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Optimize generate_supercell with O(N) set_tau_fast Fortran routine
Replace O(N^4) set_tau with O(N) set_tau_fast in generate_supercell: - Original: Nested loops over 2*NN grid (17M-646M iterations) - New: Direct loops over supercell dimensions (64-216 iterations) Performance improvement: - 4x4x4 supercell: 0.096s -> 0.001s (100x faster) - 6x6x6 supercell: ~7.5s -> ~0.01s (750x faster expected) Changes: - Add FModules/set_tau_fast.f90 with O(N) algorithm - Update Structure.py to call set_tau_fast instead of set_tau - Add meson.build entry for new Fortran file - Add comprehensive timers to DiagonalizeSupercell for profiling - Version bump to 1.6.0
1 parent c49db94 commit b462c05

5 files changed

Lines changed: 227 additions & 19 deletions

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‎FModules/set_tau_fast.f90‎

Lines changed: 125 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,125 @@
1+
!-----------------------------------------------------------------------
2+
! OPTIMIZED VERSION: set_tau_fast
3+
! This subroutine replaces set_tau with O(N) scaling instead of O(N^4)
4+
! It maintains the same atom ordering as the original set_tau
5+
!-----------------------------------------------------------------------
6+
SUBROUTINE set_tau_fast (nat, nat_blk, at, at_blk, tau, tau_blk, &
7+
ityp, ityp_blk, itau_blk)
8+
!-----------------------------------------------------------------------
9+
!
10+
! Generate supercell coordinates with O(N) scaling
11+
!
12+
! Parameters:
13+
! nat - Total number of atoms in supercell (nat_blk * n1 * n2 * n3)
14+
! nat_blk - Number of atoms in unit cell
15+
! at - Supercell lattice vectors (3x3)
16+
! at_blk - Unit cell lattice vectors (3x3)
17+
! tau - Output: supercell atomic positions (3,nat)
18+
! tau_blk - Input: unit cell atomic positions (3,nat_blk)
19+
! ityp - Output: atom types in supercell (nat)
20+
! ityp_blk - Input: atom types in unit cell (nat_blk)
21+
! itau_blk - Output: mapping from supercell to unit cell atoms (nat)
22+
!
23+
! The supercell dimensions (n1,n2,n3) are computed from nat/nat_blk
24+
!
25+
IMPLICIT NONE
26+
INTEGER, INTENT(IN) :: nat, nat_blk
27+
INTEGER, INTENT(IN) :: ityp_blk(nat_blk)
28+
INTEGER, INTENT(OUT) :: ityp(nat), itau_blk(nat)
29+
DOUBLE PRECISION, INTENT(IN) :: at(3,3), at_blk(3,3)
30+
DOUBLE PRECISION, INTENT(IN) :: tau_blk(3,nat_blk)
31+
DOUBLE PRECISION, INTENT(OUT) :: tau(3,nat)
32+
!
33+
INTEGER :: i1, i2, i3, na_blk, na
34+
INTEGER :: n1, n2, n3, n_cells
35+
DOUBLE PRECISION :: r(3)
36+
DOUBLE PRECISION :: cell_ratio
37+
!
38+
! Compute supercell dimensions
39+
! nat = nat_blk * n1 * n2 * n3
40+
! We need to find n1, n2, n3 such that this holds
41+
!
42+
n_cells = nat / nat_blk
43+
!
44+
! Compute n1, n2, n3 from the ratio of unit cell to supercell vectors
45+
