From 259ff71b89a26f16106608cf70a195363077007d Mon Sep 17 00:00:00 2001 From: Bruno Beltran Date: Tue, 29 Sep 2020 14:34:44 -0700 Subject: [PATCH] CLEANUP: make pip installable, versioneer, rm build --- .gitattributes | 2 + .gitignore | 4 + MANIFEST.in | 3 + doc/build/doctrees/environment.pickle | Bin 64605 -> 0 bytes doc/build/doctrees/index.doctree | Bin 4636 -> 0 bytes doc/build/doctrees/poly_dyn.doctree | Bin 91629 -> 0 bytes doc/build/doctrees/references.doctree | Bin 9475 -> 0 bytes doc/build/doctrees/wlcave_notes.doctree | Bin 71782 -> 0 bytes doc/build/doctrees/wlcgreen_notes.doctree | Bin 97848 -> 0 bytes doc/build/doctrees/wlcstruc_notes.doctree | Bin 36544 -> 0 bytes doc/build/doctrees/wlctheory.doctree | Bin 52607 -> 0 bytes doc/build/html/.buildinfo | 4 - doc/build/html/.nojekyll | 0 doc/build/html/_images/poly_dyn-1.png | Bin 31511 -> 0 bytes doc/build/html/_images/rouse-mscd.pdf | Bin 367343 -> 0 bytes doc/build/html/_images/wlc-model.pdf | Bin 451900 -> 0 bytes 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b/MANIFEST.in @@ -0,0 +1,3 @@ +include versioneer.py +include wlcstat/_verison.py +include wlcstat/_version.py diff --git a/doc/build/doctrees/environment.pickle b/doc/build/doctrees/environment.pickle deleted file mode 100644 index 67ee5f1099327ed1b5b2aa90c507bc61343329ad..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 64605 zcmd_T4Uim1b{+@)AbJMVJwNy%2y!U=bGZWyX@a}jT@1Ea-CZ+X zJ^jb7YG4LfNV070l6FbUlUfQ%_SvDZ9F|XE-;d&S@>x2C71D+7{BxF0;q`5t9P;|^ zbPD;T(Af^z4oUX+-pkC&s_LGZZi2KG0(Wb=^5^Bt_g=ny`SNAfcR%?jYD7Eoi$dt@~5gTIDW53Z`!Rjc(ly{Z?~I^8E0@)UqE|yQQi7^>PrpVLtSN zFyC&~*YcIMrcRwg15+hJgMLv{K`+`7bjsY~mp`l)gI2dw_Rvzf)m-wId(l2cAN{`L zs$>{~>~7ujIvu|P{2uk9Cj&3+GJ(9+&}#P^;TH-O9d$mN)#xi2-bP!(7)&Pyl7{;)2iXE z7wuGX(2I7LTkW-uzg$J?k=g0l=}G5uv$E#gW~qYYfG?n3wFQ~mpU&AIdW|+j%?pZc z^dCfz#)>Ab=SBy;)pEUC@hBS|VZKC1CMF7gd#zb2maATQrQJd&0~8*shK+hLta=R+ zhNc^KJNR*sQ%Pw3vT5ZAu~Tubxa>8(4v^@*8$GM3SX^$kmg`;-+zY~v-(2p!7d>M# 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- -
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-
-
- -

All modules for which code is available

- - -
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-
- - - - \ No newline at end of file diff --git a/doc/build/html/_modules/wlcstat/poly_dyn.html b/doc/build/html/_modules/wlcstat/poly_dyn.html deleted file mode 100644 index bc13229..0000000 --- a/doc/build/html/_modules/wlcstat/poly_dyn.html +++ /dev/null @@ -1,299 +0,0 @@ - - - - - - - - wlcstat.poly_dyn — wlcstat documentation - - - - - - - - - - - - - - - -
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- -

Source code for wlcstat.poly_dyn

-"""Rouse polymer, analytical results.
-
-Notes
------
-There are two parameterizations of the "Rouse" polymer that are commonly used,
-and they use the same variable name for two different things.
-
-In one, N is the number of Kuhn lengths, and in the other, N is the number of
-beads, each of which can represent an arbitrary number of Kuhn lengths.
-"""
-import numpy as np
-from numba import jit
-# import mpmath
-
-from functools import lru_cache
-from pathlib import Path
-import os
-
-
-
[docs]@jit -def rouse_mode(p, n, N=1): - """Eigenbasis for Rouse model. - - Indexed by p, depends only on position n/N along the polymer of length N. - N=1 by default. - - Weber, Phys Rev E, 2010 (Eq 14)""" - p = np.atleast_1d(p) - phi = np.sqrt(2)*np.cos(p*np.pi*n/N) - phi[p == 0] = 1 - return phi
- - -
[docs]@jit(nopython=True) -def rouse_mode_coef(p, b, N, kbT=1): - """k_p: Weber Phys Rev E 2010, after Eq. 18.""" - # alternate: k*pi**2/N * p**2, i.e. k = 3kbT/b**2 - return 3*np.pi**2*kbT/(N*b**2)*p**2
- - -
[docs]@jit(nopython=True) -def kp_over_kbt(p : float, b : float, N : float): - """k_p/(k_B T) : "non-dimensionalized" k_p is all that's needed for most - formulas, e.g. MSD.""" - return (3*np.pi*np.pi)/(N*b*b) * p*p
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[docs]@jit(nopython=True) -def linear_mid_msd(t, b, N, D, num_modes=20000): - """ - modified from Weber Phys Rev E 2010, Eq. 24. - """ - msd = np.zeros_like(t) - for p in range(1, num_modes+1): - k2p_norm = kp_over_kbt(2*p, b, N) - msd += (1 / k2p_norm) * (1 - np.exp(-k2p_norm * (D / N) * t)) - return 12 * msd + 6 * D * t / N
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[docs]@jit(nopython=True) -def gaussian_G(r, N, b): - """Green's function of a Gaussian chain at N Kuhn lengths of separation, - given a Kuhn length of b""" - r2 = np.power(r, 2) - return np.power(3/(2*np.pi*b*b*N), 3/2)*np.exp(-(3/2)*r2/(N*b*b))
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[docs]@jit(nopython=True) -def gaussian_Ploop(a, N, b): - """Looping probability for two loci on a Gaussian chain N kuhn lengths - apart, when the Kuhn length is b, and the capture radius is a""" - Nb2 = N*b*b - return spycial.erf(a*np.sqrt(3/2/Nb2)) - a*np.sqrt(6/np.pi/Nb2)/np.exp(3*a*a/2/Nb2)
- - -@jit(nopython=True) -def _cart_to_sph(x, y, z): - r = np.sqrt(x*x + y*y + z*z) - if r == 0.0: - return 0.0, 0.0, 0.0 - phi = np.arctan2(y, x) - theta = np.arccos(z/r) - return r, phi, theta - - -def confined_G(r, rp, N, b, a, n_max=100, l_max=50): - # first precompute the zeros of the spherical bessel functions, since our - # routine to do so is pretty slow - if l_max >= 86: # for l >= 86, |m| >= 85 returns NaN from sph_harm - raise ValueError("l_max > 85 causes NaN's from scipy.special.sph_harm") - if confined_G.zl_n is None or n_max > confined_G.zl_n.shape[1] \ - or l_max > confined_G.zl_n.shape[0]: - confined_G.zl_n = spherical_jn_zeros(l_max, n_max) - # some aliases - spherical_jn = scipy.special.spherical_jn - Ylm = scipy.special.sph_harm - zl_n = confined_G.zl_n[:l_max+1,:n_max] - # convert to spherical coordinates - r = np.array(r) - if r.ndim == 1: - x, y, z = r - xp, yp, zp = rp - # elif r.ndim == 2: - # x = r[:,0] - # y = r[:,1] - # z = r[:,2] - # xp = rp[:,0] - # yp = rp[:,1] - # zp = rp[:,2] - else: - raise ValueError("Don't understand your R vectors") - r, phi, theta = _cart_to_sph(x, y, z) - rp, phip, thetap = _cart_to_sph(xp, yp, zp) - # compute terms based on indexing (ij in meshgrid to match zl_n) - l, n = np.meshgrid(np.arange(l_max+1), np.arange(n_max), indexing='ij') - ln_term = 2*np.exp(-b**2/6 * (zl_n/a)**2 * N) - ln_term = ln_term/(a**3 * spherical_jn(l+1, zl_n)**2) - ln_term = ln_term*spherical_jn(l, zl_n/a*r)*spherical_jn(l, zl_n/a*rp) - # l,m terms - m = np.arange(-l_max, l_max+1) - l, m = np.meshgrid(np.arange(l_max+1), np.arange(-l_max, l_max+1)) - lm_term = Ylm(m, l, phi, theta)*Ylm(m, l, phip, thetap) - lm_mask = np.abs(m) <= l - lm_term[~lm_mask] = 0 - # now broadcast and sum - G = np.sum(ln_term[None,:,:] * lm_term[:,:,None]) - return G -confined_G.zl_n = None - - -
[docs]def linear_mscd(t, D, Ndel, N, b=1, num_modes=20000): - r""" - Compute mscd for two points on a linear polymer. - - Parameters - ---------- - t : (M,) float, array_like - Times at which to evaluate the MSCD - D : float - Diffusion coefficient, (in desired output length units). Equal to - :math:`k_BT/\xi` for :math:`\xi` in units of "per Kuhn length". - Ndel : float - Distance from the last linkage site to the measured site. This ends up - being (1/2)*separation between the loci (in Kuhn lengths). - N : float - The full lengh of the linear polymer (in Kuhn lengths). - b : float - The Kuhn length (in desired length units). - num_modes : int - how many Rouse modes to include in the sum - - Returns - ------- - mscd : (M,) np.array<float> - result - """ - mscd = np.zeros_like(t) - - k1 = 3 * np.pi ** 2 / (N * (b ** 2)) - sum_coeff = 48 / k1 - exp_coeff = k1 * D / N - sin_coeff = np.pi * Ndel / N - - for p in range(1, num_modes+1, 2): - mscd += (1/p**2) * (1 - np.exp(-exp_coeff * (p ** 2) * t)) \ - * np.sin(sin_coeff*p)**2 - - return sum_coeff * mscd
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[docs]def ring_mscd(t, D, Ndel, N, b=1, num_modes=20000): - r""" - Compute mscd for two points on a ring. - - Parameters - ---------- - t : (M,) float, array_like - Times at which to evaluate the MSCD. - D : float - Diffusion coefficient, (in desired output length units). Equal to - :math:`k_BT/\xi` for :math:`\xi` in units of "per Kuhn length". - Ndel : float - (1/2)*separation between the loci on loop (in Kuhn lengths) - N : float - full length of the loop (in Kuhn lengths) - b : float - The Kuhn length, in desired output length units. - num_modes : int - How many Rouse modes to include in the sum. - - Returns - ------- - mscd : (M,) np.array<float> - result - """ - mscd = np.zeros_like(t) - - k1 = 12 * np.pi ** 2 / (N * (b ** 2)) - sum_coeff = 48 / k1 - exp_coeff = k1 * D / N - sin_coeff = 2 * np.pi * Ndel / N - - for p in range(1, num_modes+1): - mscd += (1 / p ** 2) * (1 - np.exp(-exp_coeff * p ** 2 * t)) \ - * np.sin(sin_coeff * p) ** 2 - return sum_coeff * mscd
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[docs]def end_to_end_corr(t, D, N, num_modes=10000): - """Doi and Edwards, Eq. 4.35""" - mscd = np.zeros_like(t) - tau1 = N**2/(3*np.pi*np.pi*D) - for p in range(1, num_modes+1, 2): - mscd += 8/p/p/np.pi/np.pi * np.exp(-t*p**2 / tau1) - return N*mscd
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- - - - \ No newline at end of file diff --git a/doc/build/html/_modules/wlcstat/wlcave.html b/doc/build/html/_modules/wlcstat/wlcave.html deleted file mode 100644 index 5264327..0000000 --- a/doc/build/html/_modules/wlcstat/wlcave.html +++ /dev/null @@ -1,186 +0,0 @@ - - - - - - - - wlcstat.wlcave — wlcstat documentation - - - - - - - - - - - - - - - -
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Source code for wlcstat.wlcave

-import numpy as np
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[docs]def r2_ave(length_kuhn, dimensions=3): - r""" - r2_ave - Calculate the average end-to-end distance squared :math:`\langle R^{2} \rangle / (2 l_{p})^{2}` - for the wormlike chain model - - Parameters - ---------- - length_kuhn : float (array) - The length of the chain in Kuhn lengths - dimensions : int - The number of dimensions (default to 3 dimensions) - - Returns - ------- - r2 : float (array) - The mean-square end-to-end distance for the wormlike chain model (non-dimensionalized by :math:`2 l_{p})` - - Notes - ----- - See Mehraeen, et al, Phys. Rev. E, 77, 061803 (2008). (Ref [Mehraeen2008]_) - """ - r2 = 2 * (length_kuhn / (dimensions - 1) - - (1 - np.exp(-(dimensions - 1) * length_kuhn)) / (dimensions - 1) ** 2) - - return r2
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[docs]def rg2_ave(length_kuhn, dimensions=3): - r""" - rg2_ave - Calculate the radius of gyration - :math:`\langle \vec{R}_{G}^{2} \rangle / (2 l_{p})^{2}` for the wormlike chain model - - Parameters - ---------- - length_kuhn : float (array) - The length of the chain in Kuhn lengths - dimensions : int - The number of dimensions (default to 3 dimensions) - - Returns - ------- - rg2 : float (array) - The mean-square radius of gyration for the wormlike chain model (non-dimensionalized by :math:`2 l_{p})` - - Notes - ----- - See Mehraeen, et al, Phys. Rev. E, 77, 061803 (2008). (Ref [Mehraeen2008]_) - """ - rg2 = 2 * (length_kuhn / (6 * (dimensions - 1)) - 1 / (2 * (dimensions - 1) ** 2) - + length_kuhn ** -1 / (dimensions - 1) ** 3 - - length_kuhn ** -2 * (1 - np.exp(-(dimensions - 1) * length_kuhn)) / (dimensions - 1) ** 4) - - return rg2
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[docs]def rz4_ave(length_kuhn, dimensions=3): - r""" - rz4_ave - Calculate the 4th moment of the end-to-end distribution - :math:`\langle R_{z}^{4} \rangle / (2 l_{p})^{4}` for the wormlike chain model - - Parameters - ---------- - length_kuhn : float (array) - The length of the chain in Kuhn lengths - dimensions : int - The number of dimensions (default to 3 dimensions) - - Returns - ------- - rz4 : float (array) - The mean-square end-to-end distance for the wormlike chain model (non-dimensionalized by :math:`2 l_{p})` - - Notes - ----- - See Mehraeen, et al, Phys. Rev. E, 77, 061803 (2008). (Ref [Mehraeen2008]_) - """ - - # Calculate the coefficients from the ladder operations on the hyperspherical harmonics (dimensions) - a1 = np.sqrt(1 / dimensions) - a2 = np.sqrt(2 * (dimensions - 1) / ((dimensions + 2) * dimensions)) - - # Calculate the contributions from the 2 contributing stone-fence diagrams - diagram1 = (length_kuhn ** 2 / (2 * (dimensions - 1) ** 2) - 2 * length_kuhn / (dimensions - 1) ** 3 - + 3 / (dimensions - 1) ** 4 - - length_kuhn * np.exp(-(dimensions - 1) * length_kuhn) / (dimensions - 1) ** 3 - - 3 * np.exp(-(dimensions - 1) * length_kuhn) / (dimensions - 1) ** 4) - diagram1 *= a1 ** 4 - - diagram2 = (length_kuhn / (2 * dimensions * (dimensions - 1) ** 2) - - (5 * dimensions - 1) / (4 * dimensions ** 2 * (dimensions - 1) ** 3) - + np.exp(-(dimensions - 1) * length_kuhn) * ( - length_kuhn / ((dimensions + 1) * (dimensions - 1) ** 2) - + (dimensions + 3) / ((dimensions - 1) ** 3 * (dimensions + 1) ** 2)) - + np.exp(-2 * dimensions * length_kuhn) / (4 * dimensions ** 2 * (dimensions + 1) ** 2)) - diagram2 *= a1 ** 2 * a2 ** 2 - - rz4 = 24 * (diagram1 + diagram2) - - return rz4
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- - - - \ No newline at end of file diff --git a/doc/build/html/_modules/wlcstat/wlcgreen.html b/doc/build/html/_modules/wlcstat/wlcgreen.html deleted file mode 100644 index 5c4e643..0000000 --- a/doc/build/html/_modules/wlcstat/wlcgreen.html +++ /dev/null @@ -1,227 +0,0 @@ - - - - - - - - wlcstat.wlcgreen — wlcstat documentation - - - - - - - - - - - - - - - -
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Source code for wlcstat.wlcgreen

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-from wlcstat.util.wlc_poles_residues import *
-import numpy as np
-import scipy.special as sp
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[docs]def eval_poles_and_residues(k_val, mu, mu_zero_only=True, lam_zero_only=True, dimensions=3): - r""" - eval_poles_and_residues - Evaluate the poles and the residues for a given value of the - Fourier vector magnitude :math:`K` - - Parameters - ---------- - k_val : float - The value of the Fourier vector magnitude :math:`K` - mu : int - Value of the mu parameter (:math:`z`-component of the angular momentum) - mu_zero_only : boolean - Determines whether poles and residues are determined for non-zero :math:`\mu` (default True) - lam_zero_only : boolean - Determines whether residues are determined for non_zero :math:`\lambda` (default True) - dimensions : int - The number of dimensions (default to 3 dimensions) - - Returns - ------- - poles : complex float - Evaluated poles for the given :math:`K` and :math:`\mu` - residues : complex float - Evaluated residues for the given :math:`K` and :math:`\mu` - - Notes - ----- - See Mehraeen, et al, Phys. Rev. E, 77, 061803 (2008). (Ref [Mehraeen2008]_) - """ - - poles = eval_poles(k_val, mu, dimensions) - residues = eval_residues(k_val, mu, poles, lam_zero_only, dimensions) - - return poles, residues
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[docs]def gwlc_r(r_val, length_kuhn, dimensions=3, alpha_max=25, k_val_max=1e5, delta_k_val_max=0.1): - r""" - gwlc_r - Evaluate the orientation-independent Green's function for the wormlike chain model - - Parameters - ---------- - r_val : float (array) - The values of the end-to-end distance :math:`r = R/L` to be evaluated - length_kuhn : float (array) - The length of the chain in Kuhn lengths - dimensions : int - The number of dimensions (default to 3 dimensions) - alpha_max : int - Maximum number of poles evaluated (default 25) - k_val_max : float - Cutoff value of :math:`K` for numerical integration - delta_k_val_max : float - Maximum value of the integration step size - - Returns - ------- - gwlc : float - The orientation-independent Green's function [size len(r_val) x len(length_kuhn)] - - Notes - ----- - See Mehraeen, et al, Phys. Rev. E, 77, 061803 (2008). (Ref [Mehraeen2008]_) - """ - - delta_k_val = min(delta_k_val_max, 2 * np.pi / np.max(length_kuhn) / 10) - - # Eliminate 0 and 1 from the r_val array - r_val[r_val == 0] = 1e-10 - r_val[r_val == 1] = 1-1e-10 - - # Initialize the Green's function - if type(length_kuhn) == float or type(length_kuhn) == int: - gwlc = np.zeros((len(r_val)), dtype=type(1+1j)) - else: - gwlc = np.zeros((len(r_val), len(length_kuhn)), dtype=type(1+1j)) - - tolerance = 1e-15 - - k_val_output = k_val_max / 100 - k_val = delta_k_val - int_count = 0 - contains_nan = False - while k_val <= k_val_max and not contains_nan: - int_count += 1 - - poles = eval_poles(k_val, 0, dimensions, alpha_max) - residues = eval_residues(k_val, 0, poles, True, dimensions, alpha_max, alpha_max) - - if int_count == 1: - int_coef = 55 / 24 - elif int_count == 2: - int_coef = -1 / 6 - elif int_count == 3: - int_coef = 11 / 8 - else: - int_coef = 1 - - for alpha in range(0, alpha_max + 1): - gkwlc_kval = residues[alpha] * np.exp(poles[alpha] * length_kuhn) - if type(length_kuhn) == float or type(length_kuhn) == int: - integrand = (int_coef * k_val ** (dimensions / 2) - * sp.jv(dimensions / 2 - 1, k_val * r_val * length_kuhn) * gkwlc_kval) - else: - integrand = (int_coef * k_val ** (dimensions / 2) - * sp.jv(dimensions / 2 - 1, k_val * np.outer(r_val, length_kuhn)) - * np.outer(np.ones((len(r_val)), dtype=type(1+1j)), gkwlc_kval)) - if not contains_nan: - contains_nan = np.isnan(integrand).any() - if not contains_nan: - gwlc += integrand - else: - print("Encountered NaN at k_val = " + str(k_val)) - - k_val += delta_k_val - if k_val >= k_val_output: - k_val_output += k_val_max / 100 - print("Current k_val = " + str(k_val) + " with delta_k_val = " + str(delta_k_val) - + " and k_val_max = " + str(k_val_max)) - print(np.max(abs(np.exp(poles * np.min(length_kuhn))))) - - if np.min(abs(np.exp(poles * np.min(length_kuhn)))) < tolerance and alpha_max > 10 and k_val > 2840: - alpha_max -= 1 - print("Reducing alpha_max to " + str(alpha_max) + " at k_val = " - + str(k_val) + " with delta_k_val = " + str(delta_k_val)) - print(np.max(abs(np.exp(poles * np.min(length_kuhn))))) - - if np.max(abs(np.exp(poles * np.min(length_kuhn)))) < tolerance: - print("Achieved accuracy of " + str(tolerance) + " at k_val = " - + str(k_val) + " with delta_k_val = " + str(delta_k_val)) - print(np.max(abs(np.exp(poles * np.min(length_kuhn))))) - k_val = k_val_max + delta_k_val - - gwlc *= delta_k_val / (2 * np.pi) ** (dimensions / 2) * np.outer(r_val ** (-dimensions / 2 + 1), - length_kuhn ** (dimensions / 2 + 1)) - - return gwlc
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- - - - \ No newline at end of file diff --git a/doc/build/html/_modules/wlcstat/wlcstruc.html b/doc/build/html/_modules/wlcstat/wlcstruc.html deleted file mode 100644 index bdba32b..0000000 --- a/doc/build/html/_modules/wlcstat/wlcstruc.html +++ /dev/null @@ -1,145 +0,0 @@ - - - - - - - - wlcstat.wlcstruc — wlcstat documentation - - - - - - - - - - - - - - - -
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Source code for wlcstat.wlcstruc

