def get_phi_aGp(self):
setups = self.calc.wfs.setups
spos_ac = self.calc.atoms.get_scaled_positions()
kk_Gv = gemmdot(self.q_c + self.Gvec_Gc,
self.bcell_cv.copy(),
beta=0.0)
phi_aGp = {}
for a, id in enumerate(setups.id_a):
phi_aGp[a] = two_phi_planewave_integrals(kk_Gv, setups[a])
for iG in range(self.npw):
phi_aGp[a][iG] *= np.exp(
-1j * 2. * pi *
np.dot(self.q_c + self.Gvec_Gc[iG], spos_ac[a]))
# For optical limit, G == 0 part should change
if self.optical_limit:
for a, id in enumerate(setups.id_a):
nabla_iiv = setups[a].nabla_iiv
phi_aGp[a][0] = -1j * (np.dot(nabla_iiv, self.qq_v)).ravel()
self.phi_aGp = phi_aGp
self.printtxt('')
self.printtxt('Finished phi_Gp !')
return
def get_phi_aGp(self, q_c=None, parallel=True, alldir=False):
if q_c is None:
q_c = self.q_c
qq_v = self.qq_v
optical_limit = self.optical_limit
else:
optical_limit = False
if np.abs(q_c).sum() < 1e-8:
q_c = np.array([0.0001, 0, 0])
optical_limit = True
qq_v = np.dot(q_c, self.bcell_cv)
setups = self.calc.wfs.setups
spos_ac = self.calc.atoms.get_scaled_positions()
kk_Gv = gemmdot(q_c + self.Gvec_Gc, self.bcell_cv.copy(), beta=0.0)
phi_aGp = {}
phiG0_avp = {}
if parallel:
from gpaw.response.parallel import parallel_partition
npw, npw_local, Gstart, Gend = parallel_partition(self.npw,
self.comm.rank,
self.comm.size,
reshape=False)
else:
Gstart = 0
Gend = self.npw
for a, id in enumerate(setups.id_a):
phi_aGp[a] = two_phi_planewave_integrals(kk_Gv, setups[a], Gstart,
Gend)
for iG in range(Gstart, Gend):
phi_aGp[a][iG] *= np.exp(
-1j * 2. * pi * np.dot(q_c + self.Gvec_Gc[iG], spos_ac[a]))
if parallel:
self.comm.sum(phi_aGp[a])
# For optical limit, G == 0 part should change
if optical_limit:
for a, id in enumerate(setups.id_a):
nabla_iiv = setups[a].nabla_iiv
phi_aGp[a][0] = -1j * (np.dot(nabla_iiv, qq_v)).ravel()
phiG0_avp[a] = np.zeros((3, len(phi_aGp[a][0])), complex)
for dir in range(3): # 3 dimension
q2_c = np.diag((1, 1, 1))[dir] * self.qopt
qq2_v = np.dot(q2_c, self.bcell_cv) # summation over c
phiG0_avp[a][dir] = -1j * (np.dot(nabla_iiv,
qq2_v)).ravel()
if alldir:
return phi_aGp, phiG0_avp
else:
return phi_aGp
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 get_phi_aGp(self, q_c=None, parallel=True, alldir=False):
if q_c is None:
q_c = self.q_c
qq_v = self.qq_v
optical_limit = self.optical_limit
else:
optical_limit = False
if np.abs(q_c).sum() < 1e-8:
q_c = np.array([0.0001, 0, 0])
optical_limit = True
qq_v = np.dot(q_c, self.bcell_cv)
setups = self.calc.wfs.setups
spos_ac = self.calc.atoms.get_scaled_positions()
kk_Gv = gemmdot(q_c + self.Gvec_Gc, self.bcell_cv.copy(), beta=0.0)
phi_aGp = {}
phiG0_avp = {}
if parallel:
from gpaw.response.parallel import parallel_partition
npw, npw_local, Gstart, Gend = parallel_partition(
self.npw, self.comm.rank, self.comm.size, reshape=False)
else:
Gstart = 0
Gend = self.npw
for a, id in enumerate(setups.id_a):
phi_aGp[a] = two_phi_planewave_integrals(kk_Gv, setups[a], Gstart, Gend)
for iG in range(Gstart, Gend):
phi_aGp[a][iG] *= np.exp(-1j * 2. * pi *
np.dot(q_c + self.Gvec_Gc[iG], spos_ac[a]) )
if parallel:
self.comm.sum(phi_aGp[a])
# For optical limit, G == 0 part should change
if optical_limit:
for a, id in enumerate(setups.id_a):
nabla_iiv = setups[a].nabla_iiv
phi_aGp[a][0] = -1j * (np.dot(nabla_iiv, qq_v)).ravel()
phiG0_avp[a] = np.zeros((3, len(phi_aGp[a][0])), complex)
for dir in range(3): # 3 dimension
q2_c = np.diag((1,1,1))[dir] * self.qopt
qq2_v = np.dot(q2_c, self.bcell_cv) # summation over c
phiG0_avp[a][dir] = -1j * (np.dot(nabla_iiv, qq2_v)).ravel()
if alldir:
return phi_aGp, phiG0_avp
else:
return phi_aGp
def full_hilbert_transform(specfunc_wGG, Nw, dw, eta):
NwS = specfunc_wGG.shape[0]
tmp_ww = np.zeros((Nw, NwS), dtype=complex)
for iw in range(Nw):
w = iw * dw
for jw in range(NwS):
ww = jw * dw
tmp_ww[iw, jw] = 1. / (w - ww - 1j*eta) - 1. / (w + ww + 1j*eta)
chi0_wGG = gemmdot(tmp_ww, specfunc_wGG, beta = 0.)
return chi0_wGG * dw
def full_hilbert_transform(specfunc_wGG, Nw, dw, eta):
NwS = specfunc_wGG.shape[0]
tmp_ww = np.zeros((Nw, NwS), dtype=complex)
for iw in range(Nw):
w = iw * dw
for jw in range(NwS):
ww = jw * dw
tmp_ww[iw,
jw] = 1. / (w - ww - 1j * eta) - 1. / (w + ww + 1j * eta)
chi0_wGG = gemmdot(tmp_ww, specfunc_wGG, beta=0.)
return chi0_wGG * dw
def hilbert_transform(specfunc_wGG, w_w, Nw, dw, eta, fullresponse=False):
NwS = specfunc_wGG.shape[0]
tmp_ww = np.zeros((Nw, NwS), dtype=complex)
ww_w = np.linspace(0., (NwS-1)*dw, NwS)
for iw in range(Nw):
if fullresponse is False:
tmp_ww[iw] = 1. / (w_w[iw] - ww_w + 1j*eta) - 1. / (w_w[iw] + ww_w + 1j*eta)
else:
tmp_ww[iw] = 1. / (w_w[iw] - ww_w + 1j*eta) - 1. / (w_w[iw] + ww_w - 1j*eta)
chi0_wGG = gemmdot(tmp_ww, specfunc_wGG, beta = 0.)
return chi0_wGG * dw
def hilbert_transform(specfunc_wGG, w_w, Nw, dw, eta, fullresponse=False):
NwS = specfunc_wGG.shape[0]
tmp_ww = np.zeros((Nw, NwS), dtype=complex)
ww_w = np.linspace(0., (NwS - 1) * dw, NwS)
for iw in range(Nw):
if fullresponse is False:
tmp_ww[iw] = 1. / (w_w[iw] - ww_w +
1j * eta) - 1. / (w_w[iw] + ww_w + 1j * eta)
else:
tmp_ww[iw] = 1. / (w_w[iw] - ww_w +
1j * eta) - 1. / (w_w[iw] + ww_w - 1j * eta)
chi0_wGG = gemmdot(tmp_ww, specfunc_wGG, beta=0.)
return chi0_wGG * dw
def get_all_electron_IPR(paw):
density = paw.density
wfs = paw.wfs
n_G = wfs.gd.empty()
n_g = density.finegd.empty()
print()
print('inverse participation function')
print('-' * 35)
print('%5s %5s %10s %10s' % ('k', 'band', 'eps', 'ipr'))
print('-' * 35)
for k, kpt in enumerate(paw.wfs.kpt_u):
for n, (eps, psit_G) in enumerate(zip(kpt.eps_n, kpt.psit_nG)):
n_G[:] = 0.0
wfs.add_orbital_density(n_G, kpt, n)
density.interpolator.apply(n_G, n_g)
norm = density.finegd.integrate(n_g)
n_g = n_g**2
ipr = density.finegd.integrate(n_g)
for a in kpt.P_ani:
# Get xccorr for atom a
setup = paw.density.setups[a]
xccorr = setup.xc_correction
# Get D_sp for atom a
D_sp = np.array(wfs.get_orbital_density_matrix(a, kpt, n))
# density a function of L and partial wave radial pair
# density coefficient
D_sLq = gemmdot(D_sp, xccorr.B_Lqp, trans='t')
# Create pseudo/ae density iterators for integration
n_iter = xccorr.expand_density(D_sLq, xccorr.n_qg, None)
nt_iter = xccorr.expand_density(D_sLq, xccorr.nt_qg, None)
# Take the spherical average of smooth and ae radial
# xc potentials
for n_sg, nt_sg, integrator in zip(
n_iter, nt_iter, xccorr.get_integrator(None)):
ipr += integrator.weight * np.sum(
(n_sg[0]**2 - nt_sg[0]**2) * xccorr.rgd.dv_g)
norm += integrator.weight * np.sum(
(n_sg[0] - nt_sg[0]) * xccorr.rgd.dv_g)
print('%5i %5i %10.5f %10.5f' % (k, n, eps, ipr / norm**2))
print('-' * 35)
def get_all_electron_IPR(paw):
density = paw.density
wfs = paw.wfs
n_G = wfs.gd.empty()
n_g = density.finegd.empty()
print
print "inverse participation function"
print "-"*35
print "%5s %5s %10s %10s" % ("k","band","eps","ipr")
print "-"*35
for k, kpt in enumerate(paw.wfs.kpt_u):
for n, (eps, psit_G) in enumerate(zip(kpt.eps_n, kpt.psit_nG)):
n_G[:] = 0.0
wfs.add_orbital_density(n_G, kpt, n)
density.interpolator.apply(n_G, n_g)
norm = density.finegd.integrate(n_g)
n_g = n_g ** 2
ipr = density.finegd.integrate(n_g)
for a in kpt.P_ani:
# Get xccorr for atom a
setup = paw.density.setups[a]
xccorr = setup.xc_correction
# Get D_sp for atom a
D_sp = np.array(wfs.get_orbital_density_matrix(a, kpt, n))
# density a function of L and partial wave radial pair density coefficient
D_sLq = gemmdot(D_sp, xccorr.B_Lqp, trans='t')
# Create pseudo/ae density iterators for integration
n_iter = xccorr.expand_density(D_sLq, xccorr.n_qg, None)
nt_iter = xccorr.expand_density(D_sLq, xccorr.nt_qg, None)
# Take the spherical average of smooth and ae radial xc potentials
for n_sg, nt_sg, integrator in izip(n_iter,
nt_iter,
xccorr.get_integrator(None)):
ipr += integrator.weight * np.sum((n_sg[0]**2-nt_sg[0]**2) * xccorr.rgd.dv_g)
norm += integrator.weight * np.sum((n_sg[0]-nt_sg[0]) * xccorr.rgd.dv_g)
print "%5i %5i %10.5f %10.5f" % (k, n, eps, ipr/norm**2)
print "-"*35
def get_phi_aGp(self):
setups = self.calc.wfs.setups
spos_ac = self.calc.atoms.get_scaled_positions()
kk_Gv = gemmdot(self.q_c + self.Gvec_Gc, self.bcell_cv.copy(), beta=0.0)
phi_aGp = {}
for a, id in enumerate(setups.id_a):
phi_aGp[a] = two_phi_planewave_integrals(kk_Gv, setups[a])
for iG in range(self.npw):
phi_aGp[a][iG] *= np.exp(-1j * 2. * pi *
np.dot(self.q_c + self.Gvec_Gc[iG], spos_ac[a]) )
# For optical limit, G == 0 part should change
if self.optical_limit:
for a, id in enumerate(setups.id_a):
nabla_iiv = setups[a].nabla_iiv
phi_aGp[a][0] = -1j * (np.dot(nabla_iiv, self.qq_v)).ravel()
self.phi_aGp = phi_aGp
self.printtxt('')
self.printtxt('Finished phi_Gp !')
