broadcast the prior on the root processor (rank=0)
          +     distribute_prior enacts a MPI Allreduce operation.
          +    """
          +
          +    comm = self.comm
          +    MPI = self.MPI
          +
          +    if method in self._reduce_methods:
          +        op = self._reduce_methods[method]
          +    else:
          +        raise ValueError("choose one of the following methods {}".format(self._reduce_methods.keys()))
          +
          +    for key in kwargs:
          +        if key in self.prior:
          +            prior = kwargs[key]
          +            local_p  = np.array(prior[0]) # prior
          +            local_dp = np.array(prior[1]) # uncertainty
          +
          +            global_p = np.array(0.0)
          +            global_dp = np.array(0.0)
          +
          +            comm.Allreduce([local_p, MPI.DOUBLE], [global_p, MPI.DOUBLE], op=op)
          +            comm.Allreduce([local_dp, MPI.DOUBLE], [global_dp, MPI.DOUBLE], op=op)
          +            if method == 'mean':
          +                global_p  /= comm.size
          +                global_dp /= comm.size
          +
          +            self.prior[key] = (float(global_p), float(global_dp))
          +        else:
          +            raise ValueError("prior must be one of {}".format(self.prior.keys()))
          +
          +
          +
          +def subgrid(self, xc, yc, window) +
          +
          +

          Extract a subgrid from the data at a window around +the point (xc,yc)

          +

          Parameters

          +

          xc +: x coordinate +yc +: y coordinate +window +: size of window in metres

          +

          Returns

          +

          data +: subgrid

          +
          +Source code +
          def subgrid(self, xc, yc, window):
          +    """
          +    Extract a subgrid from the data at a window around
          +    the point (xc,yc)
          +    
          +    Parameters
          +    ----------
          +     xc      : x coordinate
          +     yc      : y coordinate
          +     window  : size of window in metres
          +
          +    Returns
          +    -------
          +     data    : subgrid
          +    """
          +    if window > self.max_window:
          +        raise ValueError("Max window size is {}".format(self.max_window))
          +
          +    return super(CurieParallel, self).subgrid(window, xc, yc)
          +
          +
          +
          +def sync(self, vector) +
          +
          +

          Synchronise a local vector across all processors

          +
          +Source code +
          def sync(self, vector):
          +    """
          +    Synchronise a local vector across all processors
          +    """
          +    self.lvec.setArray(vector)
          +    self.dm.localToGlobal(self.lvec, self.gvec)
          +    self.dm.globalToLocal(self.gvec, self.lvec)
          +    return self.lvec.array.copy()
          +
          +
          +
          +

          Inherited members

          + +
          +
          +
          +
          + +
          + + + + + \ No newline at end of file diff --git a/docs/therm.html b/docs/therm.html new file mode 100644 index 0000000..c4688ea --- /dev/null +++ b/docs/therm.html @@ -0,0 +1,1216 @@ + + + + + + +pycurious.therm API documentation + + + + + + + + + +
          +
          +
          +

          Module pycurious.therm

          +
          +
          +

          Copyright 2018 Ben Mather, Robert Delhaye

          +

          This file is part of PyCurious.

          +

          PyCurious is free software: you can redistribute it and/or modify +it under the terms of the GNU Lesser General Public License as published by +the Free Software Foundation, either version 3 of the License, or any later version.

          +

          PyCurious is distributed in the hope that it will be useful, +but WITHOUT ANY WARRANTY; without even the implied warranty of +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. +See the +GNU Lesser General Public License for more details.

          +

          You should have received a copy of the GNU Lesser General Public License +along with PyCurious. +If not, see http://www.gnu.org/licenses/.

          +
          +Source code +
          """
          +Copyright 2018 Ben Mather, Robert Delhaye
          +
          +This file is part of PyCurious.
          +
          +PyCurious is free software: you can redistribute it and/or modify
          +it under the terms of the GNU Lesser General Public License as published by
          +the Free Software Foundation, either version 3 of the License, or any later version.
          +
          +PyCurious is distributed in the hope that it will be useful,
          +but WITHOUT ANY WARRANTY; without even the implied warranty of
          +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
          +GNU Lesser General Public License for more details.
          +
          +You should have received a copy of the GNU Lesser General Public License
          +along with PyCurious.  If not, see <http://www.gnu.org/licenses/>.
          +"""
          +
          +import numpy as np
          +from scipy import sparse
          +from scipy.sparse.linalg import spsolve
          +from multiprocessing import Pool, Process, Queue, cpu_count
          +
          +try: range=xrange
          +except: pass
          +
          +
          +class CurieTherm(object):
          +    """
          +    Implicit 1d solver for the steady-state heat equation
          +    over a structured grid using sparse matrices.
          +
          +    Parameters
          +    ----------
          +     minZ : float, minimum Cartesian coordinate
          +     maxZ : float, maximum Cartesian coordinate
          +     resZ : int, resolution in the z direction
          +     kwargs : dict, keyword arguments to pass to control
          +       optional functionality e.g.
          +       - stencil_width=int : number of node neighbours to
          +           include in each matrix row
          +
          +    Attributes
          +    ----------
          +     diffusivity  : float shape(n,) thermal conductivity field
          +     heat_sources : float shape(n,) heat source field
          +     temperature  : float shape(n,) temperature field
          +
          +     npoints      : int, number of nodes in the mesh
          +     sizes        : (int,int) dimensions of the sparse matrix
          +     
          +    """
          +
          +    def __init__(self, minZ, maxZ, resZ, **kwargs):
          +
          +        self.npoints = resZ
          +        self.extent = (minZ, maxZ)
          +        self.coords = np.linspace(minZ, maxZ, resZ)
          +        self.nodes = np.arange(0, resZ, dtype=np.int)
          +        self.sizes = (resZ, resZ)
          +
          +        width = kwargs.pop('stencil_width', 1)
          +        self.stencil_width = 2*width + 1
          +
          +        closure = [(0,-2), (2,0), (1,-1)]
          +        self.closure = self._create_closure_object(closure)
          +
          +
          +        self._initialise_COO_vectors()
          +        self._initialise_boundary_dictionary()
          +        self.diffusivity  = np.zeros(resZ)
          +        self.heat_sources = np.zeros(resZ)
          +        self.temperature  = np.zeros(resZ)
          +
          +
          +    def _initialise_COO_vectors(self):
          +
          +        nn = self.npoints
          +
          +        index = np.empty(nn + 2, dtype=np.int)
          +        index.fill(-1)
          +        self.index = index
          +
          +        self.rows = np.empty((self.stencil_width, nn), dtype=np.int)
          +        self.cols = np.empty((self.stencil_width, nn), dtype=np.int)
          +        self.vals = np.empty((self.stencil_width, nn))
          +
          +
          +    def _initialise_boundary_dictionary(self):
          +
          +        nn = self.npoints
          +        coords = self.coords
          +        minZ, maxZ = self.extent
          +
          +        # Setup boundary dictionary
          +        bc = dict()
          +
          +        m0 = coords == minZ
          +        m1 = coords == maxZ
          +        d0 = abs(coords[1] - coords[0])
          +        d1 = abs(coords[-1] - coords[-2])
          +
          +        bc["minZ"] = {"val": 0.0, "delta": d0, "flux": True, "mask": m0}
          +        bc["maxZ"] = {"val": 0.0, "delta": d1, "flux": True, "mask": m1}
          +
          +        self.bc = bc
          +        self.dirichlet_mask = np.zeros(nn, dtype=bool)
          +
          +
          +    def _create_closure_object(self, closure):
          +
          +        nn = self.npoints
          +        obj = [[0] for i in range(self.stencil_width)]
          +
          +        for i in range(0, self.stencil_width):
          +            # construct slicing object
          +            start, end = closure[i-j]
          +            obj[i] = slice(start, nn+end+2)
          +
          +        return obj
          +
          +
          +    def update_properties(self, diffusivity, heat_sources):
          +        """
          +        Update diffusivity and heat sources
          +        """
          +        self.diffusivity[:] = diffusivity
          +        self.heat_sources[:] = heat_sources
          +        return
          +
          +
          +    def boundary_condition(self, wall, val, flux=False):
          +        """
          +        Set the boundary conditions on each wall of the domain.
          +        By default each wall is a Dirichlet condition.
          +
          +        Parameters
          +        ----------
          +         wall : str, wall to assign bc - 'minZ' or 'maxZ'
          +         val  : float or array(n,) value(s) to assign to wall
          +         flux : bool, toggle type of boundary condition
          +           True = Neumann flux boundary condition
          +           False = Dirichlet boundary condition (default)
          +
          +        Notes
          +        -----
          +         If flux=True, positive val indicates a flux vector towards the centre
          +         of the domain.
          +
          +         val can be a vector with the same number of elements as the wall
          +        """
          +        wall = str(wall)
          +
          +        if wall in self.bc:
          +            self.bc[wall]["val"]  = np.array(val, copy=True)
          +            self.bc[wall]["flux"] = flux
          +            d = self.bc[wall]
          +
          +            mask = d['mask']
          +
          +            if flux:
          +                self.dirichlet_mask[mask] = False
          +                self.bc[wall]["val"] /= -d['delta']
          +            else:
          +                self.dirichlet_mask[mask] = True
          +
          +        else:
          +            raise ValueError("Wall should be one of {}".format(self.bc.keys()))
          +
          +
          +    def construct_matrix(self):
          +        """
          +        Construct a sparse coefficient matrix
          +        i.e. matrix A in AT = b
          +
          +        Notes
          +        -----
          +         We vectorise the 7-point stencil for fast matrix insertion.
          +         An extra border of dummy values around the domain allows for automatic
          +         Neumann (flux) boundary creation.
          +         These are stomped on if there are any Dirichlet conditions.
          +        """
          +
          +        nodes = self.nodes
          +        nn = self.npoints
          +
          +        index = self.index
          +
          +        rows = self.rows
          +        cols = self.cols
          +        vals = self.vals
          +
          +        dirichlet_mask = self.dirichlet_mask
          +        coords = self.coords.reshape(-1,1)
          +
          +        u = self.diffusivity
          +
          +        k = np.zeros(nn + 2)
          +        k[1:-1] = u
          +
          +        for i in range(0, self.stencil_width):
          +            obj = self.closure[i]
          +
          +            rows[i] = nodes
          +            cols[i] = index[obj].ravel()
          +
          +            distance = np.linalg.norm(coords[cols[i]] - coords, axis=1)
          +            distance[distance==0] = 1e-12 # protect against dividing by zero
          +            delta = 1.0/(2.0*distance**2)
          +
          +            vals[i] = delta*(k[obj] + u).ravel()
          +
          +
          +        # Dirichlet boundary conditions (duplicates are summed)
          +        cols[:,dirichlet_mask] = nodes[dirichlet_mask]
          +        vals[:,dirichlet_mask] = 0.0
          +
          +        # zero off-grid coordinates
          +        vals[cols < 0] = 0.0
          +
          +        # centre point
          +        vals[-1] = 0.0
          +        vals[-1][dirichlet_mask] = -1.0
          +
          +
          +        row = rows.ravel()
          +        col = cols.ravel()
          +        val = vals.ravel()
          +
          +
          +        # mask off-grid entries and sum duplicates
          +        mask = col >= 0
          +        row = row[mask]
          +        col = col[mask]
          +        val = val[mask]
          +
          +        mat = sparse.coo_matrix((val, (row, col)), shape=self.sizes).tocsr()
          +        mat.sum_duplicates()
          +        diag = np.ravel(mat.sum(axis=1))
          +        diag *= -1
          +        mat.setdiag(diag)
          +
          +        return mat
          +
          +
          +    def construct_rhs(self):
          +        """
          +        Construct the right-hand-side vector
          +        i.e. vector b in AT = b
          +
          +        Notes
          +        -----
          +         Boundary conditions are grabbed from the dictionary and
          +         summed to the rhs.
          +         Be careful of duplicate entries on the corners!!
          +        """
          +        
          +        rhs = -1.0*self.heat_sources
          +
          +        for wall in self.bc:
          +            val  = self.bc[wall]['val']
          +            flux = self.bc[wall]['flux']
          +            mask = self.bc[wall]['mask']
          +            if flux:
          +                rhs[mask] += val
          +            else:
          +                rhs[mask] = val
          +
          +        return rhs
          +
          +
          +    def solve(self, matrix=None, rhs=None):
          +        """
          +        Construct the matrix A and vector b in AT = b and solve for T
          +        (i.e. temperature field)
          +
          +        Arguments
          +        ---------
          +         matrix : (optional) scipy sparse matrix object
          +                 build using construct_matrix()
          +         rhs    : (optional) numpy right-hand-side vector
          +                 build using construct_rhs()
          +
          +        Returns
          +        -------
          +         sol    : 1d array shape(n,) temperature solution
          +
          +        Notes
          +        -----
          +         The solution to the system of linear equations AT = b is solved
          +         with spsolve in the scipy.sparse.linalg module
          +        """
          +        if matrix is None:
          +            matrix = self.construct_matrix()
          +        if rhs is None:
          +            rhs = self.construct_rhs()
          +        # res = self.temperature
          +
          +        T = spsolve(matrix, rhs)
          +        self.temperature[:] = T
          +
          +        return T
          +
          +
          +    def gradient(self, vector, **kwargs):
          +        """
          +        Calculate gradient of a vector
          +        
          +        Arguments
          +        ---------
          +         vector : 1d array of shape(n,)
          +
          +        Returns
          +        -------
          +         dvdz   : 1d array of shape(n,)
          +                 derivative of vector in z direction
          +        """
          +        return np.gradient(vector, self.coords, **kwargs)
          +
          +
          +    def heatflux(self):
          +        """
          +        Calculate the heat flux from the conductivity field
          +        and temperature solution
          +
          +        Returns
          +        -------
          +         qz  : 1d array shape(n,) heat flux vector
          +        """
          +
          +        T = self.temperature
          +        k = self.diffusivity
          +        divT = self.gradient(T)
          +        return -k*divT
          +
          +
          +    def isosurface(self, vector, isoval, interp='linear'):
          +        """
          +        Calculate an isosurface along the z axis
          +
          +        Parameters
          +        ----------
          +         vector : array, the same size as the mesh (n,)
          +         isoval : float, isosurface value
          +         interp : str, interpolation method can be either
          +            'nearest' - nearest neighbour interpolation
          +            'linear'  - linear interpolation
          +        
          +        Returns
          +        -------
          +         z_interp : isosurface
          +        """
          +        coords = self.coords
          +        sort_idx = np.abs(vector - isoval).argsort()    
          +        i0 = sort_idx[0]
          +        z0 = coords[i0]
          +
          +        if interp == 'linear':
          +            v0 = vector[i0]
          +            
          +            # identify next nearest node
          +            i1 = sort_idx[1]
          +            z1 = coords[i1]
          +            v1 = vector[i1]
          +
          +            vmin = min(v0,v1)
          +            vmax = max(v0,v1)
          +
          +            ratio = np.array([isoval, vmin, vmax])
          +            ratio -= ratio.min()
          +            ratio /= ratio.max()
          +            z_interp = ratio[0]*z1 + (1.0 - ratio[0])*z0
          +            return z_interp
          +        elif interp == 'nearest':
          +            return z0
          +        else:
          +            raise ValueError("enter a valid interp method: 'linear' or 'nearest'")
          +
          +
          +
          +
          +
          +
          +
          +
          +
          +

          Classes

          +
          +
          +class CurieTherm +(minZ, maxZ, resZ, **kwargs) +
          +
          +

          Implicit 1d solver for the steady-state heat equation +over a structured grid using sparse matrices.

          +

          Parameters

          +

          minZ : float, minimum Cartesian coordinate +maxZ : float, maximum Cartesian coordinate +resZ : int, resolution in the z direction +kwargs : dict, keyword arguments to pass to control +optional functionality e.g. +- stencil_width=int : number of node neighbours to +include in each matrix row

          +

          Attributes

          +

          diffusivity +: float shape(n,) thermal conductivity field +heat_sources : float shape(n,) heat source field +temperature +: float shape(n,) temperature field

          +

          npoints +: int, number of nodes in the mesh +sizes +: (int,int) dimensions of the sparse matrix

          +
          +Source code +
          class CurieTherm(object):
          +    """
          +    Implicit 1d solver for the steady-state heat equation
          +    over a structured grid using sparse matrices.
          +
          +    Parameters
          +    ----------
          +     minZ : float, minimum Cartesian coordinate
          +     maxZ : float, maximum Cartesian coordinate
          +     resZ : int, resolution in the z direction
          +     kwargs : dict, keyword arguments to pass to control
          +       optional functionality e.g.
          +       - stencil_width=int : number of node neighbours to
          +           include in each matrix row
          +
          +    Attributes
          +    ----------
          +     diffusivity  : float shape(n,) thermal conductivity field
          +     heat_sources : float shape(n,) heat source field
          +     temperature  : float shape(n,) temperature field
          +
          +     npoints      : int, number of nodes in the mesh
          +     sizes        : (int,int) dimensions of the sparse matrix
          +     
          +    """
          +
          +    def __init__(self, minZ, maxZ, resZ, **kwargs):
          +
          +        self.npoints = resZ
          +        self.extent = (minZ, maxZ)
          +        self.coords = np.linspace(minZ, maxZ, resZ)
          +        self.nodes = np.arange(0, resZ, dtype=np.int)
          +        self.sizes = (resZ, resZ)
          +
          +        width = kwargs.pop('stencil_width', 1)
          +        self.stencil_width = 2*width + 1
          +
          +        closure = [(0,-2), (2,0), (1,-1)]
          +        self.closure = self._create_closure_object(closure)
          +
          +
          +        self._initialise_COO_vectors()
          +        self._initialise_boundary_dictionary()
          +        self.diffusivity  = np.zeros(resZ)
          +        self.heat_sources = np.zeros(resZ)
          +        self.temperature  = np.zeros(resZ)
          +
          +
          +    def _initialise_COO_vectors(self):
          +
          +        nn = self.npoints
          +
          +        index = np.empty(nn + 2, dtype=np.int)
          +        index.fill(-1)
          +        self.index = index
          +
          +        self.rows = np.empty((self.stencil_width, nn), dtype=np.int)
          +        self.cols = np.empty((self.stencil_width, nn), dtype=np.int)
          +        self.vals = np.empty((self.stencil_width, nn))
          +
          +
          +    def _initialise_boundary_dictionary(self):
          +
          +        nn = self.npoints
          +        coords = self.coords
          +        minZ, maxZ = self.extent
          +
          +        # Setup boundary dictionary
          +        bc = dict()
          +
          +        m0 = coords == minZ
          +        m1 = coords == maxZ
          +        d0 = abs(coords[1] - coords[0])
          +        d1 = abs(coords[-1] - coords[-2])
          +
          +        bc["minZ"] = {"val": 0.0, "delta": d0, "flux": True, "mask": m0}
          +        bc["maxZ"] = {"val": 0.0, "delta": d1, "flux": True, "mask": m1}
          +
          +        self.bc = bc
          +        self.dirichlet_mask = np.zeros(nn, dtype=bool)
          +
          +
          +    def _create_closure_object(self, closure):
          +
          +        nn = self.npoints
          +        obj = [[0] for i in range(self.stencil_width)]
          +
          +        for i in range(0, self.stencil_width):
          +            # construct slicing object
          +            start, end = closure[i-j]
          +            obj[i] = slice(start, nn+end+2)
          +
          +        return obj
          +
          +
          +    def update_properties(self, diffusivity, heat_sources):
          +        """
          +        Update diffusivity and heat sources
          +        """
          +        self.diffusivity[:] = diffusivity
          +        self.heat_sources[:] = heat_sources
          +        return
          +
          +
          +    def boundary_condition(self, wall, val, flux=False):
          +        """
          +        Set the boundary conditions on each wall of the domain.
          +        By default each wall is a Dirichlet condition.
          +
          +        Parameters
          +        ----------
          +         wall : str, wall to assign bc - 'minZ' or 'maxZ'
          +         val  : float or array(n,) value(s) to assign to wall
          +         flux : bool, toggle type of boundary condition
          +           True = Neumann flux boundary condition
          +           False = Dirichlet boundary condition (default)
          +
          +        Notes
          +        -----
          +         If flux=True, positive val indicates a flux vector towards the centre
          +         of the domain.
          +
          +         val can be a vector with the same number of elements as the wall
          +        """
          +        wall = str(wall)
          +
          +        if wall in self.bc:
          +            self.bc[wall]["val"]  = np.array(val, copy=True)
          +            self.bc[wall]["flux"] = flux
          +            d = self.bc[wall]
          +
          +            mask = d['mask']
          +
          +            if flux:
          +                self.dirichlet_mask[mask] = False
          +                self.bc[wall]["val"] /= -d['delta']
          +            else:
          +                self.dirichlet_mask[mask] = True
          +
          +        else:
          +            raise ValueError("Wall should be one of {}".format(self.bc.keys()))
          +
          +
          +    def construct_matrix(self):
          +        """
          +        Construct a sparse coefficient matrix
          +        i.e. matrix A in AT = b
          +
          +        Notes
          +        -----
          +         We vectorise the 7-point stencil for fast matrix insertion.
          +         An extra border of dummy values around the domain allows for automatic
          +         Neumann (flux) boundary creation.
          +         These are stomped on if there are any Dirichlet conditions.
          +        """
          +
          +        nodes = self.nodes
          +        nn = self.npoints
          +
          +        index = self.index
          +
          +        rows = self.rows
          +        cols = self.cols
          +        vals = self.vals
          +
          +        dirichlet_mask = self.dirichlet_mask
          +        coords = self.coords.reshape(-1,1)
          +
          +        u = self.diffusivity
          +
          +        k = np.zeros(nn + 2)
          +        k[1:-1] = u
          +
          +        for i in range(0, self.stencil_width):
          +            obj = self.closure[i]
          +
          +            rows[i] = nodes
          +            cols[i] = index[obj].ravel()
          +
          +            distance = np.linalg.norm(coords[cols[i]] - coords, axis=1)
          +            distance[distance==0] = 1e-12 # protect against dividing by zero
          +            delta = 1.0/(2.0*distance**2)
          +
          +            vals[i] = delta*(k[obj] + u).ravel()
          +
          +
          +        # Dirichlet boundary conditions (duplicates are summed)
          +        cols[:,dirichlet_mask] = nodes[dirichlet_mask]
          +        vals[:,dirichlet_mask] = 0.0
          +
          +        # zero off-grid coordinates
          +        vals[cols < 0] = 0.0
          +
          +        # centre point
          +        vals[-1] = 0.0
          +        vals[-1][dirichlet_mask] = -1.0
          +
          +
          +        row = rows.ravel()
          +        col = cols.ravel()
          +        val = vals.ravel()
          +
          +
          +        # mask off-grid entries and sum duplicates
          +        mask = col >= 0
          +        row = row[mask]
          +        col = col[mask]
          +        val = val[mask]
          +
          +        mat = sparse.coo_matrix((val, (row, col)), shape=self.sizes).tocsr()
          +        mat.sum_duplicates()
          +        diag = np.ravel(mat.sum(axis=1))
          +        diag *= -1
          +        mat.setdiag(diag)
          +
          +        return mat
          +
          +
          +    def construct_rhs(self):
          +        """
          +        Construct the right-hand-side vector
          +        i.e. vector b in AT = b
          +
          +        Notes
          +        -----
          +         Boundary conditions are grabbed from the dictionary and
          +         summed to the rhs.
          +         Be careful of duplicate entries on the corners!!
          +        """
          +        
          +        rhs = -1.0*self.heat_sources
          +
          +        for wall in self.bc:
          +            val  = self.bc[wall]['val']
          +            flux = self.bc[wall]['flux']
          +            mask = self.bc[wall]['mask']
          +            if flux:
          +                rhs[mask] += val
          +            else:
          +                rhs[mask] = val
          +
          +        return rhs
          +
          +
          +    def solve(self, matrix=None, rhs=None):
          +        """
          +        Construct the matrix A and vector b in AT = b and solve for T
          +        (i.e. temperature field)
          +
          +        Arguments
          +        ---------
          +         matrix : (optional) scipy sparse matrix object
          +                 build using construct_matrix()
          +         rhs    : (optional) numpy right-hand-side vector
          +                 build using construct_rhs()
          +
          +        Returns
          +        -------
          +         sol    : 1d array shape(n,) temperature solution
          +
          +        Notes
          +        -----
          +         The solution to the system of linear equations AT = b is solved
          +         with spsolve in the scipy.sparse.linalg module
          +        """
          +        if matrix is None:
          +            matrix = self.construct_matrix()
          +        if rhs is None:
          +            rhs = self.construct_rhs()
          +        # res = self.temperature
          +
          +        T = spsolve(matrix, rhs)
          +        self.temperature[:] = T
          +
          +        return T
          +
          +
          +    def gradient(self, vector, **kwargs):
          +        """
          +        Calculate gradient of a vector
          +        
          +        Arguments
          +        ---------
          +         vector : 1d array of shape(n,)
          +
          +        Returns
          +        -------
          +         dvdz   : 1d array of shape(n,)
          +                 derivative of vector in z direction
          +        """
          +        return np.gradient(vector, self.coords, **kwargs)
          +
          +
          +    def heatflux(self):
          +        """
          +        Calculate the heat flux from the conductivity field
          +        and temperature solution
          +
          +        Returns
          +        -------
          +         qz  : 1d array shape(n,) heat flux vector
          +        """
          +
          +        T = self.temperature
          +        k = self.diffusivity
          +        divT = self.gradient(T)
          +        return -k*divT
          +
          +
          +    def isosurface(self, vector, isoval, interp='linear'):
          +        """
          +        Calculate an isosurface along the z axis
          +
          +        Parameters
          +        ----------
          +         vector : array, the same size as the mesh (n,)
          +         isoval : float, isosurface value
          +         interp : str, interpolation method can be either
          +            'nearest' - nearest neighbour interpolation
          +            'linear'  - linear interpolation
          +        
          +        Returns
          +        -------
          +         z_interp : isosurface
          +        """
          +        coords = self.coords
          +        sort_idx = np.abs(vector - isoval).argsort()    
          +        i0 = sort_idx[0]
          +        z0 = coords[i0]
          +
          +        if interp == 'linear':
          +            v0 = vector[i0]
          +            
          +            # identify next nearest node
          +            i1 = sort_idx[1]
          +            z1 = coords[i1]
          +            v1 = vector[i1]
          +
          +            vmin = min(v0,v1)
          +            vmax = max(v0,v1)
          +
          +            ratio = np.array([isoval, vmin, vmax])
          +            ratio -= ratio.min()
          +            ratio /= ratio.max()
          +            z_interp = ratio[0]*z1 + (1.0 - ratio[0])*z0
          +            return z_interp
          +        elif interp == 'nearest':
          +            return z0
          +        else:
          +            raise ValueError("enter a valid interp method: 'linear' or 'nearest'")
          +
          +

          Methods

          +
          +
          +def boundary_condition(self, wall, val, flux=False) +
          +
          +

          Set the boundary conditions on each wall of the domain. +By default each wall is a Dirichlet condition.

          +

          Parameters

          +

          wall : str, wall to assign bc - 'minZ' or 'maxZ' +val +: float or array(n,) value(s) to assign to wall +flux : bool, toggle type of boundary condition +True = Neumann flux boundary condition +False = Dirichlet boundary condition (default)

          +

          Notes

          +

          If flux=True, positive val indicates a flux vector towards the centre +of the domain.

          +

          val can be a vector with the same number of elements as the wall

          +
          +Source code +
          def boundary_condition(self, wall, val, flux=False):
          +    """
          +    Set the boundary conditions on each wall of the domain.
          +    By default each wall is a Dirichlet condition.
          +
          +    Parameters
          +    ----------
          +     wall : str, wall to assign bc - 'minZ' or 'maxZ'
          +     val  : float or array(n,) value(s) to assign to wall
          +     flux : bool, toggle type of boundary condition
          +       True = Neumann flux boundary condition
          +       False = Dirichlet boundary condition (default)
          +
          +    Notes
          +    -----
          +     If flux=True, positive val indicates a flux vector towards the centre
          +     of the domain.
          +
          +     val can be a vector with the same number of elements as the wall
          +    """
          +    wall = str(wall)
          +
          +    if wall in self.bc:
          +        self.bc[wall]["val"]  = np.array(val, copy=True)
          +        self.bc[wall]["flux"] = flux
          +        d = self.bc[wall]
          +
          +        mask = d['mask']
          +
          +        if flux:
          +            self.dirichlet_mask[mask] = False
          +            self.bc[wall]["val"] /= -d['delta']
          +        else:
          +            self.dirichlet_mask[mask] = True
          +
          +    else:
          +        raise ValueError("Wall should be one of {}".format(self.bc.keys()))
          +
          +
          +
          +def construct_matrix(self) +
          +
          +

          Construct a sparse coefficient matrix +i.e. matrix A in AT = b

          +

          Notes

          +

          We vectorise the 7-point stencil for fast matrix insertion. +An extra border of dummy values around the domain allows for automatic +Neumann (flux) boundary creation. +These are stomped on if there are any Dirichlet conditions.

          +
          +Source code +
          def construct_matrix(self):
          +    """
          +    Construct a sparse coefficient matrix
          +    i.e. matrix A in AT = b
          +
          +    Notes
          +    -----
          +     We vectorise the 7-point stencil for fast matrix insertion.
          +     An extra border of dummy values around the domain allows for automatic
          +     Neumann (flux) boundary creation.
          +     These are stomped on if there are any Dirichlet conditions.
          +    """
          +
          +    nodes = self.nodes
          +    nn = self.npoints
          +
          +    index = self.index
          +
          +    rows = self.rows
          +    cols = self.cols
          +    vals = self.vals
          +
          +    dirichlet_mask = self.dirichlet_mask
          +    coords = self.coords.reshape(-1,1)
          +
          +    u = self.diffusivity
          +
          +    k = np.zeros(nn + 2)
          +    k[1:-1] = u
          +
          +    for i in range(0, self.stencil_width):
          +        obj = self.closure[i]
          +
          +        rows[i] = nodes
          +        cols[i] = index[obj].ravel()
          +
          +        distance = np.linalg.norm(coords[cols[i]] - coords, axis=1)
          +        distance[distance==0] = 1e-12 # protect against dividing by zero
          +        delta = 1.0/(2.0*distance**2)
          +
          +        vals[i] = delta*(k[obj] + u).ravel()
          +
          +
          +    # Dirichlet boundary conditions (duplicates are summed)
          +    cols[:,dirichlet_mask] = nodes[dirichlet_mask]
          +    vals[:,dirichlet_mask] = 0.0
          +
          +    # zero off-grid coordinates
          +    vals[cols < 0] = 0.0
          +
          +    # centre point
          +    vals[-1] = 0.0
          +    vals[-1][dirichlet_mask] = -1.0
          +
          +
          +    row = rows.ravel()
          +    col = cols.ravel()
          +    val = vals.ravel()
          +
          +
          +    # mask off-grid entries and sum duplicates
          +    mask = col >= 0
          +    row = row[mask]
          +    col = col[mask]
          +    val = val[mask]
          +
          +    mat = sparse.coo_matrix((val, (row, col)), shape=self.sizes).tocsr()
          +    mat.sum_duplicates()
          +    diag = np.ravel(mat.sum(axis=1))
          +    diag *= -1
          +    mat.setdiag(diag)
          +
          +    return mat
          +
          +
          +
          +def construct_rhs(self) +
          +
          +

          Construct the right-hand-side vector +i.e. vector b in AT = b

          +

          Notes

          +

          Boundary conditions are grabbed from the dictionary and +summed to the rhs. +Be careful of duplicate entries on the corners!!

          +
          +Source code +
          def construct_rhs(self):
          +    """
          +    Construct the right-hand-side vector
          +    i.e. vector b in AT = b
          +
          +    Notes
          +    -----
          +     Boundary conditions are grabbed from the dictionary and
          +     summed to the rhs.
          +     Be careful of duplicate entries on the corners!!
          +    """
          +    
          +    rhs = -1.0*self.heat_sources
          +
          +    for wall in self.bc:
          +        val  = self.bc[wall]['val']
          +        flux = self.bc[wall]['flux']
          +        mask = self.bc[wall]['mask']
          +        if flux:
          +            rhs[mask] += val
          +        else:
          +            rhs[mask] = val
          +
          +    return rhs
          +
          +
          +
          +def gradient(self, vector, **kwargs) +
          +
          +

          Calculate gradient of a vector

          +

          Arguments

          +

          vector : 1d array of shape(n,)

          +

          Returns

          +

          dvdz +: 1d array of shape(n,) +derivative of vector in z direction

          +
          +Source code +
          def gradient(self, vector, **kwargs):
          +    """
          +    Calculate gradient of a vector
          +    
          +    Arguments
          +    ---------
          +     vector : 1d array of shape(n,)
          +
          +    Returns
          +    -------
          +     dvdz   : 1d array of shape(n,)
          +             derivative of vector in z direction
          +    """
          +    return np.gradient(vector, self.coords, **kwargs)
          +
          +
          +
          +def heatflux(self) +
          +
          +

          Calculate the heat flux from the conductivity field +and temperature solution

          +

          Returns

          +

          qz +: 1d array shape(n,) heat flux vector

          +
          +Source code +
          def heatflux(self):
          +    """
          +    Calculate the heat flux from the conductivity field
          +    and temperature solution
          +
          +    Returns
          +    -------
          +     qz  : 1d array shape(n,) heat flux vector
          +    """
          +
          +    T = self.temperature
          +    k = self.diffusivity
          +    divT = self.gradient(T)
          +    return -k*divT
          +
          +
          +
          +def isosurface(self, vector, isoval, interp='linear') +
          +
          +

          Calculate an isosurface along the z axis

          +

          Parameters

          +

          vector : array, the same size as the mesh (n,) +isoval : float, isosurface value +interp : str, interpolation method can be either +'nearest' - nearest neighbour interpolation +'linear' +- linear interpolation

          +

          Returns

          +

          z_interp : isosurface

          +
          +Source code +
          def isosurface(self, vector, isoval, interp='linear'):
          +    """
          +    Calculate an isosurface along the z axis
          +
          +    Parameters
          +    ----------
          +     vector : array, the same size as the mesh (n,)
          +     isoval : float, isosurface value
          +     interp : str, interpolation method can be either
          +        'nearest' - nearest neighbour interpolation
          +        'linear'  - linear interpolation
          +    
          +    Returns
          +    -------
          +     z_interp : isosurface
          +    """
          +    coords = self.coords
          +    sort_idx = np.abs(vector - isoval).argsort()    
          +    i0 = sort_idx[0]
          +    z0 = coords[i0]
          +
          +    if interp == 'linear':
          +        v0 = vector[i0]
          +        
          +        # identify next nearest node
          +        i1 = sort_idx[1]
          +        z1 = coords[i1]
          +        v1 = vector[i1]
          +
          +        vmin = min(v0,v1)
          +        vmax = max(v0,v1)
          +
          +        ratio = np.array([isoval, vmin, vmax])
          +        ratio -= ratio.min()
          +        ratio /= ratio.max()
          +        z_interp = ratio[0]*z1 + (1.0 - ratio[0])*z0
          +        return z_interp
          +    elif interp == 'nearest':
          +        return z0
          +    else:
          +        raise ValueError("enter a valid interp method: 'linear' or 'nearest'")
          +
          +
          +
          +def solve(self, matrix=None, rhs=None) +
          +
          +

          Construct the matrix A and vector b in AT = b and solve for T +(i.e. temperature field)

          +

          Arguments

          +

          matrix : (optional) scipy sparse matrix object +build using construct_matrix() +rhs +: (optional) numpy right-hand-side vector +build using construct_rhs()

          +

          Returns

          +

          sol +: 1d array shape(n,) temperature solution

          +

          Notes

          +

          The solution to the system of linear equations AT = b is solved +with spsolve in the scipy.sparse.linalg module

          +
          +Source code +
          def solve(self, matrix=None, rhs=None):
          +    """
          +    Construct the matrix A and vector b in AT = b and solve for T
          +    (i.e. temperature field)
          +
          +    Arguments
          +    ---------
          +     matrix : (optional) scipy sparse matrix object
          +             build using construct_matrix()
          +     rhs    : (optional) numpy right-hand-side vector
          +             build using construct_rhs()
          +
          +    Returns
          +    -------
          +     sol    : 1d array shape(n,) temperature solution
          +
          +    Notes
          +    -----
          +     The solution to the system of linear equations AT = b is solved
          +     with spsolve in the scipy.sparse.linalg module
          +    """
          +    if matrix is None:
          +        matrix = self.construct_matrix()
          +    if rhs is None:
          +        rhs = self.construct_rhs()
          +    # res = self.temperature
          +
          +    T = spsolve(matrix, rhs)
          +    self.temperature[:] = T
          +
          +    return T
          +
          +
          +
          +def update_properties(self, diffusivity, heat_sources) +
          +
          +

          Update diffusivity and heat sources

          +
          +Source code +
          def update_properties(self, diffusivity, heat_sources):
          +    """
          +    Update diffusivity and heat sources
          +    """
          +    self.diffusivity[:] = diffusivity
          +    self.heat_sources[:] = heat_sources
          +    return
          +
          +
          +
          +
          +
          +
          +
          + +
          + + + + + \ No newline at end of file From ea3276ecb6c8f4e439893f9d2f26928696db6ca6 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Tue, 4 Jun 2019 17:23:43 +1000 Subject: [PATCH 053/170] Committing TravisCI configuration --- .travis.yml | 23 +++++++++++++++++++++++ 1 file changed, 23 insertions(+) create mode 100644 .travis.yml diff --git a/.travis.yml b/.travis.yml new file mode 100644 index 0000000..6116c2e --- /dev/null +++ b/.travis.yml @@ -0,0 +1,23 @@ +dist: bionic +language: python +python: + - "3.5" + - "3.6" + - "3.7" + + +install: + - pip3 install Cython numpy pytest git+https://github.com/lmoresi/pdoc.git + - pip3 install . + +script: + - pdoc --html -o docs --force stripy + +deploy: + provider: pages + skip_cleanup: true + github_token: $GITHUB_TOKEN # Set in the settings page of your repository, as a secure variable + keep_history: true + on: + branch: master + local_dir: docs/ From 5de863c46ece3be23de5189655dcdae160e39f0a Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Tue, 4 Jun 2019 17:36:09 +1000 Subject: [PATCH 054/170] updated travisCI script --- .travis.yml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/.travis.yml b/.travis.yml index 6116c2e..253ba04 100644 --- a/.travis.yml +++ b/.travis.yml @@ -8,7 +8,7 @@ python: install: - pip3 install Cython numpy pytest git+https://github.com/lmoresi/pdoc.git - - pip3 install . + - pip3 install -e . script: - pdoc --html -o docs --force stripy From 482034438eafd5e74d4652f269d9accbc7f3ed66 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Tue, 4 Jun 2019 18:02:57 +1000 Subject: [PATCH 055/170] Properly generate the docs --- .travis.yml | 7 ++++++- 1 file changed, 6 insertions(+), 1 deletion(-) diff --git a/.travis.yml b/.travis.yml index 253ba04..90cf8c1 100644 --- a/.travis.yml +++ b/.travis.yml @@ -11,7 +11,12 @@ install: - pip3 install -e . script: - - pdoc --html -o docs --force stripy + # generate the docs + - cd docs + - pdoc --html -o . --force pycurious + - mv pycurious/*.html . + - rm -rf pycurious/ + - cd ../ deploy: provider: pages From b5781a9d7cc08ae8d78eab58f3e394155930e46e Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Tue, 4 Jun 2019 18:09:12 +1000 Subject: [PATCH 056/170] Forgot scipy dependency --- .travis.yml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/.travis.yml b/.travis.yml index 90cf8c1..49a3f60 100644 --- a/.travis.yml +++ b/.travis.yml @@ -7,7 +7,7 @@ python: install: - - pip3 install Cython numpy pytest git+https://github.com/lmoresi/pdoc.git + - pip3 install Cython numpy scipy pytest git+https://github.com/lmoresi/pdoc.git - pip3 install -e . script: From a85d77d059d048d4dd1c69d645476096c1e71ac8 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Tue, 4 Jun 2019 18:47:13 +1000 Subject: [PATCH 057/170] Authentification works now, but 'file exists' error --- .travis.yml | 1 - 1 file changed, 1 deletion(-) diff --git a/.travis.yml b/.travis.yml index 49a3f60..7e364ee 100644 --- a/.travis.yml +++ b/.travis.yml @@ -25,4 +25,3 @@ deploy: keep_history: true on: branch: master - local_dir: docs/ From e556955bf760f3817d2296c040ff56dcd7d3c463 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Tue, 4 Jun 2019 19:11:53 +1000 Subject: [PATCH 058/170] set verbose to see what is going on --- .travis.yml | 1 + 1 file changed, 1 insertion(+) diff --git a/.travis.yml b/.travis.yml index 7e364ee..0d0bbfe 100644 --- a/.travis.yml +++ b/.travis.yml @@ -25,3 +25,4 @@ deploy: keep_history: true on: branch: master + verbose: true From fac2cdb6338b83c151c95d820c2b8b72e4ef0514 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Tue, 4 Jun 2019 19:26:40 +1000 Subject: [PATCH 059/170] Try again specifying docs folder --- .travis.yml | 1 + 1 file changed, 1 insertion(+) diff --git a/.travis.yml b/.travis.yml index 0d0bbfe..9551fdb 100644 --- a/.travis.yml +++ b/.travis.yml @@ -26,3 +26,4 @@ deploy: on: branch: master verbose: true + local_dir: docs/ From 9228facc6e1a5db603c463c9cf3f577e471105cb Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Tue, 4 Jun 2019 19:39:27 +1000 Subject: [PATCH 060/170] Hooray! Now I can delete the docs folder --- docs/documentation.html | 180 --- docs/grid.html | 2452 --------------------------------------- docs/index.html | 128 -- docs/mapping.html | 714 ------------ docs/optimise.html | 2141 ---------------------------------- docs/parallel.html | 689 ----------- docs/therm.html | 1216 ------------------- 7 files changed, 7520 deletions(-) delete mode 100644 docs/documentation.html delete mode 100644 docs/grid.html delete mode 100644 docs/index.html delete mode 100644 docs/mapping.html delete mode 100644 docs/optimise.html delete mode 100644 docs/parallel.html delete mode 100644 docs/therm.html diff --git a/docs/documentation.html b/docs/documentation.html deleted file mode 100644 index b33100b..0000000 --- a/docs/documentation.html +++ /dev/null @@ -1,180 +0,0 @@ - - - - - - -pycurious.documentation API documentation - - - - - - - - - -
          -
          -
          -

          Module pycurious.documentation

          -
          -
          -

          Copyright 2018 Ben Mather, Robert Delhaye

          -

          This file is part of PyCurious.

          -

          PyCurious is free software: you can redistribute it and/or modify -it under the terms of the GNU Lesser General Public License as published by -the Free Software Foundation, either version 3 of the License, or any later version.

          -

          PyCurious is distributed in the hope that it will be useful, -but WITHOUT ANY WARRANTY; without even the implied warranty of -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. -See the -GNU Lesser General Public License for more details.

          -

          You should have received a copy of the GNU Lesser General Public License -along with PyCurious. -If not, see http://www.gnu.org/licenses/.

          -
          -Source code -
          """
          -Copyright 2018 Ben Mather, Robert Delhaye
          -
          -This file is part of PyCurious.
          -
          -PyCurious is free software: you can redistribute it and/or modify
          -it under the terms of the GNU Lesser General Public License as published by
          -the Free Software Foundation, either version 3 of the License, or any later version.
          -
          -PyCurious is distributed in the hope that it will be useful,
          -but WITHOUT ANY WARRANTY; without even the implied warranty of
          -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
          -GNU Lesser General Public License for more details.
          -
          -You should have received a copy of the GNU Lesser General Public License
          -along with PyCurious.  If not, see <http://www.gnu.org/licenses/>.
          -"""
          -
          -import pkg_resources as _pkg_resources
          -from distutils import dir_util as _dir_util
          -import os
          -
          -
          -def install_documentation(path="./PyCurious-Examples"):
          -    """
          -    Install the examples for PyCurious in the given location.
          -
          -    WARNING: If the path exists, the files will be written into the path
          -    and will overwrite any existing files with which they collide. The default
          -    path ("./PyCurious-Examples") is chosen to make collision less likely/problematic
          -
          -    The documentation for PyCurious is in the form of jupyter notebooks.
          -
          -    Some dependencies exist for the notebooks to be useful:
          -
          -       - matplotlib: for some diagrams
          -       - cartopy: for mapping and visualisation
          -       - pyepsg: for converting between map projections
          -
          -    PyCurious dependencies may be explicitly imported in the notebooks including:
          -
          -       - numpy
          -       - scipy
          -
          -    """
          -
          -    Notebooks_Path = _pkg_resources.resource_filename("pycurious", os.path.join("Examples"))
          -
          -    ct = _dir_util.copy_tree(Notebooks_Path, path, preserve_mode=1, preserve_times=1, preserve_symlinks=1, update=0, verbose=1, dry_run=0)
          -
          -    return
          -
          -
          -
          -
          -
          -
          -
          -

          Functions

          -
          -
          -def install_documentation(path='./PyCurious-Examples') -
          -
          -

          Install the examples for PyCurious in the given location.

          -

          WARNING: If the path exists, the files will be written into the path -and will overwrite any existing files with which they collide. The default -path ("./PyCurious-Examples") is chosen to make collision less likely/problematic

          -

          The documentation for PyCurious is in the form of jupyter notebooks.

          -

          Some dependencies exist for the notebooks to be useful:

          -
            -
          • matplotlib: for some diagrams
          • -
          • cartopy: for mapping and visualisation
          • -
          • pyepsg: for converting between map projections
          • -
          -

          PyCurious dependencies may be explicitly imported in the notebooks including:

          -
            -
          • numpy
          • -
          • scipy
          • -
          -
          -Source code -
          def install_documentation(path="./PyCurious-Examples"):
          -    """
          -    Install the examples for PyCurious in the given location.
          -
          -    WARNING: If the path exists, the files will be written into the path
          -    and will overwrite any existing files with which they collide. The default
          -    path ("./PyCurious-Examples") is chosen to make collision less likely/problematic
          -
          -    The documentation for PyCurious is in the form of jupyter notebooks.
          -
          -    Some dependencies exist for the notebooks to be useful:
          -
          -       - matplotlib: for some diagrams
          -       - cartopy: for mapping and visualisation
          -       - pyepsg: for converting between map projections
          -
          -    PyCurious dependencies may be explicitly imported in the notebooks including:
          -
          -       - numpy
          -       - scipy
          -
          -    """
          -
          -    Notebooks_Path = _pkg_resources.resource_filename("pycurious", os.path.join("Examples"))
          -
          -    ct = _dir_util.copy_tree(Notebooks_Path, path, preserve_mode=1, preserve_times=1, preserve_symlinks=1, update=0, verbose=1, dry_run=0)
          -
          -    return
          -
          -
          -
          -
          -
          -
          -
          - -
          - - - - - \ No newline at end of file diff --git a/docs/grid.html b/docs/grid.html deleted file mode 100644 index 2dba02d..0000000 --- a/docs/grid.html +++ /dev/null @@ -1,2452 +0,0 @@ - - - - - - -pycurious.grid API documentation - - - - - - - - - -
          -
          -
          -

          Module pycurious.grid

          -
          -
          -

          Copyright 2018 Ben Mather, Robert Delhaye

          -

          This file is part of PyCurious.

          -

          PyCurious is free software: you can redistribute it and/or modify -it under the terms of the GNU Lesser General Public License as published by -the Free Software Foundation, either version 3 of the License, or any later version.

          -

          PyCurious is distributed in the hope that it will be useful, -but WITHOUT ANY WARRANTY; without even the implied warranty of -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. -See the -GNU Lesser General Public License for more details.

          -

          You should have received a copy of the GNU Lesser General Public License -along with PyCurious. -If not, see http://www.gnu.org/licenses/.

