def initialize(self, paw, allocate=True):
self.allocated = False
assert hasattr(paw, 'time') and hasattr(paw, 'niter'), 'Use TDDFT!'
self.time = paw.time
self.niter = paw.niter
self.world = paw.wfs.world
self.gd = paw.density.gd
self.finegd = paw.density.finegd
self.nspins = paw.density.nspins
self.stencil = paw.input_parameters.stencils[
1] # i.e. tar['InterpolationStencil']
self.interpolator = paw.density.interpolator
self.cinterpolator = Transformer(self.gd, self.finegd, self.stencil, \
dtype=self.dtype)
self.phase_cd = np.ones((3, 2), dtype=complex)
self.Ant_sG = paw.density.nt_sG.copy() # TODO in allocate instead?
# Attach to PAW-type object
paw.attach(self, self.interval, density=paw.density)
if allocate:
self.allocate()
def interpolate_pseudo_density(self, gridrefinement=2):
gd = self.gd
Fnt_wsg = self.Fnt_wsG.copy()
# Find m for
# gridrefinement = 2**m
m1 = np.log(gridrefinement) / np.log(2.)
m = int(np.round(m1))
# Check if m is really integer
if np.absolute(m - m1) < 1e-8:
for i in range(m):
gd2 = gd.refine()
# Interpolate
interpolator = Transformer(gd,
gd2,
self.stencil,
dtype=self.dtype)
Fnt2_wsg = gd2.empty((self.nw, self.nspins), dtype=self.dtype)
for w in range(self.nw):
for s in range(self.nspins):
interpolator.apply(Fnt_wsg[w][s], Fnt2_wsg[w][s],
np.ones((3, 2), dtype=complex))
gd = gd2
Fnt_wsg = Fnt2_wsg
else:
raise NotImplementedError
return Fnt_wsg, gd
def interpolate_pseudo_density(self, gridrefinement=2):
gd = self.gd
Fnt_wsg = self.Fnt_wsG.copy()
# Find m for
# gridrefinement = 2**m
m1 = np.log(gridrefinement) / np.log(2.)
m = int(np.round(m1))
# Check if m is really integer
if np.absolute(m - m1) < 1e-8:
for i in range(m):
gd2 = gd.refine()
# Interpolate
interpolator = Transformer(gd, gd2, self.stencil,
dtype=self.dtype)
Fnt2_wsg = gd2.empty((self.nw, self.nspins), dtype=self.dtype)
for w in range(self.nw):
for s in range(self.nspins):
interpolator.apply(Fnt_wsg[w][s], Fnt2_wsg[w][s],
np.ones((3, 2), dtype=complex))
gd = gd2
Fnt_wsg = Fnt2_wsg
else:
raise NotImplementedError
return Fnt_wsg, gd
def go(comm, ngpts, repeat, narrays, out, prec):
N_c = np.array((ngpts, ngpts, ngpts))
a = 10.0
gd = GridDescriptor(N_c, (a, a, a), comm=comm))
gdcoarse = gd.coarsen()
gdfine = gd.refine()
kin1 = Laplace(gd, -0.5, 1).apply
laplace = Laplace(gd, -0.5, 2)
kin2 = laplace.apply
restrict = Transformer(gd, gdcoarse, 1).apply
interpolate = Transformer(gd, gdfine, 1).apply
precondition = Preconditioner(gd, laplace, np_float)
a1 = gd.empty(narrays)
a1[:] = 1.0
a2 = gd.empty(narrays)
c = gdcoarse.empty(narrays)
f = gdfine.empty(narrays)
T = [0, 0, 0, 0, 0]
for i in range(repeat):
comm.barrier()
kin1(a1, a2)
comm.barrier()
t0a = time()
kin1(a1, a2)
t0b = time()
comm.barrier()
t1a = time()
kin2(a1, a2)
t1b = time()
comm.barrier()
t2a = time()
for A, C in zip(a1,c):
restrict(A, C)
t2b = time()
comm.barrier()
t3a = time()
for A, F in zip(a1,f):
interpolate(A, F)
t3b = time()
comm.barrier()
if prec:
t4a = time()
for A in a1:
precondition(A, None, None, None)
t4b = time()
comm.barrier()
T[0] += t0b - t0a
T[1] += t1b - t1a
T[2] += t2b - t2a
T[3] += t3b - t3a
if prec:
T[4] += t4b - t4a
if mpi.rank == 0:
out.write(' %2d %2d %2d' % tuple(gd.parsize_c))
out.write(' %12.6f %12.6f %12.6f %12.6f %12.6f\n' %
tuple([t / repeat / narrays for t in T]))
out.flush()
def set_grid_descriptor(self, gd):
self.gd = gd
self.gds = [gd]
self.dv = gd.dv
gd = self.gd
self.B = None
self.interpolators = []
self.restrictors = []
self.operators = []
level = 0
self.presmooths = [2]
self.postsmooths = [1]
self.weights = [2. / 3.]
while level < 8:
try:
gd2 = gd.coarsen()
except ValueError:
break
self.gds.append(gd2)
self.interpolators.append(Transformer(gd2, gd))
self.restrictors.append(Transformer(gd, gd2))
self.presmooths.append(4)
self.postsmooths.append(4)
self.weights.append(1.0)
level += 1
gd = gd2
self.levels = level
def set_grid_descriptor(self, gd):
# Should probably be renamed initialize
self.gd = gd
scale = -0.25 / pi
if self.nn == 'M':
if not gd.orthogonal:
raise RuntimeError('Cannot use Mehrstellen stencil with '
'non orthogonal cell.')