return
def calculate_Kxc(gd, nt_sG, npw, Gvec_Gc, nG, vol, bcell_cv, R_av, setups,
D_asp):
"""LDA kernel"""
# The soft part
assert np.abs(nt_sG[0].shape - nG).sum() == 0
xc = XC('LDA')
fxc_sg = np.zeros_like(nt_sG)
xc.calculate_fxc(gd, nt_sG, fxc_sg)
fxc_g = fxc_sg[0]
# FFT fxc(r)
nG0 = nG[0] * nG[1] * nG[2]
tmp_g = np.fft.fftn(fxc_g) * vol / nG0
r_vg = gd.get_grid_point_coordinates()
Kxc_GG = np.zeros((npw, npw), dtype=complex)
for iG in range(npw):
for jG in range(npw):
dG_c = Gvec_Gc[iG] - Gvec_Gc[jG]
if (nG / 2 - np.abs(dG_c) > 0).all():
index = (dG_c + nG) % nG
Kxc_GG[iG, jG] = tmp_g[index[0], index[1], index[2]]
else: # not in the fft index
dG_v = np.dot(dG_c, bcell_cv)
dGr_g = gemmdot(dG_v, r_vg, beta=0.0)
Kxc_GG[iG, jG] = gd.integrate(np.exp(-1j * dGr_g) * fxc_g)
KxcPAW_GG = np.zeros_like(Kxc_GG)
# The PAW part
dG_GGv = np.zeros((npw, npw, 3))
for iG in range(npw):
for jG in range(npw):
dG_c = Gvec_Gc[iG] - Gvec_Gc[jG]
dG_GGv[iG, jG] = np.dot(dG_c, bcell_cv)
for a, setup in enumerate(setups):
if rank == a % size:
rgd = setup.xc_correction.rgd
n_qg = setup.xc_correction.n_qg
nt_qg = setup.xc_correction.nt_qg
nc_g = setup.xc_correction.nc_g
nct_g = setup.xc_correction.nct_g
Y_nL = setup.xc_correction.Y_nL
dv_g = rgd.dv_g
D_sp = D_asp[a]
B_pqL = setup.xc_correction.B_pqL
D_sLq = np.inner(D_sp, B_pqL.T)
nspins = len(D_sp)
assert nspins == 1
f_sg = rgd.empty(nspins)
ft_sg = rgd.empty(nspins)
n_sLg = np.dot(D_sLq, n_qg)
nt_sLg = np.dot(D_sLq, nt_qg)
# Add core density
n_sLg[:, 0] += sqrt(4 * pi) / nspins * nc_g
nt_sLg[:, 0] += sqrt(4 * pi) / nspins * nct_g
coefatoms_GG = np.exp(-1j * np.inner(dG_GGv, R_av[a]))
for n, Y_L in enumerate(Y_nL):
w = weight_n[n]
f_sg[:] = 0.0
n_sg = np.dot(Y_L, n_sLg)
xc.calculate_fxc(rgd, n_sg, f_sg)
ft_sg[:] = 0.0
nt_sg = np.dot(Y_L, nt_sLg)
xc.calculate_fxc(rgd, nt_sg, ft_sg)
coef_GGg = np.exp(
-1j *
np.outer(np.inner(dG_GGv, R_nv[n]), rgd.r_g)).reshape(
npw, npw, rgd.ng)
KxcPAW_GG += w * np.dot(
coef_GGg, (f_sg[0] - ft_sg[0]) * dv_g) * coefatoms_GG
world.sum(KxcPAW_GG)
Kxc_GG += KxcPAW_GG
return Kxc_GG / vol
def parallel_transport(calc,
direction=0,
spinors=True,
name=None,
scale=1.0,
bands=None,
theta=0.0,
phi=0.0):
if isinstance(calc, str):
calc = GPAW(calc, txt=None, communicator=serial_comm)
if bands is None:
nv = int(calc.get_number_of_electrons())
bands = range(nv)
cell_cv = calc.wfs.gd.cell_cv
icell_cv = (2 * np.pi) * np.linalg.inv(cell_cv).T
r_g = calc.wfs.gd.get_grid_point_coordinates()
Ng = np.prod(np.shape(r_g)[1:]) * (spinors + 1)
dO_aii = []
for ia in calc.wfs.kpt_u[0].P_ani.keys():
dO_ii = calc.wfs.setups[ia].dO_ii
if spinors:
# Spinor projections require doubling of the (identical) orbitals
dO_jj = np.zeros((2 * len(dO_ii), 2 * len(dO_ii)), complex)
dO_jj[::2, ::2] = dO_ii
dO_jj[1::2, 1::2] = dO_ii
dO_aii.append(dO_jj)
else:
dO_aii.append(dO_ii)
N_c = calc.wfs.kd.N_c
assert 1 in np.delete(N_c, direction)
Nkx = N_c[0]
Nky = N_c[1]
Nkz = N_c[2]
Nk = Nkx * Nky * Nkz
Nloc = N_c[direction]
Npar = Nk // Nloc
# Parallelization stuff
myKsize = -(-Npar // (world.size))
myKrange = range(rank * myKsize, min((rank + 1) * myKsize, Npar))
myKsize = len(myKrange)
# Get array of k-point indices of the path. q index is loc direction
kpts_kq = []
for k in range(Npar):
if direction == 0:
kpts_kq.append(list(range(k, Nkx * Nky, Nky)))
if direction == 1:
if Nkz == 1:
kpts_kq.append(list(range(k * Nky, (k + 1) * Nky)))
else:
kpts_kq.append(list(range(k, Nkz * Nky, Nkz)))
if direction == 2:
kpts_kq.append(list(range(k * Nloc, (k + 1) * Nloc)))
G_c = np.array([0, 0, 0])
G_c[direction] = 1
G_v = np.dot(G_c, icell_cv)
kpts_kc = calc.get_bz_k_points()
kpts_kv = np.dot(kpts_kc, icell_cv)
if Nloc > 1:
b_c = kpts_kc[kpts_kq[0][1]] - kpts_kc[kpts_kq[0][0]]
b_v = np.dot(b_c, icell_cv)
else:
b_v = G_v
e_mk, v_knm = get_spinorbit_eigenvalues(calc,
return_wfs=True,
scale=scale,
theta=theta,
phi=phi)
phi_km = np.zeros((Npar, len(bands)), float)
S_km = np.zeros((Npar, len(bands)), float)
# Loop over the direction parallel components
for k in myKrange:
U_qmm = [np.eye(len(bands))]
print(k)
qpts_q = kpts_kq[k]
# Loop over kpoints in the phase direction
for q in range(Nloc - 1):
iq1 = qpts_q[q]
iq2 = qpts_q[q + 1]
# print(kpts_kc[iq1], kpts_kc[iq2])
if q == 0:
u1_nsG = get_spinorbit_wavefunctions(calc, iq1,
v_knm[iq1])[bands]
# Transform from psi-like to u-like
u1_nsG[:] *= np.exp(-1.0j *
gemmdot(kpts_kv[iq1], r_g, beta=0.0))
P1_ani = get_spinorbit_projections(calc, iq1, v_knm[iq1])
u2_nsG = get_spinorbit_wavefunctions(calc, iq2, v_knm[iq2])[bands]
u2_nsG[:] *= np.exp(-1.0j * gemmdot(kpts_kv[iq2], r_g, beta=0.0))
P2_ani = get_spinorbit_projections(calc, iq2, v_knm[iq2])
M_mm = get_overlap(calc, bands,
np.reshape(u1_nsG, (len(u1_nsG), Ng)),
np.reshape(u2_nsG, (len(u2_nsG), Ng)), P1_ani,
P2_ani, dO_aii, b_v)
V_mm, sing_m, W_mm = np.linalg.svd(M_mm)
U_mm = np.dot(V_mm, W_mm).conj()
u_nysxz = np.dot(U_mm, np.swapaxes(u2_nsG, 0, 3))
u_nxsyz = np.swapaxes(u_nysxz, 1, 3)
u_nsxyz = np.swapaxes(u_nxsyz, 1, 2)
u2_nsG = u_nsxyz
for a in range(len(calc.atoms)):
P2_ni = P2_ani[a][bands]
P2_ni = np.dot(U_mm, P2_ni)
P2_ani[a][bands] = P2_ni
U_qmm.append(U_mm)
u1_nsG = u2_nsG
P1_ani = P2_ani
U_qmm = np.array(U_qmm)
# Fix phases for last point
iq0 = qpts_q[0]
if Nloc == 1:
u1_nsG = get_spinorbit_wavefunctions(calc, iq0, v_knm[iq0])[bands]
u1_nsG[:] *= np.exp(-1.0j * gemmdot(kpts_kv[iq0], r_g, beta=0.0))
P1_ani = get_spinorbit_projections(calc, iq0, v_knm[iq0])
u2_nsG = get_spinorbit_wavefunctions(calc, iq0, v_knm[iq0])[bands]
u2_nsG[:] *= np.exp(-1.0j * gemmdot(kpts_kv[iq0], r_g, beta=0.0))
u2_nsG[:] *= np.exp(-1.0j * gemmdot(G_v, r_g, beta=0.0))
P2_ani = get_spinorbit_projections(calc, iq0, v_knm[iq0])
for a in range(len(calc.atoms)):
P2_ni = P2_ani[a][bands]
# P2_ni *= np.exp(-1.0j * np.dot(G_v, r_av[a]))
P2_ani[a][bands] = P2_ni
M_mm = get_overlap(calc, bands, np.reshape(u1_nsG, (len(u1_nsG), Ng)),
np.reshape(u2_nsG, (len(u2_nsG), Ng)), P1_ani,
P2_ani, dO_aii, b_v)
V_mm, sing_m, W_mm = np.linalg.svd(M_mm)
U_mm = np.dot(V_mm, W_mm).conj()
u_nysxz = np.dot(U_mm, np.swapaxes(u2_nsG, 0, 3))
u_nxsyz = np.swapaxes(u_nysxz, 1, 3)
u_nsxyz = np.swapaxes(u_nxsyz, 1, 2)
u2_nsG = u_nsxyz
for a in range(len(calc.atoms)):
P2_ni = P2_ani[a][bands]
P2_ni = np.dot(U_mm, P2_ni)
P2_ani[a][bands] = P2_ni
# Get overlap between first kpts and its smoothly translated image
u2_nsG[:] *= np.exp(1.0j * gemmdot(G_v, r_g, beta=0.0))
for a in range(len(calc.atoms)):
P2_ni = P2_ani[a][bands]
# P2_ni *= np.exp(1.0j * np.dot(G_v, r_av[a]))
P2_ani[a][bands] = P2_ni
u1_nsG = get_spinorbit_wavefunctions(calc, iq0, v_knm[iq0])[bands]
u1_nsG[:] *= np.exp(-1.0j * gemmdot(kpts_kv[iq0], r_g, beta=0.0))
P1_ani = get_spinorbit_projections(calc, iq0, v_knm[iq0])
M_mm = get_overlap(calc, bands, np.reshape(u1_nsG, (len(u1_nsG), Ng)),
np.reshape(u2_nsG, (len(u2_nsG), Ng)), P1_ani,
P2_ani, dO_aii, np.array([0.0, 0.0, 0.0]))
l_m, l_mm = np.linalg.eig(M_mm)
phi_km[k] = np.angle(l_m)
print(phi_km[k] / 2 / np.pi)
A_mm = np.zeros_like(l_mm, complex)
for q in range(Nloc):
iq = qpts_q[q]
U_mm = U_qmm[q]
v_nm = U_mm.dot(v_knm[iq][:, bands].T).T
A_mm += np.dot(v_nm[::2].T.conj(), v_nm[::2])
A_mm -= np.dot(v_nm[1::2].T.conj(), v_nm[1::2])
A_mm /= Nloc
S_km[k] = np.diag(l_mm.T.conj().dot(A_mm).dot(l_mm)).real
world.sum(phi_km)
world.sum(S_km)
np.savez('phases_%s.npz' % name, phi_km=phi_km, S_km=S_km)
def initialize(self):
self.eta /= Hartree
self.ecut /= Hartree
calc = self.calc
self.nspins = self.calc.wfs.nspins
# kpoint init
self.kd = kd = calc.wfs.kd
self.nikpt = kd.nibzkpts
self.ftol /= kd.nbzkpts
# cell init
self.acell_cv = calc.wfs.gd.cell_cv
self.acell_cv, self.bcell_cv, self.vol, self.BZvol = \
get_primitive_cell(self.acell_cv,rpad=self.rpad)
# grid init
gd = calc.wfs.gd.new_descriptor(comm=serial_comm)
self.pbc = gd.pbc_c
self.gd = gd
self.nG0 = np.prod(gd.N_c)
# Number of grid points and volume including zero padding
self.nGrpad = gd.N_c * self.rpad
self.nG0rpad = np.prod(self.nGrpad)
self.d_c = [Gradient(gd, i, n=4, dtype=complex).apply for i in range(3)]
# obtain eigenvalues, occupations
nibzkpt = kd.nibzkpts
kweight_k = kd.weight_k
self.eFermi = self.calc.occupations.get_fermi_level()
try:
self.e_skn
self.printtxt('Use eigenvalues from user.')
