def calculate_dP_aqvMi(self, wfs):
"""Overlap between LCAO basis functions and gradient of projectors.
Only the gradient wrt the atomic positions in the reference cell is
computed.
"""
nao = wfs.setups.nao
nq = len(wfs.ibzk_qc)
atoms = [self.atoms[i] for i in self.indices]
# Derivatives in reference cell
dP_aqvMi = {}
for atom, setup in zip(atoms, wfs.setups):
a = atom.index
dP_aqvMi[a] = np.zeros((nq, 3, nao, setup.ni), wfs.dtype)
# Calculate overlap between basis function and gradient of projectors
# NOTE: the derivative is calculated wrt the atomic position and not
# the real-space coordinate
calc = TwoCenterIntegralCalculator(wfs.ibzk_qc, derivative=True)
expansions = ManySiteDictionaryWrapper(wfs.tci.P_expansions, dP_aqvMi)
calc.calculate(wfs.tci.atompairs, [expansions], [dP_aqvMi])
# Extract derivatives in the reference unit cell
# dP_aqvMi = {}
# for atom in self.atoms:
# dP_aqvMi[atom.index] = dPall_aqvMi[atom.index]
return dP_aqvMi
def get_tci_dP_aMix(spos_ac, wfs, q, *args, **kwargs):
# container for spline expansions of basis function-projector pairs
# (note to self: remember to conjugate/negate because of that)
from gpaw.lcao.overlap import ManySiteDictionaryWrapper,\
TwoCenterIntegralCalculator, NewTwoCenterIntegrals
if not isinstance(wfs.tci, NewTwoCenterIntegrals):
raise RuntimeError('Please remember --gpaw=usenewtci=True')
dP_aqxMi = {}
nao = wfs.setups.nao
nq = len(wfs.ibzk_qc)
for a, setup in enumerate(wfs.setups):
dP_aqxMi[a] = np.zeros((nq, 3, nao, setup.ni), wfs.dtype)
calc = TwoCenterIntegralCalculator(wfs.ibzk_qc, derivative=True)
expansions = ManySiteDictionaryWrapper(wfs.tci.P_expansions, dP_aqxMi)
calc.calculate(wfs.tci.atompairs, [expansions], [dP_aqxMi])
dP_aMix = {}
for a in dP_aqxMi:
dP_aMix[a] = dP_aqxMi[a].transpose(0, 2, 3, 1).copy()[q] # XXX q
return dP_aMix
def newoverlap(wfs, spos_ac):
assert wfs.ksl.block_comm.size == wfs.gd.comm.size * wfs.bd.comm.size
#even_part = EvenPartitioning(wfs.gd.comm, #wfs.ksl.block_comm,
# len(wfs.atom_partition.rank_a))
#atom_partition = even_part.as_atom_partition()
# XXXXXXXXXXXXXXX
atom_partition = wfs.atom_partition
tci = wfs.tci
gd = wfs.gd
kd = wfs.kd
nq = len(kd.ibzk_qc)
# New neighbor list because we want it "both ways", heh. Or do we?
neighbors = NeighborList(tci.cutoff_a,
skin=0,
sorted=True,
self_interaction=True,
bothways=False)
atoms = Atoms('X%d' % len(tci.cutoff_a), cell=gd.cell_cv, pbc=gd.pbc_c)
atoms.set_scaled_positions(spos_ac)
neighbors.update(atoms)
# XXX
pcutoff_a = []
phicutoff_a = []
for setup in wfs.setups:
if setup.pt_j:
pcutoff = max([pt.get_cutoff() for pt in setup.pt_j])
else:
pcutoff = 0.0
if setup.phit_j:
phicutoff = max([phit.get_cutoff() for phit in setup.phit_j])
else:
phicutoff = 0.0
pcutoff_a.append(pcutoff)
phicutoff_a.append(phicutoff)
