def calculate_blocked_density_matrix(self, f_n, C_nM):
nbands = self.bd.nbands
nao = self.nao
dtype = C_nM.dtype
self.nMdescriptor.checkassert(C_nM)
if self.gd.rank == 0:
Cf_nM = (C_nM * f_n[:, None]).conj()
else:
C_nM = self.nM_unique_descriptor.zeros(dtype=dtype)
Cf_nM = self.nM_unique_descriptor.zeros(dtype=dtype)
r = Redistributor(self.block_comm, self.nM_unique_descriptor,
self.mmdescriptor)
Cf_mm = self.mmdescriptor.zeros(dtype=dtype)
r.redistribute(Cf_nM, Cf_mm, nbands, nao)
del Cf_nM
C_mm = self.mmdescriptor.zeros(dtype=dtype)
r.redistribute(C_nM, C_mm, nbands, nao)
# no use to delete C_nM as it's in the input...
rho_mm = self.mmdescriptor.zeros(dtype=dtype)
pblas_simple_gemm(self.mmdescriptor,
self.mmdescriptor,
self.mmdescriptor,
Cf_mm,
C_mm,
rho_mm,
transa='T')
return rho_mm
def scalapack_diagonalize(self, H_sS):
mb = 32
N = self.nS
g1 = BlacsGrid(world, size, 1)
g2 = BlacsGrid(world, size//2, 2)
nndesc1 = g1.new_descriptor(N, N, self.nS_local, N)
nndesc2 = g2.new_descriptor(N, N, mb, mb)
A_ss = nndesc2.empty(dtype=H_sS.dtype)
redistributor = Redistributor(world, nndesc1, nndesc2)
redistributor.redistribute(H_sS, A_ss)
# diagonalize
v_ss = nndesc2.zeros(dtype=A_ss.dtype)
w_S = np.zeros(N,dtype=float)
nndesc2.diagonalize_dc(A_ss, v_ss, w_S, 'L')
# distribute the eigenvectors to master
v_sS = np.zeros_like(H_sS)
redistributor = Redistributor(world, nndesc2, nndesc1)
redistributor.redistribute(v_ss, v_sS)
# v2_SS = np.zeros((self.nS, self.nS), dtype=complex)
# world.all_gather(v_sS, v2_SS)
return w_S, v_sS.conj()
def scalapack_diagonalize(self, H_sS):
mb = 32
N = self.nS
g1 = BlacsGrid(world, size, 1)
g2 = BlacsGrid(world, size // 2, 2)
nndesc1 = g1.new_descriptor(N, N, self.nS_local, N)
nndesc2 = g2.new_descriptor(N, N, mb, mb)
A_ss = nndesc2.empty(dtype=H_sS.dtype)
redistributor = Redistributor(world, nndesc1, nndesc2)
redistributor.redistribute(H_sS, A_ss)
# diagonalize
v_ss = nndesc2.zeros(dtype=A_ss.dtype)
w_S = np.zeros(N, dtype=float)
nndesc2.diagonalize_dc(A_ss, v_ss, w_S, 'L')
# distribute the eigenvectors to master
v_sS = np.zeros_like(H_sS)
redistributor = Redistributor(world, nndesc2, nndesc1)
redistributor.redistribute(v_ss, v_sS)
# v2_SS = np.zeros((self.nS, self.nS), dtype=complex)
# world.all_gather(v_sS, v2_SS)
return w_S, v_sS.conj()
def diagonalize(self):
print('Diagonalizing Hamiltonian', file=self.fd)
"""The t and T represent local and global
eigenstates indices respectively
"""
# Non-Hermitian matrix can only use linalg.eig
if not self.td:
print(' Using numpy.linalg.eig...', file=self.fd)
print(' Eliminated %s pair orbitals' % len(self.excludef_S),
file=self.fd)
self.H_SS = self.collect_A_SS(self.H_sS)
self.w_T = np.zeros(self.nS - len(self.excludef_S), complex)
if world.rank == 0:
self.H_SS = np.delete(self.H_SS, self.excludef_S, axis=0)
self.H_SS = np.delete(self.H_SS, self.excludef_S, axis=1)
self.w_T, self.v_ST = np.linalg.eig(self.H_SS)
world.broadcast(self.w_T, 0)
self.df_S = np.delete(self.df_S, self.excludef_S)
self.rhoG0_S = np.delete(self.rhoG0_S, self.excludef_S)
# Here the eigenvectors are returned as complex conjugated rows
else:
if world.size == 1:
print(' Using lapack...', file=self.fd)
from gpaw.utilities.lapack import diagonalize
self.w_T = np.zeros(self.nS)
diagonalize(self.H_sS, self.w_T)
self.v_St = self.H_sS.conj().T
else:
print(' Using scalapack...', file=self.fd)
nS = self.nS
ns = -(-self.kd.nbzkpts // world.size) * (self.nv * self.nc *
self.spins *
(self.spinors + 1)**2)
grid = BlacsGrid(world, world.size, 1)
desc = grid.new_descriptor(nS, nS, ns, nS)
desc2 = grid.new_descriptor(nS, nS, 2, 2)
H_tmp = desc2.zeros(dtype=complex)
r = Redistributor(world, desc, desc2)
r.redistribute(self.H_sS, H_tmp)
self.w_T = np.empty(nS)
v_tmp = desc2.empty(dtype=complex)
desc2.diagonalize_dc(H_tmp, v_tmp, self.w_T)
r = Redistributor(grid.comm, desc2, desc)
self.v_St = desc.zeros(dtype=complex)
r.redistribute(v_tmp, self.v_St)
self.v_St = self.v_St.conj().T
if self.write_v and self.td:
# Cannot use par_save without td
self.par_save('v_TS.ulm', 'v_TS', self.v_St.T)
return
def redistribute_H(self, H_sS):
g1 = BlacsGrid(world, size, 1)
g2 = BlacsGrid(world, 1, size)
N = self.nS
nndesc1 = g1.new_descriptor(N, N, self.nS_local, N)
nndesc2 = g2.new_descriptor(N, N, N, self.nS_local)
H_Ss = nndesc2.empty(dtype=H_sS.dtype)
redistributor = Redistributor(world, nndesc1, nndesc2)
redistributor.redistribute(H_sS, H_Ss)
return H_Ss
def redistribute_H(self, H_sS):
g1 = BlacsGrid(world, size, 1)
g2 = BlacsGrid(world, 1, size)
N = self.nS
nndesc1 = g1.new_descriptor(N, N, self.nS_local, N)
nndesc2 = g2.new_descriptor(N, N, N, self.nS_local)
H_Ss = nndesc2.empty(dtype=H_sS.dtype)
redistributor = Redistributor(world, nndesc1, nndesc2)
redistributor.redistribute(H_sS, H_Ss)
return H_Ss
def parallel_eigh(matrixfile, blacsgrid=(4, 2), blocksize=64):
"""Diagonalize matrix in parallel"""
assert np.prod(blacsgrid) == world.size
grid = BlacsGrid(world, *blacsgrid)
if world.rank == MASTER:
H_MM = np.load(matrixfile)
assert H_MM.ndim == 2
assert H_MM.shape[0] == H_MM.shape[1]
NM = len(H_MM)
else:
NM = 0
NM = world.sum(NM) # Distribute matrix shape to all nodes
# descriptor for the individual blocks
block_desc = grid.new_descriptor(NM, NM, blocksize, blocksize)
# descriptor for global array on MASTER
local_desc = grid.new_descriptor(NM, NM, NM, NM)
# Make some dummy array on all the slaves
if world.rank != MASTER:
H_MM = local_desc.zeros()
assert local_desc.check(H_MM)
# The local version of the matrix
H_mm = block_desc.empty()
# Distribute global array to smaller blocks
redistributor = Redistributor(world, local_desc, block_desc)
redistributor.redistribute(H_MM, H_mm)
# Allocate arrays for eigenvalues and -vectors
eps_M = np.empty(NM)
C_mm = block_desc.empty()
block_desc.diagonalize_ex(H_mm, C_mm, eps_M)
# Collect eigenvectors on MASTER
C_MM = local_desc.empty()
redistributor2 = Redistributor(world, block_desc, local_desc)
redistributor2.redistribute(C_mm, C_MM)
# Return eigenvalues and -vectors on Master
if world.rank == MASTER:
return eps_M, C_MM
else:
return None, None
def parallel_eigh(matrixfile, blacsgrid=(4, 2), blocksize=64):
"""Diagonalize matrix in parallel"""
assert np.prod(blacsgrid) == world.size
grid = BlacsGrid(world, *blacsgrid)
if world.rank == MASTER:
H_MM = np.load(matrixfile)
assert H_MM.ndim == 2
assert H_MM.shape[0] == H_MM.shape[1]
NM = len(H_MM)
else:
NM = 0
NM = world.sum(NM) # Distribute matrix shape to all nodes
# descriptor for the individual blocks
block_desc = grid.new_descriptor(NM, NM, blocksize, blocksize)
# descriptor for global array on MASTER
local_desc = grid.new_descriptor(NM, NM, NM, NM)
# Make some dummy array on all the slaves
if world.rank != MASTER:
H_MM = local_desc.zeros()
assert local_desc.check(H_MM)
# The local version of the matrix
H_mm = block_desc.empty()
# Distribute global array to smaller blocks
redistributor = Redistributor(world, local_desc, block_desc)
redistributor.redistribute(H_MM, H_mm)
# Allocate arrays for eigenvalues and -vectors
eps_M = np.empty(NM)
C_mm = block_desc.empty()
block_desc.diagonalize_ex(H_mm, C_mm, eps_M)
# Collect eigenvectors on MASTER
C_MM = local_desc.empty()
redistributor2 = Redistributor(world, block_desc, local_desc)
redistributor2.redistribute(C_mm, C_MM)
# Return eigenvalues and -vectors on Master
if world.rank == MASTER:
return eps_M, C_MM
else:
return None, None
def distribute_MM(wfs, a_MM):
ksl = wfs.ksl
if not ksl.using_blacs:
return a_MM
dtype = a_MM.dtype
ksl_comm = ksl.block_comm
NM = ksl.nao
grid = BlacsGrid(ksl_comm, 1, 1)
MM_descriptor = grid.new_descriptor(NM, NM, NM, NM)
MM2mm = Redistributor(ksl_comm, MM_descriptor, ksl.mmdescriptor)
if ksl_comm.rank != 0:
a_MM = MM_descriptor.empty(dtype=dtype)
a_mm = ksl.mmdescriptor.empty(dtype=dtype)
MM2mm.redistribute(a_MM, a_mm)
return a_mm
def redistribute(self, in_wGG, out_x=None):
"""Redistribute array.
Switch between two kinds of parallel distributions:
1) parallel over G-vectors (second dimension of in_wGG)
2) parallel over frequency (first dimension of in_wGG)
Returns new array using the memory in the 1-d array out_x.
"""
comm = self.blockcomm
if comm.size == 1:
return in_wGG
nw = len(self.omega_w)
nG = in_wGG.shape[2]
mynw = (nw + comm.size - 1) // comm.size
mynG = (nG + comm.size - 1) // comm.size
bg1 = BlacsGrid(comm, comm.size, 1)
bg2 = BlacsGrid(comm, 1, comm.size)
md1 = BlacsDescriptor(bg1, nw, nG**2, mynw, nG**2)
md2 = BlacsDescriptor(bg2, nw, nG**2, nw, mynG * nG)
if len(in_wGG) == nw:
mdin = md2
mdout = md1
else:
mdin = md1
mdout = md2
r = Redistributor(comm, mdin, mdout)
outshape = (mdout.shape[0], mdout.shape[1] // nG, nG)
if out_x is None:
out_wGG = np.empty(outshape, complex)
else:
out_wGG = out_x[:np.product(outshape)].reshape(outshape)
r.redistribute(in_wGG.reshape(mdin.shape),
out_wGG.reshape(mdout.shape))
return out_wGG
def redistribute(self, in_wGG, out_x=None):
"""Redistribute array.
Switch between two kinds of parallel distributions:
1) parallel over G-vectors (second dimension of in_wGG)
2) parallel over frequency (first dimension of in_wGG)
Returns new array using the memory in the 1-d array out_x.