except:
self.printtxt('Use eigenvalues from the calculator.')
self.e_skn = {}
self.f_skn = {}
for ispin in range(self.nspins):
self.e_skn[ispin] = np.array([calc.get_eigenvalues(kpt=k, spin=ispin)
for k in range(nibzkpt)]) / Hartree
self.f_skn[ispin] = np.array([calc.get_occupation_numbers(kpt=k, spin=ispin)
/ kweight_k[k]
for k in range(nibzkpt)]) / kd.nbzkpts
#self.printtxt('Eigenvalues(k=0) are:')
#print >> self.txt, self.e_skn[0][0] * Hartree
self.enoshift_skn = {}
for ispin in range(self.nspins):
self.enoshift_skn[ispin] = self.e_skn[ispin].copy()
if self.eshift is not None:
self.add_discontinuity(self.eshift)
self.printtxt('Shift unoccupied bands by %f eV' % (self.eshift))
# k + q init
if self.q_c is not None:
self.qq_v = np.dot(self.q_c, self.bcell_cv) # summation over c
if self.optical_limit:
kq_k = np.arange(kd.nbzkpts)
self.expqr_g = 1.
else:
r_vg = gd.get_grid_point_coordinates() # (3, nG)
qr_g = gemmdot(self.qq_v, r_vg, beta=0.0)
self.expqr_g = np.exp(-1j * qr_g)
del r_vg, qr_g
kq_k = kd.find_k_plus_q(self.q_c)
self.kq_k = kq_k
# Plane wave init
if self.G_plus_q:
self.npw, self.Gvec_Gc, self.Gindex_G = set_Gvectors(self.acell_cv,
self.bcell_cv,
self.gd.N_c,
self.ecut,
q=self.q_c)
else:
self.npw, self.Gvec_Gc, self.Gindex_G = set_Gvectors(self.acell_cv,
self.bcell_cv,
self.gd.N_c,
self.ecut)
# band init
if self.nbands is None:
self.nbands = calc.wfs.bd.nbands
self.nvalence = calc.wfs.nvalence
# Projectors init
setups = calc.wfs.setups
self.spos_ac = calc.atoms.get_scaled_positions()
if self.pwmode:
self.pt = PWLFC([setup.pt_j for setup in setups], self.calc.wfs.pd)
self.pt.set_positions(self.spos_ac)
else:
self.pt = LFC(gd, [setup.pt_j for setup in setups],
KPointDescriptor(self.kd.bzk_kc),
dtype=complex, forces=True)
self.pt.set_positions(self.spos_ac)
# Printing calculation information
self.print_stuff()
return
t = time.time()
for n in range(numreps):
BY1_pq = np.dot(B_pqL, Y_L)
t = time.time() - t
performance = numflop * numreps / t
print 'dot : %8.5f s, %8.5f Mflops' % (t, performance / 1024**2.)
assert np.abs(BY0_pq - BY1_pq).max() < 5e-12
del BY1_pq
if test_gemmdot:
BY2_pq = np.empty((P, Q), dtype)
t = time.time()
for n in range(numreps):
BY2_pq.fill(0.0)
gemmdot(B_pqL, Y_L, 1.0, beta, BY2_pq)
t = time.time() - t
performance = numflop * numreps / t
print 'gemmdot: %8.5f s, %8.5f Mflops' % (t, performance / 1024**2.)
assert np.abs(BY0_pq - BY2_pq).max() < 5e-12
del BY2_pq
BY3_pq = np.empty((P, Q), dtype)
t = time.time()
for n in range(numreps):
BY3_pq.fill(0.0)
gemv(1.0, B_pqL, Y_L, beta, BY3_pq, 't')
t = time.time() - t
performance = numflop * numreps / t
print 'gemvT : %8.5f s, %8.5f Mflops' % (t, performance / 1024**2.)
assert np.abs(BY0_pq - BY3_pq).max() < 5e-12
def get_self_energy(self, df, W_wGG):
Sigma_skn = np.zeros((self.nspins, self.gwnkpt, self.gwnband),
dtype=float)
dSigma_skn = np.zeros((self.nspins, self.gwnkpt, self.gwnband),
dtype=float)
wcomm = df.wcomm
if self.static:
W_wGG = np.array([W_wGG])
if not self.hilbert_trans: #method 1
Wbackup_wG0 = W_wGG[:, :, 0].copy()
Wbackup_w0G = W_wGG[:, 0, :].copy()
else: #method 2, perform Hilbert transform
nG = np.shape(W_wGG)[1]
coords = np.zeros(wcomm.size, dtype=int)
nG_local = nG**2 // wcomm.size
if wcomm.rank == wcomm.size - 1:
nG_local = nG**2 - (wcomm.size - 1) * nG_local
wcomm.all_gather(np.array([nG_local]), coords)
W_Wg = SliceAlongFrequency(W_wGG, coords, wcomm)
ng = np.shape(W_Wg)[1]
Nw = int(self.w_w[-1] / self.dw)
w1_ww = np.zeros((Nw, df.Nw), dtype=complex)
for iw in range(Nw):
w1 = iw * self.dw
w1_ww[iw] = 1. / (w1 + self.w_w + 1j * self.eta_w) + 1. / (
w1 - self.w_w + 1j * self.eta_w)
w1_ww[iw, 0] -= 1. / (w1 + 1j * self.eta_w[0]) # correct w'=0
w1_ww[iw] *= self.dw_w
Cplus_Wg = np.zeros((Nw, ng), dtype=complex)
Cminus_Wg = np.zeros((Nw, ng), dtype=complex)
Cplus_Wg = gemmdot(w1_ww, W_Wg, beta=0.0)
Cminus_Wg = gemmdot(w1_ww.conj(), W_Wg, beta=0.0)
for s in range(self.nspins):
for i, k in enumerate(self.gwkpt_k): # k is bzk index
if df.optical_limit:
kq_c = df.kd.bzk_kc[k]
else:
kq_c = df.kd.bzk_kc[k] - df.q_c # k - q
kq = df.kd.where_is_q(kq_c, df.kd.bzk_kc)
assert df.kq_k[kq] == k
ibzkpt1 = df.kd.bz2ibz_k[k]
ibzkpt2 = df.kd.bz2ibz_k[kq]
for j, n in enumerate(self.bands):
for m in range(self.m_start, self.m_end):
if self.e_skn[s][ibzkpt2, m] > self.eFermi:
sign = 1.
else:
sign = -1.