          -
          -Source code -
          """
          -Copyright 2018 Ben Mather, Robert Delhaye
          -
          -This file is part of PyCurious.
          -
          -PyCurious is free software: you can redistribute it and/or modify
          -it under the terms of the GNU Lesser General Public License as published by
          -the Free Software Foundation, either version 3 of the License, or any later version.
          -
          -PyCurious is distributed in the hope that it will be useful,
          -but WITHOUT ANY WARRANTY; without even the implied warranty of
          -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
          -GNU Lesser General Public License for more details.
          -
          -You should have received a copy of the GNU Lesser General Public License
          -along with PyCurious.  If not, see <http://www.gnu.org/licenses/>.
          -"""
          -
          -# -*- coding: utf-8 -*-
          -import numpy as np
          -from scipy.special import gamma, kv, lambertw
          -from scipy.optimize import minimize
          -from scipy.signal import tukey
          -import warnings
          -
          -try: range = xrange
          -except: pass
          -
          -
          -class CurieGrid(object):
          -    """
          -    Accepts a 2D array and Cartesian coordinates specifying the
          -    bounding box of the array
          -
          -    Grid must be projected in metres
          -
          -    Args:
          -     grid : 2D array of magnetic data
          -     xmin : minimum x bound in metres
          -     xmax : maximum x bound in metres
          -     ymin : minimum y bound in metres
          -     ymax : maximum y bound in metres
          -    """
          -    def __init__(self, grid, xmin, xmax, ymin, ymax):
          -        
          -        self.data = np.array(grid)
          -        ny, nx = self.data.shape
          -        self.xmin, self.xmax = xmin, xmax
          -        self.ymin, self.ymax = ymin, ymax
          -        self.xcoords, dx = np.linspace(xmin, xmax, nx, retstep=True)
          -        self.ycoords, dy = np.linspace(ymin, ymax, ny, retstep=True)
          -        self.nx, self.ny = nx, ny
          -        self.dx, self.dy = dx, dy
          -
          -        if abs(dx - dy) > 1.0:
          -            warnings.warn("node spacing should be identical {}".format((dx,dy)), RuntimeWarning)
          -
          -
          -    def subgrid(self, window, xc, yc):
          -        """
          -        Extract a subgrid from the data at a window around
          -        the point (xc,yc)
          -        
          -        Args:
          -            xc : float
          -                x coordinate
          -            yc : float
          -                y coordinate
          -            window : float
          -                size of window in metres
          -
          -        Returns:
          -            data : 2D array
          -                subgrid encompassing window size
          -        """
          -
          -        # check in coordinate in grid
          -        if xc < self.xmin or xc > self.xmax or yc < self.ymin or yc > self.ymax:
          -            raise ValueError("Point ({},{}) outside data range".format(xc,yc))
          -
          -        # find nearest index to xc,yc
          -        ix = np.abs(self.xcoords - xc).argmin()
          -        iy = np.abs(self.ycoords - yc).argmin()
          -
          -        nw = int(round(window/self.dx))
          -        n2w = nw//2
          -
          -        # extract a square window from the data
          -        imin = ix - n2w
          -        imax = ix + n2w + 1
          -        jmin = iy - n2w
          -        jmax = iy + n2w + 1
          -
          -        # safeguard if window size is larger than grid
          -        imin = max(imin, 0)
          -        imax = min(imax, self.nx)
          -        jmin = max(jmin, 0)
          -        jmax = min(jmax, self.ny)
          -        
          -        data = self.data[jmin:jmax, imin:imax]
          -
          -        return data
          -
          -
          -    def create_centroid_list(self, window, spacingX=None, spacingY=None):
          -        """
          -        Create a list of xc,yc values to extract subgrids.
          -
          -        Args:
          -            window : float
          -                size of the windows in metres
          -            spacingX : float (optional)
          -                specify spacing in metres in the X direction
          -                will default to maximum X resolution
          -            spacingY : float (optional)
          -                specify spacing in metres in the Y direction
          -                will default to maximum Y resolution
          -
          -        Returns:
          -            xc_list : 1D array
          -                array of x coordinates
          -            yc_list : 1D array
          -                array of y coordinates
          -        """
          -        
          -        nx, ny = self.nx, self.ny
          -        xcoords = self.xcoords
          -        ycoords = self.ycoords
          -        
          -        nw = int(round(window/self.dx))
          -        n2w = nw//2
          -        
          -        # this is the densest spacing possible given the data
          -        xc = xcoords[n2w:-n2w]
          -        yc = ycoords[n2w:-n2w]
          -        
          -        # but we can alter it if required
          -        if type(spacingX) != type(None):
          -            xc = np.arange(xc.min(), xc.max(), spacingX)
          -        if type(spacingY) != type(None):
          -            yc = np.arange(yc.min(), yc.max(), spacingY)
          -
          -        xq, yq = np.meshgrid(xc, yc)
          -            
          -        return xq.ravel(), yq.ravel()
          -
          -
          -    def remove_trend_linear(self, data):
          -        """
          -        Remove the best-fitting linear trend from the data
          -
          -        This may come in handy if the magnetic data has not been
          -        reduced to the pole.
          -
          -        Args:
          -            data : 2D numpy array
          -
          -        Returns:
          -         data : 2D numpy array
          -        """
          -        data = data.copy()
          -        nr, nc = data.shape
          -        xq, yq = np.meshgrid(np.arange(0, nc), np.arange(0, nr))
          -
          -        A = np.column_stack((x.flatten(), y.flatten(), np.ones(x.size)))
          -        c, resid, rank, sigma = np.linalg.lstsq(A, data.flatten())
          -
          -        data.flat[:] -= np.dot(A, c)
          -        return data
          -
          -    def radial_spectrum(self, subgrid, taper=np.hanning, scale=0.001, **kwargs):
          -        """
          -        Compute the radial spectrum for a square grid.
          -
          -        Args:
          -            subgrid : 2D array
          -                window of the original data (see subgrid method)
          -            taper : function (default=np.hanning)
          -                taper function, set to None for no taper function
          -            scale : float (default: 0.001)
          -                scaling factor to get k into rad/km
          -            kwargs : keyword arguments
          -                keyword arguments to pass to `taper`
          -
          -        Returns:
          -            k : 1D array shape (n,)
          -                wavenumber in rad/km
          -            Phi : 1D array shape (n,)
          -                Radial power spectrum
          -            sigma_Phi : 1D array shape (n,)
          -                Standard deviation of Phi
          -        """
          -
          -        data = subgrid
          -        nr, nc = data.shape
          -        nw = nr
          -
          -        if nr != nc:
          -            warnings.warn("subgrid is not square {}".format((nr,nc)), RuntimeWarning)
          -
          -
          -        # control taper
          -        if type(taper) == type(None):
          -            vtaper = 1.0
          -        else:
          -            rt = taper(nr, **kwargs)
          -            ct = taper(nc, **kwargs)
          -            xq, yq = np.meshgrid(ct, rt)
          -            vtaper = xq*yq
          -
          -        dx_scale = self.dx*scale
          -        dk = 2.0*np.pi/(nw - 1)/dx_scale
          -
          -        # fast Fourier transform and shift
          -        FT = np.abs(np.fft.fft2(data*vtaper))
          -        FT = np.fft.fftshift(FT)
          -
          -        kbins = np.arange(dk, dk*nw/2, dk)
          -        nbins = kbins.size - 1
          -
          -        S = np.empty(nbins)
          -        k = np.empty(nbins)
          -        sigma = np.empty(nbins)
          -
          -        i0 = int((nw - 1)//2)
          -        ix, iy = np.mgrid[0:nw,0:nw]
          -        kk = np.hypot((ix - i0)*dk, (iy - i0)*dk)
          -
          -        for i in range(0, nbins):
          -            mask = np.logical_and(kk >= kbins[i], kk <= kbins[i+1])
          -            rr = 2.0*np.log(FT[mask])
          -            S[i] = rr.mean()
          -            k[i] = kk[mask].mean()
          -            sigma[i] = np.std(rr)
          -
          -        return k, S, sigma
          -
          -
          -    def radial_spectrum_log(self, subgrid, taper=np.hanning, scale=0.001, **kwargs):
          -        """
          -        Compute the log of the radial spectrum for a square grid.
          -
          -        Args:
          -         subgrid : 2D array
          -            window of the original data (see subgrid method)
          -         taper : function (default=np.hanning)
          -            taper function, set to None for no taper function
          -         scale : float (detault=0.001)
          -            scaling factor to get k into rad/km
          -         kwargs : keyword arguments
          -            keyword arguments to pass to `taper`
          -
          -        Returns:
          -            k : 1D array shape (n,)
          -                wavenumber in rad/km
          -            lnPhi : 1D array
          -                log of the radial power spectrum in ln(sqrt(S))
          -            lnsigma_Phi : 1D array
          -                standard deviation of lnPhi
          -        """
          -
          -        data = subgrid
          -        nr, nc = data.shape
          -        nw = nr
          -
          -        if nr != nc:
          -            warnings.warn("subgrid is not square {}".format((nr,nc)), RuntimeWarning)
          -
          -
          -        # control taper
          -        if type(taper) == type(None):
          -            vtaper = 1.0
          -        else:
          -            rt = taper(nr, **kwargs)
          -            ct = taper(nc, **kwargs)
          -            xq, yq = np.meshgrid(ct, rt)
          -            vtaper = xq*yq
          -
          -        dx_scale = self.dx*scale
          -        dk = 2.0*np.pi/(nw - 1)/dx_scale
          -
          -        # fast Fourier transform and shift
          -        FT = np.abs(np.fft.fft2(data*vtaper))
          -        FT = np.fft.fftshift(FT)
          -
          -        kbins = np.arange(dk, dk*nw/2, dk)
          -        nbins = kbins.size - 1
          -
          -        S = np.empty(nbins)
          -        k = np.empty(nbins)
          -        sigma = np.empty(nbins)
          -
          -        i0 = int((nw - 1)//2)
          -        ix, iy = np.mgrid[0:nw,0:nw]
          -        kk = np.hypot((ix - i0)*dk, (iy - i0)*dk)
          -
          -        for i in range(0, nbins):
          -            mask = np.logical_and(kk >= kbins[i], kk <= kbins[i+1])
          -            rr = np.log(np.sqrt(FT[mask]))
          -            S[i] = rr.mean()
          -            k[i] = kk[mask].mean()
          -            sigma[i] = np.std(rr)
          -
          -        return k, S, sigma
          -        
          -        
          -    def azimuthal_spectrum(self, subgrid, taper=np.hanning, scale=0.001, theta=5.0, **kwargs):
          -        """
          -        Compute azimuthal spectrum for a square grid.
          -
          -        Args:
          -            subgrid : 2D array
          -                window of the original data (see subgrid method)
          -            taper : function (default=np.hanning)
          -                taper function, set to None for no taper function
          -            scale : float (default=0.001)
          -                scaling factor to get k into rad/km
          -            theta : float
          -                angle increment in degrees
          -            args : arguments
          -                arguments o pass to taper
          -
          -        Returns:
          -            k : 1D array shape (n,)
          -                wavenumber in rad/km
          -            Phi : 1D array shape (n,)
          -                Radial power spectrum
          -            sigma_Phi : 1D array shape (n,)
          -                Standard deviation of Phi
          -        """
          -        from pycurious import radon
          -        data = subgrid
          -        nr, nc = data.shape
          -        nw = nr
          -
          -        if nr != nc:
          -            raise RuntimeWarning("subgrid is not square {}".format((nr,nc)))
          -
          -        dx_scale = self.dx*scale
          -        dk = 2.0*np.pi/(nw - 1)/dx_scale
          -
          -        kbins = np.arange(dk, dk*nw/2, dk)
          -
          -        dtheta = np.arange(0.0, 180.0, theta)
          -        sinogram = radon.radon2d(data, np.pi*dtheta/180.0)
          -        S = np.zeros((dtheta.size, kbins.size))
          -        sigma2 = np.zeros((dtheta.size, kbins.size))
          -
          -        # control taper
          -        if taper is None:
          -            vtaper = 1.0
          -        else:
          -            vtaper = taper(sinogram.shape[0], **kwargs)
          -
          -        nk = 1 + 2*kbins.size
          -        for i in range(0, dtheta.size):
          -            PSD = np.abs(np.fft.fft(vtaper*sinogram[:,i], n=nk))
          -            S[i,:] = np.log( np.sqrt(PSD[1:kbins.size+1] ))
          -        
          -        return kbins, S, dtheta
          -
          -
          -    def reduce_to_pole(self, data, inc, dec, sinc=None, sdec=None):
          -        r"""
          -        Reduce total field magnetic anomaly data to the pole.
          -
          -        The reduction to the pole if a phase transformation that can be
          -        applied to total field magnetic anomaly data. It simulates how
          -        the data would be if both the Geomagnetic field and the
          -        magnetization of the source were vertical (Blakely, 1996).
          -
          -        Args:
          -            data : 1D array
          -                the total field anomaly data at each point.
          -            inc : float / 1D array
          -                inclination of the inducing Geomagnetic field
          -            dec : float / 1D array
          -                declination of the inducing Geomagnetic field
          -            sinc : float / 1D array (optional)
          -                inclination of the total magnetization of the anomaly source
          -            sdec : float / 1D array (optional)
          -                declination of the total magnetization of the anomaly source
          -                The total magnetization is the vector sum of the
          -                induced and remanent magnetization. If there is only induced
          -                magnetization, use the *inc* and *dec* of the Geomagnetic field.
          -
          -        Returns:
          -            rtp : 2D array
          -                the data reduced to the pole.
          -        
          -        References:
          -            Blakely, R. J. (1996), Potential Theory in Gravity and Magnetic
          -            Applications, Cambridge University Press.
          -
          -        Notes:
          -            This functions performs the reduction in the frequency domain
          -            (using the FFT). The transform filter is (in the freq domain):
          -                RTP(k_x, k_y) = \frac{|k|}{
          -                    a_1 k_x^2 + a_2 k_y^2 + a_3 k_x k_y +
          -                    i|k|(b_1 k_x + b_2 k_y)}
          -            in which k_x and k_y are the wave-numbers in the x and y
          -            directions and
          -                |k| = \sqrt{k_x^2 + k_y^2} \\
          -                a_1 = m_z f_z - m_x f_x \\
          -                a_2 = m_z f_z - m_y f_y \\
          -                a_3 = -m_y f_x - m_x f_y \\
          -                b_1 = m_x f_z + m_z f_x \\
          -                b_2 = m_y f_z + m_z f_y
          -            \mathbf{m} = (m_x, m_y, m_z)` is the unit-vector of the total
          -            magnetization of the source and
          -            \mathbf{f} = (f_x, f_y, f_z)` is the unit-vector of the
          -            Geomagnetic field.
          -        """
          -        nr, nc = data.shape
          -
          -        if nr != nc:
          -            warnings.warn("subgrid is not square {}".format((nr,nc)), RuntimeWarning)
          -
          -        fx, fy, fz = ang2vec(1.0, inc, dec)
          -        if sinc is None or sdec is None:
          -            mx, my, mz = fx, fy, fz
          -        else:
          -            mx, my, mz = ang2vec(1.0, sinc, sdec)
          -
          -        kx, ky = [k for k in _fftfreqs(self.dx, self.dy, data.shape)]
          -        kz = np.hypot(kx, ky)
          -
          -        a1 = mz*fz - mx*fx
          -        a2 = mz*fz - my*fy
          -        a3 = -my*fx - mx*fy
          -        b1 = mx*fz + mz*fx
          -        b2 = my*fz + mz*fy
          -
          -        # The division gives a RuntimeWarning because of the zero frequency term.
          -        # This suppresses the warning.
          -        with np.errstate(divide='ignore', invalid='ignore'):
          -            rtp = (kz)/(a1*kx**2 + a2*ky**2 + a3*kx*ky + \
          -                            1j*np.sqrt(kz)*(b1*kx + b2*ky))
          -        
          -        rtp[0, 0] = 0
          -        ft_pole = rtp*np.fft.fft2(data)
          -        return np.real(np.fft.ifft2(ft_pole))
          -
          -
          -    def upward_continuation(self, data, height):
          -        r"""
          -        Upward continuation of potential field data.
          -
          -        Calculates the continuation through the Fast Fourier Transform in
          -        the wavenumber domain (Blakely, 1996):
          -
          -            F\{h_{up}\} = F\{h\} e^{-\Delta z |k|}
          -
          -        and then transformed back to the space domain. :math:`h_{up}` is the
          -        upward continue data, \Delta z is the height increase, F denotes
          -        the Fourier Transform, |k| is the wavenumber modulus.
          -
          -        Args:
          -            data   : 2D array
          -                potential field at the grid points
          -            height : float
          -                height increase (delta z) in meters.
          -        
          -        Returns:
          -            cont : array
          -                upward continued data
          -
          -        Notes:
          -            It is not possible to get the FFT of a masked grid. The default
          -            :func:`fatiando.gridder.interp` call using minimum curvature will
          -            not be suitable.  Use extrapolate=True or algorithm='nearest' to
          -            get an unmasked grid.
          -
          -        References:
          -            Blakely, R. J. (1996), Potential Theory in Gravity and Magnetic
          -            Applications, Cambridge University Press.
          -        """
          -        nr, nc = data.shape
          -
          -        if nr != nc:
          -            warnings.warn("subgrid is not square {}".format((nr,nc)), RuntimeWarning)
          -
          -        if height <= 0:
          -            warnings.warn("Using 'height' <= 0 means downward continuation, " +
          -                          "which is known to be unstable.")
          -
          -        fx = 2.0*np.pi*np.fft.fftfreq(nr, self.dx)
          -        fy = 2.0*np.pi*np.fft.fftfreq(nc, self.dy)
          -
          -        kx, ky = np.meshgrid(fy, fx)[::-1]
          -        kz = np.hypot(kx, ky)
          -
          -        upcont_ft = np.fft.fft2(data)*np.exp(-height*kz)
          -        cont = np.real(np.fft.ifft2(upcont_ft))
          -        return cont
          -
          -
          -# Helper functions to calculate Curie depth
          -
          -def bouligand2009(kh, beta, zt, dz, C):
          -    """
          -    Calculate the synthetic radial power spectrum of
          -    magnetic anomalies
          -
          -    Equation (4) of Bouligand et al. (2009)
          -
          -    Args:
          -        kh : float / 1D array
          -            wavenumber in rad/km
          -        beta : float / 1D array
          -            fractal parameter
          -        zt : float / 1D array
          -            top of magnetic sources
          -        dz : float / 1D array
          -            thickness of magnetic sources
          -        C : float 1D array
          -            field constant (Maus et al., 1997)
          -
          -    Returns:
          -        Phi : float / 1D array
          -            radial power spectrum of magnetic anomalies
          -
          -    References:
          -        Bouligand, C., J. M. G. Glen, and R. J. Blakely (2009), Mapping Curie
          -        temperature depth in the western United States with a fractal model for
          -        crustal magnetization, J. Geophys. Res., 114, B11104,
          -        doi:10.1029/2009JB006494
          -
          -        Maus, S., D. Gordon, and D. Fairhead (1997), Curie temperature depth
          -        estimation using a self-similar magnetization model, Geophys. J. Int.,
          -        129, 163-168, doi:10.1111/j.1365-246X.1997.tb00945.x
          -    """
          -    # from scipy.special import kv
          -    khdz = kh*dz
          -    coshkhdz = np.cosh(khdz)
          -
          -    Phi1d = C - 2.0*kh*zt - (beta-1.0)*np.log(kh) - khdz
          -    A = np.sqrt(np.pi)/gamma(1.0+0.5*beta) * \
          -        (0.5*coshkhdz*gamma(0.5*(1.0+beta)) - \
          -        kv((-0.5*(1.0+beta)), khdz) * np.power(0.5*khdz,(0.5*(1.0+beta)) ))
          -    Phi1d += np.log(A)
          -    return Phi1d
          -
          -
          -def tanaka1999(k, lnPhi, sigma_lnPhi, kmin_range=(0.05, 0.2), kmax_range=(0.05, 0.2)):
          -    """
          -    Compute weighted linear fit of Phi over spatial frequency window kmin:kmax
          -
          -    Args:
          -        k : float / 1D-array
          -            wavenumber in rad/km
          -        lnPhi : float / 1D array
          -            log of the radial power spectrum (see power_spectrum_log)
          -            expected in ln(sqrt(S)) form
          -        sigma_lnPhi : standard deviation of lnPhi
          -        kmin_range : tuple (default:(0.05, 0.2))
          -            minimum and maximum range of spatial frequencies to fit for the 
          -            top of magnetic sources - ideally low frequency, straight line
          -        kmax_range : tuple (default:(0.05, 0.2))
          -            minimum and maximum range of spatial frequencies to fit for the
          -            bottom of magnetic source - ideally low frequency, straight line
          -
          -    Returns:
          -        upper_source : tuple
          -            (Ztr,btr,dZtr) gradient, intercept, error for the top of magnetic sources
          -        lower_source : tuple
          -            (Zor,bor,dZor) gradient, intercept, error for the bottom of magnetic sources
          -
          -    """
          -    # for now...
          -    S = lnPhi
          -    sigma2 = sigma_lnPhi**2
          -
          -    def compute_coefficients(X, Y, E):
          -        X2 = X**2
          -        Y2 = Y**2
          -        E2 = E**2
          -
          -        XY = np.multiply(X, Y)
          -        XE2sum = np.sum(X/E2)
          -        YE2sum = np.sum(Y/E2)
          -        rE2sum = np.sum(1.0/E2)
          -        X2E2sum = np.sum(X2/E2)
          -        Y2E2sum = np.sum(Y2/E2)
          -
          -        #TL = XE2sum*YE2sum - np.sum(XY/E2*rE2sum)
          -        # I think summation in second TL term needed to be split
          -        TL = XE2sum*YE2sum - np.sum(XY/E2)*rE2sum
          -        BL = XE2sum**2 - X2E2sum*rE2sum
          -
          -        Z  = TL/BL
          -        b  = (np.sum(XY/E2) - Z*X2E2sum)/XE2sum
          -        #dZ = np.sqrt( rE2sum/(X2E2sum*rE2sum - XE2sum) )
          -        ## There was a missing **2 term at end of error term.
          -        dZ = np.sqrt( rE2sum/(X2E2sum*rE2sum - XE2sum**2) )
          -        return Z, b, dZ
          -
          -
          -    sf=k/(2.0*np.pi)
          -    S2=np.log(np.exp(S)/sf)
          -
          -    # mask low wavenumbers
          -    kmin, kmax = kmin_range
          -    mask1 = np.logical_and(sf >=kmin, sf <=kmax)
          -    X1 = sf[mask1]
          -    Y1 = S[mask1]
          -    E1 = sigma2[mask1]
          -    
          -    # mask high wavenumbers
          -    kmin, kmax = kmax_range
          -    mask2 = np.logical_and(sf >=kmin, sf <=kmax)
          -    X2 = sf[mask2]
          -    Y2 = np.log(np.exp(S[mask2])/(X2*2*np.pi))
          -    E2 = np.log(np.exp(sigma2[mask2])/(X2*2*np.pi))
          -
          -    # compute top and bottom of magnetic layer
          -    Ztr, btr, dZtr = compute_coefficients(X1, Y1, E1)
          -    Zor, bor, dZor = compute_coefficients(X2, Y2, E2)
          -    return (Ztr,btr,dZtr), (Zor, bor, dZor)
          -    
          -    
          -def ComputeTanaka(Ztr, dZtr, Zor, dZor):
          -    """
          -    Compute the Curie depth from the results of tanaka1999
          -
          -    Args:
          -        Ztr : float / 1D array
          -            top of the magnetic source
          -        dZtr : float / 1D array
          -            error of Ztr
          -        Zor : float / 1D array 
          -            bottom of the magnetic source
          -        dZor : float / 1D array
          -            error of Zor
          -
          -    Returns:
          -        Zb : float / 1D array
          -            estimated Curie point depth
          -        eZb : float / 1D array
          -            error of `Zb`
          -    """
          -    Zb = 2.0*Zor - Ztr
          -    dZb  = 2.0*dZor - dZtr
          -    return abs(Zb), dZb
          -
          -
          -def maus1995(beta, zt, kh, C=0.0):
          -    """
          -    Calculate the synthetic radial power spectrum of
          -    magnetic anomalies (Maus and Dimri; 1995)
          -
          -    This is not all that useful except when testing
          -    overflow errors which occur for the second term
          -    in Bouligand et al. (2009).
          -
          -    Args:
          -        beta : float / 1D array
          -            fractal parameter
          -        zt : float / 1D array
          -            top of magnetic sources
          -        kh : float / 1D array
          -            norm of the wave number in the horizontal plane
          -        C : float / 1D array
          -            field constant (Maus et al., 1997)
          -
          -    Returns:
          -        Phi : float / 1D array
          -            radial power spectrum of magnetic anomalies
          -
          -    References:
          -        Bouligand, C., J. M. G. Glen, and R. J. Blakely (2009), Mapping Curie
          -        temperature depth in the western United States with a fractal model for
          -        crustal magnetization, J. Geophys. Res., 114, B11104,
          -        doi:10.1029/2009JB006494
          -
          -        Maus, S., D. Gordon, and D. Fairhead (1997), Curie temperature depth
          -        estimation using a self-similar magnetization model, Geophys. J. Int.,
          -        129, 163-168, doi:10.1111/j.1365-246X.1997.tb00945.x
          -    """
          -    return C - 2.0*kh*zt - (beta-1.0)*np.log(kh)
          -
          -
          -def _fftfreqs(dx, dy, shape):
          -    """
          -    Get two 2D-arrays with the wave numbers in the x and y directions.
          -    """
          -    fx = 2.0*np.pi*np.fft.fftfreq(shape[0], dx)
          -    fy = 2.0*np.pi*np.fft.fftfreq(shape[1], dy)
          -    return np.meshgrid(fy, fx)[::-1]
          -
          -def ang2vec(intensity, inc, dec):
          -    """
          -    Convert intensity, inclination and  declination to a 3-component vector
          -
          -    Args:
          -        intensity : float or 1D array
          -            The intensity (norm) of the vector
          -        inc : float
          -            The inclination of the vector (in degrees)
          -        dec : float
          -            The declination of the vector (in degrees)
          -
          -    Returns:
          -        vec : array = [x, y, z]
          -            3-component vector
          -
          -    Notes:
          -        Coordinate system is assumed to be x->North, y->East, z->Down.
          -        Inclination is positive down and declination is measured with respect
          -        to x (North).
          -
          -    Examples:
          -        >>> import numpy
          -        >>> print ang2vec(3, 45, 45)
          -        [ 1.5         1.5         2.12132034]
          -        >>> print ang2vec(numpy.arange(4), 45, 45)
          -        [[ 0.          0.          0.        ]
          -         [ 0.5         0.5         0.70710678]
          -         [ 1.          1.          1.41421356]
          -         [ 1.5         1.5         2.12132034]]
          -
          -    """
          -    return np.transpose([intensity * i for i in dircos(inc, dec)])
          -
          -
          -def dircos(inc, dec):
          -    """
          -    Returns the 3 coordinates of a unit vector given its inclination and
          -    declination.
          -
          -    Args:
          -        inc : float
          -            The inclination of the vector (in degrees)
          -        dec : float
          -            The declination of the vector (in degrees)
          -
          -    Returns:
          -        vect : list
          -            The unit vector = [x, y, z]
          -
          -    Notes:
          -        Coordinate system is assumed to be x->North, y->East, z->Down.
          -        Inclination is positive down and declination is measured with respect
          -        to x (North).
          -    """
          -    d2r = np.pi/180.0
          -    vect = [np.cos(d2r * inc) * np.cos(d2r * dec), \
          -            np.cos(d2r * inc) * np.sin(d2r * dec), \
          -            np.sin(d2r * inc)]
          -    return vect
          -
          -
          -
          -
          -
          -
          -
          -

          Functions

          -
          -
          -def ComputeTanaka(Ztr, dZtr, Zor, dZor) -
          -
          -

          Compute the Curie depth from the results of tanaka1999

          -

          Args

          -
          -
          Ztr : float / 1D array
          -
          top of the magnetic source
          -
          dZtr : float / 1D array
          -
          error of Ztr
          -
          Zor : float / 1D array
          -
          bottom of the magnetic source
          -
          dZor : float / 1D array
          -
          error of Zor
          -
          -

          Returns

          -
          -
          Zb : float / 1D array
          -
          estimated Curie point depth
          -
          eZb : float / 1D array
          -
          error of Zb
          -
          -
          -Source code -
          def ComputeTanaka(Ztr, dZtr, Zor, dZor):
          -    """
          -    Compute the Curie depth from the results of tanaka1999
          -
          -    Args:
          -        Ztr : float / 1D array
          -            top of the magnetic source
          -        dZtr : float / 1D array
          -            error of Ztr
          -        Zor : float / 1D array 
          -            bottom of the magnetic source
          -        dZor : float / 1D array
          -            error of Zor
          -
          -    Returns:
          -        Zb : float / 1D array
          -            estimated Curie point depth
          -        eZb : float / 1D array
          -            error of `Zb`
          -    """
          -    Zb = 2.0*Zor - Ztr
          -    dZb  = 2.0*dZor - dZtr
          -    return abs(Zb), dZb
          -
          -
          -
          -def ang2vec(intensity, inc, dec) -
          -
          -

          Convert intensity, inclination and -declination to a 3-component vector

          -

          Args

          -
          -
          intensity : float or 1D array
          -
          The intensity (norm) of the vector
          -
          inc : float
          -
          The inclination of the vector (in degrees)
          -
          dec : float
          -
          The declination of the vector (in degrees)
          -
          -

          Returns

          -
          -
          vec : array = [x, y, z]
          -
          3-component vector
          -
          -

          Notes

          -

          Coordinate system is assumed to be x->North, y->East, z->Down. -Inclination is positive down and declination is measured with respect -to x (North).

          -

          Examples

          -
          >>> import numpy
          ->>> print ang2vec(3, 45, 45)
          -[ 1.5         1.5         2.12132034]
          ->>> print ang2vec(numpy.arange(4), 45, 45)
          -[[ 0.          0.          0.        ]
          -
          -

          [ 0.5 -0.5 -0.70710678] -[ 1. -1. -1.41421356] -[ 1.5 -1.5 -2.12132034]]

          -
          -Source code -
          def ang2vec(intensity, inc, dec):
          -    """
          -    Convert intensity, inclination and  declination to a 3-component vector
          -
          -    Args:
          -        intensity : float or 1D array
          -            The intensity (norm) of the vector
          -        inc : float
          -            The inclination of the vector (in degrees)
          -        dec : float
          -            The declination of the vector (in degrees)
          -
          -    Returns:
          -        vec : array = [x, y, z]
          -            3-component vector
          -
          -    Notes:
          -        Coordinate system is assumed to be x->North, y->East, z->Down.
          -        Inclination is positive down and declination is measured with respect
          -        to x (North).
          -
          -    Examples:
          -        >>> import numpy
          -        >>> print ang2vec(3, 45, 45)
          -        [ 1.5         1.5         2.12132034]
          -        >>> print ang2vec(numpy.arange(4), 45, 45)
          -        [[ 0.          0.          0.        ]
          -         [ 0.5         0.5         0.70710678]
          -         [ 1.          1.          1.41421356]
          -         [ 1.5         1.5         2.12132034]]
          -
          -    """
          -    return np.transpose([intensity * i for i in dircos(inc, dec)])
          -
          -
          -
          -def bouligand2009(kh, beta, zt, dz, C) -
          -
          -

          Calculate the synthetic radial power spectrum of -magnetic anomalies

          -

          Equation (4) of Bouligand et al. (2009)

          -

          Args

          -
          -
          kh : float / 1D array
          -
          wavenumber in rad/km
          -
          beta : float / 1D array
          -
          fractal parameter
          -
          zt : float / 1D array
          -
          top of magnetic sources
          -
          dz : float / 1D array
          -
          thickness of magnetic sources
          -
          C : float 1D array
          -
          field constant (Maus et al., 1997)
          -
          -

          Returns

          -
          -
          Phi : float / 1D array
          -
          radial power spectrum of magnetic anomalies
          -
          -

          References

          -

          Bouligand, C., J. M. G. Glen, and R. J. Blakely (2009), Mapping Curie -temperature depth in the western United States with a fractal model for -crustal magnetization, J. Geophys. Res., 114, B11104, -doi:10.1029/2009JB006494

          -

          Maus, S., D. Gordon, and D. Fairhead (1997), Curie temperature depth -estimation using a self-similar magnetization model, Geophys. J. Int., -129, 163-168, doi:10.1111/j.1365-246X.1997.tb00945.x

          -
          -Source code -
          def bouligand2009(kh, beta, zt, dz, C):
          -    """
          -    Calculate the synthetic radial power spectrum of
          -    magnetic anomalies
          -
          -    Equation (4) of Bouligand et al. (2009)
          -
          -    Args:
          -        kh : float / 1D array
          -            wavenumber in rad/km
          -        beta : float / 1D array
          -            fractal parameter
          -        zt : float / 1D array
          -            top of magnetic sources
          -        dz : float / 1D array
          -            thickness of magnetic sources
          -        C : float 1D array
          -            field constant (Maus et al., 1997)
          -
          -    Returns:
          -        Phi : float / 1D array
          -            radial power spectrum of magnetic anomalies
          -
          -    References:
          -        Bouligand, C., J. M. G. Glen, and R. J. Blakely (2009), Mapping Curie
          -        temperature depth in the western United States with a fractal model for
          -        crustal magnetization, J. Geophys. Res., 114, B11104,
          -        doi:10.1029/2009JB006494
          -
          -        Maus, S., D. Gordon, and D. Fairhead (1997), Curie temperature depth
          -        estimation using a self-similar magnetization model, Geophys. J. Int.,
          -        129, 163-168, doi:10.1111/j.1365-246X.1997.tb00945.x
          -    """
          -    # from scipy.special import kv
          -    khdz = kh*dz
          -    coshkhdz = np.cosh(khdz)
          -
          -    Phi1d = C - 2.0*kh*zt - (beta-1.0)*np.log(kh) - khdz
          -    A = np.sqrt(np.pi)/gamma(1.0+0.5*beta) * \
          -        (0.5*coshkhdz*gamma(0.5*(1.0+beta)) - \
          -        kv((-0.5*(1.0+beta)), khdz) * np.power(0.5*khdz,(0.5*(1.0+beta)) ))
          -    Phi1d += np.log(A)
          -    return Phi1d
          -
          -
          -
          -def dircos(inc, dec) -
          -
          -

          Returns the 3 coordinates of a unit vector given its inclination and -declination.

          -

          Args

          -
          -
          inc : float
          -
          The inclination of the vector (in degrees)
          -
          dec : float
          -
          The declination of the vector (in degrees)
          -
          -

          Returns

          -
          -
          vect : list
          -
          The unit vector = [x, y, z]
          -
          -

          Notes

          -

          Coordinate system is assumed to be x->North, y->East, z->Down. -Inclination is positive down and declination is measured with respect -to x (North).

          -
          -Source code -
          def dircos(inc, dec):
          -    """
          -    Returns the 3 coordinates of a unit vector given its inclination and
          -    declination.
          -
          -    Args:
          -        inc : float
          -            The inclination of the vector (in degrees)
          -        dec : float
          -            The declination of the vector (in degrees)
          -
          -    Returns:
          -        vect : list
          -            The unit vector = [x, y, z]
          -
          -    Notes:
          -        Coordinate system is assumed to be x->North, y->East, z->Down.
          -        Inclination is positive down and declination is measured with respect
          -        to x (North).
          -    """
          -    d2r = np.pi/180.0
          -    vect = [np.cos(d2r * inc) * np.cos(d2r * dec), \
          -            np.cos(d2r * inc) * np.sin(d2r * dec), \
          -            np.sin(d2r * inc)]
          -    return vect
          -
          -
          -
          -def maus1995(beta, zt, kh, C=0.0) -
          -
          -

          Calculate the synthetic radial power spectrum of -magnetic anomalies (Maus and Dimri; 1995)

          -

          This is not all that useful except when testing -overflow errors which occur for the second term -in Bouligand et al. (2009).

          -

          Args

          -
          -
          beta : float / 1D array
          -
          fractal parameter
          -
          zt : float / 1D array
          -
          top of magnetic sources
          -
          kh : float / 1D array
          -
          norm of the wave number in the horizontal plane
          -
          C : float / 1D array
          -
          field constant (Maus et al., 1997)
          -
          -

          Returns

          -
          -
          Phi : float / 1D array
          -
          radial power spectrum of magnetic anomalies
          -
          -

          References

          -

          Bouligand, C., J. M. G. Glen, and R. J. Blakely (2009), Mapping Curie -temperature depth in the western United States with a fractal model for -crustal magnetization, J. Geophys. Res., 114, B11104, -doi:10.1029/2009JB006494

          -

          Maus, S., D. Gordon, and D. Fairhead (1997), Curie temperature depth -estimation using a self-similar magnetization model, Geophys. J. Int., -129, 163-168, doi:10.1111/j.1365-246X.1997.tb00945.x

          -
          -Source code -
          def maus1995(beta, zt, kh, C=0.0):
          -    """
          -    Calculate the synthetic radial power spectrum of
          -    magnetic anomalies (Maus and Dimri; 1995)
          -
          -    This is not all that useful except when testing
          -    overflow errors which occur for the second term
          -    in Bouligand et al. (2009).
          -
          -    Args:
          -        beta : float / 1D array
          -            fractal parameter
          -        zt : float / 1D array
          -            top of magnetic sources
          -        kh : float / 1D array
          -            norm of the wave number in the horizontal plane
          -        C : float / 1D array
          -            field constant (Maus et al., 1997)
          -
          -    Returns:
          -        Phi : float / 1D array
          -            radial power spectrum of magnetic anomalies
          -
          -    References:
          -        Bouligand, C., J. M. G. Glen, and R. J. Blakely (2009), Mapping Curie
          -        temperature depth in the western United States with a fractal model for
          -        crustal magnetization, J. Geophys. Res., 114, B11104,
          -        doi:10.1029/2009JB006494
          -
          -        Maus, S., D. Gordon, and D. Fairhead (1997), Curie temperature depth
          -        estimation using a self-similar magnetization model, Geophys. J. Int.,
          -        129, 163-168, doi:10.1111/j.1365-246X.1997.tb00945.x
          -    """
          -    return C - 2.0*kh*zt - (beta-1.0)*np.log(kh)
          -
          -
          -
          -def tanaka1999(k, lnPhi, sigma_lnPhi, kmin_range=(0.05, 0.2), kmax_range=(0.05, 0.2)) -
          -
          -

          Compute weighted linear fit of Phi over spatial frequency window kmin:kmax

          -

          Args

          -
          -
          k : float / 1D-array
          -
          wavenumber in rad/km
          -
          lnPhi : float / 1D array
          -
          log of the radial power spectrum (see power_spectrum_log) -expected in ln(sqrt(S)) form
          -
          sigma_lnPhi : standard deviation of lnPhi
          -
           
          -
          kmin_range : tuple (default:(0.05, 0.2))
          -
          minimum and maximum range of spatial frequencies to fit for the -top of magnetic sources - ideally low frequency, straight line
          -
          kmax_range : tuple (default:(0.05, 0.2))
          -
          minimum and maximum range of spatial frequencies to fit for the -bottom of magnetic source - ideally low frequency, straight line
          -
          -

          Returns

          -
          -
          upper_source : tuple
          -
          (Ztr,btr,dZtr) gradient, intercept, error for the top of magnetic sources
          -
          lower_source : tuple
          -
          (Zor,bor,dZor) gradient, intercept, error for the bottom of magnetic sources
          -
          -
          -Source code -
          def tanaka1999(k, lnPhi, sigma_lnPhi, kmin_range=(0.05, 0.2), kmax_range=(0.05, 0.2)):
          -    """
          -    Compute weighted linear fit of Phi over spatial frequency window kmin:kmax
          -
          -    Args:
          -        k : float / 1D-array
          -            wavenumber in rad/km
          -        lnPhi : float / 1D array
          -            log of the radial power spectrum (see power_spectrum_log)
          -            expected in ln(sqrt(S)) form
          -        sigma_lnPhi : standard deviation of lnPhi
          -        kmin_range : tuple (default:(0.05, 0.2))
          -            minimum and maximum range of spatial frequencies to fit for the 
          -            top of magnetic sources - ideally low frequency, straight line
          -        kmax_range : tuple (default:(0.05, 0.2))
          -            minimum and maximum range of spatial frequencies to fit for the
          -            bottom of magnetic source - ideally low frequency, straight line
          -
          -    Returns:
          -        upper_source : tuple
          -            (Ztr,btr,dZtr) gradient, intercept, error for the top of magnetic sources
          -        lower_source : tuple
          -            (Zor,bor,dZor) gradient, intercept, error for the bottom of magnetic sources
          -
          -    """
          -    # for now...
          -    S = lnPhi
          -    sigma2 = sigma_lnPhi**2
          -
          -    def compute_coefficients(X, Y, E):
          -        X2 = X**2
          -        Y2 = Y**2
          -        E2 = E**2
          -
          -        XY = np.multiply(X, Y)
          -        XE2sum = np.sum(X/E2)
          -        YE2sum = np.sum(Y/E2)
          -        rE2sum = np.sum(1.0/E2)
          -        X2E2sum = np.sum(X2/E2)
          -        Y2E2sum = np.sum(Y2/E2)
          -
          -        #TL = XE2sum*YE2sum - np.sum(XY/E2*rE2sum)
          -        # I think summation in second TL term needed to be split
          -        TL = XE2sum*YE2sum - np.sum(XY/E2)*rE2sum
          -        BL = XE2sum**2 - X2E2sum*rE2sum
          -
          -        Z  = TL/BL
          -        b  = (np.sum(XY/E2) - Z*X2E2sum)/XE2sum
          -        #dZ = np.sqrt( rE2sum/(X2E2sum*rE2sum - XE2sum) )
          -        ## There was a missing **2 term at end of error term.
          -        dZ = np.sqrt( rE2sum/(X2E2sum*rE2sum - XE2sum**2) )
          -        return Z, b, dZ
          -
          -
          -    sf=k/(2.0*np.pi)
          -    S2=np.log(np.exp(S)/sf)
          -
          -    # mask low wavenumbers
          -    kmin, kmax = kmin_range
          -    mask1 = np.logical_and(sf >=kmin, sf <=kmax)
          -    X1 = sf[mask1]
          -    Y1 = S[mask1]
          -    E1 = sigma2[mask1]
          -    
          -    # mask high wavenumbers
          -    kmin, kmax = kmax_range
          -    mask2 = np.logical_and(sf >=kmin, sf <=kmax)
          -    X2 = sf[mask2]
          -    Y2 = np.log(np.exp(S[mask2])/(X2*2*np.pi))
          -    E2 = np.log(np.exp(sigma2[mask2])/(X2*2*np.pi))
          -
          -    # compute top and bottom of magnetic layer
          -    Ztr, btr, dZtr = compute_coefficients(X1, Y1, E1)
          -    Zor, bor, dZor = compute_coefficients(X2, Y2, E2)
          -    return (Ztr,btr,dZtr), (Zor, bor, dZor)
          -
          -
          -
          -
          -
          -

          Classes

          -
          -
          -class CurieGrid -(grid, xmin, xmax, ymin, ymax) -
          -
          -

          Accepts a 2D array and Cartesian coordinates specifying the -bounding box of the array

          -

          Grid must be projected in metres

          -

          Args: -grid : 2D array of magnetic data -xmin : minimum x bound in metres -xmax : maximum x bound in metres -ymin : minimum y bound in metres -ymax : maximum y bound in metres

          -
          -Source code -
          class CurieGrid(object):
          -    """
          -    Accepts a 2D array and Cartesian coordinates specifying the
          -    bounding box of the array
          -
          -    Grid must be projected in metres
          -
          -    Args:
          -     grid : 2D array of magnetic data
          -     xmin : minimum x bound in metres
          -     xmax : maximum x bound in metres
          -     ymin : minimum y bound in metres
          -     ymax : maximum y bound in metres
          -    """
          -    def __init__(self, grid, xmin, xmax, ymin, ymax):
          -        
          -        self.data = np.array(grid)
          -        ny, nx = self.data.shape
          -        self.xmin, self.xmax = xmin, xmax
          -        self.ymin, self.ymax = ymin, ymax
          -        self.xcoords, dx = np.linspace(xmin, xmax, nx, retstep=True)
          -        self.ycoords, dy = np.linspace(ymin, ymax, ny, retstep=True)
          -        self.nx, self.ny = nx, ny
          -        self.dx, self.dy = dx, dy
          -
          -        if abs(dx - dy) > 1.0:
          -            warnings.warn("node spacing should be identical {}".format((dx,dy)), RuntimeWarning)
          -
          -
          -    def subgrid(self, window, xc, yc):
          -        """
          -        Extract a subgrid from the data at a window around
          -        the point (xc,yc)
          -        
          -        Args:
          -            xc : float
          -                x coordinate
          -            yc : float
          -                y coordinate
          -            window : float
          -                size of window in metres
          -
          -        Returns:
          -            data : 2D array
          -                subgrid encompassing window size
          -        """
          -
          -        # check in coordinate in grid
          -        if xc < self.xmin or xc > self.xmax or yc < self.ymin or yc > self.ymax:
          -            raise ValueError("Point ({},{}) outside data range".format(xc,yc))
          -
          -        # find nearest index to xc,yc
          -        ix = np.abs(self.xcoords - xc).argmin()
          -        iy = np.abs(self.ycoords - yc).argmin()
          -
          -        nw = int(round(window/self.dx))
          -        n2w = nw//2
          -
          -        # extract a square window from the data
          -        imin = ix - n2w
          -        imax = ix + n2w + 1
          -        jmin = iy - n2w
          -        jmax = iy + n2w + 1
          -
          -        # safeguard if window size is larger than grid
          -        imin = max(imin, 0)
          -        imax = min(imax, self.nx)
          -        jmin = max(jmin, 0)
          -        jmax = min(jmax, self.ny)
          -        
          -        data = self.data[jmin:jmax, imin:imax]
          -
          -        return data
          -
          -
          -    def create_centroid_list(self, window, spacingX=None, spacingY=None):
          -        """
          -        Create a list of xc,yc values to extract subgrids.
          -
          -        Args:
          -            window : float
          -                size of the windows in metres
          -            spacingX : float (optional)
          -                specify spacing in metres in the X direction
          -                will default to maximum X resolution
          -            spacingY : float (optional)
          -                specify spacing in metres in the Y direction
          -                will default to maximum Y resolution
          -
          -        Returns:
          -            xc_list : 1D array
          -                array of x coordinates
          -            yc_list : 1D array
          -                array of y coordinates
          -        """
          -        
          -        nx, ny = self.nx, self.ny
          -        xcoords = self.xcoords
          -        ycoords = self.ycoords
          -        
          -        nw = int(round(window/self.dx))
          -        n2w = nw//2
          -        
          -        # this is the densest spacing possible given the data
          -        xc = xcoords[n2w:-n2w]
          -        yc = ycoords[n2w:-n2w]
          -        
          -        # but we can alter it if required
          -        if type(spacingX) != type(None):
          -            xc = np.arange(xc.min(), xc.max(), spacingX)
          -        if type(spacingY) != type(None):
          -            yc = np.arange(yc.min(), yc.max(), spacingY)
          -
          -        xq, yq = np.meshgrid(xc, yc)
          -            
          -        return xq.ravel(), yq.ravel()
          -
          -
          -    def remove_trend_linear(self, data):
          -        """
          -        Remove the best-fitting linear trend from the data
          -
          -        This may come in handy if the magnetic data has not been
          -        reduced to the pole.
          -
          -        Args:
          -            data : 2D numpy array
          -
          -        Returns:
          -         data : 2D numpy array
          -        """
          -        data = data.copy()
          -        nr, nc = data.shape
          -        xq, yq = np.meshgrid(np.arange(0, nc), np.arange(0, nr))
          -
          -        A = np.column_stack((x.flatten(), y.flatten(), np.ones(x.size)))
          -        c, resid, rank, sigma = np.linalg.lstsq(A, data.flatten())
          -
          -        data.flat[:] -= np.dot(A, c)
          -        return data
          -
          -    def radial_spectrum(self, subgrid, taper=np.hanning, scale=0.001, **kwargs):
          -        """
          -        Compute the radial spectrum for a square grid.
          -
          -        Args:
          -            subgrid : 2D array
          -                window of the original data (see subgrid method)
          -            taper : function (default=np.hanning)
          -                taper function, set to None for no taper function
          -            scale : float (default: 0.001)
          -                scaling factor to get k into rad/km
          -            kwargs : keyword arguments
          -                keyword arguments to pass to `taper`
          -
          -        Returns:
          -            k : 1D array shape (n,)
          -                wavenumber in rad/km
          -            Phi : 1D array shape (n,)
          -                Radial power spectrum
          -            sigma_Phi : 1D array shape (n,)
          -                Standard deviation of Phi
          -        """
          -
          -        data = subgrid
          -        nr, nc = data.shape
          -        nw = nr
          -
          -        if nr != nc:
          -            warnings.warn("subgrid is not square {}".format((nr,nc)), RuntimeWarning)
          -
          -
          -        # control taper
          -        if type(taper) == type(None):
          -            vtaper = 1.0
          -        else:
          -            rt = taper(nr, **kwargs)
          -            ct = taper(nc, **kwargs)
          -            xq, yq = np.meshgrid(ct, rt)
          -            vtaper = xq*yq
          -
          -        dx_scale = self.dx*scale
          -        dk = 2.0*np.pi/(nw - 1)/dx_scale
          -
          -        # fast Fourier transform and shift
          -        FT = np.abs(np.fft.fft2(data*vtaper))
          -        FT = np.fft.fftshift(FT)
          -
          -        kbins = np.arange(dk, dk*nw/2, dk)
          -        nbins = kbins.size - 1
          -
          -        S = np.empty(nbins)
          -        k = np.empty(nbins)
          -        sigma = np.empty(nbins)
          -
          -        i0 = int((nw - 1)//2)
          -        ix, iy = np.mgrid[0:nw,0:nw]
          -        kk = np.hypot((ix - i0)*dk, (iy - i0)*dk)
          -
          -        for i in range(0, nbins):
          -            mask = np.logical_and(kk >= kbins[i], kk <= kbins[i+1])
          -            rr = 2.0*np.log(FT[mask])
          -            S[i] = rr.mean()
          -            k[i] = kk[mask].mean()
          -            sigma[i] = np.std(rr)
          -
          -        return k, S, sigma
          -
          -
          -    def radial_spectrum_log(self, subgrid, taper=np.hanning, scale=0.001, **kwargs):
          -        """
          -        Compute the log of the radial spectrum for a square grid.
          -
          -        Args:
          -         subgrid : 2D array
          -            window of the original data (see subgrid method)
          -         taper : function (default=np.hanning)
          -            taper function, set to None for no taper function
          -         scale : float (detault=0.001)
          -            scaling factor to get k into rad/km
          -         kwargs : keyword arguments
          -            keyword arguments to pass to `taper`
          -
          -        Returns:
          -            k : 1D array shape (n,)
          -                wavenumber in rad/km
          -            lnPhi : 1D array
          -                log of the radial power spectrum in ln(sqrt(S))
          -            lnsigma_Phi : 1D array
          -                standard deviation of lnPhi
          -        """
          -
          -        data = subgrid
          -        nr, nc = data.shape
          -        nw = nr
          -
          -        if nr != nc:
          -            warnings.warn("subgrid is not square {}".format((nr,nc)), RuntimeWarning)
          -
          -
          -        # control taper
          -        if type(taper) == type(None):
          -            vtaper = 1.0
          -        else:
          -            rt = taper(nr, **kwargs)
          -            ct = taper(nc, **kwargs)
          -            xq, yq = np.meshgrid(ct, rt)
          -            vtaper = xq*yq
          -
          -        dx_scale = self.dx*scale
          -        dk = 2.0*np.pi/(nw - 1)/dx_scale
          -
          -        # fast Fourier transform and shift
          -        FT = np.abs(np.fft.fft2(data*vtaper))
          -        FT = np.fft.fftshift(FT)
          -
          -        kbins = np.arange(dk, dk*nw/2, dk)
          -        nbins = kbins.size - 1
          -
          -        S = np.empty(nbins)
          -        k = np.empty(nbins)
          -        sigma = np.empty(nbins)
          -
          -        i0 = int((nw - 1)//2)
          -        ix, iy = np.mgrid[0:nw,0:nw]
          -        kk = np.hypot((ix - i0)*dk, (iy - i0)*dk)
          -
          -        for i in range(0, nbins):
          -            mask = np.logical_and(kk >= kbins[i], kk <= kbins[i+1])
          -            rr = np.log(np.sqrt(FT[mask]))
          -            S[i] = rr.mean()
          -            k[i] = kk[mask].mean()
          -            sigma[i] = np.std(rr)
          -
          -        return k, S, sigma
          -        
          -        
          -    def azimuthal_spectrum(self, subgrid, taper=np.hanning, scale=0.001, theta=5.0, **kwargs):
          -        """
          -        Compute azimuthal spectrum for a square grid.
          -
          -        Args:
          -            subgrid : 2D array
          -                window of the original data (see subgrid method)
          -            taper : function (default=np.hanning)
          -                taper function, set to None for no taper function
          -            scale : float (default=0.001)
          -                scaling factor to get k into rad/km
          -            theta : float
          -                angle increment in degrees
          -            args : arguments
          -                arguments o pass to taper
          -
          -        Returns:
          -            k : 1D array shape (n,)
          -                wavenumber in rad/km
          -            Phi : 1D array shape (n,)
          -                Radial power spectrum
          -            sigma_Phi : 1D array shape (n,)
          -                Standard deviation of Phi
          -        """
          -        from pycurious import radon
          -        data = subgrid
          -        nr, nc = data.shape
          -        nw = nr
          -
          -        if nr != nc:
          -            raise RuntimeWarning("subgrid is not square {}".format((nr,nc)))
          -
          -        dx_scale = self.dx*scale
          -        dk = 2.0*np.pi/(nw - 1)/dx_scale
          -
          -        kbins = np.arange(dk, dk*nw/2, dk)
          -
          -        dtheta = np.arange(0.0, 180.0, theta)
          -        sinogram = radon.radon2d(data, np.pi*dtheta/180.0)
          -        S = np.zeros((dtheta.size, kbins.size))
          -        sigma2 = np.zeros((dtheta.size, kbins.size))
          -
          -        # control taper
          -        if taper is None:
          -            vtaper = 1.0
          -        else:
          -            vtaper = taper(sinogram.shape[0], **kwargs)
          -
          -        nk = 1 + 2*kbins.size
          -        for i in range(0, dtheta.size):
          -            PSD = np.abs(np.fft.fft(vtaper*sinogram[:,i], n=nk))
          -            S[i,:] = np.log( np.sqrt(PSD[1:kbins.size+1] ))
          -        
          -        return kbins, S, dtheta
          -
          -
          -    def reduce_to_pole(self, data, inc, dec, sinc=None, sdec=None):
          -        r"""
          -        Reduce total field magnetic anomaly data to the pole.
          -
          -        The reduction to the pole if a phase transformation that can be
          -        applied to total field magnetic anomaly data. It simulates how
          -        the data would be if both the Geomagnetic field and the
          -        magnetization of the source were vertical (Blakely, 1996).
          -
          -        Args:
          -            data : 1D array
          -                the total field anomaly data at each point.
          -            inc : float / 1D array
          -                inclination of the inducing Geomagnetic field
          -            dec : float / 1D array
          -                declination of the inducing Geomagnetic field
          -            sinc : float / 1D array (optional)
          -                inclination of the total magnetization of the anomaly source
          -            sdec : float / 1D array (optional)
          -                declination of the total magnetization of the anomaly source
          -                The total magnetization is the vector sum of the
          -                induced and remanent magnetization. If there is only induced
          -                magnetization, use the *inc* and *dec* of the Geomagnetic field.
          -
          -        Returns:
          -            rtp : 2D array
          -                the data reduced to the pole.
          -        
          -        References:
          -            Blakely, R. J. (1996), Potential Theory in Gravity and Magnetic
          -            Applications, Cambridge University Press.
          -
          -        Notes:
          -            This functions performs the reduction in the frequency domain
          -            (using the FFT). The transform filter is (in the freq domain):
          -                RTP(k_x, k_y) = \frac{|k|}{
          -                    a_1 k_x^2 + a_2 k_y^2 + a_3 k_x k_y +
          -                    i|k|(b_1 k_x + b_2 k_y)}
          -            in which k_x and k_y are the wave-numbers in the x and y
          -            directions and
          -                |k| = \sqrt{k_x^2 + k_y^2} \\
          -                a_1 = m_z f_z - m_x f_x \\
          -                a_2 = m_z f_z - m_y f_y \\
          -                a_3 = -m_y f_x - m_x f_y \\
          -                b_1 = m_x f_z + m_z f_x \\
          -                b_2 = m_y f_z + m_z f_y
          -            \mathbf{m} = (m_x, m_y, m_z)` is the unit-vector of the total
          -            magnetization of the source and
          -            \mathbf{f} = (f_x, f_y, f_z)` is the unit-vector of the
          -            Geomagnetic field.
          -        """
          -        nr, nc = data.shape
          -
          -        if nr != nc:
          -            warnings.warn("subgrid is not square {}".format((nr,nc)), RuntimeWarning)
          -
          -        fx, fy, fz = ang2vec(1.0, inc, dec)
          -        if sinc is None or sdec is None:
          -            mx, my, mz = fx, fy, fz
          -        else:
          -            mx, my, mz = ang2vec(1.0, sinc, sdec)
          -
          -        kx, ky = [k for k in _fftfreqs(self.dx, self.dy, data.shape)]
          -        kz = np.hypot(kx, ky)
          -
          -        a1 = mz*fz - mx*fx
          -        a2 = mz*fz - my*fy
          -        a3 = -my*fx - mx*fy
          -        b1 = mx*fz + mz*fx
          -        b2 = my*fz + mz*fy
          -
          -        # The division gives a RuntimeWarning because of the zero frequency term.
          -        # This suppresses the warning.
          -        with np.errstate(divide='ignore', invalid='ignore'):
          -            rtp = (kz)/(a1*kx**2 + a2*ky**2 + a3*kx*ky + \
          -                            1j*np.sqrt(kz)*(b1*kx + b2*ky))
          -        
          -        rtp[0, 0] = 0
          -        ft_pole = rtp*np.fft.fft2(data)
          -        return np.real(np.fft.ifft2(ft_pole))
          -
          -
          -    def upward_continuation(self, data, height):
          -        r"""
          -        Upward continuation of potential field data.
          -
          -        Calculates the continuation through the Fast Fourier Transform in
          -        the wavenumber domain (Blakely, 1996):
          -
          -            F\{h_{up}\} = F\{h\} e^{-\Delta z |k|}
          -
          -        and then transformed back to the space domain. :math:`h_{up}` is the
          -        upward continue data, \Delta z is the height increase, F denotes
          -        the Fourier Transform, |k| is the wavenumber modulus.
          -
          -        Args:
          -            data   : 2D array
          -                potential field at the grid points
          -            height : float
          -                height increase (delta z) in meters.
          -        
          -        Returns:
          -            cont : array
          -                upward continued data
          -
          -        Notes:
          -            It is not possible to get the FFT of a masked grid. The default
          -            :func:`fatiando.gridder.interp` call using minimum curvature will
          -            not be suitable.  Use extrapolate=True or algorithm='nearest' to
          -            get an unmasked grid.
          -
          -        References:
          -            Blakely, R. J. (1996), Potential Theory in Gravity and Magnetic
          -            Applications, Cambridge University Press.
          -        """
          -        nr, nc = data.shape
          -
          -        if nr != nc:
          -            warnings.warn("subgrid is not square {}".format((nr,nc)), RuntimeWarning)
          -
          -        if height <= 0:
          -            warnings.warn("Using 'height' <= 0 means downward continuation, " +
          -                          "which is known to be unstable.")
          -
          -        fx = 2.0*np.pi*np.fft.fftfreq(nr, self.dx)
          -        fy = 2.0*np.pi*np.fft.fftfreq(nc, self.dy)
          -
          -        kx, ky = np.meshgrid(fy, fx)[::-1]
          -        kz = np.hypot(kx, ky)
          -
          -        upcont_ft = np.fft.fft2(data)*np.exp(-height*kz)
          -        cont = np.real(np.fft.ifft2(upcont_ft))
          -        return cont
          -
          -

          Subclasses

          - -

          Methods

          -
          -
          -def azimuthal_spectrum(self, subgrid, taper=, scale=0.001, theta=5.0, **kwargs) -
          -
          -

          Compute azimuthal spectrum for a square grid.