self.operators = [LaplaceA(gd, -scale)]
self.B = LaplaceB(gd)
else:
self.operators = [Laplace(gd, scale, self.nn)]
self.B = None
self.interpolators = []
self.restrictors = []
level = 0
self.presmooths = [2]
self.postsmooths = [1]
# Weights for the relaxation,
# only used if 'J' (Jacobi) is chosen as method
self.weights = [2.0 / 3.0]
while level < 8:
try:
gd2 = gd.coarsen()
except ValueError:
break
self.operators.append(Laplace(gd2, scale, 1))
self.interpolators.append(Transformer(gd2, gd))
self.restrictors.append(Transformer(gd, gd2))
self.presmooths.append(4)
self.postsmooths.append(4)
self.weights.append(1.0)
level += 1
gd = gd2
self.levels = level
if self.operators[-1].gd.N_c.max() > 36:
# Try to warn exactly once no matter how one uses the solver.
if gd.comm.parent is None:
warn = (gd.comm.rank == 0)
else:
warn = (gd.comm.parent.rank == 0)
if warn:
warntxt = '\n'.join([POISSON_GRID_WARNING, '',
self.get_description()])
else:
warntxt = ('Poisson warning from domain rank %d'
% self.gd.comm.rank)
# Warn from all ranks to avoid deadlocks.
warnings.warn(warntxt, stacklevel=2)
def get_combined_data(self, qmdata=None, cldata=None, spacing=None):
if qmdata is None:
qmdata = self.density.rhot_g
if cldata is None:
cldata = self.classical_material.charge_density
if spacing is None:
spacing = self.cl.gd.h_cv[0, 0]
spacing_au = spacing / Bohr # from Angstroms to a.u.
# Collect data from different processes
cln = self.cl.gd.collect(cldata)
qmn = self.qm.gd.collect(qmdata)
clgd = GridDescriptor(self.cl.gd.N_c, self.cl.cell, False, serial_comm,
None)
if world.rank == 0:
cln *= self.classical_material.sign
# refine classical part
while clgd.h_cv[0, 0] > spacing_au * 1.50: # 45:
cln = Transformer(clgd, clgd.refine()).apply(cln)
clgd = clgd.refine()
# refine quantum part
qmgd = GridDescriptor(self.qm.gd.N_c, self.qm.cell, False,
serial_comm, None)
while qmgd.h_cv[0, 0] < clgd.h_cv[0, 0] * 0.95:
qmn = Transformer(qmgd, qmgd.coarsen()).apply(qmn)
qmgd = qmgd.coarsen()
assert np.all(qmgd.h_cv == clgd.h_cv
), " Spacings %.8f (qm) and %.8f (cl) Angstroms" % (
qmgd.h_cv[0][0] * Bohr, clgd.h_cv[0][0] * Bohr)
# now find the corners
r_gv_cl = clgd.get_grid_point_coordinates().transpose((1, 2, 3, 0))
cind = self.qm.corner1 / np.diag(clgd.h_cv) - 1
n = qmn.shape
# print 'Corner points: ', self.qm.corner1*Bohr, ' - ', self.qm.corner2*Bohr
# print 'Calculated points: ', r_gv_cl[tuple(cind)]*Bohr, ' - ', r_gv_cl[tuple(cind+n+1)]*Bohr
cln[cind[0] + 1:cind[0] + n[0] + 1, cind[1] + 1:cind[1] + n[1] + 1,
cind[2] + 1:cind[2] + n[2] + 1] += qmn
world.barrier()
return cln, clgd
def interpolate_2d(mat):
from gpaw.grid_descriptor import GridDescriptor
from gpaw.transformers import Transformer
nn = 10
N_c = np.zeros([3], dtype=int)
N_c[1:] = mat.shape[:2]
N_c[0] = nn
bmat = np.resize(mat, N_c)
gd = GridDescriptor(N_c, N_c)
finegd = GridDescriptor(N_c * 2, N_c)
interpolator = Transformer(gd, finegd, 3)
fine_bmat = finegd.zeros()
interpolator.apply(bmat, fine_bmat)
return fine_bmat[0]
def initialize(self, density, hamiltonian, wfs, occupations):
assert wfs.kd.gamma
self.xc.initialize(density, hamiltonian, wfs, occupations)
self.kpt_comm = wfs.kd.comm
self.nspins = wfs.nspins
self.setups = wfs.setups
self.density = density
self.kpt_u = wfs.kpt_u
self.exx_s = np.zeros(self.nspins)
self.ekin_s = np.zeros(self.nspins)
self.nocc_s = np.empty(self.nspins, int)
self.gd = density.gd
self.redistributor = density.redistributor
use_charge_center = hamiltonian.poisson.use_charge_center
# XXX How do we construct a copy of the Poisson solver of the
# Hamiltonian? We don't know what class it is, etc., but gd
# may differ.
# XXX One might consider using a charged centered compensation
# charge for the PoissonSolver in the case of EXX as standard
self.poissonsolver = PoissonSolver('fd',
eps=1e-11,
use_charge_center=use_charge_center)
# self.poissonsolver = hamiltonian.poisson
if self.finegrid:
self.finegd = self.gd.refine()