-
-from wlcstat.util.wlc_poles_residues import *
-from wlcstat.util.wlc_vertex import *
-import numpy as np
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[docs]def eval_structure_factor(k_val_vector, length_kuhn, dimensions=3, alpha_max=25): - r""" - eval_structure factor - Evaluate the structure factor for the wormlike chain model - - Parameters - ---------- - k_val_vector : float (array) - The value of the Fourier vector magnitude :math:`K` - length_kuhn : float (array) - The length of the chain in Kuhn lengths - dimensions : int - The number of dimensions (default to 3 dimensions) - alpha_max : int - Maximum number of poles evaluated (default 25) - - Returns - ------- - structure_factor : float (vector) - Structure factor for the wormlike chain model for every k_val in k_val_vector - - Notes - ----- - See Mehraeen, et al, Phys. Rev. E, 77, 061803 (2008). (Ref [Mehraeen2008]_) - """ - if type(length_kuhn) == float or type(length_kuhn) == int: - structure_factor = np.zeros((len(k_val_vector)), dtype=type(1+1j)) - else: - structure_factor = np.zeros((len(k_val_vector), len(length_kuhn)), dtype=type(1+1j)) - - for ind_k_val in range(0, len(k_val_vector)): - k_val = k_val_vector[ind_k_val] - - poles = eval_poles(k_val, 0, dimensions, alpha_max) - residues = eval_residues(k_val, 0, poles, True, dimensions, alpha_max) - residue_zero, ddp_residue_zero = eval_residue_zero(k_val, dimensions) - - if type(length_kuhn) == float or type(length_kuhn) == int: - structure_factor[ind_k_val] = (length_kuhn * residue_zero + ddp_residue_zero) - for alpha in range(0, alpha_max): - structure_factor[ind_k_val] += (np.exp(poles[alpha] * length_kuhn) * - residues[alpha] / poles[alpha] ** 2) - structure_factor[ind_k_val] *= 2 / length_kuhn ** 2 - else: - for ind_length in range(0, len(length_kuhn)): - structure_factor[ind_k_val, ind_length] = (length_kuhn[ind_length] * residue_zero + ddp_residue_zero) - - for alpha in range(0, alpha_max): - structure_factor[ind_k_val, ind_length] += (np.exp(poles[alpha] * length_kuhn[ind_length]) * - residues[alpha] / poles[alpha] ** 2) - - structure_factor[ind_k_val, ind_length] *= 2 / length_kuhn[ind_length] ** 2 - - return structure_factor
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- - - - \ No newline at end of file diff --git a/doc/build/html/_sources/index.rst.txt b/doc/build/html/_sources/index.rst.txt deleted file mode 100644 index a25a33b..0000000 --- a/doc/build/html/_sources/index.rst.txt +++ /dev/null @@ -1,25 +0,0 @@ -Wormlike Chain Model Statistics (wlcstat) -=========================================== - -.. toctree:: - :maxdepth: 2 - :caption: Contents: - - Wormlike Chain Theory - - Average Quantities - - Wormlike Chain Green's Function - - Structure Factor - - Polymer Dynamics - - References - -Indices and tables -================== - -* :ref:`genindex` -* :ref:`modindex` -* :ref:`search` diff --git a/doc/build/html/_sources/poly_dyn.rst.txt b/doc/build/html/_sources/poly_dyn.rst.txt deleted file mode 100644 index 299e47c..0000000 --- a/doc/build/html/_sources/poly_dyn.rst.txt +++ /dev/null @@ -1,360 +0,0 @@ -.. _poly_dyn: -.. .. automodule:: poly_dyn - -Polymer Dynamics -================ - - - - - - -Dynamics of a linear and ring flexible Gaussian chains (Rouse model) --------------------------------------------------------------------- - -We consider a flexible polymer chain -that is subject -Brownian forces [Doi1988]_. -Our goals is to determine specific dynamic properties of a linear and ring -Gaussian chain. For example, we consider the dynamic motion of two -chain segments relative to each other. We define this relative motion -as the mean-square change in displacment (MSCD). -In this development, we present a detailed derivation for the linear chain, -and we provide the results for the ring polymer. - -.. figure:: figures/rouse-mscd.pdf - :width: 600 - :align: center - :alt: Schematic representation of the linear and ring Rouse model with definition of segments for MSCD calculation. - - Schematic representation of the linear and ring Rouse model with definition of segments for MSCD calculation. - The total chain length is :math:`N = 2 N_{s}`, and we consider two points on the chain located at - :math:`n_{1} = N_{s} - \Delta = N/2 - \Delta` and :math:`n_{2} = N_{s} + \Delta = N/2 + \Delta`. - - -We start by defining a discrete -polymer chain with bead positions -:math:`\vec{R}_{m}`, where :math:`m` runs from 0 -to :math:`n_{\mathrm{b}}`. -Each bead is connected to their -neighboring beads by Hookean springs, -resulting in a potential force -on the :math:`m`-th bead -:math:`\vec{F}_{V_{m}}` that is given by - - -.. math:: - & & \vec{F}_{V_{m}}= - \left\{ \begin{array}{c} - \frac{3 k_{B}T}{g b^{2}} \left( \vec{R}_{m+1} - 2 \vec{R}_{m} + \vec{R}_{m-1} \right), - \hspace{0.3in} - m = 1,\ldots, n_{\mathrm{b}}-1 \\ - \frac{3 k_{B}T}{g b^{2}} \left( \vec{R}_{1} - \vec{R}_{0} \right), - \hspace{2in} - m = 0 \\ - -\frac{3 k_{B}T}{g b^{2}} \left( \vec{R}_{n_{\mathrm{b}}} - \vec{R}_{n_{\mathrm{b}}-1} \right), - \hspace{1.65in} - m = n_{\mathrm{b}}, - \end{array} - \right. - -.. \label{eq:restoringforce} - -where :math:`b` is the Kuhn statistical segment length of the polymer [Doi1988]_, -and :math:`g` is the number of Kuhn lengths -per bead. We set :math:`g = N/n_{\mathrm{b}}`, giving -a total chain length of :math:`N` Kuhn lengths. - -The Langevin equation of motion for the :math:`m`-th bead is given by - -.. math:: - g \xi \frac{d\vec{R}_{m}(t)}{dt}=\vec{F}_{V_{m}} + \vec{F}_{B_{m}} - -where the drag coefficient :math:`\xi` is defined as the viscous drag per Kuhn length. -We now take the limit of -:math:`n_{\mathrm{b}} \rightarrow \infty` -for fixed chain length :math:`N`, resulting in -a continuous-chain representation -of the chain :math:`\vec{r}(n,t)` where :math:`n` -is a path-length variable that runs -from :math:`0` to :math:`N`. -The Langevin equation for the chain is -given by - -.. math:: - \xi \frac{\partial \vec{r}(n, t)}{\partial t}= - \frac{3 k_{B}T}{b^{2}} - \frac{\partial^{2} \vec{r}(n, t)}{\partial n^{2}} - + \vec{f}_{B}(n,t), - :label: eom-cont - -which is subject to the end conditions - -.. math:: - \frac{\partial \vec{r}(n=0,t)}{\partial n} = - \frac{\partial \vec{r}(n=N,t)}{\partial n} = 0. - -The Brownian forces satisfy the fluctuation dissipation theorem - -.. math:: - \langle \vec{f}_{B}(n,t)\vec{f}_{B}(n',t')\rangle = - 2k_{B}T \xi \delta (n - n') \delta(t-t') \textbf{I}. - - -It is convenient to define a set of normal coordinates that -effectively decouple the interactions implicit within the equation of motion (Eq. :eq:`eom-cont`). -We define the normal modes - -.. math:: - & & \phi_{p}(n)= - \left\{ \begin{array}{c} - \sqrt{2} \cos \left( \frac{\pi p n}{N} \right), \ \ p = 1,2,\ldots \\ - 1, \ \ \ \ \ \ \ \ \ \ p = 0. - \end{array} - \right. - -These modes represent a complete basis set that satisfy the boundary conditions for :math:`\vec{r}(n,t)`. -Orthogonality is demonstrated by noting - -.. math:: - \int_{0}^{N} \! \! dn \phi_{p}(n) \phi_{p'}(n) = N \delta_{p,p'}. - -The amplitude of the :math:`p`-th mode :math:`\vec{X}_{p}(t)` is given by - -.. math:: - \vec{X}_{p}(t) = \frac{1}{N} \int_{0}^{N} \! \! dn \, \vec{r}(n,t) \phi_{p}(n), - -and the inversion back to chain coordinates is written as - -.. math:: - \vec{r}(n,t) = \sum_{p=0}^{\infty} \vec{X}_{p}(t) \phi_{p}(n). - -Upon performing a transform to normal -coordinates, we find the governing -equation of motion - -.. math:: - \xi N \frac{d \vec{X}_{p}}{d t} = - - k_{p} \vec{X}_{p} - + \vec{f}_{B_{p}} - :label: eom-normal - -where :math:`k_{p} = \frac{3 \pi^{2} k_{B}T}{b^{2} N} p^{2}`. -The :math:`p`-mode Brownian force :math:`\vec{f}_{B_{p}}` -is given by - -.. math:: - \vec{f}_{B_{p}} = \int_{0}^{N} \! \! dn \, \vec{f}_{B}(n,t) \phi_{p}(n) - -and satisfies the fluctuation dissipation theorem - -.. math:: - \langle - \vec{f}_{B_{p}} (t) \vec{f}_{B_{p'}}(t') - \rangle = - 2 k_{B}T \xi N \delta_{pp'} \delta (t - t') \mathbf{I}. - -A similar derivation for a ring polymer results in a treatment that -is identical to the linear chain, but the normal modes for the -ring polymer are continuous across the ends [i.e. :math:`\vec{r}(n=0,t) = \vec{r}(n=N,t)`]. -Specifically, the complete normal-mode set is separated into even and odd functions, -respectively -defined by - -.. math:: - & & \phi_{p}^{(e)}(n)= - \left\{ \begin{array}{c} - \sqrt{2} \cos \left( \frac{2 p \pi n}{N} \right), \ \ p = 1,2,\ldots \\ - 1, \ \ \ \ \ \ \ \ \ \ p = 0. - \end{array} - \right. - -and - -.. math:: - \phi_{p}^{(o)}(n)= - \sqrt{2} \sin \left( \frac{2 \pi p n}{N} \right), \ \ p = 1,2,\ldots - -The even and odd normal modes satisfy the equation of motion defined in Eq. :eq:`eom-normal` -with -:math:`k_{p} = \frac{12 \pi^{2} k_{B}T}{b^{2} N} p^{2}` - -Mean-square displacement (MSD) for linear polymers -************************************************** - -The mean-square displacement of a segment of the polymer chain is define a - -.. math:: - \mathrm{MSD} = \langle \left( \vec{r}(n, t) - \vec{r}(n, 0) \right)^{2} \rangle - :label: msd - -for the nth segment of the chain with total length :math:`N`. -We insert our normal-mode representation into Eq. :eq:`msd`, -resulting in the expression - -.. math:: - \mathrm{MSD} = - \sum_{p=1}^{\infty} \sum_{p'=1}^{\infty} - \langle - \left( \vec{X}_{p}(t) - \vec{X}_{p}(0) \right) \cdot - \left( \vec{X}_{p'}(t) - \vec{X}_{p'}(0) \right) \rangle - \phi_{p}(n) \phi_{p'}(n) - -The equation of motion (Eq. :eq:`eom-normal`) can be used to determine the correlation function -:math:`\langle \vec{X}_{p}(t) \cdot \vec{X}_{p'}(0) \rangle` (detailed discussion is found in Ref. [Doi1988]_). -This results in the expression - -.. math:: - \langle \vec{X}_{p}(t) \cdot \vec{X}_{p'}(0) \rangle = 3 \frac{k_{B}T}{k_{p}} - \exp \! \left( - \frac{k_{p}}{N \xi} t \right) \delta_{pp'} - -for :math:`p \ge 1` and - -.. math:: - \langle - \left( \vec{X}_{0}(t) - \vec{X}_{0}(0) \right)^{2} \rangle = 6 \frac{k_{B}T}{N \xi} t - -We focus on the :math:`\mathrm{MSD}` for the midpoint of a linear chain, -thus :math:`n=N/2`. -Inserting this into our definition of :math:`\mathrm{MSD}` results in the -expression for the MSD of the midpoint of a linear chain - -.. math:: - \mathrm{MSD} - & = & - 6 \frac{k_{B}T}{\xi N} t + - \sum_{p \, \mathrm{even}} 12 \frac{k_{B}T}{k_{p}} - \left[ 1 - \exp \! \left( - \frac{k_{p}}{N \xi} t \right) \right] \\ - & = & - 6 \frac{k_{B}T}{\xi N} t + - \sum_{p = 1}^{\infty} 12 \frac{k_{B}T}{k_{2p}} - \left[ 1 - \exp \! \left( - \frac{k_{2p}}{N \xi} t \right) \right] \\ - -Mean-squared change in distance (MSCD) for linear and ring polymers -******************************************************************* - -We now consider the mean-square change in distance (MSCD) for a linear polymer -chain. -This quantity is defined as - -.. math:: - \mathrm{MSCD} = \langle \left( \Delta \vec{R}(t) - \Delta \vec{R}(0) \right)^{2} \rangle - :label: mscd - -where :math:`\Delta \vec{R}(t) = \vec{r}(N/2 + \Delta, t) - \vec{r}(N/2 - \Delta,t)` where -the total chain length is :math:`N = 2 N_{s}`. -We insert our normal-mode representation into Eq. :eq:`mscd` -to find - -.. math:: - \mathrm{MSCD} = - \sum_{p=1}^{\infty} \sum_{p'=1}^{\infty} - \langle - \left( \vec{X}_{p}(t) - \vec{X}_{p}(0) \right) \cdot - \left( \vec{X}_{p'}(t) - \vec{X}_{p'}(0) \right) - \rangle - \left[ \phi_{p}(N/2 + \Delta) - \phi_{p}(N/2 - \Delta) \right] - \left[ \phi_{p'}(N/2 + \Delta) - \phi_{p'}(N/2 - \Delta) \right] - -The equation of motion (Eq. :eq:`eom-normal`) can be used to determine the correlation function -:math:`\langle \vec{X}_{p}(t) \cdot \vec{X}_{p'}(0) \rangle` (detailed discussion is found in Ref. [Doi1988]_). -This results in the expression - -.. math:: - \langle \vec{X}_{p}(t) \cdot \vec{X}_{p'}(0) \rangle = 3 \frac{k_{B}T}{k_{p}} - \exp \! \left( - \frac{k_{p}}{N \xi} t \right) \delta_{pp'} - -Inserting this into our definition of :math:`\mathrm{MSCD}` results in the -expression for the linear chain - -.. math:: - \mathrm{MSCD}^{\mathrm{(linear)}} - & = & \sum_{p \, \mathrm{odd}} 48 \frac{k_{B}T}{k_{p}} - \left[ 1 - \exp \! \left( - \frac{k_{p}}{N \xi} t \right) \right] - \sin^{2} \left( \frac{\pi p \Delta}{N} \right) \\ - & = & \sum_{p = 0}^{\infty} 48 \frac{k_{B}T}{k_{2p+1}} - \left[ 1 - \exp \! \left( - \frac{k_{2p+1}}{N \xi} t \right) \right] - \sin^{2} \left[ \frac{\pi (2p+1) \Delta}{N} \right] - -where :math:`k_{p} = \frac{3 \pi^{2} k_{B}T}{b^{2} N} p^{2}` for the linear chain. - -We follow a parallel derivation for the ring polymer. -We note that only the odd set of normal modes contribute to :math:`\mathrm{MSCD}` -for the ring polymer. -Taking similar steps as in the linear case, -we arrive at the expression for the ring polymer - -.. math:: - \mathrm{MSCD}^{\mathrm{(ring)}} - = \sum_{p = 1}^{\infty} 48 \frac{k_{B}T}{k_{p}} - \left[ 1 - \exp \! \left( - \frac{k_{p}}{N \xi} t \right) \right] - \sin^{2} \left( \frac{2 \pi p \Delta}{N} \right) - -where :math:`k_{p} = \frac{12 \pi^{2} k_{B}T}{b^{2} N} p^{2}` for the ring polymer. - -Functions contained with the 'poly_dyn' module ----------------------------------------------- - -.. automodule:: wlcstat.poly_dyn - :members: - - -Example usage of 'linear_mscd' and 'ring_mscd' ----------------------------------------------- - -We show the solution for the MSCD for chain length :math:`N=100` and :math:`\Delta = 25` for both -linear and ring polymers. In this plot, we also show the MSD (using 'linear_mid_msd') multiplied by -2, which coincides with the short-time asymptotic behavior. -The long-time asymptotic behavior is found by noting - -.. math:: - \mathrm{MSCD} = \langle \left( \Delta \vec{R}(t) - \Delta \vec{R}(0) \right)^{2} \rangle = - \langle \Delta \vec{R}(t)^{2} \rangle - - 2 \langle \Delta \vec{R}(t) \cdot \Delta \vec{R}(0) \rangle - + \langle \Delta \vec{R}(0) ^{2} \rangle \rightarrow - 2 \langle \Delta \vec{R}^{2} \rangle - -which leads to the asymptotic solutions - -.. math:: - \mathrm{MSCD}^{\mathrm{(linear)}} \rightarrow 4 \Delta - -and - -.. math:: - \mathrm{MSCD}^{\mathrm{(ring)}} \rightarrow \frac{2}{\frac{1}{2 \Delta} + \frac{1}{N-2 \Delta}}. - -These asymptotic solutions are also included in the plot. - -.. plot:: - - import matplotlib.pyplot as plt - import numpy as np - from wlcstat.poly_dyn import * - - num_t = 100 - t_val_0 = 1e-4 - t_val_f = 1e6 - t_val = np.logspace(np.log10(t_val_0), np.log10(t_val_f), num_t) - N=100 - Ndel=25 - mscdl = linear_mscd(t_val, 1, Ndel, N, 1, 20000) - mscdr = ring_mscd(t_val, 1, Ndel, N, 1, 20000) - msd = linear_mid_msd(t_val, 1, N, 1, 10000) - mscdl_inf = 2 * 2 * Ndel - mscdr_inf = 2 * 1 / (1 / (2 * Ndel) + 1 / (N - 2 * Ndel)) - plt.figure(figsize=(10,8)) - font = {'family' : 'serif', - 'weight':'normal', - 'size': 18} - plt.rc('font', **font) - plt.loglog(t_val, mscdl) - plt.loglog(t_val, mscdr) - plt.loglog(t_val, 2 * msd) - plt.loglog(t_val, 2 * 6 * t_val /N,'--') - plt.loglog(t_val, mscdl_inf + 0*t_val,'--') - plt.loglog(t_val, mscdr_inf + 0*t_val,'--') - plt.xlabel(r'$t$') - plt.ylabel(r'$MSCD$') - plt.tight_layout() - plt.show() \ No newline at end of file diff --git a/doc/build/html/_sources/references.rst.txt b/doc/build/html/_sources/references.rst.txt deleted file mode 100644 index d0e555e..0000000 --- a/doc/build/html/_sources/references.rst.txt +++ /dev/null @@ -1,37 +0,0 @@ -.. _references: - - -References -========== - -.. Spakowitz Lab references - -.. [Spakowitz2004] - Spakowitz, Andrew J., and Zhen-Gang Wang. "Exact results for a semiflexible polymer chain in an aligning field." Macromolecules 37.15 (2004): 5814-5823. - -.. [Spakowitz2005] - Spakowitz, Andrew J., and Zhen-Gang Wang. "End-to-end distance vector distribution with fixed end orientations for the wormlike chain model." Physical Review E 72.4 (2005): 041802. - -.. [Spakowitz2006] - Spakowitz, A. J. "Wormlike chain statistics with twist and fixed ends." EPL (Europhysics Letters) 73.5 (2006): 684. - -.. [Mehraeen2008] - Mehraeen, Shafigh, et al. "End-to-end distribution for a wormlike chain in arbitrary dimensions." Physical Review E 77.6 (2008): 061803. - -.. Wormlike Chain references - -.. [Kratky1949] - Kratky, Otto, and Günther Porod. "Röntgenuntersuchung gelöster fadenmoleküle." Recueil des Travaux Chimiques des Pays‐Bas 68.12 (1949): 1106-1122. - -.. [Yamakawa1997] - Yamakawa, Hiromi, and Takenao Yoshizaki. Helical wormlike chains in polymer solutions. Vol. 1. Berlin: Springer, 1997. - -.. Mathematics references - -.. [Arfken1999] - Arfken, George B., and Hans J. Weber. "Mathematical methods for physicists." (1999): 165-169. - -.. Polymer dynamics references - -.. [Doi1988] - Doi, Masao, Samuel Frederick Edwards, and Samuel Frederick Edwards. The theory of polymer dynamics. Vol. 73. oxford university press, 1988. \ No newline at end of file diff --git a/doc/build/html/_sources/wlcave_notes.rst.txt b/doc/build/html/_sources/wlcave_notes.rst.txt deleted file mode 100644 index d797a69..0000000 --- a/doc/build/html/_sources/wlcave_notes.rst.txt +++ /dev/null @@ -1,277 +0,0 @@ -.. _wlcave_notes: -.. .. automodule:: wlcstat - - -Average Quantities -================== - -The orientation Green function can be used to evaluate any average quantity that can be -expressed in terms of the tangent orientations. -The Green function operates as a conditional probability, such that :math:`G(\vec{u}|\vec{u}_{0};L)` gives the -probability that a chain of length :math:`L` with an initial tangent orientation :math:`\vec{u}_{0}` will have a final -tangent orientation :math:`\vec{u}`. -We consider an arbitrary orientation-only average quantity :math:`A^{n} = -\langle A_{n}(s_{n}) A_{n-1}(s_{n-1}) \ldots A_{1}(s_{1}) \rangle`, -where :math:`A_{m}(s_{m})` is a function that is expressible only in terms of the tangent orientation at arclength -position :math:`s_{m}`. -The arclength positions are ordered such that :math:`s_{1} < s_{2} < \ldots < s_{n-1} < s_{n}`. -The average quantity :math:`A^{n}` is evaluated using the following procedure: - -- An orientation Green function :math:`G(\vec{u}_{1}|\vec{u}_{0};s_{1})` is inserted into :math:`A^{n}` to propagate from the initial orientation :math:`\vec{u}_{0}` at :math:`s=0` to the first orientation :math:`\vec{u}_{1}` at :math:`s_{1}` - -- An orientation Green function :math:`G(\vec{u}_{m+1}|\vec{u}_{m};s_{m+1}-s_{m})` is inserted into :math:`A^{n}` between :math:`A_{m+1}` and :math:`A_{m}`, resulting in a product of :math:`n-1` Green functions that propagate between the internal orientations in the average - -- An orientation Green function :math:`G(\vec{u}|\vec{u}_{n};L-s_{n})` is inserted into :math:`A^{n}` to propagate from the :math:`n` th orientation :math:`\vec{u}_{n}` at :math:`s_{n}` to the final orientation :math:`\vec{u}` at :math:`L` - -- The average :math:`A^{n}` is normalized by a factor that represents the orientational integral over the full-chain Green function, i.e. the same quantity as the average without the product of :math:`A_{m}` - -- The average is then evaluated by integrating over the orientations :math:`\vec{u}_{0}`, :math:`\vec{u}_{1}`, \ldots, :math:`\vec{u}_{n}`, and :math:`\vec{u}` - -This procedure is amenable to the evaluation of arbitrary average quantities that are expressible in terms of the -tangent orientations :math:`\vec{u}_{m}` along the chain at positions :math:`s_{m}`. - -For example, the average :math:`\langle \vec{u}(s_{2}) \cdot \vec{u}(s_{1}) \rangle` (where :math:`s_{1} < s_{2}`) is given by - -.. math:: - \langle \vec{u}(s_{2}) \cdot \vec{u}(s_{1}) \rangle & = & - \frac{1}{\mathcal{N}} - \int d \vec{u} d \vec{u}_{2} d \vec{u}_{1} d \vec{u}_{0} - G(\vec{u}|\vec{u}_{2};L-s_{2}) - G(\vec{u}_{2}|\vec{u}_{1};s_{2}-s_{1}) - G(\vec{u}_{1}|\vec{u}_{0};s_{1}) - \vec{u}_{2} \cdot \vec{u}_{1} - \nonumber \\ - & = & - \frac{3}{\mathcal{N}} - \int d \vec{u} d \vec{u}_{2} d \vec{u}_{1} d \vec{u}_{0} - G(\vec{u}|\vec{u}_{2};L-s_{2}) - G(\vec{u}_{2}|\vec{u}_{1};s_{2}-s_{1}) - G(\vec{u}_{1}|\vec{u}_{0};s_{1}) - u_{2}^{(z)} u_{1}^{(z)}, - :label: u1u2 -.. \label{eq:u1u2} - -where rotational symmetry implies -:math:`\langle u^{(x)}(s_{2}) u^{(x)}(s_{1}) \rangle =\langle u^{(y)}(s_{2}) u^{(y)}(s_{1}) \rangle = \langle u^{(z)}(s_{2}) u^{(z)}(s_{1}) \rangle` and, consequently, :math:`\langle \vec{u}(s_{2}) \cdot \vec{u}(s_{1}) \rangle = 3 \langle u^{(z)}(s_{2}) u^{(z)}(s_{1}) \rangle`. -The normalization factor :math:`\mathcal{N}` is given by - -.. math:: - \mathcal{N} = \int d \vec{u} d \vec{u}_{0} G(\vec{u}|\vec{u}_{0};L) = 4 \pi. - -Inserting :eq:`guwlc` into :eq:`u1u2` gives - -.. math:: - \langle \vec{u}(s_{2}) \cdot \vec{u}(s_{1}) \rangle & = & - \frac{3}{4 \pi} \int d \vec{u} d \vec{u}_{2} d \vec{u}_{1} d - \vec{u}_{0} \sum_{l_{2}=0}^{\infty} \sum_{m_{2}=-l_{2}}^{l_{2}} - \sum_{l_{1}=0}^{\infty} \sum_{m_{1}=-l_{1}}^{l_{1}} - \sum_{l_{0}=0}^{\infty} \sum_{m_{0}=-l_{0}}^{l_{0}} \times - \nonumber \\ & & Y_{l_{2}}^{m_{2}} (\vec{u}) - Y_{l_{2}}^{m_{2}*}(\vec{u}_{2}) Y_{l_{1}}^{m_{1}} (\vec{u}_{2}) - Y_{l_{1}}^{m_{1}*}(\vec{u}_{1}) Y_{l_{0}}^{m_{0}} (\vec{u}_{1}) - Y_{l_{0}}^{m_{0}*}(\vec{u}_{0}) \cos \theta_{2} \cos \theta_{1} - \times \nonumber \\ & & \exp \! \left[ - -l_{2}(l_{2}+1)\frac{L-s_{2}}{2l_{p}} - -l_{1}(l_{1}+1)\frac{s_{2}-s_{1}}{2l_{p}} - -l_{0}(l_{0}+1)\frac{s_{1}}{2l_{p}} \right], - -where :math:`u_{2}^{(z)}=\cos \theta_{2}`. -Using the properties of the spherical harmonics [Arfken1999]_, -we note that :math:`\cos \theta = 2 \sqrt{\pi/3} Y_{1}^{0}(\vec{u})`, -and the average is written as - -.. math:: - \langle \vec{u}(s_{2}) \cdot \vec{u}(s_{1}) \rangle & = & - \int d \vec{u} d \vec{u}_{2} d \vec{u}_{1} d \vec{u}_{0} - \sum_{l_{2}=0}^{\infty} \sum_{m_{2}=-l_{2}}^{l_{2}} - \sum_{l_{1}=0}^{\infty} \sum_{m_{1}=-l_{1}}^{l_{1}} - \sum_{l_{0}=0}^{\infty} \sum_{m_{0}=-l_{0}}^{l_{0}} \times - \nonumber \\ - & & - Y_{l_{2}}^{m_{2}} (\vec{u}) - Y_{l_{2}}^{m_{2}*}(\vec{u}_{2}) - Y_{l_{1}}^{m_{1}} (\vec{u}_{2}) - Y_{l_{1}}^{m_{1}*}(\vec{u}_{1}) - Y_{l_{0}}^{m_{0}} (\vec{u}_{1}) - Y_{l_{0}}^{m_{0}*}(\vec{u}_{0}) - Y_{1}^{0*}(\vec{u}_{2}) - Y_{1}^{0}(\vec{u}_{1}) - \times - \nonumber \\ - & & - \exp \! \left[ - -l_{2}(l_{2}+1)\frac{L-s_{2}}{2l_{p}} - -l_{1}(l_{1}+1)\frac{s_{2}-s_{1}}{2l_{p}} - -l_{0}(l_{0}+1)\frac{s_{1}}{2l_{p}} - \right] - -Integration over :math:`\vec{u}` and :math:`\vec{u}_{0}` force :math:`l_{2}=m_{2}=l_{0}=m_{0}=0`, -and the subsequent integration over :math:`\vec{u}_{1}` and :math:`\vec{u}_{2}` result in -:math:`l_{1}=1` and :math:`m_{1}=0`. -The final expression is given by - -.. math:: - \langle \vec{u}(s_{2}) \cdot \vec{u}(s_{1}) \rangle = \exp \! \left( - - \frac{s_{2} - s_{1}}{l_{p}} - \right), - -which demonstrates the role of the persistence length :math:`l_{p}` as a correlation length for -the tangent orientation. - -This average shows that the orientation statistics can be used to directly evaluate averages that are expressed in -terms of the tangent vector :math:`\vec{u}`. -However, other average quantities can be evaluated using the orientation Green function if the quantity can be expressed in terms of the -tangent orientation. -For example, the mean-square end-to-end vector is written as - -.. math:: - \langle - \vec{R}^{2} - \rangle & = & - \int_{0}^{L} \int_{0}^{L} ds_{2} ds_{1} \langle \vec{u}(s_{2}) \cdot \vec{u}(s_{1}) \rangle - = 2 \int_{0}^{L} \int_{0}^{s_{2}} ds_{2} ds_{1} \exp \! \left( - - \frac{s_{2} - s_{1}}{l_{p}} - \right) \\ - & = & - 2l_{p}^{2} \left[ - 2N - 1 + \exp \left( -2N \right) - \right], - -where :math:`N=L/(2 l_{p})`. - -An alternative approach to calculating averages is to use the Fourier-transformed Green's -function as a generator of averages -(see Refs. [Spakowitz2004]_, [Spakowitz2005]_, [Spakowitz2006]_, and [Mehraeen2008]_. -Development of this approach is provided in our -discussion of the Green's function. - -The 'wlcave.py' module provides scripts to calculate a number of -average quantities for the wormlike chain model. These include the -following: - -- The mean-square end-to-end distance :math:`\langle R^{2} \rangle` - -- The mean-square radius of gyration :math:`\langle \vec{R}_{G}^{2} \rangle` - -- The 4th moment of the end-to-end distribution :math:`\langle R_{z}^{4} \rangle / (2 l_{p})^{4}` - -Functions contained with the 'wlcave' module --------------------------------------------- - -.. automodule:: wlcstat.wlcave - :members: - - -Example usage of 'r2_ave' -------------------------- - -This example gives the mean-square end-to-end distance :math:`\langle R^{2} \rangle / (2 l_{p})^{2}` -(i.e. length non-dimensionalized by :math:`2 l_{p}`) versus -chain length :math:`N = L/(2 l_{p})` for 3 dimensions. The short-length asymptotic behavior -:math:`\langle R^{2} \rangle / (2 l_{p})^{2} \rightarrow N^{2}` -and long-length asymptotic behavior -:math:`\langle R^{2} \rangle / (2 l_{p})^{2} \rightarrow 2 N/(d-1)` are included to show the -limiting behaviors. - -.. plot:: - - import matplotlib.pyplot as plt - import numpy as np - from wlcstat.wlcave import * - - num_pts = 100 - length_kuhn_0 = 1e-3 - length_kuhn_f = 1e3 - length_kuhn = np.logspace(np.log10(length_kuhn_0), np.log10(length_kuhn_f), num_pts) - dimensions = 3 - r2 = r2_ave(length_kuhn, dimensions) - r2short = length_kuhn ** 2 - r2long = length_kuhn * 2 / (dimensions - 1) - plt.figure(figsize=(10,8)) - font = {'family' : 'serif', - 'weight':'normal', - 'size': 18} - plt.rc('font', **font) - plt.loglog(length_kuhn, r2) - plt.loglog(length_kuhn[0:60], r2short[0:60]) # Short length asymptotic solution - plt.loglog(length_kuhn[40:100], r2long[40:100]) # Long length asymptotic solution - plt.xlabel(r'Chain length $N = L/(2l_{p})$') - plt.ylabel(r'End-to-end distance $\langle R^{2} \rangle$') - plt.tight_layout() - plt.show() - -Example usage of 'rg2_ave' --------------------------- - -This example gives the mean-square radius of gyration :math:`\langle \vec{R}_{G}^{2} \rangle / (2 l_{p})^{2}` -(i.e. length non-dimensionalized by :math:`2 l_{p}`) versus -chain length :math:`N = L/(2 l_{p})` for 3 dimensions. The short-length asymptotic behavior -:math:`\langle R^{2} \rangle / (2 l_{p})^{2} \rightarrow N^{2}/12` -and long-length asymptotic behavior -:math:`\langle R^{2} \rangle / (2 l_{p})^{2} \rightarrow N/[3 (d-1)]` are included to show the -limiting behaviors. - -.. plot:: - - import matplotlib.pyplot as plt - import numpy as np - from wlcstat.wlcave import * - - num_pts = 100 - length_kuhn_0 = 1e-3 - length_kuhn_f = 1e3 - length_kuhn = np.logspace(np.log10(length_kuhn_0), np.log10(length_kuhn_f), num_pts) - dimensions = 3 - rg2 = rg2_ave(length_kuhn, dimensions) - rg2short = length_kuhn ** 2 / 12 - rg2long = length_kuhn / (3 * (dimensions - 1)) - plt.figure(figsize=(10,8)) - font = {'family' : 'serif', - 'weight':'normal', - 'size': 18} - plt.rc('font', **font) - plt.loglog(length_kuhn, rg2) - plt.loglog(length_kuhn[0:60], rg2short[0:60]) # Short length asymptotic solution - plt.loglog(length_kuhn[40:100], rg2long[40:100]) # Long length asymptotic solution - plt.xlabel(r'Chain length $N = L/(2l_{p})$') - plt.ylabel(r'Mean-square radius of gyration $\langle \vec{R}_{G}^{2} \rangle$') - plt.tight_layout() - plt.show() - -Example usage of 'rz4_ave' --------------------------- - -This example gives the 4th moment of the end-to-end distribution :math:`\langle R_{z}^{4} \rangle / (2 l_{p})^{4}` -(i.e. length non-dimensionalized by :math:`2 l_{p}`) versus -chain length :math:`N = L/(2 l_{p})` for 3 dimensions. The short-length asymptotic behavior -:math:`\langle R_{z}^{2} \rangle / (2 l_{p})^{2} \rightarrow N^{4} 3 / [d (d + 2)]` -and long-length asymptotic behavior -:math:`\langle R_{z}^{2} \rangle / (2 l_{p})^{2} \rightarrow 12 N^2/[d^2 (d-1)^2]` are included to show the -limiting behaviors. - -.. plot:: - - import matplotlib.pyplot as plt - import numpy as np - from wlcstat.wlcave import * - - num_pts = 100 - length_kuhn_0 = 1e-3 - length_kuhn_f = 1e3 - length_kuhn = np.logspace(np.log10(length_kuhn_0), np.log10(length_kuhn_f), num_pts) - dimensions = 3 - rz4 = rz4_ave(length_kuhn, dimensions) - rz4short = length_kuhn ** 4 * 3 / (dimensions * (dimensions + 2)) - rz4long = length_kuhn ** 2 * 12 / (dimensions * (dimensions - 1)) ** 2 - plt.figure(figsize=(10,8)) - font = {'family' : 'serif', - 'weight':'normal', - 'size': 18} - plt.rc('font', **font) - plt.loglog(length_kuhn, rz4) - plt.loglog(length_kuhn[0:60], rz4short[0:60]) # Short length asymptotic solution - plt.loglog(length_kuhn[40:100], rz4long[40:100]) # Long length asymptotic solution - plt.xlabel(r'Chain length $N = L/(2l_{p})$') - plt.ylabel(r'4th moment $\langle R_{z}^{4} \rangle$') - plt.tight_layout() - plt.show() diff --git a/doc/build/html/_sources/wlcgreen_notes.rst.txt b/doc/build/html/_sources/wlcgreen_notes.rst.txt deleted file mode 100644 index 2790717..0000000 --- a/doc/build/html/_sources/wlcgreen_notes.rst.txt +++ /dev/null @@ -1,424 +0,0 @@ -.. _wlcgreen_notes: -.. .. automodule:: wlcstat - -Wormlike Chain Green's Function -=============================== - -We consider the end-to-end distribution function :math:`G(\vec{R},\vec{u}|\vec{u}_{0};L)` (or Green's function), -which gives the probability that a chain that begins at the origin with initial -orientation :math:`\vec{u}_{0}` will have end position :math:`\vec{R}` and final orientation :math:`\vec{u}`. -The Green's function -:math:`G(\vec{R},\vec{u}|\vec{u}_{0};L)` is written as - -.. math:: - G(\vec{R},\vec{u}|\vec{u}_{0};L) = \int_{\vec{u}(s=0)=\vec{u}_{0}}^{\vec{u}(s=L)=\vec{u}} - \hspace{-0.3in} \mathcal{D}[\vec{u}(s)] - \exp \left\{ -\beta \mathcal{H}_{0} [\vec{u}(s)] \right\} - \delta \left( \vec{R}-\int_{0}^{L}ds \vec{u} \right), - -.. \label{eq:ORgreenfunc} - -where :math:`\delta` is a Dirac delta function that restricts the path integration -to those paths that satisfy the fixed end separation :math:`\vec{R}`. -The path integral formulation of the Green function is used to find the -governing "Schrödinger" equation [Yamakawa1997]_ - -.. math:: - \left( - \frac{\partial}{\partial L} - \frac{1}{2l_{p}} \tilde{\nabla}^{2}_{D} + \vec{u} \cdot \vec{\nabla}_{R} - \right) - G(\vec{R},\vec{u}|\vec{u}_{0};L)= - \delta \left( L \right) \delta ( \vec{R} ) \delta \left( \vec{u} - \vec{u}_{0} \right), - -.. \label{eq:schrodinger-r} - -where :math:`\tilde{\nabla}^{2}_{D}` is the :math:`D`-dimensional angular Laplacian, -and :math:`\vec{\nabla}_{R}` is the :math:`D`-dimensional gradient operator. - -Upon :math:`D`-dimensional Fourier transforming -from the variable :math:`\vec{R}` to the wavevector :math:`\vec{k}`, -our problem becomes that of a single wormlike chain -with Hamiltonian - -.. math:: - \beta \mathcal{H} = \beta \mathcal{H}_{0} + \beta \mathcal{H}_{ext} = - \frac{l_{p}}{2} \int_{0}^{L} ds - \left( \frac{\partial \vec{u}}{\partial s} \right)^{\! \! 2} - -i\vec{k} \cdot \int_{0}^{L}ds \vec{u}. - -.. \label{eq:TotalHamiltonian} - -The external Hamiltonian :math:`\beta \mathcal{H}_{ext}` -naturally emerges -in the Fourier transform of the end-to-end distribution function :math:`G(\vec{R},\vec{u}|\vec{u}_{0};L)` -due to the end-position constraint. -The corresponding "Schrödinger" equation in Fourier space is - -.. math:: - \left( - \frac{\partial}{\partial L} - \frac{1}{2l_{p}} \tilde{\nabla}^{2}_{D} - i \vec{k}\cdot \vec{u} - \right) - G(\vec{k},\vec{u}|\vec{u}_{0};L)= - \delta \left( L \right) \delta \left( \vec{u} - \vec{u}_{0} \right), - -.. \label{eq:schrodinger-k} - -which demonstrates the direct correspondence between our problem and that of a rigid rotor -in a dipole field. - -Exact results for the Green's function are provided in Refs. -[Spakowitz2004]_, [Spakowitz2005]_, [Spakowitz2006]_, and [Mehraeen2008]_, -which give solutions with and without end constraints and in arbitrary dimensions :math:`D`. -For example, the solution to the orientation-independent Green function in Fourier-Laplace space -(i.e. Fourier transformed from :math:`\vec{R}` to :math:`\vec{k}` and Laplace transformed -from :math:`N` to :math:`p`) - -.. math:: - G(\vec{K};p) = \frac{1}{P_{0}+\frac{\left(a_{1} K\right)^2}{P_{1}+ - \frac{\left(a_{2} K\right)^2}{P_{2}+\frac{\left(a_{3} K\right)^2}{\cdots}}}}, - :label: gwlc - -where :math:`\vec{K}=2l_{p} \vec{k}`, -:math:`K` is the magnitude of :math:`\vec{K}`, -:math:`P_{\lambda}=p+ \lambda (\lambda+D-2)`, and -:math:`a_{\lambda} = \left[\frac{\lambda (\lambda+D-3)}{(2\lambda+D-2)(2\lambda+D-4)}\right]^{1/2}`. -A detailed derivation of this :math:`D`-dimensional solution is found in Ref. [Mehraeen2008]_. -We note that this exact solution produces identical results as those given in -Ref. [Spakowitz2004]_ -for 2- and 3-dimensional solutions. - -Methods to Evaluate the Wormlike Chain Green's Function -------------------------------------------------------- - -The Green's function (e.g. :eq:`gwlc`) is written in Fourier-Laplace space. -Thus, evaluation of the Green's function requires inversion to real space -:math:`\vec{R}` and :math:`N`. -The python module 'wlcgreen' contains python code to numerically invert the -Fourier and Laplace transforms to render real-space solutions. -The procedure followed in this module is as follows: - -- Laplace-space inversion (from :math:`p` to :math:`N`): Numerical Laplace inversion using residue theorem based on evaluation of the singularities in :math:`G` - -- Fourier-space inversion (from :math:`\vec{k}` to :math:`\vec{R}`): Numerical Fourier inversion by numerical integration over :math:`\vec{k}` - -These steps are performed sequentially, such that Laplace inversion is first followed by Fourier inversion. -The Spakowitz lab has utilized other numerical approaches for these steps. -For example, numerical Laplace inversion can also be performed by numerical -complex integration of the Bromwich integral, but this approach is not integrated into the 'wlcgreen' module. - -The orientation-independent Green's function :math:`G(\vec{K};p)` -in :eq:`gwlc` serves as a useful example for our numerical procedures. -Below, we discuss the two steps for the real-space inversion for this function. - -Step 1: Laplace-space inversion -^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - -The Laplace-space inversion requires us to determine the poles :math:`\mathcal{E}_{\alpha}` -(all simple and generally complex). -Mathematically, this is written as - -.. math:: - j (K; p = \mathcal{E}_{\alpha}) = \frac{1}{G(K; p = \mathcal{E}_{\alpha})} = 0 - -for :math:`\alpha = 0, 1, \ldots` gives the infinite set of poles within the infinite continued -fraction. In practice, the real part of :math:`\mathcal{E}_{\alpha}` becomes increasingly negative -with increasing :math:`\alpha`, and a cutoff :math:`\alpha = \alpha_{\mathrm{max}}` is invoked for -any given :math:`N`. We note that :math:`\mathcal{E}_{\alpha} \rightarrow -\alpha (\alpha+D-2)` -(unperturbed eigenvalues of the hyperspherical harmonics) as -:math:`K \rightarrow 0` and becomes more negative with increasing :math:`K` (see Ref [Mehraeen2008]_). -We determine :math:`\alpha_{\mathrm{max}}` based on the :math:`K=0` magnitude of :math:`G` for a given :math:`N`. - -The Laplace inversion is then determined by evaluating the residues in the complex plane. -The is written as - -.. math:: - G (K; N) = \sum_{\alpha = 0}^{\alpha_{\mathrm{max}}} - \mathop{\mathrm{Res}}_{p = \mathcal{E}_{\alpha}} \left[ - G(K; p) \exp \left( p N \right) \right] - = \sum_{\alpha = 0}^{\alpha_{\mathrm{max}}} \lim_{p \rightarrow \mathcal{E}_{\alpha}} - \left[ - ( p - \mathcal{E}_{\alpha}) G(K; p) \exp \left( p N \right) \right] = - \sum_{\alpha = 0}^{\alpha_{\mathrm{max}}} \frac{1}{\partial_{p} j (K; p = \mathcal{E}_{\alpha})} - \exp \left( \mathcal{E}_{\alpha} N \right) - -The final form arises from the fact that all of the poles :math:`\mathcal{E}_{\alpha}` are simple. -From this development, the Laplace inversion requires evaluation of two quantities: -:math:`\mathcal{E}_{\alpha}` (for :math:`\alpha = 0, 1, \ldots, \alpha_{\mathrm{max}}`) -and :math:`\partial_{p} j (K; p = \mathcal{E}_{\alpha}) = \frac{\partial j (K; p = \mathcal{E}_{\alpha})}{\partial p}`. -We leverage several numerical and asymptotic methods to find the poles :math:`\mathcal{E}_{\alpha}` -(see [Mehraeen2008]_ for a detailed description of these methods). - -This basic approach is extended to Green's function evaluation with fixed end orientation -(i.e. the orientation-dependent Green's function). -Turning back to the general Green's function (i.e. including end orientations), -we have - -.. math:: - G(\vec{K},\vec{u}|\vec{u}_{0};p) = - \frac{1}{\Omega_{D}} - \sum_{\lambda} \sum_{\lambda_{0}} \sum_{\mathbf{\mu}} - Y^{(D)*}_{\lambda;\mathbf{\mu}} (\vec{u}') - Y^{(D)}_{\lambda_{0};\mathbf{\mu}}(\vec{u}_{0}') - \mathcal{G}_{\lambda_{0},\lambda}^{\mu}(K;p). - -This spherical harmonic expansion requires evaluation of the Laplace inverse -of :math:`\mathcal{G}_{\lambda_{0},\lambda}^{\mu_{1}}(K;p)` -(i.e. spherical-harmonic transform of the Green's function). -The evaluation of poles and residues of :math:`\mathcal{G}_{\lambda_{0},\lambda}^{\mu}(K;p)` -utilizes similar approaches as outlined above and discussed in detail in Ref. [Mehraeen2008]_. -The primary difference is whether the residues and poles require evaluation for non-zero -values of :math:`\mu` and the residue evaluation must account for different -:math:`\lambda` and :math:`\lambda_{0}`. -Poles and residues are evaluated -for the additional index :math:`\mu`, which defines the :math:`z`-component of the -angular momentum (noting the Quantum Mechanical analogy of our problem). -Inclusion of :math:`\mu` requires definition of the cutoff :math:`\mu = \mu_{\mathrm{max}}` -that restricts the otherwise infinite summations within the inversion. -Evaluation of the residues for all possible values of :math:`\lambda` and :math:`\lambda_{0}` -(with a cutoff :math:`\lambda_{\mathrm{max}}`) -results in a residue matrix defined by -:math:`[\partial_{p} j_{\lambda_{0},\lambda}^{\mu} (K;p = \mathcal{E}_{\alpha}^{\mu} ) ]^{-1}`, -which is a :math:`(\lambda_{\mathrm{max}} - \mu + 1) \times (\lambda_{\mathrm{max}} - \mu + 1)` -tensor for a given :math:`\mu` and :math:`\mathcal{E}_{\alpha}^{\mu}`. - -The following table shows the cases of whether non-zero values of -:math:`\mu` and :math:`\lambda` need to be evaluated for the Laplace-inversion. -We define the boolean parameters -'mu_zero_only' and 'lam_zero_only' to determine the family of residues and poles that need to -be determined for a given Green's function evaluation. - -.. table:: - :widths: 30 30 30 30 - :align: center - - +-----------------+----------------+----------------------------+------------------------------------+ - | | :math:`G(K;N)` | :math:`G(K,\vec{u}_{0};N)` | :math:`G(K,\vec{u}|\vec{u}_{0};N)` | - +=================+================+============================+====================================+ - | 'mu_zero_only' | True | True | False | - +-----------------+----------------+----------------------------+------------------------------------+ - | 'lam_zero_only' | True | False | False | - +-----------------+----------------+----------------------------+------------------------------------+ - - -We define a data structure that facilitates evaluation of the Laplace inversion -but also enables the 'wlcgreen' module to dynamically grow the data structure, -so residues and poles do not require re-evaluation if already evaluated at a given :math:`K`. -We define the 'green_properties' library as follows - -.. code:: python - - green_properties = { k_val1:[mu_zero_only, lam_zero_only, poles, residues], - k_val2:[mu_zero_only, lam_zero_only, poles, residues], ... } - -For a given key in the library 'k_val', the elements are as follows - -- 'mu_zero_only' is a boolean (True or False) that determines whether the poles and residues are evaluated for non-zero values of :math:`\mu` - -- 'lam_zero_only' is a boolean (True or False) that determines whether the residues are evaluated for non-zero :math:`\lambda` - -- 'poles' is an array of poles [size :math:`(\alpha_{\mathrm{max}} + 1) \times (\mu_{\mathrm{max}} + 1)`], which accounts for the value of 'mu_zero_only' - -- 'residues' is an array of residues [size :math:`(\alpha_{\mathrm{max}} + 1) \times (\mu_{\mathrm{max}} + 1)`] (to be discussed further) - -Step 2: Fourier-space inversion -^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - -The Fourier inversion is found by numerically performing the integral - -.. math:: - G(\vec{R};N) & = & - \frac{1}{(2\pi)^{D}} \int d\vec{k} \exp \left( - -i \vec{k} \cdot \vec{R} \right) G(K;N) - \nonumber \\ - & = & - \frac{1}{(2 l_{p})^{D}} - \frac{1}{(2 \pi)^{D/2}} - \int_{0}^{\infty} d K K^{D-1} - \frac{J_{D/2-1}(NrK)}{\left(NrK\right)^{D/2-1}} - G(K;N) - -where -:math:`\vec{K} = 2 l_{p} \vec{k}` (:math:`K = |\vec{K}|`), -:math:`\vec{r} = \vec{R}/L` (:math:`r = |\vec{r}|`), -and :math:`J_{n}(z)` is the Bessel function of the first kind. - -Integration over :math:`K` is performed numerically -from :math:`K=0` to :math:`K=K_{\mathrm{cutoff}}`, -where :math:`K_{\mathrm{cutoff}}` is a cutoff value -that is sufficiently large to achieve convergence. -The :math:`K`-step size in the numerical integration -is chosen such that it satisfies a global accuracy threshold. -In our calculation, we use a tolerance of :math:`10^{-20}`, which leads to -an overall accuracy of :math:`10^{-15}` for the real-space Green function. - -Functions contained with the 'wlcgreen' module ----------------------------------------------- - -.. automodule:: wlcstat.wlcgreen - :members: - - -Example usage of 'eval_poles_and_residues' ------------------------------------------- - -This plot shows the poles for the wormlike chain in 3 dimensions over a range of :math:`K`. -This plot is a reproduction of Fig. 1 in Ref. [Mehraeen2008]_. - -.. plot:: - - import matplotlib.pyplot as plt - import numpy as np - from wlcstat.wlcgreen import * - - num_k = 100 - k_val_0 = 1e-1 - k_val_f = 1e3 - k_val = np.logspace(np.log10(k_val_0), np.log10(k_val_f), num_k) - mu=0 - dimensions = 3 - num_poles = min(12, 26-mu) - poles = np.zeros((num_k, num_poles), dtype=type(1 + 1j)) - for i_k_val in range(num_k): - poles_k_val, resi_k_val = eval_poles_and_residues(k_val[i_k_val],mu,dimensions) - for i_pole in range(num_poles): - poles[i_k_val, i_pole] = poles_k_val[i_pole] - - plt.figure(figsize=(10,8)) - font = {'family' : 'serif', - 'weight':'normal', - 'size': 18} - plt.rc('font', **font) - - for i_pole in range(num_poles): - plt.semilogx(k_val, np.real(poles[:, i_pole])) - - plt.xlabel(r'$K = (2l_{p}) k$') - plt.ylabel(r'Real ($\mathcal{E}_{\alpha}$)') - plt.tight_layout() - plt.show() - -.. plot:: - - import matplotlib.pyplot as plt - import numpy as np - from wlcstat.wlcgreen import * - - num_k = 100 - k_val_0 = 1e-1 - k_val_f = 1e3 - k_val = np.logspace(np.log10(k_val_0), np.log10(k_val_f), num_k) - mu=0 - dimensions = 3 - num_poles = min(12, 26-mu) - poles = np.zeros((num_k, num_poles), dtype=type(1 + 1j)) - for i_k_val in range(num_k): - poles_k_val, resi_k_val = eval_poles_and_residues(k_val[i_k_val],mu,dimensions) - for i_pole in range(num_poles): - poles[i_k_val, i_pole] = poles_k_val[i_pole] - - plt.figure(figsize=(10,8)) - font = {'family' : 'serif', - 'weight':'normal', - 'size': 18} - plt.rc('font', **font) - - for i_pole in range(num_poles): - plt.semilogx(k_val, np.imag(poles[:, i_pole])) - - plt.xlabel(r'$K = (2l_{p}) k$') - plt.ylabel(r'Imag ($\mathcal{E}_{\alpha}$)') - plt.tight_layout() - plt.show() - -Another way to look at the poles is to consider the weight of the individual poles on the -Fourier inversion. We consider a chain length :math:`N=0.1`, which is quite rigid. -This plot shows the weight :math:`\exp \left[ \mathrm{Real} (\mathcal{E}_{\alpha} ) N \right)` -over a range of :math:`K`. -We note that the :math:`y`-scale in this plot is roughly coincident with machine precision -:math:`10^{-14}`, so the :math:`k`-range and the number of poles are the complete set necessary -for Laplace inversion to machine precision accuracy for this chain length. - -.. plot:: - - import matplotlib.pyplot as plt - import numpy as np - from wlcstat.wlcgreen import * - - length_kuhn = 0.1 - alpha_max = 25 - num_k = 100 - k_val_0 = 1e-1 - k_val_f = 1e5 - k_val = np.logspace(np.log10(k_val_0), np.log10(k_val_f), num_k) - mu=0 - dimensions = 3 - num_poles = min(18, alpha_max + 1 - mu) - poles = np.zeros((num_k, num_poles), dtype=type(1 + 1j)) - for i_k_val in range(num_k): - poles_k_val, resi_k_val = eval_poles_and_residues(k_val[i_k_val],mu,dimensions) - for i_pole in range(num_poles): - poles[i_k_val, i_pole] = poles_k_val[i_pole] - - plt.figure(figsize=(10,8)) - font = {'family' : 'serif', - 'weight':'normal', - 'size': 18} - plt.rc('font', **font) - - for i_pole in range(num_poles): - plt.loglog(k_val, np.exp(np.real(poles[:, i_pole]) * length_kuhn)) - - plt.ylim((10 ** -14, 1)) - plt.xlim((10 ** -1, 10 ** 5)) - plt.xlabel(r'$K = (2l_{p}) k$') - plt.ylabel(r'$\exp \left[ \mathrm{Real} (\mathcal{E}_{\alpha}) N \right]$') - plt.tight_layout() - plt.show() - -We now demonstrate the evaluation of the residues for -:math:`\lambda = \lambda_{0} = 0` and -:math:`\mu = 0` -We show the residues values for the first 10 eigenvalues :math:`\mathcal{E}_{\alpha}`. -Our numerical procedure utilizes the small-:math:`k` and intermediate-:math:`k` algorithms -given in Ref. [Mehraeen2008]_, -with a cross-over frequency of :math:`K_{\mathrm{cutoff}} = 0.01`. - -.. plot:: - - import matplotlib.pyplot as plt - import numpy as np - from wlcstat.wlcgreen import * - - num_k = 100 - k_val_0 = 1e-4 - k_val_f = 1e4 - k_val = np.logspace(np.log10(k_val_0), np.log10(k_val_f), num_k) - mu=0 - dimensions = 3 - num_poles = 10 - lam_0 = 0 - lam = 0 - - num_poles = min(num_poles, 26-mu) - poles = np.zeros((num_k, num_poles), dtype=type(1 + 1j)) - residues = np.zeros((num_k, num_poles), dtype=type(1 + 1j)) - - for i_k_val in range(num_k): - poles_k_val, resi_k_val = eval_poles_and_residues(k_val[i_k_val],mu,True,False,dimensions) - for i_pole in range(num_poles): - poles[i_k_val, i_pole] = poles_k_val[i_pole] - residues[i_k_val, i_pole] = resi_k_val[lam, lam_0, i_pole] - - plt.figure(figsize=(10,8)) - font = {'family' : 'serif', - 'weight':'normal', - 'size': 18} - plt.rc('font', **font) - - for i_pole in range(num_poles): - plt.loglog(k_val, np.real(abs(residues[:, i_pole]))) - - plt.xlabel(r'$K = (2l_{p}) k$') - plt.ylabel(r'$| \mathrm{Resi}_{\alpha} |$') - plt.tight_layout() - plt.show() diff --git a/doc/build/html/_sources/wlcstruc_notes.rst.txt b/doc/build/html/_sources/wlcstruc_notes.rst.txt deleted file mode 100644 index cbdc357..0000000 --- a/doc/build/html/_sources/wlcstruc_notes.rst.txt +++ /dev/null @@ -1,150 +0,0 @@ -.. _wlcstruc_notes: -.. .. automodule:: wlcstat - - -Structure Factor -================ - -The physical behavior of a polymer chain is frequently characterized by the -single-chain structure factor. -The structure factor is directly measured in a -scattering experiment, and correlating scattering experiments with theoretical -models provides insight into the physical behavior in -polymeric fluids. -From a theoretical perspective, the single-chain structure factor acts as an -input for treating many-chain systems including -concentration fluctuations. -Although the structure factors for both a flexible Gaussian chain -and a rigid rod are easily expressible, the structure factor of a semiflexible -polymer is considerably more difficult to predict theoretically, -largely due to the challenges in acquiring analytical expressions for the -governing chain statistics. -Our goal in this section is to apply our exact results to predict the -structure factor for the wormlike chain model that is valid over the -entire range of scattering vectors and chain lengths. - -We define the structure factor to be - -.. math:: - S(\vec{k}) = \frac{1}{L^{2}} - \int_{0}^{L} ds_{1} - \int_{0}^{L} ds_{2} - \left< \exp \left[ i \vec{k} \cdot \left( \vec{r}(s_{1})-\vec{r}(s_{2}) \right) \right] \right>, - -.. \label{eq:sk} - -where :math:`\vec{k}` is the scattering vector, and -the angular brackets denote an average with respect to the -specific model that governs the chain statistics. -Our current manuscript contains exact results that permit the evaluation of -the structure factor for the wormlike chain model without excluded volume -interactions. -Our definition for the structure factor differs from the conventional definition -by an extra factor of :math:`1/L`, thus rendering a dimensionless -structure factor that tends to one at zero scattering vector. - -For the wormlike chain model, the structure factor is given by - -.. math:: - S(\vec{k}) = \frac{2}{N^{2}} \mathcal{L}^{-1} \left[ \frac{G(K;p)}{p^{2}} \right], - -.. \label{eq:sklaplace} - -where :math:`K = 2 l_{p} | \vec{k} |`, :math:`\mathcal{L}^{-1}` implies a Laplace -inversion from :math:`p` to :math:`N=L/(2l_{p})`, and :math:`G(K;p)` is the wormlike chain -Green function. -The structure factor is expressible in terms of the magnitude of the scattering vector -due to the rotational invariance of the governing statistics. -Using results given in Sec.~\ref{sec:greal}, we write the structure factor as - -.. math:: - S(\vec{k}) = - \frac{2}{N^{2}} \left[ - \frac{N}{j_{0}^{(+)}(K;0)} - - \frac{\partial_{p} j_{0}^{(+)}(K;0)}{j_{0}^{(+)}(K;0)^{2}} - + \sum_{\alpha=0}^{\infty} - \frac{\exp \left( \mathcal{E}_{\alpha} N \right)}{\mathcal{E}_{\alpha}^{2} \partial_{p} j_{0}^{(+)}(K;\mathcal{E}_{\alpha})} - \right], - :label: skwlc - -.. \label{eq:skwlc} - -where :math:`j_{0}^{(+)}(K;p)` and :math:`\partial_{p} j_{0}^{(+)}(K;p)` are -continued-fraction functions that are defined in Sec.~\ref{sec:greal}. -Equation :eq:`skwlc` is evaluated using methods outlined in Sec.~\ref{sec:greal} -to find the eigenvalues :math:`\mathcal{E}_{l}` and to calculate -:math:`j_{0}^{(+)}` and :math:`\partial_{p} j_{0}^{(+)}`. -The structure factor given by Eq. :eq:`skwlc` is expressed in arbitrary number of -dimensions :math:`D`, which is generally useful for treating many-chain systems. - -In Ref. [Spakowitz2004]_, we present realizations of the -structure factor for the wormlike chain model in 3 dimensions, -demonstrating that our exact results -for wormlike chain statistics in 3 dimensions capture the structure factor -over all chain lengths and scattering vectors. -Equation :eq:`skwlc`, along with the techniques provided in Sec.~\ref{sec:greal}, -provide a convenient methodology for calculating the structure factor -as a comparison with scattering experiments. -Specifically, the infinite summation in Eq. :eq:`skwlc` is truncated at a finite cutoff, -and the partial summation is evaluated using methods to evaluate -:math:`\mathcal{E}_{l}` found in Sec.~\ref{sec:greal}. -For most calculations, only a couple of terms are necessary to achieve -accurate realizations of the structure factor. -For example, the structure factor in 3 dimensions for a chain -of length :math:`N=0.1` requires only 4 terms in the summation to achieve -accuracy within 1.76 percent difference from a more accurate calculation with -30 terms in the summation (\emph{i.e.} completely converged in its numerical behavior). -Since the terms in the summation decay exponentially with :math:`N`, larger :math:`N` values -require fewer terms. -To illustrate this, we note that the structure factor in 3 dimensions for a slightly -larger chain of length :math:`N=0.5` calculated with 4 terms in the summation -is within :math:`1.05 \times 10^{-4}` percent difference from the calculation -with 30 terms in the summation. -Therefore, most practical applications of Eq. :eq:`skwlc` require the inclusion of -only a couple of terms in the summation. - -Functions contained with the 'wlcstruc' module ----------------------------------------------- - -.. automodule:: wlcstat.wlcstruc - :members: - -Example usage of 'eval_structure_factor' ------------------------------------------- - -This plot shows the structure factor for the wormlike chain in 3 dimensions over a range of :math:`K` -for :math:`N = 0.1`, :math:`0.5`, and :math:`1.0`. -This plot is a reproduction of Fig. 2 in Ref. [Spakowitz2004]_. - -.. plot:: - - import matplotlib.pyplot as plt - import numpy as np - from wlcstat.wlcstruc import * - - - num_k = 100 - k_val_0 = 1e-2 - k_val_f = 20 - length_kuhn_vec = np.array([0.1, 0.5, 1]) - dimensions = 3 - - plt.figure(figsize=(10,8)) - font = {'family' : 'serif', - 'weight':'normal', - 'size': 18} - plt.rc('font', **font) - - for ind_length in range(0, len(length_kuhn_vec)): - length_kuhn = float(length_kuhn_vec[ind_length]) - k_val = np.linspace(k_val_0, k_val_f / length_kuhn, num_k) - structure_factor = eval_structure_factor(k_val, length_kuhn, dimensions) - plt.plot(k_val * length_kuhn, np.real(structure_factor * k_val * length_kuhn),'-') - - plt.xlabel(r'$Lk$') - plt.ylabel(r'Structure Factor, $k L S(K;N)$') - plt.ylim((2, 3.5)) - plt.xlim((2, 20)) - plt.tight_layout() - plt.show() - diff --git a/doc/build/html/_sources/wlctheory.rst.txt b/doc/build/html/_sources/wlctheory.rst.txt deleted file mode 100644 index ab54a62..0000000 --- a/doc/build/html/_sources/wlctheory.rst.txt +++ /dev/null @@ -1,303 +0,0 @@ -.. _wlctheory: - -Wormlike Chain Theory -===================== - -The wormlike chain model describes the polymer chain as a continuous -thread through space that resists bending deformation [Kratky1949]_. -Subjecting the chain to thermal fluctuations results in a wiggling wormlike -polymer chain. - -The polymer conformation is defined by a space curve :math:`\vec{r}(s)` where -:math:`s` runs from zero to the contour length :math:`L`. The wormlike chain model has -a fixed length (like the freely jointed chain model), which is -enforced by setting - -.. math:: - \left( \frac{\partial \vec{r}(s)}{\partial s} \right)^{\! \! 2} = - \left( \vec{u}(s) \right)^{2} - = 1 - -at all values of :math:`s` along the chain, where we define the tangent vector -:math:`\vec{u}(s) = \frac{\partial \vec{r}(s)}{\partial s}`. -The chain opposes bending deformation, and the bending energy is -quadratic in the curvature of the chain. This gives the bending energy - -.. math:: - E_{bend} = \frac{k_{B}T l_{p}}{2} \int_{0}^{L} ds \left( - \frac{\partial^{2} \vec{r}(s)}{\partial s^{2}} \right)^{\! \! 2} = - \frac{k_{B}T l_{p}}{2} \int_{0}^{L} ds \left( - \frac{\partial \vec{u}(s)}{\partial s} \right)^{\! 