          -

          Args

          -
          -
          subgrid : 2D array
          -
          window of the original data (see subgrid method)
          -
          taper : function (default=np.hanning)
          -
          taper function, set to None for no taper function
          -
          scale : float (default=0.001)
          -
          scaling factor to get k into rad/km
          -
          theta : float
          -
          angle increment in degrees
          -
          args : arguments
          -
          arguments o pass to taper
          -
          -

          Returns

          -
          -
          k : 1D array shape (n,)
          -
          wavenumber in rad/km
          -
          Phi : 1D array shape (n,)
          -
          Radial power spectrum
          -
          sigma_Phi : 1D array shape (n,)
          -
          Standard deviation of Phi
          -
          -
          -Source code -
          def azimuthal_spectrum(self, subgrid, taper=np.hanning, scale=0.001, theta=5.0, **kwargs):
          -    """
          -    Compute azimuthal spectrum for a square grid.
          -
          -    Args:
          -        subgrid : 2D array
          -            window of the original data (see subgrid method)
          -        taper : function (default=np.hanning)
          -            taper function, set to None for no taper function
          -        scale : float (default=0.001)
          -            scaling factor to get k into rad/km
          -        theta : float
          -            angle increment in degrees
          -        args : arguments
          -            arguments o pass to taper
          -
          -    Returns:
          -        k : 1D array shape (n,)
          -            wavenumber in rad/km
          -        Phi : 1D array shape (n,)
          -            Radial power spectrum
          -        sigma_Phi : 1D array shape (n,)
          -            Standard deviation of Phi
          -    """
          -    from pycurious import radon
          -    data = subgrid
          -    nr, nc = data.shape
          -    nw = nr
          -
          -    if nr != nc:
          -        raise RuntimeWarning("subgrid is not square {}".format((nr,nc)))
          -
          -    dx_scale = self.dx*scale
          -    dk = 2.0*np.pi/(nw - 1)/dx_scale
          -
          -    kbins = np.arange(dk, dk*nw/2, dk)
          -
          -    dtheta = np.arange(0.0, 180.0, theta)
          -    sinogram = radon.radon2d(data, np.pi*dtheta/180.0)
          -    S = np.zeros((dtheta.size, kbins.size))
          -    sigma2 = np.zeros((dtheta.size, kbins.size))
          -
          -    # control taper
          -    if taper is None:
          -        vtaper = 1.0
          -    else:
          -        vtaper = taper(sinogram.shape[0], **kwargs)
          -
          -    nk = 1 + 2*kbins.size
          -    for i in range(0, dtheta.size):
          -        PSD = np.abs(np.fft.fft(vtaper*sinogram[:,i], n=nk))
          -        S[i,:] = np.log( np.sqrt(PSD[1:kbins.size+1] ))
          -    
          -    return kbins, S, dtheta
          -
          -
          -
          -def create_centroid_list(self, window, spacingX=None, spacingY=None) -
          -
          -

          Create a list of xc,yc values to extract subgrids.

          -

          Args

          -
          -
          window : float
          -
          size of the windows in metres
          -
          spacingX : float (optional)
          -
          specify spacing in metres in the X direction -will default to maximum X resolution
          -
          spacingY : float (optional)
          -
          specify spacing in metres in the Y direction -will default to maximum Y resolution
          -
          -

          Returns

          -
          -
          xc_list : 1D array
          -
          array of x coordinates
          -
          yc_list : 1D array
          -
          array of y coordinates
          -
          -
          -Source code -
          def create_centroid_list(self, window, spacingX=None, spacingY=None):
          -    """
          -    Create a list of xc,yc values to extract subgrids.
          -
          -    Args:
          -        window : float
          -            size of the windows in metres
          -        spacingX : float (optional)
          -            specify spacing in metres in the X direction
          -            will default to maximum X resolution
          -        spacingY : float (optional)
          -            specify spacing in metres in the Y direction
          -            will default to maximum Y resolution
          -
          -    Returns:
          -        xc_list : 1D array
          -            array of x coordinates
          -        yc_list : 1D array
          -            array of y coordinates
          -    """
          -    
          -    nx, ny = self.nx, self.ny
          -    xcoords = self.xcoords
          -    ycoords = self.ycoords
          -    
          -    nw = int(round(window/self.dx))
          -    n2w = nw//2
          -    
          -    # this is the densest spacing possible given the data
          -    xc = xcoords[n2w:-n2w]
          -    yc = ycoords[n2w:-n2w]
          -    
          -    # but we can alter it if required
          -    if type(spacingX) != type(None):
          -        xc = np.arange(xc.min(), xc.max(), spacingX)
          -    if type(spacingY) != type(None):
          -        yc = np.arange(yc.min(), yc.max(), spacingY)
          -
          -    xq, yq = np.meshgrid(xc, yc)
          -        
          -    return xq.ravel(), yq.ravel()
          -
          -
          -
          -def radial_spectrum(self, subgrid, taper=, scale=0.001, **kwargs) -
          -
          -

          Compute the radial spectrum for a square grid.

          -

          Args

          -
          -
          subgrid : 2D array
          -
          window of the original data (see subgrid method)
          -
          taper : function (default=np.hanning)
          -
          taper function, set to None for no taper function
          -
          scale : float (default: 0.001)
          -
          scaling factor to get k into rad/km
          -
          kwargs : keyword arguments
          -
          keyword arguments to pass to taper
          -
          -

          Returns

          -
          -
          k : 1D array shape (n,)
          -
          wavenumber in rad/km
          -
          Phi : 1D array shape (n,)
          -
          Radial power spectrum
          -
          sigma_Phi : 1D array shape (n,)
          -
          Standard deviation of Phi
          -
          -
          -Source code -
          def radial_spectrum(self, subgrid, taper=np.hanning, scale=0.001, **kwargs):
          -    """
          -    Compute the radial spectrum for a square grid.
          -
          -    Args:
          -        subgrid : 2D array
          -            window of the original data (see subgrid method)
          -        taper : function (default=np.hanning)
          -            taper function, set to None for no taper function
          -        scale : float (default: 0.001)
          -            scaling factor to get k into rad/km
          -        kwargs : keyword arguments
          -            keyword arguments to pass to `taper`
          -
          -    Returns:
          -        k : 1D array shape (n,)
          -            wavenumber in rad/km
          -        Phi : 1D array shape (n,)
          -            Radial power spectrum
          -        sigma_Phi : 1D array shape (n,)
          -            Standard deviation of Phi
          -    """
          -
          -    data = subgrid
          -    nr, nc = data.shape
          -    nw = nr
          -
          -    if nr != nc:
          -        warnings.warn("subgrid is not square {}".format((nr,nc)), RuntimeWarning)
          -
          -
          -    # control taper
          -    if type(taper) == type(None):
          -        vtaper = 1.0
          -    else:
          -        rt = taper(nr, **kwargs)
          -        ct = taper(nc, **kwargs)
          -        xq, yq = np.meshgrid(ct, rt)
          -        vtaper = xq*yq
          -
          -    dx_scale = self.dx*scale
          -    dk = 2.0*np.pi/(nw - 1)/dx_scale
          -
          -    # fast Fourier transform and shift
          -    FT = np.abs(np.fft.fft2(data*vtaper))
          -    FT = np.fft.fftshift(FT)
          -
          -    kbins = np.arange(dk, dk*nw/2, dk)
          -    nbins = kbins.size - 1
          -
          -    S = np.empty(nbins)
          -    k = np.empty(nbins)
          -    sigma = np.empty(nbins)
          -
          -    i0 = int((nw - 1)//2)
          -    ix, iy = np.mgrid[0:nw,0:nw]
          -    kk = np.hypot((ix - i0)*dk, (iy - i0)*dk)
          -
          -    for i in range(0, nbins):
          -        mask = np.logical_and(kk >= kbins[i], kk <= kbins[i+1])
          -        rr = 2.0*np.log(FT[mask])
          -        S[i] = rr.mean()
          -        k[i] = kk[mask].mean()
          -        sigma[i] = np.std(rr)
          -
          -    return k, S, sigma
          -
          -
          -
          -def radial_spectrum_log(self, subgrid, taper=, scale=0.001, **kwargs) -
          -
          -

          Compute the log of the radial spectrum for a square grid.

          -

          Args: -subgrid : 2D array -window of the original data (see subgrid method) -taper : function (default=np.hanning) -taper function, set to None for no taper function -scale : float (detault=0.001) -scaling factor to get k into rad/km -kwargs : keyword arguments -keyword arguments to pass to taper

          -

          Returns

          -
          -
          k : 1D array shape (n,)
          -
          wavenumber in rad/km
          -
          lnPhi : 1D array
          -
          log of the radial power spectrum in ln(sqrt(S))
          -
          lnsigma_Phi : 1D array
          -
          standard deviation of lnPhi
          -
          -
          -Source code -
          def radial_spectrum_log(self, subgrid, taper=np.hanning, scale=0.001, **kwargs):
          -    """
          -    Compute the log of the radial spectrum for a square grid.
          -
          -    Args:
          -     subgrid : 2D array
          -        window of the original data (see subgrid method)
          -     taper : function (default=np.hanning)
          -        taper function, set to None for no taper function
          -     scale : float (detault=0.001)
          -        scaling factor to get k into rad/km
          -     kwargs : keyword arguments
          -        keyword arguments to pass to `taper`
          -
          -    Returns:
          -        k : 1D array shape (n,)
          -            wavenumber in rad/km
          -        lnPhi : 1D array
          -            log of the radial power spectrum in ln(sqrt(S))
          -        lnsigma_Phi : 1D array
          -            standard deviation of lnPhi
          -    """
          -
          -    data = subgrid
          -    nr, nc = data.shape
          -    nw = nr
          -
          -    if nr != nc:
          -        warnings.warn("subgrid is not square {}".format((nr,nc)), RuntimeWarning)
          -
          -
          -    # control taper
          -    if type(taper) == type(None):
          -        vtaper = 1.0
          -    else:
          -        rt = taper(nr, **kwargs)
          -        ct = taper(nc, **kwargs)
          -        xq, yq = np.meshgrid(ct, rt)
          -        vtaper = xq*yq
          -
          -    dx_scale = self.dx*scale
          -    dk = 2.0*np.pi/(nw - 1)/dx_scale
          -
          -    # fast Fourier transform and shift
          -    FT = np.abs(np.fft.fft2(data*vtaper))
          -    FT = np.fft.fftshift(FT)
          -
          -    kbins = np.arange(dk, dk*nw/2, dk)
          -    nbins = kbins.size - 1
          -
          -    S = np.empty(nbins)
          -    k = np.empty(nbins)
          -    sigma = np.empty(nbins)
          -
          -    i0 = int((nw - 1)//2)
          -    ix, iy = np.mgrid[0:nw,0:nw]
          -    kk = np.hypot((ix - i0)*dk, (iy - i0)*dk)
          -
          -    for i in range(0, nbins):
          -        mask = np.logical_and(kk >= kbins[i], kk <= kbins[i+1])
          -        rr = np.log(np.sqrt(FT[mask]))
          -        S[i] = rr.mean()
          -        k[i] = kk[mask].mean()
          -        sigma[i] = np.std(rr)
          -
          -    return k, S, sigma
          -
          -
          -
          -def reduce_to_pole(self, data, inc, dec, sinc=None, sdec=None) -
          -
          -

          Reduce total field magnetic anomaly data to the pole.

          -

          The reduction to the pole if a phase transformation that can be -applied to total field magnetic anomaly data. It simulates how -the data would be if both the Geomagnetic field and the -magnetization of the source were vertical (Blakely, 1996).

          -

          Args

          -
          -
          data : 1D array
          -
          the total field anomaly data at each point.
          -
          inc : float / 1D array
          -
          inclination of the inducing Geomagnetic field
          -
          dec : float / 1D array
          -
          declination of the inducing Geomagnetic field
          -
          sinc : float / 1D array (optional)
          -
          inclination of the total magnetization of the anomaly source
          -
          sdec : float / 1D array (optional)
          -
          declination of the total magnetization of the anomaly source -The total magnetization is the vector sum of the -induced and remanent magnetization. If there is only induced -magnetization, use the inc and dec of the Geomagnetic field.
          -
          -

          Returns

          -
          -
          rtp : 2D array
          -
          the data reduced to the pole.
          -
          -

          References

          -

          Blakely, R. J. (1996), Potential Theory in Gravity and Magnetic -Applications, Cambridge University Press.

          -

          Notes

          -

          This functions performs the reduction in the frequency domain -(using the FFT). The transform filter is (in the freq domain): -RTP(k_x, k_y) = \frac{|k|}{ -a_1 k_x^2 + a_2 k_y^2 + a_3 k_x k_y + -i|k|(b_1 k_x + b_2 k_y)} -in which k_x and k_y are the wave-numbers in the x and y -directions and -|k| = \sqrt{k_x^2 + k_y^2} \ -a_1 = m_z f_z - m_x f_x \ -a_2 = m_z f_z - m_y f_y \ -a_3 = -m_y f_x - m_x f_y \ -b_1 = m_x f_z + m_z f_x \ -b_2 = m_y f_z + m_z f_y -\mathbf{m} = (m_x, m_y, m_z)is the unit-vector of the total -magnetization of the source and -\mathbf{f} = (f_x, f_y, f_z) is the unit-vector of the -Geomagnetic field.

          -
          -Source code -
          def reduce_to_pole(self, data, inc, dec, sinc=None, sdec=None):
          -    r"""
          -    Reduce total field magnetic anomaly data to the pole.
          -
          -    The reduction to the pole if a phase transformation that can be
          -    applied to total field magnetic anomaly data. It simulates how
          -    the data would be if both the Geomagnetic field and the
          -    magnetization of the source were vertical (Blakely, 1996).
          -
          -    Args:
          -        data : 1D array
          -            the total field anomaly data at each point.
          -        inc : float / 1D array
          -            inclination of the inducing Geomagnetic field
          -        dec : float / 1D array
          -            declination of the inducing Geomagnetic field
          -        sinc : float / 1D array (optional)
          -            inclination of the total magnetization of the anomaly source
          -        sdec : float / 1D array (optional)
          -            declination of the total magnetization of the anomaly source
          -            The total magnetization is the vector sum of the
          -            induced and remanent magnetization. If there is only induced
          -            magnetization, use the *inc* and *dec* of the Geomagnetic field.
          -
          -    Returns:
          -        rtp : 2D array
          -            the data reduced to the pole.
          -    
          -    References:
          -        Blakely, R. J. (1996), Potential Theory in Gravity and Magnetic
          -        Applications, Cambridge University Press.
          -
          -    Notes:
          -        This functions performs the reduction in the frequency domain
          -        (using the FFT). The transform filter is (in the freq domain):
          -            RTP(k_x, k_y) = \frac{|k|}{
          -                a_1 k_x^2 + a_2 k_y^2 + a_3 k_x k_y +
          -                i|k|(b_1 k_x + b_2 k_y)}
          -        in which k_x and k_y are the wave-numbers in the x and y
          -        directions and
          -            |k| = \sqrt{k_x^2 + k_y^2} \\
          -            a_1 = m_z f_z - m_x f_x \\
          -            a_2 = m_z f_z - m_y f_y \\
          -            a_3 = -m_y f_x - m_x f_y \\
          -            b_1 = m_x f_z + m_z f_x \\
          -            b_2 = m_y f_z + m_z f_y
          -        \mathbf{m} = (m_x, m_y, m_z)` is the unit-vector of the total
          -        magnetization of the source and
          -        \mathbf{f} = (f_x, f_y, f_z)` is the unit-vector of the
          -        Geomagnetic field.
          -    """
          -    nr, nc = data.shape
          -
          -    if nr != nc:
          -        warnings.warn("subgrid is not square {}".format((nr,nc)), RuntimeWarning)
          -
          -    fx, fy, fz = ang2vec(1.0, inc, dec)
          -    if sinc is None or sdec is None:
          -        mx, my, mz = fx, fy, fz
          -    else:
          -        mx, my, mz = ang2vec(1.0, sinc, sdec)
          -
          -    kx, ky = [k for k in _fftfreqs(self.dx, self.dy, data.shape)]
          -    kz = np.hypot(kx, ky)
          -
          -    a1 = mz*fz - mx*fx
          -    a2 = mz*fz - my*fy
          -    a3 = -my*fx - mx*fy
          -    b1 = mx*fz + mz*fx
          -    b2 = my*fz + mz*fy
          -
          -    # The division gives a RuntimeWarning because of the zero frequency term.
          -    # This suppresses the warning.
          -    with np.errstate(divide='ignore', invalid='ignore'):
          -        rtp = (kz)/(a1*kx**2 + a2*ky**2 + a3*kx*ky + \
          -                        1j*np.sqrt(kz)*(b1*kx + b2*ky))
          -    
          -    rtp[0, 0] = 0
          -    ft_pole = rtp*np.fft.fft2(data)
          -    return np.real(np.fft.ifft2(ft_pole))
          -
          -
          -
          -def remove_trend_linear(self, data) -
          -
          -

          Remove the best-fitting linear trend from the data

          -

          This may come in handy if the magnetic data has not been -reduced to the pole.

          -

          Args

          -
          -
          data : 2D numpy array
          -
           
          -
          -

          Returns: -data : 2D numpy array

          -
          -Source code -
          def remove_trend_linear(self, data):
          -    """
          -    Remove the best-fitting linear trend from the data
          -
          -    This may come in handy if the magnetic data has not been
          -    reduced to the pole.
          -
          -    Args:
          -        data : 2D numpy array
          -
          -    Returns:
          -     data : 2D numpy array
          -    """
          -    data = data.copy()
          -    nr, nc = data.shape
          -    xq, yq = np.meshgrid(np.arange(0, nc), np.arange(0, nr))
          -
          -    A = np.column_stack((x.flatten(), y.flatten(), np.ones(x.size)))
          -    c, resid, rank, sigma = np.linalg.lstsq(A, data.flatten())
          -
          -    data.flat[:] -= np.dot(A, c)
          -    return data
          -
          -
          -
          -def subgrid(self, window, xc, yc) -
          -
          -

          Extract a subgrid from the data at a window around -the point (xc,yc)

          -

          Args

          -
          -
          xc : float
          -
          x coordinate
          -
          yc : float
          -
          y coordinate
          -
          window : float
          -
          size of window in metres
          -
          -

          Returns

          -
          -
          data : 2D array
          -
          subgrid encompassing window size
          -
          -
          -Source code -
          def subgrid(self, window, xc, yc):
          -    """
          -    Extract a subgrid from the data at a window around
          -    the point (xc,yc)
          -    
          -    Args:
          -        xc : float
          -            x coordinate
          -        yc : float
          -            y coordinate
          -        window : float
          -            size of window in metres
          -
          -    Returns:
          -        data : 2D array
          -            subgrid encompassing window size
          -    """
          -
          -    # check in coordinate in grid
          -    if xc < self.xmin or xc > self.xmax or yc < self.ymin or yc > self.ymax:
          -        raise ValueError("Point ({},{}) outside data range".format(xc,yc))
          -
          -    # find nearest index to xc,yc
          -    ix = np.abs(self.xcoords - xc).argmin()
          -    iy = np.abs(self.ycoords - yc).argmin()
          -
          -    nw = int(round(window/self.dx))
          -    n2w = nw//2
          -
          -    # extract a square window from the data
          -    imin = ix - n2w
          -    imax = ix + n2w + 1
          -    jmin = iy - n2w
          -    jmax = iy + n2w + 1
          -
          -    # safeguard if window size is larger than grid
          -    imin = max(imin, 0)
          -    imax = min(imax, self.nx)
          -    jmin = max(jmin, 0)
          -    jmax = min(jmax, self.ny)
          -    
          -    data = self.data[jmin:jmax, imin:imax]
          -
          -    return data
          -
          -
          -
          -def upward_continuation(self, data, height) -
          -
          -

          Upward continuation of potential field data.

          -

          Calculates the continuation through the Fast Fourier Transform in -the wavenumber domain (Blakely, 1996):

          -
          F\{h_{up}\} = F\{h\} e^{-\Delta z |k|}
          -
          -

          and then transformed back to the space domain. :math:h_{up} is the -upward continue data, \Delta z is the height increase, F denotes -the Fourier Transform, |k| is the wavenumber modulus.

          -

          Args

          -
          -
          data -: 2D array
          -
          potential field at the grid points
          -
          height : float
          -
          height increase (delta z) in meters.
          -
          -

          Returns

          -
          -
          cont : array
          -
          upward continued data
          -
          -

          Notes

          -

          It is not possible to get the FFT of a masked grid. The default -:func:fatiando.gridder.interp call using minimum curvature will -not be suitable. -Use extrapolate=True or algorithm='nearest' to -get an unmasked grid.

          -

          References

          -

          Blakely, R. J. (1996), Potential Theory in Gravity and Magnetic -Applications, Cambridge University Press.

          -
          -Source code -
          def upward_continuation(self, data, height):
          -    r"""
          -    Upward continuation of potential field data.
          -
          -    Calculates the continuation through the Fast Fourier Transform in
          -    the wavenumber domain (Blakely, 1996):
          -
          -        F\{h_{up}\} = F\{h\} e^{-\Delta z |k|}
          -
          -    and then transformed back to the space domain. :math:`h_{up}` is the
          -    upward continue data, \Delta z is the height increase, F denotes
          -    the Fourier Transform, |k| is the wavenumber modulus.
          -
          -    Args:
          -        data   : 2D array
          -            potential field at the grid points
          -        height : float
          -            height increase (delta z) in meters.
          -    
          -    Returns:
          -        cont : array
          -            upward continued data
          -
          -    Notes:
          -        It is not possible to get the FFT of a masked grid. The default
          -        :func:`fatiando.gridder.interp` call using minimum curvature will
          -        not be suitable.  Use extrapolate=True or algorithm='nearest' to
          -        get an unmasked grid.
          -
          -    References:
          -        Blakely, R. J. (1996), Potential Theory in Gravity and Magnetic
          -        Applications, Cambridge University Press.
          -    """
          -    nr, nc = data.shape
          -
          -    if nr != nc:
          -        warnings.warn("subgrid is not square {}".format((nr,nc)), RuntimeWarning)
          -
          -    if height <= 0:
          -        warnings.warn("Using 'height' <= 0 means downward continuation, " +
          -                      "which is known to be unstable.")
          -
          -    fx = 2.0*np.pi*np.fft.fftfreq(nr, self.dx)
          -    fy = 2.0*np.pi*np.fft.fftfreq(nc, self.dy)
          -
          -    kx, ky = np.meshgrid(fy, fx)[::-1]
          -    kz = np.hypot(kx, ky)
          -
          -    upcont_ft = np.fft.fft2(data)*np.exp(-height*kz)
          -    cont = np.real(np.fft.ifft2(upcont_ft))
          -    return cont
          -
          -
          -
          -
          -
          -
          -
          - -
          - - - - - \ No newline at end of file diff --git a/docs/index.html b/docs/index.html deleted file mode 100644 index fae4ccf..0000000 --- a/docs/index.html +++ /dev/null @@ -1,128 +0,0 @@ - - - - - - -pycurious API documentation - - - - - - - - - -
          -
          -
          -

          Module pycurious

          -
          -
          -

          Copyright 2018 Ben Mather, Robert Delhaye

          -

          This file is part of PyCurious.

          -

          PyCurious is free software: you can redistribute it and/or modify -it under the terms of the GNU Lesser General Public License as published by -the Free Software Foundation, either version 3 of the License, or any later version.

          -

          PyCurious is distributed in the hope that it will be useful, -but WITHOUT ANY WARRANTY; without even the implied warranty of -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. -See the -GNU Lesser General Public License for more details.

          -

          You should have received a copy of the GNU Lesser General Public License -along with PyCurious. -If not, see http://www.gnu.org/licenses/.

          -
          -Source code -
          """
          -Copyright 2018 Ben Mather, Robert Delhaye
          -
          -This file is part of PyCurious.
          -
          -PyCurious is free software: you can redistribute it and/or modify
          -it under the terms of the GNU Lesser General Public License as published by
          -the Free Software Foundation, either version 3 of the License, or any later version.
          -
          -PyCurious is distributed in the hope that it will be useful,
          -but WITHOUT ANY WARRANTY; without even the implied warranty of
          -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
          -GNU Lesser General Public License for more details.
          -
          -You should have received a copy of the GNU Lesser General Public License
          -along with PyCurious.  If not, see <http://www.gnu.org/licenses/>.
          -"""
          -
          -# -*- coding: utf-8 -*-
          -from .documentation import install_documentation
          -from .grid import CurieGrid, bouligand2009, tanaka1999, maus1995, ComputeTanaka
          -from .optimise import CurieOptimise
          -from .mapping import transform_coordinates
          -from .mapping import convert_extent
          -from .mapping import trim
          -from .mapping import grid
          -from .mapping import import_geotiff
          -
          -
          -
          -

          Sub-modules

          -
          -
          pycurious.documentation
          -
          -

          Copyright 2018 Ben Mather, Robert Delhaye …

          -
          -
          pycurious.grid
          -
          -

          Copyright 2018 Ben Mather, Robert Delhaye …

          -
          -
          pycurious.mapping
          -
          -

          Copyright 2018 Ben Mather, Robert Delhaye …

          -
          -
          pycurious.optimise
          -
          -

          Copyright 2018 Ben Mather, Robert Delhaye …

          -
          -
          pycurious.parallel
          -
          -

          Copyright 2018 Ben Mather, Robert Delhaye …

          -
          -
          pycurious.therm
          -
          -

          Copyright 2018 Ben Mather, Robert Delhaye …

          -
          -
          -
          -
          -
          -
          -
          -
          -
          -
          - -
          - - - - - \ No newline at end of file diff --git a/docs/mapping.html b/docs/mapping.html deleted file mode 100644 index c476d4e..0000000 --- a/docs/mapping.html +++ /dev/null @@ -1,714 +0,0 @@ - - - - - - -pycurious.mapping API documentation - - - - - - - - - -
          -
          -
          -

          Module pycurious.mapping

          -
          -
          -

          Copyright 2018 Ben Mather, Robert Delhaye

          -

          This file is part of PyCurious.

          -

          PyCurious is free software: you can redistribute it and/or modify -it under the terms of the GNU Lesser General Public License as published by -the Free Software Foundation, either version 3 of the License, or any later version.

          -

          PyCurious is distributed in the hope that it will be useful, -but WITHOUT ANY WARRANTY; without even the implied warranty of -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. -See the -GNU Lesser General Public License for more details.

          -

          You should have received a copy of the GNU Lesser General Public License -along with PyCurious. -If not, see http://www.gnu.org/licenses/.

          -
          -Source code -
          """
          -Copyright 2018 Ben Mather, Robert Delhaye
          -
          -This file is part of PyCurious.
          -
          -PyCurious is free software: you can redistribute it and/or modify
          -it under the terms of the GNU Lesser General Public License as published by
          -the Free Software Foundation, either version 3 of the License, or any later version.
          -
          -PyCurious is distributed in the hope that it will be useful,
          -but WITHOUT ANY WARRANTY; without even the implied warranty of
          -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
          -GNU Lesser General Public License for more details.
          -
          -You should have received a copy of the GNU Lesser General Public License
          -along with PyCurious.  If not, see <http://www.gnu.org/licenses/>.
          -"""
          -
          -# -*- coding: utf-8 -*-
          -import numpy as np
          -
          -try: range=xrange
          -except: pass
          -
          -def transform_coordinates(x, y, epsg_in, epsg_out):
          -    """
          -    Transform between any coordinate system.
          -
          -    Requires `pyproj`
          -    """
          -    import pyproj
          -    proj_in  = pyproj.Proj("+init=EPSG:"+str(epsg_in))
          -    proj_out = pyproj.Proj("+init=EPSG:"+str(epsg_out))
          -    return pyproj.transform(proj_in, proj_out, x, y)
          -
          -
          -def convert_extent(extent_in, epsg_in, epsg_out):
          -    """
          -    Transform extent from epsg_in to epsg_out
          -
          -    Args:
          -        extent_in : tuple
          -            bounding box [minX, maxX, minY, maxY]
          -        epsg_in : int
          -            CRS of extent
          -        epsg_out : int
          -            CRS of output
          -
          -    Returns:
          -        extent_out : tuple
          -            bounding box in new CRS
          -    """
          -    xmin, xmax, ymin, ymax = extent_in
          -    xi = [xmin, xmin, xmax, xmax]
          -    yi = [ymin, ymax, ymin, ymax]
          -    xo, yo = transform_coordinates(xi, yi, epsg_in, epsg_out)
          -    extent_out = [min(xo), max(xo), min(yo), max(yo)]
          -    return extent_out
          -
          -
          -def trim(coords, data, extent, buffer_amount=0.0):
          -    """
          -    Trim a smaller section of a large dataset taking into
          -    consideration transformations into various coordinate
          -    reference systems (CRS)
          -    
          -    Args:
          -        coords : array shape (n,2)
          -            geographical / projected coordinates
          -        data : array shape (n,)
          -            values corresponding to coordinates
          -        extent : tuple
          -            bounding box to trim data
          -        buffer : float
          -            amount of buffer to include (default=0.0)
          -
          -    Returns:
          -        coords_trim : array shape (l,2)
          -            trimmed coordinates
          -        data_trim : array shape (l,2)
          -            trimmed data array
          -    """
          -    xmin, xmax, ymin, ymax = extent
          -
          -    # Extract only the data within the extent
          -    data_mask = np.ones(data.shape[0], dtype=bool)
          -
          -    # Add a 1 percent buffer zone
          -    x_buffer = buffer_amount*(xmax - xmin)
          -    y_buffer = buffer_amount*(ymax - ymin)
          -
          -    mask_e = coords[:,0] < xmin - x_buffer
          -    mask_w = coords[:,0] > xmax + x_buffer
          -    mask_n = coords[:,1] < ymin - y_buffer
          -    mask_s = coords[:,1] > ymax + y_buffer
          -    data_mask[mask_n] = False
          -    data_mask[mask_s] = False
          -    data_mask[mask_e] = False
          -    data_mask[mask_w] = False
          -    
          -    data_trim = data[data_mask]
          -    coords_trim = coords[data_mask]
          -
          -    return coords_trim, data_trim
          -
          -
          -def grid(coords, data, extent, shape=None, epsg_in=None, epsg_out=None, **kwargs):
          -    """
          -    Grid a smaller section of a large dataset taking into
          -    consideration transformations into various coordinate
          -    reference systems (CRS)
          -    
          -    Args:
          -        coords : array shape (n,2)
          -            geographical coordinates
          -        data : array shape (n,) 
          -            values corresponding to coordinates
          -        extent : tuple
          -           box contained within the data in espg_out coordinates
          -        shape : tuple (nrows,ncols)
          -           size of the box, if None, shape is estimated from coords spacing
          -        epsg_in : int
          -           CRS of data (if transformation is required)
          -        epsg_out : int
          -           CRS of grid (if transformation is required)
          -        kwargs : keyword arguments
          -           keyword arguments to pass to griddata from
          -           `scipy.interpolate.griddata`
          -    
          -    Returns:
          -        grid : array shape (nrows, ncols)
          -            rectangular section of data bounded by extent
          -    """
          -    from scipy.interpolate import griddata
          -    xmin, xmax, ymin, ymax = extent
          -    
          -    if type(epsg_in) != type(None):
          -        xt, yt = transform_coordinates(np.array([xmin, xmin, xmax, xmax]),\
          -                                       np.array([ymin, ymax, ymin, ymax]),\
          -                                       epsg_out, epsg_in)
          -        # find the coordinates that will completely
          -        # engulf the extent
          -        xtmin, xtmax = min(xt), max(xt)
          -        ytmin, ytmax = min(yt), max(yt)
          -    else:
          -        xtmin, xtmax = xmin, xmax
          -        ytmin, ytmax = ymin, ymax
          -
          -    xtextent = [xtmin, xtmax, ytmin, ytmax]
          -
          -    # trim data - buffer = 5%
          -    coords_trim, data_trim = trim(coords, data, xtextent, 0.05)
          -
          -
          -    if type(epsg_in) != type(None):
          -        # convert back to output CRS
          -        xtrim, ytrim = transform_coordinates(coords_trim[:,0],\
          -                                             coords_trim[:,1],\
          -                                             epsg_in, epsg_out)
          -        coords_trim = np.column_stack([xtrim, ytrim])
          -
          -
          -    if shape == None:
          -        # estimate based on the data spacing
          -        xunique = np.unique(coords_trim[:,0])
          -        yunique = np.unique(coords_trim[:,1])
          -        dx = np.diff(xunique).mean()
          -        dy = np.diff(yunique).mean()
          -        nc = int((xtmax - xtmin)/dx)
          -        nr = int((ytmax - ytmin)/dy)
          -        print("using nrows={}, ncols={} with cell spacing of {}".format(nr,nc,(dy,dx)))
          -    else:
          -        nr, nc = shape
          -
          -    # interpolate
          -
          -    xcoords = np.linspace(xmin, xmax, nc)
          -    ycoords = np.linspace(ymin, ymax, nr)
          -    xq, yq = np.meshgrid(xcoords, ycoords)
          -
          -    vq = griddata(coords_trim, data_trim, (xq, yq), **kwargs)
          -    return vq
          -
          -
          -def import_geotiff(file_path):
          -    """
          -    Import a GeoTIFF to a numpy array and prints
          -    information of the Coordinate Reference System (CRS)
          -
          -    Args:
          -        file_path : str
          -            path to the GeoTIFF
          -
          -    Returns:
          -        data : 2D array
          -        extent : tuple
          -            extent in the projection of the GeoTIFF
          -            e.g. [xmin, xmax, ymin, ymax]
          -    """
          -    from osgeo import gdal, osr
          -    
          -    gtiff = gdal.Open(file_path)
          -    data = gtiff.ReadAsArray()
          -    gt = gtiff.GetGeoTransform()
          -    gtproj = gtiff.GetProjection()
          -
          -    inproj = osr.SpatialReference()
          -    inproj.ImportFromWkt(gtproj)
          -
          -    gtextent = (gt[0], gt[0] + gtiff.RasterXSize*gt[1],\
          -                gt[3], gt[3] + gtiff.RasterYSize*gt[5])
          -
          -    # print projection information
          -    print(inproj)
          -
          -    # this closes the geotiff
          -    gtiff = None
          -
          -    return data, gtextent
          -
          -
          -def export_geotiff(file_path, array, extent, epsg):
          -    """
          -    Export a GeoTIFF from a numpy array projected in a
          -    predefined Coordinate Reference System (CRS)
          -
          -    Args:
          -        file_path : str
          -            path to write the GeoTIFF
          -        array: 2D array
          -            array to save to GeoTiff
          -        extent : tuple
          -            extent in the projection of the GeoTIFF
          -            e.g. [xmin, xmax, ymin, ymax]
          -        epsg : int
          -            CRS of the GeoTIFF
          -            e.g. 4326 for WGS84
          -
          -    """
          -    from osgeo import gdal, osr
          -    # import ogr, gdal, osr, os
          -
          -    cols = array.shape[1]
          -    rows = array.shape[0]
          -
          -    xmin, xmax, ymin, ymax = extent
          -    spacingX = (xmax - xmin)/cols
          -    spacingY = (ymax - ymin)/rows
          -
          -    driver = gdal.GetDriverByName('GTiff')
          -    outRaster = driver.Create(file_path, cols, rows, 1, gdal.GDT_Float64)
          -    outRaster.SetGeoTransform((xmin, spacingX, 0, ymin, 0, spacingY))
          -    outband = outRaster.GetRasterBand(1)
          -    outband.WriteArray(array)
          -    outRasterSRS = osr.SpatialReference()
          -    outRasterSRS.ImportFromEPSG(epsg)
          -    outRaster.SetProjection(outRasterSRS.ExportToWkt())
          -    outband.FlushCache()
          -    return
          -
          -
          -
          -
          -
          -
          -
          -

          Functions

          -
          -
          -def convert_extent(extent_in, epsg_in, epsg_out) -
          -
          -

          Transform extent from epsg_in to epsg_out

          -

          Args

          -
          -
          extent_in : tuple
          -
          bounding box [minX, maxX, minY, maxY]
          -
          epsg_in : int
          -
          CRS of extent
          -
          epsg_out : int
          -
          CRS of output
          -
          -

          Returns

          -
          -
          extent_out : tuple
          -
          bounding box in new CRS
          -
          -
          -Source code -
          def convert_extent(extent_in, epsg_in, epsg_out):
          -    """
          -    Transform extent from epsg_in to epsg_out
          -
          -    Args:
          -        extent_in : tuple
          -            bounding box [minX, maxX, minY, maxY]
          -        epsg_in : int
          -            CRS of extent
          -        epsg_out : int
          -            CRS of output
          -
          -    Returns:
          -        extent_out : tuple
          -            bounding box in new CRS
          -    """
          -    xmin, xmax, ymin, ymax = extent_in
          -    xi = [xmin, xmin, xmax, xmax]
          -    yi = [ymin, ymax, ymin, ymax]
          -    xo, yo = transform_coordinates(xi, yi, epsg_in, epsg_out)
          -    extent_out = [min(xo), max(xo), min(yo), max(yo)]
          -    return extent_out
          -
          -
          -
          -def export_geotiff(file_path, array, extent, epsg) -
          -
          -

          Export a GeoTIFF from a numpy array projected in a -predefined Coordinate Reference System (CRS)

          -

          Args

          -
          -
          file_path : str
          -
          path to write the GeoTIFF
          -
          array
          -
          2D array -array to save to GeoTiff
          -
          extent : tuple
          -
          extent in the projection of the GeoTIFF -e.g. [xmin, xmax, ymin, ymax]
          -
          epsg : int
          -
          CRS of the GeoTIFF -e.g. 4326 for WGS84
          -
          -
          -Source code -
          def export_geotiff(file_path, array, extent, epsg):
          -    """
          -    Export a GeoTIFF from a numpy array projected in a
          -    predefined Coordinate Reference System (CRS)
          -
          -    Args:
          -        file_path : str
          -            path to write the GeoTIFF
          -        array: 2D array
          -            array to save to GeoTiff
          -        extent : tuple
          -            extent in the projection of the GeoTIFF
          -            e.g. [xmin, xmax, ymin, ymax]
          -        epsg : int
          -            CRS of the GeoTIFF
          -            e.g. 4326 for WGS84
          -
          -    """
          -    from osgeo import gdal, osr
          -    # import ogr, gdal, osr, os
          -
          -    cols = array.shape[1]
          -    rows = array.shape[0]
          -
          -    xmin, xmax, ymin, ymax = extent
          -    spacingX = (xmax - xmin)/cols
          -    spacingY = (ymax - ymin)/rows
          -
          -    driver = gdal.GetDriverByName('GTiff')
          -    outRaster = driver.Create(file_path, cols, rows, 1, gdal.GDT_Float64)
          -    outRaster.SetGeoTransform((xmin, spacingX, 0, ymin, 0, spacingY))
          -    outband = outRaster.GetRasterBand(1)
          -    outband.WriteArray(array)
          -    outRasterSRS = osr.SpatialReference()
          -    outRasterSRS.ImportFromEPSG(epsg)
          -    outRaster.SetProjection(outRasterSRS.ExportToWkt())
          -    outband.FlushCache()
          -    return
          -
          -
          -
          -def grid(coords, data, extent, shape=None, epsg_in=None, epsg_out=None, **kwargs) -
          -
          -

          Grid a smaller section of a large dataset taking into -consideration transformations into various coordinate -reference systems (CRS)

          -

          Args

          -
          -
          coords : array shape (n,2)
          -
          geographical coordinates
          -
          data : array shape (n,)
          -
          values corresponding to coordinates
          -
          extent : tuple
          -
           
          -
          box contained within the data in espg_out coordinates
          -
          shape : tuple (nrows,ncols)
          -
           
          -
          size of the box, if None, shape is estimated from coords spacing
          -
          epsg_in : int
          -
           
          -
          CRS of data (if transformation is required)
          -
          epsg_out : int
          -
           
          -
          CRS of grid (if transformation is required)
          -
          kwargs : keyword arguments
          -
           
          -
          -

          keyword arguments to pass to griddata from -scipy.interpolate.griddata

          -

          Returns

          -
          -
          grid() : array shape (nrows, ncols)
          -
          rectangular section of data bounded by extent
          -
          -
          -Source code -
          def grid(coords, data, extent, shape=None, epsg_in=None, epsg_out=None, **kwargs):
          -    """
          -    Grid a smaller section of a large dataset taking into
          -    consideration transformations into various coordinate
          -    reference systems (CRS)
          -    
          -    Args:
          -        coords : array shape (n,2)
          -            geographical coordinates
          -        data : array shape (n,) 
          -            values corresponding to coordinates
          -        extent : tuple
          -           box contained within the data in espg_out coordinates
          -        shape : tuple (nrows,ncols)
          -           size of the box, if None, shape is estimated from coords spacing
          -        epsg_in : int
          -           CRS of data (if transformation is required)
          -        epsg_out : int
          -           CRS of grid (if transformation is required)
          -        kwargs : keyword arguments
          -           keyword arguments to pass to griddata from
          -           `scipy.interpolate.griddata`
          -    
          -    Returns:
          -        grid : array shape (nrows, ncols)
          -            rectangular section of data bounded by extent
          -    """
          -    from scipy.interpolate import griddata
          -    xmin, xmax, ymin, ymax = extent
          -    
          -    if type(epsg_in) != type(None):
          -        xt, yt = transform_coordinates(np.array([xmin, xmin, xmax, xmax]),\
          -                                       np.array([ymin, ymax, ymin, ymax]),\
          -                                       epsg_out, epsg_in)
          -        # find the coordinates that will completely
          -        # engulf the extent
          -        xtmin, xtmax = min(xt), max(xt)
          -        ytmin, ytmax = min(yt), max(yt)
          -    else:
          -        xtmin, xtmax = xmin, xmax
          -        ytmin, ytmax = ymin, ymax
          -
          -    xtextent = [xtmin, xtmax, ytmin, ytmax]
          -
          -    # trim data - buffer = 5%
          -    coords_trim, data_trim = trim(coords, data, xtextent, 0.05)
          -
          -
          -    if type(epsg_in) != type(None):
          -        # convert back to output CRS
          -        xtrim, ytrim = transform_coordinates(coords_trim[:,0],\
          -                                             coords_trim[:,1],\
          -                                             epsg_in, epsg_out)
          -        coords_trim = np.column_stack([xtrim, ytrim])
          -
          -
          -    if shape == None:
          -        # estimate based on the data spacing
          -        xunique = np.unique(coords_trim[:,0])
          -        yunique = np.unique(coords_trim[:,1])
          -        dx = np.diff(xunique).mean()
          -        dy = np.diff(yunique).mean()
          -        nc = int((xtmax - xtmin)/dx)
          -        nr = int((ytmax - ytmin)/dy)
          -        print("using nrows={}, ncols={} with cell spacing of {}".format(nr,nc,(dy,dx)))
          -    else:
          -        nr, nc = shape
          -
          -    # interpolate
          -
          -    xcoords = np.linspace(xmin, xmax, nc)
          -    ycoords = np.linspace(ymin, ymax, nr)
          -    xq, yq = np.meshgrid(xcoords, ycoords)
          -
          -    vq = griddata(coords_trim, data_trim, (xq, yq), **kwargs)
          -    return vq
          -
          -
          -
          -def import_geotiff(file_path) -
          -
          -

          Import a GeoTIFF to a numpy array and prints -information of the Coordinate Reference System (CRS)

          -

          Args

          -
          -
          file_path : str
          -
          path to the GeoTIFF
          -
          -

          Returns

          -
          -
          data : 2D array
          -
           
          -
          extent : tuple
          -
          extent in the projection of the GeoTIFF -e.g. [xmin, xmax, ymin, ymax]
          -
          -
          -Source code -
          def import_geotiff(file_path):
          -    """
          -    Import a GeoTIFF to a numpy array and prints
          -    information of the Coordinate Reference System (CRS)
          -
          -    Args:
          -        file_path : str
          -            path to the GeoTIFF
          -
          -    Returns:
          -        data : 2D array
          -        extent : tuple
          -            extent in the projection of the GeoTIFF
          -            e.g. [xmin, xmax, ymin, ymax]
          -    """
          -    from osgeo import gdal, osr
          -    
          -    gtiff = gdal.Open(file_path)
          -    data = gtiff.ReadAsArray()
          -    gt = gtiff.GetGeoTransform()
          -    gtproj = gtiff.GetProjection()
          -
          -    inproj = osr.SpatialReference()
          -    inproj.ImportFromWkt(gtproj)
          -
          -    gtextent = (gt[0], gt[0] + gtiff.RasterXSize*gt[1],\
          -                gt[3], gt[3] + gtiff.RasterYSize*gt[5])
          -
          -    # print projection information
          -    print(inproj)
          -
          -    # this closes the geotiff
          -    gtiff = None
          -
          -    return data, gtextent
          -
          -
          -
          -def transform_coordinates(x, y, epsg_in, epsg_out) -
          -
          -

          Transform between any coordinate system.

