def write(self, filename, idiotproof=True):
if idiotproof and not filename.endswith('.ftd'):
raise IOError('Filename must end with `.ftd`.')
master = self.world.rank == 0
# Open writer on master and set parameters/dimensions
if master:
tar = Writer(filename)
tar['DataType'] = {float: 'Float', complex: 'Complex'}[self.dtype]
tar['Time'] = self.time
tar['TimeStep'] = self.timestep #non-essential
tar['Width'] = self.sigma
tar.dimension('nw', self.nw)
tar.dimension('nspins', self.nspins)
# Create dimensions for varioius netCDF variables:
ng = self.gd.get_size_of_global_array()
tar.dimension('ngptsx', ng[0])
tar.dimension('ngptsy', ng[1])
tar.dimension('ngptsz', ng[2])
# Write frequencies
tar.add('Frequency', ('nw', ), self.omega_w, dtype=float)
# Write cumulative phase factors
tar.add('PhaseFactor', ('nw', ), self.gamma_w, dtype=self.dtype)
# Collect average densities on master and write
if master:
tar.add('Average', (
'nspins',
'ngptsx',
'ngptsy',
'ngptsz',
),
dtype=float)
for s in range(self.nspins):
big_Ant_G = self.gd.collect(self.Ant_sG[s])
if master:
tar.fill(big_Ant_G)
# Collect fourier transforms on master and write
if master:
tar.add('FourierTransform', ('nw', 'nspins', 'ngptsx', 'ngptsy', \
'ngptsz', ), dtype=self.dtype)
for w in range(self.nw):
for s in range(self.nspins):
big_Fnt_G = self.gd.collect(self.Fnt_wsG[w, s])
if master:
tar.fill(big_Fnt_G)
# Close to flush changes
if master:
tar.close()
# Make sure slaves don't return before master is done
self.world.barrier()
def write(self, filename, idiotproof=True):
if idiotproof and not filename.endswith('.ftd'):
raise IOError('Filename must end with `.ftd`.')
master = self.world.rank == 0
# Open writer on master and set parameters/dimensions
if master:
tar = Writer(filename)
tar['DataType'] = {float:'Float', complex:'Complex'}[self.dtype]
tar['Time'] = self.time
tar['TimeStep'] = self.timestep #non-essential
tar['Width'] = self.sigma
tar.dimension('nw', self.nw)
tar.dimension('nspins', self.nspins)
# Create dimensions for varioius netCDF variables:
ng = self.gd.get_size_of_global_array()
tar.dimension('ngptsx', ng[0])
tar.dimension('ngptsy', ng[1])
tar.dimension('ngptsz', ng[2])
# Write frequencies
tar.add('Frequency', ('nw',), self.omega_w, dtype=float)
# Write cumulative phase factors
tar.add('PhaseFactor', ('nw',), self.gamma_w, dtype=self.dtype)
# Collect average densities on master and write
if master:
tar.add('Average', ('nspins', 'ngptsx', 'ngptsy',
'ngptsz', ), dtype=float)
for s in range(self.nspins):
big_Ant_G = self.gd.collect(self.Ant_sG[s])
if master:
tar.fill(big_Ant_G)
# Collect fourier transforms on master and write
if master:
tar.add('FourierTransform', ('nw', 'nspins', 'ngptsx', 'ngptsy', \
'ngptsz', ), dtype=self.dtype)
for w in range(self.nw):
for s in range(self.nspins):
big_Fnt_G = self.gd.collect(self.Fnt_wsG[w,s])
if master:
tar.fill(big_Fnt_G)
# Close to flush changes
if master:
tar.close()
# Make sure slaves don't return before master is done
self.world.barrier()
def calculate_local_kernel(self):
# Standard ALDA exchange kernel
# Use with care. Results are very difficult to converge
# Sensitive to density_cut
ns = self.calc.wfs.nspins
gd = self.gd
pd = self.pd
cell_cv = gd.cell_cv
icell_cv = 2 * np.pi * np.linalg.inv(cell_cv)
vol = np.linalg.det(cell_cv)
fxc_sg = ns * self.get_fxc_g(ns * self.n_g)
fxc_sg[np.where(self.n_g < self.density_cut)] = 0.0
r_vg = gd.get_grid_point_coordinates()
for iq in range(len(self.ibzq_qc)):
Gvec_Gc = np.dot(pd.get_reciprocal_vectors(q=iq, add_q=False),
cell_cv / (2 * np.pi))
npw = len(Gvec_Gc)
l_pw_size = -(-npw // mpi.world.size)
l_pw_range = range(mpi.world.rank * l_pw_size,
min((mpi.world.rank + 1) * l_pw_size, npw))
fhxc_sGsG = np.zeros((ns * npw, ns * npw), dtype=complex)
for s in range(ns):
for iG in l_pw_range:
for jG in range(npw):
fxc = fxc_sg[s].copy()
dG_c = Gvec_Gc[iG] - Gvec_Gc[jG]
dG_v = np.dot(dG_c, icell_cv)
dGr_g = gemmdot(dG_v, r_vg, beta=0.0)
ft_fxc = gd.integrate(np.exp(-1j * dGr_g) * fxc)
fhxc_sGsG[s * npw + iG, s * npw + jG] = ft_fxc
mpi.world.sum(fhxc_sGsG)
fhxc_sGsG /= vol
Gq2_G = self.pd.G2_qG[iq]
if (self.ibzq_qc[iq] == 0).all():
Gq2_G[0] = 1.
vq_G = 4 * np.pi / Gq2_G
fhxc_sGsG += np.tile(np.eye(npw) * vq_G, (ns, ns))
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)
w.fill(fhxc_sGsG)
w.close()
mpi.world.barrier()
prnt(file=self.fd)
def calculate_local_kernel(self):
# Standard ALDA exchange kernel
# Use with care. Results are very difficult to converge
# Sensitive to density_cut
ns = self.calc.wfs.nspins
gd = self.gd
pd = self.pd
cell_cv = gd.cell_cv
icell_cv = 2 * np.pi * np.linalg.inv(cell_cv)
vol = np.linalg.det(cell_cv)
fxc_sg = ns * self.get_fxc_g(ns * self.n_g)
fxc_sg[np.where(self.n_g < self.density_cut)] = 0.0
r_vg = gd.get_grid_point_coordinates()
for iq in range(len(self.ibzq_qc)):
Gvec_Gc = np.dot(pd.get_reciprocal_vectors(q=iq, add_q=False),
cell_cv / (2 * np.pi))
npw = len(Gvec_Gc)
l_pw_size = -(-npw // mpi.world.size)
l_pw_range = range(mpi.world.rank * l_pw_size,
min((mpi.world.rank + 1) * l_pw_size, npw))
fhxc_sGsG = np.zeros((ns * npw, ns * npw), dtype=complex)
for s in range(ns):
for iG in l_pw_range:
for jG in range(npw):
fxc = fxc_sg[s].copy()
dG_c = Gvec_Gc[iG] - Gvec_Gc[jG]
dG_v = np.dot(dG_c, icell_cv)
dGr_g = gemmdot(dG_v, r_vg, beta=0.0)
ft_fxc = gd.integrate(np.exp(-1j * dGr_g) * fxc)
fhxc_sGsG[s * npw + iG, s * npw + jG] = ft_fxc
mpi.world.sum(fhxc_sGsG)
fhxc_sGsG /= vol
Gq2_G = self.pd.G2_qG[iq]
if (self.ibzq_qc[iq] == 0).all():
Gq2_G[0] = 1.
vq_G = 4 * np.pi / Gq2_G
fhxc_sGsG += np.tile(np.eye(npw) * vq_G, (ns, ns))
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)
w.fill(fhxc_sGsG)
w.close()
mpi.world.barrier()
prnt(file=self.fd)
def dscf_save_band(filename, paw, n):
"""Extract and save all information for band `n` to a tar file."""