"""
comm = self.blockcomm
if comm.size == 1:
return in_wGG
nw = len(self.omega_w)
nG = in_wGG.shape[2]
mynw = (nw + comm.size - 1) // comm.size
mynG = (nG + comm.size - 1) // comm.size
bg1 = BlacsGrid(comm, comm.size, 1)
bg2 = BlacsGrid(comm, 1, comm.size)
md1 = BlacsDescriptor(bg1, nw, nG**2, mynw, nG**2)
md2 = BlacsDescriptor(bg2, nw, nG**2, nw, mynG * nG)
if len(in_wGG) == nw:
mdin = md2
mdout = md1
else:
mdin = md1
mdout = md2
r = Redistributor(comm, mdin, mdout)
outshape = (mdout.shape[0], mdout.shape[1] // nG, nG)
if out_x is None:
out_wGG = np.empty(outshape, complex)
else:
out_wGG = out_x[:np.product(outshape)].reshape(outshape)
r.redistribute(in_wGG.reshape(mdin.shape),
out_wGG.reshape(mdout.shape))
return out_wGG
def scal_diagonalize(A, nodes='master'):
# Diagonalize matrix A (size N*N) with scalapack
# Usage: eps, B = scal_diagonalize(A)
# eps and B and the eigenvalues and eigenvectors
# nodes = 'master': eigenvectors only available on master node
# nodes = 'all': eigenvectors broadcast to all nodes
# make sure A is N*N, and hermitian
N = A.shape[0]
assert A.shape[0] == A.shape[1]
for i in range(N):
for j in range(i, N):
assert A[i,j] == A[j,i].conj()
# create blacs descriptor
mb = 64
g = BlacsGrid(world, 2, size//2)
nndesc1 = g.new_descriptor(N, N, N, N)
nndesc2 = g.new_descriptor(N, N, mb, mb)
# distribute A to blacs grid A_
if rank != 0:
A = nndesc1.zeros(dtype=A.dtype)
A_ = nndesc2.empty(dtype=A.dtype)
redistributor = Redistributor(world, nndesc1, nndesc2)
redistributor.redistribute(A, A_)
# diagonalize
B_ = nndesc2.zeros(dtype=A.dtype)
eps = np.zeros(N,dtype=A.dtype)
nndesc2.diagonalize_dc(A_, B_, eps, 'L')
# distribute the eigenvectors to master
B = np.zeros_like(A)
redistributor = Redistributor(world, nndesc2, nndesc1)
redistributor.redistribute(B_, B)
if nodes == 'master':
return eps, B
elif nodes == 'all':
if rank != 0:
B = np.zeros((N, N))
world.broadcast(B, 0)
return eps, B
def scal_diagonalize(A, nodes='master'):
# Diagonalize matrix A (size N*N) with scalapack
# Usage: eps, B = scal_diagonalize(A)
# eps and B and the eigenvalues and eigenvectors
# nodes = 'master': eigenvectors only available on master node
# nodes = 'all': eigenvectors broadcast to all nodes
# make sure A is N*N, and hermitian
N = A.shape[0]
assert A.shape[0] == A.shape[1]
for i in range(N):
for j in range(i, N):
assert A[i, j] == A[j, i].conj()
# create blacs descriptor
mb = 64
g = BlacsGrid(world, 2, size // 2)
nndesc1 = g.new_descriptor(N, N, N, N)
nndesc2 = g.new_descriptor(N, N, mb, mb)
# distribute A to blacs grid A_
if rank != 0:
A = nndesc1.zeros(dtype=A.dtype)
A_ = nndesc2.empty(dtype=A.dtype)
redistributor = Redistributor(world, nndesc1, nndesc2)
redistributor.redistribute(A, A_)
# diagonalize
B_ = nndesc2.zeros(dtype=A.dtype)
eps = np.zeros(N, dtype=A.dtype)
nndesc2.diagonalize_dc(A_, B_, eps, 'L')
# distribute the eigenvectors to master
B = np.zeros_like(A)
redistributor = Redistributor(world, nndesc2, nndesc1)
redistributor.redistribute(B_, B)
if nodes == 'master':
return eps, B
elif nodes == 'all':
if rank != 0:
B = np.zeros((N, N))
world.broadcast(B, 0)
return eps, B
def distribute_to_columns(self, rho_mm, srcdescriptor):
redistributor = Redistributor(
self.block_comm, # XXX
srcdescriptor,
self.mM_unique_descriptor)
rho_mM = redistributor.redistribute(rho_mm)
if self.gd.rank != 0:
rho_mM = self.mMdescriptor.zeros(dtype=rho_mm.dtype)
self.gd.comm.broadcast(rho_mM, 0)
return rho_mM
def test(comm, M, N, mcpus, ncpus, mb, nb):
grid0 = BlacsGrid(comm, 1, 1)
desc0 = grid0.new_descriptor(M, N, M, N, 0, 0)
A_mn = desc0.zeros(dtype=float)
A_mn[:] = comm.size + 1
grid1 = BlacsGrid(comm, mcpus, ncpus)
desc1 = grid1.new_descriptor(M, N, mb, nb, 0, 0) # ???
B_mn = desc1.zeros(dtype=float)
B_mn[:] = comm.rank
if comm.rank == 0:
msg = 'Slices of global matrix indices by rank'
print(msg)
print('-' * len(msg))
for rank in range(comm.size):
comm.barrier()
if rank == comm.rank:
print('Rank %d:' % rank)
last_Mstart = -1
for Mstart, Mstop, Nstart, Nstop, block in desc1.my_blocks(B_mn):
if Mstart > last_Mstart and last_Mstart >= 0:
print()
print('[%3d:%3d, %3d:%3d]' % (Mstart, Mstop, Nstart, Nstop),
end=' ')
last_Mstart = Mstart
assert (block == comm.rank).all()
#print block
#print
print()
print()
comm.barrier()
redistributor = Redistributor(comm, desc1, desc0)
redistributor.redistribute(B_mn, A_mn)
if comm.rank == 0:
msg = 'Rank where each element of the global matrix is stored'
print(msg)
print('-' * len(msg))
print(A_mn)
def test(comm, M, N, mcpus, ncpus, mb, nb):
grid0 = BlacsGrid(comm, 1, 1)
desc0 = grid0.new_descriptor(M, N, M, N, 0, 0)
A_mn = desc0.zeros(dtype=float)
A_mn[:] = comm.size + 1
grid1 = BlacsGrid(comm, mcpus, ncpus)
desc1 = grid1.new_descriptor(M, N, mb, nb, 0, 0) # ???
B_mn = desc1.zeros(dtype=float)
B_mn[:] = comm.rank
if comm.rank == 0:
msg = 'Slices of global matrix indices by rank'
print msg
print '-' * len(msg)
for rank in range(comm.size):
comm.barrier()
if rank == comm.rank:
print 'Rank %d:' % rank
last_Mstart = -1
for Mstart, Mstop, Nstart, Nstop, block in desc1.my_blocks(B_mn):
if Mstart > last_Mstart and last_Mstart >= 0:
print
print '[%3d:%3d, %3d:%3d]' % (Mstart, Mstop, Nstart, Nstop),
last_Mstart = Mstart
assert (block == comm.rank).all()
#print block
#print
print
print
comm.barrier()
redistributor = Redistributor(comm, desc1, desc0)
redistributor.redistribute(B_mn, A_mn)
if comm.rank == 0:
msg = 'Rank where each element of the global matrix is stored'
print msg
print '-' * len(msg)
print A_mn
def calculate_density_matrix(self, f_n, C_nM, rho_mM=None):
"""Calculate density matrix from occupations and coefficients.
Presently this function performs the usual scalapack 3-step trick:
redistribute-numbercrunching-backdistribute.
Notes on future performance improvement.
As per the current framework, C_nM exists as copies on each
domain, i.e. this is not parallel over domains. We'd like to
correct this and have an efficient distribution using e.g. the
block communicator.
The diagonalization routine and other parts of the code should
however be changed to accommodate the following scheme:
Keep coefficients in C_mm form after the diagonalization.
rho_mm can then be directly calculated from C_mm without
redistribution, after which we only need to redistribute
rho_mm across domains.
"""
dtype = C_nM.dtype
rho_mm = self.calculate_blocked_density_matrix(f_n, C_nM)
rback = Redistributor(self.block_comm, self.mmdescriptor,
self.mM_unique_descriptor)
rho1_mM = self.mM_unique_descriptor.zeros(dtype=dtype)
rback.redistribute(rho_mm, rho1_mM)
del rho_mm
if rho_mM is None:
if self.gd.rank == 0:
rho_mM = rho1_mM
else:
rho_mM = self.mMdescriptor.zeros(dtype=dtype)
self.gd.comm.broadcast(rho_mM, 0)
return rho_mM
def collect_wuMM(wfs, a_wuMM, w, s, k):
# This function is based on
# gpaw/wavefunctions/base.py: WaveFunctions.collect_auxiliary()
dtype = a_wuMM[0][0].dtype
ksl = wfs.ksl
NM = ksl.nao
kpt_rank, u = wfs.kd.get_rank_and_index(s, k)
ksl_comm = ksl.block_comm
if wfs.kd.comm.rank == kpt_rank:
a_MM = a_wuMM[w][u]
# Collect within blacs grid
if ksl.using_blacs:
a_mm = a_MM
grid = BlacsGrid(ksl_comm, 1, 1)
MM_descriptor = grid.new_descriptor(NM, NM, NM, NM)
mm2MM = Redistributor(ksl_comm, ksl.mmdescriptor, MM_descriptor)
a_MM = MM_descriptor.empty(dtype=dtype)
mm2MM.redistribute(a_mm, a_MM)
# KSL master send a_MM to the global master
if ksl_comm.rank == 0:
if kpt_rank == 0:
assert wfs.world.rank == 0
# I have it already
return a_MM
else:
wfs.kd.comm.send(a_MM, 0, 2017)
return None
elif ksl_comm.rank == 0 and kpt_rank != 0:
assert wfs.world.rank == 0
a_MM = np.empty((NM, NM), dtype=dtype)
wfs.kd.comm.receive(a_MM, kpt_rank, 2017)
return a_MM
def distribute_frequencies(self, chi0_wGG):
"""Distribute frequencies to all cores."""
world = self.world
comm = self.blockcomm
if world.size == 1:
return chi0_wGG
nw = len(self.omega_w)
nG = chi0_wGG.shape[2]
mynw = (nw + world.size - 1) // world.size
mynG = (nG + comm.size - 1) // comm.size
wa = min(world.rank * mynw, nw)
wb = min(wa + mynw, nw)
if self.blockcomm.size == 1:
return chi0_wGG[wa:wb].copy()
if self.kncomm.rank == 0:
bg1 = BlacsGrid(comm, 1, comm.size)
in_wGG = chi0_wGG.reshape((nw, -1))
else:
bg1 = DryRunBlacsGrid(mpi.serial_comm, 1, 1)
in_wGG = np.zeros((0, 0), complex)
md1 = BlacsDescriptor(bg1, nw, nG**2, nw, mynG * nG)
bg2 = BlacsGrid(world, world.size, 1)
md2 = BlacsDescriptor(bg2, nw, nG**2, mynw, nG**2)
r = Redistributor(world, md1, md2)
shape = (wb - wa, nG, nG)
out_wGG = np.empty(shape, complex)
r.redistribute(in_wGG, out_wGG.reshape((wb - wa, nG**2)))
return out_wGG
def distribute_frequencies(self, chi0_wGG):
"""Distribute frequencies to all cores."""
world = self.world
comm = self.blockcomm
if world.size == 1:
return chi0_wGG
nw = len(self.omega_w)
nG = chi0_wGG.shape[2]
mynw = (nw + world.size - 1) // world.size
mynG = (nG + comm.size - 1) // comm.size
wa = min(world.rank * mynw, nw)
wb = min(wa + mynw, nw)
if self.blockcomm.size == 1:
return chi0_wGG[wa:wb].copy()
if self.kncomm.rank == 0:
bg1 = BlacsGrid(comm, 1, comm.size)
in_wGG = chi0_wGG.reshape((nw, -1))
else:
bg1 = DryRunBlacsGrid(mpi.serial_comm, 1, 1)
in_wGG = np.zeros((0, 0), complex)
md1 = BlacsDescriptor(bg1, nw, nG**2, nw, mynG * nG)
bg2 = BlacsGrid(world, world.size, 1)
md2 = BlacsDescriptor(bg2, nw, nG**2, mynw, nG**2)
r = Redistributor(world, md1, md2)
shape = (wb - wa, nG, nG)
out_wGG = np.empty(shape, complex)
r.redistribute(in_wGG, out_wGG.reshape((wb - wa, nG**2)))
return out_wGG
class LrTDDFTLayouts:
"""BLACS layout for distributed Omega matrix in linear response
time-dependet DFT calculations"""
def __init__(self, sl_lrtddft, nkq, dd_comm, eh_comm):
mcpus, ncpus, blocksize = tuple(sl_lrtddft)
self.world = eh_comm.parent
self.dd_comm = dd_comm
if self.world is None:
self.world = self.dd_comm
# All the ranks within domain communicator contain the omega matrix
# construct new communicator only on domain masters
eh_ranks = np.arange(eh_comm.size) * dd_comm.size
self.eh_comm2 = self.world.new_communicator(eh_ranks)
self.eh_grid = BlacsGrid(self.eh_comm2, eh_comm.size, 1)
self.eh_descr = self.eh_grid.new_descriptor(nkq, nkq, 1, nkq)
self.diag_grid = BlacsGrid(self.world, mcpus, ncpus)
self.diag_descr = self.diag_grid.new_descriptor(
nkq, nkq, blocksize, blocksize)
self.redistributor_in = Redistributor(self.world, self.eh_descr,
self.diag_descr)
self.redistributor_out = Redistributor(self.world, self.diag_descr,
self.eh_descr)
"""
# -----------------------------------------------------------------
# for SCALAPACK we need TRANSPOSED MATRIX (and vector)
# -----------------------------------------------------------------
# M = rows, N = cols
M = nkq*4; N = nkq*4; mb = nkq*4; nb = 4; Nrhs = 1
# Matrix, mp=1, np=eh_comm.size
self.eh_grid2a = BlacsGrid(self.eh_comm2, eh_comm.size, 1)
# Vector, mp=eh_comm.size, np=1
self.eh_grid2b = BlacsGrid(self.eh_comm2, 1, eh_comm.size)
self.eh_descr2a = self.eh_grid2a.new_descriptor(N, M, nb, mb)
self.eh_descr2b = self.eh_grid2b.new_descriptor(Nrhs, N, 1, nb)
self.solve_descr2a =self.diag_grid.new_descriptor(N, M,
blocksize, blocksize)
self.solve_descr2b =self.diag_grid.new_descriptor(Nrhs, N,
1, blocksize)
self.redist_solve_in_2a = Redistributor(self.world,
self.eh_descr2a,
self.solve_descr2a)
self.redist_solve_in_2b = Redistributor(self.world,
self.eh_descr2b,
self.solve_descr2b)
self.redist_solve_out_2a = Redistributor(self.world,
self.solve_descr2a,
self.eh_descr2a)
self.redist_solve_out_2b = Redistributor(self.world,
self.solve_descr2b,
self.eh_descr2b)
"""
# -----------------------------------------------------------------
# for SCALAPACK we need TRANSPOSED MATRIX (and vector)
# -----------------------------------------------------------------
# M = rows, N = cols
M = nkq * 4
N = nkq * 4
mb = 4
nb = 4
Nrhs = 1
# Matrix, mp=1, np=eh_comm.size
self.eh_grid2a = BlacsGrid(self.world, dd_comm.size, eh_comm.size)
# Vector, mp=eh_comm.size, np=1
self.eh_grid2b = BlacsGrid(self.world, 1, dd_comm.size * eh_comm.size)
self.eh_descr2a = self.eh_grid2a.new_descriptor(N, M, nb, mb)
self.eh_descr2b = self.eh_grid2b.new_descriptor(Nrhs, N, Nrhs, nb)
self.solve_descr2a = self.diag_grid.new_descriptor(
N, M, blocksize, blocksize)
self.solve_descr2b = self.diag_grid.new_descriptor(
Nrhs, N, Nrhs, blocksize)
self.redist_solve_in_2a = Redistributor(self.world, self.eh_descr2a,
self.solve_descr2a)
self.redist_solve_in_2b = Redistributor(self.world, self.eh_descr2b,
self.solve_descr2b)
self.redist_solve_out_2a = Redistributor(self.world,
self.solve_descr2a,
self.eh_descr2a)
self.redist_solve_out_2b = Redistributor(self.world,
self.solve_descr2b,
self.eh_descr2b)