rho_G = df.density_matrix(m, n, kq, spin1=s, spin2=s)
if not self.hilbert_trans: #method 1
W_wGG[:, :, 0] = Wbackup_wG0
W_wGG[:, 0, :] = Wbackup_w0G
# w1 = w - epsilon_m,k-q
w1 = self.e_skn[s][ibzkpt1,
n] - self.e_skn[s][ibzkpt2, m]
if self.ppa:
# analytical expression for Plasmon Pole Approximation
W_GG = sign * W_wGG[0] * (
1. /
(w1 + self.wt_GG - 1j * self.eta) - 1. /
(w1 - self.wt_GG + 1j * self.eta))
W_GG -= W_wGG[0] * (
1. /
(w1 + self.wt_GG + 1j * self.eta * sign) +
1. /
(w1 - self.wt_GG + 1j * self.eta * sign))
W_G = gemmdot(W_GG, rho_G, beta=0.0)
Sigma_skn[s, i, j] += np.real(
gemmdot(W_G,
rho_G,
alpha=self.alpha,
beta=0.0,
trans='c'))
W_GG = sign * W_wGG[0] * (
1. /
(w1 - self.wt_GG + 1j * self.eta)**2 - 1. /
(w1 + self.wt_GG - 1j * self.eta)**2)
W_GG += W_wGG[0] * (
1. /
(w1 - self.wt_GG + 1j * self.eta * sign)**2
+ 1. /
(w1 + self.wt_GG + 1j * self.eta * sign)**2
)
W_G = gemmdot(W_GG, rho_G, beta=0.0)
dSigma_skn[s, i, j] += np.real(
gemmdot(W_G,
rho_G,
alpha=self.alpha,
beta=0.0,
trans='c'))
elif self.static:
W1_GG = W_wGG[0] - np.eye(df.npw) * self.Kc_GG
W2_GG = W_wGG[0]
# perform W_GG * np.outer(rho_G.conj(), rho_G).sum(GG)
W_G = gemmdot(W1_GG, rho_G,
beta=0.0) # Coulomb Hole
Sigma_skn[s, i, j] += np.real(
gemmdot(W_G,
rho_G,
alpha=self.alpha * pi / 1j,
beta=0.0,
trans='c'))
if sign == -1:
W_G = gemmdot(
W2_GG, rho_G,
beta=0.0) # Screened Exchange
Sigma_skn[s, i, j] -= np.real(
gemmdot(W_G,
rho_G,
alpha=2 * self.alpha * pi / 1j,
beta=0.0,
trans='c'))
del W1_GG, W2_GG, W_G, rho_G
else:
# perform W_wGG * np.outer(rho_G.conj(), rho_G).sum(GG)
W_wG = gemmdot(W_wGG, rho_G, beta=0.0)
C_wlocal = gemmdot(W_wG,
rho_G,
alpha=self.alpha,
beta=0.0,
trans='c')
del W_wG, rho_G
C_w = np.zeros(df.Nw, dtype=complex)
wcomm.all_gather(C_wlocal, C_w)
del C_wlocal
# calculate self energy
w1_w = 1. / (w1 - self.w_w + 1j * self.eta_w *
sign) + 1. / (w1 + self.w_w + 1j *
self.eta_w * sign)
w1_w[0] -= 1. / (w1 + 1j * self.eta_w[0] * sign
) # correct w'=0
w1_w *= self.dw_w
Sigma_skn[s, i, j] += np.real(
gemmdot(C_w, w1_w, beta=0.0))
# calculate derivate of self energy with respect to w
w1_w = 1. / (w1 - self.w_w + 1j * self.eta_w *
sign)**2 + 1. / (
w1 + self.w_w +
1j * self.eta_w * sign)**2
w1_w[0] -= 1. / (w1 + 1j * self.eta_w[0] *
sign)**2 # correct w'=0
w1_w *= self.dw_w
dSigma_skn[s, i, j] -= np.real(
gemmdot(C_w, w1_w, beta=0.0))
else: #method 2
if not np.abs(self.e_skn[s][ibzkpt2, m] -
self.e_skn[s][ibzkpt1, n]) < 1e-10:
sign *= np.sign(self.e_skn[s][ibzkpt1, n] -
self.e_skn[s][ibzkpt2, m])
# find points on frequency grid
w0 = self.e_skn[s][ibzkpt1,
n] - self.e_skn[s][ibzkpt2, m]
w0_id = np.abs(int(w0 / self.dw))
w1 = w0_id * self.dw
w2 = (w0_id + 1) * self.dw
# choose plus or minus, treat optical limit:
if sign == 1:
C_Wg = Cplus_Wg[
w0_id:w0_id +
2] # only two grid points needed for each w0
if sign == -1:
C_Wg = Cminus_Wg[
w0_id:w0_id +
2] # only two grid points needed for each w0
C_wGG = GatherOrbitals(C_Wg, coords, wcomm).copy()
del C_Wg
# special treat of w0 = 0 (degenerate states):
if w0_id == 0:
Cplustmp_GG = GatherOrbitals(
Cplus_Wg[1], coords, wcomm).copy()
Cminustmp_GG = GatherOrbitals(
Cminus_Wg[1], coords, wcomm).copy()
# perform C_wGG * np.outer(rho_G.conj(), rho_G).sum(GG)
if w0_id == 0:
Sw0_G = gemmdot(C_wGG[0], rho_G, beta=0.0)
Sw0 = np.real(
gemmdot(Sw0_G,
rho_G,
alpha=self.alpha,
beta=0.0,
trans='c'))
Sw1_G = gemmdot(Cplustmp_GG, rho_G, beta=0.0)
Sw1 = np.real(
gemmdot(Sw1_G,
rho_G,
alpha=self.alpha,
beta=0.0,
trans='c'))
Sw2_G = gemmdot(Cminustmp_GG, rho_G, beta=0.0)
Sw2 = np.real(
gemmdot(Sw2_G,
rho_G,
alpha=self.alpha,
beta=0.0,
trans='c'))
Sigma_skn[s, i, j] += Sw0
dSigma_skn[s, i,
j] += (Sw1 + Sw2) / (2 * self.dw)
else:
Sw1_G = gemmdot(C_wGG[0], rho_G, beta=0.0)
Sw1 = np.real(
gemmdot(Sw1_G,
rho_G,
alpha=self.alpha,
beta=0.0,
trans='c'))
Sw2_G = gemmdot(C_wGG[1], rho_G, beta=0.0)
Sw2 = np.real(
gemmdot(Sw2_G,
rho_G,
alpha=self.alpha,
beta=0.0,
trans='c'))
Sw0 = (w2 - np.abs(w0)) / self.dw * Sw1 + (
np.abs(w0) - w1) / self.dw * Sw2
Sigma_skn[s, i, j] += np.sign(
self.e_skn[s][ibzkpt1, n] -
self.e_skn[s][ibzkpt2, m]) * Sw0
dSigma_skn[s, i, j] += (Sw2 - Sw1) / self.dw
self.ncomm.barrier()
self.ncomm.sum(Sigma_skn)
self.ncomm.sum(dSigma_skn)
return Sigma_skn, dSigma_skn
def calculate_Kxc(gd,
nt_sG,
npw,
Gvec_Gc,
nG,
vol,
bcell_cv,
R_av,
setups,
D_asp,
functional='ALDA',
density_cut=None):
"""ALDA kernel"""
# The soft part
#assert np.abs(nt_sG[0].shape - nG).sum() == 0
if functional == 'ALDA_X':
x_only = True
A_x = -3. / 4. * (3. / np.pi)**(1. / 3.)
nspins = len(nt_sG)
assert nspins in [1, 2]
fxc_sg = nspins**(1. / 3.) * 4. / 9. * A_x * nt_sG**(-2. / 3.)
else:
assert len(nt_sG) == 1
x_only = False
fxc_sg = np.zeros_like(nt_sG)
xc = XC(functional[1:])
xc.calculate_fxc(gd, nt_sG, fxc_sg)
if density_cut is not None:
fxc_sg[np.where(nt_sG * len(nt_sG) < density_cut)] = 0.0
# FFT fxc(r)
nG0 = nG[0] * nG[1] * nG[2]
tmp_sg = [np.fft.fftn(fxc_sg[s]) * vol / nG0 for s in range(len(nt_sG))]
r_vg = gd.get_grid_point_coordinates()
Kxc_sGG = np.zeros((len(fxc_sg), npw, npw), dtype=complex)
for s in range(len(fxc_sg)):
for iG in range(npw):
for jG in range(npw):
dG_c = Gvec_Gc[iG] - Gvec_Gc[jG]
if (nG / 2 - np.abs(dG_c) > 0).all():
index = (dG_c + nG) % nG
Kxc_sGG[s, iG, jG] = tmp_sg[s][index[0],
index[1],
index[2]]
else: # not in the fft index
dG_v = np.dot(dG_c, bcell_cv)
dGr_g = gemmdot(dG_v, r_vg, beta=0.0)
Kxc_sGG[s, iG, jG] = gd.integrate(np.exp(-1j * dGr_g)
* fxc_sg[s])
# The PAW part
KxcPAW_sGG = np.zeros_like(Kxc_sGG)
dG_GGv = np.zeros((npw, npw, 3))
for iG in range(npw):
for jG in range(npw):
dG_c = Gvec_Gc[iG] - Gvec_Gc[jG]
dG_GGv[iG, jG] = np.dot(dG_c, bcell_cv)
for a, setup in enumerate(setups):
if rank == a % size:
rgd = setup.xc_correction.rgd
n_qg = setup.xc_correction.n_qg
nt_qg = setup.xc_correction.nt_qg
nc_g = setup.xc_correction.nc_g
nct_g = setup.xc_correction.nct_g
Y_nL = setup.xc_correction.Y_nL
dv_g = rgd.dv_g
D_sp = D_asp[a]
B_pqL = setup.xc_correction.B_pqL
D_sLq = np.inner(D_sp, B_pqL.T)
nspins = len(D_sp)
f_sg = rgd.empty(nspins)
ft_sg = rgd.empty(nspins)
n_sLg = np.dot(D_sLq, n_qg)
nt_sLg = np.dot(D_sLq, nt_qg)
# Add core density
n_sLg[:, 0] += np.sqrt(4. * np.pi) / nspins * nc_g
nt_sLg[:, 0] += np.sqrt(4. * np.pi) / nspins * nct_g
coefatoms_GG = np.exp(-1j * np.inner(dG_GGv, R_av[a]))
for n, Y_L in enumerate(Y_nL):
w = weight_n[n]
f_sg[:] = 0.0
n_sg = np.dot(Y_L, n_sLg)
if x_only:
f_sg = nspins * (4 / 9.) * A_x * (nspins * n_sg)**(-2 / 3.)
else:
xc.calculate_fxc(rgd, n_sg, f_sg)
ft_sg[:] = 0.0
nt_sg = np.dot(Y_L, nt_sLg)
if x_only:
ft_sg = nspins * (4 / 9.) * (A_x
* (nspins * nt_sg)**(-2 / 3.))
else:
xc.calculate_fxc(rgd, nt_sg, ft_sg)
for i in range(len(rgd.r_g)):
coef_GG = np.exp(-1j * np.inner(dG_GGv, R_nv[n])
* rgd.r_g[i])
for s in range(len(f_sg)):
KxcPAW_sGG[s] += w * np.dot(coef_GG,
(f_sg[s, i] -
ft_sg[s, i])
* dv_g[i]) * coefatoms_GG
world.sum(KxcPAW_sGG)
Kxc_sGG += KxcPAW_sGG
return Kxc_sGG / vol
def initialize(self):
self.eta /= Hartree
self.ecut /= Hartree
calc = self.calc
self.nspins = self.calc.wfs.nspins
# kpoint init
self.kd = kd = calc.wfs.kd
self.nikpt = kd.nibzkpts
self.ftol /= kd.nbzkpts
# cell init
self.acell_cv = calc.wfs.gd.cell_cv
self.acell_cv, self.bcell_cv, self.vol, self.BZvol = \
get_primitive_cell(self.acell_cv,rpad=self.rpad)
# grid init
gd = calc.wfs.gd.new_descriptor(comm=serial_comm)
self.pbc = gd.pbc_c
self.gd = gd
self.nG0 = np.prod(gd.N_c)
# Number of grid points and volume including zero padding
self.nGrpad = gd.N_c * self.rpad
self.nG0rpad = np.prod(self.nGrpad)
self.d_c = [
Gradient(gd, i, n=4, dtype=complex).apply for i in range(3)
]
# obtain eigenvalues, occupations
nibzkpt = kd.nibzkpts
kweight_k = kd.weight_k
self.eFermi = self.calc.occupations.get_fermi_level()
try:
self.e_skn
self.printtxt('Use eigenvalues from user.')
except:
self.printtxt('Use eigenvalues from the calculator.')
self.e_skn = {}
self.f_skn = {}
for ispin in range(self.nspins):
self.e_skn[ispin] = np.array([
calc.get_eigenvalues(kpt=k, spin=ispin)
for k in range(nibzkpt)
]) / Hartree
self.f_skn[ispin] = np.array([
calc.get_occupation_numbers(kpt=k, spin=ispin) /
kweight_k[k] for k in range(nibzkpt)
]) / kd.nbzkpts
#self.printtxt('Eigenvalues(k=0) are:')
#print >> self.txt, self.e_skn[0][0] * Hartree
self.enoshift_skn = {}
for ispin in range(self.nspins):
self.enoshift_skn[ispin] = self.e_skn[ispin].copy()
if self.eshift is not None:
self.add_discontinuity(self.eshift)
self.printtxt('Shift unoccupied bands by %f eV' % (self.eshift))
# k + q init
if self.q_c is not None:
self.qq_v = np.dot(self.q_c, self.bcell_cv) # summation over c
if self.optical_limit:
kq_k = np.arange(kd.nbzkpts)
self.expqr_g = 1.