2} - -.. figure:: figures/wlc-model.pdf - :width: 600 - :align: center - :alt: Schematic representation of the wormlike chain model and definition of geometric parameters. - - Schematic representation of the wormlike chain model and definition of geometric parameters. - -Wormlike Chain model Green function---Path integral formulation and the Diffusion equation ------------------------------------------------------------------------------------------- - -The governing differential equation for the Wormlike Chain model [Kratky1949]_ is -given through the application of the path integral in the -necessary dimensions. -The differential Hamiltonian :math:`\mathcal{H}` of the Wormlike -chain model is given by - -.. math:: - \beta \mathcal{H} = \frac{l_{p}}{2} \left( \frac{\partial \vec{u}}{\partial s} \right)^{2} +\beta V(\vec{r}, \vec{u}), - -where the tangent :math:`\vec{u} = \frac{\partial \vec{r}}{\partial s}` -(with constraint :math:`\left| \frac{\partial \vec{r}}{\partial s} \right|=1` for all :math:`s`). -Define the Green function :math:`G(\vec{r}, \vec{u}|\vec{r}_{0},\vec{u}_{0}; L)` to be the -probability of finding the chain at location :math:`\vec{r}` with -orientation :math:`\vec{u}` at length :math:`L` given that the chain begins at -location :math:`\vec{r}_{0}` with orientation :math:`\vec{u}_{0}`. -The Markov property of the chain is written as - -.. math:: - G (\vec{r}_{C}, \vec{u}_{C}, s_{C}|\vec{r}_{A},\vec{u}_{A}, s_{A}) = \int d \vec{r}_{B} d \vec{u}_{B} G (\vec{r}_{C}, \vec{u}_{C}, s_{C}|\vec{r}_{B},\vec{u}_{B}, s_{B}) \times G (\vec{r}_{B}, \vec{u}_{B}, s_{B}|\vec{r}_{A},\vec{u}_{A}, s_{A}). - -Set :math:`s_{A}=0`, :math:`s_{B}=L`, and :math:`s_{C}=L+\delta` with -:math:`\vec{r}_{A}=\vec{r}_{0}`, -:math:`\vec{r}_{B}=\vec{r}_{1}`, and -:math:`\vec{r}_{C}=\vec{r}` to find the governing diffusion equation -for :math:`G(\vec{r},\vec{u}|\vec{r}_{0},\vec{u}_{0};L)`. - - -In the limit :math:`\delta \rightarrow 0`, the Green function -:math:`G(\vec{r},\vec{u}, N+\delta | \vec{r},\vec{u},N)` will be dominated by a single path whose action is - -.. math:: - S \approx \frac{l_{p}}{2} \delta \left( \frac{ \vec{u} - \vec{u}_{1}}{\delta} \right)^{2} + \delta \beta V \!\! \left( \frac{\vec{r}+\vec{r}_{1}}{2} \right). - -The Green function for this path is thus - -.. math:: - G(\vec{r}, \vec{u}, L + \delta| \vec{r}_{1}, \vec{u}_{1}, L) = - \frac{\delta (\vec{r} - \vec{r}_{1} - \vec{u} \delta )}{A} \exp \! - \left( \frac{l_{p}}{\delta} \vec{u} \cdot \vec{u}_{1} \right) \exp (-\delta \beta V) - -where the normalization constant :math:`A` is to be -determined in the limit of :math:`\delta` approaching zero, and -the delta function is added to the Green function to conserve the path length. -The Green function is now given by - -.. math:: - G(\vec{r}, \vec{u}, L + \delta| \vec{r}_{0}, \vec{u}_{0}, 0) = - \int \frac{\delta (\vec{r} - \vec{r}_{1} - \vec{u} \delta )}{A} - \exp \left( \frac{l_{p}}{\delta} \vec{u} \cdot \vec{u}_{1} - \right)\exp (-\delta \beta V) \times G(\vec{r}_{1}, \vec{u}_{1},L - | \vec{r}_{0}, \vec{u}_{0},0) d \vec{r}_{1} d \vec{u}_{1}. - -Assume only small deviations from :math:`\vec{r}` and :math:`\vec{u}` -will contribute to the integral. Expand the Green function -:math:`G(\vec{r}_{1}, \vec{u}_{1}, L| \vec{r}_{0},\vec{u}_{0},0)` about :math:`\vec{r}` -and :math:`\vec{u}` to quadratic order in the deviation to find the -leading order change in the propagated Green function. - -The resulting expansion is given by - -.. math:: - G(\vec{r}_{1}, \vec{u}_{1}, L| \vec{r}_{0},\vec{u}_{0},0) - & = & - G(\vec{r}, \vec{u}, L| \vec{r}_{0},\vec{u}_{0},0)- - \frac{\partial G}{\partial \vec{r}} \cdot \Delta \vec{r} - - \frac{\partial G}{\partial \vec{u}} \cdot \Delta \vec{u} \nonumber \\ - & & - \hspace{-1in} - + \frac{1}{2} \frac{\partial^{2} G}{\partial \vec{r}^{2}} - : \Delta \vec{r} \Delta \vec{r} - + \frac{1}{2} \frac{\partial^{2} G}{\partial \vec{u}^{2}} - : \Delta \vec{u} \Delta \vec{u} - + \frac{\partial^{2} G}{\partial \vec{r} \partial \vec{u}} - : \Delta \vec{r} \Delta \vec{u} - -where :math:`\Delta \vec{r} = \vec{r} - \vec{r}_{1}` and -:math:`\Delta \vec{u} = \vec{u} - \vec{u}_{1}`. -The double dot operation between two tensors acts as :math:`\textbf{A}:\textbf{B} = A_{ij} B_{ji}`. -The normalization constant is found by requiring the leading term -to approach unity as the time change :math:`\delta` approaches zero. -The following integral determines :math:`A`: - -.. math:: - \frac{1}{A} \int \delta(\vec{r} - \vec{r}_{1} - \vec{u} \delta ) - \exp \left( \frac{l_{p}}{\delta} - \vec{u} \cdot \vec{u}_{1} \right) - d \vec{u}_{1} d \vec{r}_{1} & = & \nonumber \\ - \hspace{-0.5in} - \frac{1}{A} \int \delta(\vec{r} - \vec{r}_{1} - \vec{u} \delta ) - \left[ \int_{0}^{2 \pi} \int_{0}^{\pi} - \exp \left( \frac{l_{p}}{\delta} \cos \theta \right) \sin \theta - d \theta d \phi \right] d \vec{r}_{1} & = & \nonumber \\ - \frac{1}{A} \frac{4 \pi \delta}{l_{p}} \sinh - \left( \frac{l_{p}}{\delta} \right) & = & 1 - -thus :math:`A = \frac{4 \pi \delta}{l_{p}} \sinh \left( \frac{l_{p}}{\delta} \right)`. -The leading order -response of the Green function is found by evaluating the averaged -quantities within the integrand. Define the average of a given -quantity to be - -.. math:: - \left< ... \right> = \int d \vec{u}_{1} \frac{1}{A} - \exp (h \vec{u} \cdot \vec{u}_{1}) (...), - -where :math:`h = \frac{l_{p}}{\delta}`. - -We must find the -following quantities: :math:`\left< \Delta \vec{r} \right>`, -:math:`\left< \Delta \vec{u} \right>`, and -:math:`\left< \Delta \vec{u} \Delta \vec{u} \right>`. The other averages -( :math:`\left< \Delta \vec{r} \Delta \vec{r} \right>` and -:math:`\left< \Delta \vec{r} \Delta \vec{u} \right>` ) yield -terms of quadratic order in :math:`\delta`, thus they do not contribute -to the lowest order response. -For convenience, define the vector -quantity :math:`\vec{h} = h \vec{u}` for use in this derivation. -The average quantity -:math:`\langle \Delta \vec{u} \rangle` is given by - -.. math:: - \langle \Delta \vec{u} \rangle & = & \vec{u} - \langle \vec{u}_{1} \rangle \nonumber \\ - & = & \vec{u} - \frac{1}{A} \int d \vec{u}_{1} \exp - ( \vec{h} \cdot \vec{u}_{1} ) \vec{u}_{1} \nonumber \\ - & = & \vec{u} - \frac{1}{A} %\vec{\nabla}_{h} - \frac{\partial A}{\partial \vec{h}} \nonumber \\ - & = & \vec{u} - \frac{4 \pi \vec{u}}{A} - \left( \frac{ \cosh (h) }{h} - \frac{\sinh (h)}{h^{2}} \right) \nonumber \\ - & = & \vec{u} (1 - \coth (h) + h^{-1} ). - -Thus, in the limit of :math:`h \rightarrow \infty`, the quantity -:math:`\langle \Delta \vec{u} \rangle = \frac{\vec{u} \delta}{l_{p}}`. -The average quantity :math:`\langle \Delta \vec{u} \Delta \vec{u} \rangle` -is given by - -.. math:: - \langle \Delta \vec{u} \Delta \vec{u} \rangle & = & \vec{u} \vec{u} - - \vec{u} \langle \vec{u}_{1} \rangle - \langle \vec{u}_{1} \rangle \vec{u} - + \langle \vec{u}_{1} \vec{u}_{1} \rangle \nonumber \\ - & = & \frac{2 \delta}{l_{p}} \vec{u} \vec{u} - - \vec{u} \vec{u} + \langle \vec{u}_{1} \vec{u}_{1} \rangle \nonumber \\ - & = & \frac{2 \delta}{l_{p}} \vec{u} \vec{u} - - \vec{u} \vec{u} + \frac{1}{A} - \frac{\partial^{2} A}{\partial \vec{h} \partial \vec{h}}. - -The following quantity is found to complete the derivation: - -.. math:: - \frac{\partial^{2} A}{\partial \vec{h} \partial \vec{h}} - = 4 \pi \mathbf{I} - \left( \frac{\cosh (h)}{h^{2}} - \frac{\sinh (h)}{h^{3}} \right) + - 4 \pi \vec{h} \vec{h} - \left( \frac{ \sinh (h)}{h^{3}} - \frac{3 \cosh (h)}{h^{4}} + \frac{3 \sinh (h)}{h^{5}} \right). - -This is evaluated and the limit as :math:`h` approaches infinity yields -the solution of :math:`\langle \Delta \vec{u} \Delta \vec{u} \rangle -= \frac{\delta}{l_{p}} ( \mathbf{I} - \vec{u} \vec{u} )`. -Altogether the Green function obeys - -.. math:: - G + \frac{\partial G}{\partial s} \delta = G - \beta V G \delta - - \frac{\partial G}{\partial \vec{r}} \cdot \vec{u} \delta - - \frac{\partial G}{\partial \vec{u}} \cdot \frac{\vec{u}}{l_{p}} \delta - + \frac{1}{2} \vec{\nabla}_{u} \vec{\nabla}_{u} G : - \frac{\delta}{l_{p}} ( \mathbf{I} - \vec{u} \vec{u} ) - -This differential equation is further simplified by noting that -:math:`\vec{u} \cdot \vec{\nabla}_{u} = 0` and -:math:`\vec{u} \vec{u} : \vec{\nabla}_{u} \vec{\nabla}_{u} = 0`. -The final differential equation for the Green function is given by - -.. math:: - \frac{\partial G(\vec{r}, \vec{u}, L| \vec{r}_{0}, \vec{u}_{0}, 0)}{\partial L} & = & - - \beta V G(\vec{r}, \vec{u}, L| \vec{r}_{0}, \vec{u}_{0}, 0) \nonumber \\ - & & - - \vec{u} \cdot \vec{\nabla}_{r} G(\vec{r}, \vec{u}, L| \vec{r}_{0}, \vec{u}_{0}, 0) + \frac{1}{2 l_{p}} - \vec{\nabla}_{u}^{2} G(\vec{r}, \vec{u}, L | \vec{r}_{0}, \vec{u}_{0}, 0), - -with the initial condition :math:`G(\vec{r}, \vec{u}, 0 | \vec{r}_{0}, \vec{u}_{0}, 0)= -\delta(\vec{r}-\vec{r}_{0})\delta(\vec{u}-\vec{u}_{0})`. - -Orientation statistics ----------------------- - -Consider the case :math:`V=0`. -Define the Fourier transform (and inverse transform) of a function :math:`f(\vec{r})` from :math:`\vec{r}` to :math:`\vec{k}` to be - -.. math:: - \tilde{f}(\vec{k}) = - \int d \vec{r} f(\vec{r}) \exp \left( i \vec{k} \cdot \vec{r} \right) %= \tilde{f}(\vec{k}) - \hspace{0.1in} - \mathrm{and} - \hspace{0.1in} - f(\vec{r}) = - \frac{1}{(2\pi)^{3}} \int d \vec{k} \tilde{f} ( \vec{k})\exp \left( -i \vec{k} \cdot \vec{r} \right) - -The governing differential equation for :math:`\tilde{G}(\vec{k},\vec{u}|\vec{u}_{0};L)` for :math:`V=0` is - -.. math:: - \frac{\partial \tilde{G}(\vec{k},\vec{u}|\vec{u}_{0};L)}{\partial L} = - \left(i\vec{k} \cdot \vec{u} + - \frac{1}{2 l_{p}} \vec{\nabla}_{u}^{2} - \right) - \tilde{G}(\vec{k},\vec{u}|\vec{u}_{0};L) - -with initial condition -:math:`\tilde{G}(\vec{k},\vec{u}|\vec{u}_{0};0)=\exp (i\vec{k} \cdot \vec{r}_{0}) \delta(\vec{u}-\vec{u}_{0})` - -The integral of the Green function over the position :math:`\vec{r}` is equivalent to - -.. math:: - G(\vec{u}|\vec{u}_{0};L) = \int d \vec{r} G(\vec{r}, \vec{u}, L | \vec{r}_{0}, \vec{u}_{0}, 0) - = \tilde{G}(\vec{k}=\vec{0},\vec{u}|\vec{u}_{0};L), - -which gives the orientation-only chain statistics, i.e. the probability that a chain begin with -orientation :math:`\vec{u}_{0}` and ends with orientation :math:`\vec{u}` regardless of the end positions. -The orientation Green function :math:`G(\vec{u}|\vec{u}_{0};L)` satisfies - -.. math:: - \frac{\partial G(\vec{u}|\vec{u}_{0};L)}{\partial L} = - \frac{1}{2 l_{p}} \vec{\nabla}_{u}^{2} - G(\vec{u}|\vec{u}_{0};L) - :label: gudiffeqn -.. \label{eq:gudiffeqn} - -with initial condition :math:`G(\vec{u}|\vec{u}_{0};L) = \delta(\vec{u}-\vec{u}_{0})`. - -Here, we note that the operator :math:`\vec{\nabla}_{u}^{2}` has eigenfunctions :math:`Y_{l}^{m}` that satisfy - -.. math:: - \vec{\nabla}_{u}^{2} Y_{l}^{m} = - l(l+1) Y_{l}^{m}. - -The eigenfunctions :math:`Y_{l}^{m}` are the spherical -harmonics [Arfken1999]_ that form a complete basis set for the 3-dimensional angular Laplacian :math:`\vec{\nabla}_{u}^{2}`. -This basis set is extended to arbitrary dimensions as the hyperspherical harmonics, -and we will make use of this extension in coming chapters. -The range of the indices :math:`l` and :math:`m` are :math:`l \in [0, \infty]` and :math:`m \in [-l, l]`. -The spherical harmonics satisfy - -.. math:: - \int d \vec{u} Y_{l}^{m} (\vec{u}) - Y_{l'}^{m'*}(\vec{u}) = \delta_{ll'} \delta_{mm'} - -The solution for :math:`G(\vec{u}|\vec{u}_{0};L)` is constructed as an expansion in the spherical harmonics, such that - -.. math:: - G(\vec{u}|\vec{u}_{0};L) = \sum_{l=0}^{\infty} \sum_{m=-l}^{l} - Y_{l}^{m} (\vec{u}) - Y_{l}^{m*}(\vec{u}_{0}) \exp [-l(l+1)N] - :label: guwlc -.. \label{eq:guwlc} - -where :math:`N=L/(2l_{p})`. -This form satisfies the governing Schrödinger equation (Eq. :eq:`gudiffeqn`), and the initial condition -is captured by noting that - -.. math:: - \sum_{l=0}^{\infty} \sum_{m=-l}^{l} - Y_{l}^{m} (\vec{u}) - Y_{l}^{m*}(\vec{u}_{0}) = \delta \left( \vec{u} - \vec{u}_{0} \right). - -This development enables the evaluations of average quantities (as discussed in the Average Quantities section). diff --git a/doc/build/html/_static/basic.css b/doc/build/html/_static/basic.css deleted file mode 100644 index 24bc73e..0000000 --- a/doc/build/html/_static/basic.css +++ /dev/null @@ -1,855 +0,0 @@ -/* - 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Multiple values per key are supported, - * it will always return arrays of strings for the value parts. - */ -jQuery.getQueryParameters = function(s) { - if (typeof s === 'undefined') - s = document.location.search; - var parts = s.substr(s.indexOf('?') + 1).split('&'); - var result = {}; - for (var i = 0; i < parts.length; i++) { - var tmp = parts[i].split('=', 2); - var key = jQuery.urldecode(tmp[0]); - var value = jQuery.urldecode(tmp[1]); - if (key in result) - result[key].push(value); - else - result[key] = [value]; - } - return result; -}; - -/** - * highlight a given string on a jquery object by wrapping it in - * span elements with the given class name. - */ -jQuery.fn.highlightText = function(text, className) { - function highlight(node, addItems) { - if (node.nodeType === 3) { - var val = node.nodeValue; - var pos = val.toLowerCase().indexOf(text); - if (pos >= 0 && - !jQuery(node.parentNode).hasClass(className) && - !jQuery(node.parentNode).hasClass("nohighlight")) { - var span; - var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg"); - if (isInSVG) { - span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); - } else { - span = document.createElement("span"); - span.className = className; - } - span.appendChild(document.createTextNode(val.substr(pos, text.length))); - node.parentNode.insertBefore(span, node.parentNode.insertBefore( - document.createTextNode(val.substr(pos + text.length)), - node.nextSibling)); - node.nodeValue = val.substr(0, pos); - if (isInSVG) { - var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect"); - var bbox = node.parentElement.getBBox(); - rect.x.baseVal.value = bbox.x; - rect.y.baseVal.value = bbox.y; - rect.width.baseVal.value = bbox.width; - rect.height.baseVal.value = bbox.height; - rect.setAttribute('class', className); - addItems.push({ - "parent": node.parentNode, - "target": rect}); - } - } - } - else if (!jQuery(node).is("button, select, textarea")) { - jQuery.each(node.childNodes, function() { - highlight(this, addItems); - }); - } - } - var addItems = []; - var result = this.each(function() { - highlight(this, addItems); - }); - for (var i = 0; i < addItems.length; ++i) { - jQuery(addItems[i].parent).before(addItems[i].target); - } - return result; -}; - -/* - * backward compatibility for jQuery.browser - * This will be supported until firefox bug is fixed. - */ -if (!jQuery.browser) { - jQuery.uaMatch = function(ua) { - ua = ua.toLowerCase(); - - var match = /(chrome)[ \/]([\w.]+)/.exec(ua) || - /(webkit)[ \/]([\w.]+)/.exec(ua) || - /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) || - /(msie) ([\w.]+)/.exec(ua) || - ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) || - []; - - return { - browser: match[ 1 ] || "", - version: match[ 2 ] || "0" - }; - }; - jQuery.browser = {}; - jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true; -} - -/** - * Small JavaScript module for the documentation. - */ -var Documentation = { - - init : function() { - this.fixFirefoxAnchorBug(); - this.highlightSearchWords(); - this.initIndexTable(); - if (DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) { - this.initOnKeyListeners(); - } - }, - - /** - * i18n support - */ - TRANSLATIONS : {}, - PLURAL_EXPR : function(n) { return n === 1 ? 0 : 1; }, - LOCALE : 'unknown', - - // gettext and ngettext don't access this so that the functions - // can safely bound to a different name (_ = Documentation.gettext) - gettext : function(string) { - var translated = Documentation.TRANSLATIONS[string]; - if (typeof translated === 'undefined') - return string; - return (typeof translated === 'string') ? translated : translated[0]; - }, - - ngettext : function(singular, plural, n) { - var translated = Documentation.TRANSLATIONS[singular]; - if (typeof translated === 'undefined') - return (n == 1) ? singular : plural; - return translated[Documentation.PLURALEXPR(n)]; - }, - - addTranslations : function(catalog) { - for (var key in catalog.messages) - this.TRANSLATIONS[key] = catalog.messages[key]; - this.PLURAL_EXPR = new Function('n', 'return +(' + catalog.plural_expr + ')'); - this.LOCALE = catalog.locale; - }, - - /** - * add context elements like header anchor links - */ - addContextElements : function() { - $('div[id] > :header:first').each(function() { - $('\u00B6'). - attr('href', '#' + this.id). - attr('title', _('Permalink to this headline')). - appendTo(this); - }); - $('dt[id]').each(function() { - $('\u00B6'). - attr('href', '#' + this.id). - attr('title', _('Permalink to this definition')). - appendTo(this); - }); - }, - - /** - * workaround a firefox stupidity - * see: https://bugzilla.mozilla.org/show_bug.cgi?id=645075 - */ - fixFirefoxAnchorBug : function() { - if (document.location.hash && $.browser.mozilla) - window.setTimeout(function() { - document.location.href += ''; - }, 10); - }, - - /** - * highlight the search words provided in the url in the text - */ - highlightSearchWords : function() { - var params = $.getQueryParameters(); - var terms = (params.highlight) ? params.highlight[0].split(/\s+/) : []; - if (terms.length) { - var body = $('div.body'); - if (!body.length) { - body = $('body'); - } - window.setTimeout(function() { - $.each(terms, function() { - body.highlightText(this.toLowerCase(), 'highlighted'); - }); - }, 10); - $('') - .appendTo($('#searchbox')); - } - }, - - /** - * init the domain index toggle buttons - */ - initIndexTable : function() { - var togglers = $('img.toggler').click(function() { - var src = $(this).attr('src'); - var idnum = $(this).attr('id').substr(7); - $('tr.cg-' + idnum).toggle(); - if (src.substr(-9) === 'minus.png') - $(this).attr('src', src.substr(0, src.length-9) + 'plus.png'); - else - $(this).attr('src', src.substr(0, src.length-8) + 'minus.png'); - }).css('display', ''); - if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) { - togglers.click(); - } - }, - - /** - * helper function to hide the search marks again - */ - hideSearchWords : function() { - $('#searchbox .highlight-link').fadeOut(300); - $('span.highlighted').removeClass('highlighted'); - }, - - /** - * make the url absolute - */ - makeURL : function(relativeURL) { - return DOCUMENTATION_OPTIONS.URL_ROOT + '/' + relativeURL; - }, - - /** - * get the current relative url - */ - getCurrentURL : function() { - var path = document.location.pathname; - var parts = path.split(/\//); - $.each(DOCUMENTATION_OPTIONS.URL_ROOT.split(/\//), function() { - if (this === '..') - parts.pop(); - }); - var url = parts.join('/'); - return path.substring(url.lastIndexOf('/') + 1, path.length - 1); - }, - - initOnKeyListeners: function() { - $(document).keydown(function(event) { - var activeElementType = document.activeElement.tagName; - // don't navigate when in search box or textarea - if (activeElementType !== 'TEXTAREA' && activeElementType !== 'INPUT' && activeElementType !== 'SELECT' - && !event.altKey && !event.ctrlKey && !event.metaKey && !event.shiftKey) { - switch (event.keyCode) { - case 37: // left - var prevHref = $('link[rel="prev"]').prop('href'); - if (prevHref) { - window.location.href = prevHref; - return false; - } - case 39: // right - var nextHref = $('link[rel="next"]').prop('href'); - if (nextHref) { - window.location.href = nextHref; - return false; - } - } - } - }); - } -}; - -// quick alias for translations -_ = Documentation.gettext; - -$(document).ready(function() { - Documentation.init(); -}); diff --git a/doc/build/html/_static/documentation_options.js b/doc/build/html/_static/documentation_options.js deleted file mode 100644 index 2fa8c97..0000000 --- a/doc/build/html/_static/documentation_options.js +++ /dev/null @@ -1,12 +0,0 @@ -var DOCUMENTATION_OPTIONS = { - URL_ROOT: document.getElementById("documentation_options").getAttribute('data-url_root'), - VERSION: '', - LANGUAGE: 'None', - COLLAPSE_INDEX: false, - BUILDER: 'html', - FILE_SUFFIX: '.html', - LINK_SUFFIX: '.html', - HAS_SOURCE: true, - SOURCELINK_SUFFIX: '.txt', - NAVIGATION_WITH_KEYS: false -}; \ No newline at end of file diff --git a/doc/build/html/_static/file.png b/doc/build/html/_static/file.png deleted file mode 100644 index a858a410e4faa62ce324d814e4b816fff83a6fb3..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 286 zcmV+(0pb3MP)s`hMrGg#P~ix$^RISR_I47Y|r1 z_CyJOe}D1){SET-^Amu_i71Lt6eYfZjRyw@I6OQAIXXHDfiX^GbOlHe=Ae4>0m)d(f|Me07*qoM6N<$f}vM^LjV8( diff --git a/doc/build/html/_static/jquery-3.5.1.js b/doc/build/html/_static/jquery-3.5.1.js deleted file mode 100644 index 5093733..0000000 --- a/doc/build/html/_static/jquery-3.5.1.js +++ /dev/null @@ -1,10872 +0,0 @@ -/*! - * jQuery JavaScript Library v3.5.1 - * https://jquery.com/ - * - * Includes Sizzle.js - * https://sizzlejs.com/ - * - * Copyright JS Foundation and other contributors - * Released under the MIT license - * https://jquery.org/license - * - * Date: 2020-05-04T22:49Z - */ -( function( global, factory ) { - - "use strict"; - - if ( typeof module === "object" && typeof module.exports === "object" ) { - - // For CommonJS and CommonJS-like environments where a proper `window` - // is present, execute the factory and get jQuery. - // For environments that do not have a `window` with a `document` - // (such as Node.js), expose a factory as module.exports. - // This accentuates the need for the creation of a real `window`. - // e.g. var jQuery = require("jquery")(window); - // See ticket #14549 for more info. - module.exports = global.document ? - factory( global, true ) : - function( w ) { - if ( !w.document ) { - throw new Error( "jQuery requires a window with a document" ); - } - return factory( w ); - }; - } else { - factory( global ); - } - -// Pass this if window is not defined yet -} )( typeof window !== "undefined" ? window : this, function( window, noGlobal ) { - -// Edge <= 12 - 13+, Firefox <=18 - 45+, IE 10 - 11, Safari 5.1 - 9+, iOS 6 - 9.1 -// throw exceptions when non-strict code (e.g., ASP.NET 4.5) accesses strict mode -// arguments.callee.caller (trac-13335). But as of jQuery 3.0 (2016), strict mode should be common -// enough that all such attempts are guarded in a try block. -"use strict"; - -var arr = []; - -var getProto = Object.getPrototypeOf; - -var slice = arr.slice; - -var flat = arr.flat ? function( array ) { - return arr.flat.call( array ); -} : function( array ) { - return arr.concat.apply( [], array ); -}; - - -var push = arr.push; - -var indexOf = arr.indexOf; - -var class2type = {}; - -var toString = class2type.toString; - -var hasOwn = class2type.hasOwnProperty; - -var fnToString = hasOwn.toString; - -var ObjectFunctionString = fnToString.call( Object ); - -var support = {}; - -var isFunction = function isFunction( obj ) { - - // Support: Chrome <=57, Firefox <=52 - // In some browsers, typeof returns "function" for HTML elements - // (i.e., `typeof document.createElement( "object" ) === "function"`). - // We don't want to classify *any* DOM node as a function. - return typeof obj === "function" && typeof obj.nodeType !== "number"; - }; - - -var isWindow = function isWindow( obj ) { - return obj != null && obj === obj.window; - }; - - -var document = window.document; - - - - var preservedScriptAttributes = { - type: true, - src: true, - nonce: true, - noModule: true - }; - - function DOMEval( code, node, doc ) { - doc = doc || document; - - var i, val, - script = doc.createElement( "script" ); - - script.text = code; - if ( node ) { - for ( i in preservedScriptAttributes ) { - - // Support: Firefox 64+, Edge 18+ - // Some browsers don't support the "nonce" property on scripts. - // On the other hand, just using `getAttribute` is not enough as - // the `nonce` attribute is reset to an empty string whenever it - // becomes browsing-context connected. - // See https://github.com/whatwg/html/issues/2369 - // See https://html.spec.whatwg.org/#nonce-attributes - // The `node.getAttribute` check was added for the sake of - // `jQuery.globalEval` so that it can fake a nonce-containing node - // via an object. - val = node[ i ] || node.getAttribute && node.getAttribute( i ); - if ( val ) { - script.setAttribute( i, val ); - } - } - } - doc.head.appendChild( script ).parentNode.removeChild( script ); - } - - -function toType( obj ) { - if ( obj == null ) { - return obj + ""; - } - - // Support: Android <=2.3 only (functionish RegExp) - return typeof obj === "object" || typeof obj === "function" ? - class2type[ toString.call( obj ) ] || "object" : - typeof obj; -} -/* global Symbol */ -// Defining this global in .eslintrc.json would create a danger of using the global -// unguarded in another place, it seems safer to define global only for this module - - - -var - version = "3.5.1", - - // Define a local copy of jQuery - jQuery = function( selector, context ) { - - // The jQuery object is actually just the init constructor 'enhanced' - // Need init if jQuery is called (just allow error to be thrown if not included) - return new jQuery.fn.init( selector, context ); - }; - -jQuery.fn = jQuery.prototype = { - - // The current version of jQuery being used - jquery: version, - - constructor: jQuery, - - // The default length of a jQuery object is 0 - length: 0, - - toArray: function() { - return slice.call( this ); - }, - - // Get the Nth element in the matched element set OR - // Get the whole matched element set as a clean array - get: function( num ) { - - // Return all the elements in a clean array - if ( num == null ) { - return slice.call( this ); - } - - // Return just the one element from the set - return num < 0 ? this[ num + this.length ] : this[ num ]; - }, - - // Take an array of elements and push it onto the stack - // (returning the new matched element set) - pushStack: function( elems ) { - - // Build a new jQuery matched element set - var ret = jQuery.merge( this.constructor(), elems ); - - // Add the old object onto the stack (as a reference) - ret.prevObject = this; - - // Return the newly-formed element set - return ret; - }, - - // Execute a callback for every element in the matched set. - each: function( callback ) { - return jQuery.each( this, callback ); - }, - - map: function( callback ) { - return this.pushStack( jQuery.map( this, function( elem, i ) { - return callback.call( elem, i, elem ); - } ) ); - }, - - slice: function() { - return this.pushStack( slice.apply( this, arguments ) ); - }, - - first: function() { - return this.eq( 0 ); - }, - - last: function() { - return this.eq( -1 ); - }, - - even: function() { - return this.pushStack( jQuery.grep( this, function( _elem, i ) { - return ( i + 1 ) % 2; - } ) ); - }, - - odd: function() { - return this.pushStack( jQuery.grep( this, function( _elem, i ) { - return i % 2; - } ) ); - }, - - eq: function( i ) { - var len = this.length, - j = +i + ( i < 0 ? len : 0 ); - return this.pushStack( j >= 0 && j < len ? [ this[ j ] ] : [] ); - }, - - end: function() { - return this.prevObject || this.constructor(); - }, - - // For internal use only. - // Behaves like an Array's method, not like a jQuery method. - push: push, - sort: arr.sort, - splice: arr.splice -}; - -jQuery.extend = jQuery.fn.extend = function() { - var options, name, src, copy, copyIsArray, clone, - target = arguments[ 0 ] || {}, - i = 1, - length = arguments.length, - deep = false; - - // Handle a deep copy situation - if ( typeof target === "boolean" ) { - deep = target; - - // Skip the boolean and the target - target = arguments[ i ] || {}; - i++; - } - - // Handle case when target is a string or something (possible in deep copy) - if ( typeof target !== "object" && !isFunction( target ) ) { - target = {}; - } - - // Extend jQuery itself if only one argument is passed - if ( i === length ) { - target = this; - i--; - } - - for ( ; i < length; i++ ) { - - // Only deal with non-null/undefined values - if ( ( options = arguments[ i ] ) != null ) { - - // Extend the base object - for ( name in options ) { - copy = options[ name ]; - - // Prevent Object.prototype pollution - // Prevent never-ending loop - if ( name === "__proto__" || target === copy ) { - continue; - } - - // Recurse if we're merging plain objects or arrays - if ( deep && copy && ( jQuery.isPlainObject( copy ) || - ( copyIsArray = Array.isArray( copy ) ) ) ) { - src = target[ name ]; - - // Ensure proper type for the source value - if ( copyIsArray && !Array.isArray( src ) ) { - clone = []; - } else if ( !copyIsArray && !jQuery.isPlainObject( src ) ) { - clone = {}; - } else { - clone = src; - } - copyIsArray = false; - - // Never move original objects, clone them - target[ name ] = jQuery.extend( deep, clone, copy ); - - // Don't bring in undefined values - } else if ( copy !== undefined ) { - target[ name ] = copy; - } - } - } - } - - // Return the modified object - return target; -}; - -jQuery.extend( { - - // Unique for each copy of jQuery on the page - expando: "jQuery" + ( version + Math.random() ).replace( /\D/g, "" ), - - // Assume jQuery is ready without the ready module - isReady: true, - - error: function( msg ) { - throw new Error( msg ); - }, - - noop: function() {}, - - isPlainObject: function( obj ) { - var proto, Ctor; - - // Detect obvious negatives - // Use toString instead of jQuery.type to catch host objects - if ( !obj || toString.call( obj ) !== "[object Object]" ) { - return false; - } - - proto = getProto( obj ); - - // Objects with no prototype (e.g., `Object.create( null )`) are plain - if ( !proto ) { - return true; - } - - // Objects with prototype are plain iff they were constructed by a global Object function - Ctor = hasOwn.call( proto, "constructor" ) && proto.constructor; - return typeof Ctor === "function" && fnToString.call( Ctor ) === ObjectFunctionString; - }, - - isEmptyObject: function( obj ) { - var name; - - for ( name in obj ) { - return false; - } - return true; - }, - - // Evaluates a script in a provided context; falls back to the global one - // if not specified. - globalEval: function( code, options, doc ) { - DOMEval( code, { nonce: options && options.nonce }, doc ); - }, - - each: function( obj, callback ) { - var length, i = 0; - - if ( isArrayLike( obj ) ) { - length = obj.length; - for ( ; i < length; i++ ) { - if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) { - break; - } - } - } else { - for ( i in obj ) { - if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) { - break; - } - } - } - - return obj; - }, - - // results is for internal usage only - makeArray: function( arr, results ) { - var ret = results || []; - - if ( arr != null ) { - if ( isArrayLike( Object( arr ) ) ) { - jQuery.merge( ret, - typeof arr === "string" ? - [ arr ] : arr - ); - } else { - push.call( ret, arr ); - } - } - - return ret; - }, - - inArray: function( elem, arr, i ) { - return arr == null ? -1 : indexOf.call( arr, elem, i ); - }, - - // Support: Android <=4.0 only, PhantomJS 1 only - // push.apply(_, arraylike) throws on ancient WebKit - merge: function( first, second ) { - var len = +second.length, - j = 0, - i = first.length; - - for ( ; j < len; j++ ) { - first[ i++ ] = second[ j ]; - } - - first.length = i; - - return first; - }, - - grep: function( elems, callback, invert ) { - var callbackInverse, - matches = [], - i = 0, - length = elems.length, - callbackExpect = !invert; - - // Go through the array, only saving the items - // that pass the validator function - for ( ; i < length; i++ ) { - callbackInverse = !callback( elems[ i ], i ); - if ( callbackInverse !== callbackExpect ) { - matches.push( elems[ i ] ); - } - } - - return matches; - }, - - // arg is for internal usage only - map: function( elems, callback, arg ) { - var length, value, - i = 0, - ret = []; - - // Go through the array, translating each of the items to their new values - if ( isArrayLike( elems ) ) { - length = elems.length; - for ( ; i < length; i++ ) { - value = callback( elems[ i ], i, arg ); - - if ( value != null ) { - ret.push( value ); - } - } - - // Go through every key on the object, - } else { - for ( i in elems ) { - value = callback( elems[ i ], i, arg ); - - if ( value != null ) { - ret.push( value ); - } - } - } - - // Flatten any nested arrays - return flat( ret ); - }, - - // A global GUID counter for objects - guid: 1, - - // jQuery.support is not used in Core but other projects attach their - // properties to it so it needs to exist. - support: support -} ); - -if ( typeof Symbol === "function" ) { - jQuery.fn[ Symbol.iterator ] = arr[ Symbol.iterator ]; -} - -// Populate the class2type map -jQuery.each( "Boolean Number String Function Array Date RegExp Object Error Symbol".split( " " ), -function( _i, name ) { - class2type[ "[object " + name + "]" ] = name.toLowerCase(); -} ); - -function isArrayLike( obj ) { - - // Support: real iOS 8.2 only (not reproducible in simulator) - // `in` check used to prevent JIT error (gh-2145) - // hasOwn isn't used here due to false negatives - // regarding Nodelist length in IE - var length = !!obj && "length" in obj && obj.length, - type = toType( obj ); - - if ( isFunction( obj ) || isWindow( obj ) ) { - return false; - } - - return type === "array" || length === 0 || - typeof length === "number" && length > 0 && ( length - 1 ) in obj; -} -var Sizzle = -/*! - * Sizzle CSS Selector Engine v2.3.5 - * https://sizzlejs.com/ - * - * Copyright JS Foundation and other contributors - * Released under the MIT license - * https://js.foundation/ - * - * Date: 2020-03-14 - */ -( function( window ) { -var i, - support, - Expr, - getText, - isXML, - tokenize, - compile, - select, - outermostContext, - sortInput, - hasDuplicate, - - // Local document vars - setDocument, - document, - docElem, - documentIsHTML, - rbuggyQSA, - rbuggyMatches, - matches, - contains, - - // Instance-specific data - expando = "sizzle" + 1 * new Date(), - preferredDoc = window.document, - dirruns = 0, - done = 0, - classCache = createCache(), - tokenCache = createCache(), - compilerCache = createCache(), - nonnativeSelectorCache = createCache(), - sortOrder = function( a, b ) { - if ( a === b ) { - hasDuplicate = true; - } - return 0; - }, - - // Instance methods - hasOwn = ( {} ).hasOwnProperty, - arr = [], - pop = arr.pop, - pushNative = arr.push, - push = arr.push, - slice = arr.slice, - - // Use a stripped-down indexOf as it's faster than native - // https://jsperf.com/thor-indexof-vs-for/5 - indexOf = function( list, elem ) { - var i = 0, - len = list.length; - for ( ; i < len; i++ ) { - if ( list[ i ] === elem ) { - return i; - } - } - return -1; - }, - - booleans = "checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|" + - "ismap|loop|multiple|open|readonly|required|scoped", - - // Regular expressions - - // http://www.w3.org/TR/css3-selectors/#whitespace - whitespace = "[\\x20\\t\\r\\n\\f]", - - // https://www.w3.org/TR/css-syntax-3/#ident-token-diagram - identifier = "(?:\\\\[\\da-fA-F]{1,6}" + whitespace + - "?|\\\\[^\\r\\n\\f]|[\\w-]|[^\0-\\x7f])+", - - // Attribute selectors: http://www.w3.org/TR/selectors/#attribute-selectors - attributes = "\\[" + whitespace + "*(" + identifier + ")(?:" + whitespace + - - // Operator (capture 2) - "*([*^$|!~]?=)" + whitespace + - - // "Attribute values must be CSS identifiers [capture 5] - // or strings [capture 3 or capture 4]" - "*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|(" + identifier + "))|)" + - whitespace + "*\\]", - - pseudos = ":(" + identifier + ")(?:\\((" + - - // To reduce the number of selectors needing tokenize in the preFilter, prefer arguments: - // 1. quoted (capture 3; capture 4 or capture 5) - "('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|" + - - // 2. simple (capture 6) - "((?:\\\\.|[^\\\\()[\\]]|" + attributes + ")*)|" + - - // 3. anything else (capture 2) - ".*" + - ")\\)|)", - - // Leading and non-escaped trailing whitespace, capturing some non-whitespace characters preceding the latter - rwhitespace = new RegExp( whitespace + "+", "g" ), - rtrim = new RegExp( "^" + whitespace + "+|((?:^|[^\\\\])(?:\\\\.)*)" + - whitespace + "+$", "g" ), - - rcomma = new RegExp( "^" + whitespace + "*," + whitespace + "*" ), - rcombinators = new RegExp( "^" + whitespace + "*([>+~]|" + whitespace + ")" + whitespace + - "*" ), - rdescend = new RegExp( whitespace + "|>" ), - - rpseudo = new RegExp( pseudos ), - ridentifier = new RegExp( "^" + identifier + "$" ), - - matchExpr = { - "ID": new RegExp( "^#(" + identifier + ")" ), - "CLASS": new RegExp( "^\\.(" + identifier + ")" ), - "TAG": new RegExp( "^(" + identifier + "|[*])" ), - "ATTR": new RegExp( "^" + attributes ), - "PSEUDO": new RegExp( "^" + pseudos ), - "CHILD": new RegExp( "^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\(" + - whitespace + "*(even|odd|(([+-]|)(\\d*)n|)" + whitespace + "*(?:([+-]|)" + - whitespace + "*(\\d+)|))" + whitespace + "*\\)|)", "i" ), - "bool": new RegExp( "^(?:" + booleans + ")$", "i" ), - - // For use in libraries implementing .is() - // We use this for POS matching in `select` - "needsContext": new RegExp( "^" + whitespace + - "*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\(" + whitespace + - "*((?:-\\d)?\\d*)" + whitespace + "*\\)|)(?=[^-]|$)", "i" ) - }, - - rhtml = /HTML$/i, - rinputs = /^(?:input|select|textarea|button)$/i, - rheader = /^h\d$/i, - - rnative = /^[^{]+\{\s*\[native \w/, - - // Easily-parseable/retrievable ID or TAG or CLASS selectors - rquickExpr = /^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/, - - rsibling = /[+~]/, - - // CSS escapes - // http://www.w3.org/TR/CSS21/syndata.html#escaped-characters - runescape = new RegExp( "\\\\[\\da-fA-F]{1,6}" + whitespace + "?|\\\\([^\\r\\n\\f])", "g" ), - funescape = function( escape, nonHex ) { - var high = "0x" + escape.slice( 1 ) - 0x10000; - - return nonHex ? - - // Strip the backslash prefix from a non-hex escape sequence - nonHex : - - // Replace a hexadecimal escape sequence with the encoded Unicode code point - // Support: IE <=11+ - // For values outside the Basic Multilingual Plane (BMP), manually construct a - // surrogate pair - high < 0 ? - String.fromCharCode( high + 0x10000 ) : - String.fromCharCode( high >> 10 | 0xD800, high & 0x3FF | 0xDC00 ); - }, - - // CSS string/identifier serialization - // https://drafts.csswg.org/cssom/#common-serializing-idioms - rcssescape = /([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g, - fcssescape = function( ch, asCodePoint ) { - if ( asCodePoint ) { - - // U+0000 NULL becomes U+FFFD REPLACEMENT CHARACTER - if ( ch === "\0" ) { - return "\uFFFD"; - } - - // Control characters and (dependent upon position) numbers get escaped as code points - return ch.slice( 0, -1 ) + "\\" + - ch.charCodeAt( ch.length - 1 ).toString( 16 ) + " "; - } - - // Other potentially-special ASCII characters get backslash-escaped - return "\\" + ch; - }, - - // Used for iframes - // See setDocument() - // Removing the function wrapper causes a "Permission Denied" - // error in IE - unloadHandler = function() { - setDocument(); - }, - - inDisabledFieldset = addCombinator( - function( elem ) { - return elem.disabled === true && elem.nodeName.toLowerCase() === "fieldset"; - }, - { dir: "parentNode", next: "legend" } - ); - -// Optimize for push.apply( _, NodeList ) -try { - push.apply( - ( arr = slice.call( preferredDoc.childNodes ) ), - preferredDoc.childNodes - ); - - // Support: Android<4.0 - // Detect silently failing push.apply - // eslint-disable-next-line no-unused-expressions - arr[ preferredDoc.childNodes.length ].nodeType; -} catch ( e ) { - push = { apply: arr.length ? - - // Leverage slice if possible - function( target, els ) { - pushNative.apply( target, slice.call( els ) ); - } : - - // Support: IE<9 - // Otherwise append directly - function( target, els ) { - var j = target.length, - i = 0; - - // Can't trust NodeList.length - while ( ( target[ j++ ] = els[ i++ ] ) ) {} - target.length = j - 1; - } - }; -} - -function Sizzle( selector, context, results, seed ) { - var m, i, elem, nid, match, groups, newSelector, - newContext = context && context.ownerDocument, - - // nodeType defaults to 9, since context defaults to document - nodeType = context ? context.nodeType : 9; - - results = results || []; - - // Return early from calls with invalid selector or context - if ( typeof selector !== "string" || !selector || - nodeType !== 1 && nodeType !== 9 && nodeType !== 11 ) { - - return results; - } - - // Try to shortcut find operations (as opposed to filters) in HTML documents - if ( !seed ) { - setDocument( context ); - context = context || document; - - if ( documentIsHTML ) { - - // If the selector is sufficiently simple, try using a "get*By*" DOM method - // (excepting DocumentFragment context, where the methods don't exist) - if ( nodeType !== 11 && ( match = rquickExpr.exec( selector ) ) ) { - - // ID selector - if ( ( m = match[ 1 ] ) ) { - - // Document context - if ( nodeType === 9 ) { - if ( ( elem = context.getElementById( m ) ) ) { - - // Support: IE, Opera, Webkit - // TODO: identify versions - // getElementById can match elements by name instead of ID - if ( elem.id === m ) { - results.push( elem ); - return results; - } - } else { - return results; - } - - // Element context - } else { - - // Support: IE, Opera, Webkit - // TODO: identify versions - // getElementById can match elements by name instead of ID - if ( newContext && ( elem = newContext.getElementById( m ) ) && - contains( context, elem ) && - elem.id === m ) { - - results.push( elem ); - return results; - } - } - - // Type selector - } else if ( match[ 2 ] ) { - push.apply( results, context.getElementsByTagName( selector ) ); - return results; - - // Class selector - } else if ( ( m = match[ 3 ] ) && support.getElementsByClassName && - context.getElementsByClassName ) { - - push.apply( results, context.getElementsByClassName( m ) ); - return results; - } - } - - // Take advantage of querySelectorAll - if ( support.qsa && - !nonnativeSelectorCache[ selector + " " ] && - ( !rbuggyQSA || !rbuggyQSA.test( selector ) ) && - - // Support: IE 8 only - // Exclude object elements - ( nodeType !== 1 || context.nodeName.toLowerCase() !== "object" ) ) { - - newSelector = selector; - newContext = context; - - // qSA considers elements outside a scoping root when evaluating child or - // descendant combinators, which is not what we want. - // In such cases, we work around the behavior by prefixing every selector in the - // list with an ID selector referencing the scope context. - // The technique has to be used as well when a leading combinator is used - // as such selectors are not recognized by querySelectorAll. - // Thanks to Andrew Dupont for this technique. - if ( nodeType === 1 && - ( rdescend.test( selector ) || rcombinators.test( selector ) ) ) { - - // Expand context for sibling selectors - newContext = rsibling.test( selector ) && testContext( context.parentNode ) || - context; - - // We can use :scope instead of the ID hack if the browser - // supports it & if we're not changing the context. - if ( newContext !== context || !support.scope ) { - - // Capture the context ID, setting it first if necessary - if ( ( nid = context.getAttribute( "id" ) ) ) { - nid = nid.replace( rcssescape, fcssescape ); - } else { - context.setAttribute( "id", ( nid = expando ) ); - } - } - - // Prefix every selector in the list - groups = tokenize( selector ); - i = groups.length; - while ( i-- ) { - groups[ i ] = ( nid ? "#" + nid : ":scope" ) + " " + - toSelector( groups[ i ] ); - } - newSelector = groups.join( "," ); - } - - try { - push.apply( results, - newContext.querySelectorAll( newSelector ) - ); - return results; - } catch ( qsaError ) { - nonnativeSelectorCache( selector, true ); - } finally { - if ( nid === expando ) { - context.removeAttribute( "id" ); - } - } - } - } - } - - // All others - return select( selector.replace( rtrim, "$1" ), context, results, seed ); -} - -/** - * Create key-value caches of limited size - * @returns {function(string, object)} Returns the Object data after storing it on itself with - * property name the (space-suffixed) string and (if the cache is larger than Expr.cacheLength) - * deleting the oldest entry - */ -function createCache() { - var keys = []; - - function cache( key, value ) { - - // Use (key + " ") to avoid collision with native prototype properties (see Issue #157) - if ( keys.push( key + " " ) > Expr.cacheLength ) { - - // Only keep the most recent entries - delete cache[ keys.shift() ]; - } - return ( cache[ key + " " ] = value ); - } - return cache; -} - -/** - * Mark a function for special use by Sizzle - * @param {Function} fn The function to mark - */ -function markFunction( fn ) { - fn[ expando ] = true; - return fn; -} - -/** - * Support testing using an element - * @param {Function} fn Passed the created element and returns a boolean result - */ -function assert( fn ) { - var el = document.createElement( "fieldset" ); - - try { - return !!fn( el ); - } catch ( e ) { - return false; - } finally { - - // Remove from its parent by default - if ( el.parentNode ) { - el.parentNode.removeChild( el ); - } - - // release memory in IE - el = null; - } -} - -/** - * Adds the same handler for all of the specified attrs - * @param {String} attrs Pipe-separated list of attributes - * @param {Function} handler The method that will be applied - */ -function addHandle( attrs, handler ) { - var arr = attrs.split( "|" ), - i = arr.length; - - while ( i-- ) { - Expr.attrHandle[ arr[ i ] ] = handler; - } -} - -/** - * Checks document order of two siblings - * @param {Element} a - * @param {Element} b - * @returns {Number} Returns less than 0 if a precedes b, greater than 0 if a follows b - */ -function siblingCheck( a, b ) { - var cur = b && a, - diff = cur && a.nodeType === 1 && b.nodeType === 1 && - a.sourceIndex - b.sourceIndex; - - // Use IE sourceIndex if available on both nodes - if ( diff ) { - return diff; - } - - // Check if b follows a - if ( cur ) { - while ( ( cur = cur.nextSibling ) ) { - if ( cur === b ) { - return -1; - } - } - } - - return a ? 1 : -1; -} - -/** - * Returns a function to use in pseudos for input types - * @param {String} type - */ -function createInputPseudo( type ) { - return function( elem ) { - var name = elem.nodeName.toLowerCase(); - return name === "input" && elem.type === type; - }; -} - -/** - * Returns a function to use in pseudos for buttons - * @param {String} type - */ -function createButtonPseudo( type ) { - return function( elem ) { - var name = elem.nodeName.toLowerCase(); - return ( name === "input" || name === "button" ) && elem.type === type; - }; -} - -/** - * Returns a function to use in pseudos for :enabled/:disabled - * @param {Boolean} disabled true for :disabled; false for :enabled - */ -function createDisabledPseudo( disabled ) { - - // Known :disabled false positives: fieldset[disabled] > legend:nth-of-type(n+2) :can-disable - return function( elem ) { - - // Only certain elements can match :enabled or :disabled - // https://html.spec.whatwg.org/multipage/scripting.html#selector-enabled - // https://html.spec.whatwg.org/multipage/scripting.html#selector-disabled - if ( "form" in elem ) { - - // Check for inherited disabledness on relevant non-disabled elements: - // * listed form-associated elements in a disabled fieldset - // https://html.spec.whatwg.org/multipage/forms.html#category-listed - // https://html.spec.whatwg.org/multipage/forms.html#concept-fe-disabled - // * option elements in a disabled optgroup - // https://html.spec.whatwg.org/multipage/forms.html#concept-option-disabled - // All such elements have a "form" property. - if ( elem.parentNode && elem.disabled === false ) { - - // Option elements defer to a parent optgroup if present - if ( "label" in elem ) { - if ( "label" in elem.parentNode ) { - return elem.parentNode.disabled === disabled; - } else { - return elem.disabled === disabled; - } - } - - // Support: IE 6 - 11 - // Use the isDisabled shortcut property to check for disabled fieldset ancestors - return elem.isDisabled === disabled || - - // Where there is no isDisabled, check manually - /* jshint -W018 */ - elem.isDisabled !== !disabled && - inDisabledFieldset( elem ) === disabled; - } - - return elem.disabled === disabled; - - // Try to winnow out elements that can't be disabled before trusting the disabled property. - // Some victims get caught in our net (label, legend, menu, track), but it shouldn't - // even exist on them, let alone have a boolean value. - } else if ( "label" in elem ) { - return elem.disabled === disabled; - } - - // Remaining elements are neither :enabled nor :disabled - return false; - }; -} - -/** - * Returns a function to use in pseudos for positionals - * @param {Function} fn - */ -function createPositionalPseudo( fn ) { - return markFunction( function( argument ) { - argument = +argument; - return markFunction( function( seed, matches ) { - var j, - matchIndexes = fn( [], seed.length, argument ), - i = matchIndexes.length; - - // Match elements found at the specified indexes - while ( i-- ) { - if ( seed[ ( j = matchIndexes[ i ] ) ] ) { - seed[ j ] = !( matches[ j ] = seed[ j ] ); - } - } - } ); - } ); -} - -/** - * Checks a node for validity as a Sizzle context - * @param {Element|Object=} context - * @returns {Element|Object|Boolean} The input node if acceptable, otherwise a falsy value - */ -function testContext( context ) { - return context && typeof context.getElementsByTagName !== "undefined" && context; -} - -// Expose support vars for convenience -support = Sizzle.support = {}; - -/** - * Detects XML nodes - * @param {Element|Object} elem An element or a document - * @returns {Boolean} True iff elem is a non-HTML XML node - */ -isXML = Sizzle.isXML = function( elem ) { - var namespace = elem.namespaceURI, - docElem = ( elem.ownerDocument || elem ).documentElement; - - // Support: IE <=8 - // Assume HTML when documentElement doesn't yet exist, such as inside loading iframes - // https://bugs.jquery.com/ticket/4833 - return !rhtml.test( namespace || docElem && docElem.nodeName || "HTML" ); -}; - -/** - * Sets document-related variables once based on the current document - * @param {Element|Object} [doc] An element or document object to use to set the document - * @returns {Object} Returns the current document - */ -setDocument = Sizzle.setDocument = function( node ) { - var hasCompare, subWindow, - doc = node ? node.ownerDocument || node : preferredDoc; - - // Return early if doc is invalid or already selected - // Support: IE 11+, Edge 17 - 18+ - // IE/Edge sometimes throw a "Permission denied" error when strict-comparing - // two documents; shallow comparisons work. - // eslint-disable-next-line eqeqeq - if ( doc == document || doc.nodeType !== 9 || !doc.documentElement ) { - return document; - } - - // Update global variables - document = doc; - docElem = document.documentElement; - documentIsHTML = !isXML( document ); - - // Support: IE 9 - 11+, Edge 12 - 18+ - // Accessing iframe documents after unload throws "permission denied" errors (jQuery #13936) - // Support: IE 11+, Edge 17 - 18+ - // IE/Edge sometimes throw a "Permission denied" error when strict-comparing - // two documents; shallow comparisons work. - // eslint-disable-next-line eqeqeq - if ( preferredDoc != document && - ( subWindow = document.defaultView ) && subWindow.top !== subWindow ) { - - // Support: IE 11, Edge - if ( subWindow.addEventListener ) { - subWindow.addEventListener( "unload", unloadHandler, false ); - - // Support: IE 9 - 10 only - } else if ( subWindow.attachEvent ) { - subWindow.attachEvent( "onunload", unloadHandler ); - } - } - - // Support: IE 8 - 11+, Edge 12 - 18+, Chrome <=16 - 25 only, Firefox <=3.6 - 31 only, - // Safari 4 - 5 only, Opera <=11.6 - 12.x only - // IE/Edge & older browsers don't support the :scope pseudo-class. - // Support: Safari 6.0 only - // Safari 6.0 supports :scope but it's an alias of :root there. - support.scope = assert( function( el ) { - docElem.appendChild( el ).appendChild( document.createElement( "div" ) ); - return typeof el.querySelectorAll !== "undefined" && - !el.querySelectorAll( ":scope fieldset div" ).length; - } ); - - /* Attributes - ---------------------------------------------------------------------- */ - - // Support: IE<8 - // Verify that getAttribute really returns attributes and not properties - // (excepting IE8 booleans) - support.attributes = assert( function( el ) { - el.className = "i"; - return !el.getAttribute( "className" ); - } ); - - /* getElement(s)By* - ---------------------------------------------------------------------- */ - - // Check if getElementsByTagName("*") returns only elements - support.getElementsByTagName = assert( function( el ) { - el.appendChild( document.createComment( "" ) ); - return !el.getElementsByTagName( "*" ).length; - } ); - - // Support: IE<9 - support.getElementsByClassName = rnative.test( document.getElementsByClassName ); - - // Support: IE<10 - // Check if getElementById returns elements by name - // The broken getElementById methods don't pick up programmatically-set names, - // so use a roundabout getElementsByName test - support.getById = assert( function( el ) { - docElem.appendChild( el ).id = expando; - return !document.getElementsByName || !document.getElementsByName( expando ).length; - } ); - - // ID filter and find - if ( support.getById ) { - Expr.filter[ "ID" ] = function( id ) { - var attrId = id.replace( runescape, funescape ); - return function( elem ) { - return elem.getAttribute( "id" ) === attrId; - }; - }; - Expr.find[ "ID" ] = function( id, context ) { - if ( typeof context.getElementById !== "undefined" && documentIsHTML ) { - var elem = context.getElementById( id ); - return elem ? [ elem ] : []; - } - }; - } else { - Expr.filter[ "ID" ] = function( id ) { - var attrId = id.replace( runescape, funescape ); - return function( elem ) { - var node = typeof elem.getAttributeNode !