# XXX Taking restrictor from Hamiltonian will not work in PW mode,
# will it? I think this supports only real-space mode.
# self.restrictor = hamiltonian.restrictor
self.restrictor = Transformer(self.finegd, self.gd, 3)
self.interpolator = Transformer(self.gd, self.finegd, 3)
else:
self.finegd = self.gd
self.ghat = LFC(self.finegd,
[setup.ghat_l for setup in density.setups],
integral=np.sqrt(4 * np.pi),
forces=True)
self.poissonsolver.set_grid_descriptor(self.finegd)
if self.rsf == 'Yukawa':
omega2 = self.omega**2
self.screened_poissonsolver = HelmholtzSolver(
k2=-omega2,
eps=1e-11,
nn=3,
use_charge_center=use_charge_center)
self.screened_poissonsolver.set_grid_descriptor(self.finegd)
def __init__(self,
gd,
finegd,
nspins,
setups,
timer,
xc,
world,
kptband_comm,
vext=None,
collinear=True,
psolver=None,
stencil=3):
Hamiltonian.__init__(self, gd, finegd, nspins, setups, timer, xc,
world, kptband_comm, vext, collinear)
# Solver for the Poisson equation:
if psolver is None:
psolver = PoissonSolver(nn=3, relax='J')
self.poisson = psolver
self.poisson.set_grid_descriptor(finegd)
# Restrictor function for the potential:
self.restrictor = Transformer(self.finegd, self.gd, stencil)
self.restrict = self.restrictor.apply
self.vbar = LFC(self.finegd, [[setup.vbar] for setup in setups],
forces=True)
self.vbar_g = None
def writearray(name):
if name.split('_')[0] in writes:
a_xg = getattr(self, name)
if self.fdtd.cl.gd != self.gd:
a_xg = Transformer(self.fdtd.cl.gd, self.gd, self.stencil,
a_xg.dtype).apply(a_xg)
writer.write(**{name: self.gd.collect(a_xg)})
def set_grid_descriptor(self, gd):
# Should probably be renamed initialize
self.gd = gd
self.dv = gd.dv
gd = self.gd
scale = -0.25 / pi
if self.nn == 'M':
raise ValueError('Helmholtz not defined for Mehrstellen stencil')
self.operators = [HelmholtzOperator(gd, scale, self.nn, k2=self.k2)]
self.B = None
self.interpolators = []
self.restrictors = []
level = 0
self.presmooths = [2]
self.postsmooths = [1]
# Weights for the relaxation,
# only used if 'J' (Jacobi) is chosen as method
self.weights = [2.0 / 3.0]
while level < 4:
try:
gd2 = gd.coarsen()
except ValueError:
break
self.operators.append(HelmholtzOperator(gd2, scale, 1, k2=self.k2))
self.interpolators.append(Transformer(gd2, gd))
self.restrictors.append(Transformer(gd, gd2))
self.presmooths.append(4)
self.postsmooths.append(4)
self.weights.append(1.0)
level += 1
gd = gd2
self.levels = level
if self.relax_method == 1:
self.description = 'Gauss-Seidel'
else:
self.description = 'Jacobi'
self.description += ' solver with %d multi-grid levels' % (level + 1)
self.description += '\nStencil: ' + self.operators[0].description
def initialize(self, setups, timer, magmom_av, hund):
Density.initialize(self, setups, timer, magmom_av, hund)
# Interpolation function for the density:
self.interpolator = Transformer(self.gd, self.finegd, self.stencil)
spline_aj = []
for setup in setups:
if setup.nct is None:
spline_aj.append([])
else:
spline_aj.append([setup.nct])
self.nct = LFC(self.gd, spline_aj,
integral=[setup.Nct for setup in setups],
forces=True, cut=True)
self.ghat = LFC(self.finegd, [setup.ghat_l for setup in setups],
integral=sqrt(4 * pi), forces=True)
def set_grid_descriptor(self, gd):
# Should probably be renamed initialize
self.gd = gd
self.dv = gd.dv
gd = self.gd
scale = -0.25 / pi
if self.nn == 'M':
if not gd.orthogonal:
raise RuntimeError('Cannot use Mehrstellen stencil with '
'non orthogonal cell.')
self.operators = [LaplaceA(gd, -scale, allocate=False)]
self.B = LaplaceB(gd, allocate=False)
else:
self.operators = [Laplace(gd, scale, self.nn, allocate=False)]
self.B = None
self.interpolators = []
self.restrictors = []
level = 0
self.presmooths = [2]
self.postsmooths = [1]
# Weights for the relaxation,
# only used if 'J' (Jacobi) is chosen as method
self.weights = [2.0 / 3.0]
while level < 4:
try:
gd2 = gd.coarsen()
except ValueError:
break
self.operators.append(Laplace(gd2, scale, 1, allocate=False))
self.interpolators.append(Transformer(gd2, gd, allocate=False))
self.restrictors.append(Transformer(gd, gd2, allocate=False))
self.presmooths.append(4)
self.postsmooths.append(4)
self.weights.append(1.0)
level += 1
gd = gd2
self.levels = level
def __init__(self, gd, finegd, nspins, setups, stencil, timer, xc,
psolver, vext_g):
"""Create the Hamiltonian."""