else:
r_vg = gd.get_grid_point_coordinates() # (3, nG)
qr_g = gemmdot(self.qq_v, r_vg, beta=0.0)
self.expqr_g = np.exp(-1j * qr_g)
del r_vg, qr_g
kq_k = kd.find_k_plus_q(self.q_c)
self.kq_k = kq_k
# Plane wave init
if self.G_plus_q:
self.npw, self.Gvec_Gc, self.Gindex_G = set_Gvectors(self.acell_cv,
self.bcell_cv,
self.gd.N_c,
self.ecut,
q=self.q_c)
else:
self.npw, self.Gvec_Gc, self.Gindex_G = set_Gvectors(
self.acell_cv, self.bcell_cv, self.gd.N_c, self.ecut)
# band init
if self.nbands is None:
self.nbands = calc.wfs.bd.nbands
self.nvalence = calc.wfs.nvalence
# Projectors init
setups = calc.wfs.setups
self.spos_ac = calc.atoms.get_scaled_positions()
if self.pwmode:
self.pt = PWLFC([setup.pt_j for setup in setups], self.calc.wfs.pd)
self.pt.set_positions(self.spos_ac)
else:
self.pt = LFC(gd, [setup.pt_j for setup in setups],
KPointDescriptor(self.kd.bzk_kc),
dtype=complex,
forces=True)
self.pt.set_positions(self.spos_ac)
# Printing calculation information
self.print_stuff()
return
import numpy as np
from gpaw.utilities.blas import \
gemm, axpy, r2k, rk, gemmdot, dotc
from gpaw.utilities.tools import tri2full
a = np.arange(5 * 7).reshape(5, 7) + 4.
a2 = np.arange(3 * 7).reshape(3, 7) + 3.
b = np.arange(7) - 2.
# Check gemmdot with floats
assert np.all(np.dot(a, b) == gemmdot(a, b))
assert np.all(np.dot(a, a2.T) == gemmdot(a, a2, trans='t'))
assert np.all(np.dot(a, a2.T) == gemmdot(a, a2, trans='c'))
assert np.dot(b, b) == gemmdot(b, b)
# Check gemmdot with complex arrays
a = a * (2 + 1.j)
a2 = a2 * (-1 + 3.j)
b = b * (3 - 2.j)
assert np.all(np.dot(a, b) == gemmdot(a, b))
assert np.all(np.dot(a, a2.T) == gemmdot(a, a2, trans='t'))
assert np.all(np.dot(a, a2.T.conj()) == gemmdot(a, a2, trans='c'))
assert np.dot(b, b) == gemmdot(b, b, trans='n')
assert np.dot(b, b.conj()) == gemmdot(b, b, trans='c')
assert np.vdot(a, 5.j * a) == dotc(a, 5.j * a)
# Check gemm for transa='n'
a2 = np.arange(7 * 5 * 1 * 3).reshape(7, 5, 1, 3) * (-1. + 4.j) + 3.
c = np.tensordot(a, a2, [1, 0])
gemm(1., a2, a, -1., c, 'n')
assert not c.any()
def initialize(self):
self.eta /= Hartree
self.ecut /= Hartree
calc = self.calc
# kpoint init
self.kd = kd = calc.wfs.kd
self.bzk_kc = kd.bzk_kc
self.ibzk_kc = kd.ibzk_kc
self.nkpt = kd.nbzkpts
self.ftol /= self.nkpt
# band init
if self.nbands is None:
self.nbands = calc.wfs.nbands
self.nvalence = calc.wfs.nvalence
# cell init
self.acell_cv = calc.atoms.cell / Bohr
self.bcell_cv, self.vol, self.BZvol = get_primitive_cell(self.acell_cv)
# grid init
self.nG = calc.get_number_of_grid_points()
self.nG0 = self.nG[0] * self.nG[1] * self.nG[2]
gd = GridDescriptor(self.nG, calc.wfs.gd.cell_cv, pbc_c=True, comm=serial_comm)
self.gd = gd
self.h_cv = gd.h_cv
# obtain eigenvalues, occupations
nibzkpt = kd.nibzkpts
kweight_k = kd.weight_k
try:
self.e_kn
except:
self.printtxt('Use eigenvalues from the calculator.')
self.e_kn = np.array([calc.get_eigenvalues(kpt=k)
for k in range(nibzkpt)]) / Hartree
self.printtxt('Eigenvalues(k=0) are:')
print >> self.txt, self.e_kn[0] * Hartree
self.f_kn = np.array([calc.get_occupation_numbers(kpt=k) / kweight_k[k]
for k in range(nibzkpt)]) / self.nkpt
# k + q init
assert self.q_c is not None
self.qq_v = np.dot(self.q_c, self.bcell_cv) # summation over c
if self.optical_limit:
kq_k = np.arange(self.nkpt)
self.expqr_g = 1.
else:
r_vg = gd.get_grid_point_coordinates() # (3, nG)
qr_g = gemmdot(self.qq_v, r_vg, beta=0.0)
self.expqr_g = np.exp(-1j * qr_g)
del r_vg, qr_g
kq_k = kd.find_k_plus_q(self.q_c)
self.kq_k = kq_k
# Plane wave init
self.npw, self.Gvec_Gc, self.Gindex_G = set_Gvectors(self.acell_cv, self.bcell_cv, self.nG, self.ecut)
# Projectors init
setups = calc.wfs.setups
pt = LFC(gd, [setup.pt_j for setup in setups],
dtype=calc.wfs.dtype, forces=True)
spos_ac = calc.atoms.get_scaled_positions()
pt.set_k_points(self.bzk_kc)
pt.set_positions(spos_ac)
self.pt = pt
# Printing calculation information
self.print_stuff()
return
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)
def get_phases(offset):
return overlapcalc.phaseclass(overlapcalc.ibzk_qc, offset)
# 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.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, offset in r_and_offset_aao[(a1, a2)]:
if np.linalg.norm(r) > maxdistance:
continue
disp = Displacement(a1, a2, r, 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
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:
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.kpt_comm.sum(F_av, 0)
self.timer.stop('Wait for sum')
self.timer.stop('LCAO forces')
def density_matrix(self,
n,
m,
k,
kq=None,
spin1=0,
spin2=0,
phi_aGp=None,
Gspace=True):
gd = self.gd
kd = self.kd
optical_limit = False
if kq is None:
kq = self.kq_k[k]
expqr_g = self.expqr_g
q_v = self.qq_v
optical_limit = self.optical_limit
q_c = self.q_c
else:
q_c = kd.bzk_kc[kq] - kd.bzk_kc[k]
q_c[np.where(q_c > 0.501)] -= 1
q_c[np.where(q_c < -0.499)] += 1
if (np.abs(q_c) < self.ftol).all():
optical_limit = True
q_c = self.q_c
q_v = np.dot(q_c, self.bcell_cv)
r_vg = gd.get_grid_point_coordinates() # (3, nG)
qr_g = gemmdot(q_v, r_vg, beta=0.0)
expqr_g = np.exp(-1j * qr_g)
if optical_limit:
expqr_g = 1
ibzkpt1 = kd.bz2ibz_k[k]
ibzkpt2 = kd.bz2ibz_k[kq]
psitold_g = self.get_wavefunction(ibzkpt1, n, True, spin=spin1)
psit1_g = kd.transform_wave_function(psitold_g, k)
psitold_g = self.get_wavefunction(ibzkpt2, m, True, spin=spin2)
psit2_g = kd.transform_wave_function(psitold_g, kq)
if Gspace is False:
return psit1_g.conj() * psit2_g * expqr_g
else:
tmp_g = psit1_g.conj() * psit2_g * expqr_g
# zero padding is included through the FFT
rho_g = np.fft.fftn(tmp_g, s=self.nGrpad) * self.vol / self.nG0rpad
# Here, planewave cutoff is applied
rho_G = rho_g.ravel()[self.Gindex_G]
if optical_limit:
dpsit_g = gd.empty(dtype=complex)
tmp = np.zeros((3), dtype=complex)
phase_cd = np.exp(2j * pi * gd.sdisp_cd *
kd.bzk_kc[kq, :, np.newaxis])
for ix in range(3):
self.d_c[ix](psit2_g, dpsit_g, phase_cd)
tmp[ix] = gd.integrate(psit1_g.conj() * dpsit_g)
rho_G[0] = -1j * np.dot(q_v, tmp)
calc = self.calc
pt = self.pt
if not self.pwmode:
if calc.wfs.world.size > 1 or kd.nbzkpts == 1:
P1_ai = pt.dict()
pt.integrate(psit1_g, P1_ai, k)
P2_ai = pt.dict()
pt.integrate(psit2_g, P2_ai, kq)
else:
P1_ai = self.get_P_ai(k, n, spin1)
P2_ai = self.get_P_ai(kq, m, spin2)
else:
# first calculate P_ai at ibzkpt, then rotate to k
u = self.kd.get_rank_and_index(spin1, ibzkpt1)[1]
Ptmp_ai = pt.dict()
kpt = calc.wfs.kpt_u[u]
pt.integrate(kpt.psit_nG[n], Ptmp_ai, ibzkpt1)
P1_ai = self.get_P_ai(k, n, spin1, Ptmp_ai)
u = self.kd.get_rank_and_index(spin2, ibzkpt2)[1]
Ptmp_ai = pt.dict()
kpt = calc.wfs.kpt_u[u]
pt.integrate(kpt.psit_nG[m], Ptmp_ai, ibzkpt2)
P2_ai = self.get_P_ai(kq, m, spin2, Ptmp_ai)
if phi_aGp is None:
try:
if not self.mode == 'RPA':
if optical_limit:
iq = kd.where_is_q(np.zeros(3), self.bzq_qc)
else:
iq = kd.where_is_q(q_c, self.bzq_qc)
assert np.abs(self.bzq_qc[iq] - q_c).sum() < 1e-8
phi_aGp = self.load_phi_aGp(self.reader, iq) #phi_qaGp[iq]
except AttributeError:
phi_aGp = self.phi_aGp
for a, id in enumerate(self.calc.wfs.setups.id_a):
P_p = np.outer(P1_ai[a].conj(), P2_ai[a]).ravel()
phi_Gp = np.ascontiguousarray(phi_aGp[a], complex)
gemv(1.0, phi_Gp, P_p, 1.0, rho_G)
if optical_limit:
if n == m:
rho_G[0] = 1.
elif np.abs(self.e_skn[spin2][ibzkpt2, m] -
self.e_skn[spin1][ibzkpt1, n]) < 1e-5:
rho_G[0] = 0.