== "undefined" && - elem.getAttributeNode( "id" ); - return node && node.value === attrId; - }; - }; - - // Support: IE 6 - 7 only - // getElementById is not reliable as a find shortcut - Expr.find[ "ID" ] = function( id, context ) { - if ( typeof context.getElementById !== "undefined" && documentIsHTML ) { - var node, i, elems, - elem = context.getElementById( id ); - - if ( elem ) { - - // Verify the id attribute - node = elem.getAttributeNode( "id" ); - if ( node && node.value === id ) { - return [ elem ]; - } - - // Fall back on getElementsByName - elems = context.getElementsByName( id ); - i = 0; - while ( ( elem = elems[ i++ ] ) ) { - node = elem.getAttributeNode( "id" ); - if ( node && node.value === id ) { - return [ elem ]; - } - } - } - - return []; - } - }; - } - - // Tag - Expr.find[ "TAG" ] = support.getElementsByTagName ? - function( tag, context ) { - if ( typeof context.getElementsByTagName !== "undefined" ) { - return context.getElementsByTagName( tag ); - - // DocumentFragment nodes don't have gEBTN - } else if ( support.qsa ) { - return context.querySelectorAll( tag ); - } - } : - - function( tag, context ) { - var elem, - tmp = [], - i = 0, - - // By happy coincidence, a (broken) gEBTN appears on DocumentFragment nodes too - results = context.getElementsByTagName( tag ); - - // Filter out possible comments - if ( tag === "*" ) { - while ( ( elem = results[ i++ ] ) ) { - if ( elem.nodeType === 1 ) { - tmp.push( elem ); - } - } - - return tmp; - } - return results; - }; - - // Class - Expr.find[ "CLASS" ] = support.getElementsByClassName && function( className, context ) { - if ( typeof context.getElementsByClassName !== "undefined" && documentIsHTML ) { - return context.getElementsByClassName( className ); - } - }; - - /* QSA/matchesSelector - ---------------------------------------------------------------------- */ - - // QSA and matchesSelector support - - // matchesSelector(:active) reports false when true (IE9/Opera 11.5) - rbuggyMatches = []; - - // qSa(:focus) reports false when true (Chrome 21) - // We allow this because of a bug in IE8/9 that throws an error - // whenever `document.activeElement` is accessed on an iframe - // So, we allow :focus to pass through QSA all the time to avoid the IE error - // See https://bugs.jquery.com/ticket/13378 - rbuggyQSA = []; - - if ( ( support.qsa = rnative.test( document.querySelectorAll ) ) ) { - - // Build QSA regex - // Regex strategy adopted from Diego Perini - assert( function( el ) { - - var input; - - // Select is set to empty string on purpose - // This is to test IE's treatment of not explicitly - // setting a boolean content attribute, - // since its presence should be enough - // https://bugs.jquery.com/ticket/12359 - docElem.appendChild( el ).innerHTML = "" + - ""; - - // Support: IE8, Opera 11-12.16 - // Nothing should be selected when empty strings follow ^= or $= or *= - // The test attribute must be unknown in Opera but "safe" for WinRT - // https://msdn.microsoft.com/en-us/library/ie/hh465388.aspx#attribute_section - if ( el.querySelectorAll( "[msallowcapture^='']" ).length ) { - rbuggyQSA.push( "[*^$]=" + whitespace + "*(?:''|\"\")" ); - } - - // Support: IE8 - // Boolean attributes and "value" are not treated correctly - if ( !el.querySelectorAll( "[selected]" ).length ) { - rbuggyQSA.push( "\\[" + whitespace + "*(?:value|" + booleans + ")" ); - } - - // Support: Chrome<29, Android<4.4, Safari<7.0+, iOS<7.0+, PhantomJS<1.9.8+ - if ( !el.querySelectorAll( "[id~=" + expando + "-]" ).length ) { - rbuggyQSA.push( "~=" ); - } - - // Support: IE 11+, Edge 15 - 18+ - // IE 11/Edge don't find elements on a `[name='']` query in some cases. - // Adding a temporary attribute to the document before the selection works - // around the issue. - // Interestingly, IE 10 & older don't seem to have the issue. - input = document.createElement( "input" ); - input.setAttribute( "name", "" ); - el.appendChild( input ); - if ( !el.querySelectorAll( "[name='']" ).length ) { - rbuggyQSA.push( "\\[" + whitespace + "*name" + whitespace + "*=" + - whitespace + "*(?:''|\"\")" ); - } - - // Webkit/Opera - :checked should return selected option elements - // http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked - // IE8 throws error here and will not see later tests - if ( !el.querySelectorAll( ":checked" ).length ) { - rbuggyQSA.push( ":checked" ); - } - - // Support: Safari 8+, iOS 8+ - // https://bugs.webkit.org/show_bug.cgi?id=136851 - // In-page `selector#id sibling-combinator selector` fails - if ( !el.querySelectorAll( "a#" + expando + "+*" ).length ) { - rbuggyQSA.push( ".#.+[+~]" ); - } - - // Support: Firefox <=3.6 - 5 only - // Old Firefox doesn't throw on a badly-escaped identifier. - el.querySelectorAll( "\\\f" ); - rbuggyQSA.push( "[\\r\\n\\f]" ); - } ); - - assert( function( el ) { - el.innerHTML = "" + - ""; - - // Support: Windows 8 Native Apps - // The type and name attributes are restricted during .innerHTML assignment - var input = document.createElement( "input" ); - input.setAttribute( "type", "hidden" ); - el.appendChild( input ).setAttribute( "name", "D" ); - - // Support: IE8 - // Enforce case-sensitivity of name attribute - if ( el.querySelectorAll( "[name=d]" ).length ) { - rbuggyQSA.push( "name" + whitespace + "*[*^$|!~]?=" ); - } - - // FF 3.5 - :enabled/:disabled and hidden elements (hidden elements are still enabled) - // IE8 throws error here and will not see later tests - if ( el.querySelectorAll( ":enabled" ).length !== 2 ) { - rbuggyQSA.push( ":enabled", ":disabled" ); - } - - // Support: IE9-11+ - // IE's :disabled selector does not pick up the children of disabled fieldsets - docElem.appendChild( el ).disabled = true; - if ( el.querySelectorAll( ":disabled" ).length !== 2 ) { - rbuggyQSA.push( ":enabled", ":disabled" ); - } - - // Support: Opera 10 - 11 only - // Opera 10-11 does not throw on post-comma invalid pseudos - el.querySelectorAll( "*,:x" ); - rbuggyQSA.push( ",.*:" ); - } ); - } - - if ( ( support.matchesSelector = rnative.test( ( matches = docElem.matches || - docElem.webkitMatchesSelector || - docElem.mozMatchesSelector || - docElem.oMatchesSelector || - docElem.msMatchesSelector ) ) ) ) { - - assert( function( el ) { - - // Check to see if it's possible to do matchesSelector - // on a disconnected node (IE 9) - support.disconnectedMatch = matches.call( el, "*" ); - - // This should fail with an exception - // Gecko does not error, returns false instead - matches.call( el, "[s!='']:x" ); - rbuggyMatches.push( "!=", pseudos ); - } ); - } - - rbuggyQSA = rbuggyQSA.length && new RegExp( rbuggyQSA.join( "|" ) ); - rbuggyMatches = rbuggyMatches.length && new RegExp( rbuggyMatches.join( "|" ) ); - - /* Contains - ---------------------------------------------------------------------- */ - hasCompare = rnative.test( docElem.compareDocumentPosition ); - - // Element contains another - // Purposefully self-exclusive - // As in, an element does not contain itself - contains = hasCompare || rnative.test( docElem.contains ) ? - function( a, b ) { - var adown = a.nodeType === 9 ? a.documentElement : a, - bup = b && b.parentNode; - return a === bup || !!( bup && bup.nodeType === 1 && ( - adown.contains ? - adown.contains( bup ) : - a.compareDocumentPosition && a.compareDocumentPosition( bup ) & 16 - ) ); - } : - function( a, b ) { - if ( b ) { - while ( ( b = b.parentNode ) ) { - if ( b === a ) { - return true; - } - } - } - return false; - }; - - /* Sorting - ---------------------------------------------------------------------- */ - - // Document order sorting - sortOrder = hasCompare ? - function( a, b ) { - - // Flag for duplicate removal - if ( a === b ) { - hasDuplicate = true; - return 0; - } - - // Sort on method existence if only one input has compareDocumentPosition - var compare = !a.compareDocumentPosition - !b.compareDocumentPosition; - if ( compare ) { - return compare; - } - - // Calculate position if both inputs belong to the same document - // Support: IE 11+, Edge 17 - 18+ - // IE/Edge sometimes throw a "Permission denied" error when strict-comparing - // two documents; shallow comparisons work. - // eslint-disable-next-line eqeqeq - compare = ( a.ownerDocument || a ) == ( b.ownerDocument || b ) ? - a.compareDocumentPosition( b ) : - - // Otherwise we know they are disconnected - 1; - - // Disconnected nodes - if ( compare & 1 || - ( !support.sortDetached && b.compareDocumentPosition( a ) === compare ) ) { - - // Choose the first element that is related to our preferred document - // Support: IE 11+, Edge 17 - 18+ - // IE/Edge sometimes throw a "Permission denied" error when strict-comparing - // two documents; shallow comparisons work. - // eslint-disable-next-line eqeqeq - if ( a == document || a.ownerDocument == preferredDoc && - contains( preferredDoc, a ) ) { - return -1; - } - - // Support: IE 11+, Edge 17 - 18+ - // IE/Edge sometimes throw a "Permission denied" error when strict-comparing - // two documents; shallow comparisons work. - // eslint-disable-next-line eqeqeq - if ( b == document || b.ownerDocument == preferredDoc && - contains( preferredDoc, b ) ) { - return 1; - } - - // Maintain original order - return sortInput ? - ( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) : - 0; - } - - return compare & 4 ? -1 : 1; - } : - function( a, b ) { - - // Exit early if the nodes are identical - if ( a === b ) { - hasDuplicate = true; - return 0; - } - - var cur, - i = 0, - aup = a.parentNode, - bup = b.parentNode, - ap = [ a ], - bp = [ b ]; - - // Parentless nodes are either documents or disconnected - if ( !aup || !bup ) { - - // Support: IE 11+, Edge 17 - 18+ - // IE/Edge sometimes throw a "Permission denied" error when strict-comparing - // two documents; shallow comparisons work. - /* eslint-disable eqeqeq */ - return a == document ? -1 : - b == document ? 1 : - /* eslint-enable eqeqeq */ - aup ? -1 : - bup ? 1 : - sortInput ? - ( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) : - 0; - - // If the nodes are siblings, we can do a quick check - } else if ( aup === bup ) { - return siblingCheck( a, b ); - } - - // Otherwise we need full lists of their ancestors for comparison - cur = a; - while ( ( cur = cur.parentNode ) ) { - ap.unshift( cur ); - } - cur = b; - while ( ( cur = cur.parentNode ) ) { - bp.unshift( cur ); - } - - // Walk down the tree looking for a discrepancy - while ( ap[ i ] === bp[ i ] ) { - i++; - } - - return i ? - - // Do a sibling check if the nodes have a common ancestor - siblingCheck( ap[ i ], bp[ i ] ) : - - // Otherwise nodes in our document sort first - // Support: IE 11+, Edge 17 - 18+ - // IE/Edge sometimes throw a "Permission denied" error when strict-comparing - // two documents; shallow comparisons work. - /* eslint-disable eqeqeq */ - ap[ i ] == preferredDoc ? -1 : - bp[ i ] == preferredDoc ? 1 : - /* eslint-enable eqeqeq */ - 0; - }; - - return document; -}; - -Sizzle.matches = function( expr, elements ) { - return Sizzle( expr, null, null, elements ); -}; - -Sizzle.matchesSelector = function( elem, expr ) { - setDocument( elem ); - - if ( support.matchesSelector && documentIsHTML && - !nonnativeSelectorCache[ expr + " " ] && - ( !rbuggyMatches || !rbuggyMatches.test( expr ) ) && - ( !rbuggyQSA || !rbuggyQSA.test( expr ) ) ) { - - try { - var ret = matches.call( elem, expr ); - - // IE 9's matchesSelector returns false on disconnected nodes - if ( ret || support.disconnectedMatch || - - // As well, disconnected nodes are said to be in a document - // fragment in IE 9 - elem.document && elem.document.nodeType !== 11 ) { - return ret; - } - } catch ( e ) { - nonnativeSelectorCache( expr, true ); - } - } - - return Sizzle( expr, document, null, [ elem ] ).length > 0; -}; - -Sizzle.contains = function( context, elem ) { - - // Set document vars if needed - // Support: IE 11+, Edge 17 - 18+ - // IE/Edge sometimes throw a "Permission denied" error when strict-comparing - // two documents; shallow comparisons work. - // eslint-disable-next-line eqeqeq - if ( ( context.ownerDocument || context ) != document ) { - setDocument( context ); - } - return contains( context, elem ); -}; - -Sizzle.attr = function( elem, name ) { - - // Set document vars if needed - // Support: IE 11+, Edge 17 - 18+ - // IE/Edge sometimes throw a "Permission denied" error when strict-comparing - // two documents; shallow comparisons work. - // eslint-disable-next-line eqeqeq - if ( ( elem.ownerDocument || elem ) != document ) { - setDocument( elem ); - } - - var fn = Expr.attrHandle[ name.toLowerCase() ], - - // Don't get fooled by Object.prototype properties (jQuery #13807) - val = fn && hasOwn.call( Expr.attrHandle, name.toLowerCase() ) ? - fn( elem, name, !documentIsHTML ) : - undefined; - - return val !== undefined ? - val : - support.attributes || !documentIsHTML ? - elem.getAttribute( name ) : - ( val = elem.getAttributeNode( name ) ) && val.specified ? - val.value : - null; -}; - -Sizzle.escape = function( sel ) { - return ( sel + "" ).replace( rcssescape, fcssescape ); -}; - -Sizzle.error = function( msg ) { - throw new Error( "Syntax error, unrecognized expression: " + msg ); -}; - -/** - * Document sorting and removing duplicates - * @param {ArrayLike} results - */ -Sizzle.uniqueSort = function( results ) { - var elem, - duplicates = [], - j = 0, - i = 0; - - // Unless we *know* we can detect duplicates, assume their presence - hasDuplicate = !support.detectDuplicates; - sortInput = !support.sortStable && results.slice( 0 ); - results.sort( sortOrder ); - - if ( hasDuplicate ) { - while ( ( elem = results[ i++ ] ) ) { - if ( elem === results[ i ] ) { - j = duplicates.push( i ); - } - } - while ( j-- ) { - results.splice( duplicates[ j ], 1 ); - } - } - - // Clear input after sorting to release objects - // See https://github.com/jquery/sizzle/pull/225 - sortInput = null; - - return results; -}; - -/** - * Utility function for retrieving the text value of an array of DOM nodes - * @param {Array|Element} elem - */ -getText = Sizzle.getText = function( elem ) { - var node, - ret = "", - i = 0, - nodeType = elem.nodeType; - - if ( !nodeType ) { - - // If no nodeType, this is expected to be an array - while ( ( node = elem[ i++ ] ) ) { - - // Do not traverse comment nodes - ret += getText( node ); - } - } else if ( nodeType === 1 || nodeType === 9 || nodeType === 11 ) { - - // Use textContent for elements - // innerText usage removed for consistency of new lines (jQuery #11153) - if ( typeof elem.textContent === "string" ) { - return elem.textContent; - } else { - - // Traverse its children - for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) { - ret += getText( elem ); - } - } - } else if ( nodeType === 3 || nodeType === 4 ) { - return elem.nodeValue; - } - - // Do not include comment or processing instruction nodes - - return ret; -}; - -Expr = Sizzle.selectors = { - - // Can be adjusted by the user - cacheLength: 50, - - createPseudo: markFunction, - - match: matchExpr, - - attrHandle: {}, - - find: {}, - - relative: { - ">": { dir: "parentNode", first: true }, - " ": { dir: "parentNode" }, - "+": { dir: "previousSibling", first: true }, - "~": { dir: "previousSibling" } - }, - - preFilter: { - "ATTR": function( match ) { - match[ 1 ] = match[ 1 ].replace( runescape, funescape ); - - // Move the given value to match[3] whether quoted or unquoted - match[ 3 ] = ( match[ 3 ] || match[ 4 ] || - match[ 5 ] || "" ).replace( runescape, funescape ); - - if ( match[ 2 ] === "~=" ) { - match[ 3 ] = " " + match[ 3 ] + " "; - } - - return match.slice( 0, 4 ); - }, - - "CHILD": function( match ) { - - /* matches from matchExpr["CHILD"] - 1 type (only|nth|...) - 2 what (child|of-type) - 3 argument (even|odd|\d*|\d*n([+-]\d+)?|...) - 4 xn-component of xn+y argument ([+-]?\d*n|) - 5 sign of xn-component - 6 x of xn-component - 7 sign of y-component - 8 y of y-component - */ - match[ 1 ] = match[ 1 ].toLowerCase(); - - if ( match[ 1 ].slice( 0, 3 ) === "nth" ) { - - // nth-* requires argument - if ( !match[ 3 ] ) { - Sizzle.error( match[ 0 ] ); - } - - // numeric x and y parameters for Expr.filter.CHILD - // remember that false/true cast respectively to 0/1 - match[ 4 ] = +( match[ 4 ] ? - match[ 5 ] + ( match[ 6 ] || 1 ) : - 2 * ( match[ 3 ] === "even" || match[ 3 ] === "odd" ) ); - match[ 5 ] = +( ( match[ 7 ] + match[ 8 ] ) || match[ 3 ] === "odd" ); - - // other types prohibit arguments - } else if ( match[ 3 ] ) { - Sizzle.error( match[ 0 ] ); - } - - return match; - }, - - "PSEUDO": function( match ) { - var excess, - unquoted = !match[ 6 ] && match[ 2 ]; - - if ( matchExpr[ "CHILD" ].test( match[ 0 ] ) ) { - return null; - } - - // Accept quoted arguments as-is - if ( match[ 3 ] ) { - match[ 2 ] = match[ 4 ] || match[ 5 ] || ""; - - // Strip excess characters from unquoted arguments - } else if ( unquoted && rpseudo.test( unquoted ) && - - // Get excess from tokenize (recursively) - ( excess = tokenize( unquoted, true ) ) && - - // advance to the next closing parenthesis - ( excess = unquoted.indexOf( ")", unquoted.length - excess ) - unquoted.length ) ) { - - // excess is a negative index - match[ 0 ] = match[ 0 ].slice( 0, excess ); - match[ 2 ] = unquoted.slice( 0, excess ); - } - - // Return only captures needed by the pseudo filter method (type and argument) - return match.slice( 0, 3 ); - } - }, - - filter: { - - "TAG": function( nodeNameSelector ) { - var nodeName = nodeNameSelector.replace( runescape, funescape ).toLowerCase(); - return nodeNameSelector === "*" ? - function() { - return true; - } : - function( elem ) { - return elem.nodeName && elem.nodeName.toLowerCase() === nodeName; - }; - }, - - "CLASS": function( className ) { - var pattern = classCache[ className + " " ]; - - return pattern || - ( pattern = new RegExp( "(^|" + whitespace + - ")" + className + "(" + whitespace + "|$)" ) ) && classCache( - className, function( elem ) { - return pattern.test( - typeof elem.className === "string" && elem.className || - typeof elem.getAttribute !== "undefined" && - elem.getAttribute( "class" ) || - "" - ); - } ); - }, - - "ATTR": function( name, operator, check ) { - return function( elem ) { - var result = Sizzle.attr( elem, name ); - - if ( result == null ) { - return operator === "!="; - } - if ( !operator ) { - return true; - } - - result += ""; - - /* eslint-disable max-len */ - - return operator === "=" ? result === check : - operator === "!=" ? result !== check : - operator === "^=" ? check && result.indexOf( check ) === 0 : - operator === "*=" ? check && result.indexOf( check ) > -1 : - operator === "$=" ? check && result.slice( -check.length ) === check : - operator === "~=" ? ( " " + result.replace( rwhitespace, " " ) + " " ).indexOf( check ) > -1 : - operator === "|=" ? result === check || result.slice( 0, check.length + 1 ) === check + "-" : - false; - /* eslint-enable max-len */ - - }; - }, - - "CHILD": function( type, what, _argument, first, last ) { - var simple = type.slice( 0, 3 ) !== "nth", - forward = type.slice( -4 ) !== "last", - ofType = what === "of-type"; - - return first === 1 && last === 0 ? - - // Shortcut for :nth-*(n) - function( elem ) { - return !!elem.parentNode; - } : - - function( elem, _context, xml ) { - var cache, uniqueCache, outerCache, node, nodeIndex, start, - dir = simple !== forward ? "nextSibling" : "previousSibling", - parent = elem.parentNode, - name = ofType && elem.nodeName.toLowerCase(), - useCache = !xml && !ofType, - diff = false; - - if ( parent ) { - - // :(first|last|only)-(child|of-type) - if ( simple ) { - while ( dir ) { - node = elem; - while ( ( node = node[ dir ] ) ) { - if ( ofType ? - node.nodeName.toLowerCase() === name : - node.nodeType === 1 ) { - - return false; - } - } - - // Reverse direction for :only-* (if we haven't yet done so) - start = dir = type === "only" && !start && "nextSibling"; - } - return true; - } - - start = [ forward ? parent.firstChild : parent.lastChild ]; - - // non-xml :nth-child(...) stores cache data on `parent` - if ( forward && useCache ) { - - // Seek `elem` from a previously-cached index - - // ...in a gzip-friendly way - node = parent; - outerCache = node[ expando ] || ( node[ expando ] = {} ); - - // Support: IE <9 only - // Defend against cloned attroperties (jQuery gh-1709) - uniqueCache = outerCache[ node.uniqueID ] || - ( outerCache[ node.uniqueID ] = {} ); - - cache = uniqueCache[ type ] || []; - nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ]; - diff = nodeIndex && cache[ 2 ]; - node = nodeIndex && parent.childNodes[ nodeIndex ]; - - while ( ( node = ++nodeIndex && node && node[ dir ] || - - // Fallback to seeking `elem` from the start - ( diff = nodeIndex = 0 ) || start.pop() ) ) { - - // When found, cache indexes on `parent` and break - if ( node.nodeType === 1 && ++diff && node === elem ) { - uniqueCache[ type ] = [ dirruns, nodeIndex, diff ]; - break; - } - } - - } else { - - // Use previously-cached element index if available - if ( useCache ) { - - // ...in a gzip-friendly way - node = elem; - outerCache = node[ expando ] || ( node[ expando ] = {} ); - - // Support: IE <9 only - // Defend against cloned attroperties (jQuery gh-1709) - uniqueCache = outerCache[ node.uniqueID ] || - ( outerCache[ node.uniqueID ] = {} ); - - cache = uniqueCache[ type ] || []; - nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ]; - diff = nodeIndex; - } - - // xml :nth-child(...) - // or :nth-last-child(...) or :nth(-last)?-of-type(...) - if ( diff === false ) { - - // Use the same loop as above to seek `elem` from the start - while ( ( node = ++nodeIndex && node && node[ dir ] || - ( diff = nodeIndex = 0 ) || start.pop() ) ) { - - if ( ( ofType ? - node.nodeName.toLowerCase() === name : - node.nodeType === 1 ) && - ++diff ) { - - // Cache the index of each encountered element - if ( useCache ) { - outerCache = node[ expando ] || - ( node[ expando ] = {} ); - - // Support: IE <9 only - // Defend against cloned attroperties (jQuery gh-1709) - uniqueCache = outerCache[ node.uniqueID ] || - ( outerCache[ node.uniqueID ] = {} ); - - uniqueCache[ type ] = [ dirruns, diff ]; - } - - if ( node === elem ) { - break; - } - } - } - } - } - - // Incorporate the offset, then check against cycle size - diff -= last; - return diff === first || ( diff % first === 0 && diff / first >= 0 ); - } - }; - }, - - "PSEUDO": function( pseudo, argument ) { - - // pseudo-class names are case-insensitive - // http://www.w3.org/TR/selectors/#pseudo-classes - // Prioritize by case sensitivity in case custom pseudos are added with uppercase letters - // Remember that setFilters inherits from pseudos - var args, - fn = Expr.pseudos[ pseudo ] || Expr.setFilters[ pseudo.toLowerCase() ] || - Sizzle.error( "unsupported pseudo: " + pseudo ); - - // The user may use createPseudo to indicate that - // arguments are needed to create the filter function - // just as Sizzle does - if ( fn[ expando ] ) { - return fn( argument ); - } - - // But maintain support for old signatures - if ( fn.length > 1 ) { - args = [ pseudo, pseudo, "", argument ]; - return Expr.setFilters.hasOwnProperty( pseudo.toLowerCase() ) ? - markFunction( function( seed, matches ) { - var idx, - matched = fn( seed, argument ), - i = matched.length; - while ( i-- ) { - idx = indexOf( seed, matched[ i ] ); - seed[ idx ] = !( matches[ idx ] = matched[ i ] ); - } - } ) : - function( elem ) { - return fn( elem, 0, args ); - }; - } - - return fn; - } - }, - - pseudos: { - - // Potentially complex pseudos - "not": markFunction( function( selector ) { - - // Trim the selector passed to compile - // to avoid treating leading and trailing - // spaces as combinators - var input = [], - results = [], - matcher = compile( selector.replace( rtrim, "$1" ) ); - - return matcher[ expando ] ? - markFunction( function( seed, matches, _context, xml ) { - var elem, - unmatched = matcher( seed, null, xml, [] ), - i = seed.length; - - // Match elements unmatched by `matcher` - while ( i-- ) { - if ( ( elem = unmatched[ i ] ) ) { - seed[ i ] = !( matches[ i ] = elem ); - } - } - } ) : - function( elem, _context, xml ) { - input[ 0 ] = elem; - matcher( input, null, xml, results ); - - // Don't keep the element (issue #299) - input[ 0 ] = null; - return !results.pop(); - }; - } ), - - "has": markFunction( function( selector ) { - return function( elem ) { - return Sizzle( selector, elem ).length > 0; - }; - } ), - - "contains": markFunction( function( text ) { - text = text.replace( runescape, funescape ); - return function( elem ) { - return ( elem.textContent || getText( elem ) ).indexOf( text ) > -1; - }; - } ), - - // "Whether an element is represented by a :lang() selector - // is based solely on the element's language value - // being equal to the identifier C, - // or beginning with the identifier C immediately followed by "-". - // The matching of C against the element's language value is performed case-insensitively. - // The identifier C does not have to be a valid language name." - // http://www.w3.org/TR/selectors/#lang-pseudo - "lang": markFunction( function( lang ) { - - // lang value must be a valid identifier - if ( !ridentifier.test( lang || "" ) ) { - Sizzle.error( "unsupported lang: " + lang ); - } - lang = lang.replace( runescape, funescape ).toLowerCase(); - return function( elem ) { - var elemLang; - do { - if ( ( elemLang = documentIsHTML ? - elem.lang : - elem.getAttribute( "xml:lang" ) || elem.getAttribute( "lang" ) ) ) { - - elemLang = elemLang.toLowerCase(); - return elemLang === lang || elemLang.indexOf( lang + "-" ) === 0; - } - } while ( ( elem = elem.parentNode ) && elem.nodeType === 1 ); - return false; - }; - } ), - - // Miscellaneous - "target": function( elem ) { - var hash = window.location && window.location.hash; - return hash && hash.slice( 1 ) === elem.id; - }, - - "root": function( elem ) { - return elem === docElem; - }, - - "focus": function( elem ) { - return elem === document.activeElement && - ( !document.hasFocus || document.hasFocus() ) && - !!( elem.type || elem.href || ~elem.tabIndex ); - }, - - // Boolean properties - "enabled": createDisabledPseudo( false ), - "disabled": createDisabledPseudo( true ), - - "checked": function( elem ) { - - // In CSS3, :checked should return both checked and selected elements - // http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked - var nodeName = elem.nodeName.toLowerCase(); - return ( nodeName === "input" && !!elem.checked ) || - ( nodeName === "option" && !!elem.selected ); - }, - - "selected": function( elem ) { - - // Accessing this property makes selected-by-default - // options in Safari work properly - if ( elem.parentNode ) { - // eslint-disable-next-line no-unused-expressions - elem.parentNode.selectedIndex; - } - - return elem.selected === true; - }, - - // Contents - "empty": function( elem ) { - - // http://www.w3.org/TR/selectors/#empty-pseudo - // :empty is negated by element (1) or content nodes (text: 3; cdata: 4; entity ref: 5), - // but not by others (comment: 8; processing instruction: 7; etc.) - // nodeType < 6 works because attributes (2) do not appear as children - for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) { - if ( elem.nodeType < 6 ) { - return false; - } - } - return true; - }, - - "parent": function( elem ) { - return !Expr.pseudos[ "empty" ]( elem ); - }, - - // Element/input types - "header": function( elem ) { - return rheader.test( elem.nodeName ); - }, - - "input": function( elem ) { - return rinputs.test( elem.nodeName ); - }, - - "button": function( elem ) { - var name = elem.nodeName.toLowerCase(); - return name === "input" && elem.type === "button" || name === "button"; - }, - - "text": function( elem ) { - var attr; - return elem.nodeName.toLowerCase() === "input" && - elem.type === "text" && - - // Support: IE<8 - // New HTML5 attribute values (e.g., "search") appear with elem.type === "text" - ( ( attr = elem.getAttribute( "type" ) ) == null || - attr.toLowerCase() === "text" ); - }, - - // Position-in-collection - "first": createPositionalPseudo( function() { - return [ 0 ]; - } ), - - "last": createPositionalPseudo( function( _matchIndexes, length ) { - return [ length - 1 ]; - } ), - - "eq": createPositionalPseudo( function( _matchIndexes, length, argument ) { - return [ argument < 0 ? argument + length : argument ]; - } ), - - "even": createPositionalPseudo( function( matchIndexes, length ) { - var i = 0; - for ( ; i < length; i += 2 ) { - matchIndexes.push( i ); - } - return matchIndexes; - } ), - - "odd": createPositionalPseudo( function( matchIndexes, length ) { - var i = 1; - for ( ; i < length; i += 2 ) { - matchIndexes.push( i ); - } - return matchIndexes; - } ), - - "lt": createPositionalPseudo( function( matchIndexes, length, argument ) { - var i = argument < 0 ? - argument + length : - argument > length ? - length : - argument; - for ( ; --i >= 0; ) { - matchIndexes.push( i ); - } - return matchIndexes; - } ), - - "gt": createPositionalPseudo( function( matchIndexes, length, argument ) { - var i = argument < 0 ? argument + length : argument; - for ( ; ++i < length; ) { - matchIndexes.push( i ); - } - return matchIndexes; - } ) - } -}; - -Expr.pseudos[ "nth" ] = Expr.pseudos[ "eq" ]; - -// Add button/input type pseudos -for ( i in { radio: true, checkbox: true, file: true, password: true, image: true } ) { - Expr.pseudos[ i ] = createInputPseudo( i ); -} -for ( i in { submit: true, reset: true } ) { - Expr.pseudos[ i ] = createButtonPseudo( i ); -} - -// Easy API for creating new setFilters -function setFilters() {} -setFilters.prototype = Expr.filters = Expr.pseudos; -Expr.setFilters = new setFilters(); - -tokenize = Sizzle.tokenize = function( selector, parseOnly ) { - var matched, match, tokens, type, - soFar, groups, preFilters, - cached = tokenCache[ selector + " " ]; - - if ( cached ) { - return parseOnly ? 0 : cached.slice( 0 ); - } - - soFar = selector; - groups = []; - preFilters = Expr.preFilter; - - while ( soFar ) { - - // Comma and first run - if ( !matched || ( match = rcomma.exec( soFar ) ) ) { - if ( match ) { - - // Don't consume trailing commas as valid - soFar = soFar.slice( match[ 0 ].length ) || soFar; - } - groups.push( ( tokens = [] ) ); - } - - matched = false; - - // Combinators - if ( ( match = rcombinators.exec( soFar ) ) ) { - matched = match.shift(); - tokens.push( { - value: matched, - - // Cast descendant combinators to space - type: match[ 0 ].replace( rtrim, " " ) - } ); - soFar = soFar.slice( matched.length ); - } - - // Filters - for ( type in Expr.filter ) { - if ( ( match = matchExpr[ type ].exec( soFar ) ) && ( !preFilters[ type ] || - ( match = preFilters[ type ]( match ) ) ) ) { - matched = match.shift(); - tokens.push( { - value: matched, - type: type, - matches: match - } ); - soFar = soFar.slice( matched.length ); - } - } - - if ( !matched ) { - break; - } - } - - // Return the length of the invalid excess - // if we're just parsing - // Otherwise, throw an error or return tokens - return parseOnly ? - soFar.length : - soFar ? - Sizzle.error( selector ) : - - // Cache the tokens - tokenCache( selector, groups ).slice( 0 ); -}; - -function toSelector( tokens ) { - var i = 0, - len = tokens.length, - selector = ""; - for ( ; i < len; i++ ) { - selector += tokens[ i ].value; - } - return selector; -} - -function addCombinator( matcher, combinator, base ) { - var dir = combinator.dir, - skip = combinator.next, - key = skip || dir, - checkNonElements = base && key === "parentNode", - doneName = done++; - - return combinator.first ? - - // Check against closest ancestor/preceding element - function( elem, context, xml ) { - while ( ( elem = elem[ dir ] ) ) { - if ( elem.nodeType === 1 || checkNonElements ) { - return matcher( elem, context, xml ); - } - } - return false; - } : - - // Check against all ancestor/preceding elements - function( elem, context, xml ) { - var oldCache, uniqueCache, outerCache, - newCache = [ dirruns, doneName ]; - - // We can't set arbitrary data on XML nodes, so they don't benefit from combinator caching - if ( xml ) { - while ( ( elem = elem[ dir ] ) ) { - if ( elem.nodeType === 1 || checkNonElements ) { - if ( matcher( elem, context, xml ) ) { - return true; - } - } - } - } else { - while ( ( elem = elem[ dir ] ) ) { - if ( elem.nodeType === 1 || checkNonElements ) { - outerCache = elem[ expando ] || ( elem[ expando ] = {} ); - - // Support: IE <9 only - // Defend against cloned attroperties (jQuery gh-1709) - uniqueCache = outerCache[ elem.uniqueID ] || - ( outerCache[ elem.uniqueID ] = {} ); - - if ( skip && skip === elem.nodeName.toLowerCase() ) { - elem = elem[ dir ] || elem; - } else if ( ( oldCache = uniqueCache[ key ] ) && - oldCache[ 0 ] === dirruns && oldCache[ 1 ] === doneName ) { - - // Assign to newCache so results back-propagate to previous elements - return ( newCache[ 2 ] = oldCache[ 2 ] ); - } else { - - // Reuse newcache so results back-propagate to previous elements - uniqueCache[ key ] = newCache; - - // A match means we're done; a fail means we have to keep checking - if ( ( newCache[ 2 ] = matcher( elem, context, xml ) ) ) { - return true; - } - } - } - } - } - return false; - }; -} - -function elementMatcher( matchers ) { - return matchers.length > 1 ? - function( elem, context, xml ) { - var i = matchers.length; - while ( i-- ) { - if ( !matchers[ i ]( elem, context, xml ) ) { - return false; - } - } - return true; - } : - matchers[ 0 ]; -} - -function multipleContexts( selector, contexts, results ) { - var i = 0, - len = contexts.length; - for ( ; i < len; i++ ) { - Sizzle( selector, contexts[ i ], results ); - } - return results; -} - -function condense( unmatched, map, filter, context, xml ) { - var elem, - newUnmatched = [], - i = 0, - len = unmatched.length, - mapped = map != null; - - for ( ; i < len; i++ ) { - if ( ( elem = unmatched[ i ] ) ) { - if ( !filter || filter( elem, context, xml ) ) { - newUnmatched.push( elem ); - if ( mapped ) { - map.push( i ); - } - } - } - } - - return newUnmatched; -} - -function setMatcher( preFilter, selector, matcher, postFilter, postFinder, postSelector ) { - if ( postFilter && !postFilter[ expando ] ) { - postFilter = setMatcher( postFilter ); - } - if ( postFinder && !postFinder[ expando ] ) { - postFinder = setMatcher( postFinder, postSelector ); - } - return markFunction( function( seed, results, context, xml ) { - var temp, i, elem, - preMap = [], - postMap = [], - preexisting = results.length, - - // Get initial elements from seed or context - elems = seed || multipleContexts( - selector || "*", - context.nodeType ? [ context ] : context, - [] - ), - - // Prefilter to get matcher input, preserving a map for seed-results synchronization - matcherIn = preFilter && ( seed || !selector ) ? - condense( elems, preMap, preFilter, context, xml ) : - elems, - - matcherOut = matcher ? - - // If we have a postFinder, or filtered seed, or non-seed postFilter or preexisting results, - postFinder || ( seed ? preFilter : preexisting || postFilter ) ? - - // ...intermediate processing is necessary - [] : - - // ...otherwise use results directly - results : - matcherIn; - - // Find primary matches - if ( matcher ) { - matcher( matcherIn, matcherOut, context, xml ); - } - - // Apply postFilter - if ( postFilter ) { - temp = condense( matcherOut, postMap ); - postFilter( temp, [], context, xml ); - - // Un-match failing elements by moving them back to matcherIn - i = temp.length; - while ( i-- ) { - if ( ( elem = temp[ i ] ) ) { - matcherOut[ postMap[ i ] ] = !( matcherIn[ postMap[ i ] ] = elem ); - } - } - } - - if ( seed ) { - if ( postFinder || preFilter ) { - if ( postFinder ) { - - // Get the final matcherOut by condensing this intermediate into postFinder contexts - temp = []; - i = matcherOut.length; - while ( i-- ) { - if ( ( elem = matcherOut[ i ] ) ) { - - // Restore matcherIn since elem is not yet a final match - temp.push( ( matcherIn[ i ] = elem ) ); - } - } - postFinder( null, ( matcherOut = [] ), temp, xml ); - } - - // Move matched elements from seed to results to keep them synchronized - i = matcherOut.length; - while ( i-- ) { - if ( ( elem = matcherOut[ i ] ) && - ( temp = postFinder ? indexOf( seed, elem ) : preMap[ i ] ) > -1 ) { - - seed[ temp ] = !( results[ temp ] = elem ); - } - } - } - - // Add elements to results, through postFinder if defined - } else { - matcherOut = condense( - matcherOut === results ? - matcherOut.splice( preexisting, matcherOut.length ) : - matcherOut - ); - if ( postFinder ) { - postFinder( null, results, matcherOut, xml ); - } else { - push.apply( results, matcherOut ); - } - } - } ); -} - -function matcherFromTokens( tokens ) { - var checkContext, matcher, j, - len = tokens.length, - leadingRelative = Expr.relative[ tokens[ 0 ].type ], - implicitRelative = leadingRelative || Expr.relative[ " " ], - i = leadingRelative ? 1 : 0, - - // The foundational matcher ensures that elements are reachable from top-level context(s) - matchContext = addCombinator( function( elem ) { - return elem === checkContext; - }, implicitRelative, true ), - matchAnyContext = addCombinator( function( elem ) { - return indexOf( checkContext, elem ) > -1; - }, implicitRelative, true ), - matchers = [ function( elem, context, xml ) { - var ret = ( !leadingRelative && ( xml || context !== outermostContext ) ) || ( - ( checkContext = context ).nodeType ? - matchContext( elem, context, xml ) : - matchAnyContext( elem, context, xml ) ); - - // Avoid hanging onto element (issue #299) - checkContext = null; - return ret; - } ]; - - for ( ; i < len; i++ ) { - if ( ( matcher = Expr.relative[ tokens[ i ].type ] ) ) { - matchers = [ addCombinator( elementMatcher( matchers ), matcher ) ]; - } else { - matcher = Expr.filter[ tokens[ i ].type ].apply( null, tokens[ i ].matches ); - - // Return special upon seeing a positional matcher - if ( matcher[ expando ] ) { - - // Find the next relative operator (if any) for proper handling - j = ++i; - for ( ; j < len; j++ ) { - if ( Expr.relative[ tokens[ j ].type ] ) { - break; - } - } - return setMatcher( - i > 1 && elementMatcher( matchers ), - i > 1 && toSelector( - - // If the preceding token was a descendant combinator, insert an implicit any-element `*` - tokens - .slice( 0, i - 1 ) - .concat( { value: tokens[ i - 2 ].type === " " ? "*" : "" } ) - ).replace( rtrim, "$1" ), - matcher, - i < j && matcherFromTokens( tokens.slice( i, j ) ), - j < len && matcherFromTokens( ( tokens = tokens.slice( j ) ) ), - j < len && toSelector( tokens ) - ); - } - matchers.push( matcher ); - } - } - - return elementMatcher( matchers ); -} - -function matcherFromGroupMatchers( elementMatchers, setMatchers ) { - var bySet = setMatchers.length > 0, - byElement = elementMatchers.length > 0, - superMatcher = function( seed, context, xml, results, outermost ) { - var elem, j, matcher, - matchedCount = 0, - i = "0", - unmatched = seed && [], - setMatched = [], - contextBackup = outermostContext, - - // We must always have either seed elements or outermost context - elems = seed || byElement && Expr.find[ "TAG" ]( "*", outermost ), - - // Use integer dirruns iff this is the outermost matcher - dirrunsUnique = ( dirruns += contextBackup == null ? 1 : Math.random() || 0.1 ), - len = elems.length; - - if ( outermost ) { - - // Support: IE 11+, Edge 17 - 18+ - // IE/Edge sometimes throw a "Permission denied" error when strict-comparing - // two documents; shallow comparisons work. - // eslint-disable-next-line eqeqeq - outermostContext = context == document || context || outermost; - } - - // Add elements passing elementMatchers directly to results - // Support: IE<9, Safari - // Tolerate NodeList properties (IE: "length"; Safari: ) matching elements by id - for ( ; i !== len && ( elem = elems[ i ] ) != null; i++ ) { - if ( byElement && elem ) { - j = 0; - - // Support: IE 11+, Edge 17 - 18+ - // IE/Edge sometimes throw a "Permission denied" error when strict-comparing - // two documents; shallow comparisons work. - // eslint-disable-next-line eqeqeq - if ( !context && elem.ownerDocument != document ) { - setDocument( elem ); - xml = !documentIsHTML; - } - while ( ( matcher = elementMatchers[ j++ ] ) ) { - if ( matcher( elem, context || document, xml ) ) { - results.push( elem ); - break; - } - } - if ( outermost ) { - dirruns = dirrunsUnique; - } - } - - // Track unmatched elements for set filters - if ( bySet ) { - - // They will have gone through all possible matchers - if ( ( elem = !matcher && elem ) ) { - matchedCount--; - } - - // Lengthen the array for every element, matched or not - if ( seed ) { - unmatched.push( elem ); - } - } - } - - // `i` is now the count of elements visited above, and adding it to `matchedCount` - // makes the latter nonnegative. - matchedCount += i; - - // Apply set filters to unmatched elements - // NOTE: This can be skipped if there are no unmatched elements (i.e., `matchedCount` - // equals `i`), unless we didn't visit _any_ elements in the above loop because we have - // no element matchers and no seed. - // Incrementing an initially-string "0" `i` allows `i` to remain a string only in that - // case, which will result in a "00" `matchedCount` that differs from `i` but is also - // numerically zero. - if ( bySet && i !== matchedCount ) { - j = 0; - while ( ( matcher = setMatchers[ j++ ] ) ) { - matcher( unmatched, setMatched, context, xml ); - } - - if ( seed ) { - - // Reintegrate element matches to eliminate the need for sorting - if ( matchedCount > 0 ) { - while ( i-- ) { - if ( !( unmatched[ i ] || setMatched[ i ] ) ) { - setMatched[ i ] = pop.call( results ); - } - } - } - - // Discard index placeholder values to get only actual matches - setMatched = condense( setMatched ); - } - - // Add matches to results - push.apply( results, setMatched ); - - // Seedless set matches succeeding multiple successful matchers stipulate sorting - if ( outermost && !seed && setMatched.length > 0 && - ( matchedCount + setMatchers.length ) > 1 ) { - - Sizzle.uniqueSort( results ); - } - } - - // Override manipulation of globals by nested matchers - if ( outermost ) { - dirruns = dirrunsUnique; - outermostContext = contextBackup; - } - - return unmatched; - }; - - return bySet ? - markFunction( superMatcher ) : - superMatcher; -} - -compile = Sizzle.compile = function( selector, match /* Internal Use Only */ ) { - var i, - setMatchers = [], - elementMatchers = [], - cached = compilerCache[ selector + " " ]; - - if ( !cached ) { - - // Generate a function of recursive functions that can be used to check each element - if ( !match ) { - match = tokenize( selector ); - } - i = match.length; - while ( i-- ) { - cached = matcherFromTokens( match[ i ] ); - if ( cached[ expando ] ) { - setMatchers.push( cached ); - } else { - elementMatchers.push( cached ); - } - } - - // Cache the compiled function - cached = compilerCache( - selector, - matcherFromGroupMatchers( elementMatchers, setMatchers ) - ); - - // Save selector and tokenization - cached.selector = selector; - } - return cached; -}; - -/** - * A low-level selection function that works with Sizzle's compiled - * selector functions - * @param {String|Function} selector A selector or a pre-compiled - * selector function built with Sizzle.compile - * @param {Element} context - * @param {Array} [results] - * @param {Array} [seed] A set of elements to match against - */ -select = Sizzle.select = function( selector, context, results, seed ) { - var i, tokens, token, type, find, - compiled = typeof selector === "function" && selector, - match = !seed && tokenize( ( selector = compiled.selector || selector ) ); - - results = results || []; - - // Try to minimize operations if there is only one selector in the list and no seed - // (the latter of which guarantees us context) - if ( match.length === 1 ) { - - // Reduce context if the leading compound selector is an ID - tokens = match[ 0 ] = match[ 0 ].slice( 0 ); - if ( tokens.length > 2 && ( token = tokens[ 0 ] ).type === "ID" && - context.nodeType === 9 && documentIsHTML && Expr.relative[ tokens[ 1 ].type ] ) { - - context = ( Expr.find[ "ID" ]( token.matches[ 0 ] - .replace( runescape, funescape ), context ) || [] )[ 0 ]; - if ( !context ) { - return results; - - // Precompiled matchers will still verify ancestry, so step up a level - } else if ( compiled ) { - context = context.parentNode; - } - - selector = selector.slice( tokens.shift().value.length ); - } - - // Fetch a seed set for right-to-left matching - i = matchExpr[ "needsContext" ].test( selector ) ? 0 : tokens.length; - while ( i-- ) { - token = tokens[ i ]; - - // Abort if we hit a combinator - if ( Expr.relative[ ( type = token.type ) ] ) { - break; - } - if ( ( find = Expr.find[ type ] ) ) { - - // Search, expanding context for leading sibling combinators - if ( ( seed = find( - token.matches[ 0 ].replace( runescape, funescape ), - rsibling.test( tokens[ 0 ].type ) && testContext( context.parentNode ) || - context - ) ) ) { - - // If seed is empty or no tokens remain, we can return early - tokens.splice( i, 1 ); - selector = seed.length && toSelector( tokens ); - if ( !selector ) { - push.apply( results, seed ); - return results; - } - - break; - } - } - } - } - - // Compile and execute a filtering function if one is not provided - // Provide `match` to avoid retokenization if we modified the selector above - ( compiled || compile( selector, match ) )( - seed, - context, - !documentIsHTML, - results, - !context || rsibling.test( selector ) && testContext( context.parentNode ) || context - ); - return results; -}; - -// One-time assignments - -// Sort stability -support.sortStable = expando.split( "" ).sort( sortOrder ).join( "" ) === expando; - -// Support: Chrome 14-35+ -// Always assume duplicates if they aren't passed to the comparison function -support.detectDuplicates = !!hasDuplicate; - -// Initialize against the default document -setDocument(); - -// Support: Webkit<537.32 - Safari 6.0.3/Chrome 25 (fixed in Chrome 27) -// Detached nodes confoundingly follow *each other* -support.sortDetached = assert( function( el ) { - - // Should return 1, but returns 4 (following) - return el.compareDocumentPosition( document.createElement( "fieldset" ) ) & 1; -} ); - -// Support: IE<8 -// Prevent attribute/property "interpolation" -// https://msdn.microsoft.com/en-us/library/ms536429%28VS.85%29.aspx -if ( !assert( function( el ) { - el.innerHTML = ""; - return el.firstChild.getAttribute( "href" ) === "#"; -} ) ) { - addHandle( "type|href|height|width", function( elem, name, isXML ) { - if ( !isXML ) { - return elem.getAttribute( name, name.toLowerCase() === "type" ? 1 : 2 ); - } - } ); -} - -// Support: IE<9 -// Use defaultValue in place of getAttribute("value") -if ( !support.attributes || !assert( function( el ) { - el.innerHTML = ""; - el.firstChild.setAttribute( "value", "" ); - return el.firstChild.getAttribute( "value" ) === ""; -} ) ) { - addHandle( "value", function( elem, _name, isXML ) { - if ( !isXML && elem.nodeName.toLowerCase() === "input" ) { - return elem.defaultValue; - } - } ); -} - -// Support: IE<9 -// Use getAttributeNode to fetch booleans when getAttribute lies -if ( !assert( function( el ) { - return el.getAttribute( "disabled" ) == null; -} ) ) { - addHandle( booleans, function( elem, name, isXML ) { - var val; - if ( !isXML ) { - return elem[ name ] === true ? name.toLowerCase() : - ( val = elem.getAttributeNode( name ) ) && val.specified ? - val.value : - null; - } - } ); -} - -return Sizzle; - -} )( window ); - - - -jQuery.find = Sizzle; -jQuery.expr = Sizzle.selectors; - -// Deprecated -jQuery.expr[ ":" ] = jQuery.expr.pseudos; -jQuery.uniqueSort = jQuery.unique = Sizzle.uniqueSort; -jQuery.text = Sizzle.getText; -jQuery.isXMLDoc = Sizzle.isXML; -jQuery.contains = Sizzle.contains; -jQuery.escapeSelector = Sizzle.escape; - - - - -var dir = function( elem, dir, until ) { - var matched = [], - truncate = until !== undefined; - - while ( ( elem = elem[ dir ] ) && elem.nodeType !== 9 ) { - if ( elem.nodeType === 1 ) { - if ( truncate && jQuery( elem ).is( until ) ) { - break; - } - matched.push( elem ); - } - } - return matched; -}; - - -var siblings = function( n, elem ) { - var matched = []; - - for ( ; n; n = n.nextSibling ) { - if ( n.nodeType === 1 && n !== elem ) { - matched.push( n ); - } - } - - return matched; -}; - - -var rneedsContext = jQuery.expr.match.needsContext; - - - -function nodeName( elem, name ) { - - return elem.nodeName && elem.nodeName.toLowerCase() === name.toLowerCase(); - -}; -var rsingleTag = ( /^<([a-z][^\/\0>:\x20\t\r\n\f]*)[\x20\t\r\n\f]*\/?>(?:<\/\1>|)$/i ); - - - -// Implement the identical functionality for filter and not -function winnow( elements, qualifier, not ) { - if ( isFunction( qualifier ) ) { - return jQuery.grep( elements, function( elem, i ) { - return !!qualifier.call( elem, i, elem ) !== not; - } ); - } - - // Single element - if ( qualifier.nodeType ) { - return jQuery.grep( elements, function( elem ) { - return ( elem === qualifier ) !== not; - } ); - } - - // Arraylike of elements (jQuery, arguments, Array) - if ( typeof qualifier !== "string" ) { - return jQuery.grep( elements, function( elem ) { - return ( indexOf.call( qualifier, elem ) > -1 ) !== not; - } ); - } - - // Filtered directly for both simple and complex selectors - return jQuery.filter( qualifier, elements, not ); -} - -jQuery.filter = function( expr, elems, not ) { - var elem = elems[ 0 ]; - - if ( not ) { - expr = ":not(" + expr + ")"; - } - - if ( elems.length === 1 && elem.nodeType === 1 ) { - return jQuery.find.matchesSelector( elem, expr ) ? [ elem ] : []; - } - - return jQuery.find.matches( expr, jQuery.grep( elems, function( elem ) { - return elem.nodeType === 1; - } ) ); -}; - -jQuery.fn.extend( { - find: function( selector ) { - var i, ret, - len = this.length, - self = this; - - if ( typeof selector !== "string" ) { - return this.pushStack( jQuery( selector ).filter( function() { - for ( i = 0; i < len; i++ ) { - if ( jQuery.contains( self[ i ], this ) ) { - return true; - } - } - } ) ); - } - - ret = this.pushStack( [] ); - - for ( i = 0; i < len; i++ ) { - jQuery.find( selector, self[ i ], ret ); - } - - return len > 1 ? jQuery.uniqueSort( ret ) : ret; - }, - filter: function( selector ) { - return this.pushStack( winnow( this, selector || [], false ) ); - }, - not: function( selector ) { - return this.pushStack( winnow( this, selector || [], true ) ); - }, - is: function( selector ) { - return !!winnow( - this, - - // If this is a positional/relative selector, check membership in the returned set - // so $("p:first").is("p:last") won't return true for a doc with two "p". - typeof selector === "string" && rneedsContext.test( selector ) ? - jQuery( selector ) : - selector || [], - false - ).length; - } -} ); - - -// Initialize a jQuery object - - -// A central reference to the root jQuery(document) -var rootjQuery, - - // A simple way to check for HTML strings - // Prioritize #id over to avoid XSS via location.hash (#9521) - // Strict HTML recognition (#11290: must start with <) - // Shortcut simple #id case for speed - rquickExpr = /^(?:\s*(<[\w\W]+>)[^>]*|#([\w-]+))$/, - - init = jQuery.fn.init = function( selector, context, root ) { - var match, elem; - - // HANDLE: $(""), $(null), $(undefined), $(false) - if ( !selector ) { - return this; - } - - // Method init() accepts an alternate rootjQuery - // so migrate can support jQuery.sub (gh-2101) - root = root || rootjQuery; - - // Handle HTML strings - if ( typeof selector === "string" ) { - if ( selector[ 0 ] === "<" && - selector[ selector.length - 1 ] === ">" && - selector.length >= 3 ) { - - // Assume that strings that start and end with <> are HTML and skip the regex check - match = [ null, selector, null ]; - - } else { - match = rquickExpr.exec( selector ); - } - - // Match html or make sure no context is specified for #id - if ( match && ( match[ 1 ] || !context ) ) { - - // HANDLE: $(html) -> $(array) - if ( match[ 1 ] ) { - context = context instanceof jQuery ? context[ 0 ] : context; - - // Option to run scripts is true for back-compat - // Intentionally let the error be thrown if parseHTML is not present - jQuery.merge( this, jQuery.parseHTML( - match[ 1 ], - context && context.nodeType ? context.ownerDocument || context : document, - true - ) ); - - // HANDLE: $(html, props) - if ( rsingleTag.test( match[ 1 ] ) && jQuery.isPlainObject( context ) ) { - for ( match in context ) { - - // Properties of context are called as methods if possible - if ( isFunction( this[ match ] ) ) { - this[ match ]( context[ match ] ); - - // ...and otherwise set as attributes - } else { - this.attr( match, context[ match ] ); - } - } - } - - return this; - - // HANDLE: $(#id) - } else { - elem = document.getElementById( match[ 2 ] ); - - if ( elem ) { - - // Inject the element directly into the jQuery object - this[ 0 ] = elem; - this.length = 1; - } - return this; - } - - // HANDLE: $(expr, $(...)) - } else if ( !context || context.jquery ) { - return ( context || root ).find( selector ); - - // HANDLE: $(expr, context) - // (which is just equivalent to: $(context).find(expr) - } else { - return this.constructor( context ).find( selector ); - } - - // HANDLE: $(DOMElement) - } else if ( selector.nodeType ) { - this[ 0 ] = selector; - this.length = 1; - return this; - - // HANDLE: $(function) - // Shortcut for document ready - } else if ( isFunction( selector ) ) { - return root.ready !== undefined ? - root.ready( selector ) : - - // Execute immediately if ready is not present - selector( jQuery ); - } - - return jQuery.makeArray( selector, this ); - }; - -// Give the init function the jQuery prototype for later instantiation -init.prototype = jQuery.fn; - -// Initialize central reference -rootjQuery = jQuery( document ); - - -var rparentsprev = /^(?:parents|prev(?:Until|All))/, - - // Methods guaranteed to produce a unique set when starting from a unique set - guaranteedUnique = { - children: true, - contents: true, - next: true, - prev: true - }; - -jQuery.fn.extend( { - has: function( target ) { - var targets = jQuery( target, this ), - l = targets.length; - - return this.filter( function() { - var i = 0; - for ( ; i < l; i++ ) { - if ( jQuery.contains( this, targets[ i ] ) ) { - return true; - } - } - } ); - }, - - closest: function( selectors, context ) { - var cur, - i = 0, - l = this.length, - matched = [], - targets = typeof selectors !