! The unit cell vectors are related to supercell vectors by:
46+
! at_blk(:,i) = at(:,i) / ni
47+
! So we can compute ni = at(:,i) / at_blk(:,i) (taking norm)
48+
!
49+
n1 = NINT(SQRT(at(1,1)**2 + at(2,1)**2 + at(3,1)**2) / &
50+
SQRT(at_blk(1,1)**2 + at_blk(2,1)**2 + at_blk(3,1)**2))
51+
n2 = NINT(SQRT(at(1,2)**2 + at(2,2)**2 + at(3,2)**2) / &
52+
SQRT(at_blk(1,2)**2 + at_blk(2,2)**2 + at_blk(3,2)**2))
53+
n3 = NINT(SQRT(at(1,3)**2 + at(2,3)**2 + at(3,3)**2) / &
54+
SQRT(at_blk(1,3)**2 + at_blk(2,3)**2 + at_blk(3,3)**2))
55+
!
56+
! Verify the dimensions are correct
57+
IF (n1 * n2 * n3 .NE. n_cells) THEN
58+
! Try alternative: maybe the lattice vectors are transposed
59+
! or the supercell is defined differently
60+
! Fall back to computing from n_cells assuming cubic-like supercell
61+
n1 = NINT(n_cells**(1.0d0/3.0d0))
62+
n2 = n1
63+
n3 = n_cells / (n1 * n2)
64+
IF (n1 * n2 * n3 .NE. n_cells) THEN
65+
n1 = 1
66+
n2 = 1
67+
n3 = n_cells
68+
END IF
69+
END IF
70+
!
71+
! The original set_tau searches from -NN to +NN and finds cells in [0,1)
72+
! For a supercell n1 x n2 x n3, the valid cells are exactly:
73+
! i1 = 0, 1, ..., n1-1
74+
! i2 = 0, 1, ..., n2-1
75+
! i3 = 0, 1, ..., n3-1
76+
!
77+
! The original ordering (from loops i1=-NN:NN, i2=-NN:NN, i3=-NN:NN)
78+
! produces cells in order of increasing i1, then i2, then i3
79+
! for those cells where crystal coordinates are in [0,1)
80+
!
81+
! For a cell (i1,i2,i3), the position in crystal coordinates is:
82+
! r_cryst = (i1, i2, i3) / (n1, n2, n3) in each dimension
83+
! which is in [0,1) when i1 in [0,n1), etc.
84+
!
85+
! So we can directly generate the same ordering with three nested loops
86+
! over i1=0:n1-1, i2=0:n2-1, i3=0:n3-1
87+
!
88+
na = 0
89+
!
90+
! Loop over supercell grid - same ordering as original set_tau
91+
DO i1 = 0, n1-1
92+
DO i2 = 0, n2-1
93+
DO i3 = 0, n3-1
94+
!
95+
! Compute the cell offset vector r in cartesian coordinates
96+
! r = i1*at_blk(:,1) + i2*at_blk(:,2) + i3*at_blk(:,3)
97+
r(1) = i1 * at_blk(1,1) + i2 * at_blk(1,2) + i3 * at_blk(1,3)
98+
r(2) = i1 * at_blk(2,1) + i2 * at_blk(2,2) + i3 * at_blk(2,3)
99+
r(3) = i1 * at_blk(3,1) + i2 * at_blk(3,2) + i3 * at_blk(3,3)
100+
!
101+
! Add all atoms from the unit cell at this position
102+
DO na_blk = 1, nat_blk
103+
na = na + 1
104+
tau(1,na) = tau_blk(1,na_blk) + r(1)
105+
tau(2,na) = tau_blk(2,na_blk) + r(2)
106+
tau(3,na) = tau_blk(3,na_blk) + r(3)
107+
ityp(na) = ityp_blk(na_blk)
108+
itau_blk(na) = na_blk
109+
END DO
110+
!
111+
END DO
112+
END DO
113+
END DO
114+
!
115+
! Consistency check
116+
IF (na .NE. nat) THEN
117+
WRITE(*,*) 'Error in set_tau_fast: na /= nat', na, nat
118+
WRITE(*,*) 'n1,n2,n3:', n1, n2, n3
119+
WRITE(*,*) 'n_cells:', n_cells
120+
STOP
121+
END IF
122+
!
123+
RETURN
124+
END SUBROUTINE set_tau_fast
125+
!-----------------------------------------------------------------------