def solve(self, A, b):
#if 0:
# print 'edescr2a', rank, self.eh_descr2a.asarray()
# print 'edescr2b', rank, self.eh_descr2b.asarray()
#
# sys.stdout.flush()
# self.world.barrier()
#
# print 'sdescr2a', rank, self.solve_descr2a.asarray()
# print 'sdescr2b', rank, self.solve_descr2b.asarray()
#
# sys.stdout.flush()
# self.world.barrier()
#
# print 'A ', rank, A.shape
# if b is not None:
# print 'b ', rank, b.shape
#
# sys.stdout.flush()
# self.world.barrier()
A_nn = self.solve_descr2a.empty(dtype=float)
if self.eh_descr2a.blacsgrid.is_active():
A_Nn = A
else:
A_Nn = np.empty((0, 0), dtype=float)
self.redist_solve_in_2a.redistribute(A_Nn, A_nn)
b_n = self.solve_descr2b.empty(dtype=float)
if self.eh_descr2b.blacsgrid.is_active():
b_N = b.reshape(1, len(b))
else:
b_N = np.empty((A_Nn.shape[0], 0), dtype=float)
self.redist_solve_in_2b.redistribute(b_N, b_n)
#if 0:
# print 'A_Nn ', rank, A_Nn.shape
# print 'b_N ', rank, b_N.shape
# sys.stdout.flush()
# self.world.barrier()
# print 'A_nn ', rank, A_nn.shape
# print 'b_n ', rank, b_n.shape
# sys.stdout.flush()
# self.world.barrier()
#
#
# print 'b_N ', rank, b_N
# sys.stdout.flush()
# self.world.barrier()
# print 'b_n ', rank, b_n
# sys.stdout.flush()
# self.world.barrier()
#
# print 'A_Nn ', rank, A_Nn
# sys.stdout.flush()
# self.world.barrier()
# print 'A_nn ', rank, A_nn
# sys.stdout.flush()
# self.world.barrier()
info = 0
if self.solve_descr2a.blacsgrid.is_active():
_gpaw.scalapack_solve(A_nn, self.solve_descr2a.asarray(), b_n,
self.solve_descr2b.asarray())
if info != 0:
raise RuntimeError('scalapack_solve error: %d' % info)
self.redist_solve_out_2b.redistribute(b_n, b_N)
if self.eh_descr2b.blacsgrid.is_active():
b_N = b_N.flatten()
else:
b_N = b
#self.dd_comm.broadcast(b_N, 0)
b[:] = b_N
def diagonalize(self, Om, eps_n):
O_nn = self.diag_descr.empty(dtype=float)
if self.eh_descr.blacsgrid.is_active():
O_nN = Om
else:
O_nN = np.empty((0, 0), dtype=float)
self.redistributor_in.redistribute(O_nN, O_nn)
self.diag_descr.diagonalize_dc(O_nn.copy(), O_nn, eps_n, 'L')
self.redistributor_out.redistribute(O_nn, O_nN)
self.world.broadcast(eps_n, 0)
# Broadcast eigenvectors within domains
if not self.eh_descr.blacsgrid.is_active():
O_nN = Om
self.dd_comm.broadcast(O_nN, 0)
def diagonalize_full_hamiltonian(self, ham, atoms, occupations, txt,
nbands=None,
scalapack=None):
if nbands is None:
nbands = self.pd.ngmin
assert nbands <= self.pd.ngmin
self.bd = bd = BandDescriptor(nbands, self.bd.comm)
if scalapack:
nprow, npcol, b = scalapack
bg = BlacsGrid(bd.comm, bd.comm.size, 1)
bg2 = BlacsGrid(bd.comm, nprow, npcol)
else:
nprow = npcol = 1
assert bd.comm.size == nprow * npcol
self.pt.set_positions(atoms.get_scaled_positions())
self.kpt_u[0].P_ani = None
self.allocate_arrays_for_projections(self.pt.my_atom_indices)
myslice = bd.get_slice()
for kpt in self.kpt_u:
npw = len(self.pd.Q_qG[kpt.q])
if scalapack:
mynpw = -(-npw // bd.comm.size)
md = BlacsDescriptor(bg, npw, npw, mynpw, npw)
md2 = BlacsDescriptor(bg2, npw, npw, b, b)
else:
md = md2 = MatrixDescriptor(npw, npw)
H_GG, S_GG = self.hs(ham, kpt.q, kpt.s, md)
if scalapack:
r = Redistributor(bd.comm, md, md2)
H_GG = r.redistribute(H_GG)
S_GG = r.redistribute(S_GG)
psit_nG = md2.empty(dtype=complex)
eps_n = np.empty(npw)
md2.general_diagonalize_dc(H_GG, S_GG, psit_nG, eps_n)
del H_GG, S_GG
kpt.eps_n = eps_n[myslice].copy()
if scalapack:
md3 = BlacsDescriptor(bg, npw, npw, bd.mynbands, npw)
r = Redistributor(bd.comm, md2, md3)
psit_nG = r.redistribute(psit_nG)
kpt.psit_nG = psit_nG[:bd.mynbands].copy()
del psit_nG
self.pt.integrate(kpt.psit_nG, kpt.P_ani, kpt.q)
#f_n = np.zeros_like(kpt.eps_n)
#f_n[:len(kpt.f_n)] = kpt.f_n
kpt.f_n = None
occupations.calculate(self)
def diagonalize_full_hamiltonian(self, ham, atoms, occupations, log,
nbands=None, ecut=None, scalapack=None,
expert=False):
if self.dtype != complex:
raise ValueError('Your wavefunctions are not complex as '
'required by the PW diagonalization routine.\n'
'Please supply GPAW(..., dtype=complex, ...) '
'as an argument to the calculator to enforce '
'complex wavefunctions.')
if nbands is None and ecut is None:
nbands = self.pd.ngmin // self.bd.comm.size * self.bd.comm.size
elif nbands is None:
ecut /= units.Hartree
vol = abs(np.linalg.det(self.gd.cell_cv))
nbands = int(vol * ecut**1.5 * 2**0.5 / 3 / pi**2)
else:
assert nbands <= self.pd.ngmin
if expert:
iu = nbands
else:
iu = None
self.bd = bd = BandDescriptor(nbands, self.bd.comm)
log('Diagonalizing full Hamiltonian ({0} lowest bands)'.format(nbands))
log('Matrix size (min, max): {0}, {1}'.format(self.pd.ngmin,
self.pd.ngmax))
mem = 3 * self.pd.ngmax**2 * 16 / bd.comm.size / 1024**2
log('Approximate memory usage per core: {0:.3f} MB'.format(mem))
if bd.comm.size > 1:
if isinstance(scalapack, (list, tuple)):
nprow, npcol, b = scalapack
else:
nprow = int(round(bd.comm.size**0.5))
while bd.comm.size % nprow != 0:
nprow -= 1
npcol = bd.comm.size // nprow
b = 64
log('ScaLapack grid: {0}x{1},'.format(nprow, npcol),
'block-size:', b)
bg = BlacsGrid(bd.comm, bd.comm.size, 1)
bg2 = BlacsGrid(bd.comm, nprow, npcol)
scalapack = True
else:
nprow = npcol = 1
scalapack = False
self.set_positions(atoms.get_scaled_positions())
self.kpt_u[0].P_ani = None
self.allocate_arrays_for_projections(self.pt.my_atom_indices)
myslice = bd.get_slice()
pb = ProgressBar(log.fd)
nkpt = len(self.kpt_u)
for u, kpt in enumerate(self.kpt_u):
pb.update(u / nkpt)
npw = len(self.pd.Q_qG[kpt.q])
if scalapack:
mynpw = -(-npw // bd.comm.size)
md = BlacsDescriptor(bg, npw, npw, mynpw, npw)
md2 = BlacsDescriptor(bg2, npw, npw, b, b)
else:
md = md2 = MatrixDescriptor(npw, npw)
with self.timer('Build H and S'):
H_GG, S_GG = self.hs(ham, kpt.q, kpt.s, md)
if scalapack:
r = Redistributor(bd.comm, md, md2)
H_GG = r.redistribute(H_GG)
S_GG = r.redistribute(S_GG)
psit_nG = md2.empty(dtype=complex)
eps_n = np.empty(npw)
with self.timer('Diagonalize'):
if not scalapack:
md2.general_diagonalize_dc(H_GG, S_GG, psit_nG, eps_n,
iu=iu)
else:
md2.general_diagonalize_dc(H_GG, S_GG, psit_nG, eps_n)
del H_GG, S_GG
kpt.eps_n = eps_n[myslice].copy()
if scalapack:
md3 = BlacsDescriptor(bg, npw, npw, bd.mynbands, npw)
r = Redistributor(bd.comm, md2, md3)
psit_nG = r.redistribute(psit_nG)
kpt.psit_nG = psit_nG[:bd.mynbands].copy()
del psit_nG
with self.timer('Projections'):
self.pt.integrate(kpt.psit_nG, kpt.P_ani, kpt.q)
kpt.f_n = None
pb.finish()
occupations.calculate(self)
return nbands
class BlacsOrbitalLayouts(BlacsLayouts):
"""ScaLAPACK Dense Linear Algebra.
This class is instantiated in LCAO. Not for casual use, at least for now.
Requires two distributors and three descriptors for initialization
as well as grid descriptors and band descriptors. Distributors are
for cols2blocks (1D -> 2D BLACS grid) and blocks2cols (2D -> 1D
BLACS grid). ScaLAPACK operations must occur on 2D BLACS grid for
performance and scalability.
_general_diagonalize is "hard-coded" for LCAO.
Expects both Hamiltonian and Overlap matrix to be on the 2D BLACS grid.
This is done early on to save memory.
"""
# XXX rewrite this docstring a bit!
# This class 'describes' all the LCAO Blacs-related layouts
def __init__(self,
gd,
bd,
block_comm,
dtype,
mcpus,
ncpus,
blocksize,
nao,
timer=nulltimer):
BlacsLayouts.__init__(self, gd, bd, block_comm, dtype, mcpus, ncpus,
blocksize, timer)
nbands = bd.nbands
self.blocksize = blocksize
self.mynbands = mynbands = bd.mynbands
self.orbital_comm = self.bd.comm
self.naoblocksize = naoblocksize = -((-nao) // self.orbital_comm.size)
self.nao = nao
# Range of basis functions for BLACS distribution of matrices:
self.Mmax = nao
self.Mstart = bd.comm.rank * naoblocksize
self.Mstop = min(self.Mstart + naoblocksize, self.Mmax)
self.mynao = self.Mstop - self.Mstart
# Column layout for one matrix per band rank:
self.columngrid = BlacsGrid(bd.comm, bd.comm.size, 1)
self.mMdescriptor = self.columngrid.new_descriptor(
nao, nao, naoblocksize, nao)
self.nMdescriptor = self.columngrid.new_descriptor(
nbands, nao, mynbands, nao)
#parallelprint(world, (mynao, self.mMdescriptor.shape))
# Column layout for one matrix in total (only on grid masters):
self.single_column_grid = BlacsGrid(self.column_comm, bd.comm.size, 1)
self.mM_unique_descriptor = self.single_column_grid.new_descriptor( \
nao, nao, naoblocksize, nao)
# nM_unique_descriptor is meant to hold the coefficients after
# diagonalization. BLACS requires it to be nao-by-nao, but
# we only fill meaningful data into the first nbands columns.
#
# The array will then be trimmed and broadcast across
# the grid descriptor's communicator.
self.nM_unique_descriptor = self.single_column_grid.new_descriptor( \
nbands, nao, mynbands, nao)
# Fully blocked grid for diagonalization with many CPUs:
self.mmdescriptor = self.blockgrid.new_descriptor(
nao, nao, blocksize, blocksize)
#self.nMdescriptor = nMdescriptor
self.mM2mm = Redistributor(self.block_comm, self.mM_unique_descriptor,
self.mmdescriptor)
self.mm2nM = Redistributor(self.block_comm, self.mmdescriptor,
self.nM_unique_descriptor)
def diagonalize(self, H_mm, C_nM, eps_n, S_mm):
# C_nM needs to be simultaneously compatible with:
# 1. outdescriptor
# 2. broadcast with gd.comm
# We will does this with a dummy buffer C2_nM
outdescriptor = self.mm2nM.dstdescriptor # blocks2cols
blockdescriptor = self.mM2mm.dstdescriptor # cols2blocks
dtype = S_mm.dtype
eps_M = np.empty(C_nM.shape[-1]) # empty helps us debug
subM, subN = outdescriptor.gshape
C_mm = blockdescriptor.zeros(dtype=dtype)
self.timer.start('General diagonalize')
# general_diagonalize_ex may have a buffer overflow, so
# we no longer use it
#blockdescriptor.general_diagonalize_ex(H_mm, S_mm.copy(), C_mm, eps_M,
# UL='L', iu=self.bd.nbands)
blockdescriptor.general_diagonalize_dc(H_mm,
S_mm.copy(),
C_mm,
eps_M,
UL='L')
self.timer.stop('General diagonalize')
# Make C_nM compatible with the redistributor
self.timer.start('Redistribute coefs')
if outdescriptor:
C2_nM = C_nM
else:
C2_nM = outdescriptor.empty(dtype=dtype)
assert outdescriptor.check(C2_nM)
self.mm2nM.redistribute(C_mm, C2_nM, subM, subN) # blocks2cols
self.timer.stop('Redistribute coefs')
self.timer.start('Send coefs to domains')
# eps_M is already on block_comm.rank = 0
# easier to broadcast eps_M to all and
# get the correct slice afterward.
self.block_comm.broadcast(eps_M, 0)
eps_n[:] = eps_M[self.bd.get_slice()]
self.gd.comm.broadcast(C_nM, 0)
self.timer.stop('Send coefs to domains')
def distribute_overlap_matrix(self,
S_qmM,
root=0,
add_hermitian_conjugate=False):
# Some MPI implementations need a lot of memory to do large
# reductions. To avoid trouble, we do comm.sum on smaller blocks
# of S (this code is also safe for arrays smaller than blocksize)
Sflat_x = S_qmM.ravel()
blocksize = 2**23 // Sflat_x.itemsize # 8 MiB
nblocks = -(-len(Sflat_x) // blocksize)
Mstart = 0
self.timer.start('blocked summation')
for i in range(nblocks):
self.gd.comm.sum(Sflat_x[Mstart:Mstart + blocksize], root=root)
Mstart += blocksize
assert Mstart + blocksize >= len(Sflat_x)
self.timer.stop('blocked summation')
xshape = S_qmM.shape[:-2]
nm, nM = S_qmM.shape[-2:]
S_qmM = S_qmM.reshape(-1, nm, nM)
blockdesc = self.mmdescriptor
coldesc = self.mM_unique_descriptor
S_qmm = blockdesc.zeros(len(S_qmM), S_qmM.dtype)
if not coldesc: # XXX ugly way to sort out inactive ranks
S_qmM = coldesc.zeros(len(S_qmM), S_qmM.dtype)
self.timer.start('Scalapack redistribute')
for S_mM, S_mm in zip(S_qmM, S_qmm):
self.mM2mm.redistribute(S_mM, S_mm)
if add_hermitian_conjugate:
if blockdesc.active:
pblas_tran(1.0, S_mm.copy(), 1.0, S_mm, blockdesc,
blockdesc)
self.timer.stop('Scalapack redistribute')
return S_qmm.reshape(xshape + blockdesc.shape)
def get_overlap_matrix_shape(self):
return self.mmdescriptor.shape
def calculate_blocked_density_matrix(self, f_n, C_nM):
nbands = self.bd.nbands
nao = self.nao
dtype = C_nM.dtype
self.nMdescriptor.checkassert(C_nM)
if self.gd.rank == 0:
Cf_nM = (C_nM * f_n[:, None]).conj()
else:
C_nM = self.nM_unique_descriptor.zeros(dtype=dtype)
Cf_nM = self.nM_unique_descriptor.zeros(dtype=dtype)
r = Redistributor(self.block_comm, self.nM_unique_descriptor,
self.mmdescriptor)
Cf_mm = self.mmdescriptor.zeros(dtype=dtype)
r.redistribute(Cf_nM, Cf_mm, nbands, nao)
del Cf_nM
C_mm = self.mmdescriptor.zeros(dtype=dtype)
r.redistribute(C_nM, C_mm, nbands, nao)
# no use to delete C_nM as it's in the input...
rho_mm = self.mmdescriptor.zeros(dtype=dtype)
pblas_simple_gemm(self.mmdescriptor,
self.mmdescriptor,
self.mmdescriptor,
Cf_mm,
C_mm,
rho_mm,
transa='T')
return rho_mm
def calculate_density_matrix(self, f_n, C_nM, rho_mM=None):
"""Calculate density matrix from occupations and coefficients.