          -

          Requires pyproj

          -
          -Source code -
          def transform_coordinates(x, y, epsg_in, epsg_out):
          -    """
          -    Transform between any coordinate system.
          -
          -    Requires `pyproj`
          -    """
          -    import pyproj
          -    proj_in  = pyproj.Proj("+init=EPSG:"+str(epsg_in))
          -    proj_out = pyproj.Proj("+init=EPSG:"+str(epsg_out))
          -    return pyproj.transform(proj_in, proj_out, x, y)
          -
          -
          -
          -def trim(coords, data, extent, buffer_amount=0.0) -
          -
          -

          Trim a smaller section of a large dataset taking into -consideration transformations into various coordinate -reference systems (CRS)

          -

          Args

          -
          -
          coords : array shape (n,2)
          -
          geographical / projected coordinates
          -
          data : array shape (n,)
          -
          values corresponding to coordinates
          -
          extent : tuple
          -
          bounding box to trim data
          -
          buffer : float
          -
          amount of buffer to include (default=0.0)
          -
          -

          Returns

          -
          -
          coords_trim : array shape (l,2)
          -
          trimmed coordinates
          -
          data_trim : array shape (l,2)
          -
          trimmed data array
          -
          -
          -Source code -
          def trim(coords, data, extent, buffer_amount=0.0):
          -    """
          -    Trim a smaller section of a large dataset taking into
          -    consideration transformations into various coordinate
          -    reference systems (CRS)
          -    
          -    Args:
          -        coords : array shape (n,2)
          -            geographical / projected coordinates
          -        data : array shape (n,)
          -            values corresponding to coordinates
          -        extent : tuple
          -            bounding box to trim data
          -        buffer : float
          -            amount of buffer to include (default=0.0)
          -
          -    Returns:
          -        coords_trim : array shape (l,2)
          -            trimmed coordinates
          -        data_trim : array shape (l,2)
          -            trimmed data array
          -    """
          -    xmin, xmax, ymin, ymax = extent
          -
          -    # Extract only the data within the extent
          -    data_mask = np.ones(data.shape[0], dtype=bool)
          -
          -    # Add a 1 percent buffer zone
          -    x_buffer = buffer_amount*(xmax - xmin)
          -    y_buffer = buffer_amount*(ymax - ymin)
          -
          -    mask_e = coords[:,0] < xmin - x_buffer
          -    mask_w = coords[:,0] > xmax + x_buffer
          -    mask_n = coords[:,1] < ymin - y_buffer
          -    mask_s = coords[:,1] > ymax + y_buffer
          -    data_mask[mask_n] = False
          -    data_mask[mask_s] = False
          -    data_mask[mask_e] = False
          -    data_mask[mask_w] = False
          -    
          -    data_trim = data[data_mask]
          -    coords_trim = coords[data_mask]
          -
          -    return coords_trim, data_trim
          -
          -
          -
          -
          -
          -
          -
          - -
          - - - - - \ No newline at end of file diff --git a/docs/optimise.html b/docs/optimise.html deleted file mode 100644 index b600418..0000000 --- a/docs/optimise.html +++ /dev/null @@ -1,2141 +0,0 @@ - - - - - - -pycurious.optimise API documentation - - - - - - - - - -
          -
          -
          -

          Module pycurious.optimise

          -
          -
          -

          Copyright 2018 Ben Mather, Robert Delhaye

          -

          This file is part of PyCurious.

          -

          PyCurious is free software: you can redistribute it and/or modify -it under the terms of the GNU Lesser General Public License as published by -the Free Software Foundation, either version 3 of the License, or any later version.

          -

          PyCurious is distributed in the hope that it will be useful, -but WITHOUT ANY WARRANTY; without even the implied warranty of -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. -See the -GNU Lesser General Public License for more details.

          -

          You should have received a copy of the GNU Lesser General Public License -along with PyCurious. -If not, see http://www.gnu.org/licenses/.

          -
          -Source code -
          """
          -Copyright 2018 Ben Mather, Robert Delhaye
          -
          -This file is part of PyCurious.
          -
          -PyCurious is free software: you can redistribute it and/or modify
          -it under the terms of the GNU Lesser General Public License as published by
          -the Free Software Foundation, either version 3 of the License, or any later version.
          -
          -PyCurious is distributed in the hope that it will be useful,
          -but WITHOUT ANY WARRANTY; without even the implied warranty of
          -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
          -GNU Lesser General Public License for more details.
          -
          -You should have received a copy of the GNU Lesser General Public License
          -along with PyCurious.  If not, see <http://www.gnu.org/licenses/>.
          -"""
          -
          -# -*- coding: utf-8 -*-
          -from .grid import CurieGrid, bouligand2009
          -import numpy as np
          -import warnings
          -from scipy.optimize import minimize
          -from scipy.special import polygamma
          -from scipy import stats
          -from multiprocessing import Pool, Process, Queue, cpu_count
          -
          -try: range=xrange
          -except: pass
          -
          -
          -class CurieOptimise(CurieGrid):
          -    """
          -    Extends the CurieGrid class to include optimisation routines
          -    see scipy.optimize.minimize for a description of the algorithm
          -
          -    Args:
          -        grid : 2D numpy array
          -            2D array of magnetic data
          -        xmin : float
          -            minimum x bound in metres
          -        xmax : float
          -            maximum x bound in metres
          -        ymin : float
          -            minimum y bound in metres
          -        ymax : float
          -            maximum y bound in metres
          -    
          -    Attributes:
          -        bounds : list of tuples
          -            lower and upper bounds for beta, zt, dz, C
          -        prior  : dict
          -            dictionary of priors for beta, zt, dz, C
          -    """
          -    def __init__(self, grid, xmin, xmax, ymin, ymax, **kwargs):
          -
          -        super(CurieOptimise, self).__init__(grid, xmin, xmax, ymin, ymax)
          -
          -        # initialise prior dictionary
          -        self.reset_priors()
          -
          -        # lower / upper bounds
          -        # [beta, zt, dz, C]
          -        lb = [0.0, 0.0, 0.0, None]
          -        ub = [None]*len(lb)
          -        bounds = list(zip(lb,ub))
          -        self.bounds = bounds
          -
          -        self.max_processors = kwargs.pop("max_processors", cpu_count())
          -
          -        return
          -
          -    def add_prior(self, **kwargs):
          -        """
          -        Add a prior to the dictionary (tuple)
          -        Available priors are beta, zt, dz, C
          -
          -        Assumes a normal distribution or
          -        define another distribution from scipy.stats
          -
          -        Usage:
          -            >>> add_prior(beta=(p, sigma_p))
          -
          -            >>> add_prior(beta=scipy.stats.norm(p, sigma_p))
          -        """
          -
          -        for key in kwargs:
          -            if key in self.prior:
          -                prior = kwargs[key]
          -                if type(prior) == tuple:
          -                    p, sigma_p = prior
          -                    pdf = stats.norm(p, sigma_p)
          -                elif type(prior) == stats._distn_infrastructure.rv_frozen:
          -                    pdf = prior
          -                else:
          -                    raise ValueError("Use a distribution from scipy.stats module")
          -
          -                # add prior PDF to dictionary
          -                self.prior_pdf[key] = pdf
          -                self.prior[key] = list(pdf.args)
          -
          -            else:
          -                raise ValueError("prior must be one of {}".format(self.prior.keys()))
          -
          -
          -    def reset_priors(self):
          -        """
          -        Reset priors to uniform distribution
          -        """
          -        self.prior = {'beta':None, 'zt':None, 'dz':None, 'C':None}
          -        self.prior_pdf = {'beta':None, 'zt':None, 'dz':None, 'C':None}
          -
          -
          -    def objective_routine(self, **kwargs):
          -        """
          -        Evaluate the objective routine to find the misfit with priors
          -        Only keys stored in self.prior will be added to the total misfit
          -
          -        Usage:
          -            >>> objective_routine(beta=2.5)
          -
          -        Returns:
          -            misfit  : float
          -                misfit integrated over all observations and priors
          -        """
          -        c = 0.0
          -
          -        for key in kwargs:
          -            val = kwargs[key]
          -            if key in self.prior:
          -                prior_args = self.prior[key]
          -                if prior_args is not None:
          -                    c += self.objective_function(val, *prior_args)
          -        return c
          -
          -    def objective_function(self, x, x0, sigma_x0, *args):
          -        """
          -        Objective function used in `objective_routine`
          -        Evaluates the l2-norm misfit
          -
          -        Args:
          -            x : float, ndarray
          -            x0 : float, ndarray
          -            sigma_x0 : float, ndarray
          -
          -        Returns:
          -            misfit   : float
          -        """
          -        return 0.5*np.sum((x - x0)**2/sigma_x0**2)
          -
          -
          -    def min_func(self, x, kh, Phi, sigma_Phi):
          -        """
          -        Function to minimise
          -
          -        Args:
          -            x : array shape (n,)
          -                array of variables [beta, zt, dz, C]
          -            kh : array shape (n,)
          -                wavenumbers (rad/km)
          -            Phi : array shape (n,)
          -                radial power spectrum
          -            sigma_Phi : array shape (n,)
          -                standard deviation of Phi
          -
          -        Returns:
          -            misfit    : float
          -                sum of misfit (float)
          -
          -        Notes:
          -            We purposely ignore all warnings raised by the bouligand2009
          -            function because some combinations of input parameters will
          -            trigger an out-of-range warning that will crash the minimiser.
          -            Instead, the misfit is set to a very large number when this occurs.
          -        """
          -        beta, zt, dz, C = x
          -        with warnings.catch_warnings() as w:
          -            warnings.simplefilter("ignore")
          -            Phi_syn = bouligand2009(kh, beta, zt, dz, C)
          -
          -        misfit = self.objective_function(Phi_syn, Phi, 1.0)
          -        if not np.isfinite(misfit):
          -            misfit = 1e99
          -        else:
          -            misfit += self.objective_routine(beta=beta, zt=zt, dz=dz, C=C)
          -        return misfit
          -
          -
          -    def optimise(self, window, xc, yc, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs):
          -        """
          -        Find the optimal parameters of beta, zt, dz, C for a given
          -        centroid (xc,yc) and window size.
          -
          -        Args:
          -            window  : float
          -                size of window in metres
          -            xc : float
          -                centroid x values
          -            yc : float
          -                centroid y values
          -            beta : float
          -                fractal parameter (starting value)
          -            zt : float
          -                top of magnetic layer (starting value)
          -            dz : float
          -                thickness of magnetic layer (starting value)
          -            C : float
          -                field constant (starting value)
          -            taper : taper (default=np.hanning)
          -                taper function, set to None for no taper function
          -            process_subgrids : function
          -                a custom function to process the subgrid
          -            kwargs : keyword arguments
          -                to pass to radial_spectrum.
          -
          -        Returns:
          -            beta : float
          -                fractal parameters
          -            zt : float
          -                top of magnetic layer
          -            dz : float
          -                thickness of magnetic layer
          -            C : float
          -                field constant
          -        """
          -
          -        if type(process_subgrid) == type(None):
          -            # dummy function
          -            def process_subgrid(subgrid):
          -                return subgrid
          -
          -        # initial constants for minimisation
          -        # w = 1.0 # weight low frequency?
          -
          -        x0 = np.array([beta, zt, dz, C])
          -
          -        # get subgrid
          -        subgrid = self.subgrid(window, xc, yc)
          -        subgrid = process_subgrid(subgrid)
          -
          -        # compute radial spectrum
          -        k, Phi, sigma_Phi = self.radial_spectrum(subgrid, taper=taper, **kwargs)
          -
          -        # minimise function
          -        res = minimize(self.min_func, x0, args=(k, Phi, sigma_Phi), bounds=self.bounds)
          -        return res.x
          -
          -
          -    def _func_queue(self, func, q_in, q_out, window, *args, **kwargs):
          -        """ Retrive processes from the queue """
          -        while True:
          -            pos, xc, yc = q_in.get()
          -            if pos is None:
          -                break
          -
          -            pass_args = [window, xc, yc]
          -            pass_args.extend(args)
          -
          -            res = func(*pass_args, **kwargs)
          -            q_out.put((pos, res))
          -        return
          -
          -
          -    def parallelise_routine(self, window, xc_list, yc_list, func, *args, **kwargs):
          -        """
          -        Implements shared memory multiprocessing to split multiple
          -        evaluations of a function centroids across processors.
          -
          -        Supply the window size and lists of x,y coordinates to a function
          -        along with any additional arguments or keyword arguments.
          -
          -        Args:
          -         window : float
          -            size of window in metres
          -         xc_list : array shape (l,)
          -            centroid x values
          -         yc_list : array shape (l,)
          -            centroid y values
          -         func : function
          -            Python function to evaluate in parallel
          -         args : arguments
          -            additional arguments to pass to func
          -         kwargs : keyword arguments
          -            additional keyword arguments to pass to func
          -
          -        Returns:
          -            out : list
          -                (depends on output of func - see notes)
          -
          -        Usage:
          -            An obvious use case is to compute the Curie depth for many
          -            centroids in parallel.
          -
          -            >>> self.parallelise_routine(window, xc_list, yc_list, self.optimise)
          -        
          -            Each centroid is assigned a new process and sent to a free processor
          -            to compute. In this case, the output is separate lists of shape(l,)
          -            for beta, zt, dz, and C.
          -
          -            Another example is to parallelise the sensitivity analysis:
          -
          -            >>> self.parallelise_routine(window, xc_list, yc_list, self.sensitivity, nsim)
          -
          -            This time the output will be a list of lists for beta, zt, dz, and C
          -            i.e. if nc=2 is the number of centroids and nsim=4 is the number of
          -            simulations then separatee lists [[k1, k2, k3, k4], [k1, k2, k3, k4]]
          -            will be returned for beta, zt, dz, and C.
          -        """
          -
          -        n = len(xc_list)
          -        if n != len(yc_list):
          -            raise ValueError("xc_list and yc_list must be the same size")
          -
          -        xOpt = [[] for i in range(n)]
          -        processes = []
          -        q_in = Queue(1)
          -        q_out = Queue()
          -
          -        nprocs = self.max_processors
          -
          -        for i in range(nprocs):
          -            pass_args = [func, q_in, q_out, window]
          -            pass_args.extend(args)
          -
          -            p = Process(target=self._func_queue,\
          -                        args=tuple(pass_args),\
          -                        kwargs=kwargs)
          -
          -            processes.append(p)
          -
          -        for p in processes:
          -            p.daemon = True
          -            p.start()
          -
          -        # put items in the queue
          -        sent = [q_in.put((i, xc_list[i], yc_list[i])) for i in range(n)]
          -        [q_in.put((None, None, None)) for _ in range(nprocs)]
          -
          -        # get the results
          -        for i in range(len(sent)):
          -            i, res = q_out.get()
          -            xOpt[i] = res
          -
          -
          -        # wait until each processor has finished
          -        [p.join() for p in processes]
          -
          -        # process dimensions of output
          -        ndim = np.array(res).ndim
          -
          -        if ndim == 1:
          -            # return separate lists of beta, zt, dz, C
          -            xOpt = np.vstack(xOpt)
          -            return list(xOpt.T)
          -        elif ndim > 1:
          -            # return lists of beta, zt, dz, C for each centroid
          -            xOpt = np.hstack(xOpt)
          -            out = list(xOpt)
          -            for i in range(len(out)):
          -                out[i] = np.split(out[i], n)
          -            return out
          -        else:
          -            raise ValueError("Cannot determine shape of output")
          -
          -
          -
          -    def optimise_routine(self, window, xc_list, yc_list, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs):
          -        """
          -        Iterate through a list of centroids to compute the optimal values
          -        of beta, zt, dz, C for a given window size.
          -        
          -        Args:
          -            window : float
          -                size of window in metres
          -            xc_list : ndarray shape (l,)
          -                centroid x values 
          -            yc_list : ndarray shape (l,)
          -                centroid y values 
          -            beta : float
          -                fractal parameter 
          -            zt : float
          -                top of magnetic layer
          -            dz : float
          -                thickness of magnetic layer
          -            C : float
          -                field constant
          -            taper : function
          -                taper function (default=np.hanning)
          -                set to None for no taper function
          -         process_subgrids : func
          -            a custom function to process the subgrid
          -         kwargs : keyword arguments
          -            to pass to radial_spectrum.
          -
          -        Returns:
          -            beta : ndarray shape (l,)
          -                fractal parameters
          -            zt : ndarray shape (l,)
          -                top of magnetic layer
          -            dz : ndarray shape (l,)
          -                thickness of magnetic layer
          -            C : ndarray shape (l,)
          -                field constant
          -
          -        """
          -        return self.parallelise_routine(window, xc_list, yc_list, self.optimise, beta, zt, dz, C, taper, process_subgrid, **kwargs)
          -
          -
          -    def metropolis_hastings(self, window, xc, yc, nsim, burnin, x_scale=None, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs):
          -        """
          -        MCMC algorithm using a Metropolis-Hastings sampler.
          -
          -        Evaluates a Markov-Chain for starting values of beta, zt, dz, C
          -        and returns the ensemble of model realisations.
          -        
          -        Args:
          -            window : float
          -                size of window in metres
          -            xc : float
          -                centroid x values
          -            yc : float
          -                centroid y values
          -            nsim : int
          -                number of simulations
          -            burnin : int
          -                number of burn-in simulations before to nsim
          -            x_scale: float(4) (optional)
          -                scaling factor for new proposals
          -                default is [1,1,1,1] for [beta, zt, dz, C] - see notes
          -            beta : float
          -                fractal parameter (starting value)
          -            zt : float
          -                top of magnetic layer (starting value)
          -            dz : float
          -                thickness of magnetic layer (starting value)
          -            C : float
          -                field constant (starting value)
          -
          -        Returns:
          -            beta : ndarray shape (nsim,)
          -                fractal parameter
          -            zt : ndarray shape (nsim,)
          -                top of magnetic layer
          -            dz : ndarray shape (nsim,)
          -                thickness of magnetic layer
          -            C : ndarray shape (nsim,)
          -                field constant
          -
          -        Notes:
          -            nsim, burnin, and x_scale should be tweaked for optimal performance
          -            Use starting values of beta, zt, dz, C relatively close to the solution
          -            - C can easily found from the mean of the radial power spectrum.
          -
          -            During the burn-in stage we apply tempering to the PDF to iterate closer
          -            towards the solution. This has the effect of smoothing out the posterior
          -            so that minima can be more easily found. This is necessary here because
          -            large portions of the posterior probability are zero.
          -            see see Sambridge 2013, DOI:10.1093/gji/ggt342 for more information.
          -        """
          -        if type(process_subgrid) == type(None):
          -            # dummy function
          -            def process_subgrid(subgrid):
          -                return subgrid
          -
          -
          -        samples = np.empty((nsim, 4))
          -        x0 = np.array([beta, zt, dz, C])
          -
          -        if type(x_scale) == type(None):
          -            x_scale = np.ones(4)
          -
          -
          -        # get subgrid
          -        subgrid = self.subgrid(window, xc, yc)
          -        subgrid = process_subgrid(subgrid)
          -
          -        # compute radial spectrum
          -        k, Phi, sigma_Phi = self.radial_spectrum(subgrid, taper=taper, **kwargs)
          -
          -        P0 = np.exp(-self.min_func(x0, k, Phi, sigma_Phi)/1000)
          -
          -        # Burn-in phase
          -        for i in range(burnin):
          -            # add random perturbation
          -            x1 = x0 + np.random.normal(size=4)*x_scale
          -
          -            # evaluate proposal probability + tempering
          -            P1 = np.exp(-self.min_func(x1, k, Phi, sigma_Phi)/1000)
          -
          -            # iterate towards MAP estimate
          -            if P1 > P0:
          -                x0 = x1
          -                P0 = P1
          -
          -        P0 = np.exp(-self.min_func(x0, k, Phi, sigma_Phi))
          -
          -        # Now sample posterior
          -        for i in range(nsim):
          -            # add random perturbation
          -            x1 = x0 + np.random.normal(size=4)*x_scale
          -
          -            # evaluate proposal probability
          -            P0 = max(P0, 1e-99)
          -            P1 = np.exp(-self.min_func(x1, k, Phi, sigma_Phi))
          -
          -            P = min(P1/P0, 1.0)
          -
          -            # randomly accept probability
          -            if np.random.rand() <= P:
          -                x0 = x1
          -                P0 = P1
          -
          -            samples[i] = x0
          -
          -        return list(samples.T)
          -
          -
          -
          -    def sensitivity(self, window, xc, yc, nsim, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs):
          -        """
          -        Iterate through a list of centroids to compute the mean and
          -        standard deviation of beta, zt, dz, C by perturbing their
          -        prior distributions (if provided by the user - see add_prior).
          -        
          -        Args:
          -            nsim : int
          -                number of Monte Carlo simulations
          -            window : float
          -                size of window in metres
          -            xc : float
          -                centroid x values
          -            yc : float
          -                centroid y values
          -            nsim : int
          -                - number of simulations
          -            beta : float
          -                starting fractal parameter 
          -            zt : float
          -                starting top of magnetic layer
          -            dz : float
          -                starting thickness of magnetic layer
          -            C : float
          -                starting field constant
          -
          -
          -        Returns:
          -            beta : ndarray shape (nsim,)
          -                fractal parameters
          -            zt : ndarray shape (nsim,)
          -                top of magnetic layer
          -            dz : ndarray shape (nsim,)
          -                thickness of magnetic layer
          -            C : ndarray shape (nsim,)
          -                field constant
          -        """
          -        if type(process_subgrid) == type(None):
          -            # dummy function
          -            def process_subgrid(subgrid):
          -                return subgrid
          -
          -
          -        samples = np.empty((nsim, 4))
          -        x0 = np.array([beta, zt, dz, C])
          -        
          -        use_keys = []
          -        for key in self.prior_pdf:
          -            prior_pdf = self.prior_pdf[key]
          -            if prior_pdf is not None:
          -                use_keys.append(key)
          -        
          -        # get subgrid
          -        subgrid = self.subgrid(window, xc, yc)
          -        subgrid = process_subgrid(subgrid)
          -
          -        # compute radial spectrum
          -        k, Phi, sigma_Phi = self.radial_spectrum(subgrid, taper=taper, **kwargs)
          -
          -        for sim in range(0, nsim):
          -            # randomly generate new prior values within PDF
          -            for key in use_keys:
          -                prior_pdf = self.prior_pdf[key]
          -                self.prior[key][0] = prior_pdf.rvs()
          -
          -            # minimise function
          -            rPhi = np.random.normal(Phi, sigma_Phi)
          -            res = minimize(self.min_func, x0, args=(k, rPhi, sigma_Phi), bounds=self.bounds)
          -            samples[sim] = res.x
          -
          -
          -        # restore priors
          -        for key in use_keys:
          -            prior_pdf = self.prior_pdf[key]
          -            self.prior[key] = list(prior_pdf.args)
          -
          -        return list(samples.T)
          -
          -
          -
          -
          -
          -
          -
          -
          -
          -

          Classes

          -
          -
          -class CurieOptimise -(grid, xmin, xmax, ymin, ymax, **kwargs) -
          -
          -

          Extends the CurieGrid class to include optimisation routines -see scipy.optimize.minimize for a description of the algorithm

          -

          Args

          -
          -
          grid : 2D numpy array
          -
          2D array of magnetic data
          -
          xmin : float
          -
          minimum x bound in metres
          -
          xmax : float
          -
          maximum x bound in metres
          -
          ymin : float
          -
          minimum y bound in metres
          -
          ymax : float
          -
          maximum y bound in metres
          -
          -

          Attributes

          -
          -
          bounds : list of tuples
          -
          lower and upper bounds for beta, zt, dz, C
          -
          -

          prior -: dict -dictionary of priors for beta, zt, dz, C

          -
          -Source code -
          class CurieOptimise(CurieGrid):
          -    """
          -    Extends the CurieGrid class to include optimisation routines
          -    see scipy.optimize.minimize for a description of the algorithm
          -
          -    Args:
          -        grid : 2D numpy array
          -            2D array of magnetic data
          -        xmin : float
          -            minimum x bound in metres
          -        xmax : float
          -            maximum x bound in metres
          -        ymin : float
          -            minimum y bound in metres
          -        ymax : float
          -            maximum y bound in metres
          -    
          -    Attributes:
          -        bounds : list of tuples
          -            lower and upper bounds for beta, zt, dz, C
          -        prior  : dict
          -            dictionary of priors for beta, zt, dz, C
          -    """
          -    def __init__(self, grid, xmin, xmax, ymin, ymax, **kwargs):
          -
          -        super(CurieOptimise, self).__init__(grid, xmin, xmax, ymin, ymax)
          -
          -        # initialise prior dictionary
          -        self.reset_priors()
          -
          -        # lower / upper bounds
          -        # [beta, zt, dz, C]
          -        lb = [0.0, 0.0, 0.0, None]
          -        ub = [None]*len(lb)
          -        bounds = list(zip(lb,ub))
          -        self.bounds = bounds
          -
          -        self.max_processors = kwargs.pop("max_processors", cpu_count())
          -
          -        return
          -
          -    def add_prior(self, **kwargs):
          -        """
          -        Add a prior to the dictionary (tuple)
          -        Available priors are beta, zt, dz, C
          -
          -        Assumes a normal distribution or
          -        define another distribution from scipy.stats
          -
          -        Usage:
          -            >>> add_prior(beta=(p, sigma_p))
          -
          -            >>> add_prior(beta=scipy.stats.norm(p, sigma_p))
          -        """
          -
          -        for key in kwargs:
          -            if key in self.prior:
          -                prior = kwargs[key]
          -                if type(prior) == tuple:
          -                    p, sigma_p = prior
          -                    pdf = stats.norm(p, sigma_p)
          -                elif type(prior) == stats._distn_infrastructure.rv_frozen:
          -                    pdf = prior
          -                else:
          -                    raise ValueError("Use a distribution from scipy.stats module")
          -
          -                # add prior PDF to dictionary
          -                self.prior_pdf[key] = pdf
          -                self.prior[key] = list(pdf.args)
          -
          -            else:
          -                raise ValueError("prior must be one of {}".format(self.prior.keys()))
          -
          -
          -    def reset_priors(self):
          -        """
          -        Reset priors to uniform distribution
          -        """
          -        self.prior = {'beta':None, 'zt':None, 'dz':None, 'C':None}
          -        self.prior_pdf = {'beta':None, 'zt':None, 'dz':None, 'C':None}
          -
          -
          -    def objective_routine(self, **kwargs):
          -        """
          -        Evaluate the objective routine to find the misfit with priors
          -        Only keys stored in self.prior will be added to the total misfit
          -
          -        Usage:
          -            >>> objective_routine(beta=2.5)
          -
          -        Returns:
          -            misfit  : float
          -                misfit integrated over all observations and priors
          -        """
          -        c = 0.0
          -
          -        for key in kwargs:
          -            val = kwargs[key]
          -            if key in self.prior:
          -                prior_args = self.prior[key]
          -                if prior_args is not None:
          -                    c += self.objective_function(val, *prior_args)
          -        return c
          -
          -    def objective_function(self, x, x0, sigma_x0, *args):
          -        """
          -        Objective function used in `objective_routine`
          -        Evaluates the l2-norm misfit
          -
          -        Args:
          -            x : float, ndarray
          -            x0 : float, ndarray
          -            sigma_x0 : float, ndarray
          -
          -        Returns:
          -            misfit   : float
          -        """
          -        return 0.5*np.sum((x - x0)**2/sigma_x0**2)
          -
          -
          -    def min_func(self, x, kh, Phi, sigma_Phi):
          -        """
          -        Function to minimise
          -
          -        Args:
          -            x : array shape (n,)
          -                array of variables [beta, zt, dz, C]
          -            kh : array shape (n,)
          -                wavenumbers (rad/km)
          -            Phi : array shape (n,)
          -                radial power spectrum
          -            sigma_Phi : array shape (n,)
          -                standard deviation of Phi
          -
          -        Returns:
          -            misfit    : float
          -                sum of misfit (float)
          -
          -        Notes:
          -            We purposely ignore all warnings raised by the bouligand2009
          -            function because some combinations of input parameters will
          -            trigger an out-of-range warning that will crash the minimiser.
          -            Instead, the misfit is set to a very large number when this occurs.
          -        """
          -        beta, zt, dz, C = x
          -        with warnings.catch_warnings() as w:
          -            warnings.simplefilter("ignore")
          -            Phi_syn = bouligand2009(kh, beta, zt, dz, C)
          -
          -        misfit = self.objective_function(Phi_syn, Phi, 1.0)
          -        if not np.isfinite(misfit):
          -            misfit = 1e99
          -        else:
          -            misfit += self.objective_routine(beta=beta, zt=zt, dz=dz, C=C)
          -        return misfit
          -
          -
          -    def optimise(self, window, xc, yc, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs):
          -        """
          -        Find the optimal parameters of beta, zt, dz, C for a given
          -        centroid (xc,yc) and window size.
          -
          -        Args:
          -            window  : float
          -                size of window in metres
          -            xc : float
          -                centroid x values
          -            yc : float
          -                centroid y values
          -            beta : float
          -                fractal parameter (starting value)
          -            zt : float
          -                top of magnetic layer (starting value)
          -            dz : float
          -                thickness of magnetic layer (starting value)
          -            C : float
          -                field constant (starting value)
          -            taper : taper (default=np.hanning)
          -                taper function, set to None for no taper function
          -            process_subgrids : function
          -                a custom function to process the subgrid
          -            kwargs : keyword arguments
          -                to pass to radial_spectrum.
          -
          -        Returns:
          -            beta : float
          -                fractal parameters
          -            zt : float
          -                top of magnetic layer
          -            dz : float
          -                thickness of magnetic layer
          -            C : float
          -                field constant
          -        """
          -
          -        if type(process_subgrid) == type(None):
          -            # dummy function
          -            def process_subgrid(subgrid):
          -                return subgrid
          -
          -        # initial constants for minimisation
          -        # w = 1.0 # weight low frequency?
          -
          -        x0 = np.array([beta, zt, dz, C])
          -
          -        # get subgrid
          -        subgrid = self.subgrid(window, xc, yc)
          -        subgrid = process_subgrid(subgrid)
          -
          -        # compute radial spectrum
          -        k, Phi, sigma_Phi = self.radial_spectrum(subgrid, taper=taper, **kwargs)
          -
          -        # minimise function
          -        res = minimize(self.min_func, x0, args=(k, Phi, sigma_Phi), bounds=self.bounds)
          -        return res.x
          -
          -
          -    def _func_queue(self, func, q_in, q_out, window, *args, **kwargs):
          -        """ Retrive processes from the queue """
          -        while True:
          -            pos, xc, yc = q_in.get()
          -            if pos is None:
          -                break
          -
          -            pass_args = [window, xc, yc]
          -            pass_args.extend(args)
          -
          -            res = func(*pass_args, **kwargs)
          -            q_out.put((pos, res))
          -        return
          -
          -
          -    def parallelise_routine(self, window, xc_list, yc_list, func, *args, **kwargs):
          -        """
          -        Implements shared memory multiprocessing to split multiple
          -        evaluations of a function centroids across processors.
          -
          -        Supply the window size and lists of x,y coordinates to a function
          -        along with any additional arguments or keyword arguments.
          -
          -        Args:
          -         window : float
          -            size of window in metres
          -         xc_list : array shape (l,)
          -            centroid x values
          -         yc_list : array shape (l,)
          -            centroid y values
          -         func : function
          -            Python function to evaluate in parallel
          -         args : arguments
          -            additional arguments to pass to func
          -         kwargs : keyword arguments
          -            additional keyword arguments to pass to func
          -
          -        Returns:
          -            out : list
          -                (depends on output of func - see notes)
          -
          -        Usage:
          -            An obvious use case is to compute the Curie depth for many
          -            centroids in parallel.
          -
          -            >>> self.parallelise_routine(window, xc_list, yc_list, self.optimise)
          -        
          -            Each centroid is assigned a new process and sent to a free processor
          -            to compute. In this case, the output is separate lists of shape(l,)
          -            for beta, zt, dz, and C.
          -
          -            Another example is to parallelise the sensitivity analysis:
          -
          -            >>> self.parallelise_routine(window, xc_list, yc_list, self.sensitivity, nsim)
          -
          -            This time the output will be a list of lists for beta, zt, dz, and C
          -            i.e. if nc=2 is the number of centroids and nsim=4 is the number of
          -            simulations then separatee lists [[k1, k2, k3, k4], [k1, k2, k3, k4]]
          -            will be returned for beta, zt, dz, and C.
          -        """
          -
          -        n = len(xc_list)
          -        if n != len(yc_list):
          -            raise ValueError("xc_list and yc_list must be the same size")
          -
          -        xOpt = [[] for i in range(n)]
          -        processes = []
          -        q_in = Queue(1)
          -        q_out = Queue()
          -
          -        nprocs = self.max_processors
          -
          -        for i in range(nprocs):
          -            pass_args = [func, q_in, q_out, window]
          -            pass_args.extend(args)
          -
          -            p = Process(target=self._func_queue,\
          -                        args=tuple(pass_args),\
          -                        kwargs=kwargs)
          -
          -            processes.append(p)
          -
          -        for p in processes:
          -            p.daemon = True
          -            p.start()
          -
          -        # put items in the queue
          -        sent = [q_in.put((i, xc_list[i], yc_list[i])) for i in range(n)]
          -        [q_in.put((None, None, None)) for _ in range(nprocs)]
          -
          -        # get the results
          -        for i in range(len(sent)):
          -            i, res = q_out.get()
          -            xOpt[i] = res
          -
          -
          -        # wait until each processor has finished
          -        [p.join() for p in processes]
          -
          -        # process dimensions of output
          -        ndim = np.array(res).ndim
          -
          -        if ndim == 1:
          -            # return separate lists of beta, zt, dz, C
          -            xOpt = np.vstack(xOpt)
          -            return list(xOpt.T)
          -        elif ndim > 1:
          -            # return lists of beta, zt, dz, C for each centroid
          -            xOpt = np.hstack(xOpt)
          -            out = list(xOpt)
          -            for i in range(len(out)):
          -                out[i] = np.split(out[i], n)
          -            return out
          -        else:
          -            raise ValueError("Cannot determine shape of output")
          -
          -
          -
          -    def optimise_routine(self, window, xc_list, yc_list, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs):
          -        """
          -        Iterate through a list of centroids to compute the optimal values
          -        of beta, zt, dz, C for a given window size.
          -        
          -        Args:
          -            window : float
          -                size of window in metres
          -            xc_list : ndarray shape (l,)
          -                centroid x values 
          -            yc_list : ndarray shape (l,)
          -                centroid y values 
          -            beta : float
          -                fractal parameter 
          -            zt : float
          -                top of magnetic layer
          -            dz : float
          -                thickness of magnetic layer
          -            C : float
          -                field constant
          -            taper : function
          -                taper function (default=np.hanning)
          -                set to None for no taper function
          -         process_subgrids : func
          -            a custom function to process the subgrid
          -         kwargs : keyword arguments
          -            to pass to radial_spectrum.
          -
          -        Returns:
          -            beta : ndarray shape (l,)
          -                fractal parameters
          -            zt : ndarray shape (l,)
          -                top of magnetic layer
          -            dz : ndarray shape (l,)
          -                thickness of magnetic layer
          -            C : ndarray shape (l,)
          -                field constant
          -
          -        """
          -        return self.parallelise_routine(window, xc_list, yc_list, self.optimise, beta, zt, dz, C, taper, process_subgrid, **kwargs)
          -
          -
          -    def metropolis_hastings(self, window, xc, yc, nsim, burnin, x_scale=None, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs):
          -        """
          -        MCMC algorithm using a Metropolis-Hastings sampler.
          -
          -        Evaluates a Markov-Chain for starting values of beta, zt, dz, C
          -        and returns the ensemble of model realisations.
          -        
          -        Args:
          -            window : float
          -                size of window in metres
          -            xc : float
          -                centroid x values
          -            yc : float
          -                centroid y values
          -            nsim : int
          -                number of simulations
          -            burnin : int
          -                number of burn-in simulations before to nsim
          -            x_scale: float(4) (optional)
          -                scaling factor for new proposals
          -                default is [1,1,1,1] for [beta, zt, dz, C] - see notes
          -            beta : float
          -                fractal parameter (starting value)
          -            zt : float
          -                top of magnetic layer (starting value)
          -            dz : float
          -                thickness of magnetic layer (starting value)
          -            C : float
          -                field constant (starting value)
          -
          -        Returns:
          -            beta : ndarray shape (nsim,)
          -                fractal parameter
          -            zt : ndarray shape (nsim,)
          -                top of magnetic layer
          -            dz : ndarray shape (nsim,)
          -                thickness of magnetic layer
          -            C : ndarray shape (nsim,)
          -                field constant
          -
          -        Notes:
          -            nsim, burnin, and x_scale should be tweaked for optimal performance
          -            Use starting values of beta, zt, dz, C relatively close to the solution
          -            - C can easily found from the mean of the radial power spectrum.
          -
          -            During the burn-in stage we apply tempering to the PDF to iterate closer
          -            towards the solution. This has the effect of smoothing out the posterior
          -            so that minima can be more easily found. This is necessary here because
          -            large portions of the posterior probability are zero.
          -            see see Sambridge 2013, DOI:10.1093/gji/ggt342 for more information.
          -        """
          -        if type(process_subgrid) == type(None):
          -            # dummy function
          -            def process_subgrid(subgrid):
          -                return subgrid
          -
          -
          -        samples = np.empty((nsim, 4))
          -        x0 = np.array([beta, zt, dz, C])
          -
          -        if type(x_scale) == type(None):
          -            x_scale = np.ones(4)
          -
          -
          -        # get subgrid
          -        subgrid = self.subgrid(window, xc, yc)
          -        subgrid = process_subgrid(subgrid)
          -
          -        # compute radial spectrum
          -        k, Phi, sigma_Phi = self.radial_spectrum(subgrid, taper=taper, **kwargs)
          -
          -        P0 = np.exp(-self.min_func(x0, k, Phi, sigma_Phi)/1000)
          -
          -        # Burn-in phase
          -        for i in range(burnin):
          -            # add random perturbation
          -            x1 = x0 + np.random.normal(size=4)*x_scale
          -
          -            # evaluate proposal probability + tempering
          -            P1 = np.exp(-self.min_func(x1, k, Phi, sigma_Phi)/1000)
          -
          -            # iterate towards MAP estimate
          -            if P1 > P0:
          -                x0 = x1
          -                P0 = P1
          -
          -        P0 = np.exp(-self.min_func(x0, k, Phi, sigma_Phi))
          -
          -        # Now sample posterior
          -        for i in range(nsim):
          -            # add random perturbation
          -            x1 = x0 + np.random.normal(size=4)*x_scale
          -
          -            # evaluate proposal probability
          -            P0 = max(P0, 1e-99)
          -            P1 = np.exp(-self.min_func(x1, k, Phi, sigma_Phi))
          -
          -            P = min(P1/P0, 1.0)
          -
          -            # randomly accept probability
          -            if np.random.rand() <= P:
          -                x0 = x1
          -                P0 = P1
          -
          -            samples[i] = x0
          -
          -        return list(samples.T)
          -
          -
          -
          -    def sensitivity(self, window, xc, yc, nsim, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs):
          -        """
          -        Iterate through a list of centroids to compute the mean and
          -        standard deviation of beta, zt, dz, C by perturbing their
          -        prior distributions (if provided by the user - see add_prior).
          -        
          -        Args:
          -            nsim : int
          -                number of Monte Carlo simulations
          -            window : float
          -                size of window in metres
          -            xc : float
          -                centroid x values
          -            yc : float
          -                centroid y values
          -            nsim : int
          -                - number of simulations
          -            beta : float
          -                starting fractal parameter 
          -            zt : float
          -                starting top of magnetic layer
          -            dz : float
          -                starting thickness of magnetic layer
          -            C : float
          -                starting field constant
          -
          -
          -        Returns:
          -            beta : ndarray shape (nsim,)
          -                fractal parameters
          -            zt : ndarray shape (nsim,)
          -                top of magnetic layer
          -            dz : ndarray shape (nsim,)
          -                thickness of magnetic layer
          -            C : ndarray shape (nsim,)
          -                field constant
          -        """
          -        if type(process_subgrid) == type(None):
          -            # dummy function
          -            def process_subgrid(subgrid):
          -                return subgrid
          -
          -
          -        samples = np.empty((nsim, 4))
          -        x0 = np.array([beta, zt, dz, C])
          -        
          -        use_keys = []
          -        for key in self.prior_pdf:
          -            prior_pdf = self.prior_pdf[key]
          -            if prior_pdf is not None:
          -                use_keys.append(key)
          -        
          -        # get subgrid
          -        subgrid = self.subgrid(window, xc, yc)
          -        subgrid = process_subgrid(subgrid)
          -
          -        # compute radial spectrum
          -        k, Phi, sigma_Phi = self.radial_spectrum(subgrid, taper=taper, **kwargs)
          -
          -        for sim in range(0, nsim):
          -            # randomly generate new prior values within PDF
          -            for key in use_keys:
          -                prior_pdf = self.prior_pdf[key]
          -                self.prior[key][0] = prior_pdf.rvs()
          -
          -            # minimise function
          -            rPhi = np.random.normal(Phi, sigma_Phi)
          -            res = minimize(self.min_func, x0, args=(k, rPhi, sigma_Phi), bounds=self.bounds)
          -            samples[sim] = res.x
          -
          -
          -        # restore priors
          -        for key in use_keys:
          -            prior_pdf = self.prior_pdf[key]
          -            self.prior[key] = list(prior_pdf.args)
          -
          -        return list(samples.T)
          -
          -

          Ancestors

          - -

          Subclasses

          - -

          Methods

          -
          -
          -def add_prior(self, **kwargs) -
          -
          -

          Add a prior to the dictionary (tuple) -Available priors are beta, zt, dz, C

          -

          Assumes a normal distribution or -define another distribution from scipy.stats

          -

          Usage

          -
          >>> add_prior(beta=(p, sigma_p))
          -
          -
          -
          -
          -

          add_prior(beta=scipy.stats.norm(p, sigma_p))

          -
          -
          -
          -
          -Source code -
          def add_prior(self, **kwargs):
          -    """
          -    Add a prior to the dictionary (tuple)
          -    Available priors are beta, zt, dz, C
          -
          -    Assumes a normal distribution or
          -    define another distribution from scipy.stats
          -
          -    Usage:
          -        >>> add_prior(beta=(p, sigma_p))
          -
          -        >>> add_prior(beta=scipy.stats.norm(p, sigma_p))
          -    """
          -
          -    for key in kwargs:
          -        if key in self.prior:
          -            prior = kwargs[key]
          -            if type(prior) == tuple:
          -                p, sigma_p = prior
          -                pdf = stats.norm(p, sigma_p)
          -            elif type(prior) == stats._distn_infrastructure.rv_frozen:
          -                pdf = prior
          -            else:
          -                raise ValueError("Use a distribution from scipy.stats module")
          -
          -            # add prior PDF to dictionary
          -            self.prior_pdf[key] = pdf
          -            self.prior[key] = list(pdf.args)
          -
          -        else:
          -            raise ValueError("prior must be one of {}".format(self.prior.keys()))
          -
          -
          -
          -def metropolis_hastings(self, window, xc, yc, nsim, burnin, x_scale=None, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=, process_subgrid=None, **kwargs) -
          -
          -

          MCMC algorithm using a Metropolis-Hastings sampler.

          -

          Evaluates a Markov-Chain for starting values of beta, zt, dz, C -and returns the ensemble of model realisations.

          -

          Args

          -
          -
          window : float
          -
          size of window in metres
          -
          xc : float
          -
          centroid x values
          -
          yc : float
          -
          centroid y values
          -
          nsim : int
          -
          number of simulations
          -
          burnin : int
          -
          number of burn-in simulations before to nsim
          -
          x_scale
          -
          float(4) (optional) -scaling factor for new proposals -default is [1,1,1,1] for [beta, zt, dz, C] - see notes
          -
          beta : float
          -
          fractal parameter (starting value)
          -
          zt : float
          -
          top of magnetic layer (starting value)
          -
          dz : float
          -
          thickness of magnetic layer (starting value)
          -
          C : float
          -
          field constant (starting value)
          -
          -

          Returns

          -
          -
          beta : ndarray shape (nsim,)
          -
          fractal parameter
          -
          zt : ndarray shape (nsim,)
          -
          top of magnetic layer
          -
          dz : ndarray shape (nsim,)
          -
          thickness of magnetic layer
          -
          C : ndarray shape (nsim,)
          -
          field constant
          -
          -

          Notes

          -

          nsim, burnin, and x_scale should be tweaked for optimal performance -Use starting values of beta, zt, dz, C relatively close to the solution -- C can easily found from the mean of the radial power spectrum.

          -

          During the burn-in stage we apply tempering to the PDF to iterate closer -towards the solution. This has the effect of smoothing out the posterior -so that minima can be more easily found. This is necessary here because -large portions of the posterior probability are zero. -see see Sambridge 2013, DOI:10.1093/gji/ggt342 for more information.

          -
          -Source code -
          def metropolis_hastings(self, window, xc, yc, nsim, burnin, x_scale=None, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs):
          -    """
          -    MCMC algorithm using a Metropolis-Hastings sampler.
          -
          -    Evaluates a Markov-Chain for starting values of beta, zt, dz, C
          -    and returns the ensemble of model realisations.
          -    
          -    Args:
          -        window : float
          -            size of window in metres
          -        xc : float
          -            centroid x values
          -        yc : float
          -            centroid y values
          -        nsim : int
          -            number of simulations
          -        burnin : int
          -            number of burn-in simulations before to nsim
          -        x_scale: float(4) (optional)
          -            scaling factor for new proposals
          -            default is [1,1,1,1] for [beta, zt, dz, C] - see notes
          -        beta : float
          -            fractal parameter (starting value)
          -        zt : float
          -            top of magnetic layer (starting value)
          -        dz : float
          -            thickness of magnetic layer (starting value)
          -        C : float
          -            field constant (starting value)
          -
          -    Returns:
          -        beta : ndarray shape (nsim,)
          -            fractal parameter
          -        zt : ndarray shape (nsim,)
          -            top of magnetic layer
          -        dz : ndarray shape (nsim,)
          -            thickness of magnetic layer
          -        C : ndarray shape (nsim,)
          -            field constant
          -
          -    Notes:
          -        nsim, burnin, and x_scale should be tweaked for optimal performance
          -        Use starting values of beta, zt, dz, C relatively close to the solution
          -        - C can easily found from the mean of the radial power spectrum.
          -
          -        During the burn-in stage we apply tempering to the PDF to iterate closer
          -        towards the solution. This has the effect of smoothing out the posterior
          -        so that minima can be more easily found. This is necessary here because
          -        large portions of the posterior probability are zero.
          -        see see Sambridge 2013, DOI:10.1093/gji/ggt342 for more information.
          -    """
          -    if type(process_subgrid) == type(None):
          -        # dummy function
          -        def process_subgrid(subgrid):
          -            return subgrid
          -
          -
          -    samples = np.empty((nsim, 4))
          -    x0 = np.array([beta, zt, dz, C])
          -
          -    if type(x_scale) == type(None):
          -        x_scale = np.ones(4)
          -
          -
          -    # get subgrid
          -    subgrid = self.subgrid(window, xc, yc)
          -    subgrid = process_subgrid(subgrid)
          -
          -    # compute radial spectrum
          -    k, Phi, sigma_Phi = self.radial_spectrum(subgrid, taper=taper, **kwargs)
          -
          -    P0 = np.exp(-self.min_func(x0, k, Phi, sigma_Phi)/1000)
          -
          -    # Burn-in phase
          -    for i in range(burnin):
          -        # add random perturbation
          -        x1 = x0 + np.random.normal(size=4)*x_scale
          -
          -        # evaluate proposal probability + tempering
          -        P1 = np.exp(-self.min_func(x1, k, Phi, sigma_Phi)/1000)
          -
          -        # iterate towards MAP estimate
          -        if P1 > P0:
          -            x0 = x1
          -            P0 = P1
          -
          -    P0 = np.exp(-self.min_func(x0, k, Phi, sigma_Phi))
          -
          -    # Now sample posterior
          -    for i in range(nsim):
          -        # add random perturbation
          -        x1 = x0 + np.random.normal(size=4)*x_scale
          -
          -        # evaluate proposal probability
          -        P0 = max(P0, 1e-99)
          -        P1 = np.exp(-self.min_func(x1, k, Phi, sigma_Phi))
          -
          -        P = min(P1/P0, 1.0)
          -
          -        # randomly accept probability
          -        if np.random.rand() <= P:
          -            x0 = x1
          -            P0 = P1
          -
          -        samples[i] = x0
          -
          -    return list(samples.T)
          -
          -
          -
          -def min_func(self, x, kh, Phi, sigma_Phi) -
          -
          -

          Function to minimise

          -

          Args

          -
          -
          x : array shape (n,)
          -
          array of variables [beta, zt, dz, C]
          -
          kh : array shape (n,)
          -
          wavenumbers (rad/km)
          -
          Phi : array shape (n,)
          -
          radial power spectrum
          -
          sigma_Phi : array shape (n,)
          -
          standard deviation of Phi
          -
          -

          Returns

          -
          -
          misfit -: float
          -
          sum of misfit (float)
          -
          -

          Notes

          -

          We purposely ignore all warnings raised by the bouligand2009 -function because some combinations of input parameters will -trigger an out-of-range warning that will crash the minimiser. -Instead, the misfit is set to a very large number when this occurs.

          -
          -Source code -
          def min_func(self, x, kh, Phi, sigma_Phi):
          -    """
          -    Function to minimise
          -
          -    Args:
          -        x : array shape (n,)
          -            array of variables [beta, zt, dz, C]
          -        kh : array shape (n,)
          -            wavenumbers (rad/km)
          -        Phi : array shape (n,)
          -            radial power spectrum
          -        sigma_Phi : array shape (n,)
          -            standard deviation of Phi
          -
          -    Returns:
          -        misfit    : float
          -            sum of misfit (float)
          -
          -    Notes:
          -        We purposely ignore all warnings raised by the bouligand2009
          -        function because some combinations of input parameters will
          -        trigger an out-of-range warning that will crash the minimiser.
          -        Instead, the misfit is set to a very large number when this occurs.
          -    """
          -    beta, zt, dz, C = x
          -    with warnings.catch_warnings() as w:
          -        warnings.simplefilter("ignore")
          -        Phi_syn = bouligand2009(kh, beta, zt, dz, C)
          -
          -    misfit = self.objective_function(Phi_syn, Phi, 1.0)
          -    if not np.isfinite(misfit):
          -        misfit = 1e99
          -    else:
          -        misfit += self.objective_routine(beta=beta, zt=zt, dz=dz, C=C)
          -    return misfit
          -
          -
          -
          -def objective_function(self, x, x0, sigma_x0, *args) -
          -
          -

          Objective function used in objective_routine -Evaluates the l2-norm misfit

          -

          Args

          -
          -
          x : float, ndarray
          -
           
          -
          x0 : float, ndarray
          -
           
          -
          sigma_x0 : float, ndarray
          -
           
          -
          -

          Returns

          -
          -
          misfit -: float
          -
           
          -
          -
          -Source code -
          def objective_function(self, x, x0, sigma_x0, *args):
          -    """
          -    Objective function used in `objective_routine`
          -    Evaluates the l2-norm misfit
          -
          -    Args:
          -        x : float, ndarray
          -        x0 : float, ndarray
          -        sigma_x0 : float, ndarray
          -
          -    Returns:
          -        misfit   : float
          -    """
          -    return 0.5*np.sum((x - x0)**2/sigma_x0**2)
          -
          -
          -
          -def objective_routine(self, **kwargs) -
          -
          -

          Evaluate the objective routine to find the misfit with priors -Only keys stored in self.prior will be added to the total misfit

          -

          Usage

          -
          >>> objective_routine(beta=2.5)
          -
          -

          Returns

          -
          -
          misfit -: float
          -
          misfit integrated over all observations and priors
          -
          -
          -Source code -
          def objective_routine(self, **kwargs):
          -    """
          -    Evaluate the objective routine to find the misfit with priors
          -    Only keys stored in self.prior will be added to the total misfit
          -
          -    Usage:
          -        >>> objective_routine(beta=2.5)
          -
          -    Returns:
          -        misfit  : float
          -            misfit integrated over all observations and priors
          -    """
          -    c = 0.0
          -
          -    for key in kwargs:
          -        val = kwargs[key]
          -        if key in self.prior:
          -            prior_args = self.prior[key]
          -            if prior_args is not None:
          -                c += self.objective_function(val, *prior_args)
          -    return c
          -
          -
          -
          -def optimise(self, window, xc, yc, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=, process_subgrid=None, **kwargs) -
          -
          -

          Find the optimal parameters of beta, zt, dz, C for a given -centroid (xc,yc) and window size.