self.gd = gd
self.finegd = finegd
self.nspins = nspins
self.setups = setups
self.timer = timer
self.xc = xc
# Solver for the Poisson equation:
if psolver is None:
psolver = PoissonSolver(nn=3, relax='J')
self.poisson = psolver
self.poisson.set_grid_descriptor(finegd)
self.dH_asp = None
# The external potential
self.vext_g = vext_g
self.vt_sG = None
self.vHt_g = None
self.vt_sg = None
self.vbar_g = None
self.rank_a = None
# Restrictor function for the potential:
self.restrictor = Transformer(self.finegd, self.gd, stencil,
allocate=False)
self.restrict = self.restrictor.apply
self.vbar = LFC(self.finegd, [[setup.vbar] for setup in setups],
forces=True)
self.Ekin0 = None
self.Ekin = None
self.Epot = None
self.Ebar = None
self.Eext = None
self.Exc = None
self.Etot = None
self.S = None
self.allocated = False
def __init__(self, gd0, kin0, dtype=float, block=1):
gd1 = gd0.coarsen()
gd2 = gd1.coarsen()
self.kin0 = kin0
self.kin1 = Laplace(gd1, -0.5, 1, dtype)
self.kin2 = Laplace(gd2, -0.5, 1, dtype)
self.scratch0 = gd0.zeros((2, block), dtype, False)
self.scratch1 = gd1.zeros((3, block), dtype, False)
self.scratch2 = gd2.zeros((3, block), dtype, False)
self.step = 0.66666666 / kin0.get_diagonal_element()
self.restrictor_object0 = Transformer(gd0, gd1, 1, dtype)
self.restrictor_object1 = Transformer(gd1, gd2, 1, dtype)
self.interpolator_object2 = Transformer(gd2, gd1, 1, dtype)
self.interpolator_object1 = Transformer(gd1, gd0, 1, dtype)
self.restrictor0 = self.restrictor_object0.apply
self.restrictor1 = self.restrictor_object1.apply
self.interpolator2 = self.interpolator_object2.apply
self.interpolator1 = self.interpolator_object1.apply
def get_induced_density(self, from_density, gridrefinement):
if self.gd == self.fdtd.cl.gd:
Frho_wg = self.Fn_wG.copy()
else:
Frho_wg = Transformer(self.fdtd.cl.gd,
self.gd,
self.stencil,
dtype=self.dtype).apply(self.Fn_wG)
Frho_wg, gd = self.interpolate_density(self.gd, Frho_wg,
gridrefinement)
return Frho_wg, gd
def __init__(self,
gd,
finegd,
nspins,
setups,
timer,
xc,
world,
vext=None,
psolver=None,
stencil=3,
redistributor=None):
Hamiltonian.__init__(self,
gd,
finegd,
nspins,
setups,
timer,
xc,
world,
vext=vext,
redistributor=redistributor)
# Solver for the Poisson equation:
if psolver is None:
psolver = {}
if isinstance(psolver, dict):
psolver = create_poisson_solver(**psolver)
self.poisson = psolver
self.poisson.set_grid_descriptor(self.finegd)
# Restrictor function for the potential:
self.restrictor = Transformer(self.finegd, self.redistributor.aux_gd,
stencil)
self.restrict = self.restrictor.apply
self.vbar = LFC(self.finegd, [[setup.vbar] for setup in setups],
forces=True)
self.vbar_g = None
def initialize(self, density, hamiltonian, wfs, occupations):
assert wfs.kd.gamma
self.xc.initialize(density, hamiltonian, wfs, occupations)
self.kpt_comm = wfs.kd.comm
self.nspins = wfs.nspins
self.setups = wfs.setups
self.density = density
self.kpt_u = wfs.kpt_u
self.exx_s = np.zeros(self.nspins)
self.ekin_s = np.zeros(self.nspins)
self.nocc_s = np.empty(self.nspins, int)
self.gd = density.gd
self.redistributor = density.redistributor
# XXX How do we construct a copy of the Poisson solver of the
# Hamiltonian? We don't know what class it is, etc., but gd
# may differ.
self.poissonsolver = PoissonSolver(eps=1e-11)
#self.poissonsolver = hamiltonian.poisson
if self.finegrid:
self.finegd = self.gd.refine()
# XXX Taking restrictor from Hamiltonian will not work in PW mode,
# will it? I think this supports only real-space mode.
#self.restrictor = hamiltonian.restrictor
self.restrictor = Transformer(self.finegd, self.gd, 3)
self.interpolator = Transformer(self.gd, self.finegd, 3)
else:
self.finegd = self.gd
self.ghat = LFC(self.finegd,
[setup.ghat_l for setup in density.setups],
integral=np.sqrt(4 * np.pi),
forces=True)
self.poissonsolver.set_grid_descriptor(self.finegd)
self.poissonsolver.initialize()
def initialize(self, setups, stencil, timer, magmom_a, hund):
self.timer = timer
self.setups = setups
self.hund = hund
self.magmom_a = magmom_a
# Interpolation function for the density:
self.interpolator = Transformer(self.gd, self.finegd, stencil,
allocate=False)
spline_aj = []
for setup in setups:
if setup.nct is None:
spline_aj.append([])
else:
spline_aj.append([setup.nct])
self.nct = LFC(self.gd, spline_aj,
integral=[setup.Nct for setup in setups],
forces=True, cut=True)
self.ghat = LFC(self.finegd, [setup.ghat_l for setup in setups],
integral=sqrt(4 * pi), forces=True)
if self.allocated:
self.allocated = False
self.allocate()
def initialize(self, setups, timer, magmom_av, hund):
Density.initialize(self, setups, timer, magmom_av, hund)
# Interpolation function for the density:
self.interpolator = Transformer(self.gd, self.finegd, self.stencil)
spline_aj = []
for setup in setups:
if setup.nct is None:
spline_aj.append([])
else:
spline_aj.append([setup.nct])
self.nct = LFC(self.gd, spline_aj,
integral=[setup.Nct for setup in setups],
forces=True, cut=True)
self.ghat = LFC(self.finegd, [setup.ghat_l for setup in setups],
integral=sqrt(4 * pi), forces=True)
def initialize(self, paw, allocate=True):
self.allocated = False
assert hasattr(paw, 'time') and hasattr(paw, 'niter'), 'Use TDDFT!'
self.time = paw.time
self.niter = paw.niter
self.world = paw.wfs.world
self.gd = paw.density.gd
self.finegd = paw.density.finegd
self.nspins = paw.density.nspins
self.stencil = paw.input_parameters.stencils[1] # i.e. tar['InterpolationStencil']
self.interpolator = paw.density.interpolator
self.cinterpolator = Transformer(self.gd, self.finegd, self.stencil, \
dtype=self.dtype, allocate=False)
self.phase_cd = np.ones((3, 2), dtype=complex)
self.Ant_sG = paw.density.nt_sG.copy() # TODO in allocate instead?
# Attach to PAW-type object
paw.attach(self, self.interval, density=paw.density)
if allocate:
self.allocate()
def get_all_electron_density(self, atoms, gridrefinement=2):
"""Return real all-electron density array."""