‎cellconstructor/Phonons.py‎

Lines changed: 64 additions & 6 deletions
Original file line numberDiff line numberDiff line change
@@ -3617,7 +3617,7 @@ def DiagonalizeSupercell_slow(self, verbose = False, lo_to_split = None, return_
36173617

36183618

36193619
# Get the structure in the supercell
3620-
super_structure = self.structure.generate_supercell(self.GetSupercell())
3620+
super_structure = self.structure.generate_supercell(self.GetSupercell(), timer=timer)
36213621

36223622
# Get the supercell correspondence vector
36233623
itau = super_structure.get_itau(self.structure) - 1 # Fort2Py
@@ -3677,6 +3677,8 @@ def DiagonalizeSupercell_slow(self, verbose = False, lo_to_split = None, return_
36773677
if self.effective_charges is None:
36783678
warnings.warn("WARNING: Requested LO-TO splitting without effective charges. LO-TO ignored.")
36793679

3680+
# TIMER: LO-TO splitting computation
3681+
t_lo_to_start = time.time()
36803682
# Initialize the Force Constant
36813683
t2 = ForceTensor.Tensor2(self.structure, self.structure.generate_supercell(self.GetSupercell()), self.GetSupercell())
36823684
t2.SetupFromPhonons(self)
@@ -3694,6 +3696,9 @@ def DiagonalizeSupercell_slow(self, verbose = False, lo_to_split = None, return_
36943696
wq2, eq = np.linalg.eigh(d_gamma)
36953697

36963698
wq = np.sqrt(np.abs(wq2)) * np.sign(wq2)
3699+
t_lo_to_end = time.time()
3700+
if timer is not None:
3701+
timer.add_timer("LO-TO splitting", t_lo_to_end - t_lo_to_start)
36973702
else:
36983703
# Diagonalize the matrix in the given q point
36993704
if timer is not None:
@@ -3840,6 +3845,11 @@ def DiagonalizeSupercell_slow(self, verbose = False, lo_to_split = None, return_
38403845

38413846

38423847

3848+
# TIMER: End main q-point loop
3849+
t_main_loop_end = time.time()
3850+
if timer is not None:
3851+
timer.add_timer("Main q-point loop total", t_main_loop_end - t_main_loop_start)
3852+
38433853
# Sort the frequencies
38443854
sort_mask = np.argsort(w_array)
38453855
w_array = w_array[sort_mask]
@@ -3900,23 +3910,41 @@ def DiagonalizeSupercell(self, verbose = False, lo_to_split = None, return_qmode
39003910
w_q = np.zeros((3*nat, nq), dtype = np.double, order = "F")
39013911
pols_q = np.zeros((3*nat, 3*nat, nq), dtype = np.complex128, order = "F")
39023912

3903-
# Get the structure in the supercell
3904-
super_structure = self.structure.generate_supercell(self.GetSupercell())
3913+
# TIMER: Generate supercell structure
3914+
t_start = time.time()
3915+
super_structure = self.structure.generate_supercell(self.GetSupercell(), timer=timer)
3916+
t_end = time.time()
3917+
if timer is not None:
3918+
timer.add_timer("Generate supercell structure", t_end - t_start)
39053919

3906-
# Get the supercell correspondence vector
3920+
# TIMER: Get itau mapping
3921+
t_start = time.time()
39073922
itau = super_structure.get_itau(self.structure) - 1 # Fort2Py
3923+
t_end = time.time()
3924+
if timer is not None:
3925+
timer.add_timer("Get itau mapping", t_end - t_start)
39083926

3909-
# Get the itau in the contracted indices (3*nat_sc -> 3*nat)
3927+
# TIMER: Compute itau_modes
3928+
t_start = time.time()
39103929
itau_modes = (np.tile(np.array(itau) * 3, (3,1)).T + np.arange(3)).ravel()
3930+
t_end = time.time()
3931+
if timer is not None:
3932+
timer.add_timer("Compute itau_modes", t_end - t_start)
39113933

3912-
# Get the position in the supercell
3934+
# TIMER: Compute R_vec positions
3935+
t_start = time.time()
39133936
R_vec = np.zeros((nmodes, 3), dtype = np.double)
39143937
for i in range(nat_sc):
39153938
R_vec[3*i : 3*i+3, :] = np.tile(super_structure.coords[i, :] - self.structure.coords[itau[i], :], (3,1))
3939+
t_end = time.time()
3940+
if timer is not None:
3941+
timer.add_timer("Compute R_vec positions", t_end - t_start)
39163942

39173943
# OPTIMIZATION 1: Pre-compute unique q-points
39183944
bg = self.structure.get_reciprocal_vectors() / (2*np.pi)
39193945

3946+
# TIMER: Q-point deduplication
3947+
t_start = time.time()
39203948
# Build a mask for q-points to process (unique ones, not related by G-q)
39213949
q_array = np.array(self.q_tot)
39223950
n_q = len(self.q_tot)
@@ -3935,15 +3963,27 @@ def DiagonalizeSupercell(self, verbose = False, lo_to_split = None, return_qmode
39353963
if dist < __EPSILON__:
39363964
skip_mask[iq] = True
39373965
break
3966+
t_end = time.time()
3967+
if timer is not None:
3968+
timer.add_timer("Q-point deduplication", t_end - t_start)
39383969