# Calculate the projector--basis function overlaps:
#
# a1 ~a1
# P = < p | Phi > ,
# i mu i mu
#
# i.e. projector is on a1 and basis function is on what we will call a2.
overlapcalc = TwoCenterIntegralCalculator(wfs.kd.ibzk_qc, derivative=False)
P_aaqim = {} # keys: (a1, a2). Values: matrix blocks
dists_and_offsets = DistsAndOffsets(neighbors, spos_ac, gd.cell_cv)
#ng = 2**extra_parameters.get('log2ng', 10)
#transformer = FourierTransformer(rcmax, ng)
#tsoc = TwoSiteOverlapCalculator(transformer)
#msoc = ManySiteOverlapCalculator(tsoc, I_a, I_a)
msoc = wfs.tci.msoc
phit_Ij = [setup.phit_j for setup in tci.setups_I]
l_Ij = []
for phit_j in phit_Ij:
l_Ij.append([phit.get_angular_momentum_number() for phit in phit_j])
pt_l_Ij = [setup.l_j for setup in tci.setups_I]
pt_Ij = [setup.pt_j for setup in tci.setups_I]
phit_Ijq = msoc.transform(phit_Ij)
pt_Ijq = msoc.transform(pt_Ij)
#self.Theta_expansions = msoc.calculate_expansions(l_Ij, phit_Ijq,
# l_Ij, phit_Ijq)
#self.T_expansions = msoc.calculate_kinetic_expansions(l_Ij, phit_Ijq)
P_expansions = msoc.calculate_expansions(pt_l_Ij, pt_Ijq, l_Ij, phit_Ijq)
P_neighbors_a = {}
for a1 in atom_partition.my_indices:
for a2 in range(len(wfs.setups)):
R_ca_and_offset_a = dists_and_offsets.get(a1, a2)
if R_ca_and_offset_a is None: # No overlap between a1 and a2
continue
maxdistance = pcutoff_a[a1] + phicutoff_a[a2]
expansion = P_expansions.get(a1, a2)
P_qim = expansion.zeros((nq, ), dtype=wfs.dtype)
disp = None
for R_c, offset in R_ca_and_offset_a:
r = np.linalg.norm(R_c)
if r > maxdistance:
continue
# Below lines are meant to make use of symmetry. Will not
# be relevant for P.
#remainder = (a1 + a2) % 2
#if a1 < a2 and not remainder:
# continue
# if a1 > a2 and remainder:
# continue
phases = overlapcalc.phaseclass(overlapcalc.ibzk_qc, offset)
disp = AtomicDisplacement(None, a1, a2, R_c, offset, phases)
disp.evaluate_overlap(expansion, P_qim)
if disp is not None: # there was at least one non-zero overlap
assert (a1, a2) not in P_aaqim
P_aaqim[(a1, a2)] = P_qim
P_neighbors_a.setdefault(a1, []).append(a2)
return P_neighbors_a, P_aaqim
def calculate_forces(self, hamiltonian, F_av):
self.timer.start('LCAO forces')
spos_ac = self.tci.atoms.get_scaled_positions() % 1.0
ksl = self.ksl
nao = ksl.nao
mynao = ksl.mynao
nq = len(self.kd.ibzk_qc)
dtype = self.dtype
tci = self.tci
gd = self.gd
bfs = self.basis_functions
Mstart = ksl.Mstart
Mstop = ksl.Mstop
from gpaw.kohnsham_layouts import BlacsOrbitalLayouts
isblacs = isinstance(ksl, BlacsOrbitalLayouts) # XXX
if not isblacs:
self.timer.start('TCI derivative')
dThetadR_qvMM = np.empty((nq, 3, mynao, nao), dtype)
dTdR_qvMM = np.empty((nq, 3, mynao, nao), dtype)
dPdR_aqvMi = {}
for a in self.basis_functions.my_atom_indices:
ni = self.setups[a].ni
dPdR_aqvMi[a] = np.empty((nq, 3, nao, ni), dtype)
tci.calculate_derivative(spos_ac, dThetadR_qvMM, dTdR_qvMM,
dPdR_aqvMi)
gd.comm.sum(dThetadR_qvMM)
gd.comm.sum(dTdR_qvMM)
self.timer.stop('TCI derivative')
my_atom_indices = bfs.my_atom_indices
atom_indices = bfs.atom_indices
def _slices(indices):
for a in indices:
M1 = bfs.M_a[a] - Mstart
M2 = M1 + self.setups[a].nao
if M2 > 0:
yield a, max(0, M1), M2
def slices():
return _slices(atom_indices)
def my_slices():
return _slices(my_atom_indices)