# Refinement of coarse grid, for representation of the AE-density
if gridrefinement == 1:
gd = self.gd
n_sg = self.nt_sG.copy()
elif gridrefinement == 2:
gd = self.finegd
if self.nt_sg is None:
self.interpolate()
n_sg = self.nt_sg.copy()
elif gridrefinement == 4:
# Extra fine grid
gd = self.finegd.refine()
# Interpolation function for the density:
interpolator = Transformer(self.finegd, gd, 3)
# Transfer the pseudo-density to the fine grid:
n_sg = gd.empty(self.nspins)
if self.nt_sg is None:
self.interpolate()
for s in range(self.nspins):
interpolator.apply(self.nt_sg[s], n_sg[s])
else:
raise NotImplementedError
# Add corrections to pseudo-density to get the AE-density
splines = {}
phi_aj = []
phit_aj = []
nc_a = []
nct_a = []
for a, id in enumerate(self.setups.id_a):
if id in splines:
phi_j, phit_j, nc, nct = splines[id]
else:
# Load splines:
phi_j, phit_j, nc, nct = self.setups[a].get_partial_waves()[:4]
splines[id] = (phi_j, phit_j, nc, nct)
phi_aj.append(phi_j)
phit_aj.append(phit_j)
nc_a.append([nc])
nct_a.append([nct])
# Create localized functions from splines
phi = LFC(gd, phi_aj)
phit = LFC(gd, phit_aj)
nc = LFC(gd, nc_a)
nct = LFC(gd, nct_a)
spos_ac = atoms.get_scaled_positions() % 1.0
phi.set_positions(spos_ac)
phit.set_positions(spos_ac)
nc.set_positions(spos_ac)
nct.set_positions(spos_ac)
all_D_asp = []
for a, setup in enumerate(self.setups):
D_sp = self.D_asp.get(a)
if D_sp is None:
ni = setup.ni
D_sp = np.empty((self.nspins, ni * (ni + 1) // 2))
if gd.comm.size > 1:
gd.comm.broadcast(D_sp, self.rank_a[a])
all_D_asp.append(D_sp)
for s in range(self.nspins):
I_a = np.zeros(len(atoms))
nc.add1(n_sg[s], 1.0 / self.nspins, I_a)
nct.add1(n_sg[s], -1.0 / self.nspins, I_a)
phi.add2(n_sg[s], all_D_asp, s, 1.0, I_a)
phit.add2(n_sg[s], all_D_asp, s, -1.0, I_a)
for a, D_sp in self.D_asp.items():
setup = self.setups[a]
I_a[a] -= ((setup.Nc - setup.Nct) / self.nspins +
sqrt(4 * pi) *
np.dot(D_sp[s], setup.Delta_pL[:, 0]))
gd.comm.sum(I_a)
N_c = gd.N_c
g_ac = np.around(N_c * spos_ac).astype(int) % N_c - gd.beg_c
for I, g_c in zip(I_a, g_ac):
if (g_c >= 0).all() and (g_c < gd.n_c).all():
n_sg[s][tuple(g_c)] -= I / gd.dv
return n_sg, gd
class Density:
"""Density object.
Attributes:
=============== =====================================================
``gd`` Grid descriptor for coarse grids.
``finegd`` Grid descriptor for fine grids.
``interpolate`` Function for interpolating the electron density.
``mixer`` ``DensityMixer`` object.
=============== =====================================================
Soft and smooth pseudo functions on uniform 3D grids:
========== =========================================
``nt_sG`` Electron density on the coarse grid.
``nt_sg`` Electron density on the fine grid.
``nt_g`` Electron density on the fine grid.
``rhot_g`` Charge density on the fine grid.
``nct_G`` Core electron-density on the coarse grid.
========== =========================================
"""
def __init__(self, gd, finegd, nspins, charge):
"""Create the Density object."""
self.gd = gd
self.finegd = finegd
self.nspins = nspins
self.charge = float(charge)
self.charge_eps = 1e-7
self.D_asp = None
self.Q_aL = None
self.nct_G = None
self.nt_sG = None
self.rhot_g = None
self.nt_sg = None
self.nt_g = None
self.rank_a = None
self.mixer = BaseMixer()
self.timer = nulltimer
self.allocated = False
def initialize(self, setups, stencil, timer, magmom_a, hund):
self.timer = timer
self.setups = setups
self.hund = hund
self.magmom_a = magmom_a
# Interpolation function for the density:
self.interpolator = Transformer(self.gd, self.finegd, stencil,
allocate=False)
spline_aj = []
for setup in setups:
if setup.nct is None:
spline_aj.append([])
else:
spline_aj.append([setup.nct])
self.nct = LFC(self.gd, spline_aj,
integral=[setup.Nct for setup in setups],
forces=True, cut=True)
self.ghat = LFC(self.finegd, [setup.ghat_l for setup in setups],
integral=sqrt(4 * pi), forces=True)
if self.allocated:
self.allocated = False
self.allocate()
def allocate(self):
assert not self.allocated
self.interpolator.allocate()
self.allocated = True
def reset(self):
# TODO: reset other parameters?
self.nt_sG = None
def set_positions(self, spos_ac, rank_a=None):
if not self.allocated:
self.allocate()
self.nct.set_positions(spos_ac)
self.ghat.set_positions(spos_ac)
self.mixer.reset()
self.nct_G = self.gd.zeros()
self.nct.add(self.nct_G, 1.0 / self.nspins)
#self.nt_sG = None
self.nt_sg = None
self.nt_g = None
self.rhot_g = None
self.Q_aL = None
# If both old and new atomic ranks are present, start a blank dict if
# it previously didn't exist but it will needed for the new atoms.
if (self.rank_a is not None and rank_a is not None and
self.D_asp is None and (rank_a == self.gd.comm.rank).any()):
self.D_asp = {}
if self.rank_a is not None and self.D_asp is not None:
self.timer.start('Redistribute')
requests = []
flags = (self.rank_a != rank_a)
my_incoming_atom_indices = np.argwhere(np.bitwise_and(flags, \
rank_a == self.gd.comm.rank)).ravel()
my_outgoing_atom_indices = np.argwhere(np.bitwise_and(flags, \
self.rank_a == self.gd.comm.rank)).ravel()
for a in my_incoming_atom_indices:
# Get matrix from old domain:
ni = self.setups[a].ni
D_sp = np.empty((self.nspins, ni * (ni + 1) // 2))
requests.append(self.gd.comm.receive(D_sp, self.rank_a[a],
tag=a, block=False))
assert a not in self.D_asp
self.D_asp[a] = D_sp
for a in my_outgoing_atom_indices:
# Send matrix to new domain:
D_sp = self.D_asp.pop(a)
requests.append(self.gd.comm.send(D_sp, rank_a[a],
tag=a, block=False))
self.gd.comm.waitall(requests)
self.timer.stop('Redistribute')
self.rank_a = rank_a
def calculate_pseudo_density(self, wfs):
"""Calculate nt_sG from scratch.
nt_sG will be equal to nct_G plus the contribution from
wfs.add_to_density().