== "string" && jQuery( selectors ); - - // Positional selectors never match, since there's no _selection_ context - if ( !rneedsContext.test( selectors ) ) { - for ( ; i < l; i++ ) { - for ( cur = this[ i ]; cur && cur !== context; cur = cur.parentNode ) { - - // Always skip document fragments - if ( cur.nodeType < 11 && ( targets ? - targets.index( cur ) > -1 : - - // Don't pass non-elements to Sizzle - cur.nodeType === 1 && - jQuery.find.matchesSelector( cur, selectors ) ) ) { - - matched.push( cur ); - break; - } - } - } - } - - return this.pushStack( matched.length > 1 ? jQuery.uniqueSort( matched ) : matched ); - }, - - // Determine the position of an element within the set - index: function( elem ) { - - // No argument, return index in parent - if ( !elem ) { - return ( this[ 0 ] && this[ 0 ].parentNode ) ? this.first().prevAll().length : -1; - } - - // Index in selector - if ( typeof elem === "string" ) { - return indexOf.call( jQuery( elem ), this[ 0 ] ); - } - - // Locate the position of the desired element - return indexOf.call( this, - - // If it receives a jQuery object, the first element is used - elem.jquery ? elem[ 0 ] : elem - ); - }, - - add: function( selector, context ) { - return this.pushStack( - jQuery.uniqueSort( - jQuery.merge( this.get(), jQuery( selector, context ) ) - ) - ); - }, - - addBack: function( selector ) { - return this.add( selector == null ? - this.prevObject : this.prevObject.filter( selector ) - ); - } -} ); - -function sibling( cur, dir ) { - while ( ( cur = cur[ dir ] ) && cur.nodeType !== 1 ) {} - return cur; -} - -jQuery.each( { - parent: function( elem ) { - var parent = elem.parentNode; - return parent && parent.nodeType !== 11 ? parent : null; - }, - parents: function( elem ) { - return dir( elem, "parentNode" ); - }, - parentsUntil: function( elem, _i, until ) { - return dir( elem, "parentNode", until ); - }, - next: function( elem ) { - return sibling( elem, "nextSibling" ); - }, - prev: function( elem ) { - return sibling( elem, "previousSibling" ); - }, - nextAll: function( elem ) { - return dir( elem, "nextSibling" ); - }, - prevAll: function( elem ) { - return dir( elem, "previousSibling" ); - }, - nextUntil: function( elem, _i, until ) { - return dir( elem, "nextSibling", until ); - }, - prevUntil: function( elem, _i, until ) { - return dir( elem, "previousSibling", until ); - }, - siblings: function( elem ) { - return siblings( ( elem.parentNode || {} ).firstChild, elem ); - }, - children: function( elem ) { - return siblings( elem.firstChild ); - }, - contents: function( elem ) { - if ( elem.contentDocument != null && - - // Support: IE 11+ - // elements with no `data` attribute has an object - // `contentDocument` with a `null` prototype. - getProto( elem.contentDocument ) ) { - - return elem.contentDocument; - } - - // Support: IE 9 - 11 only, iOS 7 only, Android Browser <=4.3 only - // Treat the template element as a regular one in browsers that - // don't support it. - if ( nodeName( elem, "template" ) ) { - elem = elem.content || elem; - } - - return jQuery.merge( [], elem.childNodes ); - } -}, function( name, fn ) { - jQuery.fn[ name ] = function( until, selector ) { - var matched = jQuery.map( this, fn, until ); - - if ( name.slice( -5 ) !== "Until" ) { - selector = until; - } - - if ( selector && typeof selector === "string" ) { - matched = jQuery.filter( selector, matched ); - } - - if ( this.length > 1 ) { - - // Remove duplicates - if ( !guaranteedUnique[ name ] ) { - jQuery.uniqueSort( matched ); - } - - // Reverse order for parents* and prev-derivatives - if ( rparentsprev.test( name ) ) { - matched.reverse(); - } - } - - return this.pushStack( matched ); - }; -} ); -var rnothtmlwhite = ( /[^\x20\t\r\n\f]+/g ); - - - -// Convert String-formatted options into Object-formatted ones -function createOptions( options ) { - var object = {}; - jQuery.each( options.match( rnothtmlwhite ) || [], function( _, flag ) { - object[ flag ] = true; - } ); - return object; -} - -/* - * Create a callback list using the following parameters: - * - * options: an optional list of space-separated options that will change how - * the callback list behaves or a more traditional option object - * - * By default a callback list will act like an event callback list and can be - * "fired" multiple times. - * - * Possible options: - * - * once: will ensure the callback list can only be fired once (like a Deferred) - * - * memory: will keep track of previous values and will call any callback added - * after the list has been fired right away with the latest "memorized" - * values (like a Deferred) - * - * unique: will ensure a callback can only be added once (no duplicate in the list) - * - * stopOnFalse: interrupt callings when a callback returns false - * - */ -jQuery.Callbacks = function( options ) { - - // Convert options from String-formatted to Object-formatted if needed - // (we check in cache first) - options = typeof options === "string" ? - createOptions( options ) : - jQuery.extend( {}, options ); - - var // Flag to know if list is currently firing - firing, - - // Last fire value for non-forgettable lists - memory, - - // Flag to know if list was already fired - fired, - - // Flag to prevent firing - locked, - - // Actual callback list - list = [], - - // Queue of execution data for repeatable lists - queue = [], - - // Index of currently firing callback (modified by add/remove as needed) - firingIndex = -1, - - // Fire callbacks - fire = function() { - - // Enforce single-firing - locked = locked || options.once; - - // Execute callbacks for all pending executions, - // respecting firingIndex overrides and runtime changes - fired = firing = true; - for ( ; queue.length; firingIndex = -1 ) { - memory = queue.shift(); - while ( ++firingIndex < list.length ) { - - // Run callback and check for early termination - if ( list[ firingIndex ].apply( memory[ 0 ], memory[ 1 ] ) === false && - options.stopOnFalse ) { - - // Jump to end and forget the data so .add doesn't re-fire - firingIndex = list.length; - memory = false; - } - } - } - - // Forget the data if we're done with it - if ( !options.memory ) { - memory = false; - } - - firing = false; - - // Clean up if we're done firing for good - if ( locked ) { - - // Keep an empty list if we have data for future add calls - if ( memory ) { - list = []; - - // Otherwise, this object is spent - } else { - list = ""; - } - } - }, - - // Actual Callbacks object - self = { - - // Add a callback or a collection of callbacks to the list - add: function() { - if ( list ) { - - // If we have memory from a past run, we should fire after adding - if ( memory && !firing ) { - firingIndex = list.length - 1; - queue.push( memory ); - } - - ( function add( args ) { - jQuery.each( args, function( _, arg ) { - if ( isFunction( arg ) ) { - if ( !options.unique || !self.has( arg ) ) { - list.push( arg ); - } - } else if ( arg && arg.length && toType( arg ) !== "string" ) { - - // Inspect recursively - add( arg ); - } - } ); - } )( arguments ); - - if ( memory && !firing ) { - fire(); - } - } - return this; - }, - - // Remove a callback from the list - remove: function() { - jQuery.each( arguments, function( _, arg ) { - var index; - while ( ( index = jQuery.inArray( arg, list, index ) ) > -1 ) { - list.splice( index, 1 ); - - // Handle firing indexes - if ( index <= firingIndex ) { - firingIndex--; - } - } - } ); - return this; - }, - - // Check if a given callback is in the list. - // If no argument is given, return whether or not list has callbacks attached. - has: function( fn ) { - return fn ? - jQuery.inArray( fn, list ) > -1 : - list.length > 0; - }, - - // Remove all callbacks from the list - empty: function() { - if ( list ) { - list = []; - } - return this; - }, - - // Disable .fire and .add - // Abort any current/pending executions - // Clear all callbacks and values - disable: function() { - locked = queue = []; - list = memory = ""; - return this; - }, - disabled: function() { - return !list; - }, - - // Disable .fire - // Also disable .add unless we have memory (since it would have no effect) - // Abort any pending executions - lock: function() { - locked = queue = []; - if ( !memory && !firing ) { - list = memory = ""; - } - return this; - }, - locked: function() { - return !!locked; - }, - - // Call all callbacks with the given context and arguments - fireWith: function( context, args ) { - if ( !locked ) { - args = args || []; - args = [ context, args.slice ? args.slice() : args ]; - queue.push( args ); - if ( !firing ) { - fire(); - } - } - return this; - }, - - // Call all the callbacks with the given arguments - fire: function() { - self.fireWith( this, arguments ); - return this; - }, - - // To know if the callbacks have already been called at least once - fired: function() { - return !!fired; - } - }; - - return self; -}; - - -function Identity( v ) { - return v; -} -function Thrower( ex ) { - throw ex; -} - -function adoptValue( value, resolve, reject, noValue ) { - var method; - - try { - - // Check for promise aspect first to privilege synchronous behavior - if ( value && isFunction( ( method = value.promise ) ) ) { - method.call( value ).done( resolve ).fail( reject ); - - // Other thenables - } else if ( value && isFunction( ( method = value.then ) ) ) { - method.call( value, resolve, reject ); - - // Other non-thenables - } else { - - // Control `resolve` arguments by letting Array#slice cast boolean `noValue` to integer: - // * false: [ value ].slice( 0 ) => resolve( value ) - // * true: [ value ].slice( 1 ) => resolve() - resolve.apply( undefined, [ value ].slice( noValue ) ); - } - - // For Promises/A+, convert exceptions into rejections - // Since jQuery.when doesn't unwrap thenables, we can skip the extra checks appearing in - // Deferred#then to conditionally suppress rejection. - } catch ( value ) { - - // Support: Android 4.0 only - // Strict mode functions invoked without .call/.apply get global-object context - reject.apply( undefined, [ value ] ); - } -} - -jQuery.extend( { - - Deferred: function( func ) { - var tuples = [ - - // action, add listener, callbacks, - // ... .then handlers, argument index, [final state] - [ "notify", "progress", jQuery.Callbacks( "memory" ), - jQuery.Callbacks( "memory" ), 2 ], - [ "resolve", "done", jQuery.Callbacks( "once memory" ), - jQuery.Callbacks( "once memory" ), 0, "resolved" ], - [ "reject", "fail", jQuery.Callbacks( "once memory" ), - jQuery.Callbacks( "once memory" ), 1, "rejected" ] - ], - state = "pending", - promise = { - state: function() { - return state; - }, - always: function() { - deferred.done( arguments ).fail( arguments ); - return this; - }, - "catch": function( fn ) { - return promise.then( null, fn ); - }, - - // Keep pipe for back-compat - pipe: function( /* fnDone, fnFail, fnProgress */ ) { - var fns = arguments; - - return jQuery.Deferred( function( newDefer ) { - jQuery.each( tuples, function( _i, tuple ) { - - // Map tuples (progress, done, fail) to arguments (done, fail, progress) - var fn = isFunction( fns[ tuple[ 4 ] ] ) && fns[ tuple[ 4 ] ]; - - // deferred.progress(function() { bind to newDefer or newDefer.notify }) - // deferred.done(function() { bind to newDefer or newDefer.resolve }) - // deferred.fail(function() { bind to newDefer or newDefer.reject }) - deferred[ tuple[ 1 ] ]( function() { - var returned = fn && fn.apply( this, arguments ); - if ( returned && isFunction( returned.promise ) ) { - returned.promise() - .progress( newDefer.notify ) - .done( newDefer.resolve ) - .fail( newDefer.reject ); - } else { - newDefer[ tuple[ 0 ] + "With" ]( - this, - fn ? [ returned ] : arguments - ); - } - } ); - } ); - fns = null; - } ).promise(); - }, - then: function( onFulfilled, onRejected, onProgress ) { - var maxDepth = 0; - function resolve( depth, deferred, handler, special ) { - return function() { - var that = this, - args = arguments, - mightThrow = function() { - var returned, then; - - // Support: Promises/A+ section 2.3.3.3.3 - // https://promisesaplus.com/#point-59 - // Ignore double-resolution attempts - if ( depth < maxDepth ) { - return; - } - - returned = handler.apply( that, args ); - - // Support: Promises/A+ section 2.3.1 - // https://promisesaplus.com/#point-48 - if ( returned === deferred.promise() ) { - throw new TypeError( "Thenable self-resolution" ); - } - - // Support: Promises/A+ sections 2.3.3.1, 3.5 - // https://promisesaplus.com/#point-54 - // https://promisesaplus.com/#point-75 - // Retrieve `then` only once - then = returned && - - // Support: Promises/A+ section 2.3.4 - // https://promisesaplus.com/#point-64 - // Only check objects and functions for thenability - ( typeof returned === "object" || - typeof returned === "function" ) && - returned.then; - - // Handle a returned thenable - if ( isFunction( then ) ) { - - // Special processors (notify) just wait for resolution - if ( special ) { - then.call( - returned, - resolve( maxDepth, deferred, Identity, special ), - resolve( maxDepth, deferred, Thrower, special ) - ); - - // Normal processors (resolve) also hook into progress - } else { - - // ...and disregard older resolution values - maxDepth++; - - then.call( - returned, - resolve( maxDepth, deferred, Identity, special ), - resolve( maxDepth, deferred, Thrower, special ), - resolve( maxDepth, deferred, Identity, - deferred.notifyWith ) - ); - } - - // Handle all other returned values - } else { - - // Only substitute handlers pass on context - // and multiple values (non-spec behavior) - if ( handler !== Identity ) { - that = undefined; - args = [ returned ]; - } - - // Process the value(s) - // Default process is resolve - ( special || deferred.resolveWith )( that, args ); - } - }, - - // Only normal processors (resolve) catch and reject exceptions - process = special ? - mightThrow : - function() { - try { - mightThrow(); - } catch ( e ) { - - if ( jQuery.Deferred.exceptionHook ) { - jQuery.Deferred.exceptionHook( e, - process.stackTrace ); - } - - // Support: Promises/A+ section 2.3.3.3.4.1 - // https://promisesaplus.com/#point-61 - // Ignore post-resolution exceptions - if ( depth + 1 >= maxDepth ) { - - // Only substitute handlers pass on context - // and multiple values (non-spec behavior) - if ( handler !== Thrower ) { - that = undefined; - args = [ e ]; - } - - deferred.rejectWith( that, args ); - } - } - }; - - // Support: Promises/A+ section 2.3.3.3.1 - // https://promisesaplus.com/#point-57 - // Re-resolve promises immediately to dodge false rejection from - // subsequent errors - if ( depth ) { - process(); - } else { - - // Call an optional hook to record the stack, in case of exception - // since it's otherwise lost when execution goes async - if ( jQuery.Deferred.getStackHook ) { - process.stackTrace = jQuery.Deferred.getStackHook(); - } - window.setTimeout( process ); - } - }; - } - - return jQuery.Deferred( function( newDefer ) { - - // progress_handlers.add( ... ) - tuples[ 0 ][ 3 ].add( - resolve( - 0, - newDefer, - isFunction( onProgress ) ? - onProgress : - Identity, - newDefer.notifyWith - ) - ); - - // fulfilled_handlers.add( ... ) - tuples[ 1 ][ 3 ].add( - resolve( - 0, - newDefer, - isFunction( onFulfilled ) ? - onFulfilled : - Identity - ) - ); - - // rejected_handlers.add( ... ) - tuples[ 2 ][ 3 ].add( - resolve( - 0, - newDefer, - isFunction( onRejected ) ? - onRejected : - Thrower - ) - ); - } ).promise(); - }, - - // Get a promise for this deferred - // If obj is provided, the promise aspect is added to the object - promise: function( obj ) { - return obj != null ? jQuery.extend( obj, promise ) : promise; - } - }, - deferred = {}; - - // Add list-specific methods - jQuery.each( tuples, function( i, tuple ) { - var list = tuple[ 2 ], - stateString = tuple[ 5 ]; - - // promise.progress = list.add - // promise.done = list.add - // promise.fail = list.add - promise[ tuple[ 1 ] ] = list.add; - - // Handle state - if ( stateString ) { - list.add( - function() { - - // state = "resolved" (i.e., fulfilled) - // state = "rejected" - state = stateString; - }, - - // rejected_callbacks.disable - // fulfilled_callbacks.disable - tuples[ 3 - i ][ 2 ].disable, - - // rejected_handlers.disable - // fulfilled_handlers.disable - tuples[ 3 - i ][ 3 ].disable, - - // progress_callbacks.lock - tuples[ 0 ][ 2 ].lock, - - // progress_handlers.lock - tuples[ 0 ][ 3 ].lock - ); - } - - // progress_handlers.fire - // fulfilled_handlers.fire - // rejected_handlers.fire - list.add( tuple[ 3 ].fire ); - - // deferred.notify = function() { deferred.notifyWith(...) } - // deferred.resolve = function() { deferred.resolveWith(...) } - // deferred.reject = function() { deferred.rejectWith(...) } - deferred[ tuple[ 0 ] ] = function() { - deferred[ tuple[ 0 ] + "With" ]( this === deferred ? undefined : this, arguments ); - return this; - }; - - // deferred.notifyWith = list.fireWith - // deferred.resolveWith = list.fireWith - // deferred.rejectWith = list.fireWith - deferred[ tuple[ 0 ] + "With" ] = list.fireWith; - } ); - - // Make the deferred a promise - promise.promise( deferred ); - - // Call given func if any - if ( func ) { - func.call( deferred, deferred ); - } - - // All done! - return deferred; - }, - - // Deferred helper - when: function( singleValue ) { - var - - // count of uncompleted subordinates - remaining = arguments.length, - - // count of unprocessed arguments - i = remaining, - - // subordinate fulfillment data - resolveContexts = Array( i ), - resolveValues = slice.call( arguments ), - - // the master Deferred - master = jQuery.Deferred(), - - // subordinate callback factory - updateFunc = function( i ) { - return function( value ) { - resolveContexts[ i ] = this; - resolveValues[ i ] = arguments.length > 1 ? slice.call( arguments ) : value; - if ( !( --remaining ) ) { - master.resolveWith( resolveContexts, resolveValues ); - } - }; - }; - - // Single- and empty arguments are adopted like Promise.resolve - if ( remaining <= 1 ) { - adoptValue( singleValue, master.done( updateFunc( i ) ).resolve, master.reject, - !remaining ); - - // Use .then() to unwrap secondary thenables (cf. gh-3000) - if ( master.state() === "pending" || - isFunction( resolveValues[ i ] && resolveValues[ i ].then ) ) { - - return master.then(); - } - } - - // Multiple arguments are aggregated like Promise.all array elements - while ( i-- ) { - adoptValue( resolveValues[ i ], updateFunc( i ), master.reject ); - } - - return master.promise(); - } -} ); - - -// These usually indicate a programmer mistake during development, -// warn about them ASAP rather than swallowing them by default. -var rerrorNames = /^(Eval|Internal|Range|Reference|Syntax|Type|URI)Error$/; - -jQuery.Deferred.exceptionHook = function( error, stack ) { - - // Support: IE 8 - 9 only - // Console exists when dev tools are open, which can happen at any time - if ( window.console && window.console.warn && error && rerrorNames.test( error.name ) ) { - window.console.warn( "jQuery.Deferred exception: " + error.message, error.stack, stack ); - } -}; - - - - -jQuery.readyException = function( error ) { - window.setTimeout( function() { - throw error; - } ); -}; - - - - -// The deferred used on DOM ready -var readyList = jQuery.Deferred(); - -jQuery.fn.ready = function( fn ) { - - readyList - .then( fn ) - - // Wrap jQuery.readyException in a function so that the lookup - // happens at the time of error handling instead of callback - // registration. - .catch( function( error ) { - jQuery.readyException( error ); - } ); - - return this; -}; - -jQuery.extend( { - - // Is the DOM ready to be used? Set to true once it occurs. - isReady: false, - - // A counter to track how many items to wait for before - // the ready event fires. See #6781 - readyWait: 1, - - // Handle when the DOM is ready - ready: function( wait ) { - - // Abort if there are pending holds or we're already ready - if ( wait === true ? --jQuery.readyWait : jQuery.isReady ) { - return; - } - - // Remember that the DOM is ready - jQuery.isReady = true; - - // If a normal DOM Ready event fired, decrement, and wait if need be - if ( wait !== true && --jQuery.readyWait > 0 ) { - return; - } - - // If there are functions bound, to execute - readyList.resolveWith( document, [ jQuery ] ); - } -} ); - -jQuery.ready.then = readyList.then; - -// The ready event handler and self cleanup method -function completed() { - document.removeEventListener( "DOMContentLoaded", completed ); - window.removeEventListener( "load", completed ); - jQuery.ready(); -} - -// Catch cases where $(document).ready() is called -// after the browser event has already occurred. -// Support: IE <=9 - 10 only -// Older IE sometimes signals "interactive" too soon -if ( document.readyState === "complete" || - ( document.readyState !== "loading" && !document.documentElement.doScroll ) ) { - - // Handle it asynchronously to allow scripts the opportunity to delay ready - window.setTimeout( jQuery.ready ); - -} else { - - // Use the handy event callback - document.addEventListener( "DOMContentLoaded", completed ); - - // A fallback to window.onload, that will always work - window.addEventListener( "load", completed ); -} - - - - -// Multifunctional method to get and set values of a collection -// The value/s can optionally be executed if it's a function -var access = function( elems, fn, key, value, chainable, emptyGet, raw ) { - var i = 0, - len = elems.length, - bulk = key == null; - - // Sets many values - if ( toType( key ) === "object" ) { - chainable = true; - for ( i in key ) { - access( elems, fn, i, key[ i ], true, emptyGet, raw ); - } - - // Sets one value - } else if ( value !== undefined ) { - chainable = true; - - if ( !isFunction( value ) ) { - raw = true; - } - - if ( bulk ) { - - // Bulk operations run against the entire set - if ( raw ) { - fn.call( elems, value ); - fn = null; - - // ...except when executing function values - } else { - bulk = fn; - fn = function( elem, _key, value ) { - return bulk.call( jQuery( elem ), value ); - }; - } - } - - if ( fn ) { - for ( ; i < len; i++ ) { - fn( - elems[ i ], key, raw ? - value : - value.call( elems[ i ], i, fn( elems[ i ], key ) ) - ); - } - } - } - - if ( chainable ) { - return elems; - } - - // Gets - if ( bulk ) { - return fn.call( elems ); - } - - return len ? fn( elems[ 0 ], key ) : emptyGet; -}; - - -// Matches dashed string for camelizing -var rmsPrefix = /^-ms-/, - rdashAlpha = /-([a-z])/g; - -// Used by camelCase as callback to replace() -function fcamelCase( _all, letter ) { - return letter.toUpperCase(); -} - -// Convert dashed to camelCase; used by the css and data modules -// Support: IE <=9 - 11, Edge 12 - 15 -// Microsoft forgot to hump their vendor prefix (#9572) -function camelCase( string ) { - return string.replace( rmsPrefix, "ms-" ).replace( rdashAlpha, fcamelCase ); -} -var acceptData = function( owner ) { - - // Accepts only: - // - Node - // - Node.ELEMENT_NODE - // - Node.DOCUMENT_NODE - // - Object - // - Any - return owner.nodeType === 1 || owner.nodeType === 9 || !( +owner.nodeType ); -}; - - - - -function Data() { - this.expando = jQuery.expando + Data.uid++; -} - -Data.uid = 1; - -Data.prototype = { - - cache: function( owner ) { - - // Check if the owner object already has a cache - var value = owner[ this.expando ]; - - // If not, create one - if ( !value ) { - value = {}; - - // We can accept data for non-element nodes in modern browsers, - // but we should not, see #8335. - // Always return an empty object. - if ( acceptData( owner ) ) { - - // If it is a node unlikely to be stringify-ed or looped over - // use plain assignment - if ( owner.nodeType ) { - owner[ this.expando ] = value; - - // Otherwise secure it in a non-enumerable property - // configurable must be true to allow the property to be - // deleted when data is removed - } else { - Object.defineProperty( owner, this.expando, { - value: value, - configurable: true - } ); - } - } - } - - return value; - }, - set: function( owner, data, value ) { - var prop, - cache = this.cache( owner ); - - // Handle: [ owner, key, value ] args - // Always use camelCase key (gh-2257) - if ( typeof data === "string" ) { - cache[ camelCase( data ) ] = value; - - // Handle: [ owner, { properties } ] args - } else { - - // Copy the properties one-by-one to the cache object - for ( prop in data ) { - cache[ camelCase( prop ) ] = data[ prop ]; - } - } - return cache; - }, - get: function( owner, key ) { - return key === undefined ? - this.cache( owner ) : - - // Always use camelCase key (gh-2257) - owner[ this.expando ] && owner[ this.expando ][ camelCase( key ) ]; - }, - access: function( owner, key, value ) { - - // In cases where either: - // - // 1. No key was specified - // 2. A string key was specified, but no value provided - // - // Take the "read" path and allow the get method to determine - // which value to return, respectively either: - // - // 1. The entire cache object - // 2. The data stored at the key - // - if ( key === undefined || - ( ( key && typeof key === "string" ) && value === undefined ) ) { - - return this.get( owner, key ); - } - - // When the key is not a string, or both a key and value - // are specified, set or extend (existing objects) with either: - // - // 1. An object of properties - // 2. A key and value - // - this.set( owner, key, value ); - - // Since the "set" path can have two possible entry points - // return the expected data based on which path was taken[*] - return value !== undefined ? value : key; - }, - remove: function( owner, key ) { - var i, - cache = owner[ this.expando ]; - - if ( cache === undefined ) { - return; - } - - if ( key !== undefined ) { - - // Support array or space separated string of keys - if ( Array.isArray( key ) ) { - - // If key is an array of keys... - // We always set camelCase keys, so remove that. - key = key.map( camelCase ); - } else { - key = camelCase( key ); - - // If a key with the spaces exists, use it. - // Otherwise, create an array by matching non-whitespace - key = key in cache ? - [ key ] : - ( key.match( rnothtmlwhite ) || [] ); - } - - i = key.length; - - while ( i-- ) { - delete cache[ key[ i ] ]; - } - } - - // Remove the expando if there's no more data - if ( key === undefined || jQuery.isEmptyObject( cache ) ) { - - // Support: Chrome <=35 - 45 - // Webkit & Blink performance suffers when deleting properties - // from DOM nodes, so set to undefined instead - // https://bugs.chromium.org/p/chromium/issues/detail?id=378607 (bug restricted) - if ( owner.nodeType ) { - owner[ this.expando ] = undefined; - } else { - delete owner[ this.expando ]; - } - } - }, - hasData: function( owner ) { - var cache = owner[ this.expando ]; - return cache !== undefined && !jQuery.isEmptyObject( cache ); - } -}; -var dataPriv = new Data(); - -var dataUser = new Data(); - - - -// Implementation Summary -// -// 1. Enforce API surface and semantic compatibility with 1.9.x branch -// 2. Improve the module's maintainability by reducing the storage -// paths to a single mechanism. -// 3. Use the same single mechanism to support "private" and "user" data. -// 4. _Never_ expose "private" data to user code (TODO: Drop _data, _removeData) -// 5. Avoid exposing implementation details on user objects (eg. expando properties) -// 6. Provide a clear path for implementation upgrade to WeakMap in 2014 - -var rbrace = /^(?:\{[\w\W]*\}|\[[\w\W]*\])$/, - rmultiDash = /[A-Z]/g; - -function getData( data ) { - if ( data === "true" ) { - return true; - } - - if ( data === "false" ) { - return false; - } - - if ( data === "null" ) { - return null; - } - - // Only convert to a number if it doesn't change the string - if ( data === +data + "" ) { - return +data; - } - - if ( rbrace.test( data ) ) { - return JSON.parse( data ); - } - - return data; -} - -function dataAttr( elem, key, data ) { - var name; - - // If nothing was found internally, try to fetch any - // data from the HTML5 data-* attribute - if ( data === undefined && elem.nodeType === 1 ) { - name = "data-" + key.replace( rmultiDash, "-$&" ).toLowerCase(); - data = elem.getAttribute( name ); - - if ( typeof data === "string" ) { - try { - data = getData( data ); - } catch ( e ) {} - - // Make sure we set the data so it isn't changed later - dataUser.set( elem, key, data ); - } else { - data = undefined; - } - } - return data; -} - -jQuery.extend( { - hasData: function( elem ) { - return dataUser.hasData( elem ) || dataPriv.hasData( elem ); - }, - - data: function( elem, name, data ) { - return dataUser.access( elem, name, data ); - }, - - removeData: function( elem, name ) { - dataUser.remove( elem, name ); - }, - - // TODO: Now that all calls to _data and _removeData have been replaced - // with direct calls to dataPriv methods, these can be deprecated. - _data: function( elem, name, data ) { - return dataPriv.access( elem, name, data ); - }, - - _removeData: function( elem, name ) { - dataPriv.remove( elem, name ); - } -} ); - -jQuery.fn.extend( { - data: function( key, value ) { - var i, name, data, - elem = this[ 0 ], - attrs = elem && elem.attributes; - - // Gets all values - if ( key === undefined ) { - if ( this.length ) { - data = dataUser.get( elem ); - - if ( elem.nodeType === 1 && !dataPriv.get( elem, "hasDataAttrs" ) ) { - i = attrs.length; - while ( i-- ) { - - // Support: IE 11 only - // The attrs elements can be null (#14894) - if ( attrs[ i ] ) { - name = attrs[ i ].name; - if ( name.indexOf( "data-" ) === 0 ) { - name = camelCase( name.slice( 5 ) ); - dataAttr( elem, name, data[ name ] ); - } - } - } - dataPriv.set( elem, "hasDataAttrs", true ); - } - } - - return data; - } - - // Sets multiple values - if ( typeof key === "object" ) { - return this.each( function() { - dataUser.set( this, key ); - } ); - } - - return access( this, function( value ) { - var data; - - // The calling jQuery object (element matches) is not empty - // (and therefore has an element appears at this[ 0 ]) and the - // `value` parameter was not undefined. An empty jQuery object - // will result in `undefined` for elem = this[ 0 ] which will - // throw an exception if an attempt to read a data cache is made. - if ( elem && value === undefined ) { - - // Attempt to get data from the cache - // The key will always be camelCased in Data - data = dataUser.get( elem, key ); - if ( data !== undefined ) { - return data; - } - - // Attempt to "discover" the data in - // HTML5 custom data-* attrs - data = dataAttr( elem, key ); - if ( data !== undefined ) { - return data; - } - - // We tried really hard, but the data doesn't exist. - return; - } - - // Set the data... - this.each( function() { - - // We always store the camelCased key - dataUser.set( this, key, value ); - } ); - }, null, value, arguments.length > 1, null, true ); - }, - - removeData: function( key ) { - return this.each( function() { - dataUser.remove( this, key ); - } ); - } -} ); - - -jQuery.extend( { - queue: function( elem, type, data ) { - var queue; - - if ( elem ) { - type = ( type || "fx" ) + "queue"; - queue = dataPriv.get( elem, type ); - - // Speed up dequeue by getting out quickly if this is just a lookup - if ( data ) { - if ( !queue || Array.isArray( data ) ) { - queue = dataPriv.access( elem, type, jQuery.makeArray( data ) ); - } else { - queue.push( data ); - } - } - return queue || []; - } - }, - - dequeue: function( elem, type ) { - type = type || "fx"; - - var queue = jQuery.queue( elem, type ), - startLength = queue.length, - fn = queue.shift(), - hooks = jQuery._queueHooks( elem, type ), - next = function() { - jQuery.dequeue( elem, type ); - }; - - // If the fx queue is dequeued, always remove the progress sentinel - if ( fn === "inprogress" ) { - fn = queue.shift(); - startLength--; - } - - if ( fn ) { - - // Add a progress sentinel to prevent the fx queue from being - // automatically dequeued - if ( type === "fx" ) { - queue.unshift( "inprogress" ); - } - - // Clear up the last queue stop function - delete hooks.stop; - fn.call( elem, next, hooks ); - } - - if ( !startLength && hooks ) { - hooks.empty.fire(); - } - }, - - // Not public - generate a queueHooks object, or return the current one - _queueHooks: function( elem, type ) { - var key = type + "queueHooks"; - return dataPriv.get( elem, key ) || dataPriv.access( elem, key, { - empty: jQuery.Callbacks( "once memory" ).add( function() { - dataPriv.remove( elem, [ type + "queue", key ] ); - } ) - } ); - } -} ); - -jQuery.fn.extend( { - queue: function( type, data ) { - var setter = 2; - - if ( typeof type !== "string" ) { - data = type; - type = "fx"; - setter--; - } - - if ( arguments.length < setter ) { - return jQuery.queue( this[ 0 ], type ); - } - - return data === undefined ? - this : - this.each( function() { - var queue = jQuery.queue( this, type, data ); - - // Ensure a hooks for this queue - jQuery._queueHooks( this, type ); - - if ( type === "fx" && queue[ 0 ] !== "inprogress" ) { - jQuery.dequeue( this, type ); - } - } ); - }, - dequeue: function( type ) { - return this.each( function() { - jQuery.dequeue( this, type ); - } ); - }, - clearQueue: function( type ) { - return this.queue( type || "fx", [] ); - }, - - // Get a promise resolved when queues of a certain type - // are emptied (fx is the type by default) - promise: function( type, obj ) { - var tmp, - count = 1, - defer = jQuery.Deferred(), - elements = this, - i = this.length, - resolve = function() { - if ( !( --count ) ) { - defer.resolveWith( elements, [ elements ] ); - } - }; - - if ( typeof type !== "string" ) { - obj = type; - type = undefined; - } - type = type || "fx"; - - while ( i-- ) { - tmp = dataPriv.get( elements[ i ], type + "queueHooks" ); - if ( tmp && tmp.empty ) { - count++; - tmp.empty.add( resolve ); - } - } - resolve(); - return defer.promise( obj ); - } -} ); -var pnum = ( /[+-]?(?:\d*\.|)\d+(?:[eE][+-]?\d+|)/ ).source; - -var rcssNum = new RegExp( "^(?:([+-])=|)(" + pnum + ")([a-z%]*)$", "i" ); - - -var cssExpand = [ "Top", "Right", "Bottom", "Left" ]; - -var documentElement = document.documentElement; - - - - var isAttached = function( elem ) { - return jQuery.contains( elem.ownerDocument, elem ); - }, - composed = { composed: true }; - - // Support: IE 9 - 11+, Edge 12 - 18+, iOS 10.0 - 10.2 only - // Check attachment across shadow DOM boundaries when possible (gh-3504) - // Support: iOS 10.0-10.2 only - // Early iOS 10 versions support `attachShadow` but not `getRootNode`, - // leading to errors. We need to check for `getRootNode`. - if ( documentElement.getRootNode ) { - isAttached = function( elem ) { - return jQuery.contains( elem.ownerDocument, elem ) || - elem.getRootNode( composed ) === elem.ownerDocument; - }; - } -var isHiddenWithinTree = function( elem, el ) { - - // isHiddenWithinTree might be called from jQuery#filter function; - // in that case, element will be second argument - elem = el || elem; - - // Inline style trumps all - return elem.style.display === "none" || - elem.style.display === "" && - - // Otherwise, check computed style - // Support: Firefox <=43 - 45 - // Disconnected elements can have computed display: none, so first confirm that elem is - // in the document. - isAttached( elem ) && - - jQuery.css( elem, "display" ) === "none"; - }; - - - -function adjustCSS( elem, prop, valueParts, tween ) { - var adjusted, scale, - maxIterations = 20, - currentValue = tween ? - function() { - return tween.cur(); - } : - function() { - return jQuery.css( elem, prop, "" ); - }, - initial = currentValue(), - unit = valueParts && valueParts[ 3 ] || ( jQuery.cssNumber[ prop ] ? "" : "px" ), - - // Starting value computation is required for potential unit mismatches - initialInUnit = elem.nodeType && - ( jQuery.cssNumber[ prop ] || unit !== "px" && +initial ) && - rcssNum.exec( jQuery.css( elem, prop ) ); - - if ( initialInUnit && initialInUnit[ 3 ] !== unit ) { - - // Support: Firefox <=54 - // Halve the iteration target value to prevent interference from CSS upper bounds (gh-2144) - initial = initial / 2; - - // Trust units reported by jQuery.css - unit = unit || initialInUnit[ 3 ]; - - // Iteratively approximate from a nonzero starting point - initialInUnit = +initial || 1; - - while ( maxIterations-- ) { - - // Evaluate and update our best guess (doubling guesses that zero out). - // Finish if the scale equals or crosses 1 (making the old*new product non-positive). - jQuery.style( elem, prop, initialInUnit + unit ); - if ( ( 1 - scale ) * ( 1 - ( scale = currentValue() / initial || 0.5 ) ) <= 0 ) { - maxIterations = 0; - } - initialInUnit = initialInUnit / scale; - - } - - initialInUnit = initialInUnit * 2; - jQuery.style( elem, prop, initialInUnit + unit ); - - // Make sure we update the tween properties later on - valueParts = valueParts || []; - } - - if ( valueParts ) { - initialInUnit = +initialInUnit || +initial || 0; - - // Apply relative offset (+=/-=) if specified - adjusted = valueParts[ 1 ] ? - initialInUnit + ( valueParts[ 1 ] + 1 ) * valueParts[ 2 ] : - +valueParts[ 2 ]; - if ( tween ) { - tween.unit = unit; - tween.start = initialInUnit; - tween.end = adjusted; - } - } - return adjusted; -} - - -var defaultDisplayMap = {}; - -function getDefaultDisplay( elem ) { - var temp, - doc = elem.ownerDocument, - nodeName = elem.nodeName, - display = defaultDisplayMap[ nodeName ]; - - if ( display ) { - return display; - } - - temp = doc.body.appendChild( doc.createElement( nodeName ) ); - display = jQuery.css( temp, "display" ); - - temp.parentNode.removeChild( temp ); - - if ( display === "none" ) { - display = "block"; - } - defaultDisplayMap[ nodeName ] = display; - - return display; -} - -function showHide( elements, show ) { - var display, elem, - values = [], - index = 0, - length = elements.length; - - // Determine new display value for elements that need to change - for ( ; index < length; index++ ) { - elem = elements[ index ]; - if ( !elem.style ) { - continue; - } - - display = elem.style.display; - if ( show ) { - - // Since we force visibility upon cascade-hidden elements, an immediate (and slow) - // check is required in this first loop unless we have a nonempty display value (either - // inline or about-to-be-restored) - if ( display === "none" ) { - values[ index ] = dataPriv.get( elem, "display" ) || null; - if ( !values[ index ] ) { - elem.style.display = ""; - } - } - if ( elem.style.display === "" && isHiddenWithinTree( elem ) ) { - values[ index ] = getDefaultDisplay( elem ); - } - } else { - if ( display !== "none" ) { - values[ index ] = "none"; - - // Remember what we're overwriting - dataPriv.set( elem, "display", display ); - } - } - } - - // Set the display of the elements in a second loop to avoid constant reflow - for ( index = 0; index < length; index++ ) { - if ( values[ index ] != null ) { - elements[ index ].style.display = values[ index ]; - } - } - - return elements; -} - -jQuery.fn.extend( { - show: function() { - return showHide( this, true ); - }, - hide: function() { - return showHide( this ); - }, - toggle: function( state ) { - if ( typeof state === "boolean" ) { - return state ? this.show() : this.hide(); - } - - return this.each( function() { - if ( isHiddenWithinTree( this ) ) { - jQuery( this ).show(); - } else { - jQuery( this ).hide(); - } - } ); - } -} ); -var rcheckableType = ( /^(?:checkbox|radio)$/i ); - -var rtagName = ( /<([a-z][^\/\0>\x20\t\r\n\f]*)/i ); - -var rscriptType = ( /^$|^module$|\/(?:java|ecma)script/i ); - - - -( function() { - var fragment = document.createDocumentFragment(), - div = fragment.appendChild( document.createElement( "div" ) ), - input = document.createElement( "input" ); - - // Support: Android 4.0 - 4.3 only - // Check state lost if the name is set (#11217) - // Support: Windows Web Apps (WWA) - // `name` and `type` must use .setAttribute for WWA (#14901) - input.setAttribute( "type", "radio" ); - input.setAttribute( "checked", "checked" ); - input.setAttribute( "name", "t" ); - - div.appendChild( input ); - - // Support: Android <=4.1 only - // Older WebKit doesn't clone checked state correctly in fragments - support.checkClone = div.cloneNode( true ).cloneNode( true ).lastChild.checked; - - // Support: IE <=11 only - // Make sure textarea (and checkbox) defaultValue is properly cloned - div.innerHTML = ""; - support.noCloneChecked = !!div.cloneNode( true ).lastChild.defaultValue; - - // Support: IE <=9 only - // IE <=9 replaces "; - support.option = !!div.lastChild; -} )(); - - -// We have to close these tags to support XHTML (#13200) -var wrapMap = { - - // XHTML parsers do not magically insert elements in the - // same way that tag soup parsers do. So we cannot shorten - // this by omitting or other required elements. - thead: [ 1, "", "
" ], - col: [ 2, "", "
" ], - tr: [ 2, "", "
" ], - td: [ 3, "", "
" ], - - _default: [ 0, "", "" ] -}; - -wrapMap.tbody = wrapMap.tfoot = wrapMap.colgroup = wrapMap.caption = wrapMap.thead; -wrapMap.th = wrapMap.td; - -// Support: IE <=9 only -if ( !support.option ) { - wrapMap.optgroup = wrapMap.option = [ 1, "" ]; -} - - -function getAll( context, tag ) { - - // Support: IE <=9 - 11 only - // Use typeof to avoid zero-argument method invocation on host objects (#15151) - var ret; - - if ( typeof context.getElementsByTagName !== "undefined" ) { - ret = context.getElementsByTagName( tag || "*" ); - - } else if ( typeof context.querySelectorAll !== "undefined" ) { - ret = context.querySelectorAll( tag || "*" ); - - } else { - ret = []; - } - - if ( tag === undefined || tag && nodeName( context, tag ) ) { - return jQuery.merge( [ context ], ret ); - } - - return ret; -} - - -// Mark scripts as having already been evaluated -function setGlobalEval( elems, refElements ) { - var i = 0, - l = elems.length; - - for ( ; i < l; i++ ) { - dataPriv.set( - elems[ i ], - "globalEval", - !refElements || dataPriv.get( refElements[ i ], "globalEval" ) - ); - } -} - - -var rhtml = /<|&#?\w+;/; - -function buildFragment( elems, context, scripts, selection, ignored ) { - var elem, tmp, tag, wrap, attached, j, - fragment = context.createDocumentFragment(), - nodes = [], - i = 0, - l = elems.length; - - for ( ; i < l; i++ ) { - elem = elems[ i ]; - - if ( elem || elem === 0 ) { - - // Add nodes directly - if ( toType( elem ) === "object" ) { - - // Support: Android <=4.0 only, PhantomJS 1 only - // push.apply(_, arraylike) throws on ancient WebKit - jQuery.merge( nodes, elem.nodeType ? [ elem ] : elem ); - - // Convert non-html into a text node - } else if ( !rhtml.test( elem ) ) { - nodes.push( context.createTextNode( elem ) ); - - // Convert html into DOM nodes - } else { - tmp = tmp || fragment.appendChild( context.createElement( "div" ) ); - - // Deserialize a standard representation - tag = ( rtagName.exec( elem ) || [ "", "" ] )[ 1 ].toLowerCase(); - wrap = wrapMap[ tag ] || wrapMap._default; - tmp.innerHTML = wrap[ 1 ] + jQuery.htmlPrefilter( elem ) + wrap[ 2 ]; - - // Descend through wrappers to the right content - j = wrap[ 0 ]; - while ( j-- ) { - tmp = tmp.lastChild; - } - - // Support: Android <=4.0 only, PhantomJS 1 only - // push.apply(_, arraylike) throws on ancient WebKit - jQuery.merge( nodes, tmp.childNodes ); - - // Remember the top-level container - tmp = fragment.firstChild; - - // Ensure the created nodes are orphaned (#12392) - tmp.textContent = ""; - } - } - } - - // Remove wrapper from fragment - fragment.textContent = ""; - - i = 0; - while ( ( elem = nodes[ i++ ] ) ) { - - // Skip elements already in the context collection (trac-4087) - if ( selection && jQuery.inArray( elem, selection ) > -1 ) { - if ( ignored ) { - ignored.push( elem ); - } - continue; - } - - attached = isAttached( elem ); - - // Append to fragment - tmp = getAll( fragment.appendChild( elem ), "script" ); - - // Preserve script evaluation history - if ( attached ) { - setGlobalEval( tmp ); - } - - // Capture executables - if ( scripts ) { - j = 0; - while ( ( elem = tmp[ j++ ] ) ) { - if ( rscriptType.test( elem.type || "" ) ) { - scripts.push( elem ); - } - } - } - } - - return fragment; -} - - -var - rkeyEvent = /^key/, - rmouseEvent = /^(?:mouse|pointer|contextmenu|drag|drop)|click/, - rtypenamespace = /^([^.]*)(?:\.(.+)|)/; - -function returnTrue() { - return true; -} - -function returnFalse() { - return false; -} - -// Support: IE <=9 - 11+ -// focus() and blur() are asynchronous, except when they are no-op. -// So expect focus to be synchronous when the element is already active, -// and blur to be synchronous when the element is not already active. -// (focus and blur are always synchronous in other supported browsers, -// this just defines when we can count on it). -function expectSync( elem, type ) { - return ( elem === safeActiveElement() ) === ( type === "focus" ); -} - -// Support: IE <=9 only -// Accessing document.activeElement can throw unexpectedly -// https://bugs.jquery.com/ticket/13393 -function safeActiveElement() { - try { - return document.activeElement; - } catch ( err ) { } -} - -function on( elem, types, selector, data, fn, one ) { - var origFn, type; - - // Types can be a map of types/handlers - if ( typeof types === "object" ) { - - // ( types-Object, selector, data ) - if ( typeof selector !== "string" ) { - - // ( types-Object, data ) - data = data || selector; - selector = undefined; - } - for ( type in types ) { - on( elem, type, selector, data, types[ type ], one ); - } - return elem; - } - - if ( data == null && fn == null ) { - - // ( types, fn ) - fn = selector; - data = selector = undefined; - } else if ( fn == null ) { - if ( typeof selector === "string" ) { - - // ( types, selector, fn ) - fn = data; - data = undefined; - } else { - - // ( types, data, fn ) - fn = data; - data = selector; - selector = undefined; - } - } - if ( fn === false ) { - fn = returnFalse; - } else if ( !fn ) { - return elem; - } - - if ( one === 1 ) { - origFn = fn; - fn = function( event ) { - - // Can use an empty set, since event contains the info - jQuery().off( event ); - return origFn.apply( this, arguments ); - }; - - // Use same guid so caller can remove using origFn - fn.guid = origFn.guid || ( origFn.guid = jQuery.guid++ ); - } - return elem.each( function() { - jQuery.event.add( this, types, fn, data, selector ); - } ); -} - -/* - * Helper functions for managing events -- not part of the public interface. - * Props to Dean Edwards' addEvent library for many of the ideas. - */ -jQuery.event = { - - global: {}, - - add: function( elem, types, handler, data, selector ) { - - var handleObjIn, eventHandle, tmp, - events, t, handleObj, - special, handlers, type, namespaces, origType, - elemData = dataPriv.get( elem ); - - // Only attach events to objects that accept data - if ( !acceptData( elem ) ) { - return; - } - - // Caller can pass in an object of custom data in lieu of the handler - if ( handler.handler ) { - handleObjIn = handler; - handler = handleObjIn.handler; - selector = handleObjIn.selector; - } - - // Ensure that invalid selectors throw exceptions at attach time - // Evaluate against documentElement in case elem is a non-element node (e.g., document) - if ( selector ) { - jQuery.find.matchesSelector( documentElement, selector ); - } - - // Make sure that the handler has a unique ID, used to find/remove it later - if ( !handler.guid ) { - handler.guid = jQuery.guid++; - } - - // Init the element's event structure and main handler, if this is the first - if ( !( events = elemData.events ) ) { - events = elemData.events = Object.create( null ); - } - if ( !( eventHandle = elemData.handle ) ) { - eventHandle = elemData.handle = function( e ) { - - // Discard the second event of a jQuery.event.trigger() and - // when an event is called after a page has unloaded - return typeof jQuery !== "undefined" && jQuery.event.triggered !== e.type ? - jQuery.event.dispatch.apply( elem, arguments ) : undefined; - }; - } - - // Handle multiple events separated by a space - types = ( types || "" ).match( rnothtmlwhite ) || [ "" ]; - t = types.length; - while ( t-- ) { - tmp = rtypenamespace.exec( types[ t ] ) || []; - type = origType = tmp[ 1 ]; - namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort(); - - // There *must* be a type, no attaching namespace-only handlers - if ( !type ) { - continue; - } - - // If event changes its type, use the special event handlers for the changed type - special = jQuery.event.special[ type ] || {}; - - // If selector defined, determine special event api type, otherwise given type - type = ( selector ? special.delegateType : special.bindType ) || type; - - // Update special based on newly reset type - special = jQuery.event.special[ type ] || {}; - - // handleObj is passed to all event handlers - handleObj = jQuery.extend( { - type: type, - origType: origType, - data: data, - handler: handler, - guid: handler.guid, - selector: selector, - needsContext: selector && jQuery.expr.match.needsContext.test( selector ), - namespace: namespaces.join( "." ) - }, handleObjIn ); - - // Init the event handler queue if we're the first - if ( !( handlers = events[ type ] ) ) { - handlers = events[ type ] = []; - handlers.delegateCount = 0; - - // Only use addEventListener if the special events handler returns false - if ( !special.setup || - special.setup.call( elem, data, namespaces, eventHandle ) === false ) { - - if ( elem.addEventListener ) { - elem.addEventListener( type, eventHandle ); - } - } - } - - if ( special.add ) { - special.add.call( elem, handleObj ); - - if ( !handleObj.handler.guid ) { - handleObj.handler.guid = handler.guid; - } - } - - // Add to the element's handler list, delegates in front - if ( selector ) { - handlers.splice( handlers.delegateCount++, 0, handleObj ); - } else { - handlers.push( handleObj ); - } - - // Keep track of which events have ever been used, for event optimization - jQuery.event.global[ type ] = true; - } - - }, - - // Detach an event or set of events from an element - remove: function( elem, types, handler, selector, mappedTypes ) { - - var j, origCount, tmp, - events, t, handleObj, - special, handlers, type, namespaces, origType, - elemData = dataPriv.hasData( elem ) && dataPriv.get( elem ); - - if ( !elemData || !( events = elemData.events ) ) { - return; - } - - // Once for each type.namespace in types; type may be omitted - types = ( types || "" ).match( rnothtmlwhite ) || [ "" ]; - t = types.length; - while ( t-- ) { - tmp = rtypenamespace.exec( types[ t ] ) || []; - type = origType = tmp[ 1 ]; - namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort(); - - // Unbind all events (on this namespace, if provided) for the element - if ( !type ) { - for ( type in events ) { - jQuery.event.remove( elem, type + types[ t ], handler, selector, true ); - } - continue; - } - - special = jQuery.event.special[ type ] || {}; - type = ( selector ? special.delegateType : special.bindType ) || type; - handlers = events[ type ] || []; - tmp = tmp[ 2 ] && - new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ); - - // Remove matching events - origCount = j = handlers.length; - while ( j-- ) { - handleObj = handlers[ j ]; - - if ( ( mappedTypes || origType === handleObj.origType ) && - ( !handler || handler.guid === handleObj.guid ) && - ( !tmp || tmp.test( handleObj.namespace ) ) && - ( !selector || selector === handleObj.selector || - selector === "**" && handleObj.selector ) ) { - handlers.splice( j, 1 ); - - if ( handleObj.selector ) { - handlers.delegateCount--; - } - if ( special.remove ) { - special.remove.call( elem, handleObj ); - } - } - } - - // Remove generic event handler if we removed something and no more handlers exist - // (avoids potential for endless recursion during removal of special event handlers) - if ( origCount && !handlers.length ) { - if ( !special.teardown || - special.teardown.call( elem, namespaces, elemData.handle ) === false ) { - - jQuery.removeEvent( elem, type, elemData.handle ); - } - - delete events[ type ]; - } - } - - // Remove data and the expando if it's no longer used - if ( jQuery.isEmptyObject( events ) ) { - dataPriv.remove( elem, "handle events" ); - } - }, - - dispatch: function( nativeEvent ) { - - var i, j, ret, matched, handleObj, handlerQueue, - args = new Array( arguments.length ), - - // Make a writable jQuery.Event from the native event object - event = jQuery.event.fix( nativeEvent ), - - handlers = ( - dataPriv.get( this, "events" ) || Object.create( null ) - )[ event.type ] || [], - special = jQuery.event.special[ event.type ] || {}; - - // Use the fix-ed jQuery.Event rather than the (read-only) native event - args[ 0 ] = event; - - for ( i = 1; i < arguments.length; i++ ) { - args[ i ] = arguments[ i ]; - } - - event.delegateTarget = this; - - // Call the preDispatch hook for the mapped type, and let it bail if desired - if ( special.preDispatch && special.preDispatch.call( this, event ) === false ) { - return; - } - - // Determine handlers - handlerQueue = jQuery.event.handlers.call( this, event, handlers ); - - // Run delegates first; they may want to stop propagation beneath us - i = 0; - while ( ( matched = handlerQueue[ i++ ] ) && !event.isPropagationStopped() ) { - event.currentTarget = matched.elem; - - j = 0; - while ( ( handleObj = matched.handlers[ j++ ] ) && - !event.isImmediatePropagationStopped() ) { - - // If the event is namespaced, then each handler is only invoked if it is - // specially universal or its namespaces are a superset of the event's. - if ( !event.rnamespace || handleObj.namespace === false || - event.rnamespace.test( handleObj.namespace ) ) { - - event.handleObj = handleObj; - event.data = handleObj.data; - - ret = ( ( jQuery.event.special[ handleObj.origType ] || {} ).handle || - handleObj.handler ).apply( matched.elem, args ); - - if ( ret !== undefined ) { - if ( ( event.result = ret ) === false ) { - event.preventDefault(); - event.stopPropagation(); - } - } - } - } - } - - // Call the postDispatch hook for the mapped type - if ( special.postDispatch ) { - special.postDispatch.call( this, event ); - } - - return event.result; - }, - - handlers: function( event, handlers ) { - var i, handleObj, sel, matchedHandlers, matchedSelectors, - handlerQueue = [], - delegateCount = handlers.delegateCount, - cur = event.target; - - // Find delegate handlers - if ( delegateCount && - - // Support: IE <=9 - // Black-hole SVG instance trees (trac-13180) - cur.nodeType && - - // Support: Firefox <=42 - // Suppress spec-violating clicks indicating a non-primary pointer button (trac-3861) - // https://www.w3.org/TR/DOM-Level-3-Events/#event-type-click - // Support: IE 11 only - // ...but not arrow key "clicks" of radio inputs, which can have `button` -1 (gh-2343) - !