else:
rho_G[0] /= (self.enoshift_skn[spin2][ibzkpt2, m] -
self.enoshift_skn[spin1][ibzkpt1, n])
return rho_G
def density_matrix(self, n, m, k, kq=None,
spin1=0, spin2=0, phi_aGp=None, Gspace=True):
gd = self.gd
kd = self.kd
optical_limit = False
if kq is None:
kq = self.kq_k[k]
expqr_g = self.expqr_g
q_v = self.qq_v
optical_limit = self.optical_limit
q_c = self.q_c
else:
q_c = kd.bzk_kc[kq] - kd.bzk_kc[k]
q_c[np.where(q_c>0.501)] -= 1
q_c[np.where(q_c<-0.499)] += 1
if (np.abs(q_c) < self.ftol).all():
optical_limit = True
q_c = self.q_c
q_v = np.dot(q_c, self.bcell_cv)
r_vg = gd.get_grid_point_coordinates() # (3, nG)
qr_g = gemmdot(q_v, r_vg, beta=0.0)
expqr_g = np.exp(-1j * qr_g)
if optical_limit:
expqr_g = 1
ibzkpt1 = kd.bz2ibz_k[k]
ibzkpt2 = kd.bz2ibz_k[kq]
psitold_g = self.get_wavefunction(ibzkpt1, n, True, spin=spin1)
psit1_g = kd.transform_wave_function(psitold_g, k)
psitold_g = self.get_wavefunction(ibzkpt2, m, True, spin=spin2)
psit2_g = kd.transform_wave_function(psitold_g, kq)
if Gspace is False:
return psit1_g.conj() * psit2_g * expqr_g
else:
tmp_g = psit1_g.conj()* psit2_g * expqr_g
# zero padding is included through the FFT
rho_g = np.fft.fftn(tmp_g, s=self.nGrpad) * self.vol / self.nG0rpad
# Here, planewave cutoff is applied
rho_G = rho_g.ravel()[self.Gindex_G]
if optical_limit:
dpsit_g = gd.empty(dtype=complex)
tmp = np.zeros((3), dtype=complex)
phase_cd = np.exp(2j * pi * gd.sdisp_cd * kd.bzk_kc[kq, :, np.newaxis])
for ix in range(3):
self.d_c[ix](psit2_g, dpsit_g, phase_cd)
tmp[ix] = gd.integrate(psit1_g.conj() * dpsit_g)
rho_G[0] = -1j * np.dot(q_v, tmp)
calc = self.calc
pt = self.pt
if not self.pwmode:
if calc.wfs.world.size > 1 or kd.nbzkpts == 1:
P1_ai = pt.dict()
pt.integrate(psit1_g, P1_ai, k)
P2_ai = pt.dict()
pt.integrate(psit2_g, P2_ai, kq)
else:
P1_ai = self.get_P_ai(k, n, spin1)
P2_ai = self.get_P_ai(kq, m, spin2)
else:
# first calculate P_ai at ibzkpt, then rotate to k
u = self.kd.get_rank_and_index(spin1, ibzkpt1)[1]
Ptmp_ai = pt.dict()
kpt = calc.wfs.kpt_u[u]
pt.integrate(kpt.psit_nG[n], Ptmp_ai, ibzkpt1)
P1_ai = self.get_P_ai(k, n, spin1, Ptmp_ai)
u = self.kd.get_rank_and_index(spin2, ibzkpt2)[1]
Ptmp_ai = pt.dict()
kpt = calc.wfs.kpt_u[u]
pt.integrate(kpt.psit_nG[m], Ptmp_ai, ibzkpt2)
P2_ai = self.get_P_ai(kq, m, spin2, Ptmp_ai)
if phi_aGp is None:
try:
if not self.mode == 'RPA':
if optical_limit:
iq = kd.where_is_q(np.zeros(3), self.bzq_qc)
else:
iq = kd.where_is_q(q_c, self.bzq_qc)
assert np.abs(self.bzq_qc[iq] - q_c).sum() < 1e-8
phi_aGp = self.load_phi_aGp(self.reader, iq) #phi_qaGp[iq]
except AttributeError:
phi_aGp = self.phi_aGp
for a, id in enumerate(self.calc.wfs.setups.id_a):
P_p = np.outer(P1_ai[a].conj(), P2_ai[a]).ravel()
phi_Gp = np.ascontiguousarray(phi_aGp[a], complex)
gemv(1.0, phi_Gp, P_p, 1.0, rho_G)
if optical_limit:
if n==m:
rho_G[0] = 1.
elif np.abs(self.e_skn[spin2][ibzkpt2, m] - self.e_skn[spin1][ibzkpt1, n]) < 1e-5:
rho_G[0] = 0.
else:
rho_G[0] /= (self.enoshift_skn[spin2][ibzkpt2, m] - self.enoshift_skn[spin1][ibzkpt1, n])
return rho_G
import numpy as np
from gpaw.utilities.blas import \
gemm, axpy, r2k, rk, gemmdot, rotate, dotc, dotu
from gpaw.utilities.tools import tri2full
a = np.arange(5 * 7).reshape(5, 7) + 4.
a2 = np.arange(3 * 7).reshape(3, 7) + 3.
b = np.arange(7) - 2.
# Check gemmdot with floats
assert np.all(np.dot(a, b) == gemmdot(a, b))
assert np.all(np.dot(a, a2.T) == gemmdot(a, a2, trans='t'))
assert np.all(np.dot(a, a2.T) == gemmdot(a, a2, trans='c'))
assert np.dot(b, b) == gemmdot(b, b)
# Check gemmdot with complex arrays
a = a * (2 + 1.j)
a2 = a2 * (-1 + 3.j)
b = b * (3 - 2.j)
assert np.all(np.dot(a, b) == gemmdot(a, b))
assert np.all(np.dot(a, a2.T) == gemmdot(a, a2, trans='t'))
assert np.all(np.dot(a, a2.T.conj()) == gemmdot(a, a2, trans='c'))
assert np.dot(b, b) == gemmdot(b, b, trans='n')
assert np.dot(b, b.conj()) == gemmdot(b, b, trans='c')
assert np.vdot(a, 5.j * a) == dotc(a, 5.j * a)
# Check gemm for transa='n'
a2 = np.arange(7 * 5 * 1 * 3).reshape(7, 5, 1, 3) * (-1. + 4.j) + 3.
c = np.tensordot(a, a2, [1, 0])
gemm(1., a2, a, -1., c, 'n')
assert not c.any()
def calculate_Kxc(gd, nt_sG, npw, Gvec_Gc, nG, vol,
bcell_cv, R_av, setups, D_asp):
"""LDA kernel"""
# The soft part
assert np.abs(nt_sG[0].shape - nG).sum() == 0
xc = XC('LDA')
fxc_sg = np.zeros_like(nt_sG)
xc.calculate_fxc(gd, nt_sG, fxc_sg)
fxc_g = fxc_sg[0]
# FFT fxc(r)
nG0 = nG[0] * nG[1] * nG[2]
tmp_g = np.fft.fftn(fxc_g) * vol / nG0
r_vg = gd.get_grid_point_coordinates()
Kxc_GG = np.zeros((npw, npw), dtype=complex)
for iG in range(npw):
for jG in range(npw):
dG_c = Gvec_Gc[iG] - Gvec_Gc[jG]
if (nG / 2 - np.abs(dG_c) > 0).all():
index = (dG_c + nG) % nG
Kxc_GG[iG, jG] = tmp_g[index[0], index[1], index[2]]
else: # not in the fft index
dG_v = np.dot(dG_c, bcell_cv)
dGr_g = gemmdot(dG_v, r_vg, beta=0.0)
Kxc_GG[iG, jG] = gd.integrate(np.exp(-1j*dGr_g)*fxc_g)
KxcPAW_GG = np.zeros_like(Kxc_GG)
# The PAW part
dG_GGv = np.zeros((npw, npw, 3))
for iG in range(npw):
for jG in range(npw):
dG_c = Gvec_Gc[iG] - Gvec_Gc[jG]
dG_GGv[iG, jG] = np.dot(dG_c, bcell_cv)
for a, setup in enumerate(setups):
if rank == a % size:
rgd = setup.xc_correction.rgd
n_qg = setup.xc_correction.n_qg
nt_qg = setup.xc_correction.nt_qg
nc_g = setup.xc_correction.nc_g
nct_g = setup.xc_correction.nct_g
Y_nL = setup.xc_correction.Y_nL
dv_g = rgd.dv_g
D_sp = D_asp[a]
B_pqL = setup.xc_correction.B_pqL
D_sLq = np.inner(D_sp, B_pqL.T)
nspins = len(D_sp)
assert nspins == 1
f_sg = rgd.empty(nspins)
ft_sg = rgd.empty(nspins)
n_sLg = np.dot(D_sLq, n_qg)
nt_sLg = np.dot(D_sLq, nt_qg)
# Add core density
n_sLg[:, 0] += sqrt(4 * pi) / nspins * nc_g
nt_sLg[:, 0] += sqrt(4 * pi) / nspins * nct_g
coefatoms_GG = np.exp(-1j * np.inner(dG_GGv, R_av[a]))
for n, Y_L in enumerate(Y_nL):
w = weight_n[n]
f_sg[:] = 0.0
n_sg = np.dot(Y_L, n_sLg)
xc.calculate_fxc(rgd, n_sg, f_sg)
ft_sg[:] = 0.0
nt_sg = np.dot(Y_L, nt_sLg)
xc.calculate_fxc(rgd, nt_sg, ft_sg)
coef_GGg = np.exp(-1j * np.outer(np.inner(dG_GGv, R_nv[n]),
rgd.r_g)).reshape(npw,npw,rgd.ng)
KxcPAW_GG += w * np.dot(coef_GGg, (f_sg[0]-ft_sg[0]) * dv_g) * coefatoms_GG
world.sum(KxcPAW_GG)
Kxc_GG += KxcPAW_GG
return Kxc_GG / vol
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_self_energy(self, df, W_wGG):
Sigma_skn = np.zeros((self.nspins, self.gwnkpt, self.gwnband), dtype=float)
dSigma_skn = np.zeros((self.nspins, self.gwnkpt, self.gwnband), dtype=float)
wcomm = df.wcomm
if self.static:
W_wGG = np.array([W_wGG])
if not self.hilbert_trans: #method 1
Wbackup_wG0 = W_wGG[:,:,0].copy()
Wbackup_w0G = W_wGG[:,0,:].copy()
else: #method 2, perform Hilbert transform
nG = np.shape(W_wGG)[1]
coords = np.zeros(wcomm.size, dtype=int)
nG_local = nG**2 // wcomm.size
if wcomm.rank == wcomm.size - 1:
nG_local = nG**2 - (wcomm.size - 1) * nG_local
wcomm.all_gather(np.array([nG_local]), coords)
W_Wg = SliceAlongFrequency(W_wGG, coords, wcomm)
ng = np.shape(W_Wg)[1]
Nw = int(self.w_w[-1] / self.dw)
w1_ww = np.zeros((Nw, df.Nw), dtype=complex)
for iw in range(Nw):
w1 = iw * self.dw
w1_ww[iw] = 1./(w1 + self.w_w + 1j*self.eta_w) + 1./(w1 - self.w_w + 1j*self.eta_w)
w1_ww[iw,0] -= 1./(w1 + 1j*self.eta_w[0]) # correct w'=0
w1_ww[iw] *= self.dw_w
Cplus_Wg = np.zeros((Nw, ng), dtype=complex)
Cminus_Wg = np.zeros((Nw, ng), dtype=complex)
Cplus_Wg = gemmdot(w1_ww, W_Wg, beta=0.0)
Cminus_Wg = gemmdot(w1_ww.conj(), W_Wg, beta=0.0)
for s in range(self.nspins):
for i, k in enumerate(self.gwkpt_k): # k is bzk index
if df.optical_limit:
kq_c = df.kd.bzk_kc[k]
else:
kq_c = df.kd.bzk_kc[k] - df.q_c # k - q
kq = df.kd.where_is_q(kq_c, df.kd.bzk_kc)
assert df.kq_k[kq] == k
ibzkpt1 = df.kd.bz2ibz_k[k]
ibzkpt2 = df.kd.bz2ibz_k[kq]
for j, n in enumerate(self.bands):
for m in range(self.m_start, self.m_end):
if self.e_skn[s][ibzkpt2, m] > self.eFermi:
sign = 1.