#
# ----- -----
# \ -1 \ *
# E = ) S H rho = ) c eps f c
# mu nu / mu x x z z nu / n mu n n n nu
# ----- -----
# x z n
#
# We use the transpose of that matrix. The first form is used
# if rho is given, otherwise the coefficients are used.
self.timer.start('Initial')
rhoT_uMM = []
ET_uMM = []
if not isblacs:
if self.kpt_u[0].rho_MM is None:
self.timer.start('Get density matrix')
for kpt in self.kpt_u:
rhoT_MM = ksl.get_transposed_density_matrix(
kpt.f_n, kpt.C_nM)
rhoT_uMM.append(rhoT_MM)
ET_MM = ksl.get_transposed_density_matrix(
kpt.f_n * kpt.eps_n, kpt.C_nM)
ET_uMM.append(ET_MM)
if hasattr(kpt, 'c_on'):
# XXX does this work with BLACS/non-BLACS/etc.?
assert self.bd.comm.size == 1
d_nn = np.zeros((self.bd.mynbands, self.bd.mynbands),
dtype=kpt.C_nM.dtype)
for ne, c_n in zip(kpt.ne_o, kpt.c_on):
d_nn += ne * np.outer(c_n.conj(), c_n)
rhoT_MM += ksl.get_transposed_density_matrix_delta(\
d_nn, kpt.C_nM)
ET_MM += ksl.get_transposed_density_matrix_delta(\
d_nn * kpt.eps_n, kpt.C_nM)
self.timer.stop('Get density matrix')
else:
rhoT_uMM = []
ET_uMM = []
for kpt in self.kpt_u:
H_MM = self.eigensolver.calculate_hamiltonian_matrix(\
hamiltonian, self, kpt)
tri2full(H_MM)
S_MM = kpt.S_MM.copy()
tri2full(S_MM)
ET_MM = np.linalg.solve(S_MM,
gemmdot(H_MM,
kpt.rho_MM)).T.copy()
del S_MM, H_MM
rhoT_MM = kpt.rho_MM.T.copy()
rhoT_uMM.append(rhoT_MM)
ET_uMM.append(ET_MM)
self.timer.stop('Initial')
if isblacs: # XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
from gpaw.blacs import BlacsGrid, Redistributor
def get_density_matrix(f_n, C_nM, redistributor):
rho1_mm = ksl.calculate_blocked_density_matrix(f_n,
C_nM).conj()
rho_mm = redistributor.redistribute(rho1_mm)
return rho_mm
pcutoff_a = [
max([pt.get_cutoff() for pt in setup.pt_j])
for setup in self.setups
]
phicutoff_a = [
max([phit.get_cutoff() for phit in setup.phit_j])
for setup in self.setups
]
# XXX should probably use bdsize x gdsize instead
# That would be consistent with some existing grids
grid = BlacsGrid(ksl.block_comm, self.gd.comm.size,
self.bd.comm.size)
blocksize1 = -(-nao // grid.nprow)
blocksize2 = -(-nao // grid.npcol)