Presently this function performs the usual scalapack 3-step trick:
redistribute-numbercrunching-backdistribute.
Notes on future performance improvement.
As per the current framework, C_nM exists as copies on each
domain, i.e. this is not parallel over domains. We'd like to
correct this and have an efficient distribution using e.g. the
block communicator.
The diagonalization routine and other parts of the code should
however be changed to accommodate the following scheme:
Keep coefficients in C_mm form after the diagonalization.
rho_mm can then be directly calculated from C_mm without
redistribution, after which we only need to redistribute
rho_mm across domains.
"""
dtype = C_nM.dtype
rho_mm = self.calculate_blocked_density_matrix(f_n, C_nM)
rback = Redistributor(self.block_comm, self.mmdescriptor,
self.mM_unique_descriptor)
rho1_mM = self.mM_unique_descriptor.zeros(dtype=dtype)
rback.redistribute(rho_mm, rho1_mM)
del rho_mm
if rho_mM is None:
if self.gd.rank == 0:
rho_mM = rho1_mM
else:
rho_mM = self.mMdescriptor.zeros(dtype=dtype)
self.gd.comm.broadcast(rho_mM, 0)
return rho_mM
def distribute_to_columns(self, rho_mm, srcdescriptor):
redistributor = Redistributor(
self.block_comm, # XXX
srcdescriptor,
self.mM_unique_descriptor)
rho_mM = redistributor.redistribute(rho_mm)
if self.gd.rank != 0:
rho_mM = self.mMdescriptor.zeros(dtype=rho_mm.dtype)
self.gd.comm.broadcast(rho_mM, 0)
return rho_mM
def oldcalculate_density_matrix(self, f_n, C_nM, rho_mM=None):
# This version is parallel over the band descriptor only.
# This is inefficient, but let's keep it for a while in case
# there's trouble with the more efficient version
if rho_mM is None:
rho_mM = self.mMdescriptor.zeros(dtype=C_nM.dtype)
Cf_nM = (C_nM * f_n[:, None]).conj()
pblas_simple_gemm(self.nMdescriptor,
self.nMdescriptor,
self.mMdescriptor,
Cf_nM,
C_nM,
rho_mM,
transa='T')
return rho_mM
def get_transposed_density_matrix(self, f_n, C_nM, rho_mM=None):
return self.calculate_density_matrix(f_n, C_nM, rho_mM).conj()
def get_description(self):
(title, template) = BlacsLayouts.get_description(self)
bg = self.blockgrid
desc = self.mmdescriptor
s = template % (bg.nprow, bg.npcol, desc.mb, desc.nb)
return ' '.join([title, s])
grid = BlacsGrid(world, 2, world.size // 2)
desc = grid.new_descriptor(12, 8, 2, 3)
a = desc.zeros()
a[:] = world.rank
subdesc = grid.new_descriptor(7, 7, 2, 2)
b = subdesc.zeros()
r = Redistributor(grid.comm, desc, subdesc, uplo="G")
ia = 3
ja = 2
ib = 1
jb = 1
M = 4
N = 5
r.redistribute(a, b, M, N, ia, ja, ib, jb)
a0 = desc.collect_on_master(a)
b0 = subdesc.collect_on_master(b)
if world.rank == 0:
print a0
print b0
xa = a0[ia : ia + M, ja : ja + N]
xb = b0[ib : ib + M, jb : jb + N]
assert (xa == xb).all()
def calculate_rkernel(self):
gd = self.gd
ng_c = gd.N_c
cell_cv = gd.cell_cv
icell_cv = 2 * np.pi * np.linalg.inv(cell_cv)
vol = np.linalg.det(cell_cv)
ns = self.calc.wfs.nspins
n_g = self.n_g # density on rough grid
fx_g = ns * self.get_fxc_g(n_g) # local exchange kernel
qc_g = (-4 * np.pi * ns / fx_g)**0.5 # cutoff functional
flocal_g = qc_g**3 * fx_g / (6 * np.pi**2) # ren. x-kernel for r=r'
Vlocal_g = 2 * qc_g / np.pi # ren. Hartree kernel for r=r'
ng = np.prod(ng_c) # number of grid points
r_vg = gd.get_grid_point_coordinates()
rx_g = r_vg[0].flatten()
ry_g = r_vg[1].flatten()
rz_g = r_vg[2].flatten()
prnt(' %d grid points and %d plane waves at the Gamma point' %
(ng, self.pd.ngmax), file=self.fd)
# Unit cells
R_Rv = []
weight_R = []
nR_v = self.unit_cells
nR = np.prod(nR_v)
for i in range(-nR_v[0] + 1, nR_v[0]):
for j in range(-nR_v[1] + 1, nR_v[1]):
for h in range(-nR_v[2] + 1, nR_v[2]):
R_Rv.append(i * cell_cv[0] +
j * cell_cv[1] +
h * cell_cv[2])
weight_R.append((nR_v[0] - abs(i)) *
(nR_v[1] - abs(j)) *
(nR_v[2] - abs(h)) / float(nR))
if nR > 1:
# with more than one unit cell only the exchange kernel is
# calculated on the grid. The bare Coulomb kernel is added
# in PW basis and Vlocal_g only the exchange part
dv = self.calc.density.gd.dv
gc = (3 * dv / 4 / np.pi)**(1 / 3.)
Vlocal_g -= 2 * np.pi * gc**2 / dv
prnt(' Lattice point sampling: ' +
'(%s x %s x %s)^2 ' % (nR_v[0], nR_v[1], nR_v[2]) +
' Reduced to %s lattice points' % len(R_Rv), file=self.fd)
l_g_size = -(-ng // mpi.world.size)
l_g_range = range(mpi.world.rank * l_g_size,
min((mpi.world.rank+1) * l_g_size, ng))
fhxc_qsGr = {}
for iq in range(len(self.ibzq_qc)):
fhxc_qsGr[iq] = np.zeros((ns, len(self.pd.G2_qG[iq]),
len(l_g_range)), dtype=complex)
inv_error = np.seterr()
np.seterr(invalid='ignore')
np.seterr(divide='ignore')
t0 = time()
# Loop over Lattice points
for i, R_v in enumerate(R_Rv):
# Loop over r'. f_rr and V_rr are functions of r (dim. as r_vg[0])
if i == 1:
prnt(' Finished 1 cell in %s seconds' % int(time() - t0) +
' - estimated %s seconds left' %
int((len(R_Rv) - 1) * (time() - t0)),
file=self.fd)
self.fd.flush()
if len(R_Rv) > 5:
if (i+1) % (len(R_Rv) / 5 + 1) == 0:
prnt(' Finished %s cells in %s seconds'
% (i, int(time() - t0))
+ ' - estimated %s seconds left'
% int((len(R_Rv) - i) * (time() - t0) / i),
file=self.fd)
self.fd.flush()
for g in l_g_range:
rx = rx_g[g] + R_v[0]
ry = ry_g[g] + R_v[1]
rz = rz_g[g] + R_v[2]
# |r-r'-R_i|
rr = ((r_vg[0] - rx)**2 +
(r_vg[1] - ry)**2 +
(r_vg[2] - rz)**2)**0.5
n_av = (n_g + n_g.flatten()[g]) / 2.
fx_g = ns * self.get_fxc_g(n_av, index=g)
qc_g = (-4 * np.pi * ns / fx_g)**0.5
x = qc_g * rr
osc_x = np.sin(x) - x*np.cos(x)
f_rr = fx_g * osc_x / (2 * np.pi**2 * rr**3)
if nR > 1: # include only exchange part of the kernel here
V_rr = (sici(x)[0] * 2 / np.pi - 1) / rr
else: # include the full kernel (also hartree part)
V_rr = (sici(x)[0] * 2 / np.pi) / rr
# Terms with r = r'
if (np.abs(R_v) < 0.001).all():
tmp_flat = f_rr.flatten()
tmp_flat[g] = flocal_g.flatten()[g]
f_rr = tmp_flat.reshape(ng_c)
tmp_flat = V_rr.flatten()
tmp_flat[g] = Vlocal_g.flatten()[g]
V_rr = tmp_flat.reshape(ng_c)
del tmp_flat
f_rr[np.where(n_av < self.density_cut)] = 0.0
V_rr[np.where(n_av < self.density_cut)] = 0.0
f_rr *= weight_R[i]
V_rr *= weight_R[i]
# r-r'-R_i
r_r = np.array([r_vg[0] - rx, r_vg[1] - ry, r_vg[2] - rz])
# Fourier transform of r
for iq, q in enumerate(self.ibzq_qc):
q_v = np.dot(q, icell_cv)
e_q = np.exp(-1j * gemmdot(q_v, r_r, beta=0.0))
f_q = self.pd.fft((f_rr + V_rr) * e_q, iq) * vol / ng
fhxc_qsGr[iq][0, :, g - l_g_range[0]] += f_q
if ns == 2:
f_q = self.pd.fft(V_rr * e_q, iq) * vol / ng
fhxc_qsGr[iq][1, :, g - l_g_range[0]] += f_q
mpi.world.barrier()
np.seterr(**inv_error)
for iq, q in enumerate(self.ibzq_qc):
npw = len(self.pd.G2_qG[iq])
fhxc_sGsG = np.zeros((ns * npw, ns * npw), complex)
l_pw_size = -(-npw // mpi.world.size) # parallelize over PW below
l_pw_range = range(mpi.world.rank * l_pw_size,
min((mpi.world.rank + 1) * l_pw_size, npw))
if mpi.world.size > 1:
# redistribute grid and plane waves in fhxc_qsGr[iq]
bg1 = BlacsGrid(mpi.world, 1, mpi.world.size)
bg2 = BlacsGrid(mpi.world, mpi.world.size, 1)
bd1 = bg1.new_descriptor(npw, ng, npw, - (-ng / mpi.world.size))
bd2 = bg2.new_descriptor(npw, ng, -(-npw / mpi.world.size), ng)
fhxc_Glr = np.zeros((len(l_pw_range), ng), dtype=complex)
if ns == 2:
Koff_Glr = np.zeros((len(l_pw_range), ng), dtype=complex)
r = Redistributor(bg1.comm, bd1, bd2)
r.redistribute(fhxc_qsGr[iq][0], fhxc_Glr, npw, ng)
if ns == 2:
r.redistribute(fhxc_qsGr[iq][1], Koff_Glr, npw, ng)
else:
fhxc_Glr = fhxc_qsGr[iq][0]
if ns == 2:
Koff_Glr = fhxc_qsGr[iq][1]
# Fourier transform of r'
for iG in range(len(l_pw_range)):
f_g = fhxc_Glr[iG].reshape(ng_c)
f_G = self.pd.fft(f_g.conj(), iq) * vol / ng
fhxc_sGsG[l_pw_range[0] + iG, :npw] = f_G.conj()
if ns == 2:
v_g = Koff_Glr[iG].reshape(ng_c)
v_G = self.pd.fft(v_g.conj(), iq) * vol / ng
fhxc_sGsG[npw + l_pw_range[0] + iG, :npw] = v_G.conj()
if ns == 2: # f_00 = f_11 and f_01 = f_10
fhxc_sGsG[:npw, npw:] = fhxc_sGsG[npw:, :npw]
fhxc_sGsG[npw:, npw:] = fhxc_sGsG[:npw, :npw]
mpi.world.sum(fhxc_sGsG)
fhxc_sGsG /= vol
if mpi.rank == 0:
w = Writer('fhxc_%s_%s_%s_%s.gpw' %
(self.tag, self.xc, self.ecut, iq))
w.dimension('sG', ns * npw)
w.add('fhxc_sGsG', ('sG', 'sG'), dtype=complex)
if nR > 1: # add Hartree kernel evaluated in PW basis
Gq2_G = self.pd.G2_qG[iq]
if (q == 0).all():
Gq2_G[0] = 1.