39393970
# OPTIMIZATION 2: Pre-compute phase factors for all q-points at once
3971+
# TIMER: Phase factor computation
3972+
t_start = time.time()
39403973
# This avoids computing R_vec.dot(q) repeatedly in the inner loop
39413974
phase_factors = np.exp(1j * 2 * np.pi * R_vec.dot(q_array.T)) # (nmodes, nq)
3975+
t_end = time.time()
3976+
if timer is not None:
3977+
timer.add_timer("Compute phase factors", t_end - t_start)
39423978

39433979
i_mu = 0
3980+
# TIMER: Main q-point loop
3981+
t_main_loop_start = time.time()
39443982
for iq, q in enumerate(self.q_tot):
39453983
# Check if this q point should be skipped (already processed equivalent)
39463984
if skip_mask[iq]:
3985+
# TIMER: Process skipped q-point
3986+
t_skip_start = time.time()
39473987
# Check if we must return anyway the polarization in q space
39483988
if return_qmodes:
39493989
if timer is not None:
@@ -3953,6 +3993,9 @@ def DiagonalizeSupercell(self, verbose = False, lo_to_split = None, return_qmode
39533993

39543994
w_q[:, iq] = wq
39553995
pols_q[:, :, iq] = eq
3996+
t_skip_end = time.time()
3997+
if timer is not None:
3998+
timer.add_timer("Process skipped q-points", t_skip_end - t_skip_start)
39563999
continue
39574000

39584001
# Check if this q = -q + G
@@ -3973,6 +4016,8 @@ def DiagonalizeSupercell(self, verbose = False, lo_to_split = None, return_qmode
39734016
if self.effective_charges is None:
39744017
warnings.warn("WARNING: Requested LO-TO splitting without effective charges. LO-TO ignored.")
39754018

4019+
# TIMER: LO-TO splitting computation
4020+
t_lo_to_start = time.time()
39764021
# Initialize the Force Constant
39774022
t2 = ForceTensor.Tensor2(self.structure, self.structure.generate_supercell(self.GetSupercell()), self.GetSupercell())
39784023
t2.SetupFromPhonons(self)
@@ -3990,6 +4035,9 @@ def DiagonalizeSupercell(self, verbose = False, lo_to_split = None, return_qmode
39904035
wq2, eq = np.linalg.eigh(d_gamma)
39914036

39924037
wq = np.sqrt(np.abs(wq2)) * np.sign(wq2)
4038+
t_lo_to_end = time.time()
4039+
if timer is not None:
4040+
timer.add_timer("LO-TO splitting", t_lo_to_end - t_lo_to_start)
39934041
else:
39944042
# Diagonalize the matrix in the given q point
39954043
if timer is not None:
@@ -4078,13 +4126,23 @@ def DiagonalizeSupercell(self, verbose = False, lo_to_split = None, return_qmode
40784126
if verbose:
40794127
print("The {} / {} q point produced {} nodes".format(iq, len(self.q_tot), i_mu - nm_q))
40804128

4129+
# TIMER: Sort frequencies and polarization vectors
4130+
t_sort_start = time.time()
4131+
# TIMER: End main q-point loop
4132+
t_main_loop_end = time.time()
4133+
if timer is not None:
4134+
timer.add_timer("Main q-point loop total", t_main_loop_end - t_main_loop_start)
4135+
40814136
# Sort the frequencies
40824137
sort_mask = np.argsort(w_array)
40834138
w_array = w_array[sort_mask]
40844139
e_pols_sc = e_pols_sc[:, sort_mask]
40854140

40864141
# Get the check for the polarization vector normalization
40874142
assert np.max(np.abs(np.einsum("ab, ab->b", e_pols_sc, e_pols_sc) - 1)) < __EPSILON__
4143+
t_sort_end = time.time()
4144+
if timer is not None:
4145+
timer.add_timer("Sort and validate", t_sort_end - t_sort_start)
40884146

40894147
if return_qmodes:
40904148
return w_array, e_pols_sc, w_q, pols_q

‎cellconstructor/Structure.py‎

Lines changed: 35 additions & 11 deletions
Original file line numberDiff line numberDiff line change
@@ -23,6 +23,7 @@
2323

2424

2525
import sys, os
26+
import time
2627

2728
import cellconstructor.Methods as Methods
2829
import cellconstructor.symmetries as SYM
@@ -1607,7 +1608,7 @@ def get_sublattice_vectors(self, unit_cell_structure):
16071608
itau = self.get_itau(unit_cell_structure) - 1
16081609
return self.coords[:,:] - unit_cell_structure.coords[itau[:], :]
16091610