# XXX what are rows and columns actually?
desc = grid.new_descriptor(nao, nao, blocksize1, blocksize2)
rhoT_umm = []
ET_umm = []
redistributor = Redistributor(grid.comm, ksl.mmdescriptor, desc)
Fpot_av = np.zeros_like(F_av)
for u, kpt in enumerate(self.kpt_u):
self.timer.start('Get density matrix')
rhoT_mm = get_density_matrix(kpt.f_n, kpt.C_nM, redistributor)
rhoT_umm.append(rhoT_mm)
self.timer.stop('Get density matrix')
self.timer.start('Potential')
rhoT_mM = ksl.distribute_to_columns(rhoT_mm, desc)
vt_G = hamiltonian.vt_sG[kpt.s]
Fpot_av += bfs.calculate_force_contribution(
vt_G, rhoT_mM, kpt.q)
del rhoT_mM
self.timer.stop('Potential')
self.timer.start('Get density matrix')
for kpt in self.kpt_u:
ET_mm = get_density_matrix(kpt.f_n * kpt.eps_n, kpt.C_nM,
redistributor)
ET_umm.append(ET_mm)
self.timer.stop('Get density matrix')
M1start = blocksize1 * grid.myrow
M2start = blocksize2 * grid.mycol
M1stop = min(M1start + blocksize1, nao)
M2stop = min(M2start + blocksize2, nao)
m1max = M1stop - M1start
m2max = M2stop - M2start
if not isblacs:
# Kinetic energy contribution
#
# ----- d T
# a \ mu nu
# F += 2 Re ) -------- rho
# / d R nu mu
# ----- mu nu
# mu in a; nu
#
Fkin_av = np.zeros_like(F_av)
for u, kpt in enumerate(self.kpt_u):
dEdTrhoT_vMM = (dTdR_qvMM[kpt.q] *
rhoT_uMM[u][np.newaxis]).real
for a, M1, M2 in my_slices():
Fkin_av[a, :] += \
2.0 * dEdTrhoT_vMM[:, M1:M2].sum(-1).sum(-1)
del dEdTrhoT_vMM
# Density matrix contribution due to basis overlap
#
# ----- d Theta
# a \ mu nu
# F += -2 Re ) ------------ E
# / d R nu mu
# ----- mu nu
# mu in a; nu
#
Ftheta_av = np.zeros_like(F_av)
for u, kpt in enumerate(self.kpt_u):
dThetadRE_vMM = (dThetadR_qvMM[kpt.q] *
ET_uMM[u][np.newaxis]).real
for a, M1, M2 in my_slices():
Ftheta_av[a, :] += \
-2.0 * dThetadRE_vMM[:, M1:M2].sum(-1).sum(-1)
del dThetadRE_vMM
if isblacs:
from gpaw.lcao.overlap import TwoCenterIntegralCalculator
self.timer.start('Prepare TCI loop')
M_a = bfs.M_a
Fkin2_av = np.zeros_like(F_av)
Ftheta2_av = np.zeros_like(F_av)
cell_cv = tci.atoms.cell
spos_ac = tci.atoms.get_scaled_positions() % 1.0
overlapcalc = TwoCenterIntegralCalculator(self.kd.ibzk_qc,
derivative=False)
# XXX this is not parallel *AT ALL*.
self.timer.start('Get neighbors')
nl = tci.atompairs.pairs.neighbors
r_and_offset_aao = get_r_and_offsets(nl, spos_ac, cell_cv)
atompairs = r_and_offset_aao.keys()
atompairs.sort()
self.timer.stop('Get neighbors')
T_expansions = tci.T_expansions
Theta_expansions = tci.Theta_expansions
P_expansions = tci.P_expansions
nq = len(self.kd.ibzk_qc)
dH_asp = hamiltonian.dH_asp
self.timer.start('broadcast dH')
alldH_asp = {}
for a in range(len(self.setups)):
gdrank = bfs.sphere_a[a].rank
if gdrank == gd.rank:
dH_sp = dH_asp[a]
else:
ni = self.setups[a].ni
dH_sp = np.empty((self.nspins, ni * (ni + 1) // 2))
gd.comm.broadcast(dH_sp, gdrank)
# okay, now everyone gets copies of dH_sp
alldH_asp[a] = dH_sp
self.timer.stop('broadcast dH')