"""
wfs.calculate_density_contribution(self.nt_sG)
self.nt_sG += self.nct_G
def update(self, wfs):
self.timer.start('Density')
self.timer.start('Pseudo density')
self.calculate_pseudo_density(wfs)
self.timer.stop('Pseudo density')
self.timer.start('Atomic density matrices')
wfs.calculate_atomic_density_matrices(self.D_asp)
self.timer.stop('Atomic density matrices')
self.timer.start('Multipole moments')
comp_charge = self.calculate_multipole_moments()
self.timer.stop('Multipole moments')
if isinstance(wfs, LCAOWaveFunctions):
self.timer.start('Normalize')
self.normalize(comp_charge)
self.timer.stop('Normalize')
self.timer.start('Mix')
self.mix(comp_charge)
self.timer.stop('Mix')
self.timer.stop('Density')
def normalize(self, comp_charge=None):
"""Normalize pseudo density."""
if comp_charge is None:
comp_charge = self.calculate_multipole_moments()
pseudo_charge = self.gd.integrate(self.nt_sG).sum()
if pseudo_charge + self.charge + comp_charge != 0:
if pseudo_charge != 0:
x = -(self.charge + comp_charge) / pseudo_charge
self.nt_sG *= x
else:
# Use homogeneous background:
self.nt_sG[:] = (self.charge + comp_charge) * self.gd.dv
def calculate_pseudo_charge(self, comp_charge):
self.nt_g = self.nt_sg.sum(axis=0)
self.rhot_g = self.nt_g.copy()
self.ghat.add(self.rhot_g, self.Q_aL)
if debug:
charge = self.finegd.integrate(self.rhot_g) + self.charge
if abs(charge) > self.charge_eps:
raise RuntimeError('Charge not conserved: excess=%.9f' %
charge)
def mix(self, comp_charge):
if not self.mixer.mix_rho:
self.mixer.mix(self)
comp_charge = None
self.interpolate(comp_charge)
self.calculate_pseudo_charge(comp_charge)
if self.mixer.mix_rho:
self.mixer.mix(self)
def interpolate(self, comp_charge=None):
"""Interpolate pseudo density to fine grid."""
if comp_charge is None:
comp_charge = self.calculate_multipole_moments()
if self.nt_sg is None:
self.nt_sg = self.finegd.empty(self.nspins)
for s in range(self.nspins):
self.interpolator.apply(self.nt_sG[s], self.nt_sg[s])
# With periodic boundary conditions, the interpolation will
# conserve the number of electrons.
if not self.gd.pbc_c.all():
# With zero-boundary conditions in one or more directions,
# this is not the case.
pseudo_charge = -(self.charge + comp_charge)
if abs(pseudo_charge) > 1.0e-14:
x = pseudo_charge / self.finegd.integrate(self.nt_sg).sum()
self.nt_sg *= x
def calculate_multipole_moments(self):
"""Calculate multipole moments of compensation charges.
Returns the total compensation charge in units of electron
charge, so the number will be negative because of the
dominating contribution from the nuclear charge."""
comp_charge = 0.0
self.Q_aL = {}
for a, D_sp in self.D_asp.items():
Q_L = self.Q_aL[a] = np.dot(D_sp.sum(0), self.setups[a].Delta_pL)
Q_L[0] += self.setups[a].Delta0
comp_charge += Q_L[0]
return self.gd.comm.sum(comp_charge) * sqrt(4 * pi)
def initialize_from_atomic_densities(self, basis_functions):
"""Initialize D_asp, nt_sG and Q_aL from atomic densities.
nt_sG is initialized from atomic orbitals, and will
be constructed with the specified magnetic moments and
obeying Hund's rules if ``hund`` is true."""
# XXX does this work with blacs? What should be distributed?
# Apparently this doesn't use blacs at all, so it's serial
# with respect to the blacs distribution. That means it works
# but is not particularly efficient (not that this is a time
# consuming step)
f_sM = np.empty((self.nspins, basis_functions.Mmax))
self.D_asp = {}
f_asi = {}
for a in basis_functions.atom_indices:
c = self.charge / len(self.setups) # distribute on all atoms
f_si = self.setups[a].calculate_initial_occupation_numbers(
self.magmom_a[a], self.hund, charge=c, nspins=self.nspins)
if a in basis_functions.my_atom_indices:
self.D_asp[a] = self.setups[a].initialize_density_matrix(f_si)
f_asi[a] = f_si
self.nt_sG = self.gd.zeros(self.nspins)
basis_functions.add_to_density(self.nt_sG, f_asi)
self.nt_sG += self.nct_G
self.calculate_normalized_charges_and_mix()
def initialize_from_wavefunctions(self, wfs):
"""Initialize D_asp, nt_sG and Q_aL from wave functions."""
self.nt_sG = self.gd.empty(self.nspins)
self.calculate_pseudo_density(wfs)
self.D_asp = {}
my_atom_indices = np.argwhere(wfs.rank_a == self.gd.comm.rank).ravel()
for a in my_atom_indices:
ni = self.setups[a].ni
self.D_asp[a] = np.empty((self.nspins, ni * (ni + 1) // 2))
wfs.calculate_atomic_density_matrices(self.D_asp)
self.calculate_normalized_charges_and_mix()
def initialize_directly_from_arrays(self, nt_sG, D_asp):
"""Set D_asp and nt_sG directly."""