          -

          Args

          -
          -
          window -: float
          -
          size of window in metres
          -
          xc : float
          -
          centroid x values
          -
          yc : float
          -
          centroid y values
          -
          beta : float
          -
          fractal parameter (starting value)
          -
          zt : float
          -
          top of magnetic layer (starting value)
          -
          dz : float
          -
          thickness of magnetic layer (starting value)
          -
          C : float
          -
          field constant (starting value)
          -
          taper : taper (default=np.hanning)
          -
          taper function, set to None for no taper function
          -
          process_subgrids : function
          -
          a custom function to process the subgrid
          -
          kwargs : keyword arguments
          -
          to pass to radial_spectrum.
          -
          -

          Returns

          -
          -
          beta : float
          -
          fractal parameters
          -
          zt : float
          -
          top of magnetic layer
          -
          dz : float
          -
          thickness of magnetic layer
          -
          C : float
          -
          field constant
          -
          -
          -Source code -
          def optimise(self, window, xc, yc, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs):
          -    """
          -    Find the optimal parameters of beta, zt, dz, C for a given
          -    centroid (xc,yc) and window size.
          -
          -    Args:
          -        window  : float
          -            size of window in metres
          -        xc : float
          -            centroid x values
          -        yc : float
          -            centroid y values
          -        beta : float
          -            fractal parameter (starting value)
          -        zt : float
          -            top of magnetic layer (starting value)
          -        dz : float
          -            thickness of magnetic layer (starting value)
          -        C : float
          -            field constant (starting value)
          -        taper : taper (default=np.hanning)
          -            taper function, set to None for no taper function
          -        process_subgrids : function
          -            a custom function to process the subgrid
          -        kwargs : keyword arguments
          -            to pass to radial_spectrum.
          -
          -    Returns:
          -        beta : float
          -            fractal parameters
          -        zt : float
          -            top of magnetic layer
          -        dz : float
          -            thickness of magnetic layer
          -        C : float
          -            field constant
          -    """
          -
          -    if type(process_subgrid) == type(None):
          -        # dummy function
          -        def process_subgrid(subgrid):
          -            return subgrid
          -
          -    # initial constants for minimisation
          -    # w = 1.0 # weight low frequency?
          -
          -    x0 = np.array([beta, zt, dz, C])
          -
          -    # get subgrid
          -    subgrid = self.subgrid(window, xc, yc)
          -    subgrid = process_subgrid(subgrid)
          -
          -    # compute radial spectrum
          -    k, Phi, sigma_Phi = self.radial_spectrum(subgrid, taper=taper, **kwargs)
          -
          -    # minimise function
          -    res = minimize(self.min_func, x0, args=(k, Phi, sigma_Phi), bounds=self.bounds)
          -    return res.x
          -
          -
          -
          -def optimise_routine(self, window, xc_list, yc_list, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=, process_subgrid=None, **kwargs) -
          -
          -

          Iterate through a list of centroids to compute the optimal values -of beta, zt, dz, C for a given window size.

          -

          Args

          -
          -
          window : float
          -
          size of window in metres
          -
          xc_list : ndarray shape (l,)
          -
          centroid x values
          -
          yc_list : ndarray shape (l,)
          -
          centroid y values
          -
          beta : float
          -
          fractal parameter
          -
          zt : float
          -
          top of magnetic layer
          -
          dz : float
          -
          thickness of magnetic layer
          -
          C : float
          -
          field constant
          -
          taper : function
          -
          taper function (default=np.hanning) -set to None for no taper function
          -
          -

          process_subgrids : func -a custom function to process the subgrid -kwargs : keyword arguments -to pass to radial_spectrum.

          -

          Returns

          -
          -
          beta : ndarray shape (l,)
          -
          fractal parameters
          -
          zt : ndarray shape (l,)
          -
          top of magnetic layer
          -
          dz : ndarray shape (l,)
          -
          thickness of magnetic layer
          -
          C : ndarray shape (l,)
          -
          field constant
          -
          -
          -Source code -
          def optimise_routine(self, window, xc_list, yc_list, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs):
          -    """
          -    Iterate through a list of centroids to compute the optimal values
          -    of beta, zt, dz, C for a given window size.
          -    
          -    Args:
          -        window : float
          -            size of window in metres
          -        xc_list : ndarray shape (l,)
          -            centroid x values 
          -        yc_list : ndarray shape (l,)
          -            centroid y values 
          -        beta : float
          -            fractal parameter 
          -        zt : float
          -            top of magnetic layer
          -        dz : float
          -            thickness of magnetic layer
          -        C : float
          -            field constant
          -        taper : function
          -            taper function (default=np.hanning)
          -            set to None for no taper function
          -     process_subgrids : func
          -        a custom function to process the subgrid
          -     kwargs : keyword arguments
          -        to pass to radial_spectrum.
          -
          -    Returns:
          -        beta : ndarray shape (l,)
          -            fractal parameters
          -        zt : ndarray shape (l,)
          -            top of magnetic layer
          -        dz : ndarray shape (l,)
          -            thickness of magnetic layer
          -        C : ndarray shape (l,)
          -            field constant
          -
          -    """
          -    return self.parallelise_routine(window, xc_list, yc_list, self.optimise, beta, zt, dz, C, taper, process_subgrid, **kwargs)
          -
          -
          -
          -def parallelise_routine(self, window, xc_list, yc_list, func, *args, **kwargs) -
          -
          -

          Implements shared memory multiprocessing to split multiple -evaluations of a function centroids across processors.

          -

          Supply the window size and lists of x,y coordinates to a function -along with any additional arguments or keyword arguments.

          -

          Args: -window : float -size of window in metres -xc_list : array shape (l,) -centroid x values -yc_list : array shape (l,) -centroid y values -func : function -Python function to evaluate in parallel -args : arguments -additional arguments to pass to func -kwargs : keyword arguments -additional keyword arguments to pass to func

          -

          Returns

          -
          -
          out : list
          -
          (depends on output of func - see notes)
          -
          -

          Usage

          -

          An obvious use case is to compute the Curie depth for many -centroids in parallel.

          -
          >>> self.parallelise_routine(window, xc_list, yc_list, self.optimise)
          -
          -

          Each centroid is assigned a new process and sent to a free processor -to compute. In this case, the output is separate lists of shape(l,) -for beta, zt, dz, and C.

          -

          Another example is to parallelise the sensitivity analysis:

          -
          >>> self.parallelise_routine(window, xc_list, yc_list, self.sensitivity, nsim)
          -
          -

          This time the output will be a list of lists for beta, zt, dz, and C -i.e. if nc=2 is the number of centroids and nsim=4 is the number of -simulations then separatee lists [[k1, k2, k3, k4], [k1, k2, k3, k4]] -will be returned for beta, zt, dz, and C.

          -
          -Source code -
          def parallelise_routine(self, window, xc_list, yc_list, func, *args, **kwargs):
          -    """
          -    Implements shared memory multiprocessing to split multiple
          -    evaluations of a function centroids across processors.
          -
          -    Supply the window size and lists of x,y coordinates to a function
          -    along with any additional arguments or keyword arguments.
          -
          -    Args:
          -     window : float
          -        size of window in metres
          -     xc_list : array shape (l,)
          -        centroid x values
          -     yc_list : array shape (l,)
          -        centroid y values
          -     func : function
          -        Python function to evaluate in parallel
          -     args : arguments
          -        additional arguments to pass to func
          -     kwargs : keyword arguments
          -        additional keyword arguments to pass to func
          -
          -    Returns:
          -        out : list
          -            (depends on output of func - see notes)
          -
          -    Usage:
          -        An obvious use case is to compute the Curie depth for many
          -        centroids in parallel.
          -
          -        >>> self.parallelise_routine(window, xc_list, yc_list, self.optimise)
          -    
          -        Each centroid is assigned a new process and sent to a free processor
          -        to compute. In this case, the output is separate lists of shape(l,)
          -        for beta, zt, dz, and C.
          -
          -        Another example is to parallelise the sensitivity analysis:
          -
          -        >>> self.parallelise_routine(window, xc_list, yc_list, self.sensitivity, nsim)
          -
          -        This time the output will be a list of lists for beta, zt, dz, and C
          -        i.e. if nc=2 is the number of centroids and nsim=4 is the number of
          -        simulations then separatee lists [[k1, k2, k3, k4], [k1, k2, k3, k4]]
          -        will be returned for beta, zt, dz, and C.
          -    """
          -
          -    n = len(xc_list)
          -    if n != len(yc_list):
          -        raise ValueError("xc_list and yc_list must be the same size")
          -
          -    xOpt = [[] for i in range(n)]
          -    processes = []
          -    q_in = Queue(1)
          -    q_out = Queue()
          -
          -    nprocs = self.max_processors
          -
          -    for i in range(nprocs):
          -        pass_args = [func, q_in, q_out, window]
          -        pass_args.extend(args)
          -
          -        p = Process(target=self._func_queue,\
          -                    args=tuple(pass_args),\
          -                    kwargs=kwargs)
          -
          -        processes.append(p)
          -
          -    for p in processes:
          -        p.daemon = True
          -        p.start()
          -
          -    # put items in the queue
          -    sent = [q_in.put((i, xc_list[i], yc_list[i])) for i in range(n)]
          -    [q_in.put((None, None, None)) for _ in range(nprocs)]
          -
          -    # get the results
          -    for i in range(len(sent)):
          -        i, res = q_out.get()
          -        xOpt[i] = res
          -
          -
          -    # wait until each processor has finished
          -    [p.join() for p in processes]
          -
          -    # process dimensions of output
          -    ndim = np.array(res).ndim
          -
          -    if ndim == 1:
          -        # return separate lists of beta, zt, dz, C
          -        xOpt = np.vstack(xOpt)
          -        return list(xOpt.T)
          -    elif ndim > 1:
          -        # return lists of beta, zt, dz, C for each centroid
          -        xOpt = np.hstack(xOpt)
          -        out = list(xOpt)
          -        for i in range(len(out)):
          -            out[i] = np.split(out[i], n)
          -        return out
          -    else:
          -        raise ValueError("Cannot determine shape of output")
          -
          -
          -
          -def reset_priors(self) -
          -
          -

          Reset priors to uniform distribution

          -
          -Source code -
          def reset_priors(self):
          -    """
          -    Reset priors to uniform distribution
          -    """
          -    self.prior = {'beta':None, 'zt':None, 'dz':None, 'C':None}
          -    self.prior_pdf = {'beta':None, 'zt':None, 'dz':None, 'C':None}
          -
          -
          -
          -def sensitivity(self, window, xc, yc, nsim, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=, process_subgrid=None, **kwargs) -
          -
          -

          Iterate through a list of centroids to compute the mean and -standard deviation of beta, zt, dz, C by perturbing their -prior distributions (if provided by the user - see add_prior).

          -

          Args

          -
          -
          nsim : int
          -
          number of Monte Carlo simulations
          -
          window : float
          -
          size of window in metres
          -
          xc : float
          -
          centroid x values
          -
          yc : float
          -
          centroid y values
          -
          nsim : int
          -
          -
            -
          • number of simulations
          • -
          -
          -
          beta : float
          -
          starting fractal parameter
          -
          zt : float
          -
          starting top of magnetic layer
          -
          dz : float
          -
          starting thickness of magnetic layer
          -
          C : float
          -
          starting field constant
          -
          -

          Returns

          -
          -
          beta : ndarray shape (nsim,)
          -
          fractal parameters
          -
          zt : ndarray shape (nsim,)
          -
          top of magnetic layer
          -
          dz : ndarray shape (nsim,)
          -
          thickness of magnetic layer
          -
          C : ndarray shape (nsim,)
          -
          field constant
          -
          -
          -Source code -
          def sensitivity(self, window, xc, yc, nsim, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs):
          -    """
          -    Iterate through a list of centroids to compute the mean and
          -    standard deviation of beta, zt, dz, C by perturbing their
          -    prior distributions (if provided by the user - see add_prior).
          -    
          -    Args:
          -        nsim : int
          -            number of Monte Carlo simulations
          -        window : float
          -            size of window in metres
          -        xc : float
          -            centroid x values
          -        yc : float
          -            centroid y values
          -        nsim : int
          -            - number of simulations
          -        beta : float
          -            starting fractal parameter 
          -        zt : float
          -            starting top of magnetic layer
          -        dz : float
          -            starting thickness of magnetic layer
          -        C : float
          -            starting field constant
          -
          -
          -    Returns:
          -        beta : ndarray shape (nsim,)
          -            fractal parameters
          -        zt : ndarray shape (nsim,)
          -            top of magnetic layer
          -        dz : ndarray shape (nsim,)
          -            thickness of magnetic layer
          -        C : ndarray shape (nsim,)
          -            field constant
          -    """
          -    if type(process_subgrid) == type(None):
          -        # dummy function
          -        def process_subgrid(subgrid):
          -            return subgrid
          -
          -
          -    samples = np.empty((nsim, 4))
          -    x0 = np.array([beta, zt, dz, C])
          -    
          -    use_keys = []
          -    for key in self.prior_pdf:
          -        prior_pdf = self.prior_pdf[key]
          -        if prior_pdf is not None:
          -            use_keys.append(key)
          -    
          -    # get subgrid
          -    subgrid = self.subgrid(window, xc, yc)
          -    subgrid = process_subgrid(subgrid)
          -
          -    # compute radial spectrum
          -    k, Phi, sigma_Phi = self.radial_spectrum(subgrid, taper=taper, **kwargs)
          -
          -    for sim in range(0, nsim):
          -        # randomly generate new prior values within PDF
          -        for key in use_keys:
          -            prior_pdf = self.prior_pdf[key]
          -            self.prior[key][0] = prior_pdf.rvs()
          -
          -        # minimise function
          -        rPhi = np.random.normal(Phi, sigma_Phi)
          -        res = minimize(self.min_func, x0, args=(k, rPhi, sigma_Phi), bounds=self.bounds)
          -        samples[sim] = res.x
          -
          -
          -    # restore priors
          -    for key in use_keys:
          -        prior_pdf = self.prior_pdf[key]
          -        self.prior[key] = list(prior_pdf.args)
          -
          -    return list(samples.T)
          -
          -
          -
          -

          Inherited members

          - -
          -
          -
          -
          - -
          - - - - - \ No newline at end of file diff --git a/docs/parallel.html b/docs/parallel.html deleted file mode 100644 index c8b6e69..0000000 --- a/docs/parallel.html +++ /dev/null @@ -1,689 +0,0 @@ - - - - - - -pycurious.parallel API documentation - - - - - - - - - -
          -
          -
          -

          Module pycurious.parallel

          -
          -
          -

          Copyright 2018 Ben Mather, Robert Delhaye

          -

          This file is part of PyCurious.

          -

          PyCurious is free software: you can redistribute it and/or modify -it under the terms of the GNU Lesser General Public License as published by -the Free Software Foundation, either version 3 of the License, or any later version.

          -

          PyCurious is distributed in the hope that it will be useful, -but WITHOUT ANY WARRANTY; without even the implied warranty of -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. -See the -GNU Lesser General Public License for more details.

          -

          You should have received a copy of the GNU Lesser General Public License -along with PyCurious. -If not, see http://www.gnu.org/licenses/.

          -
          -Source code -
          """
          -Copyright 2018 Ben Mather, Robert Delhaye
          -
          -This file is part of PyCurious.
          -
          -PyCurious is free software: you can redistribute it and/or modify
          -it under the terms of the GNU Lesser General Public License as published by
          -the Free Software Foundation, either version 3 of the License, or any later version.
          -
          -PyCurious is distributed in the hope that it will be useful,
          -but WITHOUT ANY WARRANTY; without even the implied warranty of
          -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
          -GNU Lesser General Public License for more details.
          -
          -You should have received a copy of the GNU Lesser General Public License
          -along with PyCurious.  If not, see <http://www.gnu.org/licenses/>.
          -"""
          -
          -# -*- coding: utf-8 -*-
          -import numpy as np
          -import warnings
          -from .optimise import CurieOptimise
          -
          -try: range=xrange
          -except: pass
          -
          -
          -class CurieParallel(CurieOptimise):
          -    """
          -    A parallel implementation built on the PETSc DMDA mesh structure
          -    Almost a trivially parallel problem: each processor works locally
          -    on their portion of the grid. A stipulation being that the window
          -    size must not exceed the thickness of shadow zones or else the
          -    subgrid will be truncated.
          -
          -    This inherits from CurieOptimise and CurieGrid classes.
          -
          -
          -    Parameters
          -    ----------
          -     grid       : 2D array of magnetic data
          -     xmin       : minimum x bound in metres
          -     xmax       : maximum x bound in metres
          -     ymin       : minimum y bound in metres
          -     ymax       : maximum y bound in metres
          -     max_window : maximum size of the windows
          -                : this will be enforced for all methods
          -    
          -    Attributes
          -    ----------
          -     bounds     : lower and upper bounds for beta, zt, dz, C
          -     prior      : dictionary of priors for beta, zt, dz, C
          -     coords     : local xy coordinates
          -    """
          -
          -    def __init__(self, grid, xmin, xmax, ymin, ymax, max_window):
          -
          -        from petsc4py import PETSc
          -        from mpi4py import MPI
          -        comm = MPI.COMM_WORLD
          -        self.comm = comm
          -        self.MPI = MPI
          -
          -        # super(CurieParallel, self).__init__(grid, xmin, xmax, ymin, ymax)
          -
          -        # determine stencil width (should be window size/2)
          -        ny, nx = grid.shape
          -        dx = (xmax - xmin)/nx
          -        dy = (ymax - ymin)/ny
          -        nw = max_window/dx
          -        n2w = int(nw/2) + 1 # add some buffer
          -
          -        if abs(dx - dy) > 1.0:
          -            warnings.warn("node spacing should be identical {}".format((dx,dy)), RuntimeWarning)
          -
          -
          -        dm = PETSc.DMDA().create(dim=2, sizes=(nx,ny), stencil_width=n2w, comm=comm)
          -        dm.setUniformCoordinates(xmin, xmax, ymin, ymax)
          -
          -        self.dm = dm
          -        self.lgmap = dm.getLGMap()
          -        self.lvec = dm.createLocalVector()
          -        self.gvec = dm.createGlobalVector()
          -
          -        coords = dm.getCoordinatesLocal().array.reshape(-1, 2)
          -        xmin, ymin = coords.min(axis=0)
          -        xmax, ymax = coords.max(axis=0)
          -        self.coords = coords
          -        self.max_window = max_window
          -
          -        (imin, imax), (jmin, jmax) = dm.getGhostRanges()
          -
          -        # now decompose grid for each processor
          -
          -        grid_chunk = grid[jmin:jmax, imin:imax]
          -
          -        super(CurieParallel, self).__init__(grid_chunk, xmin, xmax, ymin, ymax)
          -
          -        reduce_methods = {'sum': MPI.SUM, 'max': MPI.MAX, 'min': MPI.MIN, 'mean': MPI.SUM}
          -        self._reduce_methods = reduce_methods
          -
          -
          -    def subgrid(self, xc, yc, window):
          -        """
          -        Extract a subgrid from the data at a window around
          -        the point (xc,yc)
          -        
          -        Parameters
          -        ----------
          -         xc      : x coordinate
          -         yc      : y coordinate
          -         window  : size of window in metres
          -
          -        Returns
          -        -------
          -         data    : subgrid
          -        """
          -        if window > self.max_window:
          -            raise ValueError("Max window size is {}".format(self.max_window))
          -
          -        return super(CurieParallel, self).subgrid(window, xc, yc)
          -
          -    
          -    def sync(self, vector):
          -        """
          -        Synchronise a local vector across all processors
          -        """
          -        self.lvec.setArray(vector)
          -        self.dm.localToGlobal(self.lvec, self.gvec)
          -        self.dm.globalToLocal(self.gvec, self.lvec)
          -        return self.lvec.array.copy()
          -
          -
          -    def add_parallel_prior(self, **kwargs):
          -        """
          -        Add a prior to the dictionary (tuple)
          -        This version broadcasts just the values from the root processor
          -
          -        Available priors are beta, zt, dz, C
          -
          -        Usage
          -        -----
          -         add_parallel_prior(beta=(p, sigma_p))
          -        """
          -
          -        comm = self.comm
          -        MPI = self.MPI
          -
          -        for key in kwargs:
          -            if key in self.prior:
          -                prior = kwargs[key]
          -                p  = np.array(prior[0]) # prior
          -                dp = np.array(prior[1]) # uncertainty
          -
          -                comm.Bcast([p, MPI.DOUBLE], root=0)
          -                comm.Bcast([dp,MPI.DOUBLE], root=0)
          -
          -                self.prior[key] = (float(p), float(dp))
          -            else:
          -                raise ValueError("prior must be one of {}".format(self.prior.keys()))
          -
          -
          -    def distribute_prior(self, method, **kwargs):
          -        """
          -        Distribute priors across all processors using a specific method.
          -
          -        Parameters
          -        ----------
          -         method  : operation to reduce the local priors to a single value
          -                 : choose from one of 'sum', 'mean', 'min', 'max'
          -         kwargs  : (prior, sigma_prior) tuple
          -
          -        Notes
          -        -----
          -         add_prior will broadcast the prior on the root processor (rank=0)
          -         distribute_prior enacts a MPI Allreduce operation.
          -        """
          -
          -        comm = self.comm
          -        MPI = self.MPI
          -
          -        if method in self._reduce_methods:
          -            op = self._reduce_methods[method]
          -        else:
          -            raise ValueError("choose one of the following methods {}".format(self._reduce_methods.keys()))
          -
          -        for key in kwargs:
          -            if key in self.prior:
          -                prior = kwargs[key]
          -                local_p  = np.array(prior[0]) # prior
          -                local_dp = np.array(prior[1]) # uncertainty
          -
          -                global_p = np.array(0.0)
          -                global_dp = np.array(0.0)
          -
          -                comm.Allreduce([local_p, MPI.DOUBLE], [global_p, MPI.DOUBLE], op=op)
          -                comm.Allreduce([local_dp, MPI.DOUBLE], [global_dp, MPI.DOUBLE], op=op)
          -                if method == 'mean':
          -                    global_p  /= comm.size
          -                    global_dp /= comm.size
          -
          -                self.prior[key] = (float(global_p), float(global_dp))
          -            else:
          -                raise ValueError("prior must be one of {}".format(self.prior.keys()))
          -
          -
          -
          -
          -
          -
          -
          -
          -
          -

          Classes

          -
          -
          -class CurieParallel -(grid, xmin, xmax, ymin, ymax, max_window) -
          -
          -

          A parallel implementation built on the PETSc DMDA mesh structure -Almost a trivially parallel problem: each processor works locally -on their portion of the grid. A stipulation being that the window -size must not exceed the thickness of shadow zones or else the -subgrid will be truncated.

          -

          This inherits from CurieOptimise and CurieGrid classes.

          -

          Parameters

          -

          grid -: 2D array of magnetic data -xmin -: minimum x bound in metres -xmax -: maximum x bound in metres -ymin -: minimum y bound in metres -ymax -: maximum y bound in metres -max_window : maximum size of the windows -: this will be enforced for all methods

          -

          Attributes

          -

          bounds -: lower and upper bounds for beta, zt, dz, C -prior -: dictionary of priors for beta, zt, dz, C -coords -: local xy coordinates

          -
          -Source code -
          class CurieParallel(CurieOptimise):
          -    """
          -    A parallel implementation built on the PETSc DMDA mesh structure
          -    Almost a trivially parallel problem: each processor works locally
          -    on their portion of the grid. A stipulation being that the window
          -    size must not exceed the thickness of shadow zones or else the
          -    subgrid will be truncated.
          -
          -    This inherits from CurieOptimise and CurieGrid classes.
          -
          -
          -    Parameters
          -    ----------
          -     grid       : 2D array of magnetic data
          -     xmin       : minimum x bound in metres
          -     xmax       : maximum x bound in metres
          -     ymin       : minimum y bound in metres
          -     ymax       : maximum y bound in metres
          -     max_window : maximum size of the windows
          -                : this will be enforced for all methods
          -    
          -    Attributes
          -    ----------
          -     bounds     : lower and upper bounds for beta, zt, dz, C
          -     prior      : dictionary of priors for beta, zt, dz, C
          -     coords     : local xy coordinates
          -    """
          -
          -    def __init__(self, grid, xmin, xmax, ymin, ymax, max_window):
          -
          -        from petsc4py import PETSc
          -        from mpi4py import MPI
          -        comm = MPI.COMM_WORLD
          -        self.comm = comm
          -        self.MPI = MPI
          -
          -        # super(CurieParallel, self).__init__(grid, xmin, xmax, ymin, ymax)
          -
          -        # determine stencil width (should be window size/2)
          -        ny, nx = grid.shape
          -        dx = (xmax - xmin)/nx
          -        dy = (ymax - ymin)/ny
          -        nw = max_window/dx
          -        n2w = int(nw/2) + 1 # add some buffer
          -
          -        if abs(dx - dy) > 1.0:
          -            warnings.warn("node spacing should be identical {}".format((dx,dy)), RuntimeWarning)
          -
          -
          -        dm = PETSc.DMDA().create(dim=2, sizes=(nx,ny), stencil_width=n2w, comm=comm)
          -        dm.setUniformCoordinates(xmin, xmax, ymin, ymax)
          -
          -        self.dm = dm
          -        self.lgmap = dm.getLGMap()
          -        self.lvec = dm.createLocalVector()
          -        self.gvec = dm.createGlobalVector()
          -
          -        coords = dm.getCoordinatesLocal().array.reshape(-1, 2)
          -        xmin, ymin = coords.min(axis=0)
          -        xmax, ymax = coords.max(axis=0)
          -        self.coords = coords
          -        self.max_window = max_window
          -
          -        (imin, imax), (jmin, jmax) = dm.getGhostRanges()
          -
          -        # now decompose grid for each processor
          -
          -        grid_chunk = grid[jmin:jmax, imin:imax]
          -
          -        super(CurieParallel, self).__init__(grid_chunk, xmin, xmax, ymin, ymax)
          -
          -        reduce_methods = {'sum': MPI.SUM, 'max': MPI.MAX, 'min': MPI.MIN, 'mean': MPI.SUM}
          -        self._reduce_methods = reduce_methods
          -
          -
          -    def subgrid(self, xc, yc, window):
          -        """
          -        Extract a subgrid from the data at a window around
          -        the point (xc,yc)
          -        
          -        Parameters
          -        ----------
          -         xc      : x coordinate
          -         yc      : y coordinate
          -         window  : size of window in metres
          -
          -        Returns
          -        -------
          -         data    : subgrid
          -        """
          -        if window > self.max_window:
          -            raise ValueError("Max window size is {}".format(self.max_window))
          -
          -        return super(CurieParallel, self).subgrid(window, xc, yc)
          -
          -    
          -    def sync(self, vector):
          -        """
          -        Synchronise a local vector across all processors
          -        """
          -        self.lvec.setArray(vector)
          -        self.dm.localToGlobal(self.lvec, self.gvec)
          -        self.dm.globalToLocal(self.gvec, self.lvec)
          -        return self.lvec.array.copy()
          -
          -
          -    def add_parallel_prior(self, **kwargs):
          -        """
          -        Add a prior to the dictionary (tuple)
          -        This version broadcasts just the values from the root processor
          -
          -        Available priors are beta, zt, dz, C
          -
          -        Usage
          -        -----
          -         add_parallel_prior(beta=(p, sigma_p))
          -        """
          -
          -        comm = self.comm
          -        MPI = self.MPI
          -
          -        for key in kwargs:
          -            if key in self.prior:
          -                prior = kwargs[key]
          -                p  = np.array(prior[0]) # prior
          -                dp = np.array(prior[1]) # uncertainty
          -
          -                comm.Bcast([p, MPI.DOUBLE], root=0)
          -                comm.Bcast([dp,MPI.DOUBLE], root=0)
          -
          -                self.prior[key] = (float(p), float(dp))
          -            else:
          -                raise ValueError("prior must be one of {}".format(self.prior.keys()))
          -
          -
          -    def distribute_prior(self, method, **kwargs):
          -        """
          -        Distribute priors across all processors using a specific method.
          -
          -        Parameters
          -        ----------
          -         method  : operation to reduce the local priors to a single value
          -                 : choose from one of 'sum', 'mean', 'min', 'max'
          -         kwargs  : (prior, sigma_prior) tuple
          -
          -        Notes
          -        -----
          -         add_prior will broadcast the prior on the root processor (rank=0)
          -         distribute_prior enacts a MPI Allreduce operation.
          -        """
          -
          -        comm = self.comm
          -        MPI = self.MPI
          -
          -        if method in self._reduce_methods:
          -            op = self._reduce_methods[method]
          -        else:
          -            raise ValueError("choose one of the following methods {}".format(self._reduce_methods.keys()))
          -
          -        for key in kwargs:
          -            if key in self.prior:
          -                prior = kwargs[key]
          -                local_p  = np.array(prior[0]) # prior
          -                local_dp = np.array(prior[1]) # uncertainty
          -
          -                global_p = np.array(0.0)
          -                global_dp = np.array(0.0)
          -
          -                comm.Allreduce([local_p, MPI.DOUBLE], [global_p, MPI.DOUBLE], op=op)
          -                comm.Allreduce([local_dp, MPI.DOUBLE], [global_dp, MPI.DOUBLE], op=op)
          -                if method == 'mean':
          -                    global_p  /= comm.size
          -                    global_dp /= comm.size
          -
          -                self.prior[key] = (float(global_p), float(global_dp))
          -            else:
          -                raise ValueError("prior must be one of {}".format(self.prior.keys()))
          -
          -

          Ancestors

          - -

          Methods

          -
          -
          -def add_parallel_prior(self, **kwargs) -
          -
          -

          Add a prior to the dictionary (tuple) -This version broadcasts just the values from the root processor

          -

          Available priors are beta, zt, dz, C

          -

          Usage

          -

          add_parallel_prior(beta=(p, sigma_p))

          -
          -Source code -
          def add_parallel_prior(self, **kwargs):
          -    """
          -    Add a prior to the dictionary (tuple)
          -    This version broadcasts just the values from the root processor
          -
          -    Available priors are beta, zt, dz, C
          -
          -    Usage
          -    -----
          -     add_parallel_prior(beta=(p, sigma_p))
          -    """
          -
          -    comm = self.comm
          -    MPI = self.MPI
          -
          -    for key in kwargs:
          -        if key in self.prior:
          -            prior = kwargs[key]
          -            p  = np.array(prior[0]) # prior
          -            dp = np.array(prior[1]) # uncertainty
          -
          -            comm.Bcast([p, MPI.DOUBLE], root=0)
          -            comm.Bcast([dp,MPI.DOUBLE], root=0)
          -
          -            self.prior[key] = (float(p), float(dp))
          -        else:
          -            raise ValueError("prior must be one of {}".format(self.prior.keys()))
          -
          -
          -
          -def distribute_prior(self, method, **kwargs) -
          -
          -

          Distribute priors across all processors using a specific method.

          -

          Parameters

          -

          method -: operation to reduce the local priors to a single value -: choose from one of 'sum', 'mean', 'min', 'max' -kwargs -: (prior, sigma_prior) tuple

          -

          Notes

          -

          add_prior will broadcast the prior on the root processor (rank=0) -distribute_prior enacts a MPI Allreduce operation.

          -
          -Source code -
          def distribute_prior(self, method, **kwargs):
          -    """
          -    Distribute priors across all processors using a specific method.
          -
          -    Parameters
          -    ----------
          -     method  : operation to reduce the local priors to a single value
          -             : choose from one of 'sum', 'mean', 'min', 'max'
          -     kwargs  : (prior, sigma_prior) tuple
          -
          -    Notes
          -    -----
          -     add_prior will broadcast the prior on the root processor (rank=0)
          -     distribute_prior enacts a MPI Allreduce operation.
          -    """
          -
          -    comm = self.comm
          -    MPI = self.MPI
          -
          -    if method in self._reduce_methods:
          -        op = self._reduce_methods[method]
          -    else:
          -        raise ValueError("choose one of the following methods {}".format(self._reduce_methods.keys()))
          -
          -    for key in kwargs:
          -        if key in self.prior:
          -            prior = kwargs[key]
          -            local_p  = np.array(prior[0]) # prior
          -            local_dp = np.array(prior[1]) # uncertainty
          -
          -            global_p = np.array(0.0)
          -            global_dp = np.array(0.0)
          -
          -            comm.Allreduce([local_p, MPI.DOUBLE], [global_p, MPI.DOUBLE], op=op)
          -            comm.Allreduce([local_dp, MPI.DOUBLE], [global_dp, MPI.DOUBLE], op=op)
          -            if method == 'mean':
          -                global_p  /= comm.size
          -                global_dp /= comm.size
          -
          -            self.prior[key] = (float(global_p), float(global_dp))
          -        else:
          -            raise ValueError("prior must be one of {}".format(self.prior.keys()))
          -
          -
          -
          -def subgrid(self, xc, yc, window) -
          -
          -

          Extract a subgrid from the data at a window around -the point (xc,yc)

          -

          Parameters

          -

          xc -: x coordinate -yc -: y coordinate -window -: size of window in metres

          -

          Returns

          -

          data -: subgrid

          -
          -Source code -
          def subgrid(self, xc, yc, window):
          -    """
          -    Extract a subgrid from the data at a window around
          -    the point (xc,yc)
          -    
          -    Parameters
          -    ----------
          -     xc      : x coordinate
          -     yc      : y coordinate
          -     window  : size of window in metres
          -
          -    Returns
          -    -------
          -     data    : subgrid
          -    """
          -    if window > self.max_window:
          -        raise ValueError("Max window size is {}".format(self.max_window))
          -
          -    return super(CurieParallel, self).subgrid(window, xc, yc)
          -
          -
          -
          -def sync(self, vector) -
          -
          -

          Synchronise a local vector across all processors

          -
          -Source code -
          def sync(self, vector):
          -    """
          -    Synchronise a local vector across all processors
          -    """
          -    self.lvec.setArray(vector)
          -    self.dm.localToGlobal(self.lvec, self.gvec)
          -    self.dm.globalToLocal(self.gvec, self.lvec)
          -    return self.lvec.array.copy()
          -
          -
          -
          -

          Inherited members

          - -
          -
          -
          -
          - -
          - - - - - \ No newline at end of file diff --git a/docs/therm.html b/docs/therm.html deleted file mode 100644 index c4688ea..0000000 --- a/docs/therm.html +++ /dev/null @@ -1,1216 +0,0 @@ - - - - - - -pycurious.therm API documentation - - - - - - - - - -
          -
          -
          -

          Module pycurious.therm

          -
          -
          -

          Copyright 2018 Ben Mather, Robert Delhaye

          -

          This file is part of PyCurious.

          -

          PyCurious is free software: you can redistribute it and/or modify -it under the terms of the GNU Lesser General Public License as published by -the Free Software Foundation, either version 3 of the License, or any later version.

          -

          PyCurious is distributed in the hope that it will be useful, -but WITHOUT ANY WARRANTY; without even the implied warranty of -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. -See the -GNU Lesser General Public License for more details.

          -

          You should have received a copy of the GNU Lesser General Public License -along with PyCurious. -If not, see http://www.gnu.org/licenses/.

          -
          -Source code -
          """
          -Copyright 2018 Ben Mather, Robert Delhaye
          -
          -This file is part of PyCurious.
          -
          -PyCurious is free software: you can redistribute it and/or modify
          -it under the terms of the GNU Lesser General Public License as published by
          -the Free Software Foundation, either version 3 of the License, or any later version.
          -
          -PyCurious is distributed in the hope that it will be useful,
          -but WITHOUT ANY WARRANTY; without even the implied warranty of
          -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
          -GNU Lesser General Public License for more details.
          -
          -You should have received a copy of the GNU Lesser General Public License
          -along with PyCurious.  If not, see <http://www.gnu.org/licenses/>.
          -"""
          -
          -import numpy as np
          -from scipy import sparse
          -from scipy.sparse.linalg import spsolve
          -from multiprocessing import Pool, Process, Queue, cpu_count
          -
          -try: range=xrange
          -except: pass
          -
          -
          -class CurieTherm(object):
          -    """
          -    Implicit 1d solver for the steady-state heat equation
          -    over a structured grid using sparse matrices.
          -
          -    Parameters
          -    ----------
          -     minZ : float, minimum Cartesian coordinate
          -     maxZ : float, maximum Cartesian coordinate
          -     resZ : int, resolution in the z direction
          -     kwargs : dict, keyword arguments to pass to control
          -       optional functionality e.g.
          -       - stencil_width=int : number of node neighbours to
          -           include in each matrix row
          -
          -    Attributes
          -    ----------
          -     diffusivity  : float shape(n,) thermal conductivity field
          -     heat_sources : float shape(n,) heat source field
          -     temperature  : float shape(n,) temperature field
          -
          -     npoints      : int, number of nodes in the mesh
          -     sizes        : (int,int) dimensions of the sparse matrix
          -     
          -    """
          -
          -    def __init__(self, minZ, maxZ, resZ, **kwargs):
          -
          -        self.npoints = resZ
          -        self.extent = (minZ, maxZ)
          -        self.coords = np.linspace(minZ, maxZ, resZ)
          -        self.nodes = np.arange(0, resZ, dtype=np.int)
          -        self.sizes = (resZ, resZ)
          -
          -        width = kwargs.pop('stencil_width', 1)
          -        self.stencil_width = 2*width + 1
          -
          -        closure = [(0,-2), (2,0), (1,-1)]
          -        self.closure = self._create_closure_object(closure)
          -
          -
          -        self._initialise_COO_vectors()
          -        self._initialise_boundary_dictionary()
          -        self.diffusivity  = np.zeros(resZ)
          -        self.heat_sources = np.zeros(resZ)
          -        self.temperature  = np.zeros(resZ)
          -
          -
          -    def _initialise_COO_vectors(self):
          -
          -        nn = self.npoints
          -
          -        index = np.empty(nn + 2, dtype=np.int)
          -        index.fill(-1)
          -        self.index = index
          -
          -        self.rows = np.empty((self.stencil_width, nn), dtype=np.int)
          -        self.cols = np.empty((self.stencil_width, nn), dtype=np.int)
          -        self.vals = np.empty((self.stencil_width, nn))
          -
          -
          -    def _initialise_boundary_dictionary(self):
          -
          -        nn = self.npoints
          -        coords = self.coords
          -        minZ, maxZ = self.extent
          -
          -        # Setup boundary dictionary
          -        bc = dict()
          -
          -        m0 = coords == minZ
          -        m1 = coords == maxZ
          -        d0 = abs(coords[1] - coords[0])
          -        d1 = abs(coords[-1] - coords[-2])
          -
          -        bc["minZ"] = {"val": 0.0, "delta": d0, "flux": True, "mask": m0}
          -        bc["maxZ"] = {"val": 0.0, "delta": d1, "flux": True, "mask": m1}
          -
          -        self.bc = bc
          -        self.dirichlet_mask = np.zeros(nn, dtype=bool)
          -
          -
          -    def _create_closure_object(self, closure):
          -
          -        nn = self.npoints
          -        obj = [[0] for i in range(self.stencil_width)]
          -
          -        for i in range(0, self.stencil_width):
          -            # construct slicing object
          -            start, end = closure[i-j]
          -            obj[i] = slice(start, nn+end+2)
          -
          -        return obj
          -
          -
          -    def update_properties(self, diffusivity, heat_sources):
          -        """
          -        Update diffusivity and heat sources
          -        """
          -        self.diffusivity[:] = diffusivity
          -        self.heat_sources[:] = heat_sources
          -        return
          -
          -
          -    def boundary_condition(self, wall, val, flux=False):
          -        """
          -        Set the boundary conditions on each wall of the domain.
          -        By default each wall is a Dirichlet condition.
          -
          -        Parameters
          -        ----------
          -         wall : str, wall to assign bc - 'minZ' or 'maxZ'
          -         val  : float or array(n,) value(s) to assign to wall
          -         flux : bool, toggle type of boundary condition
          -           True = Neumann flux boundary condition
          -           False = Dirichlet boundary condition (default)
          -
          -        Notes
          -        -----
          -         If flux=True, positive val indicates a flux vector towards the centre
          -         of the domain.
          -
          -         val can be a vector with the same number of elements as the wall
          -        """
          -        wall = str(wall)
          -
          -        if wall in self.bc:
          -            self.bc[wall]["val"]  = np.array(val, copy=True)
          -            self.bc[wall]["flux"] = flux
          -            d = self.bc[wall]
          -
          -            mask = d['mask']
          -
          -            if flux:
          -                self.dirichlet_mask[mask] = False
          -                self.bc[wall]["val"] /= -d['delta']
          -            else:
          -                self.dirichlet_mask[mask] = True
          -
          -        else:
          -            raise ValueError("Wall should be one of {}".format(self.bc.keys()))
          -
          -
          -    def construct_matrix(self):
          -        """
          -        Construct a sparse coefficient matrix
          -        i.e. matrix A in AT = b
          -
          -        Notes
          -        -----
          -         We vectorise the 7-point stencil for fast matrix insertion.
          -         An extra border of dummy values around the domain allows for automatic
          -         Neumann (flux) boundary creation.
          -         These are stomped on if there are any Dirichlet conditions.
          -        """
          -
          -        nodes = self.nodes
          -        nn = self.npoints
          -
          -        index = self.index
          -
          -        rows = self.rows
          -        cols = self.cols
          -        vals = self.vals
          -
          -        dirichlet_mask = self.dirichlet_mask
          -        coords = self.coords.reshape(-1,1)
          -
          -        u = self.diffusivity
          -
          -        k = np.zeros(nn + 2)
          -        k[1:-1] = u
          -
          -        for i in range(0, self.stencil_width):
          -            obj = self.closure[i]
          -
          -            rows[i] = nodes
          -            cols[i] = index[obj].ravel()
          -
          -            distance = np.linalg.norm(coords[cols[i]] - coords, axis=1)
          -            distance[distance==0] = 1e-12 # protect against dividing by zero
          -            delta = 1.0/(2.0*distance**2)
          -
          -            vals[i] = delta*(k[obj] + u).ravel()
          -
          -
          -        # Dirichlet boundary conditions (duplicates are summed)
          -        cols[:,dirichlet_mask] = nodes[dirichlet_mask]
          -        vals[:,dirichlet_mask] = 0.0
          -
          -        # zero off-grid coordinates
          -        vals[cols < 0] = 0.0
          -
          -        # centre point
          -        vals[-1] = 0.0
          -        vals[-1][dirichlet_mask] = -1.0
          -
          -
          -        row = rows.ravel()
          -        col = cols.ravel()
          -        val = vals.ravel()
          -
          -
          -        # mask off-grid entries and sum duplicates
          -        mask = col >= 0
          -        row = row[mask]
          -        col = col[mask]
          -        val = val[mask]
          -
          -        mat = sparse.coo_matrix((val, (row, col)), shape=self.sizes).tocsr()
          -        mat.sum_duplicates()
          -        diag = np.ravel(mat.sum(axis=1))
          -        diag *= -1
          -        mat.setdiag(diag)
          -
          -        return mat
          -
          -
          -    def construct_rhs(self):
          -        """
          -        Construct the right-hand-side vector
          -        i.e. vector b in AT = b
          -
          -        Notes
          -        -----
          -         Boundary conditions are grabbed from the dictionary and
          -         summed to the rhs.
          -         Be careful of duplicate entries on the corners!!
          -        """
          -        
          -        rhs = -1.0*self.heat_sources
          -
          -        for wall in self.bc:
          -            val  = self.bc[wall]['val']
          -            flux = self.bc[wall]['flux']
          -            mask = self.bc[wall]['mask']
          -            if flux:
          -                rhs[mask] += val
          -            else:
          -                rhs[mask] = val
          -
          -        return rhs
          -
          -
          -    def solve(self, matrix=None, rhs=None):
          -        """
          -        Construct the matrix A and vector b in AT = b and solve for T
          -        (i.e. temperature field)
          -
          -        Arguments
          -        ---------
          -         matrix : (optional) scipy sparse matrix object
          -                 build using construct_matrix()
          -         rhs    : (optional) numpy right-hand-side vector
          -                 build using construct_rhs()
          -
          -        Returns
          -        -------
          -         sol    : 1d array shape(n,) temperature solution
          -
          -        Notes
          -        -----
          -         The solution to the system of linear equations AT = b is solved
          -         with spsolve in the scipy.sparse.linalg module
          -        """
          -        if matrix is None:
          -            matrix = self.construct_matrix()
          -        if rhs is None:
          -            rhs = self.construct_rhs()
          -        # res = self.temperature
          -
          -        T = spsolve(matrix, rhs)
          -        self.temperature[:] = T
          -
          -        return T
          -
          -
          -    def gradient(self, vector, **kwargs):
          -        """
          -        Calculate gradient of a vector
          -        
          -        Arguments
          -        ---------
          -         vector : 1d array of shape(n,)
          -
          -        Returns
          -        -------
          -         dvdz   : 1d array of shape(n,)
          -                 derivative of vector in z direction
          -        """
          -        return np.gradient(vector, self.coords, **kwargs)
          -
          -
          -    def heatflux(self):
          -        """
          -        Calculate the heat flux from the conductivity field
          -        and temperature solution
          -
          -        Returns
          -        -------
          -         qz  : 1d array shape(n,) heat flux vector
          -        """
          -
          -        T = self.temperature
          -        k = self.diffusivity
          -        divT = self.gradient(T)
          -        return -k*divT
          -
          -
          -    def isosurface(self, vector, isoval, interp='linear'):
          -        """
          -        Calculate an isosurface along the z axis
          -
          -        Parameters
          -        ----------
          -         vector : array, the same size as the mesh (n,)
          -         isoval : float, isosurface value
          -         interp : str, interpolation method can be either
          -            'nearest' - nearest neighbour interpolation
          -            'linear'  - linear interpolation
          -        
          -        Returns
          -        -------
          -         z_interp : isosurface
          -        """
          -        coords = self.coords
          -        sort_idx = np.abs(vector - isoval).argsort()    
          -        i0 = sort_idx[0]
          -        z0 = coords[i0]
          -
          -        if interp == 'linear':
          -            v0 = vector[i0]
          -            
          -            # identify next nearest node
          -            i1 = sort_idx[1]
          -            z1 = coords[i1]
          -            v1 = vector[i1]
          -
          -            vmin = min(v0,v1)
          -            vmax = max(v0,v1)
          -
          -            ratio = np.array([isoval, vmin, vmax])
          -            ratio -= ratio.min()
          -            ratio /= ratio.max()
          -            z_interp = ratio[0]*z1 + (1.0 - ratio[0])*z0
          -            return z_interp
          -        elif interp == 'nearest':
          -            return z0
          -        else:
          -            raise ValueError("enter a valid interp method: 'linear' or 'nearest'")
          -
          -
          -
          -
          -
          -
          -
          -
          -
          -

          Classes

          -
          -
          -class CurieTherm -(minZ, maxZ, resZ, **kwargs) -
          -
          -

          Implicit 1d solver for the steady-state heat equation -over a structured grid using sparse matrices.