( event.type === "click" && event.button >= 1 ) ) { - - for ( ; cur !== this; cur = cur.parentNode || this ) { - - // Don't check non-elements (#13208) - // Don't process clicks on disabled elements (#6911, #8165, #11382, #11764) - if ( cur.nodeType === 1 && !( event.type === "click" && cur.disabled === true ) ) { - matchedHandlers = []; - matchedSelectors = {}; - for ( i = 0; i < delegateCount; i++ ) { - handleObj = handlers[ i ]; - - // Don't conflict with Object.prototype properties (#13203) - sel = handleObj.selector + " "; - - if ( matchedSelectors[ sel ] === undefined ) { - matchedSelectors[ sel ] = handleObj.needsContext ? - jQuery( sel, this ).index( cur ) > -1 : - jQuery.find( sel, this, null, [ cur ] ).length; - } - if ( matchedSelectors[ sel ] ) { - matchedHandlers.push( handleObj ); - } - } - if ( matchedHandlers.length ) { - handlerQueue.push( { elem: cur, handlers: matchedHandlers } ); - } - } - } - } - - // Add the remaining (directly-bound) handlers - cur = this; - if ( delegateCount < handlers.length ) { - handlerQueue.push( { elem: cur, handlers: handlers.slice( delegateCount ) } ); - } - - return handlerQueue; - }, - - addProp: function( name, hook ) { - Object.defineProperty( jQuery.Event.prototype, name, { - enumerable: true, - configurable: true, - - get: isFunction( hook ) ? - function() { - if ( this.originalEvent ) { - return hook( this.originalEvent ); - } - } : - function() { - if ( this.originalEvent ) { - return this.originalEvent[ name ]; - } - }, - - set: function( value ) { - Object.defineProperty( this, name, { - enumerable: true, - configurable: true, - writable: true, - value: value - } ); - } - } ); - }, - - fix: function( originalEvent ) { - return originalEvent[ jQuery.expando ] ? - originalEvent : - new jQuery.Event( originalEvent ); - }, - - special: { - load: { - - // Prevent triggered image.load events from bubbling to window.load - noBubble: true - }, - click: { - - // Utilize native event to ensure correct state for checkable inputs - setup: function( data ) { - - // For mutual compressibility with _default, replace `this` access with a local var. - // `|| data` is dead code meant only to preserve the variable through minification. - var el = this || data; - - // Claim the first handler - if ( rcheckableType.test( el.type ) && - el.click && nodeName( el, "input" ) ) { - - // dataPriv.set( el, "click", ... ) - leverageNative( el, "click", returnTrue ); - } - - // Return false to allow normal processing in the caller - return false; - }, - trigger: function( data ) { - - // For mutual compressibility with _default, replace `this` access with a local var. - // `|| data` is dead code meant only to preserve the variable through minification. - var el = this || data; - - // Force setup before triggering a click - if ( rcheckableType.test( el.type ) && - el.click && nodeName( el, "input" ) ) { - - leverageNative( el, "click" ); - } - - // Return non-false to allow normal event-path propagation - return true; - }, - - // For cross-browser consistency, suppress native .click() on links - // Also prevent it if we're currently inside a leveraged native-event stack - _default: function( event ) { - var target = event.target; - return rcheckableType.test( target.type ) && - target.click && nodeName( target, "input" ) && - dataPriv.get( target, "click" ) || - nodeName( target, "a" ); - } - }, - - beforeunload: { - postDispatch: function( event ) { - - // Support: Firefox 20+ - // Firefox doesn't alert if the returnValue field is not set. - if ( event.result !== undefined && event.originalEvent ) { - event.originalEvent.returnValue = event.result; - } - } - } - } -}; - -// Ensure the presence of an event listener that handles manually-triggered -// synthetic events by interrupting progress until reinvoked in response to -// *native* events that it fires directly, ensuring that state changes have -// already occurred before other listeners are invoked. -function leverageNative( el, type, expectSync ) { - - // Missing expectSync indicates a trigger call, which must force setup through jQuery.event.add - if ( !expectSync ) { - if ( dataPriv.get( el, type ) === undefined ) { - jQuery.event.add( el, type, returnTrue ); - } - return; - } - - // Register the controller as a special universal handler for all event namespaces - dataPriv.set( el, type, false ); - jQuery.event.add( el, type, { - namespace: false, - handler: function( event ) { - var notAsync, result, - saved = dataPriv.get( this, type ); - - if ( ( event.isTrigger & 1 ) && this[ type ] ) { - - // Interrupt processing of the outer synthetic .trigger()ed event - // Saved data should be false in such cases, but might be a leftover capture object - // from an async native handler (gh-4350) - if ( !saved.length ) { - - // Store arguments for use when handling the inner native event - // There will always be at least one argument (an event object), so this array - // will not be confused with a leftover capture object. - saved = slice.call( arguments ); - dataPriv.set( this, type, saved ); - - // Trigger the native event and capture its result - // Support: IE <=9 - 11+ - // focus() and blur() are asynchronous - notAsync = expectSync( this, type ); - this[ type ](); - result = dataPriv.get( this, type ); - if ( saved !== result || notAsync ) { - dataPriv.set( this, type, false ); - } else { - result = {}; - } - if ( saved !== result ) { - - // Cancel the outer synthetic event - event.stopImmediatePropagation(); - event.preventDefault(); - return result.value; - } - - // If this is an inner synthetic event for an event with a bubbling surrogate - // (focus or blur), assume that the surrogate already propagated from triggering the - // native event and prevent that from happening again here. - // This technically gets the ordering wrong w.r.t. to `.trigger()` (in which the - // bubbling surrogate propagates *after* the non-bubbling base), but that seems - // less bad than duplication. - } else if ( ( jQuery.event.special[ type ] || {} ).delegateType ) { - event.stopPropagation(); - } - - // If this is a native event triggered above, everything is now in order - // Fire an inner synthetic event with the original arguments - } else if ( saved.length ) { - - // ...and capture the result - dataPriv.set( this, type, { - value: jQuery.event.trigger( - - // Support: IE <=9 - 11+ - // Extend with the prototype to reset the above stopImmediatePropagation() - jQuery.extend( saved[ 0 ], jQuery.Event.prototype ), - saved.slice( 1 ), - this - ) - } ); - - // Abort handling of the native event - event.stopImmediatePropagation(); - } - } - } ); -} - -jQuery.removeEvent = function( elem, type, handle ) { - - // This "if" is needed for plain objects - if ( elem.removeEventListener ) { - elem.removeEventListener( type, handle ); - } -}; - -jQuery.Event = function( src, props ) { - - // Allow instantiation without the 'new' keyword - if ( !( this instanceof jQuery.Event ) ) { - return new jQuery.Event( src, props ); - } - - // Event object - if ( src && src.type ) { - this.originalEvent = src; - this.type = src.type; - - // Events bubbling up the document may have been marked as prevented - // by a handler lower down the tree; reflect the correct value. - this.isDefaultPrevented = src.defaultPrevented || - src.defaultPrevented === undefined && - - // Support: Android <=2.3 only - src.returnValue === false ? - returnTrue : - returnFalse; - - // Create target properties - // Support: Safari <=6 - 7 only - // Target should not be a text node (#504, #13143) - this.target = ( src.target && src.target.nodeType === 3 ) ? - src.target.parentNode : - src.target; - - this.currentTarget = src.currentTarget; - this.relatedTarget = src.relatedTarget; - - // Event type - } else { - this.type = src; - } - - // Put explicitly provided properties onto the event object - if ( props ) { - jQuery.extend( this, props ); - } - - // Create a timestamp if incoming event doesn't have one - this.timeStamp = src && src.timeStamp || Date.now(); - - // Mark it as fixed - this[ jQuery.expando ] = true; -}; - -// jQuery.Event is based on DOM3 Events as specified by the ECMAScript Language Binding -// https://www.w3.org/TR/2003/WD-DOM-Level-3-Events-20030331/ecma-script-binding.html -jQuery.Event.prototype = { - constructor: jQuery.Event, - isDefaultPrevented: returnFalse, - isPropagationStopped: returnFalse, - isImmediatePropagationStopped: returnFalse, - isSimulated: false, - - preventDefault: function() { - var e = this.originalEvent; - - this.isDefaultPrevented = returnTrue; - - if ( e && !this.isSimulated ) { - e.preventDefault(); - } - }, - stopPropagation: function() { - var e = this.originalEvent; - - this.isPropagationStopped = returnTrue; - - if ( e && !this.isSimulated ) { - e.stopPropagation(); - } - }, - stopImmediatePropagation: function() { - var e = this.originalEvent; - - this.isImmediatePropagationStopped = returnTrue; - - if ( e && !this.isSimulated ) { - e.stopImmediatePropagation(); - } - - this.stopPropagation(); - } -}; - -// Includes all common event props including KeyEvent and MouseEvent specific props -jQuery.each( { - altKey: true, - bubbles: true, - cancelable: true, - changedTouches: true, - ctrlKey: true, - detail: true, - eventPhase: true, - metaKey: true, - pageX: true, - pageY: true, - shiftKey: true, - view: true, - "char": true, - code: true, - charCode: true, - key: true, - keyCode: true, - button: true, - buttons: true, - clientX: true, - clientY: true, - offsetX: true, - offsetY: true, - pointerId: true, - pointerType: true, - screenX: true, - screenY: true, - targetTouches: true, - toElement: true, - touches: true, - - which: function( event ) { - var button = event.button; - - // Add which for key events - if ( event.which == null && rkeyEvent.test( event.type ) ) { - return event.charCode != null ? event.charCode : event.keyCode; - } - - // Add which for click: 1 === left; 2 === middle; 3 === right - if ( !event.which && button !== undefined && rmouseEvent.test( event.type ) ) { - if ( button & 1 ) { - return 1; - } - - if ( button & 2 ) { - return 3; - } - - if ( button & 4 ) { - return 2; - } - - return 0; - } - - return event.which; - } -}, jQuery.event.addProp ); - -jQuery.each( { focus: "focusin", blur: "focusout" }, function( type, delegateType ) { - jQuery.event.special[ type ] = { - - // Utilize native event if possible so blur/focus sequence is correct - setup: function() { - - // Claim the first handler - // dataPriv.set( this, "focus", ... ) - // dataPriv.set( this, "blur", ... ) - leverageNative( this, type, expectSync ); - - // Return false to allow normal processing in the caller - return false; - }, - trigger: function() { - - // Force setup before trigger - leverageNative( this, type ); - - // Return non-false to allow normal event-path propagation - return true; - }, - - delegateType: delegateType - }; -} ); - -// Create mouseenter/leave events using mouseover/out and event-time checks -// so that event delegation works in jQuery. -// Do the same for pointerenter/pointerleave and pointerover/pointerout -// -// Support: Safari 7 only -// Safari sends mouseenter too often; see: -// https://bugs.chromium.org/p/chromium/issues/detail?id=470258 -// for the description of the bug (it existed in older Chrome versions as well). -jQuery.each( { - mouseenter: "mouseover", - mouseleave: "mouseout", - pointerenter: "pointerover", - pointerleave: "pointerout" -}, function( orig, fix ) { - jQuery.event.special[ orig ] = { - delegateType: fix, - bindType: fix, - - handle: function( event ) { - var ret, - target = this, - related = event.relatedTarget, - handleObj = event.handleObj; - - // For mouseenter/leave call the handler if related is outside the target. - // NB: No relatedTarget if the mouse left/entered the browser window - if ( !related || ( related !== target && !jQuery.contains( target, related ) ) ) { - event.type = handleObj.origType; - ret = handleObj.handler.apply( this, arguments ); - event.type = fix; - } - return ret; - } - }; -} ); - -jQuery.fn.extend( { - - on: function( types, selector, data, fn ) { - return on( this, types, selector, data, fn ); - }, - one: function( types, selector, data, fn ) { - return on( this, types, selector, data, fn, 1 ); - }, - off: function( types, selector, fn ) { - var handleObj, type; - if ( types && types.preventDefault && types.handleObj ) { - - // ( event ) dispatched jQuery.Event - handleObj = types.handleObj; - jQuery( types.delegateTarget ).off( - handleObj.namespace ? - handleObj.origType + "." + handleObj.namespace : - handleObj.origType, - handleObj.selector, - handleObj.handler - ); - return this; - } - if ( typeof types === "object" ) { - - // ( types-object [, selector] ) - for ( type in types ) { - this.off( type, selector, types[ type ] ); - } - return this; - } - if ( selector === false || typeof selector === "function" ) { - - // ( types [, fn] ) - fn = selector; - selector = undefined; - } - if ( fn === false ) { - fn = returnFalse; - } - return this.each( function() { - jQuery.event.remove( this, types, fn, selector ); - } ); - } -} ); - - -var - - // Support: IE <=10 - 11, Edge 12 - 13 only - // In IE/Edge using regex groups here causes severe slowdowns. - // See https://connect.microsoft.com/IE/feedback/details/1736512/ - rnoInnerhtml = /\s*$/g; - -// Prefer a tbody over its parent table for containing new rows -function manipulationTarget( elem, content ) { - if ( nodeName( elem, "table" ) && - nodeName( content.nodeType !== 11 ? content : content.firstChild, "tr" ) ) { - - return jQuery( elem ).children( "tbody" )[ 0 ] || elem; - } - - return elem; -} - -// Replace/restore the type attribute of script elements for safe DOM manipulation -function disableScript( elem ) { - elem.type = ( elem.getAttribute( "type" ) !== null ) + "/" + elem.type; - return elem; -} -function restoreScript( elem ) { - if ( ( elem.type || "" ).slice( 0, 5 ) === "true/" ) { - elem.type = elem.type.slice( 5 ); - } else { - elem.removeAttribute( "type" ); - } - - return elem; -} - -function cloneCopyEvent( src, dest ) { - var i, l, type, pdataOld, udataOld, udataCur, events; - - if ( dest.nodeType !== 1 ) { - return; - } - - // 1. Copy private data: events, handlers, etc. - if ( dataPriv.hasData( src ) ) { - pdataOld = dataPriv.get( src ); - events = pdataOld.events; - - if ( events ) { - dataPriv.remove( dest, "handle events" ); - - for ( type in events ) { - for ( i = 0, l = events[ type ].length; i < l; i++ ) { - jQuery.event.add( dest, type, events[ type ][ i ] ); - } - } - } - } - - // 2. Copy user data - if ( dataUser.hasData( src ) ) { - udataOld = dataUser.access( src ); - udataCur = jQuery.extend( {}, udataOld ); - - dataUser.set( dest, udataCur ); - } -} - -// Fix IE bugs, see support tests -function fixInput( src, dest ) { - var nodeName = dest.nodeName.toLowerCase(); - - // Fails to persist the checked state of a cloned checkbox or radio button. - if ( nodeName === "input" && rcheckableType.test( src.type ) ) { - dest.checked = src.checked; - - // Fails to return the selected option to the default selected state when cloning options - } else if ( nodeName === "input" || nodeName === "textarea" ) { - dest.defaultValue = src.defaultValue; - } -} - -function domManip( collection, args, callback, ignored ) { - - // Flatten any nested arrays - args = flat( args ); - - var fragment, first, scripts, hasScripts, node, doc, - i = 0, - l = collection.length, - iNoClone = l - 1, - value = args[ 0 ], - valueIsFunction = isFunction( value ); - - // We can't cloneNode fragments that contain checked, in WebKit - if ( valueIsFunction || - ( l > 1 && typeof value === "string" && - !support.checkClone && rchecked.test( value ) ) ) { - return collection.each( function( index ) { - var self = collection.eq( index ); - if ( valueIsFunction ) { - args[ 0 ] = value.call( this, index, self.html() ); - } - domManip( self, args, callback, ignored ); - } ); - } - - if ( l ) { - fragment = buildFragment( args, collection[ 0 ].ownerDocument, false, collection, ignored ); - first = fragment.firstChild; - - if ( fragment.childNodes.length === 1 ) { - fragment = first; - } - - // Require either new content or an interest in ignored elements to invoke the callback - if ( first || ignored ) { - scripts = jQuery.map( getAll( fragment, "script" ), disableScript ); - hasScripts = scripts.length; - - // Use the original fragment for the last item - // instead of the first because it can end up - // being emptied incorrectly in certain situations (#8070). - for ( ; i < l; i++ ) { - node = fragment; - - if ( i !== iNoClone ) { - node = jQuery.clone( node, true, true ); - - // Keep references to cloned scripts for later restoration - if ( hasScripts ) { - - // Support: Android <=4.0 only, PhantomJS 1 only - // push.apply(_, arraylike) throws on ancient WebKit - jQuery.merge( scripts, getAll( node, "script" ) ); - } - } - - callback.call( collection[ i ], node, i ); - } - - if ( hasScripts ) { - doc = scripts[ scripts.length - 1 ].ownerDocument; - - // Reenable scripts - jQuery.map( scripts, restoreScript ); - - // Evaluate executable scripts on first document insertion - for ( i = 0; i < hasScripts; i++ ) { - node = scripts[ i ]; - if ( rscriptType.test( node.type || "" ) && - !dataPriv.access( node, "globalEval" ) && - jQuery.contains( doc, node ) ) { - - if ( node.src && ( node.type || "" ).toLowerCase() !== "module" ) { - - // Optional AJAX dependency, but won't run scripts if not present - if ( jQuery._evalUrl && !node.noModule ) { - jQuery._evalUrl( node.src, { - nonce: node.nonce || node.getAttribute( "nonce" ) - }, doc ); - } - } else { - DOMEval( node.textContent.replace( rcleanScript, "" ), node, doc ); - } - } - } - } - } - } - - return collection; -} - -function remove( elem, selector, keepData ) { - var node, - nodes = selector ? jQuery.filter( selector, elem ) : elem, - i = 0; - - for ( ; ( node = nodes[ i ] ) != null; i++ ) { - if ( !keepData && node.nodeType === 1 ) { - jQuery.cleanData( getAll( node ) ); - } - - if ( node.parentNode ) { - if ( keepData && isAttached( node ) ) { - setGlobalEval( getAll( node, "script" ) ); - } - node.parentNode.removeChild( node ); - } - } - - return elem; -} - -jQuery.extend( { - htmlPrefilter: function( html ) { - return html; - }, - - clone: function( elem, dataAndEvents, deepDataAndEvents ) { - var i, l, srcElements, destElements, - clone = elem.cloneNode( true ), - inPage = isAttached( elem ); - - // Fix IE cloning issues - if ( !support.noCloneChecked && ( elem.nodeType === 1 || elem.nodeType === 11 ) && - !jQuery.isXMLDoc( elem ) ) { - - // We eschew Sizzle here for performance reasons: https://jsperf.com/getall-vs-sizzle/2 - destElements = getAll( clone ); - srcElements = getAll( elem ); - - for ( i = 0, l = srcElements.length; i < l; i++ ) { - fixInput( srcElements[ i ], destElements[ i ] ); - } - } - - // Copy the events from the original to the clone - if ( dataAndEvents ) { - if ( deepDataAndEvents ) { - srcElements = srcElements || getAll( elem ); - destElements = destElements || getAll( clone ); - - for ( i = 0, l = srcElements.length; i < l; i++ ) { - cloneCopyEvent( srcElements[ i ], destElements[ i ] ); - } - } else { - cloneCopyEvent( elem, clone ); - } - } - - // Preserve script evaluation history - destElements = getAll( clone, "script" ); - if ( destElements.length > 0 ) { - setGlobalEval( destElements, !inPage && getAll( elem, "script" ) ); - } - - // Return the cloned set - return clone; - }, - - cleanData: function( elems ) { - var data, elem, type, - special = jQuery.event.special, - i = 0; - - for ( ; ( elem = elems[ i ] ) !== undefined; i++ ) { - if ( acceptData( elem ) ) { - if ( ( data = elem[ dataPriv.expando ] ) ) { - if ( data.events ) { - for ( type in data.events ) { - if ( special[ type ] ) { - jQuery.event.remove( elem, type ); - - // This is a shortcut to avoid jQuery.event.remove's overhead - } else { - jQuery.removeEvent( elem, type, data.handle ); - } - } - } - - // Support: Chrome <=35 - 45+ - // Assign undefined instead of using delete, see Data#remove - elem[ dataPriv.expando ] = undefined; - } - if ( elem[ dataUser.expando ] ) { - - // Support: Chrome <=35 - 45+ - // Assign undefined instead of using delete, see Data#remove - elem[ dataUser.expando ] = undefined; - } - } - } - } -} ); - -jQuery.fn.extend( { - detach: function( selector ) { - return remove( this, selector, true ); - }, - - remove: function( selector ) { - return remove( this, selector ); - }, - - text: function( value ) { - return access( this, function( value ) { - return value === undefined ? - jQuery.text( this ) : - this.empty().each( function() { - if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { - this.textContent = value; - } - } ); - }, null, value, arguments.length ); - }, - - append: function() { - return domManip( this, arguments, function( elem ) { - if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { - var target = manipulationTarget( this, elem ); - target.appendChild( elem ); - } - } ); - }, - - prepend: function() { - return domManip( this, arguments, function( elem ) { - if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { - var target = manipulationTarget( this, elem ); - target.insertBefore( elem, target.firstChild ); - } - } ); - }, - - before: function() { - return domManip( this, arguments, function( elem ) { - if ( this.parentNode ) { - this.parentNode.insertBefore( elem, this ); - } - } ); - }, - - after: function() { - return domManip( this, arguments, function( elem ) { - if ( this.parentNode ) { - this.parentNode.insertBefore( elem, this.nextSibling ); - } - } ); - }, - - empty: function() { - var elem, - i = 0; - - for ( ; ( elem = this[ i ] ) != null; i++ ) { - if ( elem.nodeType === 1 ) { - - // Prevent memory leaks - jQuery.cleanData( getAll( elem, false ) ); - - // Remove any remaining nodes - elem.textContent = ""; - } - } - - return this; - }, - - clone: function( dataAndEvents, deepDataAndEvents ) { - dataAndEvents = dataAndEvents == null ? false : dataAndEvents; - deepDataAndEvents = deepDataAndEvents == null ? dataAndEvents : deepDataAndEvents; - - return this.map( function() { - return jQuery.clone( this, dataAndEvents, deepDataAndEvents ); - } ); - }, - - html: function( value ) { - return access( this, function( value ) { - var elem = this[ 0 ] || {}, - i = 0, - l = this.length; - - if ( value === undefined && elem.nodeType === 1 ) { - return elem.innerHTML; - } - - // See if we can take a shortcut and just use innerHTML - if ( typeof value === "string" && !rnoInnerhtml.test( value ) && - !wrapMap[ ( rtagName.exec( value ) || [ "", "" ] )[ 1 ].toLowerCase() ] ) { - - value = jQuery.htmlPrefilter( value ); - - try { - for ( ; i < l; i++ ) { - elem = this[ i ] || {}; - - // Remove element nodes and prevent memory leaks - if ( elem.nodeType === 1 ) { - jQuery.cleanData( getAll( elem, false ) ); - elem.innerHTML = value; - } - } - - elem = 0; - - // If using innerHTML throws an exception, use the fallback method - } catch ( e ) {} - } - - if ( elem ) { - this.empty().append( value ); - } - }, null, value, arguments.length ); - }, - - replaceWith: function() { - var ignored = []; - - // Make the changes, replacing each non-ignored context element with the new content - return domManip( this, arguments, function( elem ) { - var parent = this.parentNode; - - if ( jQuery.inArray( this, ignored ) < 0 ) { - jQuery.cleanData( getAll( this ) ); - if ( parent ) { - parent.replaceChild( elem, this ); - } - } - - // Force callback invocation - }, ignored ); - } -} ); - -jQuery.each( { - appendTo: "append", - prependTo: "prepend", - insertBefore: "before", - insertAfter: "after", - replaceAll: "replaceWith" -}, function( name, original ) { - jQuery.fn[ name ] = function( selector ) { - var elems, - ret = [], - insert = jQuery( selector ), - last = insert.length - 1, - i = 0; - - for ( ; i <= last; i++ ) { - elems = i === last ? this : this.clone( true ); - jQuery( insert[ i ] )[ original ]( elems ); - - // Support: Android <=4.0 only, PhantomJS 1 only - // .get() because push.apply(_, arraylike) throws on ancient WebKit - push.apply( ret, elems.get() ); - } - - return this.pushStack( ret ); - }; -} ); -var rnumnonpx = new RegExp( "^(" + pnum + ")(?!px)[a-z%]+$", "i" ); - -var getStyles = function( elem ) { - - // Support: IE <=11 only, Firefox <=30 (#15098, #14150) - // IE throws on elements created in popups - // FF meanwhile throws on frame elements through "defaultView.getComputedStyle" - var view = elem.ownerDocument.defaultView; - - if ( !view || !view.opener ) { - view = window; - } - - return view.getComputedStyle( elem ); - }; - -var swap = function( elem, options, callback ) { - var ret, name, - old = {}; - - // Remember the old values, and insert the new ones - for ( name in options ) { - old[ name ] = elem.style[ name ]; - elem.style[ name ] = options[ name ]; - } - - ret = callback.call( elem ); - - // Revert the old values - for ( name in options ) { - elem.style[ name ] = old[ name ]; - } - - return ret; -}; - - -var rboxStyle = new RegExp( cssExpand.join( "|" ), "i" ); - - - -( function() { - - // Executing both pixelPosition & boxSizingReliable tests require only one layout - // so they're executed at the same time to save the second computation. - function computeStyleTests() { - - // This is a singleton, we need to execute it only once - if ( !div ) { - return; - } - - container.style.cssText = "position:absolute;left:-11111px;width:60px;" + - "margin-top:1px;padding:0;border:0"; - div.style.cssText = - "position:relative;display:block;box-sizing:border-box;overflow:scroll;" + - "margin:auto;border:1px;padding:1px;" + - "width:60%;top:1%"; - documentElement.appendChild( container ).appendChild( div ); - - var divStyle = window.getComputedStyle( div ); - pixelPositionVal = divStyle.top !== "1%"; - - // Support: Android 4.0 - 4.3 only, Firefox <=3 - 44 - reliableMarginLeftVal = roundPixelMeasures( divStyle.marginLeft ) === 12; - - // Support: Android 4.0 - 4.3 only, Safari <=9.1 - 10.1, iOS <=7.0 - 9.3 - // Some styles come back with percentage values, even though they shouldn't - div.style.right = "60%"; - pixelBoxStylesVal = roundPixelMeasures( divStyle.right ) === 36; - - // Support: IE 9 - 11 only - // Detect misreporting of content dimensions for box-sizing:border-box elements - boxSizingReliableVal = roundPixelMeasures( divStyle.width ) === 36; - - // Support: IE 9 only - // Detect overflow:scroll screwiness (gh-3699) - // Support: Chrome <=64 - // Don't get tricked when zoom affects offsetWidth (gh-4029) - div.style.position = "absolute"; - scrollboxSizeVal = roundPixelMeasures( div.offsetWidth / 3 ) === 12; - - documentElement.removeChild( container ); - - // Nullify the div so it wouldn't be stored in the memory and - // it will also be a sign that checks already performed - div = null; - } - - function roundPixelMeasures( measure ) { - return Math.round( parseFloat( measure ) ); - } - - var pixelPositionVal, boxSizingReliableVal, scrollboxSizeVal, pixelBoxStylesVal, - reliableTrDimensionsVal, reliableMarginLeftVal, - container = document.createElement( "div" ), - div = document.createElement( "div" ); - - // Finish early in limited (non-browser) environments - if ( !div.style ) { - return; - } - - // Support: IE <=9 - 11 only - // Style of cloned element affects source element cloned (#8908) - div.style.backgroundClip = "content-box"; - div.cloneNode( true ).style.backgroundClip = ""; - support.clearCloneStyle = div.style.backgroundClip === "content-box"; - - jQuery.extend( support, { - boxSizingReliable: function() { - computeStyleTests(); - return boxSizingReliableVal; - }, - pixelBoxStyles: function() { - computeStyleTests(); - return pixelBoxStylesVal; - }, - pixelPosition: function() { - computeStyleTests(); - return pixelPositionVal; - }, - reliableMarginLeft: function() { - computeStyleTests(); - return reliableMarginLeftVal; - }, - scrollboxSize: function() { - computeStyleTests(); - return scrollboxSizeVal; - }, - - // Support: IE 9 - 11+, Edge 15 - 18+ - // IE/Edge misreport `getComputedStyle` of table rows with width/height - // set in CSS while `offset*` properties report correct values. - // Behavior in IE 9 is more subtle than in newer versions & it passes - // some versions of this test; make sure not to make it pass there! - reliableTrDimensions: function() { - var table, tr, trChild, trStyle; - if ( reliableTrDimensionsVal == null ) { - table = document.createElement( "table" ); - tr = document.createElement( "tr" ); - trChild = document.createElement( "div" ); - - table.style.cssText = "position:absolute;left:-11111px"; - tr.style.height = "1px"; - trChild.style.height = "9px"; - - documentElement - .appendChild( table ) - .appendChild( tr ) - .appendChild( trChild ); - - trStyle = window.getComputedStyle( tr ); - reliableTrDimensionsVal = parseInt( trStyle.height ) > 3; - - documentElement.removeChild( table ); - } - return reliableTrDimensionsVal; - } - } ); -} )(); - - -function curCSS( elem, name, computed ) { - var width, minWidth, maxWidth, ret, - - // Support: Firefox 51+ - // Retrieving style before computed somehow - // fixes an issue with getting wrong values - // on detached elements - style = elem.style; - - computed = computed || getStyles( elem ); - - // getPropertyValue is needed for: - // .css('filter') (IE 9 only, #12537) - // .css('--customProperty) (#3144) - if ( computed ) { - ret = computed.getPropertyValue( name ) || computed[ name ]; - - if ( ret === "" && !isAttached( elem ) ) { - ret = jQuery.style( elem, name ); - } - - // A tribute to the "awesome hack by Dean Edwards" - // Android Browser returns percentage for some values, - // but width seems to be reliably pixels. - // This is against the CSSOM draft spec: - // https://drafts.csswg.org/cssom/#resolved-values - if ( !support.pixelBoxStyles() && rnumnonpx.test( ret ) && rboxStyle.test( name ) ) { - - // Remember the original values - width = style.width; - minWidth = style.minWidth; - maxWidth = style.maxWidth; - - // Put in the new values to get a computed value out - style.minWidth = style.maxWidth = style.width = ret; - ret = computed.width; - - // Revert the changed values - style.width = width; - style.minWidth = minWidth; - style.maxWidth = maxWidth; - } - } - - return ret !== undefined ? - - // Support: IE <=9 - 11 only - // IE returns zIndex value as an integer. - ret + "" : - ret; -} - - -function addGetHookIf( conditionFn, hookFn ) { - - // Define the hook, we'll check on the first run if it's really needed. - return { - get: function() { - if ( conditionFn() ) { - - // Hook not needed (or it's not possible to use it due - // to missing dependency), remove it. - delete this.get; - return; - } - - // Hook needed; redefine it so that the support test is not executed again. - return ( this.get = hookFn ).apply( this, arguments ); - } - }; -} - - -var cssPrefixes = [ "Webkit", "Moz", "ms" ], - emptyStyle = document.createElement( "div" ).style, - vendorProps = {}; - -// Return a vendor-prefixed property or undefined -function vendorPropName( name ) { - - // Check for vendor prefixed names - var capName = name[ 0 ].toUpperCase() + name.slice( 1 ), - i = cssPrefixes.length; - - while ( i-- ) { - name = cssPrefixes[ i ] + capName; - if ( name in emptyStyle ) { - return name; - } - } -} - -// Return a potentially-mapped jQuery.cssProps or vendor prefixed property -function finalPropName( name ) { - var final = jQuery.cssProps[ name ] || vendorProps[ name ]; - - if ( final ) { - return final; - } - if ( name in emptyStyle ) { - return name; - } - return vendorProps[ name ] = vendorPropName( name ) || name; -} - - -var - - // Swappable if display is none or starts with table - // except "table", "table-cell", or "table-caption" - // See here for display values: https://developer.mozilla.org/en-US/docs/CSS/display - rdisplayswap = /^(none|table(?!-c[ea]).+)/, - rcustomProp = /^--/, - cssShow = { position: "absolute", visibility: "hidden", display: "block" }, - cssNormalTransform = { - letterSpacing: "0", - fontWeight: "400" - }; - -function setPositiveNumber( _elem, value, subtract ) { - - // Any relative (+/-) values have already been - // normalized at this point - var matches = rcssNum.exec( value ); - return matches ? - - // Guard against undefined "subtract", e.g., when used as in cssHooks - Math.max( 0, matches[ 2 ] - ( subtract || 0 ) ) + ( matches[ 3 ] || "px" ) : - value; -} - -function boxModelAdjustment( elem, dimension, box, isBorderBox, styles, computedVal ) { - var i = dimension === "width" ? 1 : 0, - extra = 0, - delta = 0; - - // Adjustment may not be necessary - if ( box === ( isBorderBox ? "border" : "content" ) ) { - return 0; - } - - for ( ; i < 4; i += 2 ) { - - // Both box models exclude margin - if ( box === "margin" ) { - delta += jQuery.css( elem, box + cssExpand[ i ], true, styles ); - } - - // If we get here with a content-box, we're seeking "padding" or "border" or "margin" - if ( !isBorderBox ) { - - // Add padding - delta += jQuery.css( elem, "padding" + cssExpand[ i ], true, styles ); - - // For "border" or "margin", add border - if ( box !== "padding" ) { - delta += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); - - // But still keep track of it otherwise - } else { - extra += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); - } - - // If we get here with a border-box (content + padding + border), we're seeking "content" or - // "padding" or "margin" - } else { - - // For "content", subtract padding - if ( box === "content" ) { - delta -= jQuery.css( elem, "padding" + cssExpand[ i ], true, styles ); - } - - // For "content" or "padding", subtract border - if ( box !== "margin" ) { - delta -= jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); - } - } - } - - // Account for positive content-box scroll gutter when requested by providing computedVal - if ( !isBorderBox && computedVal >= 0 ) { - - // offsetWidth/offsetHeight is a rounded sum of content, padding, scroll gutter, and border - // Assuming integer scroll gutter, subtract the rest and round down - delta += Math.max( 0, Math.ceil( - elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] - - computedVal - - delta - - extra - - 0.5 - - // If offsetWidth/offsetHeight is unknown, then we can't determine content-box scroll gutter - // Use an explicit zero to avoid NaN (gh-3964) - ) ) || 0; - } - - return delta; -} - -function getWidthOrHeight( elem, dimension, extra ) { - - // Start with computed style - var styles = getStyles( elem ), - - // To avoid forcing a reflow, only fetch boxSizing if we need it (gh-4322). - // Fake content-box until we know it's needed to know the true value. - boxSizingNeeded = !support.boxSizingReliable() || extra, - isBorderBox = boxSizingNeeded && - jQuery.css( elem, "boxSizing", false, styles ) === "border-box", - valueIsBorderBox = isBorderBox, - - val = curCSS( elem, dimension, styles ), - offsetProp = "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ); - - // Support: Firefox <=54 - // Return a confounding non-pixel value or feign ignorance, as appropriate. - if ( rnumnonpx.test( val ) ) { - if ( !extra ) { - return val; - } - val = "auto"; - } - - - // Support: IE 9 - 11 only - // Use offsetWidth/offsetHeight for when box sizing is unreliable. - // In those cases, the computed value can be trusted to be border-box. - if ( ( !support.boxSizingReliable() && isBorderBox || - - // Support: IE 10 - 11+, Edge 15 - 18+ - // IE/Edge misreport `getComputedStyle` of table rows with width/height - // set in CSS while `offset*` properties report correct values. - // Interestingly, in some cases IE 9 doesn't suffer from this issue. - !support.reliableTrDimensions() && nodeName( elem, "tr" ) || - - // Fall back to offsetWidth/offsetHeight when value is "auto" - // This happens for inline elements with no explicit setting (gh-3571) - val === "auto" || - - // Support: Android <=4.1 - 4.3 only - // Also use offsetWidth/offsetHeight for misreported inline dimensions (gh-3602) - !parseFloat( val ) && jQuery.css( elem, "display", false, styles ) === "inline" ) && - - // Make sure the element is visible & connected - elem.getClientRects().length ) { - - isBorderBox = jQuery.css( elem, "boxSizing", false, styles ) === "border-box"; - - // Where available, offsetWidth/offsetHeight approximate border box dimensions. - // Where not available (e.g., SVG), assume unreliable box-sizing and interpret the - // retrieved value as a content box dimension. - valueIsBorderBox = offsetProp in elem; - if ( valueIsBorderBox ) { - val = elem[ offsetProp ]; - } - } - - // Normalize "" and auto - val = parseFloat( val ) || 0; - - // Adjust for the element's box model - return ( val + - boxModelAdjustment( - elem, - dimension, - extra || ( isBorderBox ? "border" : "content" ), - valueIsBorderBox, - styles, - - // Provide the current computed size to request scroll gutter calculation (gh-3589) - val - ) - ) + "px"; -} - -jQuery.extend( { - - // Add in style property hooks for overriding the default - // behavior of getting and setting a style property - cssHooks: { - opacity: { - get: function( elem, computed ) { - if ( computed ) { - - // We should always get a number back from opacity - var ret = curCSS( elem, "opacity" ); - return ret === "" ? "1" : ret; - } - } - } - }, - - // Don't automatically add "px" to these possibly-unitless properties - cssNumber: { - "animationIterationCount": true, - "columnCount": true, - "fillOpacity": true, - "flexGrow": true, - "flexShrink": true, - "fontWeight": true, - "gridArea": true, - "gridColumn": true, - "gridColumnEnd": true, - "gridColumnStart": true, - "gridRow": true, - "gridRowEnd": true, - "gridRowStart": true, - "lineHeight": true, - "opacity": true, - "order": true, - "orphans": true, - "widows": true, - "zIndex": true, - "zoom": true - }, - - // Add in properties whose names you wish to fix before - // setting or getting the value - cssProps: {}, - - // Get and set the style property on a DOM Node - style: function( elem, name, value, extra ) { - - // Don't set styles on text and comment nodes - if ( !elem || elem.nodeType === 3 || elem.nodeType === 8 || !elem.style ) { - return; - } - - // Make sure that we're working with the right name - var ret, type, hooks, - origName = camelCase( name ), - isCustomProp = rcustomProp.test( name ), - style = elem.style; - - // Make sure that we're working with the right name. We don't - // want to query the value if it is a CSS custom property - // since they are user-defined. - if ( !isCustomProp ) { - name = finalPropName( origName ); - } - - // Gets hook for the prefixed version, then unprefixed version - hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ]; - - // Check if we're setting a value - if ( value !== undefined ) { - type = typeof value; - - // Convert "+=" or "-=" to relative numbers (#7345) - if ( type === "string" && ( ret = rcssNum.exec( value ) ) && ret[ 1 ] ) { - value = adjustCSS( elem, name, ret ); - - // Fixes bug #9237 - type = "number"; - } - - // Make sure that null and NaN values aren't set (#7116) - if ( value == null || value !== value ) { - return; - } - - // If a number was passed in, add the unit (except for certain CSS properties) - // The isCustomProp check can be removed in jQuery 4.0 when we only auto-append - // "px" to a few hardcoded values. - if ( type === "number" && !isCustomProp ) { - value += ret && ret[ 3 ] || ( jQuery.cssNumber[ origName ] ? "" : "px" ); - } - - // background-* props affect original clone's values - if ( !support.clearCloneStyle && value === "" && name.indexOf( "background" ) === 0 ) { - style[ name ] = "inherit"; - } - - // If a hook was provided, use that value, otherwise just set the specified value - if ( !hooks || !( "set" in hooks ) || - ( value = hooks.set( elem, value, extra ) ) !== undefined ) { - - if ( isCustomProp ) { - style.setProperty( name, value ); - } else { - style[ name ] = value; - } - } - - } else { - - // If a hook was provided get the non-computed value from there - if ( hooks && "get" in hooks && - ( ret = hooks.get( elem, false, extra ) ) !== undefined ) { - - return ret; - } - - // Otherwise just get the value from the style object - return style[ name ]; - } - }, - - css: function( elem, name, extra, styles ) { - var val, num, hooks, - origName = camelCase( name ), - isCustomProp = rcustomProp.test( name ); - - // Make sure that we're working with the right name. We don't - // want to modify the value if it is a CSS custom property - // since they are user-defined. - if ( !isCustomProp ) { - name = finalPropName( origName ); - } - - // Try prefixed name followed by the unprefixed name - hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ]; - - // If a hook was provided get the computed value from there - if ( hooks && "get" in hooks ) { - val = hooks.get( elem, true, extra ); - } - - // Otherwise, if a way to get the computed value exists, use that - if ( val === undefined ) { - val = curCSS( elem, name, styles ); - } - - // Convert "normal" to computed value - if ( val === "normal" && name in cssNormalTransform ) { - val = cssNormalTransform[ name ]; - } - - // Make numeric if forced or a qualifier was provided and val looks numeric - if ( extra === "" || extra ) { - num = parseFloat( val ); - return extra === true || isFinite( num ) ? num || 0 : val; - } - - return val; - } -} ); - -jQuery.each( [ "height", "width" ], function( _i, dimension ) { - jQuery.cssHooks[ dimension ] = { - get: function( elem, computed, extra ) { - if ( computed ) { - - // Certain elements can have dimension info if we invisibly show them - // but it must have a current display style that would benefit - return rdisplayswap.test( jQuery.css( elem, "display" ) ) && - - // Support: Safari 8+ - // Table columns in Safari have non-zero offsetWidth & zero - // getBoundingClientRect().width unless display is changed. - // Support: IE <=11 only - // Running getBoundingClientRect on a disconnected node - // in IE throws an error. - ( !elem.getClientRects().length || !elem.getBoundingClientRect().width ) ? - swap( elem, cssShow, function() { - return getWidthOrHeight( elem, dimension, extra ); - } ) : - getWidthOrHeight( elem, dimension, extra ); - } - }, - - set: function( elem, value, extra ) { - var matches, - styles = getStyles( elem ), - - // Only read styles.position if the test has a chance to fail - // to avoid forcing a reflow. - scrollboxSizeBuggy = !support.scrollboxSize() && - styles.position === "absolute", - - // To avoid forcing a reflow, only fetch boxSizing if we need it (gh-3991) - boxSizingNeeded = scrollboxSizeBuggy || extra, - isBorderBox = boxSizingNeeded && - jQuery.css( elem, "boxSizing", false, styles ) === "border-box", - subtract = extra ? - boxModelAdjustment( - elem, - dimension, - extra, - isBorderBox, - styles - ) : - 0; - - // Account for unreliable border-box dimensions by comparing offset* to computed and - // faking a content-box to get border and padding (gh-3699) - if ( isBorderBox && scrollboxSizeBuggy ) { - subtract -= Math.ceil( - elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] - - parseFloat( styles[ dimension ] ) - - boxModelAdjustment( elem, dimension, "border", false, styles ) - - 0.5 - ); - } - - // Convert to pixels if value adjustment is needed - if ( subtract && ( matches = rcssNum.exec( value ) ) && - ( matches[ 3 ] || "px" ) !== "px" ) { - - elem.style[ dimension ] = value; - value = jQuery.css( elem, dimension ); - } - - return setPositiveNumber( elem, value, subtract ); - } - }; -} ); - -jQuery.cssHooks.marginLeft = addGetHookIf( support.reliableMarginLeft, - function( elem, computed ) { - if ( computed ) { - return ( parseFloat( curCSS( elem, "marginLeft" ) ) || - elem.getBoundingClientRect().left - - swap( elem, { marginLeft: 0 }, function() { - return elem.getBoundingClientRect().left; - } ) - ) + "px"; - } - } -); - -// These hooks are used by animate to expand properties -jQuery.each( { - margin: "", - padding: "", - border: "Width" -}, function( prefix, suffix ) { - jQuery.cssHooks[ prefix + suffix ] = { - expand: function( value ) { - var i = 0, - expanded = {}, - - // Assumes a single number if not a string - parts = typeof value === "string" ? value.split( " " ) : [ value ]; - - for ( ; i < 4; i++ ) { - expanded[ prefix + cssExpand[ i ] + suffix ] = - parts[ i ] || parts[ i - 2 ] || parts[ 0 ]; - } - - return expanded; - } - }; - - if ( prefix !== "margin" ) { - jQuery.cssHooks[ prefix + suffix ].set = setPositiveNumber; - } -} ); - -jQuery.fn.extend( { - css: function( name, value ) { - return access( this, function( elem, name, value ) { - var styles, len, - map = {}, - i = 0; - - if ( Array.isArray( name ) ) { - styles = getStyles( elem ); - len = name.length; - - for ( ; i < len; i++ ) { - map[ name[ i ] ] = jQuery.css( elem, name[ i ], false, styles ); - } - - return map; - } - - return value !== undefined ? - jQuery.style( elem, name, value ) : - jQuery.css( elem, name ); - }, name, value, arguments.length > 1 ); - } -} ); - - -function Tween( elem, options, prop, end, easing ) { - return new Tween.prototype.init( elem, options, prop, end, easing ); -} -jQuery.Tween = Tween; - -Tween.prototype = { - constructor: Tween, - init: function( elem, options, prop, end, easing, unit ) { - this.elem = elem; - this.prop = prop; - this.easing = easing || jQuery.easing._default; - this.options = options; - this.start = this.now = this.cur(); - this.end = end; - this.unit = unit || ( jQuery.cssNumber[ prop ] ? "" : "px" ); - }, - cur: function() { - var hooks = Tween.propHooks[ this.prop ]; - - return hooks && hooks.get ? - hooks.get( this ) : - Tween.propHooks._default.get( this ); - }, - run: function( percent ) { - var eased, - hooks = Tween.propHooks[ this.prop ]; - - if ( this.options.duration ) { - this.pos = eased = jQuery.easing[ this.easing ]( - percent, this.options.duration * percent, 0, 1, this.options.duration - ); - } else { - this.pos = eased = percent; - } - this.now = ( this.end - this.start ) * eased + this.start; - - if ( this.options.step ) { - this.options.step.call( this.elem, this.now, this ); - } - - if ( hooks && hooks.set ) { - hooks.set( this ); - } else { - Tween.propHooks._default.set( this ); - } - return this; - } -}; - -Tween.prototype.init.prototype = Tween.prototype; - -Tween.propHooks = { - _default: { - get: function( tween ) { - var result; - - // Use a property on the element directly when it is not a DOM element, - // or when there is no matching style property that exists. - if ( tween.elem.nodeType !== 1 || - tween.elem[ tween.prop ] != null && tween.elem.style[ tween.prop ] == null ) { - return tween.elem[ tween.prop ]; - } - - // Passing an empty string as a 3rd parameter to .css will automatically - // attempt a parseFloat and fallback to a string if the parse fails. - // Simple values such as "10px" are parsed to Float; - // complex values such as "rotate(1rad)" are returned as-is. - result = jQuery.css( tween.elem, tween.prop, "" ); - - // Empty strings, null, undefined and "auto" are converted to 0. - return !result || result === "auto" ? 0 : result; - }, - set: function( tween ) { - - // Use step hook for back compat. - // Use cssHook if its there. - // Use .style if available and use plain properties where available. - if ( jQuery.fx.step[ tween.prop ] ) { - jQuery.fx.step[ tween.prop ]( tween ); - } else if ( tween.elem.nodeType === 1 && ( - jQuery.cssHooks[ tween.prop ] || - tween.elem.style[ finalPropName( tween.prop ) ] != null ) ) { - jQuery.style( tween.elem, tween.prop, tween.now + tween.unit ); - } else { - tween.elem[ tween.prop ] = tween.now; - } - } - } -}; - -// Support: IE <=9 only -// Panic based approach to setting things on disconnected nodes -Tween.propHooks.scrollTop = Tween.propHooks.scrollLeft = { - set: function( tween ) { - if ( tween.elem.nodeType && tween.elem.parentNode ) { - tween.elem[ tween.prop ] = tween.now; - } - } -}; - -jQuery.easing = { - linear: function( p ) { - return p; - }, - swing: function( p ) { - return 0.5 - Math.cos( p * Math.PI ) / 2; - }, - _default: "swing" -}; - -jQuery.fx = Tween.prototype.init; - -// Back compat <1.8 extension point -jQuery.fx.step = {}; - - - - -var - fxNow, inProgress, - rfxtypes = /^(?:toggle|show|hide)$/, - rrun = /queueHooks$/; - -function schedule() { - if ( inProgress ) { - if ( document.hidden === false && window.requestAnimationFrame ) { - window.requestAnimationFrame( schedule ); - } else { - window.setTimeout( schedule, jQuery.fx.interval ); - } - - jQuery.fx.tick(); - } -} - -// Animations created synchronously will run synchronously -function createFxNow() { - window.setTimeout( function() { - fxNow = undefined; - } ); - return ( fxNow = Date.now() ); -} - -// Generate parameters to create a standard animation -function genFx( type, includeWidth ) { - var which, - i = 0, - attrs = { height: type }; - - // If we include width, step value is 1 to do all cssExpand values, - // otherwise step value is 2 to skip over Left and Right - includeWidth = includeWidth ? 1 : 0; - for ( ; i < 4; i += 2 - includeWidth ) { - which = cssExpand[ i ]; - attrs[ "margin" + which ] = attrs[ "padding" + which ] = type; - } - - if ( includeWidth ) { - attrs.opacity = attrs.width = type; - } - - return attrs; -} - -function createTween( value, prop, animation ) { - var tween, - collection = ( Animation.tweeners[ prop ] || [] ).concat( Animation.tweeners[ "*" ] ), - index = 0, - length = collection.length; - for ( ; index < length; index++ ) { - if ( ( tween = collection[ index ].call( animation, prop, value ) ) ) { - - // We're done with this property - return tween; - } - } -} - -function defaultPrefilter( elem, props, opts ) { - var prop, value, toggle, hooks, oldfire, propTween, restoreDisplay, display, - isBox = "width" in props || "height" in props, - anim = this, - orig = {}, - style = elem.style, - hidden = elem.nodeType && isHiddenWithinTree( elem ), - dataShow = dataPriv.get( elem, "fxshow" ); - - // Queue-skipping animations hijack the fx hooks - if ( !opts.queue ) { - hooks = jQuery._queueHooks( elem, "fx" ); - if ( hooks.unqueued == null ) { - hooks.unqueued = 0; - oldfire = hooks.empty.fire; - hooks.empty.fire = function() { - if ( !hooks.unqueued ) { - oldfire(); - } - }; - } - hooks.unqueued++; - - anim.always( function() { - - // Ensure the complete handler is called before this completes - anim.always( function() { - hooks.unqueued--; - if ( !jQuery.queue( elem, "fx" ).length ) { - hooks.empty.fire(); - } - } ); - } ); - } - - // Detect show/hide animations - for ( prop in props ) { - value = props[ prop ]; - if ( rfxtypes.test( value ) ) { - delete props[ prop ]; - toggle = toggle || value === "toggle"; - if ( value === ( hidden ? "hide" : "show" ) ) { - - // Pretend to be hidden if this is a "show" and - // there is still data from a stopped show/hide - if ( value === "show" && dataShow && dataShow[ prop ] !== undefined ) { - hidden = true; - - // Ignore all other no-op show/hide data - } else { - continue; - } - } - orig[ prop ] = dataShow && dataShow[ prop ] || jQuery.style( elem, prop ); - } - } - - // Bail out if this is a no-op like .hide().hide() - propTween = !jQuery.isEmptyObject( props ); - if ( !propTween && jQuery.isEmptyObject( orig ) ) { - return; - } - - // Restrict "overflow" and "display" styles during box animations - if ( isBox && elem.nodeType === 1 ) { - - // Support: IE <=9 - 11, Edge 12 - 15 - // Record all 3 overflow attributes because IE does not infer the shorthand - // from identically-valued overflowX and overflowY and Edge just mirrors - // the overflowX value there. - opts.overflow = [ style.overflow, style.overflowX, style.overflowY ]; - - // Identify a display type, preferring old show/hide data over the CSS cascade - restoreDisplay = dataShow && dataShow.display; - if ( restoreDisplay == null ) { - restoreDisplay = dataPriv.get( elem, "display" ); - } - display = jQuery.css( elem, "display" ); - if ( display === "none" ) { - if ( restoreDisplay ) { - display = restoreDisplay; - } else { - - // Get nonempty value(s) by temporarily forcing visibility - showHide( [ elem ], true ); - restoreDisplay = elem.style.display || restoreDisplay; - display = jQuery.css( elem, "display" ); - showHide( [ elem ] ); - } - } - - // Animate inline elements as inline-block - if ( display === "inline" || display === "inline-block" && restoreDisplay != null ) { - if ( jQuery.css( elem, "float" ) === "none" ) { - - // Restore the original display value at the end of pure show/hide animations - if ( !propTween ) { - anim.done( function() { - style.display = restoreDisplay; - } ); - if ( restoreDisplay == null ) { - display = style.display; - restoreDisplay = display === "none" ? "" : display; - } - } - style.display = "inline-block"; - } - } - } - - if ( opts.overflow ) { - style.overflow = "hidden"; - anim.always( function() { - style.overflow = opts.overflow[ 0 ]; - style.overflowX = opts.overflow[ 1 ]; - style.overflowY = opts.overflow[ 2 ]; - } ); - } - - // Implement show/hide animations - propTween = false; - for ( prop in orig ) { - - // General show/hide setup for this element animation - if ( !propTween ) { - if ( dataShow ) { - if ( "hidden" in dataShow ) { - hidden = dataShow.hidden; - } - } else { - dataShow = dataPriv.access( elem, "fxshow", { display: restoreDisplay } ); - } - - // Store hidden/visible for toggle so `.stop().toggle()` "reverses" - if ( toggle ) { - dataShow.hidden = !hidden; - } - - // Show elements before animating them - if ( hidden ) { - showHide( [ elem ], true ); - } - - /* eslint-disable no-loop-func */ - - anim.done( function() { - - /* eslint-enable no-loop-func */ - - // The final step of a "hide" animation is actually hiding the element - if ( !hidden ) { - showHide( [ elem ] ); - } - dataPriv.remove( elem, "fxshow" ); - for ( prop in orig ) { - jQuery.style( elem, prop, orig[ prop ] ); - } - } ); - } - - // Per-property setup - propTween = createTween( hidden ? dataShow[ prop ] : 0, prop, anim ); - if ( !