vq_G = 4 * np.pi / Gq2_G
fhxc_sGsG += np.tile(np.eye(npw) * vq_G, (ns, ns))
w.fill(fhxc_sGsG)
w.close()
mpi.world.barrier()
prnt(file=self.fd)
class ECNPropagator(LCAOPropagator):
def __init__(self):
LCAOPropagator.__init__(self)
def initialize(self, paw, hamiltonian=None):
LCAOPropagator.initialize(self, paw)
if hamiltonian is not None:
self.hamiltonian = hamiltonian
ksl = self.wfs.ksl
self.blacs = ksl.using_blacs
if self.blacs:
from gpaw.blacs import Redistributor
self.log('BLACS Parallelization')
# Parallel grid descriptors
grid = ksl.blockgrid
assert grid.nprow * grid.npcol == ksl.block_comm.size
self.mm_block_descriptor = ksl.mmdescriptor
self.Cnm_block_descriptor = grid.new_descriptor(ksl.bd.nbands,
ksl.nao,
ksl.blocksize,
ksl.blocksize)
self.CnM_unique_descriptor = ksl.nM_unique_descriptor
# Redistributors
self.Cnm2nM = Redistributor(ksl.block_comm,
self.Cnm_block_descriptor,
self.CnM_unique_descriptor)
self.CnM2nm = Redistributor(ksl.block_comm,
self.CnM_unique_descriptor,
self.Cnm_block_descriptor)
if debug:
nao = ksl.nao
self.MM_descriptor = grid.new_descriptor(nao, nao, nao, nao)
self.mm2MM = Redistributor(ksl.block_comm,
self.mm_block_descriptor,
self.MM_descriptor)
self.MM2mm = Redistributor(ksl.block_comm,
self.MM_descriptor,
self.mm_block_descriptor)
for kpt in self.wfs.kpt_u:
scalapack_zero(self.mm_block_descriptor, kpt.S_MM, 'U')
scalapack_zero(self.mm_block_descriptor, kpt.T_MM, 'U')
def kick(self, hamiltonian, time):
# Propagate
get_matrix = self.wfs.eigensolver.calculate_hamiltonian_matrix
for kpt in self.wfs.kpt_u:
Vkick_MM = get_matrix(hamiltonian, self.wfs, kpt,
add_kinetic=False, root=-1)
for i in range(10):
self.propagate_wfs(kpt.C_nM, kpt.C_nM, kpt.S_MM, Vkick_MM, 0.1)
# Update Hamiltonian (and density)
self.hamiltonian.update()
def propagate(self, time, time_step):
for kpt in self.wfs.kpt_u:
H_MM = self.hamiltonian.get_hamiltonian_matrix(kpt)
self.propagate_wfs(kpt.C_nM, kpt.C_nM, kpt.S_MM, H_MM, time_step)
self.hamiltonian.update()
return time + time_step
def propagate_wfs(self, sourceC_nM, targetC_nM, S_MM, H_MM, dt):
self.timer.start('Linear solve')
if self.blacs:
# XXX, Preallocate
target_blockC_nm = self.Cnm_block_descriptor.empty(dtype=complex)
temp_blockC_nm = self.Cnm_block_descriptor.empty(dtype=complex)
temp_block_mm = self.mm_block_descriptor.empty(dtype=complex)
if self.density.gd.comm.rank != 0:
# XXX Fake blacks nbands, nao, nbands, nao grid because some
# weird asserts
# (these are 0,x or x,0 arrays)
sourceC_nM = self.CnM_unique_descriptor.zeros(dtype=complex)
# 1. target = (S+0.5j*H*dt) * source
# Wave functions to target
self.CnM2nm.redistribute(sourceC_nM, temp_blockC_nm)
# XXX It can't be this f'n hard to symmetrize a matrix (tri2full)
# Remove upper diagonal
scalapack_zero(self.mm_block_descriptor, H_MM, 'U')
# Lower diagonal matrix:
temp_block_mm[:] = S_MM - (0.5j * dt) * H_MM
scalapack_set(self.mm_block_descriptor, temp_block_mm, 0, 0, 'U')
# Note it's strictly lower diagonal matrix
# Add transpose of H
pblas_tran(-0.5j * dt, H_MM, 1.0, temp_block_mm,
self.mm_block_descriptor, self.mm_block_descriptor)
# Add transpose of S
pblas_tran(1.0, S_MM, 1.0, temp_block_mm,
self.mm_block_descriptor, self.mm_block_descriptor)
pblas_simple_gemm(self.Cnm_block_descriptor,
self.mm_block_descriptor,
self.Cnm_block_descriptor,
temp_blockC_nm,
temp_block_mm,
target_blockC_nm)
# 2. target = (S-0.5j*H*dt)^-1 * target
# temp_block_mm[:] = S_MM + (0.5j*dt) * H_MM
# XXX It can't be this f'n hard to symmetrize a matrix (tri2full)
# Lower diagonal matrix:
temp_block_mm[:] = S_MM + (0.5j * dt) * H_MM
# Not it's stricly lower diagonal matrix:
scalapack_set(self.mm_block_descriptor, temp_block_mm, 0, 0, 'U')
# Add transpose of H:
pblas_tran(+0.5j * dt, H_MM, 1.0, temp_block_mm,
self.mm_block_descriptor, self.mm_block_descriptor)
# Add transpose of S
pblas_tran(1.0, S_MM, 1.0, temp_block_mm,
self.mm_block_descriptor, self.mm_block_descriptor)
scalapack_solve(self.mm_block_descriptor,
self.Cnm_block_descriptor,
temp_block_mm,
target_blockC_nm)
if self.density.gd.comm.rank != 0: # XXX is this correct?
# XXX Fake blacks nbands, nao, nbands, nao grid because some
# weird asserts
# (these are 0,x or x,0 arrays)
target = self.CnM_unique_descriptor.zeros(dtype=complex)
else:
target = targetC_nM
self.Cnm2nM.redistribute(target_blockC_nm, target)
self.density.gd.comm.broadcast(targetC_nM, 0) # Is this required?
else:
# Note: The full equation is conjugated (therefore -+, not +-)
targetC_nM[:] = \
solve(S_MM - 0.5j * H_MM * dt,
np.dot(S_MM + 0.5j * H_MM * dt,
sourceC_nM.T.conjugate())).T.conjugate()
self.timer.stop('Linear solve')
def blacs_mm_to_global(self, H_mm):
if not debug:
raise RuntimeError('Use debug mode')
# Someone could verify that this works and remove the error.
raise NotImplementedError('Method untested and thus unreliable')
target = self.MM_descriptor.empty(dtype=complex)
self.mm2MM.redistribute(H_mm, target)
self.wfs.world.barrier()
return target
def blacs_nm_to_global(self, C_nm):
# Someone could verify that this works and remove the error.
raise NotImplementedError('Method untested and thus unreliable')
target = self.CnM_unique_descriptor.empty(dtype=complex)
self.Cnm2nM.redistribute(C_nm, target)
self.wfs.world.barrier()
return target
def todict(self):
return {'name': 'ecn'}
class LrTDDFPTSolveLayout:
"""BLACS layouts for distributed TD-DFPT"""
def __init__(self, sl_lrtddft, nrows, lr_comms):
self.mprocs, self.nprocs, self.block_size = tuple(sl_lrtddft)
self.lr_comms = lr_comms
# for SCALAPACK we need TRANSPOSED MATRIX (and vector)
#
# -----------------------------------------------------------------
# matrix
# original grid, ie, how matrix is stored
self.orig_matrix_grid = BlacsGrid(self.lr_comms.parent_comm,
self.lr_comms.dd_comm.size,
self.lr_comms.eh_comm.size)
# solve grid
self.solve_matrix_grid = BlacsGrid(self.lr_comms.parent_comm,
self.mprocs, self.nprocs)
# M = rows, N = cols
M = nrows * 4
N = nrows * 4
mb = 4
nb = 4
self.orig_matrix_descr = self.orig_matrix_grid.new_descriptor(
N, M, nb, mb)
bs = self.block_size
self.solve_matrix_descr = self.solve_matrix_grid.new_descriptor(
N, M, bs, bs)
self.matrix_in_redist = Redistributor(self.lr_comms.parent_comm,
self.orig_matrix_descr,
self.solve_matrix_descr)
# -----------------------------------------------------------------
# vector
# original grid, ie, how vector is stored
self.orig_vector_grid = BlacsGrid(
self.lr_comms.parent_comm, 1,
(self.lr_comms.dd_comm.size * self.lr_comms.eh_comm.size))
# solve grid
#self.solve_vector_grid = BlacsGrid(self.lr_comms.parent_comm, self.mprocs, self.nprocs)
# M = rows, N = cols
M = nrows * 4
Nrhs = 1
mb = 4
nb = 1
self.orig_vector_descr = self.orig_vector_grid.new_descriptor(
Nrhs, M, nb, mb)
bs = self.block_size
self.solve_vector_descr = self.solve_matrix_grid.new_descriptor(
Nrhs, M, 1, bs)
self.vector_in_redist = Redistributor(self.lr_comms.parent_comm,
self.orig_vector_descr,
self.solve_vector_descr)
self.vector_out_redist = Redistributor(self.lr_comms.parent_comm,
self.solve_vector_descr,
self.orig_vector_descr)
def solve(self, A_orig, b_orig):
"""Solve TD-DFPT equation using Scalapack.
"""
A_solve = self.solve_matrix_descr.empty(dtype=float)
if not self.orig_matrix_descr.blacsgrid.is_active():
A_orig = np.empty((0, 0), dtype=float)
self.matrix_in_redist.redistribute(A_orig, A_solve)
b_solve = self.solve_vector_descr.empty(dtype=float)
if not self.orig_vector_descr.blacsgrid.is_active():
b_orig = np.empty((0, 0), dtype=float)
self.vector_in_redist.redistribute(b_orig, b_solve)
#if False:
# np.set_printoptions(precision=5, suppress=True)
# for i in range(self.lr_comms.parent_comm.size):
# if ( self.lr_comms.parent_comm.rank == i ):
# print 'rank ', i
# print A_orig
# print A_solve
# print
# print b_orig
# print b_solve
# print
# print
# print self.solve_matrix_descr.asarray()
# print self.solve_vector_descr.asarray()
# print
# print '---'
# print
# self.lr_comms.parent_comm.barrier()
info = 0
if self.solve_matrix_descr.blacsgrid.is_active():
_gpaw.scalapack_solve(A_solve, self.solve_matrix_descr.asarray(),
b_solve, self.solve_vector_descr.asarray())
if info != 0:
raise RuntimeError('scalapack_solve error: %d' % info)
self.vector_out_redist.redistribute(b_solve, b_orig)
#if False:
# for i in range(self.lr_comms.parent_comm.size):
# if ( self.lr_comms.parent_comm.rank == i ):
# print 'rank ', i
# print A_orig
# print A_solve
# print
# print b_orig
# print b_solve
# print
# print
# self.lr_comms.parent_comm.barrier()
return b_orig
def diagonalize_full_hamiltonian(self, ham, atoms, occupations, txt,
nbands=None, scalapack=None, expert=False):
assert self.dtype == complex
if nbands is None:
nbands = self.pd.ngmin // self.bd.comm.size * self.bd.comm.size
else:
assert nbands <= self.pd.ngmin
if expert:
iu = nbands
else:
iu = None
self.bd = bd = BandDescriptor(nbands, self.bd.comm)
p = functools.partial(print, file=txt)
p('Diagonalizing full Hamiltonian ({0} lowest bands)'.format(nbands))
p('Matrix size (min, max): {0}, {1}'.format(self.pd.ngmin,
self.pd.ngmax))
mem = 3 * self.pd.ngmax**2 * 16 / bd.comm.size / 1024**2
p('Approximate memory usage per core: {0:.3f} MB'.format(mem))
if bd.comm.size > 1:
if isinstance(scalapack, (list, tuple)):
nprow, npcol, b = scalapack
else:
nprow = int(round(bd.comm.size**0.5))
while bd.comm.size % nprow != 0:
nprow -= 1
npcol = bd.comm.size // nprow
b = 64
p('ScaLapack grid: {0}x{1},'.format(nprow, npcol),
'block-size:', b)
bg = BlacsGrid(bd.comm, bd.comm.size, 1)
bg2 = BlacsGrid(bd.comm, nprow, npcol)
scalapack = True
else:
nprow = npcol = 1
scalapack = False
self.pt.set_positions(atoms.get_scaled_positions())
self.kpt_u[0].P_ani = None
self.allocate_arrays_for_projections(self.pt.my_atom_indices)
myslice = bd.get_slice()
pb = ProgressBar(txt)
nkpt = len(self.kpt_u)
for u, kpt in enumerate(self.kpt_u):
pb.update(u / nkpt)
npw = len(self.pd.Q_qG[kpt.q])
if scalapack:
mynpw = -(-npw // bd.comm.size)
md = BlacsDescriptor(bg, npw, npw, mynpw, npw)
md2 = BlacsDescriptor(bg2, npw, npw, b, b)
else:
md = md2 = MatrixDescriptor(npw, npw)
with self.timer('Build H and S'):
H_GG, S_GG = self.hs(ham, kpt.q, kpt.s, md)
if scalapack:
r = Redistributor(bd.comm, md, md2)
H_GG = r.redistribute(H_GG)
S_GG = r.redistribute(S_GG)
psit_nG = md2.empty(dtype=complex)
eps_n = np.empty(npw)
with self.timer('Diagonalize'):
if not scalapack:
md2.general_diagonalize_dc(H_GG, S_GG, psit_nG, eps_n,
iu=iu)
else:
md2.general_diagonalize_dc(H_GG, S_GG, psit_nG, eps_n)
del H_GG, S_GG
kpt.eps_n = eps_n[myslice].copy()
if scalapack:
md3 = BlacsDescriptor(bg, npw, npw, bd.mynbands, npw)
r = Redistributor(bd.comm, md2, md3)
psit_nG = r.redistribute(psit_nG)
kpt.psit_nG = psit_nG[:bd.mynbands].copy()
del psit_nG
with self.timer('Projections'):
self.pt.integrate(kpt.psit_nG, kpt.P_ani, kpt.q)
kpt.f_n = None
pb.finish()
occupations.calculate(self)
def main(N=73, seed=42, mprocs=2, nprocs=2, dtype=float):
gen = np.random.RandomState(seed)
grid = BlacsGrid(world, mprocs, nprocs)
if (dtype==complex):
epsilon = 1.0j
else:
epsilon = 0.0
# Create descriptors for matrices on master:
glob = grid.new_descriptor(N, N, N, N)
# print globA.asarray()
# Populate matrices local to master:
H0 = glob.zeros(dtype=dtype) + gen.rand(*glob.shape)
S0 = glob.zeros(dtype=dtype) + gen.rand(*glob.shape)
C0 = glob.empty(dtype=dtype)
if rank == 0:
# Complex case must have real numbers on the diagonal.
# We make a simple complex Hermitian matrix below.
H0 = H0 + epsilon * (0.1*np.tri(N, N, k= -N // nprocs) + 0.3*np.tri(N, N, k=-1))
S0 = S0 + epsilon * (0.2*np.tri(N, N, k= -N // nprocs) + 0.4*np.tri(N, N, k=-1))
# Make matrices symmetric
rk(1.0, H0.copy(), 0.0, H0)
rk(1.0, S0.copy(), 0.0, S0)
# Overlap matrix must be semi-positive definite
S0 = S0 + 50.0*np.eye(N, N, 0)
# Hamiltonian is usually diagonally dominant
H0 = H0 + 75.0*np.eye(N, N, 0)
C0 = S0.copy()
# Local result matrices
W0 = np.empty((N),dtype=float)
W0_g = np.empty((N),dtype=float)
# Calculate eigenvalues
if rank == 0:
diagonalize(H0.copy(), W0)
general_diagonalize(H0.copy(), W0_g, S0.copy())
inverse_cholesky(C0) # result returned in lower triangle
# tri2full(C0) # symmetrize
assert glob.check(H0) and glob.check(S0) and glob.check(C0)
# Create distributed destriptors with various block sizes:
dist = grid.new_descriptor(N, N, 8, 8)