self.nt_sG = nt_sG
self.D_asp = D_asp
#self.calculate_normalized_charges_and_mix()
# No calculate multipole moments? Tests will fail because of
# improperly initialized mixer
def calculate_normalized_charges_and_mix(self):
comp_charge = self.calculate_multipole_moments()
self.normalize(comp_charge)
self.mix(comp_charge)
def set_mixer(self, mixer):
if mixer is not None:
if self.nspins == 1 and isinstance(mixer, MixerSum):
raise RuntimeError('Cannot use MixerSum with nspins==1')
self.mixer = mixer
else:
if self.gd.pbc_c.any():
beta = 0.1
weight = 50.0
else:
beta = 0.25
weight = 1.0
if self.nspins == 2:
self.mixer = MixerSum(beta=beta, weight=weight)
else:
self.mixer = Mixer(beta=beta, weight=weight)
self.mixer.initialize(self)
def estimate_magnetic_moments(self):
magmom_a = np.zeros_like(self.magmom_a)
if self.nspins == 2:
for a, D_sp in self.D_asp.items():
magmom_a[a] = np.dot(D_sp[0] - D_sp[1], self.setups[a].N0_p)
self.gd.comm.sum(magmom_a)
return magmom_a
def get_correction(self, a, spin):
"""Integrated atomic density correction.
Get the integrated correction to the pseuso density relative to
the all-electron density.
"""
setup = self.setups[a]
return sqrt(4 * pi) * (
np.dot(self.D_asp[a][spin], setup.Delta_pL[:, 0])
+ setup.Delta0 / self.nspins)
def get_density_array(self):
XXX
# XXX why not replace with get_spin_density and get_total_density?
"""Return pseudo-density array."""
if self.nspins == 2:
return self.nt_sG
else:
return self.nt_sG[0]
def get_all_electron_density(self, atoms, gridrefinement=2):
"""Return real all-electron density array."""
# Refinement of coarse grid, for representation of the AE-density
if gridrefinement == 1:
gd = self.gd
n_sg = self.nt_sG.copy()
elif gridrefinement == 2:
gd = self.finegd
if self.nt_sg is None:
self.interpolate()
n_sg = self.nt_sg.copy()
elif gridrefinement == 4:
# Extra fine grid
gd = self.finegd.refine()
# Interpolation function for the density:
interpolator = Transformer(self.finegd, gd, 3)
# Transfer the pseudo-density to the fine grid:
n_sg = gd.empty(self.nspins)
if self.nt_sg is None:
self.interpolate()
for s in range(self.nspins):
interpolator.apply(self.nt_sg[s], n_sg[s])
else:
raise NotImplementedError
# Add corrections to pseudo-density to get the AE-density
splines = {}
phi_aj = []
phit_aj = []
nc_a = []
nct_a = []
for a, id in enumerate(self.setups.id_a):
if id in splines:
phi_j, phit_j, nc, nct = splines[id]
else:
# Load splines:
phi_j, phit_j, nc, nct = self.setups[a].get_partial_waves()[:4]
splines[id] = (phi_j, phit_j, nc, nct)
phi_aj.append(phi_j)
phit_aj.append(phit_j)
nc_a.append([nc])
nct_a.append([nct])
# Create localized functions from splines
phi = LFC(gd, phi_aj)
phit = LFC(gd, phit_aj)
nc = LFC(gd, nc_a)
nct = LFC(gd, nct_a)
spos_ac = atoms.get_scaled_positions() % 1.0
phi.set_positions(spos_ac)
phit.set_positions(spos_ac)
nc.set_positions(spos_ac)
nct.set_positions(spos_ac)
all_D_asp = []
for a, setup in enumerate(self.setups):
D_sp = self.D_asp.get(a)
if D_sp is None:
ni = setup.ni
D_sp = np.empty((self.nspins, ni * (ni + 1) // 2))
if gd.comm.size > 1:
gd.comm.broadcast(D_sp, self.rank_a[a])
all_D_asp.append(D_sp)
for s in range(self.nspins):
I_a = np.zeros(len(atoms))
nc.add1(n_sg[s], 1.0 / self.nspins, I_a)
nct.add1(n_sg[s], -1.0 / self.nspins, I_a)
phi.add2(n_sg[s], all_D_asp, s, 1.0, I_a)
phit.add2(n_sg[s], all_D_asp, s, -1.0, I_a)
for a, D_sp in self.D_asp.items():
setup = self.setups[a]
I_a[a] -= ((setup.Nc - setup.Nct) / self.nspins +
sqrt(4 * pi) *
np.dot(D_sp[s], setup.Delta_pL[:, 0]))
gd.comm.sum(I_a)
N_c = gd.N_c
g_ac = np.around(N_c * spos_ac).astype(int) % N_c - gd.beg_c
for I, g_c in zip(I_a, g_ac):
if (g_c >= 0).all() and (g_c < gd.n_c).all():
n_sg[s][tuple(g_c)] -= I / gd.dv
return n_sg, gd
def new_get_all_electron_density(self, atoms, gridrefinement=2):
"""Return real all-electron density array."""