          -

          Parameters

          -

          minZ : float, minimum Cartesian coordinate -maxZ : float, maximum Cartesian coordinate -resZ : int, resolution in the z direction -kwargs : dict, keyword arguments to pass to control -optional functionality e.g. -- stencil_width=int : number of node neighbours to -include in each matrix row

          -

          Attributes

          -

          diffusivity -: float shape(n,) thermal conductivity field -heat_sources : float shape(n,) heat source field -temperature -: float shape(n,) temperature field

          -

          npoints -: int, number of nodes in the mesh -sizes -: (int,int) dimensions of the sparse matrix

          -
          -Source code -
          class CurieTherm(object):
          -    """
          -    Implicit 1d solver for the steady-state heat equation
          -    over a structured grid using sparse matrices.
          -
          -    Parameters
          -    ----------
          -     minZ : float, minimum Cartesian coordinate
          -     maxZ : float, maximum Cartesian coordinate
          -     resZ : int, resolution in the z direction
          -     kwargs : dict, keyword arguments to pass to control
          -       optional functionality e.g.
          -       - stencil_width=int : number of node neighbours to
          -           include in each matrix row
          -
          -    Attributes
          -    ----------
          -     diffusivity  : float shape(n,) thermal conductivity field
          -     heat_sources : float shape(n,) heat source field
          -     temperature  : float shape(n,) temperature field
          -
          -     npoints      : int, number of nodes in the mesh
          -     sizes        : (int,int) dimensions of the sparse matrix
          -     
          -    """
          -
          -    def __init__(self, minZ, maxZ, resZ, **kwargs):
          -
          -        self.npoints = resZ
          -        self.extent = (minZ, maxZ)
          -        self.coords = np.linspace(minZ, maxZ, resZ)
          -        self.nodes = np.arange(0, resZ, dtype=np.int)
          -        self.sizes = (resZ, resZ)
          -
          -        width = kwargs.pop('stencil_width', 1)
          -        self.stencil_width = 2*width + 1
          -
          -        closure = [(0,-2), (2,0), (1,-1)]
          -        self.closure = self._create_closure_object(closure)
          -
          -
          -        self._initialise_COO_vectors()
          -        self._initialise_boundary_dictionary()
          -        self.diffusivity  = np.zeros(resZ)
          -        self.heat_sources = np.zeros(resZ)
          -        self.temperature  = np.zeros(resZ)
          -
          -
          -    def _initialise_COO_vectors(self):
          -
          -        nn = self.npoints
          -
          -        index = np.empty(nn + 2, dtype=np.int)
          -        index.fill(-1)
          -        self.index = index
          -
          -        self.rows = np.empty((self.stencil_width, nn), dtype=np.int)
          -        self.cols = np.empty((self.stencil_width, nn), dtype=np.int)
          -        self.vals = np.empty((self.stencil_width, nn))
          -
          -
          -    def _initialise_boundary_dictionary(self):
          -
          -        nn = self.npoints
          -        coords = self.coords
          -        minZ, maxZ = self.extent
          -
          -        # Setup boundary dictionary
          -        bc = dict()
          -
          -        m0 = coords == minZ
          -        m1 = coords == maxZ
          -        d0 = abs(coords[1] - coords[0])
          -        d1 = abs(coords[-1] - coords[-2])
          -
          -        bc["minZ"] = {"val": 0.0, "delta": d0, "flux": True, "mask": m0}
          -        bc["maxZ"] = {"val": 0.0, "delta": d1, "flux": True, "mask": m1}
          -
          -        self.bc = bc
          -        self.dirichlet_mask = np.zeros(nn, dtype=bool)
          -
          -
          -    def _create_closure_object(self, closure):
          -
          -        nn = self.npoints
          -        obj = [[0] for i in range(self.stencil_width)]
          -
          -        for i in range(0, self.stencil_width):
          -            # construct slicing object
          -            start, end = closure[i-j]
          -            obj[i] = slice(start, nn+end+2)
          -
          -        return obj
          -
          -
          -    def update_properties(self, diffusivity, heat_sources):
          -        """
          -        Update diffusivity and heat sources
          -        """
          -        self.diffusivity[:] = diffusivity
          -        self.heat_sources[:] = heat_sources
          -        return
          -
          -
          -    def boundary_condition(self, wall, val, flux=False):
          -        """
          -        Set the boundary conditions on each wall of the domain.
          -        By default each wall is a Dirichlet condition.
          -
          -        Parameters
          -        ----------
          -         wall : str, wall to assign bc - 'minZ' or 'maxZ'
          -         val  : float or array(n,) value(s) to assign to wall
          -         flux : bool, toggle type of boundary condition
          -           True = Neumann flux boundary condition
          -           False = Dirichlet boundary condition (default)
          -
          -        Notes
          -        -----
          -         If flux=True, positive val indicates a flux vector towards the centre
          -         of the domain.
          -
          -         val can be a vector with the same number of elements as the wall
          -        """
          -        wall = str(wall)
          -
          -        if wall in self.bc:
          -            self.bc[wall]["val"]  = np.array(val, copy=True)
          -            self.bc[wall]["flux"] = flux
          -            d = self.bc[wall]
          -
          -            mask = d['mask']
          -
          -            if flux:
          -                self.dirichlet_mask[mask] = False
          -                self.bc[wall]["val"] /= -d['delta']
          -            else:
          -                self.dirichlet_mask[mask] = True
          -
          -        else:
          -            raise ValueError("Wall should be one of {}".format(self.bc.keys()))
          -
          -
          -    def construct_matrix(self):
          -        """
          -        Construct a sparse coefficient matrix
          -        i.e. matrix A in AT = b
          -
          -        Notes
          -        -----
          -         We vectorise the 7-point stencil for fast matrix insertion.
          -         An extra border of dummy values around the domain allows for automatic
          -         Neumann (flux) boundary creation.
          -         These are stomped on if there are any Dirichlet conditions.
          -        """
          -
          -        nodes = self.nodes
          -        nn = self.npoints
          -
          -        index = self.index
          -
          -        rows = self.rows
          -        cols = self.cols
          -        vals = self.vals
          -
          -        dirichlet_mask = self.dirichlet_mask
          -        coords = self.coords.reshape(-1,1)
          -
          -        u = self.diffusivity
          -
          -        k = np.zeros(nn + 2)
          -        k[1:-1] = u
          -
          -        for i in range(0, self.stencil_width):
          -            obj = self.closure[i]
          -
          -            rows[i] = nodes
          -            cols[i] = index[obj].ravel()
          -
          -            distance = np.linalg.norm(coords[cols[i]] - coords, axis=1)
          -            distance[distance==0] = 1e-12 # protect against dividing by zero
          -            delta = 1.0/(2.0*distance**2)
          -
          -            vals[i] = delta*(k[obj] + u).ravel()
          -
          -
          -        # Dirichlet boundary conditions (duplicates are summed)
          -        cols[:,dirichlet_mask] = nodes[dirichlet_mask]
          -        vals[:,dirichlet_mask] = 0.0
          -
          -        # zero off-grid coordinates
          -        vals[cols < 0] = 0.0
          -
          -        # centre point
          -        vals[-1] = 0.0
          -        vals[-1][dirichlet_mask] = -1.0
          -
          -
          -        row = rows.ravel()
          -        col = cols.ravel()
          -        val = vals.ravel()
          -
          -
          -        # mask off-grid entries and sum duplicates
          -        mask = col >= 0
          -        row = row[mask]
          -        col = col[mask]
          -        val = val[mask]
          -
          -        mat = sparse.coo_matrix((val, (row, col)), shape=self.sizes).tocsr()
          -        mat.sum_duplicates()
          -        diag = np.ravel(mat.sum(axis=1))
          -        diag *= -1
          -        mat.setdiag(diag)
          -
          -        return mat
          -
          -
          -    def construct_rhs(self):
          -        """
          -        Construct the right-hand-side vector
          -        i.e. vector b in AT = b
          -
          -        Notes
          -        -----
          -         Boundary conditions are grabbed from the dictionary and
          -         summed to the rhs.
          -         Be careful of duplicate entries on the corners!!
          -        """
          -        
          -        rhs = -1.0*self.heat_sources
          -
          -        for wall in self.bc:
          -            val  = self.bc[wall]['val']
          -            flux = self.bc[wall]['flux']
          -            mask = self.bc[wall]['mask']
          -            if flux:
          -                rhs[mask] += val
          -            else:
          -                rhs[mask] = val
          -
          -        return rhs
          -
          -
          -    def solve(self, matrix=None, rhs=None):
          -        """
          -        Construct the matrix A and vector b in AT = b and solve for T
          -        (i.e. temperature field)
          -
          -        Arguments
          -        ---------
          -         matrix : (optional) scipy sparse matrix object
          -                 build using construct_matrix()
          -         rhs    : (optional) numpy right-hand-side vector
          -                 build using construct_rhs()
          -
          -        Returns
          -        -------
          -         sol    : 1d array shape(n,) temperature solution
          -
          -        Notes
          -        -----
          -         The solution to the system of linear equations AT = b is solved
          -         with spsolve in the scipy.sparse.linalg module
          -        """
          -        if matrix is None:
          -            matrix = self.construct_matrix()
          -        if rhs is None:
          -            rhs = self.construct_rhs()
          -        # res = self.temperature
          -
          -        T = spsolve(matrix, rhs)
          -        self.temperature[:] = T
          -
          -        return T
          -
          -
          -    def gradient(self, vector, **kwargs):
          -        """
          -        Calculate gradient of a vector
          -        
          -        Arguments
          -        ---------
          -         vector : 1d array of shape(n,)
          -
          -        Returns
          -        -------
          -         dvdz   : 1d array of shape(n,)
          -                 derivative of vector in z direction
          -        """
          -        return np.gradient(vector, self.coords, **kwargs)
          -
          -
          -    def heatflux(self):
          -        """
          -        Calculate the heat flux from the conductivity field
          -        and temperature solution
          -
          -        Returns
          -        -------
          -         qz  : 1d array shape(n,) heat flux vector
          -        """
          -
          -        T = self.temperature
          -        k = self.diffusivity
          -        divT = self.gradient(T)
          -        return -k*divT
          -
          -
          -    def isosurface(self, vector, isoval, interp='linear'):
          -        """
          -        Calculate an isosurface along the z axis
          -
          -        Parameters
          -        ----------
          -         vector : array, the same size as the mesh (n,)
          -         isoval : float, isosurface value
          -         interp : str, interpolation method can be either
          -            'nearest' - nearest neighbour interpolation
          -            'linear'  - linear interpolation
          -        
          -        Returns
          -        -------
          -         z_interp : isosurface
          -        """
          -        coords = self.coords
          -        sort_idx = np.abs(vector - isoval).argsort()    
          -        i0 = sort_idx[0]
          -        z0 = coords[i0]
          -
          -        if interp == 'linear':
          -            v0 = vector[i0]
          -            
          -            # identify next nearest node
          -            i1 = sort_idx[1]
          -            z1 = coords[i1]
          -            v1 = vector[i1]
          -
          -            vmin = min(v0,v1)
          -            vmax = max(v0,v1)
          -
          -            ratio = np.array([isoval, vmin, vmax])
          -            ratio -= ratio.min()
          -            ratio /= ratio.max()
          -            z_interp = ratio[0]*z1 + (1.0 - ratio[0])*z0
          -            return z_interp
          -        elif interp == 'nearest':
          -            return z0
          -        else:
          -            raise ValueError("enter a valid interp method: 'linear' or 'nearest'")
          -
          -

          Methods

          -
          -
          -def boundary_condition(self, wall, val, flux=False) -
          -
          -

          Set the boundary conditions on each wall of the domain. -By default each wall is a Dirichlet condition.

          -

          Parameters

          -

          wall : str, wall to assign bc - 'minZ' or 'maxZ' -val -: float or array(n,) value(s) to assign to wall -flux : bool, toggle type of boundary condition -True = Neumann flux boundary condition -False = Dirichlet boundary condition (default)

          -

          Notes

          -

          If flux=True, positive val indicates a flux vector towards the centre -of the domain.

          -

          val can be a vector with the same number of elements as the wall

          -
          -Source code -
          def boundary_condition(self, wall, val, flux=False):
          -    """
          -    Set the boundary conditions on each wall of the domain.
          -    By default each wall is a Dirichlet condition.
          -
          -    Parameters
          -    ----------
          -     wall : str, wall to assign bc - 'minZ' or 'maxZ'
          -     val  : float or array(n,) value(s) to assign to wall
          -     flux : bool, toggle type of boundary condition
          -       True = Neumann flux boundary condition
          -       False = Dirichlet boundary condition (default)
          -
          -    Notes
          -    -----
          -     If flux=True, positive val indicates a flux vector towards the centre
          -     of the domain.
          -
          -     val can be a vector with the same number of elements as the wall
          -    """
          -    wall = str(wall)
          -
          -    if wall in self.bc:
          -        self.bc[wall]["val"]  = np.array(val, copy=True)
          -        self.bc[wall]["flux"] = flux
          -        d = self.bc[wall]
          -
          -        mask = d['mask']
          -
          -        if flux:
          -            self.dirichlet_mask[mask] = False
          -            self.bc[wall]["val"] /= -d['delta']
          -        else:
          -            self.dirichlet_mask[mask] = True
          -
          -    else:
          -        raise ValueError("Wall should be one of {}".format(self.bc.keys()))
          -
          -
          -
          -def construct_matrix(self) -
          -
          -

          Construct a sparse coefficient matrix -i.e. matrix A in AT = b

          -

          Notes

          -

          We vectorise the 7-point stencil for fast matrix insertion. -An extra border of dummy values around the domain allows for automatic -Neumann (flux) boundary creation. -These are stomped on if there are any Dirichlet conditions.

          -
          -Source code -
          def construct_matrix(self):
          -    """
          -    Construct a sparse coefficient matrix
          -    i.e. matrix A in AT = b
          -
          -    Notes
          -    -----
          -     We vectorise the 7-point stencil for fast matrix insertion.
          -     An extra border of dummy values around the domain allows for automatic
          -     Neumann (flux) boundary creation.
          -     These are stomped on if there are any Dirichlet conditions.
          -    """
          -
          -    nodes = self.nodes
          -    nn = self.npoints
          -
          -    index = self.index
          -
          -    rows = self.rows
          -    cols = self.cols
          -    vals = self.vals
          -
          -    dirichlet_mask = self.dirichlet_mask
          -    coords = self.coords.reshape(-1,1)
          -
          -    u = self.diffusivity
          -
          -    k = np.zeros(nn + 2)
          -    k[1:-1] = u
          -
          -    for i in range(0, self.stencil_width):
          -        obj = self.closure[i]
          -
          -        rows[i] = nodes
          -        cols[i] = index[obj].ravel()
          -
          -        distance = np.linalg.norm(coords[cols[i]] - coords, axis=1)
          -        distance[distance==0] = 1e-12 # protect against dividing by zero
          -        delta = 1.0/(2.0*distance**2)
          -
          -        vals[i] = delta*(k[obj] + u).ravel()
          -
          -
          -    # Dirichlet boundary conditions (duplicates are summed)
          -    cols[:,dirichlet_mask] = nodes[dirichlet_mask]
          -    vals[:,dirichlet_mask] = 0.0
          -
          -    # zero off-grid coordinates
          -    vals[cols < 0] = 0.0
          -
          -    # centre point
          -    vals[-1] = 0.0
          -    vals[-1][dirichlet_mask] = -1.0
          -
          -
          -    row = rows.ravel()
          -    col = cols.ravel()
          -    val = vals.ravel()
          -
          -
          -    # mask off-grid entries and sum duplicates
          -    mask = col >= 0
          -    row = row[mask]
          -    col = col[mask]
          -    val = val[mask]
          -
          -    mat = sparse.coo_matrix((val, (row, col)), shape=self.sizes).tocsr()
          -    mat.sum_duplicates()
          -    diag = np.ravel(mat.sum(axis=1))
          -    diag *= -1
          -    mat.setdiag(diag)
          -
          -    return mat
          -
          -
          -
          -def construct_rhs(self) -
          -
          -

          Construct the right-hand-side vector -i.e. vector b in AT = b

          -

          Notes

          -

          Boundary conditions are grabbed from the dictionary and -summed to the rhs. -Be careful of duplicate entries on the corners!!

          -
          -Source code -
          def construct_rhs(self):
          -    """
          -    Construct the right-hand-side vector
          -    i.e. vector b in AT = b
          -
          -    Notes
          -    -----
          -     Boundary conditions are grabbed from the dictionary and
          -     summed to the rhs.
          -     Be careful of duplicate entries on the corners!!
          -    """
          -    
          -    rhs = -1.0*self.heat_sources
          -
          -    for wall in self.bc:
          -        val  = self.bc[wall]['val']
          -        flux = self.bc[wall]['flux']
          -        mask = self.bc[wall]['mask']
          -        if flux:
          -            rhs[mask] += val
          -        else:
          -            rhs[mask] = val
          -
          -    return rhs
          -
          -
          -
          -def gradient(self, vector, **kwargs) -
          -
          -

          Calculate gradient of a vector

          -

          Arguments

          -

          vector : 1d array of shape(n,)

          -

          Returns

          -

          dvdz -: 1d array of shape(n,) -derivative of vector in z direction

          -
          -Source code -
          def gradient(self, vector, **kwargs):
          -    """
          -    Calculate gradient of a vector
          -    
          -    Arguments
          -    ---------
          -     vector : 1d array of shape(n,)
          -
          -    Returns
          -    -------
          -     dvdz   : 1d array of shape(n,)
          -             derivative of vector in z direction
          -    """
          -    return np.gradient(vector, self.coords, **kwargs)
          -
          -
          -
          -def heatflux(self) -
          -
          -

          Calculate the heat flux from the conductivity field -and temperature solution

          -

          Returns

          -

          qz -: 1d array shape(n,) heat flux vector

          -
          -Source code -
          def heatflux(self):
          -    """
          -    Calculate the heat flux from the conductivity field
          -    and temperature solution
          -
          -    Returns
          -    -------
          -     qz  : 1d array shape(n,) heat flux vector
          -    """
          -
          -    T = self.temperature
          -    k = self.diffusivity
          -    divT = self.gradient(T)
          -    return -k*divT
          -
          -
          -
          -def isosurface(self, vector, isoval, interp='linear') -
          -
          -

          Calculate an isosurface along the z axis

          -

          Parameters

          -

          vector : array, the same size as the mesh (n,) -isoval : float, isosurface value -interp : str, interpolation method can be either -'nearest' - nearest neighbour interpolation -'linear' -- linear interpolation

          -

          Returns

          -

          z_interp : isosurface

          -
          -Source code -
          def isosurface(self, vector, isoval, interp='linear'):
          -    """
          -    Calculate an isosurface along the z axis
          -
          -    Parameters
          -    ----------
          -     vector : array, the same size as the mesh (n,)
          -     isoval : float, isosurface value
          -     interp : str, interpolation method can be either
          -        'nearest' - nearest neighbour interpolation
          -        'linear'  - linear interpolation
          -    
          -    Returns
          -    -------
          -     z_interp : isosurface
          -    """
          -    coords = self.coords
          -    sort_idx = np.abs(vector - isoval).argsort()    
          -    i0 = sort_idx[0]
          -    z0 = coords[i0]
          -
          -    if interp == 'linear':
          -        v0 = vector[i0]
          -        
          -        # identify next nearest node
          -        i1 = sort_idx[1]
          -        z1 = coords[i1]
          -        v1 = vector[i1]
          -
          -        vmin = min(v0,v1)
          -        vmax = max(v0,v1)
          -
          -        ratio = np.array([isoval, vmin, vmax])
          -        ratio -= ratio.min()
          -        ratio /= ratio.max()
          -        z_interp = ratio[0]*z1 + (1.0 - ratio[0])*z0
          -        return z_interp
          -    elif interp == 'nearest':
          -        return z0
          -    else:
          -        raise ValueError("enter a valid interp method: 'linear' or 'nearest'")
          -
          -
          -
          -def solve(self, matrix=None, rhs=None) -
          -
          -

          Construct the matrix A and vector b in AT = b and solve for T -(i.e. temperature field)

          -

          Arguments

          -

          matrix : (optional) scipy sparse matrix object -build using construct_matrix() -rhs -: (optional) numpy right-hand-side vector -build using construct_rhs()

          -

          Returns

          -

          sol -: 1d array shape(n,) temperature solution

          -

          Notes

          -

          The solution to the system of linear equations AT = b is solved -with spsolve in the scipy.sparse.linalg module

          -
          -Source code -
          def solve(self, matrix=None, rhs=None):
          -    """
          -    Construct the matrix A and vector b in AT = b and solve for T
          -    (i.e. temperature field)
          -
          -    Arguments
          -    ---------
          -     matrix : (optional) scipy sparse matrix object
          -             build using construct_matrix()
          -     rhs    : (optional) numpy right-hand-side vector
          -             build using construct_rhs()
          -
          -    Returns
          -    -------
          -     sol    : 1d array shape(n,) temperature solution
          -
          -    Notes
          -    -----
          -     The solution to the system of linear equations AT = b is solved
          -     with spsolve in the scipy.sparse.linalg module
          -    """
          -    if matrix is None:
          -        matrix = self.construct_matrix()
          -    if rhs is None:
          -        rhs = self.construct_rhs()
          -    # res = self.temperature
          -
          -    T = spsolve(matrix, rhs)
          -    self.temperature[:] = T
          -
          -    return T
          -
          -
          -
          -def update_properties(self, diffusivity, heat_sources) -
          -
          -