# Distributed matrices:
# We can use empty here, but end up with garbage on
# on the other half of the triangle when we redistribute.
# This is fine because ScaLAPACK does not care.
H = dist.empty(dtype=dtype)
S = dist.empty(dtype=dtype)
Z = dist.empty(dtype=dtype)
C = dist.empty(dtype=dtype)
# Eigenvalues are non-BLACS matrices
W = np.empty((N), dtype=float)
W_dc = np.empty((N), dtype=float)
W_mr3 = np.empty((N), dtype=float)
W_g = np.empty((N), dtype=float)
W_g_dc = np.empty((N), dtype=float)
W_g_mr3 = np.empty((N), dtype=float)
Glob2dist = Redistributor(world, glob, dist)
Glob2dist.redistribute(H0, H, uplo='L')
Glob2dist.redistribute(S0, S, uplo='L')
Glob2dist.redistribute(S0, C, uplo='L') # C0 was previously overwritten
# we don't test the expert drivers anymore since there
# might be a buffer overflow error
## scalapack_diagonalize_ex(dist, H.copy(), Z, W, 'L')
scalapack_diagonalize_dc(dist, H.copy(), Z, W_dc, 'L')
## scalapack_diagonalize_mr3(dist, H.copy(), Z, W_mr3, 'L')
## scalapack_general_diagonalize_ex(dist, H.copy(), S.copy(), Z, W_g, 'L')
scalapack_general_diagonalize_dc(dist, H.copy(), S.copy(), Z, W_g_dc, 'L')
## scalapack_general_diagonalize_mr3(dist, H.copy(), S.copy(), Z, W_g_mr3, 'L')
scalapack_inverse_cholesky(dist, C, 'L')
# Undo redistribute
C_test = glob.empty(dtype=dtype)
Dist2glob = Redistributor(world, dist, glob)
Dist2glob.redistribute(C, C_test)
if rank == 0:
## diag_ex_err = abs(W - W0).max()
diag_dc_err = abs(W_dc - W0).max()
## diag_mr3_err = abs(W_mr3 - W0).max()
## general_diag_ex_err = abs(W_g - W0_g).max()
general_diag_dc_err = abs(W_g_dc - W0_g).max()
## general_diag_mr3_err = abs(W_g_mr3 - W0_g).max()
inverse_chol_err = abs(C_test-C0).max()
## print 'diagonalize ex err', diag_ex_err
print 'diagonalize dc err', diag_dc_err
## print 'diagonalize mr3 err', diag_mr3_err
## print 'general diagonalize ex err', general_diag_ex_err
print 'general diagonalize dc err', general_diag_dc_err
## print 'general diagonalize mr3 err', general_diag_mr3_err
print 'inverse chol err', inverse_chol_err
else:
## diag_ex_err = 0.0
diag_dc_err = 0.0
## diag_mr3_err = 0.0
## general_diag_ex_err = 0.0
general_diag_dc_err = 0.0
## general_diag_mr3_err = 0.0
inverse_chol_err = 0.0
# We don't like exceptions on only one cpu
## diag_ex_err = world.sum(diag_ex_err)
diag_dc_err = world.sum(diag_dc_err)
## diag_mr3_err = world.sum(diag_mr3_err)
## general_diag_ex_err = world.sum(general_diag_ex_err)
general_diag_dc_err = world.sum(general_diag_dc_err)
## general_diag_mr3_err = world.sum(general_diag_mr3_err)
inverse_chol_err = world.sum(inverse_chol_err)
## assert diag_ex_err < tol
assert diag_dc_err < tol
## assert diag_mr3_err < tol
## assert general_diag_ex_err < tol
assert general_diag_dc_err < tol
## assert general_diag_mr3_err < tol
assert inverse_chol_err < tol
def calculate_rkernel(self):
gd = self.gd
ng_c = gd.N_c
cell_cv = gd.cell_cv
icell_cv = 2 * np.pi * np.linalg.inv(cell_cv)
vol = np.linalg.det(cell_cv)
ns = self.calc.wfs.nspins
n_g = self.n_g # density on rough grid
fx_g = ns * self.get_fxc_g(n_g) # local exchange kernel
qc_g = (-4 * np.pi * ns / fx_g)**0.5 # cutoff functional
flocal_g = qc_g**3 * fx_g / (6 * np.pi**2) # ren. x-kernel for r=r'
Vlocal_g = 2 * qc_g / np.pi # ren. Hartree kernel for r=r'
ng = np.prod(ng_c) # number of grid points
r_vg = gd.get_grid_point_coordinates()
rx_g = r_vg[0].flatten()
ry_g = r_vg[1].flatten()
rz_g = r_vg[2].flatten()
prnt(' %d grid points and %d plane waves at the Gamma point' %
(ng, self.pd.ngmax),
file=self.fd)
# Unit cells
R_Rv = []
weight_R = []
nR_v = self.unit_cells
nR = np.prod(nR_v)
for i in range(-nR_v[0] + 1, nR_v[0]):
for j in range(-nR_v[1] + 1, nR_v[1]):
for h in range(-nR_v[2] + 1, nR_v[2]):
R_Rv.append(i * cell_cv[0] + j * cell_cv[1] +
h * cell_cv[2])
weight_R.append((nR_v[0] - abs(i)) * (nR_v[1] - abs(j)) *
(nR_v[2] - abs(h)) / float(nR))
if nR > 1:
# with more than one unit cell only the exchange kernel is
# calculated on the grid. The bare Coulomb kernel is added
# in PW basis and Vlocal_g only the exchange part
dv = self.calc.density.gd.dv
gc = (3 * dv / 4 / np.pi)**(1 / 3.)
Vlocal_g -= 2 * np.pi * gc**2 / dv
prnt(' Lattice point sampling: ' + '(%s x %s x %s)^2 ' %
(nR_v[0], nR_v[1], nR_v[2]) +
' Reduced to %s lattice points' % len(R_Rv),
file=self.fd)
l_g_size = -(-ng // mpi.world.size)
l_g_range = range(mpi.world.rank * l_g_size,
min((mpi.world.rank + 1) * l_g_size, ng))
fhxc_qsGr = {}
for iq in range(len(self.ibzq_qc)):
fhxc_qsGr[iq] = np.zeros(
(ns, len(self.pd.G2_qG[iq]), len(l_g_range)), dtype=complex)
inv_error = np.seterr()
np.seterr(invalid='ignore')
np.seterr(divide='ignore')
t0 = time()
# Loop over Lattice points
for i, R_v in enumerate(R_Rv):
# Loop over r'. f_rr and V_rr are functions of r (dim. as r_vg[0])
if i == 1:
prnt(' Finished 1 cell in %s seconds' % int(time() - t0) +
' - estimated %s seconds left' % int(
(len(R_Rv) - 1) * (time() - t0)),
file=self.fd)
self.fd.flush()
if len(R_Rv) > 5:
if (i + 1) % (len(R_Rv) / 5 + 1) == 0:
prnt(' Finished %s cells in %s seconds' %
(i, int(time() - t0)) +
' - estimated %s seconds left' % int(
(len(R_Rv) - i) * (time() - t0) / i),
file=self.fd)
self.fd.flush()
for g in l_g_range:
rx = rx_g[g] + R_v[0]
ry = ry_g[g] + R_v[1]
rz = rz_g[g] + R_v[2]
# |r-r'-R_i|
rr = ((r_vg[0] - rx)**2 + (r_vg[1] - ry)**2 +
(r_vg[2] - rz)**2)**0.5
n_av = (n_g + n_g.flatten()[g]) / 2.
fx_g = ns * self.get_fxc_g(n_av, index=g)
qc_g = (-4 * np.pi * ns / fx_g)**0.5
x = qc_g * rr
osc_x = np.sin(x) - x * np.cos(x)
f_rr = fx_g * osc_x / (2 * np.pi**2 * rr**3)
if nR > 1: # include only exchange part of the kernel here
V_rr = (sici(x)[0] * 2 / np.pi - 1) / rr
else: # include the full kernel (also hartree part)
V_rr = (sici(x)[0] * 2 / np.pi) / rr
# Terms with r = r'
if (np.abs(R_v) < 0.001).all():
tmp_flat = f_rr.flatten()
tmp_flat[g] = flocal_g.flatten()[g]
f_rr = tmp_flat.reshape(ng_c)
tmp_flat = V_rr.flatten()
tmp_flat[g] = Vlocal_g.flatten()[g]
V_rr = tmp_flat.reshape(ng_c)
del tmp_flat
f_rr[np.where(n_av < self.density_cut)] = 0.0
V_rr[np.where(n_av < self.density_cut)] = 0.0
f_rr *= weight_R[i]
V_rr *= weight_R[i]
# r-r'-R_i
r_r = np.array([r_vg[0] - rx, r_vg[1] - ry, r_vg[2] - rz])
# Fourier transform of r
for iq, q in enumerate(self.ibzq_qc):
q_v = np.dot(q, icell_cv)
e_q = np.exp(-1j * gemmdot(q_v, r_r, beta=0.0))
f_q = self.pd.fft((f_rr + V_rr) * e_q, iq) * vol / ng
fhxc_qsGr[iq][0, :, g - l_g_range[0]] += f_q
if ns == 2:
f_q = self.pd.fft(V_rr * e_q, iq) * vol / ng
fhxc_qsGr[iq][1, :, g - l_g_range[0]] += f_q
mpi.world.barrier()
np.seterr(**inv_error)
for iq, q in enumerate(self.ibzq_qc):
npw = len(self.pd.G2_qG[iq])
fhxc_sGsG = np.zeros((ns * npw, ns * npw), complex)
l_pw_size = -(-npw // mpi.world.size) # parallelize over PW below
l_pw_range = range(mpi.world.rank * l_pw_size,
min((mpi.world.rank + 1) * l_pw_size, npw))
if mpi.world.size > 1:
# redistribute grid and plane waves in fhxc_qsGr[iq]
bg1 = BlacsGrid(mpi.world, 1, mpi.world.size)
bg2 = BlacsGrid(mpi.world, mpi.world.size, 1)
bd1 = bg1.new_descriptor(npw, ng, npw, -(-ng / mpi.world.size))
bd2 = bg2.new_descriptor(npw, ng, -(-npw / mpi.world.size), ng)
fhxc_Glr = np.zeros((len(l_pw_range), ng), dtype=complex)
if ns == 2:
Koff_Glr = np.zeros((len(l_pw_range), ng), dtype=complex)
r = Redistributor(bg1.comm, bd1, bd2)
r.redistribute(fhxc_qsGr[iq][0], fhxc_Glr, npw, ng)
if ns == 2:
r.redistribute(fhxc_qsGr[iq][1], Koff_Glr, npw, ng)
else:
fhxc_Glr = fhxc_qsGr[iq][0]
if ns == 2:
Koff_Glr = fhxc_qsGr[iq][1]
# Fourier transform of r'
for iG in range(len(l_pw_range)):
f_g = fhxc_Glr[iG].reshape(ng_c)
f_G = self.pd.fft(f_g.conj(), iq) * vol / ng
fhxc_sGsG[l_pw_range[0] + iG, :npw] = f_G.conj()
if ns == 2:
v_g = Koff_Glr[iG].reshape(ng_c)
v_G = self.pd.fft(v_g.conj(), iq) * vol / ng
fhxc_sGsG[npw + l_pw_range[0] + iG, :npw] = v_G.conj()
if ns == 2: # f_00 = f_11 and f_01 = f_10
fhxc_sGsG[:npw, npw:] = fhxc_sGsG[npw:, :npw]
fhxc_sGsG[npw:, npw:] = fhxc_sGsG[:npw, :npw]
mpi.world.sum(fhxc_sGsG)
fhxc_sGsG /= vol
if mpi.rank == 0:
w = Writer('fhxc_%s_%s_%s_%s.gpw' %
(self.tag, self.xc, self.ecut, iq))
w.dimension('sG', ns * npw)
w.add('fhxc_sGsG', ('sG', 'sG'), dtype=complex)
if nR > 1: # add Hartree kernel evaluated in PW basis
Gq2_G = self.pd.G2_qG[iq]
if (q == 0).all():
Gq2_G[0] = 1.