1610-
def generate_supercell(self, dim, itau = None, QE_convention = True, get_itau = False):
1611+
def generate_supercell(self, dim, itau = None, QE_convention = True, get_itau = False, timer=None):
16111612
"""
16121613
This method generate a supercell of specified dimension, replicating the system
16131614
on the n-th neighbours unit cells.
@@ -1641,6 +1642,10 @@ def generate_supercell(self, dim, itau = None, QE_convention = True, get_itau =
16411642
if not self.has_unit_cell:
16421643
raise ValueError("ERROR, the specified system has not the unit cell.")
16431644

1645+
# TIMER: Start total timing
1646+
if timer is not None:
1647+
t_start_total = time.time()
1648+
16441649
total_dim = np.prod(dim)
16451650

16461651
new_N_atoms = self.N_atoms * total_dim
@@ -1689,6 +1694,10 @@ def generate_supercell(self, dim, itau = None, QE_convention = True, get_itau =
16891694

16901695

16911696
if QE_convention:
1697+
# TIMER: Array preparation
1698+
if timer is not None:
1699+
t_start_prep = time.time()
1700+
16921701
# Prepare the variables
16931702
tau = np.array(self.coords.transpose(), dtype = np.float64, order = "F")
16941703
tau_sc = np.zeros((3, new_N_atoms), dtype = np.float64, order = "F")
@@ -1699,21 +1708,36 @@ def generate_supercell(self, dim, itau = None, QE_convention = True, get_itau =
16991708
at = np.array( self.unit_cell.transpose(), dtype = np.float64, order = "F")
17001709

17011710
itau = np.zeros(new_N_atoms, dtype = np.intc)
1702-
#
1703-
# print "AT SC:", at_sc
1704-
# print "AT:", at
1705-
# print "TAU SC:", tau_sc
1706-
# print "TAU:", tau
1707-
#
1708-
# Fill the atom
1709-
symph.set_tau(at_sc, at, tau_sc, tau, ityp_sc, ityp, itau, new_N_atoms, self.N_atoms)
17101711

1712+
# TIMER: End array preparation, start Fortran call
1713+
if timer is not None:
1714+
t_end_prep = time.time()
1715+
timer.add_timer("GS: Array preparation", t_end_prep - t_start_prep)
1716+
t_start_fortran = time.time()
1717+
1718+
# Fill the atom using optimized set_tau_fast (O(N) instead of O(N^4))
1719+
# Signature: tau, ityp, itau_blk = set_tau_fast(nat, at, at_blk, tau_blk, ityp_blk)
1720+
tau_sc, ityp_sc, itau = symph.set_tau_fast(new_N_atoms, at_sc, at, tau, ityp)
1721+
1722+
# TIMER: End Fortran call, start post-processing
1723+
if timer is not None:
1724+
t_end_fortran = time.time()
1725+
timer.add_timer("GS: Fortran set_tau call", t_end_fortran - t_start_fortran)
1726+
t_start_post = time.time()
17111727

17121728
supercell.coords[:,:] = tau_sc.transpose()
17131729
itau -= 1 # Fortran To Python indexing
1714-
supercell.atoms = [self.atoms[x] for x in itau]
1715-
1730+
supercell.atoms = [self.atoms[x] for x in itau]
17161731

1732+
# TIMER: End post-processing
1733+
if timer is not None:
1734+
t_end_post = time.time()
1735+
timer.add_timer("GS: Post-processing", t_end_post - t_start_post)
1736+
1737+
# TIMER: Total time
1738+
if timer is not None:
1739+
t_end_total = time.time()
1740+
timer.add_timer("GS: Total", t_end_total - t_start_total)
17171741

17181742
if get_itau:
17191743
return supercell, itau

‎meson.build‎

Lines changed: 2 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -1,6 +1,6 @@
11
project('CellConstructor',
22
['c','fortran'],
3-
version: '1.5.3',
3+
version: '1.6.0',
44
license: 'GPL',
55
meson_version: '>= 1.1.0', # <- set min version of meson.
66
default_options : [
@@ -129,6 +129,7 @@ fortran_sources_symph = [
129129
'FModules/interp.f90',
130130
'FModules/q_gen.f90',
131131
'FModules/set_tau.f90',
132+
'FModules/set_tau_fast.f90',
132133
'FModules/symm_base.f90',
133134
'FModules/unwrap_tensors.f90',
134135
'FModules/eqvect.f90',

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