# This will get sort of hairy. We need to account for some
# three-center overlaps, such as:
#
# a1
# Phi ~a3 a3 ~a3 a2 a2,a1
# < ---- |p > dH <p |Phi > rho
# dR
#
# To this end we will loop over all pairs of atoms (a1, a3),
# and then a sub-loop over (a3, a2).
from gpaw.lcao.overlap import DerivativeAtomicDisplacement
class Displacement(DerivativeAtomicDisplacement):
def __init__(self, a1, a2, R_c, offset):
phases = overlapcalc.phaseclass(overlapcalc.ibzk_qc,
offset)
DerivativeAtomicDisplacement.__init__(
self, None, a1, a2, R_c, offset, phases)
# Cache of Displacement objects with spherical harmonics with
# evaluated spherical harmonics.
disp_aao = {}
def get_displacements(a1, a2, maxdistance):
# XXX the way maxdistance is handled it can lead to
# bad caching when different maxdistances are passed
# to subsequent calls with same pair of atoms
disp_o = disp_aao.get((a1, a2))
if disp_o is None:
disp_o = []
for R_c, offset in r_and_offset_aao[(a1, a2)]:
if np.linalg.norm(R_c) > maxdistance:
continue
disp = Displacement(a1, a2, R_c, offset)
disp_o.append(disp)
disp_aao[(a1, a2)] = disp_o
return [disp for disp in disp_o if disp.r < maxdistance]
self.timer.stop('Prepare TCI loop')
self.timer.start('Not so complicated loop')
for (a1, a2) in atompairs:
if a1 >= a2:
# Actually this leads to bad load balance.
# We should take a1 > a2 or a1 < a2 equally many times.
# Maybe decide which of these choices
# depending on whether a2 % 1 == 0
continue
m1start = M_a[a1] - M1start
m2start = M_a[a2] - M2start
if m1start >= blocksize1 or m2start >= blocksize2:
continue # (we have only one block per CPU)
T_expansion = T_expansions.get(a1, a2)
Theta_expansion = Theta_expansions.get(a1, a2)
#P_expansion = P_expansions.get(a1, a2)
nm1, nm2 = T_expansion.shape
m1stop = min(m1start + nm1, m1max)
m2stop = min(m2start + nm2, m2max)
if m1stop <= 0 or m2stop <= 0:
continue
m1start = max(m1start, 0)
m2start = max(m2start, 0)
J1start = max(0, M1start - M_a[a1])
J2start = max(0, M2start - M_a[a2])
M1stop = J1start + m1stop - m1start
J2stop = J2start + m2stop - m2start
dTdR_qvmm = T_expansion.zeros((nq, 3), dtype=dtype)
dThetadR_qvmm = Theta_expansion.zeros((nq, 3), dtype=dtype)
disp_o = get_displacements(a1, a2,
phicutoff_a[a1] + phicutoff_a[a2])
for disp in disp_o:
disp.evaluate_overlap(T_expansion, dTdR_qvmm)
disp.evaluate_overlap(Theta_expansion, dThetadR_qvmm)
for u, kpt in enumerate(self.kpt_u):
rhoT_mm = rhoT_umm[u][m1start:m1stop, m2start:m2stop]
ET_mm = ET_umm[u][m1start:m1stop, m2start:m2stop]
Fkin_v = 2.0 * (
dTdR_qvmm[kpt.q][:, J1start:M1stop, J2start:J2stop] *