else:
sign = -1.
rho_G = df.density_matrix(m, n, kq, spin1=s, spin2=s)
if not self.hilbert_trans: #method 1
W_wGG[:,:,0] = Wbackup_wG0
W_wGG[:,0,:] = Wbackup_w0G
# w1 = w - epsilon_m,k-q
w1 = self.e_skn[s][ibzkpt1,n] - self.e_skn[s][ibzkpt2,m]
if self.ppa:
# analytical expression for Plasmon Pole Approximation
W_GG = sign * W_wGG[0] * (1./(w1 + self.wt_GG - 1j*self.eta) -
1./(w1 - self.wt_GG + 1j*self.eta))
W_GG -= W_wGG[0] * (1./(w1 + self.wt_GG + 1j*self.eta*sign) +
1./(w1 - self.wt_GG + 1j*self.eta*sign))
W_G = gemmdot(W_GG, rho_G, beta=0.0)
Sigma_skn[s,i,j] += np.real(gemmdot(W_G, rho_G, alpha=self.alpha, beta=0.0,trans='c'))
W_GG = sign * W_wGG[0] * (1./(w1 - self.wt_GG + 1j*self.eta)**2 -
1./(w1 + self.wt_GG - 1j*self.eta)**2)
W_GG += W_wGG[0] * (1./(w1 - self.wt_GG + 1j*self.eta*sign)**2 +
1./(w1 + self.wt_GG + 1j*self.eta*sign)**2)
W_G = gemmdot(W_GG, rho_G, beta=0.0)
dSigma_skn[s,i,j] += np.real(gemmdot(W_G, rho_G, alpha=self.alpha, beta=0.0,trans='c'))
elif self.static:
W1_GG = W_wGG[0] - np.eye(df.npw)*self.Kc_GG
W2_GG = W_wGG[0]
# perform W_GG * np.outer(rho_G.conj(), rho_G).sum(GG)
W_G = gemmdot(W1_GG, rho_G, beta=0.0) # Coulomb Hole
Sigma_skn[s,i,j] += np.real(gemmdot(W_G, rho_G, alpha=self.alpha*pi/1j, beta=0.0,trans='c'))
if sign == -1:
W_G = gemmdot(W2_GG, rho_G, beta=0.0) # Screened Exchange
Sigma_skn[s,i,j] -= np.real(gemmdot(W_G, rho_G, alpha=2*self.alpha*pi/1j, beta=0.0,trans='c'))
del W1_GG, W2_GG, W_G, rho_G
else:
# perform W_wGG * np.outer(rho_G.conj(), rho_G).sum(GG)
W_wG = gemmdot(W_wGG, rho_G, beta=0.0)
C_wlocal = gemmdot(W_wG, rho_G, alpha=self.alpha, beta=0.0,trans='c')
del W_wG, rho_G
C_w = np.zeros(df.Nw, dtype=complex)
wcomm.all_gather(C_wlocal, C_w)
del C_wlocal
# calculate self energy
w1_w = 1./(w1 - self.w_w + 1j*self.eta_w*sign) + 1./(w1 + self.w_w + 1j*self.eta_w*sign)
w1_w[0] -= 1./(w1 + 1j*self.eta_w[0]*sign) # correct w'=0
w1_w *= self.dw_w
Sigma_skn[s,i,j] += np.real(gemmdot(C_w, w1_w, beta=0.0))
# calculate derivate of self energy with respect to w
w1_w = 1./(w1 - self.w_w + 1j*self.eta_w*sign)**2 + 1./(w1 + self.w_w + 1j*self.eta_w*sign)**2
w1_w[0] -= 1./(w1 + 1j*self.eta_w[0]*sign)**2 # correct w'=0
w1_w *= self.dw_w
dSigma_skn[s,i,j] -= np.real(gemmdot(C_w, w1_w, beta=0.0))
else: #method 2
if not np.abs(self.e_skn[s][ibzkpt2,m] - self.e_skn[s][ibzkpt1,n]) < 1e-10:
sign *= np.sign(self.e_skn[s][ibzkpt1,n] - self.e_skn[s][ibzkpt2,m])
# find points on frequency grid
w0 = self.e_skn[s][ibzkpt1,n] - self.e_skn[s][ibzkpt2,m]
w0_id = np.abs(int(w0 / self.dw))
w1 = w0_id * self.dw
w2 = (w0_id + 1) * self.dw
# choose plus or minus, treat optical limit:
if sign == 1:
C_Wg = Cplus_Wg[w0_id:w0_id+2] # only two grid points needed for each w0
if sign == -1:
C_Wg = Cminus_Wg[w0_id:w0_id+2] # only two grid points needed for each w0
C_wGG = GatherOrbitals(C_Wg, coords, wcomm).copy()
del C_Wg
# special treat of w0 = 0 (degenerate states):
if w0_id == 0:
Cplustmp_GG = GatherOrbitals(Cplus_Wg[1], coords, wcomm).copy()
Cminustmp_GG = GatherOrbitals(Cminus_Wg[1], coords, wcomm).copy()
# perform C_wGG * np.outer(rho_G.conj(), rho_G).sum(GG)
if w0_id == 0:
Sw0_G = gemmdot(C_wGG[0], rho_G, beta=0.0)
Sw0 = np.real(gemmdot(Sw0_G, rho_G, alpha=self.alpha, beta=0.0, trans='c'))
Sw1_G = gemmdot(Cplustmp_GG, rho_G, beta=0.0)
Sw1 = np.real(gemmdot(Sw1_G, rho_G, alpha=self.alpha, beta=0.0, trans='c'))
Sw2_G = gemmdot(Cminustmp_GG, rho_G, beta=0.0)
Sw2 = np.real(gemmdot(Sw2_G, rho_G, alpha=self.alpha, beta=0.0, trans='c'))
Sigma_skn[s,i,j] += Sw0
dSigma_skn[s,i,j] += (Sw1 + Sw2)/(2*self.dw)
else:
Sw1_G = gemmdot(C_wGG[0], rho_G, beta=0.0)
Sw1 = np.real(gemmdot(Sw1_G, rho_G, alpha=self.alpha, beta=0.0, trans='c'))
Sw2_G = gemmdot(C_wGG[1], rho_G, beta=0.0)
Sw2 = np.real(gemmdot(Sw2_G, rho_G, alpha=self.alpha, beta=0.0, trans='c'))
Sw0 = (w2-np.abs(w0))/self.dw * Sw1 + (np.abs(w0)-w1)/self.dw * Sw2
Sigma_skn[s,i,j] += np.sign(self.e_skn[s][ibzkpt1,n] - self.e_skn[s][ibzkpt2,m]) * Sw0
dSigma_skn[s,i,j] += (Sw2 - Sw1)/self.dw
self.ncomm.barrier()
self.ncomm.sum(Sigma_skn)
self.ncomm.sum(dSigma_skn)
return Sigma_skn, dSigma_skn
def initialize(self):
self.eta /= Hartree
self.ecut /= Hartree
calc = self.calc
# kpoint init
self.kd = kd = calc.wfs.kd
self.bzk_kc = kd.bzk_kc
self.ibzk_kc = kd.ibzk_kc
self.nkpt = kd.nbzkpts
self.ftol /= self.nkpt
# band init
if self.nbands is None:
self.nbands = calc.wfs.nbands
self.nvalence = calc.wfs.nvalence
# cell init
self.acell_cv = calc.atoms.cell / Bohr
self.bcell_cv, self.vol, self.BZvol = get_primitive_cell(self.acell_cv)
# grid init
self.nG = calc.get_number_of_grid_points()
self.nG0 = self.nG[0] * self.nG[1] * self.nG[2]
gd = GridDescriptor(self.nG,
calc.wfs.gd.cell_cv,
pbc_c=True,
comm=serial_comm)
self.gd = gd
self.h_cv = gd.h_cv
# obtain eigenvalues, occupations
nibzkpt = kd.nibzkpts
kweight_k = kd.weight_k
try:
self.e_kn
except:
self.printtxt('Use eigenvalues from the calculator.')
self.e_kn = np.array(
[calc.get_eigenvalues(kpt=k)
for k in range(nibzkpt)]) / Hartree
self.printtxt('Eigenvalues(k=0) are:')
print >> self.txt, self.e_kn[0] * Hartree
self.f_kn = np.array([
calc.get_occupation_numbers(kpt=k) / kweight_k[k]
for k in range(nibzkpt)
]) / self.nkpt
# k + q init
assert self.q_c is not None
self.qq_v = np.dot(self.q_c, self.bcell_cv) # summation over c
if self.optical_limit:
kq_k = np.arange(self.nkpt)
self.expqr_g = 1.
else:
r_vg = gd.get_grid_point_coordinates() # (3, nG)
qr_g = gemmdot(self.qq_v, r_vg, beta=0.0)
self.expqr_g = np.exp(-1j * qr_g)
del r_vg, qr_g
kq_k = kd.find_k_plus_q(self.q_c)
self.kq_k = kq_k
# Plane wave init
self.npw, self.Gvec_Gc, self.Gindex_G = set_Gvectors(
self.acell_cv, self.bcell_cv, self.nG, self.ecut)
# Projectors init
setups = calc.wfs.setups
pt = LFC(gd, [setup.pt_j for setup in setups],
dtype=calc.wfs.dtype,
forces=True)
spos_ac = calc.atoms.get_scaled_positions()
pt.set_k_points(self.bzk_kc)
pt.set_positions(spos_ac)
self.pt = pt
# Printing calculation information
self.print_stuff()
return
t = time.time()
for n in range(numreps):
BY1_pq = np.dot(B_pqL, Y_L)
t = time.time()-t
performance = numflop*numreps/t
print 'dot : %8.5f s, %8.5f Mflops' % (t,performance/1024**2.)
assert np.abs(BY0_pq-BY1_pq).max()<5e-12
del BY1_pq
if test_gemmdot:
BY2_pq = np.empty((P,Q), dtype)
t = time.time()
for n in range(numreps):
BY2_pq.fill(0.0)
gemmdot(B_pqL, Y_L, 1.0, beta, BY2_pq)
t = time.time()-t
performance = numflop*numreps/t
print 'gemmdot: %8.5f s, %8.5f Mflops' % (t,performance/1024**2.)
assert np.abs(BY0_pq-BY2_pq).max()<5e-12
del BY2_pq
BY3_pq = np.empty((P,Q), dtype)
t = time.time()
for n in range(numreps):
BY3_pq.fill(0.0)
gemv(1.0, B_pqL, Y_L, beta, BY3_pq, 't')
t = time.time()-t
performance = numflop*numreps/t
print 'gemvT : %8.5f s, %8.5f Mflops' % (t,performance/1024**2.)
assert np.abs(BY0_pq-BY3_pq).max()<5e-12
def calculate_Kxc(gd,
nt_sG,
npw,
Gvec_Gc,
nG,
vol,
bcell_cv,
R_av,
setups,
D_asp,
functional='ALDA',
density_cut=None):
"""ALDA kernel"""
# The soft part
#assert np.abs(nt_sG[0].shape - nG).sum() == 0
if functional == 'ALDA_X':
x_only = True
A_x = -3. / 4. * (3. / np.pi)**(1. / 3.)