world, bd, gd, kd = paw.wfs.world, paw.wfs.bd, paw.wfs.gd, \
KPointDescriptor(paw.wfs.nspins, paw.wfs.nibzkpts, paw.wfs.kpt_comm, \
paw.wfs.gamma, paw.wfs.dtype)
if world.rank == 0:
# Minimal amount of information needed:
w = Writer(filename)
w.dimension('nspins', kd.nspins)
w.dimension('nibzkpts', kd.nibzkpts)
w.dimension('nproj', sum([setup.ni for setup in paw.wfs.setups]))
ng = gd.get_size_of_global_array()
w.dimension('ngptsx', ng[0])
w.dimension('ngptsy', ng[1])
w.dimension('ngptsz', ng[2])
# Write projections:
if world.rank == 0:
w.add('Projection', ('nspins', 'nibzkpts', 'nproj'), dtype=kd.dtype)
for s in range(kd.nspins):
for k in range(kd.nibzkpts):
all_P_ni = paw.wfs.collect_projections(k, s) # gets all bands
if world.rank == 0:
w.fill(all_P_ni[n])
# Write wave functions:
if world.rank == 0:
w.add('PseudoWaveFunction', ('nspins', 'nibzkpts',
'ngptsx', 'ngptsy', 'ngptsz'),
dtype=kd.dtype)
for s in range(kd.nspins):
for k in range(kd.nibzkpts):
psit_G = paw.wfs.get_wave_function_array(n, k, s)
if world.rank == 0:
w.fill(psit_G)
if world.rank == 0:
# Close the file here to ensure that the last wave function is
# written to disk:
w.close()
# We don't want the slaves to start reading before the master has
# finished writing:
world.barrier()
def dscf_save_band(filename, paw, n):
"""Extract and save all information for band `n` to a tar file."""
world, bd, gd, kd = paw.wfs.world, paw.wfs.bd, paw.wfs.gd, \
KPointDescriptor(paw.wfs.nspins, paw.wfs.nibzkpts, paw.wfs.kpt_comm, \
paw.wfs.gamma, paw.wfs.dtype)
if world.rank == 0:
# Minimal amount of information needed:
w = Writer(filename)
w.dimension('nspins', kd.nspins)
w.dimension('nibzkpts', kd.nibzkpts)
w.dimension('nproj', sum([setup.ni for setup in paw.wfs.setups]))
ng = gd.get_size_of_global_array()
w.dimension('ngptsx', ng[0])
w.dimension('ngptsy', ng[1])
w.dimension('ngptsz', ng[2])
# Write projections:
if world.rank == 0:
w.add('Projection', ('nspins', 'nibzkpts', 'nproj'), dtype=kd.dtype)
for s in range(kd.nspins):
for k in range(kd.nibzkpts):
all_P_ni = paw.wfs.collect_projections(k, s) # gets all bands
if world.rank == 0:
w.fill(all_P_ni[n])
# Write wave functions:
if world.rank == 0:
w.add('PseudoWaveFunction',
('nspins', 'nibzkpts', 'ngptsx', 'ngptsy', 'ngptsz'),
dtype=kd.dtype)
for s in range(kd.nspins):
for k in range(kd.nibzkpts):
psit_G = paw.wfs.get_wave_function_array(n, k, s)
if world.rank == 0:
w.fill(psit_G)
if world.rank == 0:
# Close the file here to ensure that the last wave function is
# written to disk:
w.close()
# We don't want the slaves to start reading before the master has
# finished writing:
world.barrier()
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 get_phi_qaGp(self):
N1_max = 0
N2_max = 0
natoms = len(self.calc.wfs.setups)
for id in range(natoms):
N1 = self.npw
N2 = self.calc.wfs.setups[id].ni**2
if N1 > N1_max:
N1_max = N1
if N2 > N2_max:
N2_max = N2
nbzq = self.kd.nbzkpts
nbzq, nq_local, q_start, q_end = parallel_partition(
nbzq, world.rank, world.size, reshape=False)
phimax_qaGp = np.zeros((nq_local, natoms, N1_max, N2_max), dtype=complex)
#phimax_qaGp = np.zeros((nbzq, natoms, N1_max, N2_max), dtype=complex)
t0 = time()
for iq in range(nq_local):
q_c = self.bzq_qc[iq + q_start]
tmp_aGp = self.get_phi_aGp(q_c, parallel=False)
for id in range(natoms):
N1, N2 = tmp_aGp[id].shape
phimax_qaGp[iq, id, :N1, :N2] = tmp_aGp[id]
self.timing(iq*world.size, t0, nq_local, 'iq')
world.barrier()
# Write to disk
filename = 'phi_qaGp'
if world.rank == 0:
w = Writer(filename)
w.dimension('nbzq', nbzq)
w.dimension('natoms', natoms)
w.dimension('nG', N1_max)
w.dimension('nii', N2_max)
w.add('phi_qaGp', ('nbzq', 'natoms', 'nG', 'nii',), dtype=complex)
for q in range(nbzq):
residual = nbzq % size
N_local = nbzq // size
if q < residual * (N_local + 1):
qrank = q // (N_local + 1)
else:
qrank = (q - residual * (N_local + 1)) // N_local + residual
if qrank == 0:
if world.rank == 0:
phi_aGp = phimax_qaGp[q - q_start]
else:
if world.rank == qrank:
phi_aGp = phimax_qaGp[q - q_start]
world.send(phi_aGp, 0, q)
elif world.rank == 0:
world.receive(phi_aGp, qrank, q)
if world.rank == 0:
w.fill(phi_aGp)
world.barrier()
if world.rank == 0:
w.close()
return
def get_phi_qaGp(self):
N1_max = 0
N2_max = 0
natoms = len(self.calc.wfs.setups)
for id in range(natoms):
N1 = self.npw
N2 = self.calc.wfs.setups[id].ni**2
if N1 > N1_max:
N1_max = N1
if N2 > N2_max:
N2_max = N2
nbzq = self.kd.nbzkpts
nbzq, nq_local, q_start, q_end = parallel_partition(nbzq,
world.rank,
world.size,
reshape=False)
phimax_qaGp = np.zeros((nq_local, natoms, N1_max, N2_max),
dtype=complex)
#phimax_qaGp = np.zeros((nbzq, natoms, N1_max, N2_max), dtype=complex)
t0 = time()
for iq in range(nq_local):
q_c = self.bzq_qc[iq + q_start]
tmp_aGp = self.get_phi_aGp(q_c, parallel=False)
for id in range(natoms):
N1, N2 = tmp_aGp[id].shape
phimax_qaGp[iq, id, :N1, :N2] = tmp_aGp[id]
self.timing(iq * world.size, t0, nq_local, 'iq')
world.barrier()
# Write to disk
filename = 'phi_qaGp'
if world.rank == 0:
w = Writer(filename)
w.dimension('nbzq', nbzq)
w.dimension('natoms', natoms)
w.dimension('nG', N1_max)
w.dimension('nii', N2_max)
w.add('phi_qaGp', (
'nbzq',
'natoms',
'nG',
'nii',
), dtype=complex)
for q in range(nbzq):
residual = nbzq % size
N_local = nbzq // size
if q < residual * (N_local + 1):
qrank = q // (N_local + 1)
else:
qrank = (q - residual * (N_local + 1)) // N_local + residual
if qrank == 0:
if world.rank == 0:
phi_aGp = phimax_qaGp[q - q_start]
else:
if world.rank == qrank:
phi_aGp = phimax_qaGp[q - q_start]
world.send(phi_aGp, 0, q)
elif world.rank == 0:
world.receive(phi_aGp, qrank, q)
if world.rank == 0:
w.fill(phi_aGp)
if world.rank == 0:
w.close()
world.barrier()
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)