rhoT_mm[np.newaxis]).real.sum(-1).sum(-1)
Ftheta_v = 2.0 * (dThetadR_qvmm[kpt.q][:, J1start:M1stop,
J2start:J2stop] *
ET_mm[np.newaxis]).real.sum(-1).sum(-1)
Fkin2_av[a1] += Fkin_v
Fkin2_av[a2] -= Fkin_v
Ftheta2_av[a1] -= Ftheta_v
Ftheta2_av[a2] += Ftheta_v
Fkin_av = Fkin2_av
Ftheta_av = Ftheta2_av
self.timer.stop('Not so complicated loop')
dHP_and_dSP_aauim = {}
a2values = {}
for (a2, a3) in atompairs:
if not a3 in a2values:
a2values[a3] = []
a2values[a3].append(a2)
Fatom_av = np.zeros_like(F_av)
Frho_av = np.zeros_like(F_av)
self.timer.start('Complicated loop')
for a1, a3 in atompairs:
if a1 == a3:
# Functions reside on same atom, so their overlap
# does not change when atom is displaced
continue
m1start = M_a[a1] - M1start
if m1start >= blocksize1:
continue
P_expansion = P_expansions.get(a1, a3)
nm1 = P_expansion.shape[0]
m1stop = min(m1start + nm1, m1max)
if m1stop <= 0:
continue
m1start = max(m1start, 0)
J1start = max(0, M1start - M_a[a1])
J1stop = J1start + m1stop - m1start
disp_o = get_displacements(a1, a3,
phicutoff_a[a1] + pcutoff_a[a3])
if len(disp_o) == 0:
continue
dPdR_qvmi = P_expansion.zeros((nq, 3), dtype=dtype)
for disp in disp_o:
disp.evaluate_overlap(P_expansion, dPdR_qvmi)
dPdR_qvmi = dPdR_qvmi[:, :, J1start:J1stop, :].copy()
for a2 in a2values[a3]:
m2start = M_a[a2] - M2start
if m2start >= blocksize2:
continue
P_expansion2 = P_expansions.get(a2, a3)
nm2 = P_expansion2.shape[0]
m2stop = min(m2start + nm2, m2max)
if m2stop <= 0:
continue
disp_o = get_displacements(a2, a3,
phicutoff_a[a2] + pcutoff_a[a3])
if len(disp_o) == 0:
continue
m2start = max(m2start, 0)
J2start = max(0, M2start - M_a[a2])
J2stop = J2start + m2stop - m2start
if (a2, a3) in dHP_and_dSP_aauim:
dHP_uim, dSP_uim = dHP_and_dSP_aauim[(a2, a3)]
else:
P_qmi = P_expansion2.zeros((nq, ), dtype=dtype)
for disp in disp_o:
disp.evaluate_direct(P_expansion2, P_qmi)
P_qmi = P_qmi[:, J2start:J2stop].copy()
dH_sp = alldH_asp[a3]
dS_ii = self.setups[a3].dO_ii
dHP_uim = []
dSP_uim = []
for u, kpt in enumerate(self.kpt_u):
dH_ii = unpack(dH_sp[kpt.s])
dHP_im = np.dot(P_qmi[kpt.q], dH_ii).T.conj()
# XXX only need nq of these
dSP_im = np.dot(P_qmi[kpt.q], dS_ii).T.conj()
dHP_uim.append(dHP_im)
dSP_uim.append(dSP_im)
dHP_and_dSP_aauim[(a2, a3)] = dHP_uim, dSP_uim
for u, kpt in enumerate(self.kpt_u):
rhoT_mm = rhoT_umm[u][m1start:m1stop, m2start:m2stop]
ET_mm = ET_umm[u][m1start:m1stop, m2start:m2stop]
dPdRdHP_vmm = np.dot(dPdR_qvmi[kpt.q], dHP_uim[u])
dPdRdSP_vmm = np.dot(dPdR_qvmi[kpt.q], dSP_uim[u])
Fatom_c = 2.0 * (dPdRdHP_vmm *
rhoT_mm).real.sum(-1).sum(-1)
Frho_c = 2.0 * (dPdRdSP_vmm *