nspins = len(nt_sG)
assert nspins in [1, 2]
fxc_sg = nspins**(1. / 3.) * 4. / 9. * A_x * nt_sG**(-2. / 3.)
else:
assert len(nt_sG) == 1
x_only = False
fxc_sg = np.zeros_like(nt_sG)
xc = XC(functional[1:])
xc.calculate_fxc(gd, nt_sG, fxc_sg)
if density_cut is not None:
fxc_sg[np.where(nt_sG * len(nt_sG) < density_cut)] = 0.0
# FFT fxc(r)
nG0 = nG[0] * nG[1] * nG[2]
tmp_sg = [np.fft.fftn(fxc_sg[s]) * vol / nG0 for s in range(len(nt_sG))]
r_vg = gd.get_grid_point_coordinates()
Kxc_sGG = np.zeros((len(fxc_sg), npw, npw), dtype=complex)
for s in range(len(fxc_sg)):
for iG in range(npw):
for jG in range(npw):
dG_c = Gvec_Gc[iG] - Gvec_Gc[jG]
if (nG / 2 - np.abs(dG_c) > 0).all():
index = (dG_c + nG) % nG
Kxc_sGG[s, iG, jG] = tmp_sg[s][index[0], index[1],
index[2]]
else: # not in the fft index
dG_v = np.dot(dG_c, bcell_cv)
dGr_g = gemmdot(dG_v, r_vg, beta=0.0)
Kxc_sGG[s, iG, jG] = gd.integrate(
np.exp(-1j * dGr_g) * fxc_sg[s])
# The PAW part
KxcPAW_sGG = np.zeros_like(Kxc_sGG)
dG_GGv = np.zeros((npw, npw, 3))
for iG in range(npw):
for jG in range(npw):
dG_c = Gvec_Gc[iG] - Gvec_Gc[jG]
dG_GGv[iG, jG] = np.dot(dG_c, bcell_cv)
for a, setup in enumerate(setups):
if rank == a % size:
rgd = setup.xc_correction.rgd
n_qg = setup.xc_correction.n_qg
nt_qg = setup.xc_correction.nt_qg
nc_g = setup.xc_correction.nc_g
nct_g = setup.xc_correction.nct_g
Y_nL = setup.xc_correction.Y_nL
dv_g = rgd.dv_g
D_sp = D_asp[a]
B_pqL = setup.xc_correction.B_pqL
D_sLq = np.inner(D_sp, B_pqL.T)
nspins = len(D_sp)
f_sg = rgd.empty(nspins)
ft_sg = rgd.empty(nspins)
n_sLg = np.dot(D_sLq, n_qg)
nt_sLg = np.dot(D_sLq, nt_qg)
# Add core density
n_sLg[:, 0] += np.sqrt(4. * np.pi) / nspins * nc_g
nt_sLg[:, 0] += np.sqrt(4. * np.pi) / nspins * nct_g
coefatoms_GG = np.exp(-1j * np.inner(dG_GGv, R_av[a]))
for n, Y_L in enumerate(Y_nL):
w = weight_n[n]
f_sg[:] = 0.0
n_sg = np.dot(Y_L, n_sLg)
if x_only:
f_sg = nspins * (4 / 9.) * A_x * (nspins * n_sg)**(-2 / 3.)
else:
xc.calculate_fxc(rgd, n_sg, f_sg)
ft_sg[:] = 0.0
nt_sg = np.dot(Y_L, nt_sLg)
if x_only:
ft_sg = nspins * (4 / 9.) * (A_x *
(nspins * nt_sg)**(-2 / 3.))
else:
xc.calculate_fxc(rgd, nt_sg, ft_sg)
for i in range(len(rgd.r_g)):
coef_GG = np.exp(-1j * np.inner(dG_GGv, R_nv[n]) *
rgd.r_g[i])
for s in range(len(f_sg)):
KxcPAW_sGG[s] += w * np.dot(coef_GG,
(f_sg[s, i] - ft_sg[s, i])
* dv_g[i]) * coefatoms_GG
world.sum(KxcPAW_sGG)
Kxc_sGG += KxcPAW_sGG
return Kxc_sGG / vol
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 write_overlaps(calc, seed=None, spin=0, v_knm=None):
if seed is None:
seed = calc.atoms.get_chemical_formula()
if v_knm is None:
spinors = False
else:
spinors = True
bands = get_bands(seed)
Nn = len(bands)
kpts_kc = calc.get_bz_k_points()
Nk = len(kpts_kc)
nnkp = open(seed + '.nnkp', 'r')
lines = nnkp.readlines()
for il, line in enumerate(lines):
if len(line.split()) > 1:
if line.split()[0] == 'begin' and line.split()[1] == 'nnkpts':
Nb = eval(lines[il + 1].split()[0])
i0 = il + 2
break
f = open(seed + '.mmn', 'w')
print('Kohn-Sham input generated from GPAW calculation', file=f)
print('%10d %6d %6d' % (Nn, Nk, Nb), file=f)
icell_cv = (2 * np.pi) * np.linalg.inv(calc.wfs.gd.cell_cv).T
r_g = calc.wfs.gd.get_grid_point_coordinates()
Ng = np.prod(np.shape(r_g)[1:]) * (spinors + 1)
dO_aii = []
for ia in calc.wfs.kpt_u[0].P_ani.keys():
dO_ii = calc.wfs.setups[ia].dO_ii
if spinors:
# Spinor projections require doubling of the (identical) orbitals
dO_jj = np.zeros((2 * len(dO_ii), 2 * len(dO_ii)), complex)
dO_jj[::2, ::2] = dO_ii
dO_jj[1::2, 1::2] = dO_ii
dO_aii.append(dO_jj)
else:
dO_aii.append(dO_ii)
wfs = calc.wfs
u_knG = []
for ik in range(Nk):
if spinors:
# For spinors, G denotes spin and grid: G = (s, gx, gy, gz)
u_nG = get_spinorbit_wavefunctions(calc, ik, v_knm[ik])
u_knG.append(u_nG[bands])
else:
# For non-spinors, G denotes grid: G = (gx, gy, gz)
u_knG.append(
np.array(
[wfs.get_wave_function_array(n, ik, spin) for n in bands]))
P_kani = []
for ik in range(Nk):
if spinors:
P_kani.append(get_spinorbit_projections(calc, ik, v_knm[ik]))
else:
P_kani.append(calc.wfs.kpt_u[spin * Nk + ik].P_ani)
for ik1 in range(Nk):
u1_nG = u_knG[ik1]
for ib in range(Nb):
# b denotes nearest neighbor k-points
line = lines[i0 + ik1 * Nb + ib].split()
ik2 = int(line[1]) - 1
u2_nG = u_knG[ik2]
G_c = np.array([int(line[i]) for i in range(2, 5)])
bG_c = kpts_kc[ik2] - kpts_kc[ik1] + G_c
bG_v = np.dot(bG_c, icell_cv)
u2_nG = u2_nG * np.exp(-1.0j * gemmdot(bG_v, r_g, beta=0.0))
M_mm = get_overlap(calc, bands, np.reshape(u1_nG,
(len(u1_nG), Ng)),
np.reshape(u2_nG, (len(u2_nG), Ng)),
P_kani[ik1], P_kani[ik2], dO_aii, bG_v)
indices = (ik1 + 1, ik2 + 1, G_c[0], G_c[1], G_c[2])
print('%3d %3d %4d %3d %3d' % indices, file=f)
for m1 in range(len(M_mm)):
for m2 in range(len(M_mm)):
M = M_mm[m2, m1]
print('%20.12f %20.12f' % (M.real, M.imag), file=f)
f.close()
def calculate_forces_by_kpoint(self, kpt, hamiltonian,
F_av, tci, P_aqMi,
dThetadR_vMM, dTdR_vMM, dPdR_aqvMi):
k = kpt.k
q = kpt.q
mynao = self.ksl.mynao
nao = self.ksl.nao
dtype = self.dtype
Mstart = self.ksl.Mstart
Mstop = self.ksl.Mstop
basis_functions = self.basis_functions
my_atom_indices = basis_functions.my_atom_indices
atom_indices = basis_functions.atom_indices
def _slices(indices):
for a in indices:
M1 = basis_functions.M_a[a] - Mstart
M2 = M1 + self.setups[a].niAO
yield a, 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('LCAO forces: initial')
if kpt.rho_MM is None:
rhoT_MM = self.ksl.get_transposed_density_matrix(kpt.f_n, kpt.C_nM)
ET_MM = self.ksl.get_transposed_density_matrix(kpt.f_n * kpt.eps_n,
kpt.C_nM)
if hasattr(kpt, 'c_on'):
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 += self.ksl.get_transposed_density_matrix_delta(d_nn, kpt.C_nM)
ET_MM+=self.ksl.get_transposed_density_matrix_delta(d_nn*kpt.eps_n, kpt.C_nM)
else:
H_MM = self.eigensolver.calculate_hamiltonian_matrix(hamiltonian,
self,
kpt)
tri2full(H_MM)
S_MM = self.S_qMM[q].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()
self.timer.stop('LCAO forces: initial')
# 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)
dEdTrhoT_vMM = (dTdR_vMM * rhoT_MM[np.newaxis]).real
for a, M1, M2 in my_slices():
Fkin_av[a, :] = 2 * dEdTrhoT_vMM[:, M1:M2].sum(-1).sum(-1)
del dEdTrhoT_vMM
# 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('LCAO forces: potential')
Fpot_av = np.zeros_like(F_av)
vt_G = hamiltonian.vt_sG[kpt.s]
DVt_vMM = np.zeros((3, mynao, nao), dtype)
# Note that DVt_vMM contains dPhi(r) / dr = - dPhi(r) / dR^a
basis_functions.calculate_potential_matrix_derivative(vt_G, DVt_vMM, q)
for a, M1, M2 in slices():
for v in range(3):
Fpot_av[a, v] = 2 * (DVt_vMM[v, M1:M2, :]
* rhoT_MM[M1:M2, :]).real.sum()
del DVt_vMM
self.timer.stop('LCAO forces: potential')
# 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
#
Frho_av = np.zeros_like(F_av)
dThetadRE_vMM = (dThetadR_vMM * ET_MM[np.newaxis]).real
for a, M1, M2 in my_slices():
Frho_av[a, :] = -2 * dThetadRE_vMM[:, M1:M2].sum(-1).sum(-1)
del dThetadRE_vMM
# 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('LCAO forces: paw correction')
dPdR_avMi = dict([(a, dPdR_aqvMi[a][q]) for a in my_atom_indices])
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][q], dO_ii, 0.0, dOP_iM, 'c')
for v in range(3):
gemm(1.0, dOP_iM, dPdR_avMi[b][v][Mstart:Mstop], 0.0,
work_MM, 'n')
ZE_MM = (work_MM * ET_MM).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('LCAO forces: 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('LCAO forces: atomic density')
Fatom_av = np.zeros_like(F_av)
for b in my_atom_indices:
H_ii = np.asarray(unpack(hamiltonian.dH_asp[b][kpt.s]), dtype)
HP_iM = gemmdot(H_ii, np.conj(self.P_aqMi[b][q].T))
for v in range(3):
dPdR_Mi = dPdR_avMi[b][v][Mstart:Mstop]
ArhoT_MM = (gemmdot(dPdR_Mi, HP_iM) * rhoT_MM).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('LCAO forces: atomic density')
F_av += Fkin_av + Fpot_av + Frho_av + Fatom_av
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')