vq_G = 4 * np.pi / Gq2_G
fhxc_sGsG += np.tile(np.eye(npw) * vq_G, (ns, ns))
w.fill(fhxc_sGsG)
w.close()
mpi.world.barrier()
prnt(file=self.fd)
def calculate_blocked_density_matrix(self, f_n, C_nM):
nbands = self.bd.nbands
nao = self.nao
dtype = C_nM.dtype
self.nMdescriptor.checkassert(C_nM)
if self.gd.rank == 0:
Cf_nM = (C_nM * f_n[:, None])
else:
C_nM = self.nM_unique_descriptor.zeros(dtype=dtype)
Cf_nM = self.nM_unique_descriptor.zeros(dtype=dtype)
r = Redistributor(self.block_comm, self.nM_unique_descriptor,
self.mmdescriptor)
Cf_mm = self.mmdescriptor.zeros(dtype=dtype)
r.redistribute(Cf_nM, Cf_mm, nbands, nao)
del Cf_nM
C_mm = self.mmdescriptor.zeros(dtype=dtype)
r.redistribute(C_nM, C_mm, nbands, nao)
# no use to delete C_nM as it's in the input...
rho_mm = self.mmdescriptor.zeros(dtype=dtype)
if 1: # if self.libelpa is None:
pblas_simple_gemm(self.mmdescriptor,
self.mmdescriptor,
self.mmdescriptor,
Cf_mm,
C_mm,
rho_mm,
transa='C')
else:
# elpa_hermitian_multiply was not faster than the ordinary
# multiplication in the test. The way we have things distributed,
# we need to transpose things at the moment.
#
# Rather than enabling this, we should store the coefficients
# in an appropriate 2D block cyclic format (c_nm) and not the
# current C_nM format. This makes it possible to avoid
# redistributing the coefficients at all. But we don't have time
# to implement this at the moment.
mul = self.libelpa.hermitian_multiply
desc = self.mmdescriptor
from gpaw.utilities.scalapack import pblas_tran
def T(array):
tmp = array.copy()
pblas_tran(alpha=1.0,
a_MN=tmp,
beta=0.0,
c_NM=array,
desca=desc,
descc=desc)
T(C_mm)
T(Cf_mm)
mul(C_mm, Cf_mm, rho_mm, desc, desc, desc, uplo_a='X', uplo_c='X')
return rho_mm
def main(N=72, seed=42, mprocs=2, nprocs=2, dtype=float):
gen = np.random.RandomState(seed)
grid = BlacsGrid(world, mprocs, nprocs)
if (dtype == complex):
epsilon = 1.0j
else:
epsilon = 0.0
# Create descriptors for matrices on master:
glob = grid.new_descriptor(N, N, N, N)
# print globA.asarray()
# Populate matrices local to master:
H0 = glob.zeros(dtype=dtype) + gen.rand(*glob.shape)
S0 = glob.zeros(dtype=dtype) + gen.rand(*glob.shape)
C0 = glob.empty(dtype=dtype)
if rank == 0:
# Complex case must have real numbers on the diagonal.
# We make a simple complex Hermitian matrix below.
H0 = H0 + epsilon * (0.1 * np.tri(N, N, k=-N // nprocs) +
0.3 * np.tri(N, N, k=-1))
S0 = S0 + epsilon * (0.2 * np.tri(N, N, k=-N // nprocs) +
0.4 * np.tri(N, N, k=-1))
# Make matrices symmetric
rk(1.0, H0.copy(), 0.0, H0)
rk(1.0, S0.copy(), 0.0, S0)
# Overlap matrix must be semi-positive definite
S0 = S0 + 50.0 * np.eye(N, N, 0)
# Hamiltonian is usually diagonally dominant
H0 = H0 + 75.0 * np.eye(N, N, 0)
C0 = S0.copy()
S0_inv = S0.copy()
# Local result matrices
W0 = np.empty((N), dtype=float)
W0_g = np.empty((N), dtype=float)
# Calculate eigenvalues / other serial results
if rank == 0:
diagonalize(H0.copy(), W0)
general_diagonalize(H0.copy(), W0_g, S0.copy())
inverse_cholesky(C0) # result returned in lower triangle
tri2full(S0_inv, 'L')
S0_inv = inv(S0_inv)
# tri2full(C0) # symmetrize
assert glob.check(H0) and glob.check(S0) and glob.check(C0)
# Create distributed destriptors with various block sizes:
dist = grid.new_descriptor(N, N, 8, 8)
# Distributed matrices:
# We can use empty here, but end up with garbage on
# on the other half of the triangle when we redistribute.
# This is fine because ScaLAPACK does not care.
H = dist.empty(dtype=dtype)
S = dist.empty(dtype=dtype)
Sinv = dist.empty(dtype=dtype)
Z = dist.empty(dtype=dtype)
C = dist.empty(dtype=dtype)
Sinv = dist.empty(dtype=dtype)
# Eigenvalues are non-BLACS matrices
W = np.empty((N), dtype=float)
W_dc = np.empty((N), dtype=float)
W_mr3 = np.empty((N), dtype=float)
W_g = np.empty((N), dtype=float)
W_g_dc = np.empty((N), dtype=float)
W_g_mr3 = np.empty((N), dtype=float)
Glob2dist = Redistributor(world, glob, dist)
Glob2dist.redistribute(H0, H, uplo='L')
Glob2dist.redistribute(S0, S, uplo='L')
Glob2dist.redistribute(S0, C, uplo='L') # C0 was previously overwritten
Glob2dist.redistribute(S0, Sinv, uplo='L')
# we don't test the expert drivers anymore since there
# might be a buffer overflow error
## scalapack_diagonalize_ex(dist, H.copy(), Z, W, 'L')
scalapack_diagonalize_dc(dist, H.copy(), Z, W_dc, 'L')
## scalapack_diagonalize_mr3(dist, H.copy(), Z, W_mr3, 'L')
## scalapack_general_diagonalize_ex(dist, H.copy(), S.copy(), Z, W_g, 'L')
scalapack_general_diagonalize_dc(dist, H.copy(), S.copy(), Z, W_g_dc, 'L')
## scalapack_general_diagonalize_mr3(dist, H.copy(), S.copy(), Z, W_g_mr3, 'L')
scalapack_inverse_cholesky(dist, C, 'L')
if dtype == complex: # Only supported for complex for now
scalapack_inverse(dist, Sinv, 'L')
# Undo redistribute
C_test = glob.empty(dtype=dtype)
Sinv_test = glob.empty(dtype=dtype)
Dist2glob = Redistributor(world, dist, glob)
Dist2glob.redistribute(C, C_test)
Dist2glob.redistribute(Sinv, Sinv_test)
if rank == 0:
## diag_ex_err = abs(W - W0).max()
diag_dc_err = abs(W_dc - W0).max()
## diag_mr3_err = abs(W_mr3 - W0).max()
## general_diag_ex_err = abs(W_g - W0_g).max()
general_diag_dc_err = abs(W_g_dc - W0_g).max()
## general_diag_mr3_err = abs(W_g_mr3 - W0_g).max()
inverse_chol_err = abs(C_test - C0).max()
tri2full(Sinv_test, 'L')
inverse_err = abs(Sinv_test - S0_inv).max()
## print 'diagonalize ex err', diag_ex_err
print('diagonalize dc err', diag_dc_err)
## print 'diagonalize mr3 err', diag_mr3_err
## print 'general diagonalize ex err', general_diag_ex_err
print('general diagonalize dc err', general_diag_dc_err)
## print 'general diagonalize mr3 err', general_diag_mr3_err
print('inverse chol err', inverse_chol_err)
if dtype == complex:
print('inverse err', inverse_err)
else:
## diag_ex_err = 0.0
diag_dc_err = 0.0
## diag_mr3_err = 0.0
## general_diag_ex_err = 0.0
general_diag_dc_err = 0.0
## general_diag_mr3_err = 0.0
inverse_chol_err = 0.0
inverse_err = 0.0
# We don't like exceptions on only one cpu
## diag_ex_err = world.sum(diag_ex_err)
diag_dc_err = world.sum(diag_dc_err)
## diag_mr3_err = world.sum(diag_mr3_err)
## general_diag_ex_err = world.sum(general_diag_ex_err)
general_diag_dc_err = world.sum(general_diag_dc_err)
## general_diag_mr3_err = world.sum(general_diag_mr3_err)
inverse_chol_err = world.sum(inverse_chol_err)
inverse_err = world.sum(inverse_err)
## assert diag_ex_err < tol
assert diag_dc_err < tol
## assert diag_mr3_err < tol
## assert general_diag_ex_err < tol
assert general_diag_dc_err < tol
## assert general_diag_mr3_err < tol
assert inverse_chol_err < tol
if dtype == complex:
assert inverse_err < tol
class LCAOTDDFT(GPAW):
def __init__(self, filename=None, propagator_debug=False,
propagator='cn', fxc=None, **kwargs):
self.time = 0.0
self.niter = 0
self.kick_strength = [0.0, 0.0, 0.0]
GPAW.__init__(self, filename, **kwargs)
self.propagator_debug = propagator_debug
self.tddft_initialized = False
self.fxc = fxc
self.propagator = propagator
# Restarting from a file
if filename is not None:
self.initialize()
self.set_positions()
def propagate_wfs(self, sourceC_nm, targetC_nm, S_MM, H_MM, dt):
if self.propagator == 'cn':
return self.linear_propagator(sourceC_nm, targetC_nm, S_MM, H_MM, dt)
raise NotImplementedError
def linear_propagator(self, sourceC_nM, targetC_nM, S_MM, H_MM, dt):
self.timer.start('Linear solve')
# XXX Debugging stuff. Remove
if self.propagator_debug:
if self.blacs:
globalH_MM = self.blacs_mm_to_global(H_MM)
globalS_MM = self.blacs_mm_to_global(S_MM)
if world.rank == 0:
tri2full(globalS_MM, 'L')
tri2full(globalH_MM, 'L')
U_MM = dot(inv(globalS_MM-0.5j*globalH_MM*dt), globalS_MM+0.5j*globalH_MM*dt)
debugC_nM = dot(sourceC_nM, U_MM.T.conjugate())
#print 'PASS PROPAGATOR'
#debugC_nM = sourceC_nM.copy()
else:
if world.rank == 0:
U_MM = dot(inv(S_MM-0.5j*H_MM*dt), S_MM+0.5j*H_MM*dt)
debugC_nM = dot(sourceC_nM, U_MM.T.conjugate())
#print 'PASS PROPAGATOR'
#debugC_nM = sourceC_nM.copy()
if self.blacs:
target_blockC_nm = self.Cnm_block_descriptor.empty(dtype=complex) # XXX, Preallocate
temp_blockC_nm = self.Cnm_block_descriptor.empty(dtype=complex) # XXX, Preallocate
temp_block_mm = self.mm_block_descriptor.empty(dtype=complex)
if self.density.gd.comm.rank != 0:
# XXX Fake blacks nbands, nao, nbands, nao grid because some weird asserts
# (these are 0,x or x,0 arrays)
sourceC_nM = self.CnM_unique_descriptor.zeros(dtype=complex)
# 1. target = (S+0.5j*H*dt) * source
# Wave functions to target
self.CnM2nm.redistribute(sourceC_nM, temp_blockC_nm)
# XXX It can't be this f'n hard to symmetrize a matrix (tri2full)
scalapack_zero(self.mm_block_descriptor, H_MM, 'U') # Remove upper diagonal
temp_block_mm[:] = S_MM - (0.5j*dt) * H_MM # Lower diagonal matrix
scalapack_set(self.mm_block_descriptor, temp_block_mm, 0, 0, 'U')
# Note it's stricly lower diagonal matrix
pblas_tran(-0.5j*dt, H_MM, 1.0, temp_block_mm, self.mm_block_descriptor, self.mm_block_descriptor) # Add transpose of H
pblas_tran(1.0, S_MM, 1.0, temp_block_mm, self.mm_block_descriptor, self.mm_block_descriptor) # Add transpose of S
pblas_simple_gemm(self.Cnm_block_descriptor,
self.mm_block_descriptor,
self.Cnm_block_descriptor,
temp_blockC_nm,
temp_block_mm,
target_blockC_nm)
# 2. target = (S-0.5j*H*dt)^-1 * target
#temp_block_mm[:] = S_MM + (0.5j*dt) * H_MM
# XXX It can't be this f'n hard to symmetrize a matrix (tri2full)
temp_block_mm[:] = S_MM + (0.5j*dt) * H_MM # Lower diagonal matrix
scalapack_set(self.mm_block_descriptor, temp_block_mm, 0, 0, 'U') # Not it's stricly lower diagonal matrix
pblas_tran(+0.5j*dt, H_MM, 1.0, temp_block_mm, self.mm_block_descriptor, self.mm_block_descriptor) # Add transpose of H
pblas_tran(1.0, S_MM, 1.0, temp_block_mm, self.mm_block_descriptor, self.mm_block_descriptor) # Add transpose of S
scalapack_solve(self.mm_block_descriptor,
self.Cnm_block_descriptor,
temp_block_mm,
target_blockC_nm)
if self.density.gd.comm.rank != 0: # XXX is this correct?
# XXX Fake blacks nbands, nao, nbands, nao grid because some weird asserts
# (these are 0,x or x,0 arrays)
target = self.CnM_unique_descriptor.zeros(dtype=complex)
else:
target = targetC_nM
self.Cnm2nM.redistribute(target_blockC_nm, target)
self.density.gd.comm.broadcast(targetC_nM, 0) # Is this required?
else:
# Note: The full equation is conjugated (therefore -+, not +-)
targetC_nM[:] = solve(S_MM-0.5j*H_MM*dt, np.dot(S_MM+0.5j*H_MM*dt, sourceC_nM.T.conjugate())).T.conjugate()
# XXX Debugging stuff. Remove
if self.propagator_debug:
if world.rank == 0:
verify(targetC_nM, debugC_nM,
'Linear solver propagator vs. reference')
self.timer.stop('Linear solve')
def taylor_propagator(self, sourceC_nM, targetC_nM, S_MM, H_MM, dt):
self.timer.start('Taylor propagator')
# XXX Debugging stuff. Remove
if self.propagator_debug:
if self.blacs:
globalH_MM = self.blacs_mm_to_global(H_MM)
globalS_MM = self.blacs_mm_to_global(S_MM)
if world.rank == 0:
tri2full(globalS_MM, 'L')
tri2full(globalH_MM, 'L')
U_MM = dot(inv(globalS_MM-0.5j*globalH_MM*dt), globalS_MM+0.5j*globalH_MM*dt)
debugC_nM = dot(sourceC_nM, U_MM.T.conjugate())
#print 'PASS PROPAGATOR'
#debugC_nM = sourceC_nM.copy()
else:
if world.rank == 0:
U_MM = dot(inv(S_MM - 0.5j * H_MM * dt),
S_MM + 0.5j * H_MM * dt)
debugC_nM = dot(sourceC_nM, U_MM.T.conjugate())
#print 'PASS PROPAGATOR'
#debugC_nM = sourceC_nM.copy()
if self.blacs:
target_blockC_nm = self.Cnm_block_descriptor.empty(dtype=complex) # XXX, Preallocate
if self.density.gd.comm.rank != 0:
# XXX Fake blacks nbands, nao, nbands, nao grid because some weird asserts
# (these are 0,x or x,0 arrays)
sourceC_nM = self.CnM_unique_descriptor.zeros(dtype=complex)
# Zeroth order taylor to target
self.CnM2nm.redistribute(sourceC_nM, target_blockC_nm)
# XXX, preallocate, optimize use of temporal arrays
temp_blockC_nm = target_blockC_nm.copy()
temp2_blockC_nm = target_blockC_nm.copy()
order = 4
assert self.wfs.kd.comm.size == 1
for n in range(order):
# Multiply with hamiltonian
pblas_simple_hemm(self.mm_block_descriptor,
self.Cnm_block_descriptor,
self.Cnm_block_descriptor,
H_MM,
temp_blockC_nm,
temp2_blockC_nm, side='R')
# XXX: replace with not simple gemm
temp2_blockC_nm *= -1j*dt/(n+1)
# Multiply with inverse overlap
pblas_simple_hemm(self.mm_block_descriptor,
self.Cnm_block_descriptor,
self.Cnm_block_descriptor,
self.wfs.kpt_u[0].invS_MM, # XXX
temp2_blockC_nm,
temp_blockC_nm, side='R')
target_blockC_nm += temp_blockC_nm
if self.density.gd.comm.rank != 0: # Todo: Change to gd.rank
# XXX Fake blacks nbands, nao, nbands, nao grid because some weird asserts
# (these are 0,x or x,0 arrays)
target = self.CnM_unique_descriptor.zeros(dtype=complex)
else:
target = targetC_nM
self.Cnm2nM.redistribute(target_blockC_nm, target)
self.density.gd.comm.broadcast(targetC_nM, 0)
else:
assert self.wfs.kd.comm.size == 1
if self.density.gd.comm.rank == 0:
targetC_nM[:] = sourceC_nM[:]
tempC_nM = sourceC_nM.copy()
order = 4
for n in range(order):
tempC_nM[:] = np.dot(self.wfs.kpt_u[0].invS, np.dot(H_MM, 1j*dt/(n+1)*tempC_nM.T.conjugate())).T.conjugate()
targetC_nM += tempC_nM
self.density.gd.comm.broadcast(targetC_nM, 0)
if self.propagator_debug:
if world.rank == 0:
verify(targetC_nM, debugC_nM,
'Linear solver propagator vs. reference')
self.timer.stop('Taylor propagator')
def kick(self, strength):
self.tddft_init()
self.timer.start('Kick')
self.kick_strength = strength
# magnitude
magnitude = np.sqrt(strength[0]*strength[0]
+ strength[1]*strength[1]
+ strength[2]*strength[2])
# normalize
direction = strength / magnitude
self.text('Applying absorbtion kick')
self.text('Magnitude: %.8f ' % magnitude)
self.text('Direction: %.4f %.4f %.4f' % tuple(direction))
# Create hamiltonian object for absorbtion kick
kick_hamiltonian = KickHamiltonian(self, ConstantElectricField(magnitude, direction=direction))
for k, kpt in enumerate(self.wfs.kpt_u):
Vkick_MM = self.wfs.eigensolver.calculate_hamiltonian_matrix(kick_hamiltonian, self.wfs, kpt, add_kinetic=False, root=-1)
for i in range(10):
self.propagate_wfs(kpt.C_nM, kpt.C_nM, kpt.S_MM, Vkick_MM, 0.1)
self.timer.stop('Kick')
def blacs_mm_to_global(self, H_mm):
target = self.MM_descriptor.empty(dtype=complex)
self.mm2MM.redistribute(H_mm, target)
world.barrier()
return target
def blacs_nm_to_global(self, C_nm):
target = self.CnM_unique_descriptor.empty(dtype=complex)
self.Cnm2nM.redistribute(C_nm, target)
world.barrier()
return target
def tddft_init(self):
if not self.tddft_initialized:
if world.rank == 0:
print('Initializing real time LCAO TD-DFT calculation.')