          Update diffusivity and heat sources

          -
          -Source code -
          def update_properties(self, diffusivity, heat_sources):
          -    """
          -    Update diffusivity and heat sources
          -    """
          -    self.diffusivity[:] = diffusivity
          -    self.heat_sources[:] = heat_sources
          -    return
          -
          -
          -
          -
          -
          -
          -
          - -
          - - - - - \ No newline at end of file From 5271a66b3dcf5ef8e6e896070a37b13e868163eb Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Tue, 4 Jun 2019 19:41:26 +1000 Subject: [PATCH 061/170] We have to create docs folder to put the docs in... --- .travis.yml | 1 + 1 file changed, 1 insertion(+) diff --git a/.travis.yml b/.travis.yml index 9551fdb..0e4658c 100644 --- a/.travis.yml +++ b/.travis.yml @@ -12,6 +12,7 @@ install: script: # generate the docs + - mkdir docs - cd docs - pdoc --html -o . --force pycurious - mv pycurious/*.html . From 0acb6dfcd67e1e9a361415b5a7a2c50e814f79ca Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Thu, 6 Jun 2019 18:16:21 +1000 Subject: [PATCH 062/170] try testing on diffferent o/s --- .travis.yml | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/.travis.yml b/.travis.yml index 0e4658c..55e9541 100644 --- a/.travis.yml +++ b/.travis.yml @@ -1,5 +1,7 @@ -dist: bionic language: python +os: + - linux + - osx python: - "3.5" - "3.6" From 433ee9c22f3d7322a0cf13f83196cb8571771837 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Thu, 6 Jun 2019 18:43:40 +1000 Subject: [PATCH 063/170] More elaborate travis build system --- .travis.yml | 36 ++++++++++++++++++++++++++++-------- 1 file changed, 28 insertions(+), 8 deletions(-) diff --git a/.travis.yml b/.travis.yml index 55e9541..f4acf1c 100644 --- a/.travis.yml +++ b/.travis.yml @@ -1,12 +1,31 @@ language: python -os: - - linux - - osx -python: - - "3.5" - - "3.6" - - "3.7" +# define global environment variables +env: + global: + -DEPLOY_DOCS=false + -DEPLOY_PYPI=false + +matrix: + include: + - os: linux + dist: trusty + python: 3.5 + env: + - DEPLOY_DOCS=true + - DEPLOY_PYPI=true + - os: linux + dist: bionic + python: + - "3.5" + - "3.6" + - "3.7" + - os: osx + osx_image: xcode10.2 + python: + - "3.5" + - "3.6" + - "3.7" install: - pip3 install Cython numpy scipy pytest git+https://github.com/lmoresi/pdoc.git @@ -18,8 +37,8 @@ script: - cd docs - pdoc --html -o . --force pycurious - mv pycurious/*.html . - - rm -rf pycurious/ - cd ../ + - rm -rf docs/ deploy: provider: pages @@ -28,5 +47,6 @@ deploy: keep_history: true on: branch: master + condition: '$DEPLOY_DOCS == "true"' verbose: true local_dir: docs/ From 3e4f95f014a2e00ef6fbc3c1b13412b0c962baf2 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Thu, 6 Jun 2019 18:48:20 +1000 Subject: [PATCH 064/170] Multiple python nestings do not work --- .travis.yml | 12 +++--------- 1 file changed, 3 insertions(+), 9 deletions(-) diff --git a/.travis.yml b/.travis.yml index f4acf1c..7834289 100644 --- a/.travis.yml +++ b/.travis.yml @@ -16,16 +16,10 @@ matrix: - DEPLOY_PYPI=true - os: linux dist: bionic - python: - - "3.5" - - "3.6" - - "3.7" + python: 3.7 - os: osx osx_image: xcode10.2 - python: - - "3.5" - - "3.6" - - "3.7" + python: 3.5 install: - pip3 install Cython numpy scipy pytest git+https://github.com/lmoresi/pdoc.git @@ -37,8 +31,8 @@ script: - cd docs - pdoc --html -o . --force pycurious - mv pycurious/*.html . + - rm -rf pycurious/ - cd ../ - - rm -rf docs/ deploy: provider: pages From f0d528a2fa768381631cea8eb415162fc5629806 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Thu, 6 Jun 2019 18:53:00 +1000 Subject: [PATCH 065/170] update osx to python3.7 --- .travis.yml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/.travis.yml b/.travis.yml index 7834289..cfdfe47 100644 --- a/.travis.yml +++ b/.travis.yml @@ -19,7 +19,7 @@ matrix: python: 3.7 - os: osx osx_image: xcode10.2 - python: 3.5 + python: 3.7 install: - pip3 install Cython numpy scipy pytest git+https://github.com/lmoresi/pdoc.git From bf2d9b98d27b85816ba80bc95e8df90292c52896 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Thu, 6 Jun 2019 18:58:34 +1000 Subject: [PATCH 066/170] OSX doesn't come with python installed - why!?!? --- .travis.yml | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/.travis.yml b/.travis.yml index cfdfe47..88e0a02 100644 --- a/.travis.yml +++ b/.travis.yml @@ -21,6 +21,10 @@ matrix: osx_image: xcode10.2 python: 3.7 +before_install: + - if [ "$TRAVIS_OS_NAME" = "osx" ]; then brew update ; fi + - if [ "$TRAVIS_OS_NAME" = "osx" ]; then brew install python --universal --framework ; fi + install: - pip3 install Cython numpy scipy pytest git+https://github.com/lmoresi/pdoc.git - pip3 install -e . From 4749717933b08d02153c3eb4f5a961c887d0da87 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Thu, 6 Jun 2019 19:03:25 +1000 Subject: [PATCH 067/170] Try making osx language generic --- .travis.yml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/.travis.yml b/.travis.yml index 88e0a02..d7efca9 100644 --- a/.travis.yml +++ b/.travis.yml @@ -19,7 +19,7 @@ matrix: python: 3.7 - os: osx osx_image: xcode10.2 - python: 3.7 + language: generic before_install: - if [ "$TRAVIS_OS_NAME" = "osx" ]; then brew update ; fi From cc25ecd184479c9f9c14c4dd5927a538260f73fc Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Thu, 6 Jun 2019 19:09:24 +1000 Subject: [PATCH 068/170] I think I got it this time --- .travis.yml | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/.travis.yml b/.travis.yml index d7efca9..275dfb0 100644 --- a/.travis.yml +++ b/.travis.yml @@ -23,11 +23,11 @@ matrix: before_install: - if [ "$TRAVIS_OS_NAME" = "osx" ]; then brew update ; fi - - if [ "$TRAVIS_OS_NAME" = "osx" ]; then brew install python --universal --framework ; fi + - if [ "$TRAVIS_OS_NAME" = "osx" ]; then brew install python3 ; fi install: - - pip3 install Cython numpy scipy pytest git+https://github.com/lmoresi/pdoc.git - - pip3 install -e . + - python3 -m pip install Cython numpy scipy pytest git+https://github.com/lmoresi/pdoc.git + - python3 -m pip install -e . script: # generate the docs From 3cae9ccafeb7465a6551a0c64c6893fad648b269 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Thu, 6 Jun 2019 23:39:40 +1000 Subject: [PATCH 069/170] First iteration of JOSS paper --- paper/paper.md | 66 ++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 66 insertions(+) create mode 100644 paper/paper.md diff --git a/paper/paper.md b/paper/paper.md new file mode 100644 index 0000000..b121955 --- /dev/null +++ b/paper/paper.md @@ -0,0 +1,66 @@ +--- +title: 'PyCurious: A Python module for computing the Curie depth from the magnetic anomaly.' +tags: + - Python + - Curie depth + - magnetism + - magnetic anomaly + - Bayesian inference +authors: + - name: Ben Mather + orcid: 0000-0003-3566-1557 + affiliation: "1,2" # (Multiple affiliations must be quoted) + - name: Robert Delhaye + orcid: 0000-0000-0000-0000 + affiliation: "2" +affiliations: + - name: School of Geoscience, The University of Sydney + index: 1 + - name: School of Cosmic Physics, Dublin Institute for Advanced Studies + index: 2 +date: 30 April 2019 +bibliography: paper.bib +--- + +![Figure](figure.png) + +**Figure 1.** Samples meshes on the sphere produced by `pycurious` based on the octahedron with added points at the face centroids (far left), and the icosahedron with with face points (left). An icosahedron grid with refinement in regions where ocean age-grid information is available [@MullerEtAl2008], and an icosahedral mesh refined to create a smooth heat-map of seismic activity and average earthquake depth from a global catalogue of earthquakes of magnitude > 5.5 since 1990 from the IRIS online catalogue + +# Summary + +Magnetic data is one of the most prevelant geophysical datasets available on the surface of the Earth. Curie depth is the depth at which rocks lose their magnetism. The most prevalent magnetic mineral is magnetite, which has a Curie point of 580°C, thus the Curie depth is often interpreted as the 580°C isotherm. Current methods to derive Curie depth first compute the (fast) Fourier transform over a square window of a magnetic anomaly that has been reduced to the pole. The depth and thickness of magnetic sources is estimated from the slope of the radial power spectrum. + +Our package, `pycurious`, is a Python-based implements the Tanaka et al. (1999) and Bouligand et al. (2009) methods for computing the thickness of a buried magnetic source. The former selects portions of the radial power spectrum in the low and high frequency domain to compute the depth of magneic sources, while the latter fits an analytical solution to the entire power spectrum. We cast the Bouligand et al. (2009) method within a Bayesian framwork to estimate the uncertainty of Curie depth calculations. + +`pycurious` is an object-oriented package that accepts grids of the Earth's magnetic anomaly and computes the Curie depth using a specified window size. The computation is distributed across all available processors to improve efficiency over large study areas. A mapping module includes a set of fucntions that help to wrangle maps of the magnetic anomaly into a useable form for `pycurious`. + +`pycurious` includes the following functionality: + +- Importing and exporting GeoTiffs +- Converting between geospatial coordinate reference systems +- Selection of window sizes over which to compute Curie depth +- Parallel computation of curie depth across computing resources +- Bayesian inversion framework and sensitivity analysis + + +## Documentation + +`pycurious` is bundled with a linked collection of jupyter notebooks that can act as a user guide and an introduction to the package. The notebooks are split into matching sets for frequentist and Bayesian estimates of Curie depth. The notebooks cover: + +- Plotting the radial and azimuthal power spectrum +- Computing Curie depth from a synthetic magnetic anomaly +- Exploring parameter sensitivity +- Posing the inverse problem and objective function +- Mapping Curie depth using the EMAG2 magnetic anomaly dataset + +All documentation can be accessed from within the module via a python function that installs the notebooks at a filesystem location specified by the user at run time. + +## Installation, Dependencies and Usage + +`pycurious` requires `numpy` and `Cython` to compile C routines that are included with the distribution. The documentation is supplied in the form of jupyter notebooks (the jupyter environment is a dependency) which also have optional dependencies for the `cartopy` mapping package. `pycurious` and all python dependencies can be installed through the pypi.org `pip` package. However, several of the dependencies for `cartopy` may cause problems for inexperienced users. We therefore provided a fully build docker image and a deployment of the documentation / examples on [mybinder.org](https://mybinder.org/v2/gh/brmather/pycurious/binder?filepath=Notebooks%2F0-StartHere.ipynb) + +# Acknowledgements + +Development of `pycurious` was inspired from [`pycpd`](https://github.com/groupeLIAMG/pycpd) and [`fatiando a terra`](https://github.com/fatiando/fatiando). + +# References From 63aa7af29a5393ad4bd1be0971647ab5861f3635 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Thu, 6 Jun 2019 23:45:08 +1000 Subject: [PATCH 070/170] updated Dockerfile --- Docker/Dockerfile | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) diff --git a/Docker/Dockerfile b/Docker/Dockerfile index f899d9b..4775efe 100644 --- a/Docker/Dockerfile +++ b/Docker/Dockerfile @@ -11,10 +11,14 @@ FROM ${FROMIMG_ARG} USER root WORKDIR /home/jovyan/ +RUN python3 -m pip install --no-cache-dir --upgrade \ + jupyter \ + pytest + ### PyCurious - Notebooks ENV MODULE_DIR="pycurious-src" -ADD --chown=jovyan:jovyan $MODULE_DIR $MODULE_DIR +ADD --chown=jovyan:jovyan . / pycurious-src/ RUN cd $MODULE_DIR && python3 -m pip install --no-cache-dir --upgrade --no-deps . RUN ipython3 -c 'import pycurious; pycurious.documentation.install_documentation(path="Notebooks")' From bed4551b994d58b224d0a83c3a56bbccbafa0185 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Sat, 15 Jun 2019 12:18:06 +1000 Subject: [PATCH 071/170] Add download functionality To pull EMAG2v3 from Zenodo --- Docker/Dockerfile | 3 +- README.md | 2 + pycurious/__init__.py | 7 +-- pycurious/download.py | 133 ++++++++++++++++++++++++++++++++++++++++++ setup.py | 55 +++++++++++++++-- 5 files changed, 188 insertions(+), 12 deletions(-) create mode 100644 pycurious/download.py diff --git a/Docker/Dockerfile b/Docker/Dockerfile index 4775efe..a2ce312 100644 --- a/Docker/Dockerfile +++ b/Docker/Dockerfile @@ -13,7 +13,8 @@ WORKDIR /home/jovyan/ RUN python3 -m pip install --no-cache-dir --upgrade \ jupyter \ - pytest + pytest \ + git+https://github.com/lmoresi/pdoc.git ### PyCurious - Notebooks diff --git a/README.md b/README.md index 390cb00..74cb3b5 100644 --- a/README.md +++ b/README.md @@ -2,6 +2,8 @@ [![Docker Cloud Automated build](https://img.shields.io/docker/cloud/automated/brmather/pycurious.svg)](https://hub.docker.com/r/brmather/pycurious) [![PyPI](https://img.shields.io/pypi/v/pycurious.svg)](https://pypi.org/project/pycurious/) +[![DOI](https://zenodo.org/badge/123281222.svg)](https://zenodo.org/badge/latestdoi/123281222) +[![Build Status](https://travis-ci.org/brmather/pycurious.svg?branch=master)](https://travis-ci.org/brmather/pycurious) Magnetic data is one of the most common geophysics datasets available on the surface of the Earth. Curie depth is the depth at which rocks lose their magnetism. The most prevalent magnetic mineral is magnetite, which has a Curie point of 580C, thus the Curie depth is often interpreted as the 580C isotherm. diff --git a/pycurious/__init__.py b/pycurious/__init__.py index 9aeb2f7..51783ff 100644 --- a/pycurious/__init__.py +++ b/pycurious/__init__.py @@ -20,8 +20,5 @@ from .documentation import install_documentation from .grid import CurieGrid, bouligand2009, tanaka1999, maus1995, ComputeTanaka from .optimise import CurieOptimise -from .mapping import transform_coordinates -from .mapping import convert_extent -from .mapping import trim -from .mapping import grid -from .mapping import import_geotiff \ No newline at end of file +from . import mapping +from . import download \ No newline at end of file diff --git a/pycurious/download.py b/pycurious/download.py new file mode 100644 index 0000000..bec09d5 --- /dev/null +++ b/pycurious/download.py @@ -0,0 +1,133 @@ +""" +Copyright 2018 Ben Mather, Robert Delhaye + +This file is part of PyCurious. + +PyCurious is free software: you can redistribute it and/or modify +it under the terms of the GNU Lesser General Public License as published by +the Free Software Foundation, either version 3 of the License, or any later version. + +PyCurious is distributed in the hope that it will be useful, +but WITHOUT ANY WARRANTY; without even the implied warranty of +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +GNU Lesser General Public License for more details. + +You should have received a copy of the GNU Lesser General Public License +along with PyCurious. If not, see . +""" + +## Here are some functions to download or install files. + +def download_file(url, local_filename, expected_size="Unknown"): + """ + Download files from a URL to a local filename. + + Args: + url : str + URL that points to the file to be downloaded + local_filename : str + download content to this filename + """ + import requests + import os + import time + import shutil + + # We might want to bundle some files if they are small / compressed or not readily available for download + + if (os.path.isfile(url)): + shutil.copy(url, local_filename) + + else: + r = requests.get(url, stream=True) + + start_time = time.time() + last_time = start_time + datasize = 0 + + with open(local_filename, 'wb') as f: + for chunk in r.iter_content(chunk_size=10000000): + if chunk: # filter out keep-alive new chunks + f.write(chunk) + f.flush() + datasize += len(chunk) + if (time.time() - last_time) > 2.5: + print ("{:.1f} Mb in {:.1f}s / {}".format(datasize / 1.0e6, time.time() - start_time, expected_size)) + last_time = time.time() + + return + + +def md5sum(filename): + """ + Returns the checksum for a given file + """ + import hashlib + from functools import partial + + with open(filename, mode='rb') as f: + d = hashlib.md5() + for buf in iter(partial(f.read, 4096), b''): + d.update(buf) + return d.hexdigest() + + +def download_cached_file(location_url, local_file, expected_md5, expected_size="Unknown"): + """ + Download files from a URL to a local filename. + + Same as `download_file()` but checks whether the file has already + been downloaded from its checksum. + + Args: + location_url : str + URL that points to the file to be downloaded + local_file : str + download content to this filename + expected_md5 : str + checksum belonging to that file + expected_size : float / int / str (optional) + optional size of file (default="Unknown") + """ + import sys + + try: + assert md5sum(local_file) == expected_md5 + print ("Using cached file - {}".format(local_file)) + return(2) + + except (IOError, AssertionError) as error_info: + # No file or the wrong file ... best go download it + # print "Assertion failed - {}".format(sys.exc_info()) + + try: + data_file = download_file(location_url, local_file, expected_size) + print ("Downloaded from {}".format( location_url )) + return(1) + + except: + print ("Unable to download {} [{}] ".format( location_url, sys.exc_info() )) + return(0) + + +def report_cached_file(local_file, expected_md5): + """ + Report whether the local file matches its checksum + + Args: + local_file : str + string pointing to the local file + expected_md5 : str + checksum assigned to `local_file`. + """ + import os + import os.path + + if not os.path.isfile(local_file): + print ("Local file {} does not exist".format(local_file)) + else: + if len(expected_md5) == 0 or md5sum(local_file) == expected_md5: + print ("Cached file {} is valid".format(local_file)) + else: + print ("Cached file {} failed, checksum {}".format(local_file, md5sum(local_file))) + diff --git a/setup.py b/setup.py index da6e6cd..854f975 100644 --- a/setup.py +++ b/setup.py @@ -1,14 +1,53 @@ +## To install locally: python setup.py build && python setup.py install +## (If there are problems with installation of the documentation, it may be that +## the egg file is out of sync and will need to be manually deleted - see error message +## for details of the corrupted zip file. ) +## +## To push a version through to pip. +## - Make sure it installs correctly locally as above +## - Update the version information in this file +## - python setup.py sdist upload -r pypitest # for the test version +## - python setup.py sdist upload -r pypi # for the real version +## +## (see http://peterdowns.com/posts/first-time-with-pypi.html) -# python3 setup.py build_ext --inplace import numpy as np -from setuptools import setup -from setuptools import Extension -# from distutils.core import setup -# from distutils.extension import Extension +from setuptools import setup, Extension from Cython.Build import cythonize from os import path +import io +## in development set version to none and ... +PYPI_VERSION = "0.3" + +# Return the git revision as a string (from numpy) +def git_version(): + def _minimal_ext_cmd(cmd): + # construct minimal environment + env = {} + for k in ['SYSTEMROOT', 'PATH']: + v = os.environ.get(k) + if v is not None: + env[k] = v + # LANGUAGE is used on win32 + env['LANGUAGE'] = 'C' + env['LANG'] = 'C' + env['LC_ALL'] = 'C' + out = subprocess.Popen(cmd, stdout = subprocess.PIPE, env=env).communicate()[0] + return out + + try: + out = _minimal_ext_cmd(['git', 'rev-parse', '--short', 'HEAD']) + GIT_REVISION = out.strip().decode('ascii') + except OSError: + GIT_REVISION = "Unknown" + + return GIT_REVISION + + +if PYPI_VERSION is None: + PYPI_VERSION = git_version() this_directory = path.abspath(path.dirname(__file__)) with open(path.join(this_directory, 'README.md')) as f: @@ -28,9 +67,13 @@ author = "Ben Mather", author_email = "brmather1@gmail.com", url = "https://github.com/brmather/pycurious", - version = "0.4", + version = PYPI_VERSION, description = "Python tool for computing the Curie depth from magnetic data", ext_modules = cythonize([ext]), + install_requires = ['numpy', 'scipy>=0.15.0', 'Cython>=0.25.2'], + python_requires = '>=2.7, >=3.5', + setup_requires = ['pytest-runner', 'webdav'], + tests_require = ['pytest', 'webdav'], packages = ['pycurious'], package_data = {'pycurious': ['Examples/data/*', 'Examples/*.ipynb', From b63a5b3407440cdaf51358c6423285b031066f3b Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Sat, 15 Jun 2019 20:51:12 +1000 Subject: [PATCH 072/170] Updated README.md with link to docs --- Docker/Dockerfile | 9 +++-- README.md | 87 +++++++++++++++++++++++++++-------------------- 2 files changed, 56 insertions(+), 40 deletions(-) diff --git a/Docker/Dockerfile b/Docker/Dockerfile index a2ce312..00e6baf 100644 --- a/Docker/Dockerfile +++ b/Docker/Dockerfile @@ -11,10 +11,13 @@ FROM ${FROMIMG_ARG} USER root WORKDIR /home/jovyan/ +RUN apk add \ + libxml2-dev \ + libxslt-dev + RUN python3 -m pip install --no-cache-dir --upgrade \ - jupyter \ - pytest \ - git+https://github.com/lmoresi/pdoc.git + jupyter \ + pytest ### PyCurious - Notebooks diff --git a/README.md b/README.md index 74cb3b5..4792bee 100644 --- a/README.md +++ b/README.md @@ -17,7 +17,14 @@ Launch the demonstration at [mybinder.org](https://mybinder.org/v2/gh/brmather/p ## Navigation / Notebooks -There are two matching sets of `pycurious` notebooks - one set for the [Tanaka](#Tanaka) and one for [Bouligand](#Bouligand) implementations. The Bouligand set of noteboks are a natural choice for Bayesian inference applications. +There are two matching sets of Jupyter notebooks - one set for the [Tanaka](#Tanaka) and one for [Bouligand](#Bouligand) implementations. The Bouligand set of noteboks are a natural choice for Bayesian inference applications. + +Note, these examples can be installed from the package itself by running: + +```python +import pycurious +pycurious.install_documentation(path="Notebooks") +``` ### Tanaka @@ -33,13 +40,43 @@ There are two matching sets of `pycurious` notebooks - one set for the [Tanaka]( - [Ex4-Spatial-variation-of-Curie-depth.ipynb](pycurious-src/pycurious/Examples/Notebooks/Bouligand/Ex4-Spatial-variation-of-Curie-depth.ipynb) - [Ex5-Mapping-Curie-depth-EMAG2.ipynb](pycurious-src/pycurious/Examples/Notebooks/Bouligand/Ex5-Mapping-Curie-depth-EMAG2.ipynb) -## Examples -Note, these examples can be installed from the package itself by running: +## Installation -```python -import pycurious -pycurious.install_documentation(path="Notebooks") +### Dependencies + +You will need **Python 2.7 or 3.5+**. +Also, the following packages are required: + +- [`numpy`](http://numpy.org) +- [`scipy`](https://scipy.org) +- [`cython`](https://cython.org/) + +__Optional dependencies__ for mapping module and running the Notebooks: + +- [`matplotlib`](https://matplotlib.org/) +- [`pyproj`](https://github.com/jswhit/pyproj) +- [`cartopy`](https://scitools.org.uk/cartopy/docs/latest/) + +### Installing using pip + +You can install `pycurious` using the +[`pip package manager`](https://pypi.org/project/pip/) with either version of Python: + +```bash +python2 -m pip install pycurious +python3 -m pip install pycurious +``` +All the dependencies will be automatically installed by `pip`. + +### Installing using Docker + +A more straightforward installation for `pycurious` and all of its dependencies may be deployed with [Docker](https://www.docker.com). +To install the docker image and start the Jupyter notebook examples: + +```bash +docker pull brmather/pycurious:latest +docker run --name pycurious -p 8888:8888 brmather/pycurious:latest ``` ## Usage @@ -66,43 +103,19 @@ subgrid = grid.subgrid(window_size, x, y) k, Phi, sigma_Phi = grid.radial_spectrum(subgrid) ``` -## Installation - -To install with **setuptools**: +A series of tests are located in the *tests* subdirectory. +In order to perform these tests, clone the repository and run [`pytest`](https://pypi.org/project/pytest/): ```bash -python setup.py install --user +git checkout https://github.com/brmather/pycurious.git +cd pycurious +pytest -v ``` -This will compile all C source code and install them to the user directory (omit the `--user` flag to install to the system directory). Remember to delete the build folder if you are upgrading this package. - -Alternatively, install using **pip**: +### API Documentation -```bash -pip install pycurious --user -``` +The API for all functions and classes in `pycurious` can be accessed from [https://brmather.github.io/pycurious/](https://brmather.github.io/pycurious/). -### Dependencies - -- Python 2.7+ and 3.6+ -- Numpy 1.9+ -- Scipy 0.14+ -- Cython - -Optional dependencies for mapping module: - -- Matplotlib -- [pyproj](https://github.com/jswhit/pyproj) -- [Cartopy](http://scitools.org.uk/cartopy/docs/latest/index.html) - -### Docker - -A more straightforward installation for `pycurious` and all of its dependencies may be deployed with [Docker](https://www.docker.com). To install the docker image and test it is working: - -```bash -docker pull brmather/pycurious:latest -docker run --rm brmather/pycurious:latest help -``` ## References From f1d8518539016fc09451e327e09da88fc4e66aa2 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Mon, 17 Jun 2019 16:28:29 +1000 Subject: [PATCH 073/170] Updated Ex5 with download scripts Downloads: - EMAG2 v3 from Zenodo - Li et al 2017 from Nature Scientific Reports --- .../Ex5-Mapping-Curie-depth-EMAG2.ipynb | 118 ++++++++++-------- 1 file changed, 69 insertions(+), 49 deletions(-) diff --git a/pycurious/Examples/Notebooks/Bouligand/Ex5-Mapping-Curie-depth-EMAG2.ipynb b/pycurious/Examples/Notebooks/Bouligand/Ex5-Mapping-Curie-depth-EMAG2.ipynb index 9a4604e..fc84c24 100644 --- a/pycurious/Examples/Notebooks/Bouligand/Ex5-Mapping-Curie-depth-EMAG2.ipynb +++ b/pycurious/Examples/Notebooks/Bouligand/Ex5-Mapping-Curie-depth-EMAG2.ipynb @@ -37,7 +37,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -59,45 +59,36 @@ "source": [ "## Import EMAG2 data\n", "\n", - "The latest data can be downloaded from the [NOAA web page](https://www.ngdc.noaa.gov/geomag/emag2.html) in CSV format. Download it to a local directory (may take some time).\n", - "\n", - "Once loaded, we trim the data to a region of interest - being careful to allow some buffer to accommodate the maximum window size. We save this to a compressed `.npz` file to avoid the costly repitition of reloading the same data in the future.\n", - "\n", - "**EMAG2_V3_20170530.csv**\n", + "The [EMAG2 (v3)](https://www.ngdc.noaa.gov/geomag/emag2.html) Earth magnetic anomaly grid$^1$ has been reformatted from a CSV file to a compressed `.npz` NumPy archive to efficiently load within Python workflows. This dataset can be downloaded from [Zenodo](https://zenodo.org/record/3245551). We have added some download tools accessed under `pycurious.download` to ease the download process and checksum validation.\n", "\n", - "- Column 1: i ; grid column/longitude index\n", - "- Column 2: j ; grid row/latitude index\n", - "- Column 3: LON ; Geographic Longitude WGS84 (decimal degrees)\n", - "- Column 4: LAT ; Geographic Latitude WGS84 (decimal degrees)\n", - "- Column 5: SeaLevel ; Magnetic Anomaly Value at Sea Level(nT)\n", - "- Column 6: UpCont ; Magnetic Anomaly Value at continuous 4km altitude (nT)\n", - "- Column 7: Code ; Data Source Code (see table below)\n", - "- Column 8: Error ; Error estimate (nT)\n", + "### References\n", "\n", - "Code 888 is assigned in certain cells on grid edges where the data source is ambiguous and assigned an error of -888 nT\n", - "\n", - "Code 999 is assigned in cells where no data is reported with the anomaly value assigned 99999 nT and an error of -999 nT" + "$^1$ Brian Meyer, Richard Saltus, Arnaud Chulliat (2017): EMAG2: Earth Magnetic Anomaly Grid (2-arc-minute resolution) Version 3. National Centers for Environmental Information, NOAA. Model. doi:[10.7289/V5H70CVX](https://data.nodc.noaa.gov/cgi-bin/iso?id=gov.noaa.ngdc.mgg.geophysical_models:EMAG2_V3)" ] }, { "cell_type": "code", "execution_count": null, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ - "filedir = '/path/to/directory/'\n", - "emag2_name = 'EMAG2_V3_20170530'\n", - "\n", - "try:\n", - " with np.load(filedir+emag2_name+'.npz') as f:\n", - " mag_data = f['data']\n", - "except:\n", - " mag_data = np.loadtxt(filedir+emag2_name+'.csv', delimiter=',', usecols=(2,3,4,5,7))\n", - " lon_mask = mag_data[:,0] > 180.0\n", - " mag_data[lon_mask,0] -= 360.0\n", - " np.savez_compressed(filedir+emag2_name+'.npz', data=mag_data.astype(np.float32))" + "file_resources = [\n", + " # EMAG2 v3\n", + " {\n", + " \"local_file\":\"../../data/EMAG2_V3_20170530.npz\",\n", + " \"md5\":'c0898b6a91efb3f13783873a8b67380c',\n", + " \"url\":\"https://zenodo.org/record/3245551/files/EMAG2_V3_20170530.npz?download=1\",\n", + " \"expected_size\":\"500Mb\"\n", + " },\n", + " \n", + " # Li et al. 2017\n", + " {\n", + " \"local_file\":\"../../data/Li_et_al_2017.txt\",\n", + " \"md5\":'5f0ea0af3e27c6c21cd7b776c979aa80',\n", + " \"url\":\"https://media.nature.com/original/nature-assets/srep/2017/170321/srep45129/extref/srep45129-s1.txt?download=1\",\n", + " \"expected_size\":\"15Mb\"\n", + " }, \n", + "]" ] }, { @@ -106,6 +97,43 @@ "metadata": {}, "outputs": [], "source": [ + "from pycurious.download import download_cached_file\n", + "\n", + "for resource in file_resources:\n", + " print (\"\\nDownloading {:s}\".format(resource[\"local_file\"]))\n", + " download_cached_file(resource[\"url\"], resource[\"local_file\"], resource[\"md5\"], resource[\"expected_size\"])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Once loaded, we trim the data to a region of interest - being careful to allow some buffer to accommodate the maximum window size.\n", + "\n", + "**EMAG2_V3_20170530.npz** contains the following columns:\n", + "\n", + "1. LON ; Geographic Longitude WGS84 (decimal degrees)\n", + "2. LAT ; Geographic Latitude WGS84 (decimal degrees)\n", + "3. SeaLevel ; Magnetic Anomaly Value at Sea Level(nT)\n", + "4. UpCont ; Magnetic Anomaly Value at continuous 4km altitude (nT)\n", + "5. Code ; Data Source Code (see table below)\n", + "6. Error ; Error estimate (nT)\n", + "\n", + "Code 888 is assigned in certain cells on grid edges where the data source is ambiguous and assigned an error of -888 nT\n", + "\n", + "Code 999 is assigned in cells where no data is reported with the anomaly value assigned 99999 nT and an error of -999 nT" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "emag2_file = file_resources[0][\"local_file\"]\n", + "with np.load(emag2_file) as f:\n", + " mag_data = f['data']\n", + "\n", "# filter NaNs\n", "mag_data = mag_data[mag_data[:,3] != 99999.]\n", "mag_data = mag_data[mag_data[:,4] != -888.]\n", @@ -116,7 +144,7 @@ "maxcols = mag_data.max(axis=0)\n", "\n", "fmt = \"min/max {:5.2f} -> {:5.2f}\"\n", - "for col in xrange(mag_data.shape[1]):\n", + "for col in range(mag_data.shape[1]):\n", " print(fmt.format(mincols[col], maxcols[col]))" ] }, @@ -134,9 +162,7 @@ { "cell_type": "code", "execution_count": null, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "# grid extent - grid of the British Isles in Irenet 95 grid projection\n", @@ -156,9 +182,7 @@ { "cell_type": "code", "execution_count": null, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "dx, dy = 1e3, 1e3 # 1 km grid resolution\n", @@ -186,7 +210,7 @@ "ax.gridlines()\n", "\n", "im1 = ax.imshow(mag_sphere, extent=extent_sphere, transform=ccrs.PlateCarree(),\n", - " vmin=-200, vmax=200, zorder=0)\n", + " cmap='Spectral_r', vmin=-200, vmax=200, zorder=0)\n", "\n", "fig.colorbar(im1, label='nT')" ] @@ -221,9 +245,7 @@ { "cell_type": "code", "execution_count": null, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "curie_depth = zt + dz\n", @@ -266,12 +288,12 @@ { "cell_type": "code", "execution_count": null, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ - "li_cpd = np.loadtxt(filedir + 'Li_2017_curiedepth.txt')\n", + "li2017_cpd_file = file_resources[1]['local_file']\n", + "\n", + "li_cpd = np.loadtxt(li2017_cpd_file, skiprows=1)\n", "li_cpd = li_cpd[~np.isnan(li_cpd[:,2])]\n", "\n", "li_grid = mapping.grid(li_cpd[:,:2], li_cpd[:,2], extent_sphere, shape=(ny,nx))" @@ -309,9 +331,7 @@ { "cell_type": "code", "execution_count": null, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "mapping.export_geotiff(\"my-curie-depth.tiff\", curie_depth_sphere, extent_sphere, epsg=4326)" From 9e1e6cafac146c7545efdf3ab0a07ed9a7578752 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Mon, 17 Jun 2019 16:36:08 +1000 Subject: [PATCH 074/170] Updated manifest and added contribution guide --- CONTRIBUTING.md | 34 ++++++++++++++++++++++++++++++++++ MANIFEST.in | 4 +--- 2 files changed, 35 insertions(+), 3 deletions(-) create mode 100644 CONTRIBUTING.md diff --git a/CONTRIBUTING.md b/CONTRIBUTING.md new file mode 100644 index 0000000..ded1122 --- /dev/null +++ b/CONTRIBUTING.md @@ -0,0 +1,34 @@ +# Contributing to pycurious + +We welcome contributions to `pycurious`, large or small [\*](#footnote1). That can be in the form of new code, improvements to the documentation, +helping with a missing test, or it may even just be pointing out a bug or potential improvement to the team. + +For bugs and suggestions, the most effective way to reach the team is by raising an issue on the github issue tracker. Github +allows you to classify your issues so that we know if it is a bug report, feature request or feedback to the authors. + +If you wish to contribute some changes to the code then you should submit a *pull request*. On github we can review the code that you are contributing and discuss it before the changes are merged into the development version of the code. Before embarking on changes to the code, please first take a look at the [`dev` branch](https://github.com/brmather/pycurious/tree/dev) which is where unreleased changes are staged: we may have +been working on something similar already. + +## How to create a Pull Request (PR) + +Create your own fork of the project on github: log into your github account, navigate to the [`pycurious` repository](https://github.com/brmather/pycurious/tree/dev) +and click on the *fork* button at the top right corner of this repository. You can find detailed instructions and a discussion of how to fork a repository, clone it locally and work on the changes +[in the GitHub guides](https://guides.github.com/activities/forking/). + +## When to make your pull request + +It is much easier to merge in small changes to the code than extensive ones that touch multiple files. If a small incremental change is possible, please issue a request for that change rather than saving everything up. + +It is a good idea to commit frequently and with commit messages that refer to the changes that have been make and why they have been made. The commit message is usually browsed without seeing the actual changes themselves and which sections of the code have been altered so a helpful message provides relevant details. + +## Tests + +We use `pytest` for the unit testing framework in `pycurious`. In the source directory this means running: + +```bash +python setup.py test +``` + +The existing tests should be passing before you start coding (help us out with an issue if that is not the case !) and when you have finished. Any new functionality should also have tests that we can use to verify the code. It is important that you make it clear if the original tests have had to change to accomodate new code / functionality. + +* _Small changes are our favorites as they are much easier to quickly merge into the existing code. Proofreading typos, bug fixes, ... the little stuff is especially welcome._ diff --git a/MANIFEST.in b/MANIFEST.in index 1e73e56..3d647bf 100644 --- a/MANIFEST.in +++ b/MANIFEST.in @@ -1,5 +1,6 @@ include README.md include MANIFEST.in +include CONTRIBUTING.md include COPYING include COPYING.LESSER include setup.cfg @@ -7,7 +8,4 @@ include src/* include __init__.py recursive-include pycurious/*.py recursive-include pycurious/*.ipynb -include docs/* include tests/*.py - - From f5138be46866af5b7fd5e77cd052d3753998ae1e Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Tue, 18 Jun 2019 13:40:32 +1000 Subject: [PATCH 075/170] Add PyPI deployment --- .travis.yml | 27 ++++++++++++++++++--------- 1 file changed, 18 insertions(+), 9 deletions(-) diff --git a/.travis.yml b/.travis.yml index 275dfb0..5c323d5 100644 --- a/.travis.yml +++ b/.travis.yml @@ -30,6 +30,8 @@ install: - python3 -m pip install -e . script: + # generate the release + - python3 setup.py sdist # generate the docs - mkdir docs - cd docs @@ -39,12 +41,19 @@ script: - cd ../ deploy: - provider: pages - skip_cleanup: true - github_token: $GITHUB_TOKEN # Set in the settings page of your repository, as a secure variable - keep_history: true - on: - branch: master - condition: '$DEPLOY_DOCS == "true"' - verbose: true - local_dir: docs/ + - provider: pages + skip_cleanup: true + github_token: $GITHUB_TOKEN # Set in the settings page of your repository, as a secure variable + keep_history: true + on: + branch: master + condition: '$DEPLOY_DOCS == "true"' + verbose: true + local_dir: docs/ + - provider: pypi + user: $PYPI_USERNAME + password: $PYPI_PASSWORD + on: + tags: true + condition: '$DEPLOY_PYPI == true' + skip_cleanup: true \ No newline at end of file From c0aa7b9e070c8a4b8e963de85b8bf6bc7d7c45d8 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Tue, 18 Jun 2019 14:11:45 +1000 Subject: [PATCH 076/170] First lot of tests --- tests/test_0_imports.py | 43 +++++++++++++++++++++++++++ tests/test_routines.py | 64 +++++++++++++++++++++++++++++++++++++++++ 2 files changed, 107 insertions(+) create mode 100644 tests/test_0_imports.py create mode 100644 tests/test_routines.py diff --git a/tests/test_0_imports.py b/tests/test_0_imports.py new file mode 100644 index 0000000..bdd6081 --- /dev/null +++ b/tests/test_0_imports.py @@ -0,0 +1,43 @@ +import pytest + +## =================== + +def test_numpy_import(): + import numpy + return + +def test_scipy_import(): + import scipy + print("\t\t You have scipy version {}".format(scipy.__version__)) + +def test_cython_import(): + import Cython + return + +def test_pycurious_modules(): + import pycurious + from pycurious import documentation + from pycurious import CurieGrid + from pycurious import CurieOptimise + from pycurious import mapping + from pycurious import download + + +# def test_jupyter_available(): +# from subprocess import check_output +# try: +# result = str(check_output(['which', 'jupyter']))[2:-3] +# except: +# assert False, "jupyter notebook system is not installed" + +# def test_documentation_dependencies(): +# import matplotlib +# import cartopy +# import pyproj + + +if __name__ == "__main__": + test_numpy_import() + test_scipy_import() + test_cython_import() + test_pycurious_modules() \ No newline at end of file diff --git a/tests/test_routines.py b/tests/test_routines.py new file mode 100644 index 0000000..4f2479e --- /dev/null +++ b/tests/test_routines.py @@ -0,0 +1,64 @@ +import pytest +import pycurious +import numpy as np +from time import time + +# global variables +max_window = 100e3 + +# square grid 100km x 100km +xmin = 0.0 +xmax = 100e3 +ymin = 0.0 +ymax = 100e3 + +nx = 100 +ny = 100 + +# random noise +mag_grid = np.random.randn(ny,nx) + + +def time_routine(routine, *args, **kwargs): + t = time() + routine(*args, **kwargs) + str_fmt = "- {:30} completed in {:1.6f} seconds" + print(str_fmt.format(str(routine.__name__), time()-t)) + + +## +## Test PyCurious routines +## + +def test_CurieGrid_routines(): + cpd = pycurious.CurieGrid(mag_grid, xmin, xmax, ymin, ymax) + xc = 50e3 + yc = 50e3 + + time_routine(cpd.__init__, mag_grid, xmin, xmax, ymin, ymax) + time_routine(cpd.subgrid, max_window, xc, yc) + time_routine(cpd.create_centroid_list, 0.1*max_window) + time_routine(cpd.remove_trend_linear, cpd.data) + time_routine(cpd.radial_spectrum, cpd.data) + time_routine(cpd.radial_spectrum_log, cpd.data) + time_routine(cpd.azimuthal_spectrum, cpd.data) + time_routine(cpd.reduce_to_pole, cpd.data, 30., 30.) + time_routine(cpd.upward_continuation, cpd.data, 10e3) + + +def test_CurieOptimise_routines(): + cpd = pycurious.CurieOptimise(mag_grid, xmin, xmax, ymin, ymax) + xc_list, yc_list = cpd.create_centroid_list(0.5*max_window, spacingX=5e3, spacingY=5e3) + xc = xc_list[0] + yc = yc_list[0] + + time_routine(cpd.add_prior, beta=(3.0, 0.5)) + time_routine(cpd.optimise, 0.5*max_window, xc, yc) + time_routine(cpd.optimise_routine, 0.5*max_window, xc_list, yc_list) + time_routine(cpd.metropolis_hastings, 0.5*max_window, xc, yc, 100, 10) + time_routine(cpd.sensitivity, 0.5*max_window, xc, yc, 100) + + +if __name__ == "__main__": + test_CurieGrid_routines() + test_CurieOptimise_routines() \ No newline at end of file From 5a9d1fcb6598edb334671a226cca9e1aab332a15 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Tue, 18 Jun 2019 15:07:55 +1000 Subject: [PATCH 077/170] Updated with some more tests Deleted ones that don't work or are pointless --- .../Examples/Scripts}/Bouligand_forward.py | 0 pycurious/grid.py | 4 +- tests/optimise_test.py | 97 --------------- tests/parallel_test.py | 53 --------- tests/test_multiprocessing.py | 64 ---------- tests/test_optimise.py | 94 +++++++++++++++ tests/valid_numbers.py | 111 ------------------ 7 files changed, 96 insertions(+), 327 deletions(-) rename {tests => pycurious/Examples/Scripts}/Bouligand_forward.py (100%) delete mode 100644 tests/optimise_test.py delete mode 100644 tests/parallel_test.py delete mode 100644 tests/test_multiprocessing.py create mode 100644 tests/test_optimise.py delete mode 100644 tests/valid_numbers.py diff --git a/tests/Bouligand_forward.py b/pycurious/Examples/Scripts/Bouligand_forward.py similarity index 100% rename from tests/Bouligand_forward.py rename to pycurious/Examples/Scripts/Bouligand_forward.py diff --git a/pycurious/grid.py b/pycurious/grid.py index d8185c5..72bd171 100644 --- a/pycurious/grid.py +++ b/pycurious/grid.py @@ -162,8 +162,8 @@ def remove_trend_linear(self, data): nr, nc = data.shape xq, yq = np.meshgrid(np.arange(0, nc), np.arange(0, nr)) - A = np.column_stack((x.flatten(), y.flatten(), np.ones(x.size))) - c, resid, rank, sigma = np.linalg.lstsq(A, data.flatten()) + A = np.c_[xq.ravel(), yq.ravel(), np.ones(xq.size)] + c, resid, rank, sigma = np.linalg.lstsq(A, data.ravel(), rcond=None) data.flat[:] -= np.dot(A, c) return data diff --git a/tests/optimise_test.py b/tests/optimise_test.py deleted file mode 100644 index 952e33e..0000000 --- a/tests/optimise_test.py +++ /dev/null @@ -1,97 +0,0 @@ -# coding: utf-8 - -import numpy as np -import matplotlib.pyplot as plt -import pycurious -import time - - -# initialise CurieOptimise object -max_window = 100e3 - - -# square grid 100km x 100km - -xmin = 0.0 -xmax = 100e3 -ymin = 0.0 -ymax = 100e3 - -nx = 100 -ny = 100 - -# random noise -mag_grid = np.random.randn(ny,nx) - -cpd = pycurious.CurieOptimise(mag_grid, xmin, xmax, ymin, ymax) - - -# compute centroid -xc = 0.5*(xmin + xmax) -yc = 0.5*(ymin + ymax) - -xc_list, yc_list = cpd.create_centroid_list(0.5*max_window, spacingX=5e3, spacingY=5e3) -print("number of centroids = {}".format(len(xc_list))) - - - -t = time.time() -betaN, ztN, dzN, CN = cpd.optimise_routine(0.5*max_window, xc_list, yc_list, taper=None) -print("\nfirst optimisation - no priors\ntime = {:.3f} sec".format(time.time() - t)) - - - -xc = np.unique(xc_list) -yc = np.unique(yc_list) - -nr, nc = yc.size, xc.size - -plot_helper = [(betaN, 'beta'), (ztN, 'zt'), (dzN, 'dz'), (CN, 'C')] - -fig, (ax1,ax2,ax3,ax4) = plt.subplots(1, 4, sharey=True, figsize=(16,3.5)) -for i, ax in enumerate([ax1, ax2, ax3, ax4]): - title = plot_helper[i][1] - data = plot_helper[i][0] - mask = np.isfinite(data) - - ax.set_title(title) - sci = ax.scatter(xc_list[mask]/1e3, yc_list[mask]/1e3, c=data[mask]) - fig.colorbar(sci, ax=ax) - fig.savefig('CPD_initial.png', bbox_inches='tight') - - print("{:5} mean={:.2f} std={:.2f}".format(title, data.mean(), np.std(data))) - - - -beta_mu, beta_std = np.mean(betaN), np.std(betaN) -zt_mu, zt_std = np.mean(ztN), np.std(ztN) -dz_mu, dz_std = np.mean(dzN), np.std(dzN) -C_mu, C_std = np.mean(CN), np.std(CN) - -cpd.reset_priors() -cpd.add_prior(beta=(beta_mu, beta_std)) -cpd.add_prior(zt=(zt_mu, zt_std)) -cpd.add_prior(dz=(dz_mu, dz_std)) -cpd.add_prior(C=(C_mu, C_std)) - - -t = time.time() -betaOpt, ztOpt, dzOpt, COpt = cpd.optimise_routine(0.5*max_window, xc_list, yc_list, taper=None) -print("\nsecond optimisation - with priors\ntime = {:.3f} sec".format(time.time() - t)) - - - -plot_helper = [(betaOpt, 'beta'), (ztOpt, 'zt'), (dzOpt, 'dz'), (COpt, 'C')] - -fig, (ax1,ax2,ax3,ax4) = plt.subplots(1, 4, sharey=True, figsize=(16,3.5)) -for i, ax in enumerate([ax1, ax2, ax3, ax4]): - title = plot_helper[i][1] - data = plot_helper[i][0] - mask = np.isfinite(data) - - ax.set_title(title) - sci = ax.scatter(xc_list[mask]/1e3, yc_list[mask]/1e3, c=data[mask]) - fig.colorbar(sci, ax=ax) - fig.savefig('CPD_optimised.png', bbox_inches='tight') - - print("{:5} mean={:.2f} std={:.2f}".format(title, data.mean(), np.std(data))) diff --git a/tests/parallel_test.py b/tests/parallel_test.py deleted file mode 100644 index 0df83f5..0000000 --- a/tests/parallel_test.py +++ /dev/null @@ -1,53 +0,0 @@ -import matplotlib.pyplot as plt -import numpy as np -import pycurious - -xmin = -1.0 -xmax = 1.0 -ymin = -1.0 -ymax = 1.0 - -nx = 10 -ny = 10 - -xcoords = np.linspace(xmin, xmax, nx) -ycoords = np.linspace(ymin, ymax, ny) -xq, yq = np.meshgrid(xcoords, ycoords) - -grid = xq**2 + yq**2 - -max_window_size = 0.5 -print("window size {}".format(max_window_size)) - - -cpd = pycurious.CurieParallel(grid, xmin, xmax, ymin, ymax, max_window_size) - -fig = plt.figure() -ax1 = fig.add_subplot(111) -im1 = ax1.imshow(grid, extent=[xmin, xmax, ymin, ymax]) -fig.colorbar(im1) -fig.savefig('{}_whole_grid.png'.format(cpd.comm.rank)) - - - - - -print("{} ghost range {}".format(cpd.comm.rank, cpd.dm.getGhostRanges())) -print("{} min {}".format(cpd.comm.rank, cpd.coords.min(axis=0))) -print("{} max {}".format(cpd.comm.rank, cpd.coords.max(axis=0))) - - -fig = plt.figure() -ax1 = fig.add_subplot(111) -im1 = ax1.imshow(cpd.data, extent=[cpd.xmin, cpd.xmax, cpd.ymin, cpd.ymax], origin='lower') -fig.colorbar(im1) -fig.savefig('{}_decomposed_grid.png'.format(cpd.comm.rank)) - - - -xc_list, yc_list = cpd.create_centroid_list(max_window_size) - -cpd.reset_priors() -betaN, ztN, dzN, CN = cpd.optimise_routine(max_window_size, xc_list, yc_list, 3.0, 1.0, 20.0, 5.0, taper=None) - -print("{} min/max dz {}".format(cpd.comm.rank, (dzN.min(), dzN.max()))) \ No newline at end of file diff --git a/tests/test_multiprocessing.py b/tests/test_multiprocessing.py deleted file mode 100644 index 3b98f89..0000000 --- a/tests/test_multiprocessing.py +++ /dev/null @@ -1,64 +0,0 @@ -import numpy as np -import pycurious - -# load x,y,anomaly -mag_data = np.loadtxt("../pycurious/Examples/data/test_mag_data.txt") - -nx, ny = 305, 305 - -x = mag_data[:,0] -y = mag_data[:,1] -d = mag_data[:,2].reshape(ny,nx) - -xmin, xmax = x.min(), x.max() -ymin, ymax = y.min(), y.max() - -# initialise CurieOptimise object -grid = pycurious.CurieOptimise(d, xmin, xmax, ymin, ymax) - - -# get centroids -window_size = 200e3 -xc_list, yc_list = grid.create_centroid_list(window_size, spacingX=10e3, spacingY=10e3) - -print("number of centroids = {}".format(len(xc_list))) - - -beta, zt, dz, C = grid.optimise_routine(window_size, xc_list, yc_list) -print "done with optimise_routine" - -result = grid.parallelise_routine(window_size, xc_list, yc_list, grid.sensitivity, 5) -print result -result1 = np.array(result) -print result1.shape -# print result1[:,0] -# print result1[:,1] -# print result1[:,:,0] - -# result2 = np.hstack(result) -# print result2.shape -# print result2[0] - -# print grid.sensitivity(window_size, xc_list[0], yc_list[0], 5) - - - -import matplotlib.pyplot as plt -# get dimensions of domain -xcoords = np.unique(xc_list) -ycoords = np.unique(yc_list) -nc, nr = xcoords.size, ycoords.size - -fig, (ax1, ax2, ax3, ax4) = plt.subplots(1, 4, sharex=True, sharey=True, figsize=(17,3.)) - -im1 = ax1.imshow(beta.reshape(nr,nc)) -im2 = ax2.imshow(zt.reshape(nr,nc)) -im3 = ax3.imshow(dz.reshape(nr,nc)) -im4 = ax4.imshow(C.reshape(nr,nc)) - -fig.colorbar(im1, ax=ax1, label=r"$\beta$") -fig.colorbar(im2, ax=ax2, label=r"$z_t$") -fig.colorbar(im3, ax=ax3, label=r"$\Delta z$") -fig.colorbar(im4, ax=ax4, label=r"$C$") - -fig.savefig("curie_depth.png") \ No newline at end of file diff --git a/tests/test_optimise.py b/tests/test_optimise.py new file mode 100644 index 0000000..5139e73 --- /dev/null +++ b/tests/test_optimise.py @@ -0,0 +1,94 @@ + +import pytest +import pycurious +import numpy as np +from scipy.optimize import minimize + +# global variables +max_window = 100e3 + +# square grid 100km x 100km +xmin = 0.0 +xmax = 100e3 +ymin = 0.0 +ymax = 100e3 + +nx = 100 +ny = 100 + +# random noise +mag_grid = np.random.randn(ny,nx) + +xc = 50e3 +yc = 50e3 + + +def test_optimisation(): + grid = pycurious.CurieOptimise(mag_grid, xmin, xmax, ymin, ymax) + beta, zt, dz, C = grid.optimise(max_window, xc, yc) + +def test_priors(): + grid = pycurious.CurieOptimise(mag_grid, xmin, xmax, ymin, ymax) + beta0, zt0, dz0, C0 = grid.optimise(max_window, xc, yc) + + grid.add_prior(beta=(1.0, 0.1)) + beta1, zt1, dz1, C1 = grid.optimise(max_window, xc, yc) + + if abs(beta1 - 1.0) < abs(beta0 - 1.0): + print("PASSED! Optimisation is sensitive to prior information") + else: + assert False, "FAILED! Optimisation with priors failed" + +def test_valid_numbers(): + S = np.array([ 22.16409774, 19.95258494, 18.27873722, 17.10575637,\ + 16.53959747, 16.31539575, 15.69619005, 15.29953307,\ + 14.83475976, 14.54031396, 14.33361716, 13.81764026,\ + 13.5176055 , 13.27386563, 13.03493328, 12.88581369,\ + 12.61998358, 12.48616749, 12.11261083, 12.13079154,\ + 11.85440661, 11.79244826, 11.66823202, 11.40231744,\ + 11.32521296, 11.13634007, 11.10650999, 10.94822598,\ + 10.78032794, 10.66593304, 10.55815845, 10.56805594,\ + 10.33514462, 10.22026537, 10.22945756, 10.09275259,\ + 10.11562101, 9.85061009, 9.87165772, 9.85976847,\ + 9.73954992, 9.72021054, 9.52959744, 9.59582531,\ + 9.50927273, 9.44691364, 9.39293966, 9.33097387, 9.33191784]) + + k = np.array([ 0.09237068, 0.15443902, 0.21486191, 0.282031 , 0.33452175,\ + 0.4020083 , 0.46381582, 0.5290359 , 0.59611689, 0.65875047,\ + 0.71442694, 0.77929408, 0.84320843, 0.90939865, 0.96863721,\ + 1.03155349, 1.09130906, 1.15699532, 1.22338685, 1.28109263,\ + 1.34606572, 1.40861721, 1.46920824, 1.53421046, 1.59675833,\ + 1.66109235, 1.7233503 , 1.78492941, 1.84835837, 1.90933735,\ + 1.973275 , 2.03650008, 2.0983359 , 2.16386249, 2.22416603,\ + 2.2876692 , 2.34841931, 2.41225232, 2.47774604, 2.5379226 ,\ + 2.59980401, 2.66346692, 2.72735801, 2.79146076, 2.85220715,\ + 2.91443307, 2.97643404, 3.04008782, 3.10369815]) + + sigma_S = np.ones_like(S) + + grid = pycurious.CurieOptimise(mag_grid, xmin, xmax, ymin, ymax) + + beta0 = 3.0 + zt0 = 1.0 + dz0 = 40.0 + C0 = 5.0 + x0 = np.array([beta0, zt0, dz0, C0]) + + lower_bound = np.zeros_like(x0) + upper_bound = [None]*len(lower_bound) + + # xi = func([5, 0., 45., 6.], S, k) + xi = grid.min_func(x0, k, S, sigma_S) + + res = minimize(grid.min_func, x0, args=(k, S, sigma_S), method='TNC', bounds=list(zip(lower_bound,upper_bound))) + print("beta={:.2f}, zt={:.2f}, dz={:.2f}, C={:.2f}".format(*res.x)) + + if np.isfinite(res.x).all(): + print("PASSED! All numbers are finite") + else: + assert False, "FAILED! Not all numbers are finite" + +if __name__ == "__main__": + test_optimisation() + test_priors() + test_valid_numbers() \ No newline at end of file diff --git a/tests/valid_numbers.py b/tests/valid_numbers.py deleted file mode 100644 index 5511f05..0000000 --- a/tests/valid_numbers.py +++ /dev/null @@ -1,111 +0,0 @@ -import numpy as np -from scipy.optimize import minimize -from scipy.special import gamma, kv, lambertw -import warnings - -def func(x, Phi_exp, kh): - """ - Function to minimise - """ - beta = x[0] - zt = x[1] - dz = x[2] - C = x[3] - with warnings.catch_warnings() as w: - warnings.simplefilter("ignore") - Phi_syn = bouligand2009(beta, zt, dz, kh, C) - if np.isnan(Phi_syn).any(): - Phi_syn.fill(1e5) - - misfit = np.linalg.norm((Phi_exp - Phi_syn))**2 - - # print (Phi_syn), misfit -# misfit = np.sum((Phi_exp - pycurious.bouligand2009(beta, zt, dz, kh, C))**2/np.sqrt(sigma2)**2) - misfit += (beta - 5.44)**2/0.62**2 - misfit += (zt - 0.14)**2/0.28**2 - misfit += (dz - 22.73)**2/29.63**2 - misfit += (C - 11.88)**2/1.38**2 - return misfit - -def bouligand2009(beta, zt, dz, kh, C=0.0): - """ - Calculate the synthetic radial power spectrum of - magnetic anomalies - - Equation (4) of Bouligand et al. (2009) - - Parameters - ---------- - beta : fractal parameter - zt : top of magnetic sources - dz : thickness of magnetic sources - kh : norm of the wave number in the horizontal plane - C : field constant (Maus et al., 1997) - - Returns - ------- - Phi : radial power spectrum of magnetic anomalies - - References - ---------- - Bouligand, C., J. M. G. Glen, and R. J. Blakely (2009), Mapping Curie - temperature depth in the western United States with a fractal model for - crustal magnetization, J. Geophys. Res., 114, B11104, - doi:10.1029/2009JB006494 - Maus, S., D. Gordon, and D. Fairhead (1997), Curie temperature depth - estimation using a self-similar magnetization model, Geophys. J. Int., - 129, 163-168, doi:10.1111/j.1365-246X.1997.tb00945.x - """ - khdz = kh*dz - coshkhdz = np.cosh(khdz) - - Phi1d = C - 2.0*kh*zt - (beta-1.0)*np.log(kh) - khdz - A = np.sqrt(np.pi)/gamma(1.0+0.5*beta) * \ - (0.5*coshkhdz*gamma(0.5*(1.0+beta)) - \ - kv((-0.5*(1.0+beta)), khdz) * np.power(0.5*khdz,(0.5*(1.0+beta)) )) - Phi1d += np.log(A) - return Phi1d - - -S = np.array([ 22.16409774, 19.95258494, 18.27873722, 17.10575637,\ - 16.53959747, 16.31539575, 15.69619005, 15.29953307,\ - 14.83475976, 14.54031396, 14.33361716, 13.81764026,\ - 13.5176055 , 13.27386563, 13.03493328, 12.88581369,\ - 12.61998358, 12.48616749, 12.11261083, 12.13079154,\ - 11.85440661, 11.79244826, 11.66823202, 11.40231744,\ - 11.32521296, 11.13634007, 11.10650999, 10.94822598,\ - 10.78032794, 10.66593304, 10.55815845, 10.56805594,\ - 10.33514462, 10.22026537, 10.22945756, 10.09275259,\ - 10.11562101, 9.85061009, 9.87165772, 9.85976847,\ - 9.73954992, 9.72021054, 9.52959744, 9.59582531,\ - 9.50927273, 9.44691364, 9.39293966, 9.33097387, 9.33191784]) - -k = np.array([ 0.09237068, 0.15443902, 0.21486191, 0.282031 , 0.33452175,\ - 0.4020083 , 0.46381582, 0.5290359 , 0.59611689, 0.65875047,\ - 0.71442694, 0.77929408, 0.84320843, 0.90939865, 0.96863721,\ - 1.03155349, 1.09130906, 1.15699532, 1.22338685, 1.28109263,\ - 1.34606572, 1.40861721, 1.46920824, 1.53421046, 1.59675833,\ - 1.66109235, 1.7233503 , 1.78492941, 1.84835837, 1.90933735,\ - 1.973275 , 2.03650008, 2.0983359 , 2.16386249, 2.22416603,\ - 2.2876692 , 2.34841931, 2.41225232, 2.47774604, 2.5379226 ,\ - 2.59980401, 2.66346692, 2.72735801, 2.79146076, 2.85220715,\ - 2.91443307, 2.97643404, 3.04008782, 3.10369815]) - -w = 1.0 - -beta0 = 3.0 -zt0 = 1.0 -dz0 = 40.0 -C0 = 5.0 -x0 = np.array([beta0, zt0, dz0, C0]) - -lb = np.zeros_like(x0) -ub = np.zeros_like(x0) -# ub = np.array([50., 1, 100, 1e99]) -ub = [None]*len(lb) - -# xi = func([5, 0., 45., 6.], S, k) -xi = func(x0, S, k) - -res = minimize(func, x0, args=(S, k), method='TNC', bounds=list(zip(lb,ub))) -print("beta={:.2f}, zt={:.2f}, dz={:.2f}, C={:.2f}".format(*res.x)) \ No newline at end of file From a5654ce2aa8e8c0ad61ca949afe4fbd9ac2bc5aa Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Tue, 18 Jun 2019 15:14:58 +1000 Subject: [PATCH 078/170] Remove matplotlib dependency from Bouligand_forward.py Causes import errors with pdoc --- pycurious/Examples/Scripts/Bouligand_forward.py | 5 ++--- 1 file changed, 2 insertions(+), 3 deletions(-) diff --git a/pycurious/Examples/Scripts/Bouligand_forward.py b/pycurious/Examples/Scripts/Bouligand_forward.py index d039a07..6d995db 100644 --- a/pycurious/Examples/Scripts/Bouligand_forward.py +++ b/pycurious/Examples/Scripts/Bouligand_forward.py @@ -1,4 +1,4 @@ -## Code to generate test magnetic data for testing of PyCurious methods +## Code to generate test magnetic data for PyCurious examples ## Converted from MATLAB code by R Delhaye. #Original code: #Claire Bouligand @@ -7,7 +7,6 @@ #Modified to use less memory import numpy as np -import matplotlib.pyplot as plt import pycurious import time @@ -123,7 +122,7 @@ x=np.arange(0.5,0.5+dlx*(nx),dlx)*1000 y=np.arange(0.5,0.5+dly*(nx),dly)*1000 -fid=open("test_mag_data.txt","w+") +fid=open("../data/test_mag_data.txt","w+") for i in range(0,nx): for j in range(0,ny): fid.write(' '.join([str(x[i]),str(y[j]),str(np.real(ANO[i,j])),"\n"])) From 123ffad8642444914b1b032c73afff75669a1997 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Tue, 18 Jun 2019 15:34:11 +1000 Subject: [PATCH 079/170] Now running tests with Travis-CI --- .travis.yml | 2 + .../Examples/Scripts/Bouligand_forward.py | 154 ----------------- tests/Bouligand_forward.py | 156 ++++++++++++++++++ 3 files changed, 158 insertions(+), 154 deletions(-) delete mode 100644 pycurious/Examples/Scripts/Bouligand_forward.py create mode 100644 tests/Bouligand_forward.py diff --git a/.travis.yml b/.travis.yml index 5c323d5..ddaa2c7 100644 --- a/.travis.yml +++ b/.travis.yml @@ -30,6 +30,8 @@ install: - python3 -m pip install -e . script: + # run the tests + - pytest tests/ # generate the release - python3 setup.py sdist # generate the docs diff --git a/pycurious/Examples/Scripts/Bouligand_forward.py b/pycurious/Examples/Scripts/Bouligand_forward.py deleted file mode 100644 index 6d995db..0000000 --- a/pycurious/Examples/Scripts/Bouligand_forward.py +++ /dev/null @@ -1,154 +0,0 @@ -## Code to generate test magnetic data for PyCurious examples -## Converted from MATLAB code by R Delhaye. -#Original code: -#Claire Bouligand -#03-19-2007 -#05-09-2014 -#Modified to use less memory - -import numpy as np -import pycurious -import time - -start_time=time.time() -cm=1e-7 - -########################################################## -#A VERIFIER: multiplier facteur cm par 4*pi -## TO VERIFY: multiplication factor "cm for 4*pi" -########################################################### -## Degree of fractal -b=-3.0 -## Dimension of pixels (km), should be multiples of the smallest -dlx=1.0 -dly=1.0 -dlz=1.0 -dl=min([dlx,dly,dlz]) -dx=dlx/dl -dy=dly/dl -dz=dlz/dl - -#nombre de pixels -## Number of pixels. -nx=305 -ny=305 -nz=10 -nmax=int(max([nx*dx,ny*dy,nz*dz])) - -#texte="dimensions x : %d / y : %d / z : %d" % (nx*dlx,ny*dly,nz*dlz) -#print(texte) -#disp(texte) - -#Parametres de l'aimantation -## Parameters of magnetisation -#M1=1 # aimantation moyenne = 1 A/m ## Average magnetisation -#M2=10^(0.25) # std de l'aimantation = 10^(0.25) A/m ## Standard dev of -#magnetisation -M1=0 -M2=0.2 -#prof sommet zt # Depth Zt -zt=0.305 -#prof base zb ## Depth Zb -zb=zt+nz*dlz - -############################################################ -#GENERATION DE LA DISTRIB 3D D'AIMANTATION FRACTAL -#A PARTIR VOLUME DE DIM ID. (nmax,dl) SELON X, Y ET Z - -M=np.zeros((nmax,nmax,nmax)) -l=[0,(nmax-1)*dl,dl] - -#x=np.arange(0,dlx*(nx-1),dlx) -#y=np.arange(0,dly*(nx-1),dly) -#z=np.arange(0,dlz*(nx-1),dlz) - -df=1.0/(nmax*dl) -dfx=1.0/(nx*dlx) -dfy=1.0/(ny*dly) -dfz=1.0/(nz*dlz) - -#Center indices of matrix = Nyquist -c=(nmax+1)/2 -f=np.zeros((int(np.floor((nmax+1))),1)) -fx=np.zeros((int(np.floor((nmax+1))),1)) -fy=np.zeros((int(np.floor((nmax+1))),1)) -fz=np.zeros((int(np.floor((nmax+1))),1)) -for i in range(0,int(np.floor((nmax+1)/2))-1): - f[i]=(i)*df -for i in range(int(np.floor((nmax+1)/2))-1,int(nmax)): - f[i]=-1.0*(nmax-i)*df -for i in range(0,int(np.floor((nx+1)/2))-1): - fx[i]=(i)*dfx -for i in range(int(np.floor((nx+1)/2))-1,int(nx)): - fx[i]=-1.0*(nx-i)*dfx -for i in range(1,int(np.floor((ny+1)/2))-1): - fy[i]=(i)*dfy -for i in range(int(np.floor((ny+1)/2))-1,int(ny)): - fy[i]=-1.0*(ny-i)*dfy -for i in range(1,int(np.floor((nz+1)/2))-1): - fz[i]=(i)*dfz -for i in range(int(np.floor((nz+1)/2))-1,int(nz)): - fz[i]=-1.0*(nz-i)*dfz - -# Normal distribution -M=M2*np.random.randn(nmax,nmax,nmax)+M1 - -Mf=np.fft.fftn(M) -for i in range(0,nmax-1): - for k in range(0,nmax-1): - for l in range(0,nmax-1): - Mf[i,k,l]=Mf[i,k,l]*((f[i])**2+(f[k])**2+(f[l])**2+0.0000001)**(b/4) -## DC correction - not needed in python, req. in MATLAB -##Mf(1,1,1)=mean([Mf(2,1,1) Mf(1,2,1) Mf(1,1,2)]) - -Mi=np.fft.ifftn(Mf) -TFANO=np.zeros((nx,ny), dtype=np.complex) -ANO=np.zeros((nx,ny), dtype=np.complex) -#input("Press Enter to continue.") -## executes fine up to here. -for k in range(0,nz): - TFHM=np.fft.fft2(Mi[:,:,k]) - z1=zt+k*dlz - z2=z1+dlz -# disp(z1) -# disp(z2) - for i in range(0,nx): - for j in range(0,ny): - fH=float(np.sqrt((fx[i])**2+(fy[j])**2)) - TFANO[i,j]=TFHM[i,j]*2*np.pi*cm*(np.exp(-2*np.pi*fH*z1)-np.exp(-2*np.pi*fH*z2)) - ANO=ANO+np.fft.ifft2(TFANO) - -print("--- %s seconds ---" % (time.time() - start_time)) - -x=np.arange(0.5,0.5+dlx*(nx),dlx)*1000 -y=np.arange(0.5,0.5+dly*(nx),dly)*1000 -fid=open("../data/test_mag_data.txt","w+") -for i in range(0,nx): - for j in range(0,ny): - fid.write(' '.join([str(x[i]),str(y[j]),str(np.real(ANO[i,j])),"\n"])) - -fid.close() -#plt.pcolor(np.real(ANO)) -#plt.show() -#clear TFHM TFANO - -#figure (7) -## RD - PROBLEM! "Data inputs must be real". Trying abs(), or real() -##pcolor(ANO) -#pcolor(log10(abs(ANO))) -#shading flat -#colorbar - -##Sauvegarde carte : -#ncol=nx #Number of columns -#nrow=ny #Number of rows -#xleft=x(1) #x coordinate for left hand corner of grid -#dx=dlx #delta x -#yleft=y(1) #y coordinate for left hand corner of grid -#dy=dly #delta y -#gridC=ANO - -##save carte_synth_format.mat ncol nrow xleft yleft dx dy gridC -##save carte_synth.mat b M1 M2 dlx dly dlz zt zb MM2 ANO - - diff --git a/tests/Bouligand_forward.py b/tests/Bouligand_forward.py new file mode 100644 index 0000000..d78b039 --- /dev/null +++ b/tests/Bouligand_forward.py @@ -0,0 +1,156 @@ +## Code to generate test magnetic data for PyCurious examples +## Converted from MATLAB code by R Delhaye. +#Original code: +#Claire Bouligand +#03-19-2007 +#05-09-2014 +#Modified to use less memory + +import numpy as np +import pycurious +import time + +start_time=time.time() +cm=1e-7 + +########################################################## +#A VERIFIER: multiplier facteur cm par 4*pi +## TO VERIFY: multiplication factor "cm for 4*pi" +########################################################### +## Degree of fractal +b=-3.0 +## Dimension of pixels (km), should be multiples of the smallest +dlx=1.0 +dly=1.0 +dlz=1.0 +dl=min([dlx,dly,dlz]) +dx=dlx/dl +dy=dly/dl +dz=dlz/dl + +#nombre de pixels +## Number of pixels. +nx=305 +ny=305 +nz=10 +nmax=int(max([nx*dx,ny*dy,nz*dz])) + +#texte="dimensions x : %d / y : %d / z : %d" % (nx*dlx,ny*dly,nz*dlz) +#print(texte) +#disp(texte) + +#Parametres de l'aimantation +## Parameters of magnetisation +#M1=1 # aimantation moyenne = 1 A/m ## Average magnetisation +#M2=10^(0.25) # std de l'aimantation = 10^(0.25) A/m ## Standard dev of +#magnetisation +M1=0 +M2=0.2 +#prof sommet zt # Depth Zt +zt=0.305 +#prof base zb ## Depth Zb +zb=zt+nz*dlz + +############################################################ +#GENERATION DE LA DISTRIB 3D D'AIMANTATION FRACTAL +#A PARTIR VOLUME DE DIM ID. (nmax,dl) SELON X, Y ET Z + +if __name__ == "__main__": + + M=np.zeros((nmax,nmax,nmax)) + l=[0,(nmax-1)*dl,dl] + + #x=np.arange(0,dlx*(nx-1),dlx) + #y=np.arange(0,dly*(nx-1),dly) + #z=np.arange(0,dlz*(nx-1),dlz) + + df=1.0/(nmax*dl) + dfx=1.0/(nx*dlx) + dfy=1.0/(ny*dly) + dfz=1.0/(nz*dlz) + + #Center indices of matrix = Nyquist + c=(nmax+1)/2 + f=np.zeros((int(np.floor((nmax+1))),1)) + fx=np.zeros((int(np.floor((nmax+1))),1)) + fy=np.zeros((int(np.floor((nmax+1))),1)) + fz=np.zeros((int(np.floor((nmax+1))),1)) + for i in range(0,int(np.floor((nmax+1)/2))-1): + f[i]=(i)*df + for i in range(int(np.floor((nmax+1)/2))-1,int(nmax)): + f[i]=-1.0*(nmax-i)*df + for i in range(0,int(np.floor((nx+1)/2))-1): + fx[i]=(i)*dfx + for i in range(int(np.floor((nx+1)/2))-1,int(nx)): + fx[i]=-1.0*(nx-i)*dfx + for i in range(1,int(np.floor((ny+1)/2))-1): + fy[i]=(i)*dfy + for i in range(int(np.floor((ny+1)/2))-1,int(ny)): + fy[i]=-1.0*(ny-i)*dfy + for i in range(1,int(np.floor((nz+1)/2))-1): + fz[i]=(i)*dfz + for i in range(int(np.floor((nz+1)/2))-1,int(nz)): + fz[i]=-1.0*(nz-i)*dfz + + # Normal distribution + M=M2*np.random.randn(nmax,nmax,nmax)+M1 + + Mf=np.fft.fftn(M) + for i in range(0,nmax-1): + for k in range(0,nmax-1): + for l in range(0,nmax-1): + Mf[i,k,l]=Mf[i,k,l]*((f[i])**2+(f[k])**2+(f[l])**2+0.0000001)**(b/4) + ## DC correction - not needed in python, req. in MATLAB + ##Mf(1,1,1)=mean([Mf(2,1,1) Mf(1,2,1) Mf(1,1,2)]) + + Mi=np.fft.ifftn(Mf) + TFANO=np.zeros((nx,ny), dtype=np.complex) + ANO=np.zeros((nx,ny), dtype=np.complex) + #input("Press Enter to continue.") + ## executes fine up to here. + for k in range(0,nz): + TFHM=np.fft.fft2(Mi[:,:,k]) + z1=zt+k*dlz + z2=z1+dlz + # disp(z1) + # disp(z2) + for i in range(0,nx): + for j in range(0,ny): + fH=float(np.sqrt((fx[i])**2+(fy[j])**2)) + TFANO[i,j]=TFHM[i,j]*2*np.pi*cm*(np.exp(-2*np.pi*fH*z1)-np.exp(-2*np.pi*fH*z2)) + ANO=ANO+np.fft.ifft2(TFANO) + + print("--- %s seconds ---" % (time.time() - start_time)) + + x=np.arange(0.5,0.5+dlx*(nx),dlx)*1000 + y=np.arange(0.5,0.5+dly*(nx),dly)*1000 + fid=open("test_mag_data.txt","w+") + for i in range(0,nx): + for j in range(0,ny): + fid.write(' '.join([str(x[i]),str(y[j]),str(np.real(ANO[i,j])),"\n"])) + + fid.close() + #plt.pcolor(np.real(ANO)) + #plt.show() + #clear TFHM TFANO + + #figure (7) + ## RD - PROBLEM! "Data inputs must be real". Trying abs(), or real() + ##pcolor(ANO) + #pcolor(log10(abs(ANO))) + #shading flat + #colorbar + + ##Sauvegarde carte : + #ncol=nx #Number of columns + #nrow=ny #Number of rows + #xleft=x(1) #x coordinate for left hand corner of grid + #dx=dlx #delta x + #yleft=y(1) #y coordinate for left hand corner of grid + #dy=dly #delta y + #gridC=ANO + + ##save carte_synth_format.mat ncol nrow xleft yleft dx dy gridC + ##save carte_synth.mat b M1 M2 dlx dly dlz zt zb MM2 ANO + + From 66553289f30884d860bb892b62b626b0b15c0a18 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Tue, 18 Jun 2019 15:40:41 +1000 Subject: [PATCH 080/170] Run tests in Dockerfile We don't want to override latest or dev with a broken build --- Docker/Dockerfile | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/Docker/Dockerfile b/Docker/Dockerfile index 00e6baf..9e00b1f 100644 --- a/Docker/Dockerfile +++ b/Docker/Dockerfile @@ -34,6 +34,10 @@ RUN chown -R jovyan:jovyan /home/jovyan USER jovyan +# Run the tests with PyTest +RUN cd $MODULE_DIR && pytest tests/ + + ## These are supplied by the build script ## build-dockerfile.sh From 790d4ddad391120f60af8e3bea5c8030499c4f92 Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Thu, 20 Jun 2019 10:54:27 +1000 Subject: [PATCH 081/170] Updated a lot of docstrings incremented PyPI version to 0.3.1 --- MANIFEST.in | 1 - README.md | 18 +- pycurious/Examples/0-StartHere.ipynb | 88 ++++--- pycurious/__init__.py | 129 ++++++++- pycurious/documentation.py | 42 +-- pycurious/download.py | 49 +++- pycurious/grid.py | 95 ++++--- pycurious/mapping.py | 87 +++++-- pycurious/optimise.py | 166 +++++++----- pycurious/parallel.py | 204 --------------- pycurious/therm.py | 377 --------------------------- setup.cfg | 5 + setup.py | 2 +- 13 files changed, 481 insertions(+), 782 deletions(-) delete mode 100644 pycurious/parallel.py delete mode 100644 pycurious/therm.py diff --git a/MANIFEST.in b/MANIFEST.in index 3d647bf..efb6c1c 100644 --- a/MANIFEST.in +++ b/MANIFEST.in @@ -5,7 +5,6 @@ include COPYING include COPYING.LESSER include setup.cfg include src/* -include __init__.py recursive-include pycurious/*.py recursive-include pycurious/*.ipynb include tests/*.py diff --git a/README.md b/README.md index 4792bee..059fa0e 100644 --- a/README.md +++ b/README.md @@ -5,7 +5,7 @@ [![DOI](https://zenodo.org/badge/123281222.svg)](https://zenodo.org/badge/latestdoi/123281222) [![Build Status](https://travis-ci.org/brmather/pycurious.svg?branch=master)](https://travis-ci.org/brmather/pycurious) -Magnetic data is one of the most common geophysics datasets available on the surface of the Earth. Curie depth is the depth at which rocks lose their magnetism. The most prevalent magnetic mineral is magnetite, which has a Curie point of 580C, thus the Curie depth is often interpreted as the 580C isotherm. +Magnetic data is one of the most common geophysics datasets available on the surface of the Earth. Curie depth is the depth at which rocks lose their magnetism. The most prevalent magnetic mineral is magnetite, which has a Curie point of 580°C, thus the Curie depth is often interpreted as the 580°C isotherm. Current methods to derive Curie depth first compute the (fast) Fourier transform over a square window of a magnetic anomaly that has been reduced to the pole. The depth and thickness of magnetic sources is estimated from the slope of the radial power spectrum. `pycurious` implements the Tanaka *et al.