( prop in dataShow ) ) { - dataShow[ prop ] = propTween.start; - if ( hidden ) { - propTween.end = propTween.start; - propTween.start = 0; - } - } - } -} - -function propFilter( props, specialEasing ) { - var index, name, easing, value, hooks; - - // camelCase, specialEasing and expand cssHook pass - for ( index in props ) { - name = camelCase( index ); - easing = specialEasing[ name ]; - value = props[ index ]; - if ( Array.isArray( value ) ) { - easing = value[ 1 ]; - value = props[ index ] = value[ 0 ]; - } - - if ( index !== name ) { - props[ name ] = value; - delete props[ index ]; - } - - hooks = jQuery.cssHooks[ name ]; - if ( hooks && "expand" in hooks ) { - value = hooks.expand( value ); - delete props[ name ]; - - // Not quite $.extend, this won't overwrite existing keys. - // Reusing 'index' because we have the correct "name" - for ( index in value ) { - if ( !( index in props ) ) { - props[ index ] = value[ index ]; - specialEasing[ index ] = easing; - } - } - } else { - specialEasing[ name ] = easing; - } - } -} - -function Animation( elem, properties, options ) { - var result, - stopped, - index = 0, - length = Animation.prefilters.length, - deferred = jQuery.Deferred().always( function() { - - // Don't match elem in the :animated selector - delete tick.elem; - } ), - tick = function() { - if ( stopped ) { - return false; - } - var currentTime = fxNow || createFxNow(), - remaining = Math.max( 0, animation.startTime + animation.duration - currentTime ), - - // Support: Android 2.3 only - // Archaic crash bug won't allow us to use `1 - ( 0.5 || 0 )` (#12497) - temp = remaining / animation.duration || 0, - percent = 1 - temp, - index = 0, - length = animation.tweens.length; - - for ( ; index < length; index++ ) { - animation.tweens[ index ].run( percent ); - } - - deferred.notifyWith( elem, [ animation, percent, remaining ] ); - - // If there's more to do, yield - if ( percent < 1 && length ) { - return remaining; - } - - // If this was an empty animation, synthesize a final progress notification - if ( !length ) { - deferred.notifyWith( elem, [ animation, 1, 0 ] ); - } - - // Resolve the animation and report its conclusion - deferred.resolveWith( elem, [ animation ] ); - return false; - }, - animation = deferred.promise( { - elem: elem, - props: jQuery.extend( {}, properties ), - opts: jQuery.extend( true, { - specialEasing: {}, - easing: jQuery.easing._default - }, options ), - originalProperties: properties, - originalOptions: options, - startTime: fxNow || createFxNow(), - duration: options.duration, - tweens: [], - createTween: function( prop, end ) { - var tween = jQuery.Tween( elem, animation.opts, prop, end, - animation.opts.specialEasing[ prop ] || animation.opts.easing ); - animation.tweens.push( tween ); - return tween; - }, - stop: function( gotoEnd ) { - var index = 0, - - // If we are going to the end, we want to run all the tweens - // otherwise we skip this part - length = gotoEnd ? animation.tweens.length : 0; - if ( stopped ) { - return this; - } - stopped = true; - for ( ; index < length; index++ ) { - animation.tweens[ index ].run( 1 ); - } - - // Resolve when we played the last frame; otherwise, reject - if ( gotoEnd ) { - deferred.notifyWith( elem, [ animation, 1, 0 ] ); - deferred.resolveWith( elem, [ animation, gotoEnd ] ); - } else { - deferred.rejectWith( elem, [ animation, gotoEnd ] ); - } - return this; - } - } ), - props = animation.props; - - propFilter( props, animation.opts.specialEasing ); - - for ( ; index < length; index++ ) { - result = Animation.prefilters[ index ].call( animation, elem, props, animation.opts ); - if ( result ) { - if ( isFunction( result.stop ) ) { - jQuery._queueHooks( animation.elem, animation.opts.queue ).stop = - result.stop.bind( result ); - } - return result; - } - } - - jQuery.map( props, createTween, animation ); - - if ( isFunction( animation.opts.start ) ) { - animation.opts.start.call( elem, animation ); - } - - // Attach callbacks from options - animation - .progress( animation.opts.progress ) - .done( animation.opts.done, animation.opts.complete ) - .fail( animation.opts.fail ) - .always( animation.opts.always ); - - jQuery.fx.timer( - jQuery.extend( tick, { - elem: elem, - anim: animation, - queue: animation.opts.queue - } ) - ); - - return animation; -} - -jQuery.Animation = jQuery.extend( Animation, { - - tweeners: { - "*": [ function( prop, value ) { - var tween = this.createTween( prop, value ); - adjustCSS( tween.elem, prop, rcssNum.exec( value ), tween ); - return tween; - } ] - }, - - tweener: function( props, callback ) { - if ( isFunction( props ) ) { - callback = props; - props = [ "*" ]; - } else { - props = props.match( rnothtmlwhite ); - } - - var prop, - index = 0, - length = props.length; - - for ( ; index < length; index++ ) { - prop = props[ index ]; - Animation.tweeners[ prop ] = Animation.tweeners[ prop ] || []; - Animation.tweeners[ prop ].unshift( callback ); - } - }, - - prefilters: [ defaultPrefilter ], - - prefilter: function( callback, prepend ) { - if ( prepend ) { - Animation.prefilters.unshift( callback ); - } else { - Animation.prefilters.push( callback ); - } - } -} ); - -jQuery.speed = function( speed, easing, fn ) { - var opt = speed && typeof speed === "object" ? jQuery.extend( {}, speed ) : { - complete: fn || !fn && easing || - isFunction( speed ) && speed, - duration: speed, - easing: fn && easing || easing && !isFunction( easing ) && easing - }; - - // Go to the end state if fx are off - if ( jQuery.fx.off ) { - opt.duration = 0; - - } else { - if ( typeof opt.duration !== "number" ) { - if ( opt.duration in jQuery.fx.speeds ) { - opt.duration = jQuery.fx.speeds[ opt.duration ]; - - } else { - opt.duration = jQuery.fx.speeds._default; - } - } - } - - // Normalize opt.queue - true/undefined/null -> "fx" - if ( opt.queue == null || opt.queue === true ) { - opt.queue = "fx"; - } - - // Queueing - opt.old = opt.complete; - - opt.complete = function() { - if ( isFunction( opt.old ) ) { - opt.old.call( this ); - } - - if ( opt.queue ) { - jQuery.dequeue( this, opt.queue ); - } - }; - - return opt; -}; - -jQuery.fn.extend( { - fadeTo: function( speed, to, easing, callback ) { - - // Show any hidden elements after setting opacity to 0 - return this.filter( isHiddenWithinTree ).css( "opacity", 0 ).show() - - // Animate to the value specified - .end().animate( { opacity: to }, speed, easing, callback ); - }, - animate: function( prop, speed, easing, callback ) { - var empty = jQuery.isEmptyObject( prop ), - optall = jQuery.speed( speed, easing, callback ), - doAnimation = function() { - - // Operate on a copy of prop so per-property easing won't be lost - var anim = Animation( this, jQuery.extend( {}, prop ), optall ); - - // Empty animations, or finishing resolves immediately - if ( empty || dataPriv.get( this, "finish" ) ) { - anim.stop( true ); - } - }; - doAnimation.finish = doAnimation; - - return empty || optall.queue === false ? - this.each( doAnimation ) : - this.queue( optall.queue, doAnimation ); - }, - stop: function( type, clearQueue, gotoEnd ) { - var stopQueue = function( hooks ) { - var stop = hooks.stop; - delete hooks.stop; - stop( gotoEnd ); - }; - - if ( typeof type !== "string" ) { - gotoEnd = clearQueue; - clearQueue = type; - type = undefined; - } - if ( clearQueue ) { - this.queue( type || "fx", [] ); - } - - return this.each( function() { - var dequeue = true, - index = type != null && type + "queueHooks", - timers = jQuery.timers, - data = dataPriv.get( this ); - - if ( index ) { - if ( data[ index ] && data[ index ].stop ) { - stopQueue( data[ index ] ); - } - } else { - for ( index in data ) { - if ( data[ index ] && data[ index ].stop && rrun.test( index ) ) { - stopQueue( data[ index ] ); - } - } - } - - for ( index = timers.length; index--; ) { - if ( timers[ index ].elem === this && - ( type == null || timers[ index ].queue === type ) ) { - - timers[ index ].anim.stop( gotoEnd ); - dequeue = false; - timers.splice( index, 1 ); - } - } - - // Start the next in the queue if the last step wasn't forced. - // Timers currently will call their complete callbacks, which - // will dequeue but only if they were gotoEnd. - if ( dequeue || !gotoEnd ) { - jQuery.dequeue( this, type ); - } - } ); - }, - finish: function( type ) { - if ( type !== false ) { - type = type || "fx"; - } - return this.each( function() { - var index, - data = dataPriv.get( this ), - queue = data[ type + "queue" ], - hooks = data[ type + "queueHooks" ], - timers = jQuery.timers, - length = queue ? queue.length : 0; - - // Enable finishing flag on private data - data.finish = true; - - // Empty the queue first - jQuery.queue( this, type, [] ); - - if ( hooks && hooks.stop ) { - hooks.stop.call( this, true ); - } - - // Look for any active animations, and finish them - for ( index = timers.length; index--; ) { - if ( timers[ index ].elem === this && timers[ index ].queue === type ) { - timers[ index ].anim.stop( true ); - timers.splice( index, 1 ); - } - } - - // Look for any animations in the old queue and finish them - for ( index = 0; index < length; index++ ) { - if ( queue[ index ] && queue[ index ].finish ) { - queue[ index ].finish.call( this ); - } - } - - // Turn off finishing flag - delete data.finish; - } ); - } -} ); - -jQuery.each( [ "toggle", "show", "hide" ], function( _i, name ) { - var cssFn = jQuery.fn[ name ]; - jQuery.fn[ name ] = function( speed, easing, callback ) { - return speed == null || typeof speed === "boolean" ? - cssFn.apply( this, arguments ) : - this.animate( genFx( name, true ), speed, easing, callback ); - }; -} ); - -// Generate shortcuts for custom animations -jQuery.each( { - slideDown: genFx( "show" ), - slideUp: genFx( "hide" ), - slideToggle: genFx( "toggle" ), - fadeIn: { opacity: "show" }, - fadeOut: { opacity: "hide" }, - fadeToggle: { opacity: "toggle" } -}, function( name, props ) { - jQuery.fn[ name ] = function( speed, easing, callback ) { - return this.animate( props, speed, easing, callback ); - }; -} ); - -jQuery.timers = []; -jQuery.fx.tick = function() { - var timer, - i = 0, - timers = jQuery.timers; - - fxNow = Date.now(); - - for ( ; i < timers.length; i++ ) { - timer = timers[ i ]; - - // Run the timer and safely remove it when done (allowing for external removal) - if ( !timer() && timers[ i ] === timer ) { - timers.splice( i--, 1 ); - } - } - - if ( !timers.length ) { - jQuery.fx.stop(); - } - fxNow = undefined; -}; - -jQuery.fx.timer = function( timer ) { - jQuery.timers.push( timer ); - jQuery.fx.start(); -}; - -jQuery.fx.interval = 13; -jQuery.fx.start = function() { - if ( inProgress ) { - return; - } - - inProgress = true; - schedule(); -}; - -jQuery.fx.stop = function() { - inProgress = null; -}; - -jQuery.fx.speeds = { - slow: 600, - fast: 200, - - // Default speed - _default: 400 -}; - - -// Based off of the plugin by Clint Helfers, with permission. -// https://web.archive.org/web/20100324014747/http://blindsignals.com/index.php/2009/07/jquery-delay/ -jQuery.fn.delay = function( time, type ) { - time = jQuery.fx ? jQuery.fx.speeds[ time ] || time : time; - type = type || "fx"; - - return this.queue( type, function( next, hooks ) { - var timeout = window.setTimeout( next, time ); - hooks.stop = function() { - window.clearTimeout( timeout ); - }; - } ); -}; - - -( function() { - var input = document.createElement( "input" ), - select = document.createElement( "select" ), - opt = select.appendChild( document.createElement( "option" ) ); - - input.type = "checkbox"; - - // Support: Android <=4.3 only - // Default value for a checkbox should be "on" - support.checkOn = input.value !== ""; - - // Support: IE <=11 only - // Must access selectedIndex to make default options select - support.optSelected = opt.selected; - - // Support: IE <=11 only - // An input loses its value after becoming a radio - input = document.createElement( "input" ); - input.value = "t"; - input.type = "radio"; - support.radioValue = input.value === "t"; -} )(); - - -var boolHook, - attrHandle = jQuery.expr.attrHandle; - -jQuery.fn.extend( { - attr: function( name, value ) { - return access( this, jQuery.attr, name, value, arguments.length > 1 ); - }, - - removeAttr: function( name ) { - return this.each( function() { - jQuery.removeAttr( this, name ); - } ); - } -} ); - -jQuery.extend( { - attr: function( elem, name, value ) { - var ret, hooks, - nType = elem.nodeType; - - // Don't get/set attributes on text, comment and attribute nodes - if ( nType === 3 || nType === 8 || nType === 2 ) { - return; - } - - // Fallback to prop when attributes are not supported - if ( typeof elem.getAttribute === "undefined" ) { - return jQuery.prop( elem, name, value ); - } - - // Attribute hooks are determined by the lowercase version - // Grab necessary hook if one is defined - if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) { - hooks = jQuery.attrHooks[ name.toLowerCase() ] || - ( jQuery.expr.match.bool.test( name ) ? boolHook : undefined ); - } - - if ( value !== undefined ) { - if ( value === null ) { - jQuery.removeAttr( elem, name ); - return; - } - - if ( hooks && "set" in hooks && - ( ret = hooks.set( elem, value, name ) ) !== undefined ) { - return ret; - } - - elem.setAttribute( name, value + "" ); - return value; - } - - if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) { - return ret; - } - - ret = jQuery.find.attr( elem, name ); - - // Non-existent attributes return null, we normalize to undefined - return ret == null ? undefined : ret; - }, - - attrHooks: { - type: { - set: function( elem, value ) { - if ( !support.radioValue && value === "radio" && - nodeName( elem, "input" ) ) { - var val = elem.value; - elem.setAttribute( "type", value ); - if ( val ) { - elem.value = val; - } - return value; - } - } - } - }, - - removeAttr: function( elem, value ) { - var name, - i = 0, - - // Attribute names can contain non-HTML whitespace characters - // https://html.spec.whatwg.org/multipage/syntax.html#attributes-2 - attrNames = value && value.match( rnothtmlwhite ); - - if ( attrNames && elem.nodeType === 1 ) { - while ( ( name = attrNames[ i++ ] ) ) { - elem.removeAttribute( name ); - } - } - } -} ); - -// Hooks for boolean attributes -boolHook = { - set: function( elem, value, name ) { - if ( value === false ) { - - // Remove boolean attributes when set to false - jQuery.removeAttr( elem, name ); - } else { - elem.setAttribute( name, name ); - } - return name; - } -}; - -jQuery.each( jQuery.expr.match.bool.source.match( /\w+/g ), function( _i, name ) { - var getter = attrHandle[ name ] || jQuery.find.attr; - - attrHandle[ name ] = function( elem, name, isXML ) { - var ret, handle, - lowercaseName = name.toLowerCase(); - - if ( !isXML ) { - - // Avoid an infinite loop by temporarily removing this function from the getter - handle = attrHandle[ lowercaseName ]; - attrHandle[ lowercaseName ] = ret; - ret = getter( elem, name, isXML ) != null ? - lowercaseName : - null; - attrHandle[ lowercaseName ] = handle; - } - return ret; - }; -} ); - - - - -var rfocusable = /^(?:input|select|textarea|button)$/i, - rclickable = /^(?:a|area)$/i; - -jQuery.fn.extend( { - prop: function( name, value ) { - return access( this, jQuery.prop, name, value, arguments.length > 1 ); - }, - - removeProp: function( name ) { - return this.each( function() { - delete this[ jQuery.propFix[ name ] || name ]; - } ); - } -} ); - -jQuery.extend( { - prop: function( elem, name, value ) { - var ret, hooks, - nType = elem.nodeType; - - // Don't get/set properties on text, comment and attribute nodes - if ( nType === 3 || nType === 8 || nType === 2 ) { - return; - } - - if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) { - - // Fix name and attach hooks - name = jQuery.propFix[ name ] || name; - hooks = jQuery.propHooks[ name ]; - } - - if ( value !== undefined ) { - if ( hooks && "set" in hooks && - ( ret = hooks.set( elem, value, name ) ) !== undefined ) { - return ret; - } - - return ( elem[ name ] = value ); - } - - if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) { - return ret; - } - - return elem[ name ]; - }, - - propHooks: { - tabIndex: { - get: function( elem ) { - - // Support: IE <=9 - 11 only - // elem.tabIndex doesn't always return the - // correct value when it hasn't been explicitly set - // https://web.archive.org/web/20141116233347/http://fluidproject.org/blog/2008/01/09/getting-setting-and-removing-tabindex-values-with-javascript/ - // Use proper attribute retrieval(#12072) - var tabindex = jQuery.find.attr( elem, "tabindex" ); - - if ( tabindex ) { - return parseInt( tabindex, 10 ); - } - - if ( - rfocusable.test( elem.nodeName ) || - rclickable.test( elem.nodeName ) && - elem.href - ) { - return 0; - } - - return -1; - } - } - }, - - propFix: { - "for": "htmlFor", - "class": "className" - } -} ); - -// Support: IE <=11 only -// Accessing the selectedIndex property -// forces the browser to respect setting selected -// on the option -// The getter ensures a default option is selected -// when in an optgroup -// eslint rule "no-unused-expressions" is disabled for this code -// since it considers such accessions noop -if ( !support.optSelected ) { - jQuery.propHooks.selected = { - get: function( elem ) { - - /* eslint no-unused-expressions: "off" */ - - var parent = elem.parentNode; - if ( parent && parent.parentNode ) { - parent.parentNode.selectedIndex; - } - return null; - }, - set: function( elem ) { - - /* eslint no-unused-expressions: "off" */ - - var parent = elem.parentNode; - if ( parent ) { - parent.selectedIndex; - - if ( parent.parentNode ) { - parent.parentNode.selectedIndex; - } - } - } - }; -} - -jQuery.each( [ - "tabIndex", - "readOnly", - "maxLength", - "cellSpacing", - "cellPadding", - "rowSpan", - "colSpan", - "useMap", - "frameBorder", - "contentEditable" -], function() { - jQuery.propFix[ this.toLowerCase() ] = this; -} ); - - - - - // Strip and collapse whitespace according to HTML spec - // https://infra.spec.whatwg.org/#strip-and-collapse-ascii-whitespace - function stripAndCollapse( value ) { - var tokens = value.match( rnothtmlwhite ) || []; - return tokens.join( " " ); - } - - -function getClass( elem ) { - return elem.getAttribute && elem.getAttribute( "class" ) || ""; -} - -function classesToArray( value ) { - if ( Array.isArray( value ) ) { - return value; - } - if ( typeof value === "string" ) { - return value.match( rnothtmlwhite ) || []; - } - return []; -} - -jQuery.fn.extend( { - addClass: function( value ) { - var classes, elem, cur, curValue, clazz, j, finalValue, - i = 0; - - if ( isFunction( value ) ) { - return this.each( function( j ) { - jQuery( this ).addClass( value.call( this, j, getClass( this ) ) ); - } ); - } - - classes = classesToArray( value ); - - if ( classes.length ) { - while ( ( elem = this[ i++ ] ) ) { - curValue = getClass( elem ); - cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " ); - - if ( cur ) { - j = 0; - while ( ( clazz = classes[ j++ ] ) ) { - if ( cur.indexOf( " " + clazz + " " ) < 0 ) { - cur += clazz + " "; - } - } - - // Only assign if different to avoid unneeded rendering. - finalValue = stripAndCollapse( cur ); - if ( curValue !== finalValue ) { - elem.setAttribute( "class", finalValue ); - } - } - } - } - - return this; - }, - - removeClass: function( value ) { - var classes, elem, cur, curValue, clazz, j, finalValue, - i = 0; - - if ( isFunction( value ) ) { - return this.each( function( j ) { - jQuery( this ).removeClass( value.call( this, j, getClass( this ) ) ); - } ); - } - - if ( !arguments.length ) { - return this.attr( "class", "" ); - } - - classes = classesToArray( value ); - - if ( classes.length ) { - while ( ( elem = this[ i++ ] ) ) { - curValue = getClass( elem ); - - // This expression is here for better compressibility (see addClass) - cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " ); - - if ( cur ) { - j = 0; - while ( ( clazz = classes[ j++ ] ) ) { - - // Remove *all* instances - while ( cur.indexOf( " " + clazz + " " ) > -1 ) { - cur = cur.replace( " " + clazz + " ", " " ); - } - } - - // Only assign if different to avoid unneeded rendering. - finalValue = stripAndCollapse( cur ); - if ( curValue !== finalValue ) { - elem.setAttribute( "class", finalValue ); - } - } - } - } - - return this; - }, - - toggleClass: function( value, stateVal ) { - var type = typeof value, - isValidValue = type === "string" || Array.isArray( value ); - - if ( typeof stateVal === "boolean" && isValidValue ) { - return stateVal ? this.addClass( value ) : this.removeClass( value ); - } - - if ( isFunction( value ) ) { - return this.each( function( i ) { - jQuery( this ).toggleClass( - value.call( this, i, getClass( this ), stateVal ), - stateVal - ); - } ); - } - - return this.each( function() { - var className, i, self, classNames; - - if ( isValidValue ) { - - // Toggle individual class names - i = 0; - self = jQuery( this ); - classNames = classesToArray( value ); - - while ( ( className = classNames[ i++ ] ) ) { - - // Check each className given, space separated list - if ( self.hasClass( className ) ) { - self.removeClass( className ); - } else { - self.addClass( className ); - } - } - - // Toggle whole class name - } else if ( value === undefined || type === "boolean" ) { - className = getClass( this ); - if ( className ) { - - // Store className if set - dataPriv.set( this, "__className__", className ); - } - - // If the element has a class name or if we're passed `false`, - // then remove the whole classname (if there was one, the above saved it). - // Otherwise bring back whatever was previously saved (if anything), - // falling back to the empty string if nothing was stored. - if ( this.setAttribute ) { - this.setAttribute( "class", - className || value === false ? - "" : - dataPriv.get( this, "__className__" ) || "" - ); - } - } - } ); - }, - - hasClass: function( selector ) { - var className, elem, - i = 0; - - className = " " + selector + " "; - while ( ( elem = this[ i++ ] ) ) { - if ( elem.nodeType === 1 && - ( " " + stripAndCollapse( getClass( elem ) ) + " " ).indexOf( className ) > -1 ) { - return true; - } - } - - return false; - } -} ); - - - - -var rreturn = /\r/g; - -jQuery.fn.extend( { - val: function( value ) { - var hooks, ret, valueIsFunction, - elem = this[ 0 ]; - - if ( !arguments.length ) { - if ( elem ) { - hooks = jQuery.valHooks[ elem.type ] || - jQuery.valHooks[ elem.nodeName.toLowerCase() ]; - - if ( hooks && - "get" in hooks && - ( ret = hooks.get( elem, "value" ) ) !== undefined - ) { - return ret; - } - - ret = elem.value; - - // Handle most common string cases - if ( typeof ret === "string" ) { - return ret.replace( rreturn, "" ); - } - - // Handle cases where value is null/undef or number - return ret == null ? "" : ret; - } - - return; - } - - valueIsFunction = isFunction( value ); - - return this.each( function( i ) { - var val; - - if ( this.nodeType !== 1 ) { - return; - } - - if ( valueIsFunction ) { - val = value.call( this, i, jQuery( this ).val() ); - } else { - val = value; - } - - // Treat null/undefined as ""; convert numbers to string - if ( val == null ) { - val = ""; - - } else if ( typeof val === "number" ) { - val += ""; - - } else if ( Array.isArray( val ) ) { - val = jQuery.map( val, function( value ) { - return value == null ? "" : value + ""; - } ); - } - - hooks = jQuery.valHooks[ this.type ] || jQuery.valHooks[ this.nodeName.toLowerCase() ]; - - // If set returns undefined, fall back to normal setting - if ( !hooks || !( "set" in hooks ) || hooks.set( this, val, "value" ) === undefined ) { - this.value = val; - } - } ); - } -} ); - -jQuery.extend( { - valHooks: { - option: { - get: function( elem ) { - - var val = jQuery.find.attr( elem, "value" ); - return val != null ? - val : - - // Support: IE <=10 - 11 only - // option.text throws exceptions (#14686, #14858) - // Strip and collapse whitespace - // https://html.spec.whatwg.org/#strip-and-collapse-whitespace - stripAndCollapse( jQuery.text( elem ) ); - } - }, - select: { - get: function( elem ) { - var value, option, i, - options = elem.options, - index = elem.selectedIndex, - one = elem.type === "select-one", - values = one ? null : [], - max = one ? index + 1 : options.length; - - if ( index < 0 ) { - i = max; - - } else { - i = one ? index : 0; - } - - // Loop through all the selected options - for ( ; i < max; i++ ) { - option = options[ i ]; - - // Support: IE <=9 only - // IE8-9 doesn't update selected after form reset (#2551) - if ( ( option.selected || i === index ) && - - // Don't return options that are disabled or in a disabled optgroup - !option.disabled && - ( !option.parentNode.disabled || - !nodeName( option.parentNode, "optgroup" ) ) ) { - - // Get the specific value for the option - value = jQuery( option ).val(); - - // We don't need an array for one selects - if ( one ) { - return value; - } - - // Multi-Selects return an array - values.push( value ); - } - } - - return values; - }, - - set: function( elem, value ) { - var optionSet, option, - options = elem.options, - values = jQuery.makeArray( value ), - i = options.length; - - while ( i-- ) { - option = options[ i ]; - - /* eslint-disable no-cond-assign */ - - if ( option.selected = - jQuery.inArray( jQuery.valHooks.option.get( option ), values ) > -1 - ) { - optionSet = true; - } - - /* eslint-enable no-cond-assign */ - } - - // Force browsers to behave consistently when non-matching value is set - if ( !optionSet ) { - elem.selectedIndex = -1; - } - return values; - } - } - } -} ); - -// Radios and checkboxes getter/setter -jQuery.each( [ "radio", "checkbox" ], function() { - jQuery.valHooks[ this ] = { - set: function( elem, value ) { - if ( Array.isArray( value ) ) { - return ( elem.checked = jQuery.inArray( jQuery( elem ).val(), value ) > -1 ); - } - } - }; - if ( !support.checkOn ) { - jQuery.valHooks[ this ].get = function( elem ) { - return elem.getAttribute( "value" ) === null ? "on" : elem.value; - }; - } -} ); - - - - -// Return jQuery for attributes-only inclusion - - -support.focusin = "onfocusin" in window; - - -var rfocusMorph = /^(?:focusinfocus|focusoutblur)$/, - stopPropagationCallback = function( e ) { - e.stopPropagation(); - }; - -jQuery.extend( jQuery.event, { - - trigger: function( event, data, elem, onlyHandlers ) { - - var i, cur, tmp, bubbleType, ontype, handle, special, lastElement, - eventPath = [ elem || document ], - type = hasOwn.call( event, "type" ) ? event.type : event, - namespaces = hasOwn.call( event, "namespace" ) ? event.namespace.split( "." ) : []; - - cur = lastElement = tmp = elem = elem || document; - - // Don't do events on text and comment nodes - if ( elem.nodeType === 3 || elem.nodeType === 8 ) { - return; - } - - // focus/blur morphs to focusin/out; ensure we're not firing them right now - if ( rfocusMorph.test( type + jQuery.event.triggered ) ) { - return; - } - - if ( type.indexOf( "." ) > -1 ) { - - // Namespaced trigger; create a regexp to match event type in handle() - namespaces = type.split( "." ); - type = namespaces.shift(); - namespaces.sort(); - } - ontype = type.indexOf( ":" ) < 0 && "on" + type; - - // Caller can pass in a jQuery.Event object, Object, or just an event type string - event = event[ jQuery.expando ] ? - event : - new jQuery.Event( type, typeof event === "object" && event ); - - // Trigger bitmask: & 1 for native handlers; & 2 for jQuery (always true) - event.isTrigger = onlyHandlers ? 2 : 3; - event.namespace = namespaces.join( "." ); - event.rnamespace = event.namespace ? - new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ) : - null; - - // Clean up the event in case it is being reused - event.result = undefined; - if ( !event.target ) { - event.target = elem; - } - - // Clone any incoming data and prepend the event, creating the handler arg list - data = data == null ? - [ event ] : - jQuery.makeArray( data, [ event ] ); - - // Allow special events to draw outside the lines - special = jQuery.event.special[ type ] || {}; - if ( !onlyHandlers && special.trigger && special.trigger.apply( elem, data ) === false ) { - return; - } - - // Determine event propagation path in advance, per W3C events spec (#9951) - // Bubble up to document, then to window; watch for a global ownerDocument var (#9724) - if ( !onlyHandlers && !special.noBubble && !isWindow( elem ) ) { - - bubbleType = special.delegateType || type; - if ( !rfocusMorph.test( bubbleType + type ) ) { - cur = cur.parentNode; - } - for ( ; cur; cur = cur.parentNode ) { - eventPath.push( cur ); - tmp = cur; - } - - // Only add window if we got to document (e.g., not plain obj or detached DOM) - if ( tmp === ( elem.ownerDocument || document ) ) { - eventPath.push( tmp.defaultView || tmp.parentWindow || window ); - } - } - - // Fire handlers on the event path - i = 0; - while ( ( cur = eventPath[ i++ ] ) && !event.isPropagationStopped() ) { - lastElement = cur; - event.type = i > 1 ? - bubbleType : - special.bindType || type; - - // jQuery handler - handle = ( - dataPriv.get( cur, "events" ) || Object.create( null ) - )[ event.type ] && - dataPriv.get( cur, "handle" ); - if ( handle ) { - handle.apply( cur, data ); - } - - // Native handler - handle = ontype && cur[ ontype ]; - if ( handle && handle.apply && acceptData( cur ) ) { - event.result = handle.apply( cur, data ); - if ( event.result === false ) { - event.preventDefault(); - } - } - } - event.type = type; - - // If nobody prevented the default action, do it now - if ( !onlyHandlers && !event.isDefaultPrevented() ) { - - if ( ( !special._default || - special._default.apply( eventPath.pop(), data ) === false ) && - acceptData( elem ) ) { - - // Call a native DOM method on the target with the same name as the event. - // Don't do default actions on window, that's where global variables be (#6170) - if ( ontype && isFunction( elem[ type ] ) && !isWindow( elem ) ) { - - // Don't re-trigger an onFOO event when we call its FOO() method - tmp = elem[ ontype ]; - - if ( tmp ) { - elem[ ontype ] = null; - } - - // Prevent re-triggering of the same event, since we already bubbled it above - jQuery.event.triggered = type; - - if ( event.isPropagationStopped() ) { - lastElement.addEventListener( type, stopPropagationCallback ); - } - - elem[ type ](); - - if ( event.isPropagationStopped() ) { - lastElement.removeEventListener( type, stopPropagationCallback ); - } - - jQuery.event.triggered = undefined; - - if ( tmp ) { - elem[ ontype ] = tmp; - } - } - } - } - - return event.result; - }, - - // Piggyback on a donor event to simulate a different one - // Used only for `focus(in | out)` events - simulate: function( type, elem, event ) { - var e = jQuery.extend( - new jQuery.Event(), - event, - { - type: type, - isSimulated: true - } - ); - - jQuery.event.trigger( e, null, elem ); - } - -} ); - -jQuery.fn.extend( { - - trigger: function( type, data ) { - return this.each( function() { - jQuery.event.trigger( type, data, this ); - } ); - }, - triggerHandler: function( type, data ) { - var elem = this[ 0 ]; - if ( elem ) { - return jQuery.event.trigger( type, data, elem, true ); - } - } -} ); - - -// Support: Firefox <=44 -// Firefox doesn't have focus(in | out) events -// Related ticket - https://bugzilla.mozilla.org/show_bug.cgi?id=687787 -// -// Support: Chrome <=48 - 49, Safari <=9.0 - 9.1 -// focus(in | out) events fire after focus & blur events, -// which is spec violation - http://www.w3.org/TR/DOM-Level-3-Events/#events-focusevent-event-order -// Related ticket - https://bugs.chromium.org/p/chromium/issues/detail?id=449857 -if ( !support.focusin ) { - jQuery.each( { focus: "focusin", blur: "focusout" }, function( orig, fix ) { - - // Attach a single capturing handler on the document while someone wants focusin/focusout - var handler = function( event ) { - jQuery.event.simulate( fix, event.target, jQuery.event.fix( event ) ); - }; - - jQuery.event.special[ fix ] = { - setup: function() { - - // Handle: regular nodes (via `this.ownerDocument`), window - // (via `this.document`) & document (via `this`). - var doc = this.ownerDocument || this.document || this, - attaches = dataPriv.access( doc, fix ); - - if ( !attaches ) { - doc.addEventListener( orig, handler, true ); - } - dataPriv.access( doc, fix, ( attaches || 0 ) + 1 ); - }, - teardown: function() { - var doc = this.ownerDocument || this.document || this, - attaches = dataPriv.access( doc, fix ) - 1; - - if ( !attaches ) { - doc.removeEventListener( orig, handler, true ); - dataPriv.remove( doc, fix ); - - } else { - dataPriv.access( doc, fix, attaches ); - } - } - }; - } ); -} -var location = window.location; - -var nonce = { guid: Date.now() }; - -var rquery = ( /\?/ ); - - - -// Cross-browser xml parsing -jQuery.parseXML = function( data ) { - var xml; - if ( !data || typeof data !== "string" ) { - return null; - } - - // Support: IE 9 - 11 only - // IE throws on parseFromString with invalid input. - try { - xml = ( new window.DOMParser() ).parseFromString( data, "text/xml" ); - } catch ( e ) { - xml = undefined; - } - - if ( !xml || xml.getElementsByTagName( "parsererror" ).length ) { - jQuery.error( "Invalid XML: " + data ); - } - return xml; -}; - - -var - rbracket = /\[\]$/, - rCRLF = /\r?\n/g, - rsubmitterTypes = /^(?:submit|button|image|reset|file)$/i, - rsubmittable = /^(?:input|select|textarea|keygen)/i; - -function buildParams( prefix, obj, traditional, add ) { - var name; - - if ( Array.isArray( obj ) ) { - - // Serialize array item. - jQuery.each( obj, function( i, v ) { - if ( traditional || rbracket.test( prefix ) ) { - - // Treat each array item as a scalar. - add( prefix, v ); - - } else { - - // Item is non-scalar (array or object), encode its numeric index. - buildParams( - prefix + "[" + ( typeof v === "object" && v != null ? i : "" ) + "]", - v, - traditional, - add - ); - } - } ); - - } else if ( !traditional && toType( obj ) === "object" ) { - - // Serialize object item. - for ( name in obj ) { - buildParams( prefix + "[" + name + "]", obj[ name ], traditional, add ); - } - - } else { - - // Serialize scalar item. - add( prefix, obj ); - } -} - -// Serialize an array of form elements or a set of -// key/values into a query string -jQuery.param = function( a, traditional ) { - var prefix, - s = [], - add = function( key, valueOrFunction ) { - - // If value is a function, invoke it and use its return value - var value = isFunction( valueOrFunction ) ? - valueOrFunction() : - valueOrFunction; - - s[ s.length ] = encodeURIComponent( key ) + "=" + - encodeURIComponent( value == null ? "" : value ); - }; - - if ( a == null ) { - return ""; - } - - // If an array was passed in, assume that it is an array of form elements. - if ( Array.isArray( a ) || ( a.jquery && !jQuery.isPlainObject( a ) ) ) { - - // Serialize the form elements - jQuery.each( a, function() { - add( this.name, this.value ); - } ); - - } else { - - // If traditional, encode the "old" way (the way 1.3.2 or older - // did it), otherwise encode params recursively. - for ( prefix in a ) { - buildParams( prefix, a[ prefix ], traditional, add ); - } - } - - // Return the resulting serialization - return s.join( "&" ); -}; - -jQuery.fn.extend( { - serialize: function() { - return jQuery.param( this.serializeArray() ); - }, - serializeArray: function() { - return this.map( function() { - - // Can add propHook for "elements" to filter or add form elements - var elements = jQuery.prop( this, "elements" ); - return elements ? jQuery.makeArray( elements ) : this; - } ) - .filter( function() { - var type = this.type; - - // Use .is( ":disabled" ) so that fieldset[disabled] works - return this.name && !jQuery( this ).is( ":disabled" ) && - rsubmittable.test( this.nodeName ) && !rsubmitterTypes.test( type ) && - ( this.checked || !rcheckableType.test( type ) ); - } ) - .map( function( _i, elem ) { - var val = jQuery( this ).val(); - - if ( val == null ) { - return null; - } - - if ( Array.isArray( val ) ) { - return jQuery.map( val, function( val ) { - return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) }; - } ); - } - - return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) }; - } ).get(); - } -} ); - - -var - r20 = /%20/g, - rhash = /#.*$/, - rantiCache = /([?&])_=[^&]*/, - rheaders = /^(.*?):[ \t]*([^\r\n]*)$/mg, - - // #7653, #8125, #8152: local protocol detection - rlocalProtocol = /^(?:about|app|app-storage|.+-extension|file|res|widget):$/, - rnoContent = /^(?:GET|HEAD)$/, - rprotocol = /^\/\//, - - /* Prefilters - * 1) They are useful to introduce custom dataTypes (see ajax/jsonp.js for an example) - * 2) These are called: - * - BEFORE asking for a transport - * - AFTER param serialization (s.data is a string if s.processData is true) - * 3) key is the dataType - * 4) the catchall symbol "*" can be used - * 5) execution will start with transport dataType and THEN continue down to "*" if needed - */ - prefilters = {}, - - /* Transports bindings - * 1) key is the dataType - * 2) the catchall symbol "*" can be used - * 3) selection will start with transport dataType and THEN go to "*" if needed - */ - transports = {}, - - // Avoid comment-prolog char sequence (#10098); must appease lint and evade compression - allTypes = "*/".concat( "*" ), - - // Anchor tag for parsing the document origin - originAnchor = document.createElement( "a" ); - originAnchor.href = location.href; - -// Base "constructor" for jQuery.ajaxPrefilter and jQuery.ajaxTransport -function addToPrefiltersOrTransports( structure ) { - - // dataTypeExpression is optional and defaults to "*" - return function( dataTypeExpression, func ) { - - if ( typeof dataTypeExpression !== "string" ) { - func = dataTypeExpression; - dataTypeExpression = "*"; - } - - var dataType, - i = 0, - dataTypes = dataTypeExpression.toLowerCase().match( rnothtmlwhite ) || []; - - if ( isFunction( func ) ) { - - // For each dataType in the dataTypeExpression - while ( ( dataType = dataTypes[ i++ ] ) ) { - - // Prepend if requested - if ( dataType[ 0 ] === "+" ) { - dataType = dataType.slice( 1 ) || "*"; - ( structure[ dataType ] = structure[ dataType ] || [] ).unshift( func ); - - // Otherwise append - } else { - ( structure[ dataType ] = structure[ dataType ] || [] ).push( func ); - } - } - } - }; -} - -// Base inspection function for prefilters and transports -function inspectPrefiltersOrTransports( structure, options, originalOptions, jqXHR ) { - - var inspected = {}, - seekingTransport = ( structure === transports ); - - function inspect( dataType ) { - var selected; - inspected[ dataType ] = true; - jQuery.each( structure[ dataType ] || [], function( _, prefilterOrFactory ) { - var dataTypeOrTransport = prefilterOrFactory( options, originalOptions, jqXHR ); - if ( typeof dataTypeOrTransport === "string" && - !seekingTransport && !inspected[ dataTypeOrTransport ] ) { - - options.dataTypes.unshift( dataTypeOrTransport ); - inspect( dataTypeOrTransport ); - return false; - } else if ( seekingTransport ) { - return !( selected = dataTypeOrTransport ); - } - } ); - return selected; - } - - return inspect( options.dataTypes[ 0 ] ) || !inspected[ "*" ] && inspect( "*" ); -} - -// A special extend for ajax options -// that takes "flat" options (not to be deep extended) -// Fixes #9887 -function ajaxExtend( target, src ) { - var key, deep, - flatOptions = jQuery.ajaxSettings.flatOptions || {}; - - for ( key in src ) { - if ( src[ key ] !== undefined ) { - ( flatOptions[ key ] ? target : ( deep || ( deep = {} ) ) )[ key ] = src[ key ]; - } - } - if ( deep ) { - jQuery.extend( true, target, deep ); - } - - return target; -} - -/* Handles responses to an ajax request: - * - finds the right dataType (mediates between content-type and expected dataType) - * - returns the corresponding response - */ -function ajaxHandleResponses( s, jqXHR, responses ) { - - var ct, type, finalDataType, firstDataType, - contents = s.contents, - dataTypes = s.dataTypes; - - // Remove auto dataType and get content-type in the process - while ( dataTypes[ 0 ] === "*" ) { - dataTypes.shift(); - if ( ct === undefined ) { - ct = s.mimeType || jqXHR.getResponseHeader( "Content-Type" ); - } - } - - // Check if we're dealing with a known content-type - if ( ct ) { - for ( type in contents ) { - if ( contents[ type ] && contents[ type ].test( ct ) ) { - dataTypes.unshift( type ); - break; - } - } - } - - // Check to see if we have a response for the expected dataType - if ( dataTypes[ 0 ] in responses ) { - finalDataType = dataTypes[ 0 ]; - } else { - - // Try convertible dataTypes - for ( type in responses ) { - if ( !dataTypes[ 0 ] || s.converters[ type + " " + dataTypes[ 0 ] ] ) { - finalDataType = type; - break; - } - if ( !firstDataType ) { - firstDataType = type; - } - } - - // Or just use first one - finalDataType = finalDataType || firstDataType; - } - - // If we found a dataType - // We add the dataType to the list if needed - // and return the corresponding response - if ( finalDataType ) { - if ( finalDataType !== dataTypes[ 0 ] ) { - dataTypes.unshift( finalDataType ); - } - return responses[ finalDataType ]; - } -} - -/* Chain conversions given the request and the original response - * Also sets the responseXXX fields on the jqXHR instance - */ -function ajaxConvert( s, response, jqXHR, isSuccess ) { - var conv2, current, conv, tmp, prev, - converters = {}, - - // Work with a copy of dataTypes in case we need to modify it for conversion - dataTypes = s.dataTypes.slice(); - - // Create converters map with lowercased keys - if ( dataTypes[ 1 ] ) { - for ( conv in s.converters ) { - converters[ conv.toLowerCase() ] = s.converters[ conv ]; - } - } - - current = dataTypes.shift(); - - // Convert to each sequential dataType - while ( current ) { - - if ( s.responseFields[ current ] ) { - jqXHR[ s.responseFields[ current ] ] = response; - } - - // Apply the dataFilter if provided - if ( !prev && isSuccess && s.dataFilter ) { - response = s.dataFilter( response, s.dataType ); - } - - prev = current; - current = dataTypes.shift(); - - if ( current ) { - - // There's only work to do if current dataType is non-auto - if ( current === "*" ) { - - current = prev; - - // Convert response if prev dataType is non-auto and differs from current - } else if ( prev !== "*" && prev !== current ) { - - // Seek a direct converter - conv = converters[ prev + " " + current ] || converters[ "* " + current ]; - - // If none found, seek a pair - if ( !conv ) { - for ( conv2 in converters ) { - - // If conv2 outputs current - tmp = conv2.split( " " ); - if ( tmp[ 1 ] === current ) { - - // If prev can be converted to accepted input - conv = converters[ prev + " " + tmp[ 0 ] ] || - converters[ "* " + tmp[ 0 ] ]; - if ( conv ) { - - // Condense equivalence converters - if ( conv === true ) { - conv = converters[ conv2 ]; - - // Otherwise, insert the intermediate dataType - } else if ( converters[ conv2 ] !== true ) { - current = tmp[ 0 ]; - dataTypes.unshift( tmp[ 1 ] ); - } - break; - } - } - } - } - - // Apply converter (if not an equivalence) - if ( conv !== true ) { - - // Unless errors are allowed to bubble, catch and return them - if ( conv && s.throws ) { - response = conv( response ); - } else { - try { - response = conv( response ); - } catch ( e ) { - return { - state: "parsererror", - error: conv ? e : "No conversion from " + prev + " to " + current - }; - } - } - } - } - } - } - - return { state: "success", data: response }; -} - -jQuery.extend( { - - // Counter for holding the number of active queries - active: 0, - - // Last-Modified header cache for next request - lastModified: {}, - etag: {}, - - ajaxSettings: { - url: location.href, - type: "GET", - isLocal: rlocalProtocol.test( location.protocol ), - global: true, - processData: true, - async: true, - contentType: "application/x-www-form-urlencoded; charset=UTF-8", - - /* - timeout: 0, - data: null, - dataType: null, - username: null, - password: null, - cache: null, - throws: false, - traditional: false, - headers: {}, - */ - - accepts: { - "*": allTypes, - text: "text/plain", - html: "text/html", - xml: "application/xml, text/xml", - json: "application/json, text/javascript" - }, - - contents: { - xml: /\bxml\b/, - html: /\bhtml/, - json: /\bjson\b/ - }, - - responseFields: { - xml: "responseXML", - text: "responseText", - json: "responseJSON" - }, - - // Data converters - // Keys separate source (or catchall "*") and destination types with a single space - converters: { - - // Convert anything to text - "* text": String, - - // Text to html (true = no transformation) - "text html": true, - - // Evaluate text as a json expression - "text json": JSON.parse, - - // Parse text as xml - "text xml": jQuery.parseXML - }, - - // For options that shouldn't be deep extended: - // you can add your own custom options here if - // and when you create one that shouldn't be - // deep extended (see ajaxExtend) - flatOptions: { - url: true, - context: true - } - }, - - // Creates a full fledged settings object into target - // with both ajaxSettings and settings fields. - // If target is omitted, writes into ajaxSettings. - ajaxSetup: function( target, settings ) { - return settings ? - - // Building a settings object - ajaxExtend( ajaxExtend( target, jQuery.ajaxSettings ), settings ) : - - // Extending ajaxSettings - ajaxExtend( jQuery.ajaxSettings, target ); - }, - - ajaxPrefilter: addToPrefiltersOrTransports( prefilters ), - ajaxTransport: addToPrefiltersOrTransports( transports ), - - // Main method - ajax: function( url, options ) { - - // If url is an object, simulate pre-1.5 signature - if ( typeof url === "object" ) { - options = url; - url = undefined; - } - - // Force options to be an object - options = options || {}; - - var transport, - - // URL without anti-cache param - cacheURL, - - // Response headers - responseHeadersString, - responseHeaders, - - // timeout handle - timeoutTimer, - - // Url cleanup var - urlAnchor, - - // Request state (becomes false upon send and true upon completion) - completed, - - // To know if global events are to be dispatched - fireGlobals, - - // Loop variable - i, - - // uncached part of the url - uncached, - - // Create the final options object - s = jQuery.ajaxSetup( {}, options ), - - // Callbacks context - callbackContext = s.context || s, - - // Context for global events is callbackContext if it is a DOM node or jQuery collection - globalEventContext = s.context && - ( callbackContext.nodeType || callbackContext.jquery ) ? - jQuery( callbackContext ) : - jQuery.event, - - // Deferreds - deferred = jQuery.Deferred(), - completeDeferred = jQuery.Callbacks( "once memory" ), - - // Status-dependent callbacks - statusCode = s.statusCode || {}, - - // Headers (they are sent all at once) - requestHeaders = {}, - requestHeadersNames = {}, - - // Default abort message - strAbort = "canceled", - - // Fake xhr - jqXHR = { - readyState: 0, - - // Builds headers hashtable if needed - getResponseHeader: function( key ) { - var match; - if ( completed ) { - if ( !responseHeaders ) { - responseHeaders = {}; - while ( ( match = rheaders.exec( responseHeadersString ) ) ) { - responseHeaders[ match[ 1 ].toLowerCase() + " " ] = - ( responseHeaders[ match[ 1 ].toLowerCase() + " " ] || [] ) - .concat( match[ 2 ] ); - } - } - match = responseHeaders[ key.toLowerCase() + " " ]; - } - return match == null ? null : match.join( ", " ); - }, - - // Raw string - getAllResponseHeaders: function() { - return completed ? responseHeadersString : null; - }, - - // Caches the header - setRequestHeader: function( name, value ) { - if ( completed == null ) { - name = requestHeadersNames[ name.toLowerCase() ] = - requestHeadersNames[ name.toLowerCase() ] || name; - requestHeaders[ name ] = value; - } - return this; - }, - - // Overrides response content-type header - overrideMimeType: function( type ) { - if ( completed == null ) { - s.mimeType = type; - } - return this; - }, - - // Status-dependent callbacks - statusCode: function( map ) { - var code; - if ( map ) { - if ( completed ) { - - // Execute the appropriate callbacks - jqXHR.always( map[ jqXHR.status ] ); - } else { - - // Lazy-add the new callbacks in a way that preserves old ones - for ( code in map ) { - statusCode[ code ] = [ statusCode[ code ], map[ code ] ]; - } - } - } - return this; - }, - - // Cancel the request - abort: function( statusText ) { - var finalText = statusText || strAbort; - if ( transport ) { - transport.abort( finalText ); - } - done( 0, finalText ); - return this; - } - }; - - // Attach deferreds - deferred.promise( jqXHR ); - - // Add protocol if not provided (prefilters might expect it) - // Handle falsy url in the settings object (#10093: consistency with old signature) - // We also use the url parameter if available - s.url = ( ( url || s.url || location.href ) + "" ) - .replace( rprotocol, location.protocol + "//" ); - - // Alias method option to type as per ticket #12004 - s.type = options.method || options.type || s.method || s.type; - - // Extract dataTypes list - s.dataTypes = ( s.dataType || "*" ).toLowerCase().match( rnothtmlwhite ) || [ "" ]; - - // A cross-domain request is in order when the origin doesn't match the current origin. - if ( s.crossDomain == null ) { - urlAnchor = document.createElement( "a" ); - - // Support: IE <=8 - 11, Edge 12 - 15 - // IE throws exception on accessing the href property if url is malformed, - // e.g. http://example.com:80x/ - try { - urlAnchor.href = s.url; - - // Support: IE <=8 - 11 only - // Anchor's host property isn't correctly set when s.url is relative - urlAnchor.href = urlAnchor.href; - s.crossDomain = originAnchor.protocol + "//" + originAnchor.host !== - urlAnchor.protocol + "//" + urlAnchor.host; - } catch ( e ) { - - // If there is an error parsing the URL, assume it is crossDomain, - // it can be rejected by the transport if it is invalid - s.crossDomain = true; - } - } - - // Convert data if not already a string - if ( s.data && s.processData && typeof s.data !== "string" ) { - s.data = jQuery.param( s.data, s.traditional ); - } - - // Apply prefilters - inspectPrefiltersOrTransports( prefilters, s, options, jqXHR ); - - // If request was aborted inside a prefilter, stop there - if ( completed ) { - return jqXHR; - } - - // We can fire global events as of now if asked to - // Don't fire events if jQuery.event is undefined in an AMD-usage scenario (#15118) - fireGlobals = jQuery.event && s.global; - - // Watch for a new set of requests - if ( fireGlobals && jQuery.active++ === 0 ) { - jQuery.event.trigger( "ajaxStart" ); - } - - // Uppercase the type - s.type = s.type.toUpperCase(); - - // Determine if request has content - s.hasContent = !rnoContent.test( s.type ); - - // Save the URL in case we're toying with the If-Modified-Since - // and/or If-None-Match header later on - // Remove hash to simplify url manipulation - cacheURL = s.url.replace( rhash, "" ); - - // More options handling for requests with no content - if ( !s.hasContent ) { - - // Remember the hash so we can put it back - uncached = s.url.slice( cacheURL.length ); - - // If data is available and should be processed, append data to url - if ( s.data && ( s.processData || typeof s.data === "string" ) ) { - cacheURL += ( rquery.test( cacheURL ) ? "&" : "?" ) + s.data; - - // #9682: remove data so that it's not used in an eventual retry - delete s.data; - } - - // Add or update anti-cache param if needed - if ( s.cache === false ) { - cacheURL = cacheURL.replace( rantiCache, "$1" ); - uncached = ( rquery.test( cacheURL ) ? "&" : "?" ) + "_=" + ( nonce.guid++ ) + - uncached; - } - - // Put hash and anti-cache on the URL that will be requested (gh-1732) - s.url = cacheURL + uncached; - - // Change '%20' to '+' if this is encoded form body content (gh-2658) - } else if ( s.data && s.processData && - ( s.contentType || "" ).indexOf( "application/x-www-form-urlencoded" ) === 0 ) { - s.data = s.data.replace( r20, "+" ); - } - - // Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode. - if ( s.ifModified ) { - if ( jQuery.lastModified[ cacheURL ] ) { - jqXHR.setRequestHeader( "If-Modified-Since", jQuery.lastModified[ cacheURL ] ); - } - if ( jQuery.etag[ cacheURL ] ) { - jqXHR.setRequestHeader( "If-None-Match", jQuery.etag[ cacheURL ] ); - } - } - - // Set the correct header, if data is being sent - if ( s.data && s.hasContent && s.contentType !== false || options.contentType ) { - jqXHR.setRequestHeader( "Content-Type", s.contentType ); - } - - // Set the Accepts header for the server, depending on the dataType - jqXHR.setRequestHeader( - "Accept", - s.dataTypes[ 0 ] && s.accepts[ s.dataTypes[ 0 ] ] ? - s.accepts[ s.dataTypes[ 0 ] ] + - ( s.dataTypes[ 0 ] !== "*" ? 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ztHZ8{e*Ui=*-K*UON=xNhkk?f^(30s9|8nM2Mb;wVM3s|eg6wclRbap8~`k;)?g|C zcKhVmSg>YC@X-PbG{7)C?_s_OeK-o))z!ZK{+g@VaCQTmi@@3QE8q%uEpEK0S-O@ayrzjDKJ^}RDdAK4zLPE$*HKl1)SZXn8GGE zSiA9I%F8GuWG9A9<6)19@n^x{weop4HI4(N}=Py7vsCnO|*@ITDqZTH3pj~Os)A%JM%gT9vf`K+23x!Zlfb1*3q z1k!D2<$--)gfj#t)S1+&YGL{~wvL)-eD8 diff --git a/doc/build/html/poly_dyn-1.py b/doc/build/html/poly_dyn-1.py deleted file mode 100644 index 4c2d16d..0000000 --- a/doc/build/html/poly_dyn-1.py +++ /dev/null @@ -1,30 +0,0 @@ -import matplotlib.pyplot as plt -import numpy as np -from wlcstat.poly_dyn import * - -num_t = 100 -t_val_0 = 1e-4 -t_val_f = 1e6 -t_val = np.logspace(np.log10(t_val_0), np.log10(t_val_f), num_t) -N=100 -Ndel=25 -mscdl = linear_mscd(t_val, 1, Ndel, N, 1, 20000) -mscdr = ring_mscd(t_val, 1, Ndel, N, 1, 20000) -msd = linear_mid_msd(t_val, 1, N, 1, 10000) -mscdl_inf = 2 * 2 * Ndel -mscdr_inf = 2 * 1 / (1 / (2 * Ndel) + 1 / (N - 2 * Ndel)) -plt.figure(figsize=(10,8)) -font = {'family' : 'serif', - 'weight':'normal', - 'size': 18} -plt.rc('font', **font) -plt.loglog(t_val, mscdl) -plt.loglog(t_val, mscdr) -plt.loglog(t_val, 2 * msd) -plt.loglog(t_val, 2 * 6 * t_val /N,'--') -plt.loglog(t_val, mscdl_inf + 0*t_val,'--') -plt.loglog(t_val, mscdr_inf + 0*t_val,'--') -plt.xlabel(r'$t$') -plt.ylabel(r'$MSCD$') -plt.tight_layout() -plt.show() \ No newline at end of file diff --git a/doc/build/html/poly_dyn.html b/doc/build/html/poly_dyn.html deleted file mode 100644 index ad053b4..0000000 --- a/doc/build/html/poly_dyn.html +++ /dev/null @@ -1,475 +0,0 @@ - - - - - - - - Polymer Dynamics — wlcstat documentation - - - - - - - - - - - - - - - -