print('XXX Warning: Array use not optimal for memory.')
print('XXX Taylor propagator probably doesn\'t work')
print('XXX ...and no arrays are listed in memory estimate yet.')
self.blacs = self.wfs.ksl.using_blacs
if self.blacs:
self.ksl = ksl = self.wfs.ksl
nao = ksl.nao
nbands = ksl.bd.nbands
mynbands = ksl.bd.mynbands
blocksize = ksl.blocksize
from gpaw.blacs import Redistributor
if world.rank == 0:
print('BLACS Parallelization')
# Parallel grid descriptors
self.MM_descriptor = ksl.blockgrid.new_descriptor(nao, nao, nao, nao) # FOR DEBUG
self.mm_block_descriptor = ksl.blockgrid.new_descriptor(nao, nao, blocksize, blocksize)
self.Cnm_block_descriptor = ksl.blockgrid.new_descriptor(nbands, nao, blocksize, blocksize)
#self.CnM_descriptor = ksl.blockgrid.new_descriptor(nbands, nao, mynbands, nao)
self.mM_column_descriptor = ksl.single_column_grid.new_descriptor(nao, nao, ksl.naoblocksize, nao)
self.CnM_unique_descriptor = ksl.single_column_grid.new_descriptor(nbands, nao, mynbands, nao)
# Redistributors
self.mm2MM = Redistributor(ksl.block_comm,
self.mm_block_descriptor,
self.MM_descriptor) # XXX FOR DEBUG
self.MM2mm = Redistributor(ksl.block_comm,
self.MM_descriptor,
self.mm_block_descriptor) # XXX FOR DEBUG
self.Cnm2nM = Redistributor(ksl.block_comm,
self.Cnm_block_descriptor,
self.CnM_unique_descriptor)
self.CnM2nm = Redistributor(ksl.block_comm,
self.CnM_unique_descriptor,
self.Cnm_block_descriptor)
self.mM2mm = Redistributor(ksl.block_comm,
self.mM_column_descriptor,
self.mm_block_descriptor)
for kpt in self.wfs.kpt_u:
scalapack_zero(self.mm_block_descriptor, kpt.S_MM,'U')
scalapack_zero(self.mm_block_descriptor, kpt.T_MM,'U')
# XXX to propagator class
if self.propagator == 'taylor' and self.blacs:
# cholS_mm = self.mm_block_descriptor.empty(dtype=complex)
for kpt in self.wfs.kpt_u:
kpt.invS_MM = kpt.S_MM.copy()
scalapack_inverse(self.mm_block_descriptor,
kpt.invS_MM, 'L')
if self.propagator_debug:
if world.rank == 0:
print('XXX Doing serial inversion of overlap matrix.')
self.timer.start('Invert overlap (serial)')
invS2_MM = self.MM_descriptor.empty(dtype=complex)
for kpt in self.wfs.kpt_u:
#kpt.S_MM[:] = 128.0*(2**world.rank)
self.mm2MM.redistribute(self.wfs.S_qMM[kpt.q], invS2_MM)
world.barrier()
if world.rank == 0:
tri2full(invS2_MM,'L')
invS2_MM[:] = inv(invS2_MM.copy())
self.invS2_MM = invS2_MM
kpt.invS2_MM = ksl.mmdescriptor.empty(dtype=complex)
self.MM2mm.redistribute(invS2_MM, kpt.invS2_MM)
verify(kpt.invS_MM, kpt.invS2_MM, 'overlap par. vs. serial', 'L')
self.timer.stop('Invert overlap (serial)')
if world.rank == 0:
print('XXX Overlap inverted.')
if self.propagator == 'taylor' and not self.blacs:
tmp = inv(self.wfs.kpt_u[0].S_MM)
self.wfs.kpt_u[0].invS = tmp
# Reset the density mixer
self.density.mixer = DummyMixer()
self.tddft_initialized = True
for k, kpt in enumerate(self.wfs.kpt_u):
kpt.C2_nM = kpt.C_nM.copy()
#kpt.firstC_nM = kpt.C_nM.copy()
def update_projectors(self):
self.timer.start('LCAO update projectors')
# Loop over all k-points
for k, kpt in enumerate(self.wfs.kpt_u):
for a, P_ni in kpt.P_ani.items():
print('Update projector: Rank:', world.rank, 'a', a)
P_ni.fill(117)
gemm(1.0, kpt.P_aMi[a], kpt.C_nM, 0.0, P_ni, 'n')
self.timer.stop('LCAO update projectors')
def save_wfs(self):
for k, kpt in enumerate(self.wfs.kpt_u):
kpt.C2_nM[:] = kpt.C_nM
def update_hamiltonian(self):
self.update_projectors()
self.density.update(self.wfs)
self.hamiltonian.update(self.density)
def propagate(self, time_step=10, iterations=2000, out='lcao.dm',
dump_interval=50):
assert self.wfs.dtype == complex
time_step *= attosec_to_autime
self.time_step = time_step
self.dump_interval = dump_interval
maxiter = self.niter + iterations
if self.time < self.time_step:
self.dm_file = paropen(out,'w') # XXXX
# Bug: will fail if world != self.wfs.world. -askhl
header = '# Kick = [%22.12le, %22.12le, %22.12le]\n' \
% (self.kick_strength[0], self.kick_strength[1], \
self.kick_strength[2])
header += '# %15s %15s %22s %22s %22s\n' \
% ('time', 'norm', 'dmx', 'dmy', 'dmz')
self.dm_file.write(header)
self.dm_file.flush()
self.text('About to do %d propagation steps.' % iterations)
else:
self.dm_file = paropen(out,'a') # XXXX
self.text('About to continue from iteration %d and do %d propagation steps' % (self.niter, maxiter))
self.tddft_init()
dm0 = None # Initial dipole moment
self.timer.start('Propagate')
while self.niter < maxiter:
dm = self.density.finegd.calculate_dipole_moment(self.density.rhot_g)
if dm0 is None:
dm0 = dm
norm = self.density.finegd.integrate(self.density.rhot_g)
line = '%20.8lf %20.8le %22.12le %22.12le %22.12le' % (self.time, norm, dm[0], dm[1], dm[2])
T = localtime()
if world.rank == 0:
print(line, file=self.dm_file)
if world.rank == 0 and self.niter%10==0:
print('iter: %3d %02d:%02d:%02d %11.2f %9.1f %12.8f' % (self.niter,
T[3], T[4], T[5],
self.time * autime_to_attosec,
log(abs(norm)+1e-16)/log(10),
np.sqrt(dm[0]**2+dm[1]**2+dm[2]**2)))
self.dm_file.flush()
# ----------------------------------------------------------------------------
# Predictor step
# ----------------------------------------------------------------------------
# 1. Calculate H(t)
self.save_wfs() # kpt.C2_nM = kpt.C_nM
# 2. H_MM(t) = <M|H(t)|H>
# Solve Psi(t+dt) from (S_MM - 0.5j*H_MM(t)*dt) Psi(t+dt) = (S_MM + 0.5j*H_MM(t)*dt) Psi(t)
for k, kpt in enumerate(self.wfs.kpt_u):
if self.fxc is not None:
if self.time == 0.0:
kpt.deltaXC_H_MM = self.wfs.eigensolver.calculate_hamiltonian_matrix(\
self.hamiltonian, self.wfs, kpt, root=-1)
self.hamiltonian.xc = XC(self.fxc)
self.update_hamiltonian()
assert len(self.wfs.kpt_u) == 1
kpt.deltaXC_H_MM -= self.wfs.eigensolver.calculate_hamiltonian_matrix(\
self.hamiltonian, self.wfs, kpt, root=-1)
self.update_hamiltonian()
for k, kpt in enumerate(self.wfs.kpt_u):
kpt.H0_MM = self.wfs.eigensolver.calculate_hamiltonian_matrix(self.hamiltonian, self.wfs, kpt, root=-1)
if self.fxc is not None:
kpt.H0_MM += kpt.deltaXC_H_MM
self.propagate_wfs(kpt.C_nM, kpt.C_nM, kpt.S_MM, kpt.H0_MM, self.time_step)
# ----------------------------------------------------------------------------
# Propagator step
# ----------------------------------------------------------------------------
# 1. Calculate H(t+dt)
self.update_hamiltonian()
# 2. Estimate H(t+0.5*dt) ~ H(t) + H(t+dT)
for k, kpt in enumerate(self.wfs.kpt_u):
kpt.H0_MM *= 0.5
if self.fxc is not None:
# Store this to H0_MM and maybe save one extra H_MM of memory?
kpt.H0_MM += 0.5 * (self.wfs.eigensolver.calculate_hamiltonian_matrix( \
self.hamiltonian, self.wfs, kpt, root=-1) +\
kpt.deltaXC_H_MM)
else:
# Store this to H0_MM and maybe save one extra H_MM of memory?
kpt.H0_MM += 0.5 * self.wfs.eigensolver.calculate_hamiltonian_matrix( \
self.hamiltonian, self.wfs, kpt, root=-1)
# 3. Solve Psi(t+dt) from (S_MM - 0.5j*H_MM(t+0.5*dt)*dt) Psi(t+dt) = (S_MM + 0.5j*H_MM(t+0.5*dt)*dt) Psi(t)
self.propagate_wfs(kpt.C2_nM, kpt.C_nM, kpt.S_MM, kpt.H0_MM, self.time_step)
self.niter += 1
self.time += self.time_step
# Call registered callback functions
self.call_observers(self.niter)
self.call_observers(self.niter, final=True)
self.dm_file.close()
self.timer.stop('Propagate')
class LrDiagonalizeLayout:
"""BLACS layout for distributed Omega matrix in linear response
time-dependet DFT calculations"""
def __init__(self, sl_lrtddft, nrows, lr_comms):
self.mprocs, self.nprocs, self.block_size = tuple(sl_lrtddft)
self.lr_comms = lr_comms
# original grid, ie, how matrix is stored
self.matrix_grid = BlacsGrid(self.lr_comms.parent_comm,
self.lr_comms.dd_comm.size,
self.lr_comms.eh_comm.size)
# diagonalization grid
self.diag_grid = BlacsGrid(self.lr_comms.parent_comm, self.mprocs,
self.nprocs)
# -----------------------------------------------------------------
# for SCALAPACK we need TRANSPOSED MATRIX (and vector)
#
# M = rows, N = cols
M = nrows
N = nrows
mb = 1
nb = 1
self.matrix_descr = self.matrix_grid.new_descriptor(N, M, nb, mb)
bs = self.block_size
self.diag_descr = self.diag_grid.new_descriptor(N, M, bs, bs)
self.diag_in_redist = Redistributor(self.lr_comms.parent_comm,
self.matrix_descr, self.diag_descr)
self.diag_out_redist = Redistributor(self.lr_comms.parent_comm,
self.diag_descr,
self.matrix_descr)
def diagonalize(self, eigenvectors, eigenvalues):
"""Diagonalize symmetric distributed Casida matrix using Scalapack.
Parameters:
eigenvectors
distributed Casida matrix on input, distributed eigenvectors on output
eigenvalues
zero array on input, eigenvalues on output
"""
O_diag = self.diag_descr.empty(dtype=float)
if self.matrix_descr.blacsgrid.is_active():
O_orig = eigenvectors
else:
O_orig = np.empty((0, 0), dtype=float)
self.diag_in_redist.redistribute(O_orig, O_diag)
#print O_diag
self.diag_descr.diagonalize_dc(O_diag.copy(), O_diag, eigenvalues, 'L')
self.diag_out_redist.redistribute(O_diag, O_orig)
self.lr_comms.parent_comm.broadcast(eigenvalues, 0)
grid = BlacsGrid(world, 2, world.size // 2)
desc = grid.new_descriptor(12, 8, 2, 3)
a = desc.zeros()
a[:] = world.rank
subdesc = grid.new_descriptor(7, 7, 2, 2)
b = subdesc.zeros()
r = Redistributor(grid.comm, desc, subdesc, uplo='G')
ia = 3
ja = 2
ib = 1
jb = 1
M = 4
N = 5
r.redistribute(a, b, M, N, ia, ja, ib, jb)
a0 = desc.collect_on_master(a)
b0 = subdesc.collect_on_master(b)
if world.rank == 0:
print a0
print b0
xa = a0[ia:ia + M, ja:ja + N]
xb = b0[ib:ib + M, jb:jb + N]
assert (xa == xb).all()