ET_mm).real.sum(-1).sum(-1)
Fatom_av[a1] += Fatom_c
Fatom_av[a3] -= Fatom_c
Frho_av[a1] -= Frho_c
Frho_av[a3] += Frho_c
self.timer.stop('Complicated loop')
if not isblacs:
# Potential contribution
#
# ----- / d Phi (r)
# a \ | mu ~
# F += -2 Re ) | ---------- v (r) Phi (r) dr rho
# / | d R nu nu mu
# ----- / a
# mu in a; nu
#
self.timer.start('Potential')
Fpot_av = np.zeros_like(F_av)
for u, kpt in enumerate(self.kpt_u):
vt_G = hamiltonian.vt_sG[kpt.s]
Fpot_av += bfs.calculate_force_contribution(
vt_G, rhoT_uMM[u], kpt.q)
self.timer.stop('Potential')
# Density matrix contribution from PAW correction
#
# ----- -----
# a \ a \ b
# F += 2 Re ) Z E - 2 Re ) Z E
# / mu nu nu mu / mu nu nu mu
# ----- -----
# mu nu b; mu in a; nu
#
# with
# b*
# ----- dP
# b \ i mu b b
# Z = ) -------- dS P
# mu nu / dR ij j nu
# ----- b mu
# ij
#
self.timer.start('Paw correction')
Frho_av = np.zeros_like(F_av)
for u, kpt in enumerate(self.kpt_u):
work_MM = np.zeros((mynao, nao), dtype)
ZE_MM = None
for b in my_atom_indices:
setup = self.setups[b]
dO_ii = np.asarray(setup.dO_ii, dtype)
dOP_iM = np.zeros((setup.ni, nao), dtype)
gemm(1.0, self.P_aqMi[b][kpt.q], dO_ii, 0.0, dOP_iM, 'c')
for v in range(3):
gemm(1.0, dOP_iM,
dPdR_aqvMi[b][kpt.q][v][Mstart:Mstop], 0.0,
work_MM, 'n')
ZE_MM = (work_MM * ET_uMM[u]).real
for a, M1, M2 in slices():
dE = 2 * ZE_MM[M1:M2].sum()
Frho_av[a, v] -= dE # the "b; mu in a; nu" term
Frho_av[b, v] += dE # the "mu nu" term
del work_MM, ZE_MM
self.timer.stop('Paw correction')
# Atomic density contribution
# ----- -----
# a \ a \ b
# F += -2 Re ) A rho + 2 Re ) A rho
# / mu nu nu mu / mu nu nu mu
# ----- -----
# mu nu b; mu in a; nu
#
# b*
# ----- d P
# b \ i mu b b
# A = ) ------- dH P
# mu nu / d R ij j nu
# ----- b mu
# ij
#
self.timer.start('Atomic Hamiltonian force')
Fatom_av = np.zeros_like(F_av)
for u, kpt in enumerate(self.kpt_u):
for b in my_atom_indices:
H_ii = np.asarray(unpack(hamiltonian.dH_asp[b][kpt.s]),
dtype)
HP_iM = gemmdot(
H_ii,
np.ascontiguousarray(self.P_aqMi[b][kpt.q].T.conj()))
for v in range(3):
dPdR_Mi = dPdR_aqvMi[b][kpt.q][v][Mstart:Mstop]
ArhoT_MM = (gemmdot(dPdR_Mi, HP_iM) * rhoT_uMM[u]).real
for a, M1, M2 in slices():
dE = 2 * ArhoT_MM[M1:M2].sum()
Fatom_av[a, v] += dE # the "b; mu in a; nu" term
Fatom_av[b, v] -= dE # the "mu nu" term
self.timer.stop('Atomic Hamiltonian force')
F_av += Fkin_av + Fpot_av + Ftheta_av + Frho_av + Fatom_av
self.timer.start('Wait for sum')
ksl.orbital_comm.sum(F_av)
if self.bd.comm.rank == 0:
self.kd.comm.sum(F_av, 0)
self.timer.stop('Wait for sum')
self.timer.stop('LCAO forces')