- -
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- -
-

Polymer Dynamics

-
-

Dynamics of a linear and ring flexible Gaussian chains (Rouse model)

-

We consider a flexible polymer chain -that is subject -Brownian forces [Doi1988]. -Our goals is to determine specific dynamic properties of a linear and ring -Gaussian chain. For example, we consider the dynamic motion of two -chain segments relative to each other. We define this relative motion -as the mean-square change in displacment (MSCD). -In this development, we present a detailed derivation for the linear chain, -and we provide the results for the ring polymer.

-
-Schematic representation of the linear and ring Rouse model with definition of segments for MSCD calculation. -

Schematic representation of the linear and ring Rouse model with definition of segments for MSCD calculation. -The total chain length is \(N = 2 N_{s}\), and we consider two points on the chain located at -\(n_{1} = N_{s} - \Delta = N/2 - \Delta\) and \(n_{2} = N_{s} + \Delta = N/2 + \Delta\).

-
-

We start by defining a discrete -polymer chain with bead positions -\(\vec{R}_{m}\), where \(m\) runs from 0 -to \(n_{\mathrm{b}}\). -Each bead is connected to their -neighboring beads by Hookean springs, -resulting in a potential force -on the \(m\)-th bead -\(\vec{F}_{V_{m}}\) that is given by

-
-\[\begin{split}& & \vec{F}_{V_{m}}= -\left\{ \begin{array}{c} - \frac{3 k_{B}T}{g b^{2}} \left( \vec{R}_{m+1} - 2 \vec{R}_{m} + \vec{R}_{m-1} \right), - \hspace{0.3in} - m = 1,\ldots, n_{\mathrm{b}}-1 \\ - \frac{3 k_{B}T}{g b^{2}} \left( \vec{R}_{1} - \vec{R}_{0} \right), - \hspace{2in} - m = 0 \\ - -\frac{3 k_{B}T}{g b^{2}} \left( \vec{R}_{n_{\mathrm{b}}} - \vec{R}_{n_{\mathrm{b}}-1} \right), - \hspace{1.65in} - m = n_{\mathrm{b}}, - \end{array} - \right.\end{split}\]
-

where \(b\) is the Kuhn statistical segment length of the polymer [Doi1988], -and \(g\) is the number of Kuhn lengths -per bead. We set \(g = N/n_{\mathrm{b}}\), giving -a total chain length of \(N\) Kuhn lengths.

-

The Langevin equation of motion for the \(m\)-th bead is given by

-
-\[g \xi \frac{d\vec{R}_{m}(t)}{dt}=\vec{F}_{V_{m}} + \vec{F}_{B_{m}}\]
-

where the drag coefficient \(\xi\) is defined as the viscous drag per Kuhn length. -We now take the limit of -\(n_{\mathrm{b}} \rightarrow \infty\) -for fixed chain length \(N\), resulting in -a continuous-chain representation -of the chain \(\vec{r}(n,t)\) where \(n\) -is a path-length variable that runs -from \(0\) to \(N\). -The Langevin equation for the chain is -given by

-
-(1)\[\xi \frac{\partial \vec{r}(n, t)}{\partial t}= -\frac{3 k_{B}T}{b^{2}} -\frac{\partial^{2} \vec{r}(n, t)}{\partial n^{2}} -+ \vec{f}_{B}(n,t),\]
-

which is subject to the end conditions

-
-\[\frac{\partial \vec{r}(n=0,t)}{\partial n} = -\frac{\partial \vec{r}(n=N,t)}{\partial n} = 0.\]
-

The Brownian forces satisfy the fluctuation dissipation theorem

-
-\[\langle \vec{f}_{B}(n,t)\vec{f}_{B}(n',t')\rangle = -2k_{B}T \xi \delta (n - n') \delta(t-t') \textbf{I}.\]
-

It is convenient to define a set of normal coordinates that -effectively decouple the interactions implicit within the equation of motion (Eq. (1)). -We define the normal modes

-
-\[\begin{split}& & \phi_{p}(n)= -\left\{ \begin{array}{c} - \sqrt{2} \cos \left( \frac{\pi p n}{N} \right), \ \ p = 1,2,\ldots \\ - 1, \ \ \ \ \ \ \ \ \ \ p = 0. - \end{array} - \right.\end{split}\]
-

These modes represent a complete basis set that satisfy the boundary conditions for \(\vec{r}(n,t)\). -Orthogonality is demonstrated by noting

-
-\[\int_{0}^{N} \! \! dn \phi_{p}(n) \phi_{p'}(n) = N \delta_{p,p'}.\]
-

The amplitude of the \(p\)-th mode \(\vec{X}_{p}(t)\) is given by

-
-\[\vec{X}_{p}(t) = \frac{1}{N} \int_{0}^{N} \! \! dn \, \vec{r}(n,t) \phi_{p}(n),\]
-

and the inversion back to chain coordinates is written as

-
-\[\vec{r}(n,t) = \sum_{p=0}^{\infty} \vec{X}_{p}(t) \phi_{p}(n).\]
-

Upon performing a transform to normal -coordinates, we find the governing -equation of motion

-
-(2)\[\xi N \frac{d \vec{X}_{p}}{d t} = -- k_{p} \vec{X}_{p} -+ \vec{f}_{B_{p}}\]
-

where \(k_{p} = \frac{3 \pi^{2} k_{B}T}{b^{2} N} p^{2}\). -The \(p\)-mode Brownian force \(\vec{f}_{B_{p}}\) -is given by

-
-\[\vec{f}_{B_{p}} = \int_{0}^{N} \! \! dn \, \vec{f}_{B}(n,t) \phi_{p}(n)\]
-

and satisfies the fluctuation dissipation theorem

-
-\[\langle -\vec{f}_{B_{p}} (t) \vec{f}_{B_{p'}}(t') -\rangle = -2 k_{B}T \xi N \delta_{pp'} \delta (t - t') \mathbf{I}.\]
-

A similar derivation for a ring polymer results in a treatment that -is identical to the linear chain, but the normal modes for the -ring polymer are continuous across the ends [i.e. \(\vec{r}(n=0,t) = \vec{r}(n=N,t)\)]. -Specifically, the complete normal-mode set is separated into even and odd functions, -respectively -defined by

-
-\[\begin{split}& & \phi_{p}^{(e)}(n)= -\left\{ \begin{array}{c} - \sqrt{2} \cos \left( \frac{2 p \pi n}{N} \right), \ \ p = 1,2,\ldots \\ - 1, \ \ \ \ \ \ \ \ \ \ p = 0. - \end{array} - \right.\end{split}\]
-

and

-
-\[\phi_{p}^{(o)}(n)= - \sqrt{2} \sin \left( \frac{2 \pi p n}{N} \right), \ \ p = 1,2,\ldots\]
-

The even and odd normal modes satisfy the equation of motion defined in Eq. (2) -with -\(k_{p} = \frac{12 \pi^{2} k_{B}T}{b^{2} N} p^{2}\)

-
-

Mean-square displacement (MSD) for linear polymers

-

The mean-square displacement of a segment of the polymer chain is define a

-
-(3)\[\mathrm{MSD} = \langle \left( \vec{r}(n, t) - \vec{r}(n, 0) \right)^{2} \rangle\]
-

for the nth segment of the chain with total length \(N\). -We insert our normal-mode representation into Eq. (3), -resulting in the expression

-
-\[\mathrm{MSD} = -\sum_{p=1}^{\infty} \sum_{p'=1}^{\infty} -\langle -\left( \vec{X}_{p}(t) - \vec{X}_{p}(0) \right) \cdot -\left( \vec{X}_{p'}(t) - \vec{X}_{p'}(0) \right) \rangle -\phi_{p}(n) \phi_{p'}(n)\]
-

The equation of motion (Eq. (2)) can be used to determine the correlation function -\(\langle \vec{X}_{p}(t) \cdot \vec{X}_{p'}(0) \rangle\) (detailed discussion is found in Ref. [Doi1988]). -This results in the expression

-
-\[\langle \vec{X}_{p}(t) \cdot \vec{X}_{p'}(0) \rangle = 3 \frac{k_{B}T}{k_{p}} -\exp \! \left( - \frac{k_{p}}{N \xi} t \right) \delta_{pp'}\]
-

for \(p \ge 1\) and

-
-\[\langle -\left( \vec{X}_{0}(t) - \vec{X}_{0}(0) \right)^{2} \rangle = 6 \frac{k_{B}T}{N \xi} t\]
-

We focus on the \(\mathrm{MSD}\) for the midpoint of a linear chain, -thus \(n=N/2\). -Inserting this into our definition of \(\mathrm{MSD}\) results in the -expression for the MSD of the midpoint of a linear chain

-
-\[\begin{split}\mathrm{MSD} -& = & -6 \frac{k_{B}T}{\xi N} t + -\sum_{p \, \mathrm{even}} 12 \frac{k_{B}T}{k_{p}} -\left[ 1 - \exp \! \left( - \frac{k_{p}}{N \xi} t \right) \right] \\ -& = & -6 \frac{k_{B}T}{\xi N} t + -\sum_{p = 1}^{\infty} 12 \frac{k_{B}T}{k_{2p}} -\left[ 1 - \exp \! \left( - \frac{k_{2p}}{N \xi} t \right) \right] \\\end{split}\]
-
-
-

Mean-squared change in distance (MSCD) for linear and ring polymers

-

We now consider the mean-square change in distance (MSCD) for a linear polymer -chain. -This quantity is defined as

-
-(4)\[\mathrm{MSCD} = \langle \left( \Delta \vec{R}(t) - \Delta \vec{R}(0) \right)^{2} \rangle\]
-

where \(\Delta \vec{R}(t) = \vec{r}(N/2 + \Delta, t) - \vec{r}(N/2 - \Delta,t)\) where -the total chain length is \(N = 2 N_{s}\). -We insert our normal-mode representation into Eq. (4) -to find

-
-\[\mathrm{MSCD} = -\sum_{p=1}^{\infty} \sum_{p'=1}^{\infty} -\langle -\left( \vec{X}_{p}(t) - \vec{X}_{p}(0) \right) \cdot -\left( \vec{X}_{p'}(t) - \vec{X}_{p'}(0) \right) -\rangle -\left[ \phi_{p}(N/2 + \Delta) - \phi_{p}(N/2 - \Delta) \right] -\left[ \phi_{p'}(N/2 + \Delta) - \phi_{p'}(N/2 - \Delta) \right]\]
-

The equation of motion (Eq. (2)) can be used to determine the correlation function -\(\langle \vec{X}_{p}(t) \cdot \vec{X}_{p'}(0) \rangle\) (detailed discussion is found in Ref. [Doi1988]). -This results in the expression

-
-\[\langle \vec{X}_{p}(t) \cdot \vec{X}_{p'}(0) \rangle = 3 \frac{k_{B}T}{k_{p}} -\exp \! \left( - \frac{k_{p}}{N \xi} t \right) \delta_{pp'}\]
-

Inserting this into our definition of \(\mathrm{MSCD}\) results in the -expression for the linear chain

-
-\[\begin{split}\mathrm{MSCD}^{\mathrm{(linear)}} -& = & \sum_{p \, \mathrm{odd}} 48 \frac{k_{B}T}{k_{p}} -\left[ 1 - \exp \! \left( - \frac{k_{p}}{N \xi} t \right) \right] -\sin^{2} \left( \frac{\pi p \Delta}{N} \right) \\ -& = & \sum_{p = 0}^{\infty} 48 \frac{k_{B}T}{k_{2p+1}} -\left[ 1 - \exp \! \left( - \frac{k_{2p+1}}{N \xi} t \right) \right] -\sin^{2} \left[ \frac{\pi (2p+1) \Delta}{N} \right]\end{split}\]
-

where \(k_{p} = \frac{3 \pi^{2} k_{B}T}{b^{2} N} p^{2}\) for the linear chain.

-

We follow a parallel derivation for the ring polymer. -We note that only the odd set of normal modes contribute to \(\mathrm{MSCD}\) -for the ring polymer. -Taking similar steps as in the linear case, -we arrive at the expression for the ring polymer

-
-\[\mathrm{MSCD}^{\mathrm{(ring)}} -= \sum_{p = 1}^{\infty} 48 \frac{k_{B}T}{k_{p}} -\left[ 1 - \exp \! \left( - \frac{k_{p}}{N \xi} t \right) \right] -\sin^{2} \left( \frac{2 \pi p \Delta}{N} \right)\]
-

where \(k_{p} = \frac{12 \pi^{2} k_{B}T}{b^{2} N} p^{2}\) for the ring polymer.

-
-
-
-

Functions contained with the ‘poly_dyn’ module

-

Rouse polymer, analytical results.

-

Notes

-

There are two parameterizations of the “Rouse” polymer that are commonly used, -and they use the same variable name for two different things.

-

In one, N is the number of Kuhn lengths, and in the other, N is the number of -beads, each of which can represent an arbitrary number of Kuhn lengths.

-
-
-wlcstat.poly_dyn.end_to_end_corr(t, D, N, num_modes=10000)[source]
-

Doi and Edwards, Eq. 4.35

-
- -
-
-wlcstat.poly_dyn.gaussian_G(r, N, b)[source]
-

Green’s function of a Gaussian chain at N Kuhn lengths of separation, -given a Kuhn length of b

-
- -
-
-wlcstat.poly_dyn.gaussian_Ploop(a, N, b)[source]
-

Looping probability for two loci on a Gaussian chain N kuhn lengths -apart, when the Kuhn length is b, and the capture radius is a

-
- -
-
-wlcstat.poly_dyn.kp_over_kbt(p: float, b: float, N: float)[source]
-

k_p/(k_B T) : “non-dimensionalized” k_p is all that’s needed for most -formulas, e.g. MSD.

-
- -
-
-wlcstat.poly_dyn.linear_mid_msd(t, b, N, D, num_modes=20000)[source]
-

modified from Weber Phys Rev E 2010, Eq. 24.

-
- -
-
-wlcstat.poly_dyn.linear_mscd(t, D, Ndel, N, b=1, num_modes=20000)[source]
-

Compute mscd for two points on a linear polymer.

-
-
Parameters
-
    -
  • t ((M,) float, array_like) – Times at which to evaluate the MSCD

  • -
  • D (float) – Diffusion coefficient, (in desired output length units). Equal to -\(k_BT/\xi\) for \(\xi\) in units of “per Kuhn length”.

  • -
  • Ndel (float) – Distance from the last linkage site to the measured site. This ends up -being (1/2)*separation between the loci (in Kuhn lengths).

  • -
  • N (float) – The full lengh of the linear polymer (in Kuhn lengths).

  • -
  • b (float) – The Kuhn length (in desired length units).

  • -
  • num_modes (int) – how many Rouse modes to include in the sum

  • -
-
-
Returns
-

mscd – result

-
-
Return type
-

(M,) np.array<float>

-
-
-
- -
-
-wlcstat.poly_dyn.ring_mscd(t, D, Ndel, N, b=1, num_modes=20000)[source]
-

Compute mscd for two points on a ring.

-
-
Parameters
-
    -
  • t ((M,) float, array_like) – Times at which to evaluate the MSCD.

  • -
  • D (float) – Diffusion coefficient, (in desired output length units). Equal to -\(k_BT/\xi\) for \(\xi\) in units of “per Kuhn length”.

  • -
  • Ndel (float) – (1/2)*separation between the loci on loop (in Kuhn lengths)

  • -
  • N (float) – full length of the loop (in Kuhn lengths)

  • -
  • b (float) – The Kuhn length, in desired output length units.

  • -
  • num_modes (int) – How many Rouse modes to include in the sum.

  • -
-
-
Returns
-

mscd – result

-
-
Return type
-

(M,) np.array<float>

-
-
-
- -
-
-wlcstat.poly_dyn.rouse_mode(p, n, N=1)[source]
-

Eigenbasis for Rouse model.

-

Indexed by p, depends only on position n/N along the polymer of length N. -N=1 by default.

-

Weber, Phys Rev E, 2010 (Eq 14)

-
- -
-
-wlcstat.poly_dyn.rouse_mode_coef(p, b, N, kbT=1)[source]
-

k_p: Weber Phys Rev E 2010, after Eq. 18.

-
- -
-
-

Example usage of ‘linear_mscd’ and ‘ring_mscd’

-

We show the solution for the MSCD for chain length \(N=100\) and \(\Delta = 25\) for both -linear and ring polymers. In this plot, we also show the MSD (using ‘linear_mid_msd’) multiplied by -2, which coincides with the short-time asymptotic behavior. -The long-time asymptotic behavior is found by noting

-
-\[\mathrm{MSCD} = \langle \left( \Delta \vec{R}(t) - \Delta \vec{R}(0) \right)^{2} \rangle = -\langle \Delta \vec{R}(t)^{2} \rangle -- 2 \langle \Delta \vec{R}(t) \cdot \Delta \vec{R}(0) \rangle -+ \langle \Delta \vec{R}(0) ^{2} \rangle \rightarrow -2 \langle \Delta \vec{R}^{2} \rangle\]
-

which leads to the asymptotic solutions

-
-\[\mathrm{MSCD}^{\mathrm{(linear)}} \rightarrow 4 \Delta\]
-

and

-
-\[\mathrm{MSCD}^{\mathrm{(ring)}} \rightarrow \frac{2}{\frac{1}{2 \Delta} + \frac{1}{N-2 \Delta}}.\]
-

These asymptotic solutions are also included in the plot.

-

(Source code, png, hires.png, pdf)

-
-_images/poly_dyn-1.png -
-
-
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-
-
-
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References

-
-
Spakowitz2004
-

Spakowitz, Andrew J., and Zhen-Gang Wang. “Exact results for a semiflexible polymer chain in an aligning field.” Macromolecules 37.15 (2004): 5814-5823.

-
-
Spakowitz2005
-

Spakowitz, Andrew J., and Zhen-Gang Wang. “End-to-end distance vector distribution with fixed end orientations for the wormlike chain model.” Physical Review E 72.4 (2005): 041802.

-
-
Spakowitz2006
-

Spakowitz, A. J. “Wormlike chain statistics with twist and fixed ends.” EPL (Europhysics Letters) 73.5 (2006): 684.

-
-
Mehraeen2008
-

Mehraeen, Shafigh, et al. “End-to-end distribution for a wormlike chain in arbitrary dimensions.” Physical Review E 77.6 (2008): 061803.

-
-
-
-
Kratky1949
-

Kratky, Otto, and Günther Porod. “Röntgenuntersuchung gelöster fadenmoleküle.” Recueil des Travaux Chimiques des Pays‐Bas 68.12 (1949): 1106-1122.

-
-
Yamakawa1997
-

Yamakawa, Hiromi, and Takenao Yoshizaki. Helical wormlike chains in polymer solutions. Vol. 1. Berlin: Springer, 1997.

-
-
-
-
Arfken1999
-

Arfken, George B., and Hans J. Weber. “Mathematical methods for physicists.” (1999): 165-169.

-
-
-
-
Doi1988
-

Doi, Masao, Samuel Frederick Edwards, and Samuel Frederick Edwards. The theory of polymer dynamics. Vol. 73. oxford university press, 1988.

-
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zgT)~MT|InH`m6tbx@2l$VZE7;1!Dr91=u+qoBL1Zoh;DA2}%{$=th!ul_d^oCx^< diff --git a/doc/build/html/wlcave_notes-1.py b/doc/build/html/wlcave_notes-1.py deleted file mode 100644 index 412df9e..0000000 --- a/doc/build/html/wlcave_notes-1.py +++ /dev/null @@ -1,24 +0,0 @@ -import matplotlib.pyplot as plt -import numpy as np -from wlcstat.wlcave import * - -num_pts = 100 -length_kuhn_0 = 1e-3 -length_kuhn_f = 1e3 -length_kuhn = np.logspace(np.log10(length_kuhn_0), np.log10(length_kuhn_f), num_pts) -dimensions = 3 -r2 = r2_ave(length_kuhn, dimensions) -r2short = length_kuhn ** 2 -r2long = length_kuhn * 2 / (dimensions - 1) -plt.figure(figsize=(10,8)) -font = {'family' : 'serif', - 'weight':'normal', - 'size': 18} -plt.rc('font', **font) -plt.loglog(length_kuhn, r2) -plt.loglog(length_kuhn[0:60], r2short[0:60]) # Short length asymptotic solution -plt.loglog(length_kuhn[40:100], r2long[40:100]) # Long length asymptotic solution -plt.xlabel(r'Chain length $N = L/(2l_{p})$') -plt.ylabel(r'End-to-end distance $\langle R^{2} \rangle$') -plt.tight_layout() -plt.show() \ No newline at end of file diff --git a/doc/build/html/wlcave_notes-2.hires.png b/doc/build/html/wlcave_notes-2.hires.png deleted file mode 100644 index 2da7ea3a3190c2db8e65c29a9e696b48cc30cecf..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 127429 zcmeFZWmr{P_ddMUgMq|RL8T2q8U>LKMY=ZKaFFf>X)I6_P*NJCTj|~^f&vnf(kR^$ zn@#f{OGSA;yx-oBzkOXEuYKHW%{Av7bBuf3;~wh?T3&(>pBx{BLJ>+y-c~}PjvtklqSL3(pF4-DJ?NymvQ$IUuMF$`F*s?8 znC7&vUp1tZnj%=oXJ@rPKfymoc+U6M8`niW=b6sTGQ&T=eJi)SK1%F7_w`MgAqkVs zw}a+ic9=@!Vy0TI*4nJ_?z-r^ckk+6B2MGiN9^17#!9a%T}=fI6Dyn|l7Q?4H)=}C zoW5eqbB5&mKSPleXKy97-`6fXczFKrVEv!__&+E4ztJbmUQ_L<-i~q5TCA|*fFk;{ zz*GJ|rwD~2ITkaR=IXO2K1>zI9J5j2qBD@3un?s;@CNu|>{0z*zI~|-iJRb@Pt@b61Z>Y-Bi{{(h z#k_1!q8&MSQd5U~h_|zFC0-dMRH3phrUJQGu7V}11wy~mj}Ambk<8-dDYa_s*0BKY zwaVCQ+Lq={wGvp*U^_QA_p)nL(&Ybh)0Q+&kJaG7#o1TZ{!L_|T#}b(o^>>Ni8r-2 zH3d$il_2b_sRH7?3`*KUreYNcfu|Oi?d0bWY 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1e3 -length_kuhn = np.logspace(np.log10(length_kuhn_0), np.log10(length_kuhn_f), num_pts) -dimensions = 3 -rz4 = rz4_ave(length_kuhn, dimensions) -rz4short = length_kuhn ** 4 * 3 / (dimensions * (dimensions + 2)) -rz4long = length_kuhn ** 2 * 12 / (dimensions * (dimensions - 1)) ** 2 -plt.figure(figsize=(10,8)) -font = {'family' : 'serif', - 'weight':'normal', - 'size': 18} -plt.rc('font', **font) -plt.loglog(length_kuhn, rz4) -plt.loglog(length_kuhn[0:60], rz4short[0:60]) # Short length asymptotic solution -plt.loglog(length_kuhn[40:100], rz4long[40:100]) # Long length asymptotic solution -plt.xlabel(r'Chain length $N = L/(2l_{p})$') -plt.ylabel(r'4th moment $\langle R_{z}^{4} \rangle$') -plt.tight_layout() -plt.show() \ No newline at end of file diff --git a/doc/build/html/wlcave_notes.html b/doc/build/html/wlcave_notes.html deleted file mode 100644 index 8c41bbd..0000000 --- a/doc/build/html/wlcave_notes.html +++ /dev/null @@ -1,362 +0,0 @@ - - - - - - - - Average Quantities — wlcstat documentation - - - - - - - - - - - - - - - -

- -
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-
- -
-

Average Quantities

-

The orientation Green function can be used to evaluate any average quantity that can be -expressed in terms of the tangent orientations. -The Green function operates as a conditional probability, such that \(G(\vec{u}|\vec{u}_{0};L)\) gives the -probability that a chain of length \(L\) with an initial tangent orientation \(\vec{u}_{0}\) will have a final -tangent orientation \(\vec{u}\). -We consider an arbitrary orientation-only average quantity \(A^{n} = -\langle A_{n}(s_{n}) A_{n-1}(s_{n-1}) \ldots A_{1}(s_{1}) \rangle\), -where \(A_{m}(s_{m})\) is a function that is expressible only in terms of the tangent orientation at arclength -position \(s_{m}\). -The arclength positions are ordered such that \(s_{1} < s_{2} < \ldots < s_{n-1} < s_{n}\). -The average quantity \(A^{n}\) is evaluated using the following procedure:

-
    -
  • An orientation Green function \(G(\vec{u}_{1}|\vec{u}_{0};s_{1})\) is inserted into \(A^{n}\) to propagate from the initial orientation \(\vec{u}_{0}\) at \(s=0\) to the first orientation \(\vec{u}_{1}\) at \(s_{1}\)

  • -
  • An orientation Green function \(G(\vec{u}_{m+1}|\vec{u}_{m};s_{m+1}-s_{m})\) is inserted into \(A^{n}\) between \(A_{m+1}\) and \(A_{m}\), resulting in a product of \(n-1\) Green functions that propagate between the internal orientations in the average

  • -
  • An orientation Green function \(G(\vec{u}|\vec{u}_{n};L-s_{n})\) is inserted into \(A^{n}\) to propagate from the \(n\) th orientation \(\vec{u}_{n}\) at \(s_{n}\) to the final orientation \(\vec{u}\) at \(L\)

  • -
  • The average \(A^{n}\) is normalized by a factor that represents the orientational integral over the full-chain Green function, i.e. the same quantity as the average without the product of \(A_{m}\)

  • -
  • The average is then evaluated by integrating over the orientations \(\vec{u}_{0}\), \(\vec{u}_{1}\), ldots, \(\vec{u}_{n}\), and \(\vec{u}\)

  • -
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This procedure is amenable to the evaluation of arbitrary average quantities that are expressible in terms of the -tangent orientations \(\vec{u}_{m}\) along the chain at positions \(s_{m}\).

-

For example, the average \(\langle \vec{u}(s_{2}) \cdot \vec{u}(s_{1}) \rangle\) (where \(s_{1} < s_{2}\)) is given by

-
-(1)\[\begin{split}\langle \vec{u}(s_{2}) \cdot \vec{u}(s_{1}) \rangle & = & -\frac{1}{\mathcal{N}} -\int d \vec{u} d \vec{u}_{2} d \vec{u}_{1} d \vec{u}_{0} -G(\vec{u}|\vec{u}_{2};L-s_{2}) -G(\vec{u}_{2}|\vec{u}_{1};s_{2}-s_{1}) -G(\vec{u}_{1}|\vec{u}_{0};s_{1}) -\vec{u}_{2} \cdot \vec{u}_{1} -\nonumber \\ -& = & -\frac{3}{\mathcal{N}} -\int d \vec{u} d \vec{u}_{2} d \vec{u}_{1} d \vec{u}_{0} -G(\vec{u}|\vec{u}_{2};L-s_{2}) -G(\vec{u}_{2}|\vec{u}_{1};s_{2}-s_{1}) -G(\vec{u}_{1}|\vec{u}_{0};s_{1}) -u_{2}^{(z)} u_{1}^{(z)},\end{split}\]
-

where rotational symmetry implies -\(\langle u^{(x)}(s_{2}) u^{(x)}(s_{1}) \rangle =\langle u^{(y)}(s_{2}) u^{(y)}(s_{1}) \rangle = \langle u^{(z)}(s_{2}) u^{(z)}(s_{1}) \rangle\) and, consequently, \(\langle \vec{u}(s_{2}) \cdot \vec{u}(s_{1}) \rangle = 3 \langle u^{(z)}(s_{2}) u^{(z)}(s_{1}) \rangle\). -The normalization factor \(\mathcal{N}\) is given by

-
-\[\mathcal{N} = \int d \vec{u} d \vec{u}_{0} G(\vec{u}|\vec{u}_{0};L) = 4 \pi.\]
-

Inserting (2) into (1) gives

-
-\[\begin{split}\langle \vec{u}(s_{2}) \cdot \vec{u}(s_{1}) \rangle & = & -\frac{3}{4 \pi} \int d \vec{u} d \vec{u}_{2} d \vec{u}_{1} d -\vec{u}_{0} \sum_{l_{2}=0}^{\infty} \sum_{m_{2}=-l_{2}}^{l_{2}} -\sum_{l_{1}=0}^{\infty} \sum_{m_{1}=-l_{1}}^{l_{1}} -\sum_{l_{0}=0}^{\infty} \sum_{m_{0}=-l_{0}}^{l_{0}} \times -\nonumber \\ & & Y_{l_{2}}^{m_{2}} (\vec{u}) -Y_{l_{2}}^{m_{2}*}(\vec{u}_{2}) Y_{l_{1}}^{m_{1}} (\vec{u}_{2}) -Y_{l_{1}}^{m_{1}*}(\vec{u}_{1}) Y_{l_{0}}^{m_{0}} (\vec{u}_{1}) -Y_{l_{0}}^{m_{0}*}(\vec{u}_{0}) \cos \theta_{2} \cos \theta_{1} -\times \nonumber \\ & & \exp \! \left[ --l_{2}(l_{2}+1)\frac{L-s_{2}}{2l_{p}} --l_{1}(l_{1}+1)\frac{s_{2}-s_{1}}{2l_{p}} --l_{0}(l_{0}+1)\frac{s_{1}}{2l_{p}} \right],\end{split}\]
-

where \(u_{2}^{(z)}=\cos \theta_{2}\). -Using the properties of the spherical harmonics [Arfken1999], -we note that \(\cos \theta = 2 \sqrt{\pi/3} Y_{1}^{0}(\vec{u})\), -and the average is written as

-
-\[\begin{split}\langle \vec{u}(s_{2}) \cdot \vec{u}(s_{1}) \rangle & = & -\int d \vec{u} d \vec{u}_{2} d \vec{u}_{1} d \vec{u}_{0} - \sum_{l_{2}=0}^{\infty} \sum_{m_{2}=-l_{2}}^{l_{2}} - \sum_{l_{1}=0}^{\infty} \sum_{m_{1}=-l_{1}}^{l_{1}} - \sum_{l_{0}=0}^{\infty} \sum_{m_{0}=-l_{0}}^{l_{0}} \times - \nonumber \\ - & & - Y_{l_{2}}^{m_{2}} (\vec{u}) - Y_{l_{2}}^{m_{2}*}(\vec{u}_{2}) - Y_{l_{1}}^{m_{1}} (\vec{u}_{2}) - Y_{l_{1}}^{m_{1}*}(\vec{u}_{1}) - Y_{l_{0}}^{m_{0}} (\vec{u}_{1}) - Y_{l_{0}}^{m_{0}*}(\vec{u}_{0}) - Y_{1}^{0*}(\vec{u}_{2}) - Y_{1}^{0}(\vec{u}_{1}) - \times - \nonumber \\ - & & - \exp \! \left[ - -l_{2}(l_{2}+1)\frac{L-s_{2}}{2l_{p}} - -l_{1}(l_{1}+1)\frac{s_{2}-s_{1}}{2l_{p}} - -l_{0}(l_{0}+1)\frac{s_{1}}{2l_{p}} - \right]\end{split}\]
-

Integration over \(\vec{u}\) and \(\vec{u}_{0}\) force \(l_{2}=m_{2}=l_{0}=m_{0}=0\), -and the subsequent integration over \(\vec{u}_{1}\) and \(\vec{u}_{2}\) result in -\(l_{1}=1\) and \(m_{1}=0\). -The final expression is given by

-
-\[\langle \vec{u}(s_{2}) \cdot \vec{u}(s_{1}) \rangle = \exp \! \left( -- \frac{s_{2} - s_{1}}{l_{p}} -\right),\]
-

which demonstrates the role of the persistence length \(l_{p}\) as a correlation length for -the tangent orientation.

-

This average shows that the orientation statistics can be used to directly evaluate averages that are expressed in -terms of the tangent vector \(\vec{u}\). -However, other average quantities can be evaluated using the orientation Green function if the quantity can be expressed in terms of the -tangent orientation. -For example, the mean-square end-to-end vector is written as

-
-\[\begin{split}\langle -\vec{R}^{2} -\rangle & = & -\int_{0}^{L} \int_{0}^{L} ds_{2} ds_{1} \langle \vec{u}(s_{2}) \cdot \vec{u}(s_{1}) \rangle -= 2 \int_{0}^{L} \int_{0}^{s_{2}} ds_{2} ds_{1} \exp \! \left( -- \frac{s_{2} - s_{1}}{l_{p}} -\right) \\ -& = & -2l_{p}^{2} \left[ -2N - 1 + \exp \left( -2N \right) -\right],\end{split}\]
-

where \(N=L/(2 l_{p})\).

-

An alternative approach to calculating averages is to use the Fourier-transformed Green’s -function as a generator of averages -(see Refs. [Spakowitz2004], [Spakowitz2005], [Spakowitz2006], and [Mehraeen2008]. -Development of this approach is provided in our -discussion of the Green’s function.

-

The ‘wlcave.py’ module provides scripts to calculate a number of -average quantities for the wormlike chain model. These include the -following:

-
    -
  • The mean-square end-to-end distance \(\langle R^{2} \rangle\)

  • -
  • The mean-square radius of gyration \(\langle \vec{R}_{G}^{2} \rangle\)

  • -
  • The 4th moment of the end-to-end distribution \(\langle R_{z}^{4} \rangle / (2 l_{p})^{4}\)

  • -
-
-

Functions contained with the ‘wlcave’ module

-
-
-wlcstat.wlcave.r2_ave(length_kuhn, dimensions=3)[source]
-

r2_ave - Calculate the average end-to-end distance squared \(\langle R^{2} \rangle / (2 l_{p})^{2}\) -for the wormlike chain model

-
-
Parameters
-
    -
  • length_kuhn (float (array)) – The length of the chain in Kuhn lengths

  • -
  • dimensions (int) – The number of dimensions (default to 3 dimensions)

  • -
-
-
Returns
-

r2 – The mean-square end-to-end distance for the wormlike chain model (non-dimensionalized by \(2 l_{p})\)

-
-
Return type
-

float (array)

-
-
-

Notes

-

See Mehraeen, et al, Phys. Rev. E, 77, 061803 (2008). (Ref [Mehraeen2008])

-
- -
-
-wlcstat.wlcave.rg2_ave(length_kuhn, dimensions=3)[source]
-

rg2_ave - Calculate the radius of gyration -\(\langle \vec{R}_{G}^{2} \rangle / (2 l_{p})^{2}\) for the wormlike chain model

-
-
Parameters
-
    -
  • length_kuhn (float (array)) – The length of the chain in Kuhn lengths

  • -
  • dimensions (int) – The number of dimensions (default to 3 dimensions)

  • -
-
-
Returns
-

rg2 – The mean-square radius of gyration for the wormlike chain model (non-dimensionalized by \(2 l_{p})\)

-
-
Return type
-

float (array)

-
-
-

Notes

-

See Mehraeen, et al, Phys. Rev. E, 77, 061803 (2008). (Ref [Mehraeen2008])

-
- -
-
-wlcstat.wlcave.rz4_ave(length_kuhn, dimensions=3)[source]
-

rz4_ave - Calculate the 4th moment of the end-to-end distribution -\(\langle R_{z}^{4} \rangle / (2 l_{p})^{4}\) for the wormlike chain model

-
-
Parameters
-
    -
  • length_kuhn (float (array)) – The length of the chain in Kuhn lengths

  • -
  • dimensions (int) – The number of dimensions (default to 3 dimensions)

  • -
-
-
Returns
-

rz4 – The mean-square end-to-end distance for the wormlike chain model (non-dimensionalized by \(2 l_{p})\)

-
-
Return type
-

float (array)

-
-
-

Notes

-

See Mehraeen, et al, Phys. Rev. E, 77, 061803 (2008). (Ref [Mehraeen2008])

-
- -
-
-

Example usage of ‘r2_ave’

-

This example gives the mean-square end-to-end distance \(\langle R^{2} \rangle / (2 l_{p})^{2}\) -(i.e. length non-dimensionalized by \(2 l_{p}\)) versus -chain length \(N = L/(2 l_{p})\) for 3 dimensions. The short-length asymptotic behavior -\(\langle R^{2} \rangle / (2 l_{p})^{2} \rightarrow N^{2}\) -and long-length asymptotic behavior -\(\langle R^{2} \rangle / (2 l_{p})^{2} \rightarrow 2 N/(d-1)\) are included to show the -limiting behaviors.

-

(Source code, png, hires.png, pdf)

-
-_images/wlcave_notes-1.png -
-
-
-

Example usage of ‘rg2_ave’

-

This example gives the mean-square radius of gyration \(\langle \vec{R}_{G}^{2} \rangle / (2 l_{p})^{2}\) -(i.e. length non-dimensionalized by \(2 l_{p}\)) versus -chain length \(N = L/(2 l_{p})\) for 3 dimensions. The short-length asymptotic behavior -\(\langle R^{2} \rangle / (2 l_{p})^{2} \rightarrow N^{2}/12\) -and long-length asymptotic behavior -\(\langle R^{2} \rangle / (2 l_{p})^{2} \rightarrow N/[3 (d-1)]\) are included to show the -limiting behaviors.

-

(Source code, png, hires.png, pdf)

-
-_images/wlcave_notes-2.png -
-
-
-

Example usage of ‘rz4_ave’

-

This example gives the 4th moment of the end-to-end distribution \(\langle R_{z}^{4} \rangle / (2 l_{p})^{4}\) -(i.e. length non-dimensionalized by \(2 l_{p}\)) versus -chain length \(N = L/(2 l_{p})\) for 3 dimensions. The short-length asymptotic behavior -\(\langle R_{z}^{2} \rangle / (2 l_{p})^{2} \rightarrow N^{4} 3 / [d (d + 2)]\) -and long-length asymptotic behavior -\(\langle R_{z}^{2} \rangle / (2 l_{p})^{2} \rightarrow 12 N^2/[d^2 (d-1)^2]\) are included to show the -limiting behaviors.

-

(Source code, png, hires.png, pdf)

-
-_images/wlcave_notes-3.png -
-
-
- - -
-
-
-
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