* (1999) and Bouligand *et al.* (2009) methods for computing the thickness of a buried magnetic source, which are covered within Jupyter notebooks. @@ -28,17 +28,17 @@ pycurious.install_documentation(path="Notebooks") ### Tanaka -- [Ex1-Plot-power-spectrum.ipynb](pycurious-src/pycurious/Examples/Notebooks/Tanaka/Ex1-Plot-power-spectrum.ipynb) -- [Ex2-Compute-Curie-depth.ipynb](pycurious-src/pycurious/Examples/Notebooks/Tanaka/Ex2-Compute-Curie-depth.ipynb) -- [Ex3-Parameter-exploration.ipynb](pycurious-src/pycurious/Examples/Notebooks/Tanaka/Ex3-Parameter-exploration.ipynb) +- [Ex1-Plot-power-spectrum.ipynb](pycurious/Examples/Notebooks/Tanaka/Ex1-Plot-power-spectrum.ipynb) +- [Ex2-Compute-Curie-depth.ipynb](pycurious/Examples/Notebooks/Tanaka/Ex2-Compute-Curie-depth.ipynb) +- [Ex3-Parameter-exploration.ipynb](pycurious/Examples/Notebooks/Tanaka/Ex3-Parameter-exploration.ipynb) ### Bouligand -- [Ex1-Plot-power-spectrum.ipynb](pycurious-src/pycurious/Examples/Notebooks/Bouligand/Ex1-Plot-power-spectrum.ipynb) -- [Ex2-Compute-Curie-depth.ipynb](pycurious-src/pycurious/Examples/Notebooks/Bouligand/Ex2-Compute-Curie-depth.ipynb) -- [Ex3-Posing-the-inverse-problem.ipynb](pycurious-src/pycurious/Examples/Notebooks/Bouligand/Ex3-Posing-the-inverse-problem.ipynb) -- [Ex4-Spatial-variation-of-Curie-depth.ipynb](pycurious-src/pycurious/Examples/Notebooks/Bouligand/Ex4-Spatial-variation-of-Curie-depth.ipynb) -- [Ex5-Mapping-Curie-depth-EMAG2.ipynb](pycurious-src/pycurious/Examples/Notebooks/Bouligand/Ex5-Mapping-Curie-depth-EMAG2.ipynb) +- [Ex1-Plot-power-spectrum.ipynb](pycurious/Examples/Notebooks/Bouligand/Ex1-Plot-power-spectrum.ipynb) +- [Ex2-Compute-Curie-depth.ipynb](pycurious/Examples/Notebooks/Bouligand/Ex2-Compute-Curie-depth.ipynb) +- [Ex3-Posing-the-inverse-problem.ipynb](pycurious/Examples/Notebooks/Bouligand/Ex3-Posing-the-inverse-problem.ipynb) +- [Ex4-Spatial-variation-of-Curie-depth.ipynb](pycurious/Examples/Notebooks/Bouligand/Ex4-Spatial-variation-of-Curie-depth.ipynb) +- [Ex5-Mapping-Curie-depth-EMAG2.ipynb](pycurious/Examples/Notebooks/Bouligand/Ex5-Mapping-Curie-depth-EMAG2.ipynb) ## Installation diff --git a/pycurious/Examples/0-StartHere.ipynb b/pycurious/Examples/0-StartHere.ipynb index d1df166..9d7c998 100644 --- a/pycurious/Examples/0-StartHere.ipynb +++ b/pycurious/Examples/0-StartHere.ipynb @@ -14,9 +14,18 @@ "\n", "Launch the demonstration at [mybinder.org](https://mybinder.org/v2/gh/brmather/pycurious/binder?filepath=Notebooks%2F0-StartHere.ipynb)\n", "\n", + "\n", "## Navigation / Notebooks\n", "\n", - "There are two matching sets of `pycurious` notebooks - one set for the [Tanaka](#Tanaka) and one for [Bouligand](#Bouligand) implementations. The Bouligand set of noteboks are a natural choice for Bayesian inference applications.\n", + "There are two matching sets of Jupyter notebooks - one set for the [Tanaka](#Tanaka) and one for [Bouligand](#Bouligand) implementations. The Bouligand set of noteboks are a natural choice for Bayesian inference applications.\n", + "\n", + "Note, these examples can be installed from the package itself by running:\n", + "\n", + "```python\n", + "import pycurious\n", + "pycurious.install_documentation(path=\"Notebooks\")\n", + "```\n", + "\n", "\n", "### Tanaka\n", "\n", @@ -32,13 +41,42 @@ "- [Ex4-Spatial-variation-of-Curie-depth.ipynb](./Notebooks/Bouligand/Ex4-Spatial-variation-of-Curie-depth.ipynb)\n", "- [Ex5-Mapping-Curie-depth-EMAG2.ipynb](./Notebooks/Bouligand/Ex5-Mapping-Curie-depth-EMAG2.ipynb)\n", "\n", - "### Examples\n", + "## Installation\n", "\n", - "Note, these examples can be installed from the package itself by running:\n", + "### Dependencies\n", "\n", - "```python\n", - "import pycurious\n", - "pycurious.install_documentation(path=\"Notebooks\")\n", + "You will need **Python 2.7 or 3.5+**.\n", + "Also, the following packages are required:\n", + "\n", + "- [`numpy`](http://numpy.org)\n", + "- [`scipy`](https://scipy.org)\n", + "- [`cython`](https://cython.org/)\n", + "\n", + "__Optional dependencies__ for mapping module and running the Notebooks:\n", + "\n", + "- [`matplotlib`](https://matplotlib.org/)\n", + "- [`pyproj`](https://github.com/jswhit/pyproj)\n", + "- [`cartopy`](https://scitools.org.uk/cartopy/docs/latest/)\n", + "\n", + "### Installing using pip\n", + "\n", + "You can install `pycurious` using the\n", + "[`pip package manager`](https://pypi.org/project/pip/) with either version of Python:\n", + "\n", + "```bash\n", + "python2 -m pip install pycurious\n", + "python3 -m pip install pycurious\n", + "```\n", + "All the dependencies will be automatically installed by `pip`.\n", + "\n", + "### Installing using Docker\n", + "\n", + "A more straightforward installation for `pycurious` and all of its dependencies may be deployed with [Docker](https://www.docker.com).\n", + "To install the docker image and start the Jupyter notebook examples:\n", + "\n", + "```bash\n", + "docker pull brmather/pycurious:latest\n", + "docker run --name pycurious -p 8888:8888 brmather/pycurious:latest\n", "```\n", "\n", "## Usage\n", @@ -65,43 +103,19 @@ "k, Phi, sigma_Phi = grid.radial_spectrum(subgrid)\n", "```\n", "\n", - "## Installation\n", - "\n", - "To install with **setuptools**:\n", + "A series of tests are located in the *tests* subdirectory.\n", + "In order to perform these tests, clone the repository and run [`pytest`](https://pypi.org/project/pytest/):\n", "\n", "```bash\n", - "python setup.py install --user\n", + "git checkout https://github.com/brmather/pycurious.git\n", + "cd pycurious\n", + "pytest -v\n", "```\n", "\n", - "This will compile all C source code and install them to the user directory (omit the `--user` flag to install to the system directory). Remember to delete the build folder if you are upgrading this package.\n", - "\n", - "Alternatively, install using **pip**:\n", + "### API Documentation\n", "\n", - "```bash\n", - "pip install pycurious --user\n", - "```\n", + "The API for all functions and classes in `pycurious` can be accessed from [https://brmather.github.io/pycurious/](https://brmather.github.io/pycurious/).\n", "\n", - "### Dependencies\n", - "\n", - "- Python 2.7+ and 3.6+\n", - "- Numpy 1.9+\n", - "- Scipy 0.14+\n", - "- Cython\n", - "\n", - "Optional dependencies for mapping module:\n", - "\n", - "- Matplotlib\n", - "- [pyproj](https://github.com/jswhit/pyproj)\n", - "- [Cartopy](http://scitools.org.uk/cartopy/docs/latest/index.html)\n", - "\n", - "### Docker\n", - "\n", - "A more straightforward installation for `pycurious` and all of its dependencies may be deployed with [Docker](https://www.docker.com). To install the docker image and test it is working:\n", - "\n", - "```bash\n", - "docker pull brmather/pycurious:latest\n", - "docker run --rm brmather/pycurious:latest help\n", - "```\n", "\n", "## References\n", "\n", diff --git a/pycurious/__init__.py b/pycurious/__init__.py index 51783ff..a5dfd8b 100644 --- a/pycurious/__init__.py +++ b/pycurious/__init__.py @@ -1,7 +1,26 @@ +# Copyright 2018-2019 Ben Mather, Robert Delhaye +# +# This file is part of PyCurious. +# +# PyCurious is free software: you can redistribute it and/or modify +# it under the terms of the GNU Lesser General Public License as published by +# the Free Software Foundation, either version 3 of the License, or any later version. +# +# PyCurious is distributed in the hope that it will be useful, +# but WITHOUT ANY WARRANTY; without even the implied warranty of +# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +# GNU Lesser General Public License for more details. +# +# You should have received a copy of the GNU Lesser General Public License +# along with PyCurious. If not, see . + """ -Copyright 2018 Ben Mather, Robert Delhaye -This file is part of PyCurious. +> PyCurious is a Python package for computing the Curie depth from the magnetic anomaly. + +## Licence + +Copyright 2018-2019 Ben Mather, Robert Delhaye PyCurious is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by @@ -14,6 +33,112 @@ You should have received a copy of the GNU Lesser General Public License along with PyCurious. If not, see . + +## Installation + +### Dependencies + +You will need **Python 2.7 or 3.5+**. +Also, the following packages are required: + +- [`numpy`](http://numpy.org) +- [`scipy`](https://scipy.org) +- [`cython`](https://cython.org/) + +__Optional dependencies__ for mapping module and running the Notebooks: + +- [`matplotlib`](https://matplotlib.org/) +- [`pyproj`](https://github.com/jswhit/pyproj) +- [`cartopy`](https://scitools.org.uk/cartopy/docs/latest/) + +### Installing using pip + +You can install `pycurious` using the +[`pip package manager`](https://pypi.org/project/pip/) with either +version of Python: + +>>> python2 -m pip install pycurious +>>> python3 -m pip install pycurious + +All the dependencies will be automatically installed by `pip`. + +### Installing using Docker + +A more straightforward installation for `pycurious` and all of its +dependencies may be deployed with [Docker](https://www.docker.com). +To install the docker image and start the Jupyter notebook examples: + +>>> docker pull brmather/pycurious:latest +>>> docker run --name pycurious -p 8888:8888 brmather/pycurious:latest + +## Documenation / Notebooks + +Jupyter notebooks that demonstrate the functionality of PyCurious and +some common workflows may be installed to a local directory with + +```python +import pycurious +pycurious.install_documentation(path="Notebooks") +``` + +## Contributing to pycurious + +We welcome contributions to `pycurious`, large or small [\\*](#footnote1). +That can be in the form of new code, improvements to the documentation, +helping with a missing test, or it may even just be pointing out a bug or +potential improvement to the team. + +For bugs and suggestions, the most effective way to reach the team is by +raising an issue on the github issue tracker. Github allows you to classify +your issues so that we know if it is a bug report, feature request or +feedback to the authors. + +If you wish to contribute some changes to the code then you should submit a +*pull request*. On GitHub we can review the code that you are contributing +and discuss it before the changes are merged into the development version of +the code. Before embarking on changes to the code, please first take a look +at the [`dev` branch](https://github.com/brmather/pycurious/tree/dev) which +is where unreleased changes are staged: we may have been working on something +similar already. + +### How to create a Pull Request (PR) + +Create your own fork of the project on github: log into your github account, +navigate to the [`pycurious` repository](https://github.com/brmather/pycurious/tree/dev) +and click on the *fork* button at the top right corner of this repository. +You can find detailed instructions and a discussion of how to fork a +repository, clone it locally and work on the changes +[in the GitHub guides](https://guides.github.com/activities/forking/). + +### When to make your pull request + +It is much easier to merge in small changes to the code than extensive ones +that touch multiple files. If a small incremental change is possible, please +issue a request for that change rather than saving everything up. + +It is a good idea to commit frequently and with commit messages that refer +to the changes that have been make and why they have been made. The commit +message is usually browsed without seeing the actual changes themselves and +which sections of the code have been altered so a helpful message provides +relevant details. + +### Tests + +We use [`pytest`](https://pypi.org/project/pytest/) for the unit testing +framework in `pycurious`. In the source directory this means running: + +>>> python setup.py test + +The existing tests should be passing before you start coding (help us out with +an issue if that is not the case !) and when you have finished. Any new +functionality should also have tests that we can use to verify the code. +It is important that you make it clear if the original tests have had to +change to accomodate new code / functionality. + +* _Small changes are our favorites as they are much +easier to quickly merge into the existing code. Proofreading typos, bug fixes, +... the little stuff is especially welcome._ + """ # -*- coding: utf-8 -*- diff --git a/pycurious/documentation.py b/pycurious/documentation.py index ff346ed..95d63e8 100644 --- a/pycurious/documentation.py +++ b/pycurious/documentation.py @@ -1,19 +1,23 @@ -""" -Copyright 2018 Ben Mather, Robert Delhaye - -This file is part of PyCurious. +# Copyright 2018-2019 Ben Mather, Robert Delhaye +# +# This file is part of PyCurious. +# +# PyCurious is free software: you can redistribute it and/or modify +# it under the terms of the GNU Lesser General Public License as published by +# the Free Software Foundation, either version 3 of the License, or any later version. +# +# PyCurious is distributed in the hope that it will be useful, +# but WITHOUT ANY WARRANTY; without even the implied warranty of +# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +# GNU Lesser General Public License for more details. +# +# You should have received a copy of the GNU Lesser General Public License +# along with PyCurious. If not, see . -PyCurious is free software: you can redistribute it and/or modify -it under the terms of the GNU Lesser General Public License as published by -the Free Software Foundation, either version 3 of the License, or any later version. - -PyCurious is distributed in the hope that it will be useful, -but WITHOUT ANY WARRANTY; without even the implied warranty of -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -GNU Lesser General Public License for more details. +""" +Use the `pycurious.documentation.install_documentation` function to copy all +Jupyter Notebooks and example data to a local directory. -You should have received a copy of the GNU Lesser General Public License -along with PyCurious. If not, see . """ import pkg_resources as _pkg_resources @@ -33,14 +37,14 @@ def install_documentation(path="./PyCurious-Examples"): Some dependencies exist for the notebooks to be useful: - - matplotlib: for some diagrams - - cartopy: for mapping and visualisation - - pyepsg: for converting between map projections + - `matplotlib`: for some diagrams + - `cartopy`: for mapping and visualisation + - `pyepsg`: for converting between map projections PyCurious dependencies may be explicitly imported in the notebooks including: - - numpy - - scipy + - `numpy` + - `scipy` """ diff --git a/pycurious/download.py b/pycurious/download.py index bec09d5..06a16b1 100644 --- a/pycurious/download.py +++ b/pycurious/download.py @@ -1,22 +1,45 @@ +# Copyright 2018-2019 Ben Mather, Robert Delhaye +# +# This file is part of PyCurious. +# +# PyCurious is free software: you can redistribute it and/or modify +# it under the terms of the GNU Lesser General Public License as published by +# the Free Software Foundation, either version 3 of the License, or any later version. +# +# PyCurious is distributed in the hope that it will be useful, +# but WITHOUT ANY WARRANTY; without even the implied warranty of +# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +# GNU Lesser General Public License for more details. +# +# You should have received a copy of the GNU Lesser General Public License +# along with PyCurious. If not, see . + """ -Copyright 2018 Ben Mather, Robert Delhaye +This module provides some simple functions to download or install files. -This file is part of PyCurious. +It is good practise to store a checksum for each file. A checksum is a +unique signature used to identify a file, and ensure that the data +contained within the file is legitimate. Here is a sample workflow for +downloading EMAG2 (v3) and evaluating its checksum: -PyCurious is free software: you can redistribute it and/or modify -it under the terms of the GNU Lesser General Public License as published by -the Free Software Foundation, either version 3 of the License, or any later version. +```python +resource = { + "local_file":"../../data/EMAG2_V3_20170530.npz", + "md5":'c0898b6a91efb3f13783873a8b67380c', + "url":"https://zenodo.org/record/3245551/files/EMAG2_V3_20170530.npz?download=1", + "expected_size":"500Mb" + } -PyCurious is distributed in the hope that it will be useful, -but WITHOUT ANY WARRANTY; without even the implied warranty of -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -GNU Lesser General Public License for more details. +download_cached_file(resource["url"], resource["local_file"], resource["md5"], resource["expected_size"]) +``` -You should have received a copy of the GNU Lesser General Public License -along with PyCurious. If not, see . -""" +The file will commence downloading if it does not already exist in the local directory +or if the checksum (md5) does not match. If you do not know the checksum for a file, run -## Here are some functions to download or install files. +>>> md5sum(filename) + +to return its unique identifier. +""" def download_file(url, local_filename, expected_size="Unknown"): """ diff --git a/pycurious/grid.py b/pycurious/grid.py index 72bd171..df849b4 100644 --- a/pycurious/grid.py +++ b/pycurious/grid.py @@ -1,19 +1,38 @@ +# Copyright 2018-2019 Ben Mather, Robert Delhaye +# +# This file is part of PyCurious. +# +# PyCurious is free software: you can redistribute it and/or modify +# it under the terms of the GNU Lesser General Public License as published by +# the Free Software Foundation, either version 3 of the License, or any later version. +# +# PyCurious is distributed in the hope that it will be useful, +# but WITHOUT ANY WARRANTY; without even the implied warranty of +# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +# GNU Lesser General Public License for more details. +# +# You should have received a copy of the GNU Lesser General Public License +# along with PyCurious. If not, see . + """ -Copyright 2018 Ben Mather, Robert Delhaye +This PyCurious module contains the `pycurious.grid.CurieGrid` class, +which can be initialised with a magnetic grid of equal spacing in the x and y direction. +It contains methods for the following functionality: -This file is part of PyCurious. +- Decomposition of subgrids for processing square windows of the magnetic anomaly +- Removing linear trends from the magnetic anomaly +- Upward continuation +- Reduction to the pole -PyCurious is free software: you can redistribute it and/or modify -it under the terms of the GNU Lesser General Public License as published by -the Free Software Foundation, either version 3 of the License, or any later version. +Other functions within this module are useful to compute analytical solutions +of the radial power spectrum, \\( \\Phi \\) according to Bouligand *et al.* (2009), +Maus and Dimri (1995), and the decomposition of \\( \\Phi \\) from the magnetic +anomaly according to Tanaka *et al.* (1999): -PyCurious is distributed in the hope that it will be useful, -but WITHOUT ANY WARRANTY; without even the implied warranty of -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -GNU Lesser General Public License for more details. +- `bouligand2009`: analytic solution used in `pycurious.optimise.CurieOptimise` +- `maus1995`: simplified version of `pycurious.bouligand2009` without higher order integration. +- `tanaka1999`: to be used in conjunction with `pycurious.ComputeTanaka` -You should have received a copy of the GNU Lesser General Public License -along with PyCurious. If not, see . """ # -*- coding: utf-8 -*- @@ -361,7 +380,7 @@ def azimuthal_spectrum(self, subgrid, taper=np.hanning, scale=0.001, theta=5.0, def reduce_to_pole(self, data, inc, dec, sinc=None, sdec=None): - r""" + """ Reduce total field magnetic anomaly data to the pole. The reduction to the pole if a phase transformation that can be @@ -395,20 +414,29 @@ def reduce_to_pole(self, data, inc, dec, sinc=None, sdec=None): Notes: This functions performs the reduction in the frequency domain (using the FFT). The transform filter is (in the freq domain): - RTP(k_x, k_y) = \frac{|k|}{ - a_1 k_x^2 + a_2 k_y^2 + a_3 k_x k_y + - i|k|(b_1 k_x + b_2 k_y)} - in which k_x and k_y are the wave-numbers in the x and y + + \\( RTP(k_x, k_y) = \\frac{|k|}{ + a_1 k_x^2 + a_2 k_y^2 + a_3 k_x k_y + + i|k|(b_1 k_x + b_2 k_y)} \\) + + in which \\( k_x, k_y \\) are the wave-numbers in the x and y directions and - |k| = \sqrt{k_x^2 + k_y^2} \\ - a_1 = m_z f_z - m_x f_x \\ - a_2 = m_z f_z - m_y f_y \\ - a_3 = -m_y f_x - m_x f_y \\ - b_1 = m_x f_z + m_z f_x \\ - b_2 = m_y f_z + m_z f_y - \mathbf{m} = (m_x, m_y, m_z)` is the unit-vector of the total + + \\( |k| = \\sqrt{k_x^2 + k_y^2} \\) + + \\( a_1 = m_z f_z - m_x f_x \\) + + \\( a_2 = m_z f_z - m_y f_y \\) + + \\( a_3 = -m_y f_x - m_x f_y \\) + + \\( b_1 = m_x f_z + m_z f_x \\) + + \\( b_2 = m_y f_z + m_z f_y \\) + + \\( \\mathbf{m} = (m_x, m_y, m_z) \\) is the unit-vector of the total magnetization of the source and - \mathbf{f} = (f_x, f_y, f_z)` is the unit-vector of the + \\( \\mathbf{f} = (f_x, f_y, f_z) \\) is the unit-vector of the Geomagnetic field. """ nr, nc = data.shape @@ -443,20 +471,21 @@ def reduce_to_pole(self, data, inc, dec, sinc=None, sdec=None): def upward_continuation(self, data, height): - r""" + """ Upward continuation of potential field data. Calculates the continuation through the Fast Fourier Transform in the wavenumber domain (Blakely, 1996): - F\{h_{up}\} = F\{h\} e^{-\Delta z |k|} + \\( F\\{h_{up}\\} = F\\{h\\} e^{-\\Delta z |k|} \\) - and then transformed back to the space domain. :math:`h_{up}` is the - upward continue data, \Delta z is the height increase, F denotes - the Fourier Transform, |k| is the wavenumber modulus. + and then transformed back to the space domain. \\( h_{up} \\) is the + upward continue data, \\( \\Delta z \\) is the height increase, + \\( F \\) denotes the Fourier Transform, + \\( |k| \\) is the wavenumber modulus. Args: - data : 2D array + data : 2D array potential field at the grid points height : float height increase (delta z) in meters. @@ -465,12 +494,6 @@ def upward_continuation(self, data, height): cont : array upward continued data - Notes: - It is not possible to get the FFT of a masked grid. The default - :func:`fatiando.gridder.interp` call using minimum curvature will - not be suitable. Use extrapolate=True or algorithm='nearest' to - get an unmasked grid. - References: Blakely, R. J. (1996), Potential Theory in Gravity and Magnetic Applications, Cambridge University Press. diff --git a/pycurious/mapping.py b/pycurious/mapping.py index 6513265..88c2527 100644 --- a/pycurious/mapping.py +++ b/pycurious/mapping.py @@ -1,19 +1,46 @@ +# Copyright 2018-2019 Ben Mather, Robert Delhaye +# +# This file is part of PyCurious. +# +# PyCurious is free software: you can redistribute it and/or modify +# it under the terms of the GNU Lesser General Public License as published by +# the Free Software Foundation, either version 3 of the License, or any later version. +# +# PyCurious is distributed in the hope that it will be useful, +# but WITHOUT ANY WARRANTY; without even the implied warranty of +# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +# GNU Lesser General Public License for more details. +# +# You should have received a copy of the GNU Lesser General Public License +# along with PyCurious. If not, see . + """ -Copyright 2018 Ben Mather, Robert Delhaye +The `pycurious.mapping` module of PyCurious contains various functions to help +manipulate geospatial data into common formats. It handles commonly encounted +operations, such as: + +- Gridding scattered data points +- Converting between coordinate reference systems (CRS) +- Importing and exporting GeoTiff files + +It requires some **additional dependencies**: + +- [`matplotlib`](https://matplotlib.org/) - for plotting +- [`pyproj`](https://github.com/jswhit/pyproj) - for transforming CRS +- [`cartopy`](https://scitools.org.uk/cartopy/docs/latest/) - for mapping -This file is part of PyCurious. +Beware that most global data are georeferenced in WGS84 (EPSG: 4326). +The radial power spectrum must be in rad/km, which requires a transformation +from longitude / latitude to a local projection in eastings / northings. -PyCurious is free software: you can redistribute it and/or modify -it under the terms of the GNU Lesser General Public License as published by -the Free Software Foundation, either version 3 of the License, or any later version. +For example, EMAG2 is a global compilation of the magnetic anomaly +georeferenced in WGS84 longitude / latitude. This will need to be projected +in a local CRS to use with PyCurious. If we are interested in a region +across Ireland we could use the IRENET95 local CRS (EPSG: 2157), -PyCurious is distributed in the hope that it will be useful, -but WITHOUT ANY WARRANTY; without even the implied warranty of -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -GNU Lesser General Public License for more details. +>>> transform_coordinates(lons, lats, epsg_in=4326, epsg_out=2157) -You should have received a copy of the GNU Lesser General Public License -along with PyCurious. If not, see . +which would return a list of eastings and northings in IRENET95 projection. """ # -*- coding: utf-8 -*- @@ -26,7 +53,23 @@ def transform_coordinates(x, y, epsg_in, epsg_out): """ Transform between any coordinate system. - Requires `pyproj` + **Requires `pyproj`** - install using pip. + + Args: + x : float / 1D array + x coordinates (may be in degrees or metres/eastings) + y : float / 1D array + y coordinates (may be in degrees or metres/northings) + epsg_in : int + CRS of x and y coordinates + epsg_out : int + CRS of output + + Returns: + x_out : float / list of floats + x coordinates projected in `epsg_out` + y_out : float / list of floats + y coordinates projected in `epsg_out` """ import pyproj proj_in = pyproj.Proj("+init=EPSG:"+str(epsg_in)) @@ -62,7 +105,7 @@ def trim(coords, data, extent, buffer_amount=0.0): """ Trim a smaller section of a large dataset taking into consideration transformations into various coordinate - reference systems (CRS) + reference systems (CRS). Args: coords : array shape (n,2) @@ -108,7 +151,9 @@ def grid(coords, data, extent, shape=None, epsg_in=None, epsg_out=None, **kwargs """ Grid a smaller section of a large dataset taking into consideration transformations into various coordinate - reference systems (CRS) + reference systems (CRS). + + **Requires `scipy.interpolate.griddata`** Args: coords : array shape (n,2) @@ -116,7 +161,7 @@ def grid(coords, data, extent, shape=None, epsg_in=None, epsg_out=None, **kwargs data : array shape (n,) values corresponding to coordinates extent : tuple - box contained within the data in espg_out coordinates + bounding box in espg_out coordinates shape : tuple (nrows,ncols) size of the box, if None, shape is estimated from coords spacing epsg_in : int @@ -185,7 +230,9 @@ def grid(coords, data, extent, shape=None, epsg_in=None, epsg_out=None, **kwargs def import_geotiff(file_path): """ Import a GeoTIFF to a numpy array and prints - information of the Coordinate Reference System (CRS) + information of the Coordinate Reference System (CRS). + + **Requires `osgeo`.** Args: file_path : str @@ -194,7 +241,7 @@ def import_geotiff(file_path): Returns: data : 2D array extent : tuple - extent in the projection of the GeoTIFF + bounding box in the projection of the GeoTIFF e.g. [xmin, xmax, ymin, ymax] """ from osgeo import gdal, osr @@ -222,7 +269,9 @@ def import_geotiff(file_path): def export_geotiff(file_path, array, extent, epsg): """ Export a GeoTIFF from a numpy array projected in a - predefined Coordinate Reference System (CRS) + predefined Coordinate Reference System (CRS). + + **Requires `osgeo`.** Args: file_path : str @@ -230,7 +279,7 @@ def export_geotiff(file_path, array, extent, epsg): array: 2D array array to save to GeoTiff extent : tuple - extent in the projection of the GeoTIFF + bounding box in the projection of the GeoTIFF e.g. [xmin, xmax, ymin, ymax] epsg : int CRS of the GeoTIFF diff --git a/pycurious/optimise.py b/pycurious/optimise.py index 6de0f10..b0a4f75 100644 --- a/pycurious/optimise.py +++ b/pycurious/optimise.py @@ -1,19 +1,35 @@ +# Copyright 2018-2019 Ben Mather, Robert Delhaye +# +# This file is part of PyCurious. +# +# PyCurious is free software: you can redistribute it and/or modify +# it under the terms of the GNU Lesser General Public License as published by +# the Free Software Foundation, either version 3 of the License, or any later version. +# +# PyCurious is distributed in the hope that it will be useful, +# but WITHOUT ANY WARRANTY; without even the implied warranty of +# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +# GNU Lesser General Public License for more details. +# +# You should have received a copy of the GNU Lesser General Public License +# along with PyCurious. If not, see . + """ -Copyright 2018 Ben Mather, Robert Delhaye +This PyCurious module contains the `pycurious.optimise.CurieOptimise` class, +which inherits the `pycurious.grid.CurieGrid` class with added functionality for: -This file is part of PyCurious. +- Fitting the synthetic power spectrum \\( \\Phi \\) computed with `pycurious.grid.bouligand2009` +- Defining an objective function with a flexible interface for adding *a priori* and likelihood functions +- Parallel decomposition of routines to compute the optimal radial power spectrum, and thus Curie depth +- Metropolis-Hastings algorithm and sensitivity analysis to estimate the uncertainty of the posterior -PyCurious is free software: you can redistribute it and/or modify -it under the terms of the GNU Lesser General Public License as published by -the Free Software Foundation, either version 3 of the License, or any later version. +The posterior is defined as -PyCurious is distributed in the hope that it will be useful, -but WITHOUT ANY WARRANTY; without even the implied warranty of -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -GNU Lesser General Public License for more details. +\\( P(\\mathbf{m}|\\mathbf{d}) = P(\\beta, z_t, \\Delta z, C|\\Phi_d) \\) -You should have received a copy of the GNU Lesser General Public License -along with PyCurious. If not, see . +where \\( \\beta, z_t, \\Delta z, C \\) are input parameters to `pycurious.grid.bouligand2009` and +\\( \\Phi_d \\) is the radial power spectrum computed from a FFT over square windows of the magnetic +anomaly in `pycurious.grid.CurieGrid.radial_spectrum`. """ # -*- coding: utf-8 -*- @@ -31,8 +47,9 @@ class CurieOptimise(CurieGrid): """ - Extends the CurieGrid class to include optimisation routines - see scipy.optimize.minimize for a description of the algorithm + Extends the `pycurious.grid.CurieGrid` class to include + optimisation routines see `scipy.optimize.minimize` for + a description of the algorithm. Args: grid : 2D numpy array @@ -48,9 +65,9 @@ class CurieOptimise(CurieGrid): Attributes: bounds : list of tuples - lower and upper bounds for beta, zt, dz, C - prior : dict - dictionary of priors for beta, zt, dz, C + lower and upper bounds for \\( \\beta, z_t, \\Delta z, C \\) + prior : dict + dictionary of priors for \\( \\beta, z_t, \\Delta z, C \\) """ def __init__(self, grid, xmin, xmax, ymin, ymax, **kwargs): @@ -73,10 +90,10 @@ def __init__(self, grid, xmin, xmax, ymin, ymax, **kwargs): def add_prior(self, **kwargs): """ Add a prior to the dictionary (tuple) - Available priors are beta, zt, dz, C + Available priors are \\( \\beta, z_t, \\Delta z, C \\) Assumes a normal distribution or - define another distribution from scipy.stats + define another distribution from `scipy.stats` Usage: >>> add_prior(beta=(p, sigma_p)) @@ -120,7 +137,7 @@ def objective_routine(self, **kwargs): >>> objective_routine(beta=2.5) Returns: - misfit : float + misfit : float misfit integrated over all observations and priors """ c = 0.0 @@ -144,7 +161,7 @@ def objective_function(self, x, x0, sigma_x0, *args): sigma_x0 : float, ndarray Returns: - misfit : float + misfit : float """ return 0.5*np.sum((x - x0)**2/sigma_x0**2) @@ -155,20 +172,20 @@ def min_func(self, x, kh, Phi, sigma_Phi): Args: x : array shape (n,) - array of variables [beta, zt, dz, C] + array of variables \\( \\beta, z_t, \\Delta z, C \\) kh : array shape (n,) wavenumbers (rad/km) Phi : array shape (n,) - radial power spectrum + radial power spectrum \\( \\Phi \\) sigma_Phi : array shape (n,) - standard deviation of Phi + standard deviation of Phi, \\( \\sigma_{\\Phi} \\) Returns: - misfit : float - sum of misfit (float) + misfit : float + sum of misfit (scalar) Notes: - We purposely ignore all warnings raised by the bouligand2009 + We purposely ignore all warnings raised by the `pycurious.grid.bouligand2009` function because some combinations of input parameters will trigger an out-of-range warning that will crash the minimiser. Instead, the misfit is set to a very large number when this occurs. @@ -188,11 +205,11 @@ def min_func(self, x, kh, Phi, sigma_Phi): def optimise(self, window, xc, yc, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs): """ - Find the optimal parameters of beta, zt, dz, C for a given - centroid (xc,yc) and window size. + Find the optimal parameters of \\( \\beta, z_t, \\Delta z, C \\) + for a given centroid (xc,yc) and window size. Args: - window : float + window : float size of window in metres xc : float centroid x values @@ -206,7 +223,7 @@ def optimise(self, window, xc, yc, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.ha thickness of magnetic layer (starting value) C : float field constant (starting value) - taper : taper (default=np.hanning) + taper : taper (default=`numpy.hanning`) taper function, set to None for no taper function process_subgrids : function a custom function to process the subgrid @@ -270,22 +287,22 @@ def parallelise_routine(self, window, xc_list, yc_list, func, *args, **kwargs): along with any additional arguments or keyword arguments. Args: - window : float - size of window in metres - xc_list : array shape (l,) - centroid x values - yc_list : array shape (l,) - centroid y values - func : function - Python function to evaluate in parallel - args : arguments - additional arguments to pass to func - kwargs : keyword arguments - additional keyword arguments to pass to func + window : float + size of window in metres + xc_list : array shape (l,) + centroid x values + yc_list : array shape (l,) + centroid y values + func : function + Python function to evaluate in parallel + args : arguments + additional arguments to pass to `func` + kwargs : keyword arguments + additional keyword arguments to pass to `func` Returns: - out : list - (depends on output of func - see notes) + out : list of lists + (depends on output of `func` - see notes) Usage: An obvious use case is to compute the Curie depth for many @@ -295,16 +312,33 @@ def parallelise_routine(self, window, xc_list, yc_list, func, *args, **kwargs): Each centroid is assigned a new process and sent to a free processor to compute. In this case, the output is separate lists of shape(l,) - for beta, zt, dz, and C. + for \\( \\beta, z_t, \\Delta z, C \\). If `len(xc_list)=2` then, + + >>> self.parallelise_routine(window, [x1,x2], [y1, y2], self.optimise) + [[beta1 beta2], [zt1 zt2], [dz1 dz2], [C1 C2]] Another example is to parallelise the sensitivity analysis: >>> self.parallelise_routine(window, xc_list, yc_list, self.sensitivity, nsim) - This time the output will be a list of lists for beta, zt, dz, and C - i.e. if nc=2 is the number of centroids and nsim=4 is the number of - simulations then separatee lists [[k1, k2, k3, k4], [k1, k2, k3, k4]] - will be returned for beta, zt, dz, and C. + This time the output will be a list of lists for \\( \\beta, z_t, \\Delta z, C \\) + i.e. if `len(xc_list)=2` is the number of centroids and `nsim=4` is the number of + simulations then separatee lists will be returned for \\( \\beta, z_t, \\Delta z, C \\). + + >>> self.parallelise_routine(window, [x1,x2], [y1,y2], self.sensitivity, 4) + + which would return: + + ```python + [[[ beta1a , beta1b , beta1c , beta1d ], # centroid 1 (x1,y1) + [ beta2a , beta2b , beta2c , beta2d ]], # centroid 2 (x2,y2) + [[ zt1a , zt1b , zt1c , zt1d ], # centroid 1 (x1,y1) + [ zt2a , zt2b , zt2c , zt2d ]], # centroid 2 (x2,y2) + [[ dz1a , dz1b , dz1c , dz1d ], # centroid 1 (x1,y1) + [ dz2a , dz2b , dz2c , dz2d ]] # centroid 2 (x2,y2) + [[ C1a , C1b , C1c , C1d ], # centroid 1 (x1,y1) + [ C2a , C2b , C2c , C2d ]]] # centroid 2 (x2,y2) + ``` """ n = len(xc_list) @@ -367,7 +401,7 @@ def parallelise_routine(self, window, xc_list, yc_list, func, *args, **kwargs): def optimise_routine(self, window, xc_list, yc_list, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs): """ Iterate through a list of centroids to compute the optimal values - of beta, zt, dz, C for a given window size. + of \\( \\beta, z_t, \\Delta z, C \\) for a given window size. Args: window : float @@ -385,12 +419,12 @@ def optimise_routine(self, window, xc_list, yc_list, beta=3.0, zt=1.0, dz=10.0, C : float field constant taper : function - taper function (default=np.hanning) + taper function (default=`numpy.hanning`) set to None for no taper function - process_subgrids : func - a custom function to process the subgrid - kwargs : keyword arguments - to pass to radial_spectrum. + process_subgrids : func + a custom function to process the subgrid + kwargs : keyword arguments + to pass to radial_spectrum. Returns: beta : ndarray shape (l,) @@ -410,8 +444,9 @@ def metropolis_hastings(self, window, xc, yc, nsim, burnin, x_scale=None, beta=3 """ MCMC algorithm using a Metropolis-Hastings sampler. - Evaluates a Markov-Chain for starting values of beta, zt, dz, C - and returns the ensemble of model realisations. + Evaluates a Markov-Chain for starting values of + \\( \\beta, z_t, \\Delta z, C \\) and returns the + ensemble of model realisations. Args: window : float @@ -426,7 +461,8 @@ def metropolis_hastings(self, window, xc, yc, nsim, burnin, x_scale=None, beta=3 number of burn-in simulations before to nsim x_scale: float(4) (optional) scaling factor for new proposals - default is [1,1,1,1] for [beta, zt, dz, C] - see notes + (default=`[1,1,1,1]` for `[beta, zt, dz, C]`) + - see notes beta : float fractal parameter (starting value) zt : float @@ -447,9 +483,10 @@ def metropolis_hastings(self, window, xc, yc, nsim, burnin, x_scale=None, beta=3 field constant Notes: - nsim, burnin, and x_scale should be tweaked for optimal performance - Use starting values of beta, zt, dz, C relatively close to the solution - - C can easily found from the mean of the radial power spectrum. + `nsim`, `burnin`, and `x_scale` should be tweaked for optimal performance + Use starting values of \\( \\beta, z_t, \\Delta z, C \\) relatively + close to the solution - \\( C \\) can easily found from the mean of the + radial power spectrum. During the burn-in stage we apply tempering to the PDF to iterate closer towards the solution. This has the effect of smoothing out the posterior @@ -519,8 +556,9 @@ def process_subgrid(subgrid): def sensitivity(self, window, xc, yc, nsim, beta=3.0, zt=1.0, dz=10.0, C=5.0, taper=np.hanning, process_subgrid=None, **kwargs): """ Iterate through a list of centroids to compute the mean and - standard deviation of beta, zt, dz, C by perturbing their - prior distributions (if provided by the user - see add_prior). + standard deviation of \\( \\beta, z_t, \\Delta z, C \\) by + perturbing their prior distributions + (if provided by the user - see add_prior). Args: nsim : int @@ -532,7 +570,7 @@ def sensitivity(self, window, xc, yc, nsim, beta=3.0, zt=1.0, dz=10.0, C=5.0, ta yc : float centroid y values nsim : int - - number of simulations + number of simulations beta : float starting fractal parameter zt : float diff --git a/pycurious/parallel.py b/pycurious/parallel.py deleted file mode 100644 index cb75af7..0000000 --- a/pycurious/parallel.py +++ /dev/null @@ -1,204 +0,0 @@ -""" -Copyright 2018 Ben Mather, Robert Delhaye - -This file is part of PyCurious. - -PyCurious is free software: you can redistribute it and/or modify -it under the terms of the GNU Lesser General Public License as published by -the Free Software Foundation, either version 3 of the License, or any later version. - -PyCurious is distributed in the hope that it will be useful, -but WITHOUT ANY WARRANTY; without even the implied warranty of -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -GNU Lesser General Public License for more details. - -You should have received a copy of the GNU Lesser General Public License -along with PyCurious. If not, see . -""" - -# -*- coding: utf-8 -*- -import numpy as np -import warnings -from .optimise import CurieOptimise - -try: range=xrange -except: pass - - -class CurieParallel(CurieOptimise): - """ - A parallel implementation built on the PETSc DMDA mesh structure - Almost a trivially parallel problem: each processor works locally - on their portion of the grid. A stipulation being that the window - size must not exceed the thickness of shadow zones or else the - subgrid will be truncated. - - This inherits from CurieOptimise and CurieGrid classes. - - - Parameters - ---------- - grid : 2D array of magnetic data - xmin : minimum x bound in metres - xmax : maximum x bound in metres - ymin : minimum y bound in metres - ymax : maximum y bound in metres - max_window : maximum size of the windows - : this will be enforced for all methods - - Attributes - ---------- - bounds : lower and upper bounds for beta, zt, dz, C - prior : dictionary of priors for beta, zt, dz, C - coords : local xy coordinates - """ - - def __init__(self, grid, xmin, xmax, ymin, ymax, max_window): - - from petsc4py import PETSc - from mpi4py import MPI - comm = MPI.COMM_WORLD - self.comm = comm - self.MPI = MPI - - # super(CurieParallel, self).__init__(grid, xmin, xmax, ymin, ymax) - - # determine stencil width (should be window size/2) - ny, nx = grid.shape - dx = (xmax - xmin)/nx - dy = (ymax - ymin)/ny - nw = max_window/dx - n2w = int(nw/2) + 1 # add some buffer - - if abs(dx - dy) > 1.0: - warnings.warn("node spacing should be identical {}".format((dx,dy)), RuntimeWarning) - - - dm = PETSc.DMDA().create(dim=2, sizes=(nx,ny), stencil_width=n2w, comm=comm) - dm.setUniformCoordinates(xmin, xmax, ymin, ymax) - - self.dm = dm - self.lgmap = dm.getLGMap() - self.lvec = dm.createLocalVector() - self.gvec = dm.createGlobalVector() - - coords = dm.getCoordinatesLocal().array.reshape(-1, 2) - xmin, ymin = coords.min(axis=0) - xmax, ymax = coords.max(axis=0) - self.coords = coords - self.max_window = max_window - - (imin, imax), (jmin, jmax) = dm.getGhostRanges() - - # now decompose grid for each processor - - grid_chunk = grid[jmin:jmax, imin:imax] - - super(CurieParallel, self).__init__(grid_chunk, xmin, xmax, ymin, ymax) - - reduce_methods = {'sum': MPI.SUM, 'max': MPI.MAX, 'min': MPI.MIN, 'mean': MPI.SUM} - self._reduce_methods = reduce_methods - - - def subgrid(self, xc, yc, window): - """ - Extract a subgrid from the data at a window around - the point (xc,yc) - - Parameters - ---------- - xc : x coordinate - yc : y coordinate - window : size of window in metres - - Returns - ------- - data : subgrid - """ - if window > self.max_window: - raise ValueError("Max window size is {}".format(self.max_window)) - - return super(CurieParallel, self).subgrid(window, xc, yc) - - - def sync(self, vector): - """ - Synchronise a local vector across all processors - """ - self.lvec.setArray(vector) - self.dm.localToGlobal(self.lvec, self.gvec) - self.dm.globalToLocal(self.gvec, self.lvec) - return self.lvec.array.copy() - - - def add_parallel_prior(self, **kwargs): - """ - Add a prior to the dictionary (tuple) - This version broadcasts just the values from the root processor - - Available priors are beta, zt, dz, C - - Usage - ----- - add_parallel_prior(beta=(p, sigma_p)) - """ - - comm = self.comm - MPI = self.MPI - - for key in kwargs: - if key in self.prior: - prior = kwargs[key] - p = np.array(prior[0]) # prior - dp = np.array(prior[1]) # uncertainty - - comm.Bcast([p, MPI.DOUBLE], root=0) - comm.Bcast([dp,MPI.DOUBLE], root=0) - - self.prior[key] = (float(p), float(dp)) - else: - raise ValueError("prior must be one of {}".format(self.prior.keys())) - - - def distribute_prior(self, method, **kwargs): - """ - Distribute priors across all processors using a specific method. - - Parameters - ---------- - method : operation to reduce the local priors to a single value - : choose from one of 'sum', 'mean', 'min', 'max' - kwargs : (prior, sigma_prior) tuple - - Notes - ----- - add_prior will broadcast the prior on the root processor (rank=0) - distribute_prior enacts a MPI Allreduce operation. - """ - - comm = self.comm - MPI = self.MPI - - if method in self._reduce_methods: - op = self._reduce_methods[method] - else: - raise ValueError("choose one of the following methods {}".format(self._reduce_methods.keys())) - - for key in kwargs: - if key in self.prior: - prior = kwargs[key] - local_p = np.array(prior[0]) # prior - local_dp = np.array(prior[1]) # uncertainty - - global_p = np.array(0.0) - global_dp = np.array(0.0) - - comm.Allreduce([local_p, MPI.DOUBLE], [global_p, MPI.DOUBLE], op=op) - comm.Allreduce([local_dp, MPI.DOUBLE], [global_dp, MPI.DOUBLE], op=op) - if method == 'mean': - global_p /= comm.size - global_dp /= comm.size - - self.prior[key] = (float(global_p), float(global_dp)) - else: - raise ValueError("prior must be one of {}".format(self.prior.keys())) \ No newline at end of file diff --git a/pycurious/therm.py b/pycurious/therm.py deleted file mode 100644 index ceba4d3..0000000 --- a/pycurious/therm.py +++ /dev/null @@ -1,377 +0,0 @@ -""" -Copyright 2018 Ben Mather, Robert Delhaye - -This file is part of PyCurious. - -PyCurious is free software: you can redistribute it and/or modify -it under the terms of the GNU Lesser General Public License as published by -the Free Software Foundation, either version 3 of the License, or any later version. - -PyCurious is distributed in the hope that it will be useful, -but WITHOUT ANY WARRANTY; without even the implied warranty of -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -GNU Lesser General Public License for more details. - -You should have received a copy of the GNU Lesser General Public License -along with PyCurious. If not, see . -""" - -import numpy as np -from scipy import sparse -from scipy.sparse.linalg import spsolve -from multiprocessing import Pool, Process, Queue, cpu_count - -try: range=xrange -except: pass - - -class CurieTherm(object): - """ - Implicit 1d solver for the steady-state heat equation - over a structured grid using sparse matrices. - - Parameters - ---------- - minZ : float, minimum Cartesian coordinate - maxZ : float, maximum Cartesian coordinate - resZ : int, resolution in the z direction - kwargs : dict, keyword arguments to pass to control - optional functionality e.g. - - stencil_width=int : number of node neighbours to - include in each matrix row - - Attributes - ---------- - diffusivity : float shape(n,) thermal conductivity field - heat_sources : float shape(n,) heat source field - temperature : float shape(n,) temperature field - - npoints : int, number of nodes in the mesh - sizes : (int,int) dimensions of the sparse matrix - - """ - - def __init__(self, minZ, maxZ, resZ, **kwargs): - - self.npoints = resZ - self.extent = (minZ, maxZ) - self.coords = np.linspace(minZ, maxZ, resZ) - self.nodes = np.arange(0, resZ, dtype=np.int) - self.sizes = (resZ, resZ) - - width = kwargs.pop('stencil_width', 1) - self.stencil_width = 2*width + 1 - - closure = [(0,-2), (2,0), (1,-1)] - self.closure = self._create_closure_object(closure) - - - self._initialise_COO_vectors() - self._initialise_boundary_dictionary() - self.diffusivity = np.zeros(resZ) - self.heat_sources = np.zeros(resZ) - self.temperature = np.zeros(resZ) - - - def _initialise_COO_vectors(self): - - nn = self.npoints - - index = np.empty(nn + 2, dtype=np.int) - index.fill(-1) - self.index = index - - self.rows = np.empty((self.stencil_width, nn), dtype=np.int) - self.cols = np.empty((self.stencil_width, nn), dtype=np.int) - self.vals = np.empty((self.stencil_width, nn)) - - - def _initialise_boundary_dictionary(self): - - nn = self.npoints - coords = self.coords - minZ, maxZ = self.extent - - # Setup boundary dictionary - bc = dict() - - m0 = coords == minZ - m1 = coords == maxZ - d0 = abs(coords[1] - coords[0]) - d1 = abs(coords[-1] - coords[-2]) - - bc["minZ"] = {"val": 0.0, "delta": d0, "flux": True, "mask": m0} - bc["maxZ"] = {"val": 0.0, "delta": d1, "flux": True, "mask": m1} - - self.bc = bc - self.dirichlet_mask = np.zeros(nn, dtype=bool) - - - def _create_closure_object(self, closure): - - nn = self.npoints - obj = [[0] for i in range(self.stencil_width)] - - for i in range(0, self.stencil_width): - # construct slicing object - start, end = closure[i-j] - obj[i] = slice(start, nn+end+2) - - return obj - - - def update_properties(self, diffusivity, heat_sources): - """ - Update diffusivity and heat sources - """ - self.diffusivity[:] = diffusivity - self.heat_sources[:] = heat_sources - return - - - def boundary_condition(self, wall, val, flux=False): - """ - Set the boundary conditions on each wall of the domain. - By default each wall is a Dirichlet condition. - - Parameters - ---------- - wall : str, wall to assign bc - 'minZ' or 'maxZ' - val : float or array(n,) value(s) to assign to wall - flux : bool, toggle type of boundary condition - True = Neumann flux boundary condition - False = Dirichlet boundary condition (default) - - Notes - ----- - If flux=True, positive val indicates a flux vector towards the centre - of the domain. - - val can be a vector with the same number of elements as the wall - """ - wall = str(wall) - - if wall in self.bc: - self.bc[wall]["val"] = np.array(val, copy=True) - self.bc[wall]["flux"] = flux - d = self.bc[wall] - - mask = d['mask'] - - if flux: - self.dirichlet_mask[mask] = False - self.bc[wall]["val"] /= -d['delta'] - else: - self.dirichlet_mask[mask] = True - - else: - raise ValueError("Wall should be one of {}".format(self.bc.keys())) - - - def construct_matrix(self): - """ - Construct a sparse coefficient matrix - i.e. matrix A in AT = b - - Notes - ----- - We vectorise the 7-point stencil for fast matrix insertion. - An extra border of dummy values around the domain allows for automatic - Neumann (flux) boundary creation. - These are stomped on if there are any Dirichlet conditions. - """ - - nodes = self.nodes - nn = self.npoints - - index = self.index - - rows = self.rows - cols = self.cols - vals = self.vals - - dirichlet_mask = self.dirichlet_mask - coords = self.coords.reshape(-1,1) - - u = self.diffusivity - - k = np.zeros(nn + 2) - k[1:-1] = u - - for i in range(0, self.stencil_width): - obj = self.closure[i] - - rows[i] = nodes - cols[i] = index[obj].ravel() - - distance = np.linalg.norm(coords[cols[i]] - coords, axis=1) - distance[distance==0] = 1e-12 # protect against dividing by zero - delta = 1.0/(2.0*distance**2) - - vals[i] = delta*(k[obj] + u).ravel() - - - # Dirichlet boundary conditions (duplicates are summed) - cols[:,dirichlet_mask] = nodes[dirichlet_mask] - vals[:,dirichlet_mask] = 0.0 - - # zero off-grid coordinates - vals[cols < 0] = 0.0 - - # centre point - vals[-1] = 0.0 - vals[-1][dirichlet_mask] = -1.0 - - - row = rows.ravel() - col = cols.ravel() - val = vals.ravel() - - - # mask off-grid entries and sum duplicates - mask = col >= 0 - row = row[mask] - col = col[mask] - val = val[mask] - - mat = sparse.coo_matrix((val, (row, col)), shape=self.sizes).tocsr() - mat.sum_duplicates() - diag = np.ravel(mat.sum(axis=1)) - diag *= -1 - mat.setdiag(diag) - - return mat - - - def construct_rhs(self): - """ - Construct the right-hand-side vector - i.e. vector b in AT = b - - Notes - ----- - Boundary conditions are grabbed from the dictionary and - summed to the rhs. - Be careful of duplicate entries on the corners!! - """ - - rhs = -1.0*self.heat_sources - - for wall in self.bc: - val = self.bc[wall]['val'] - flux = self.bc[wall]['flux'] - mask = self.bc[wall]['mask'] - if flux: - rhs[mask] += val - else: - rhs[mask] = val - - return rhs - - - def solve(self, matrix=None, rhs=None): - """ - Construct the matrix A and vector b in AT = b and solve for T - (i.e. temperature field) - - Arguments - --------- - matrix : (optional) scipy sparse matrix object - build using construct_matrix() - rhs : (optional) numpy right-hand-side vector - build using construct_rhs() - - Returns - ------- - sol : 1d array shape(n,) temperature solution - - Notes - ----- - The solution to the system of linear equations AT = b is solved - with spsolve in the scipy.sparse.linalg module - """ - if matrix is None: - matrix = self.construct_matrix() - if rhs is None: - rhs = self.construct_rhs() - # res = self.temperature - - T = spsolve(matrix, rhs) - self.temperature[:] = T - - return T - - - def gradient(self, vector, **kwargs): - """ - Calculate gradient of a vector - - Arguments - --------- - vector : 1d array of shape(n,) - - Returns - ------- - dvdz : 1d array of shape(n,) - derivative of vector in z direction - """ - return np.gradient(vector, self.coords, **kwargs) - - - def heatflux(self): - """ - Calculate the heat flux from the conductivity field - and temperature solution - - Returns - ------- - qz : 1d array shape(n,) heat flux vector - """ - - T = self.temperature - k = self.diffusivity - divT = self.gradient(T) - return -k*divT - - - def isosurface(self, vector, isoval, interp='linear'): - """ - Calculate an isosurface along the z axis - - Parameters - ---------- - vector : array, the same size as the mesh (n,) - isoval : float, isosurface value - interp : str, interpolation method can be either - 'nearest' - nearest neighbour interpolation - 'linear' - linear interpolation - - Returns - ------- - z_interp : isosurface - """ - coords = self.coords - sort_idx = np.abs(vector - isoval).argsort() - i0 = sort_idx[0] - z0 = coords[i0] - - if interp == 'linear': - v0 = vector[i0] - - # identify next nearest node - i1 = sort_idx[1] - z1 = coords[i1] - v1 = vector[i1] - - vmin = min(v0,v1) - vmax = max(v0,v1) - - ratio = np.array([isoval, vmin, vmax]) - ratio -= ratio.min() - ratio /= ratio.max() - z_interp = ratio[0]*z1 + (1.0 - ratio[0])*z0 - return z_interp - elif interp == 'nearest': - return z0 - else: - raise ValueError("enter a valid interp method: 'linear' or 'nearest'") diff --git a/setup.cfg b/setup.cfg index 52985f1..7295b60 100644 --- a/setup.cfg +++ b/setup.cfg @@ -1,7 +1,12 @@ +[aliases] +test=pytest + [bdist_wheel] + # This flag says that the code is written to work on both Python 2 and Python # 3. If at all possible, it is good practice to do this. If you cannot, you # will need to generate wheels for each Python version that you support. + universal=1 [metadata] description-file = README.md diff --git a/setup.py b/setup.py index 854f975..0def317 100644 --- a/setup.py +++ b/setup.py @@ -19,7 +19,7 @@ import io ## in development set version to none and ... -PYPI_VERSION = "0.3" +PYPI_VERSION = "0.3.1" # Return the git revision as a string (from numpy) def git_version(): From 17489a89fdef516dc07ddcad4082196de11fd71b Mon Sep 17 00:00:00 2001 From: Ben Mather Date: Thu, 20 Jun 2019 17:05:43 +1000 Subject: [PATCH 082/170] Adding PyCurious logo --- README.md | 2 +- pycurious/Examples/Images/pycurious-logo.pdf | Bin 0 -> 1536715 bytes pycurious/Examples/Images/pycurious-logo.png | Bin 0 -> 233328 bytes 3 files changed, 1 insertion(+), 1 deletion(-) create mode 100644 pycurious/Examples/Images/pycurious-logo.pdf create mode 100644 pycurious/Examples/Images/pycurious-logo.png diff --git a/README.md b/README.md index 059fa0e..34df2be 100644 --- a/README.md +++ b/README.md @@ -1,4 +1,4 @@ -# PyCurious +![PyCurious](https://github.com/brmather/pycurious/blob/master/pycurious/Examples/Images/pycurious-logo.png?raw=true) [![Docker Cloud Automated build](https://img.shields.io/docker/cloud/automated/brmather/pycurious.svg)](https://hub.docker.com/r/brmather/pycurious) [![PyPI](https://img.shields.io/pypi/v/pycurious.svg)](https://pypi.org/project/pycurious/) diff --git a/pycurious/Examples/Images/pycurious-logo.pdf b/pycurious/Examples/Images/pycurious-logo.pdf new file mode 100644 index 0000000000000000000000000000000000000000..52b5a3f1e1dd5d726c7741436b243722dc5a3e1d GIT binary patch literal 1536715 zcmce-WmFwa(>5C1Ay{w^792M2?oMzC&c>bKZo%E%A-KB*_l>)|yTc*(b3gC*9r<<6 zT4&a*nd#cqJykVTGgo!jCRY#p zkd)wwiHRA+fR>KN_8(_UeMe&vV?!GwV|YG3cn3#&V|^?5pXr|JBNgPFs4LGj=5S#Z zc2B2te!OJ$e{czy{3op@5%C_}NlC5dn*j!5M-F5oQ6Aiut)y@71`kEE+ygNtt-9+y z44VVTNuL{ko@MF1+rJ(@ar327JauBf_hxP1Uh`KHz0FpvzmvTbFD8S6b*R@li$;c< 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