# Refinement of coarse grid, for representation of the AE-density
if gridrefinement == 1:
gd = self.gd
n_sg = self.nt_sG.copy()
elif gridrefinement == 2:
gd = self.finegd
if self.nt_sg is None:
self.interpolate()
n_sg = self.nt_sg.copy()
elif gridrefinement == 4:
# Extra fine grid
gd = self.finegd.refine()
# Interpolation function for the density:
interpolator = Transformer(self.finegd, gd, 3)
# Transfer the pseudo-density to the fine grid:
n_sg = gd.empty(self.nspins)
if self.nt_sg is None:
self.interpolate()
for s in range(self.nspins):
interpolator.apply(self.nt_sg[s], n_sg[s])
else:
raise NotImplementedError
# Add corrections to pseudo-density to get the AE-density
splines = {}
phi_aj = []
phit_aj = []
nc_a = []
nct_a = []
for a, id in enumerate(self.setups.id_a):
if id in splines:
phi_j, phit_j, nc, nct = splines[id]
else:
# Load splines:
phi_j, phit_j, nc, nct = self.setups[a].get_partial_waves()[:4]
splines[id] = (phi_j, phit_j, nc, nct)
phi_aj.append(phi_j)
phit_aj.append(phit_j)
nc_a.append([nc])
nct_a.append([nct])
# Create localized functions from splines
phi = BasisFunctions(gd, phi_aj)
phit = BasisFunctions(gd, phit_aj)
nc = LFC(gd, nc_a)
nct = LFC(gd, nct_a)
spos_ac = atoms.get_scaled_positions() % 1.0
phi.set_positions(spos_ac)
phit.set_positions(spos_ac)
nc.set_positions(spos_ac)
nct.set_positions(spos_ac)
I_sa = np.zeros((self.nspins, len(atoms)))
a_W = np.empty(len(phi.M_W), np.int32)
W = 0
for a in phi.atom_indices:
nw = len(phi.sphere_a[a].M_w)
a_W[W:W + nw] = a
W += nw
rho_MM = np.zeros((phi.Mmax, phi.Mmax))
for s, I_a in enumerate(I_sa):
M1 = 0
for a, setup in enumerate(self.setups):
ni = setup.ni
D_sp = self.D_asp.get(a)
if D_sp is None:
D_sp = np.empty((self.nspins, ni * (ni + 1) // 2))
else:
I_a[a] = ((setup.Nct - setup.Nc) / self.nspins -
sqrt(4 * pi) *
np.dot(D_sp[s], setup.Delta_pL[:, 0]))
if gd.comm.size > 1:
gd.comm.broadcast(D_sp, self.rank_a[a])
M2 = M1 + ni
rho_MM[M1:M2, M1:M2] = unpack2(D_sp[s])
M1 = M2
phi.lfc.ae_valence_density_correction(rho_MM, n_sg[s], a_W, I_a)
phit.lfc.ae_valence_density_correction(-rho_MM, n_sg[s], a_W, I_a)
a_W = np.empty(len(nc.M_W), np.int32)
W = 0
for a in nc.atom_indices:
nw = len(nc.sphere_a[a].M_w)
a_W[W:W + nw] = a
W += nw
scale = 1.0 / self.nspins
for s, I_a in enumerate(I_sa):
nc.lfc.ae_core_density_correction(scale, n_sg[s], a_W, I_a)
nct.lfc.ae_core_density_correction(-scale, n_sg[s], a_W, I_a)
gd.comm.sum(I_a)
N_c = gd.N_c
g_ac = np.around(N_c * spos_ac).astype(int) % N_c - gd.beg_c
for I, g_c in zip(I_a, g_ac):
if (g_c >= 0).all() and (g_c < gd.n_c).all():
n_sg[s][tuple(g_c)] -= I / gd.dv
return n_sg, gd
if extra_parameters.get('usenewlfc', True):
get_all_electron_density = new_get_all_electron_density
def estimate_memory(self, mem):
nspins = self.nspins
nbytes = self.gd.bytecount()
nfinebytes = self.finegd.bytecount()
arrays = mem.subnode('Arrays')
for name, size in [('nt_sG', nbytes * nspins),
('nt_sg', nfinebytes * nspins),
('nt_g', nfinebytes),
('rhot_g', nfinebytes),
('nct_G', nbytes)]:
arrays.subnode(name, size)
lfs = mem.subnode('Localized functions')
for name, obj in [('nct', self.nct),
('ghat', self.ghat)]:
obj.estimate_memory(lfs.subnode(name))
self.mixer.estimate_memory(mem.subnode('Mixer'), self.gd)
# TODO
# The implementation of interpolator memory use is not very
# accurate; 20 MiB vs 13 MiB estimated in one example, probably
# worse for parallel calculations.
self.interpolator.estimate_memory(mem.subnode('Interpolator'))
def get_spin_contamination(self, atoms, majority_spin=0):
"""Calculate the spin contamination.
Spin contamination is defined as the integral over the
spin density difference, where it is negative (i.e. the
minority spin density is larger than the majority spin density.
"""
if majority_spin == 0:
smaj = 0
smin = 1
else:
smaj = 1
smin = 0
nt_sg, gd = self.get_all_electron_density(atoms)
dt_sg = nt_sg[smin] - nt_sg[smaj]
dt_sg = np.where(dt_sg > 0, dt_sg, 0.0)
return gd.integrate(dt_sg)
def __init__(self, calc, wfs, poisson_solver=None, dtype=float, **kwargs):
"""Store calculator etc.
Parameters
----------
calc: Calculator
Calculator instance containing a ground-state calculation
(calc.set_positions must have been called before this point!).
wfs: WaveFunctions
Class taking care of wave-functions, projectors, k-point related
quantities and symmetries.
poisson_solver: PoissonSolver
Multigrid or FFT poisson solver (not required if the
``Perturbation`` to be solved for has a ``solve_poisson`` member
function).
dtype: ...
dtype of the density response.
"""
# Store ground-state quantities
self.hamiltonian = calc.hamiltonian
self.density = calc.density
self.wfs = wfs
# Get list of k-point containers
self.kpt_u = wfs.kpt_u
# Poisson solver
if poisson_solver is None:
# Solver must be provided by the perturbation
self.poisson = None
self.solve_poisson = None
else:
self.poisson = poisson_solver
self.solve_poisson = self.poisson.solve_neutral
# Store grid-descriptors
self.gd = calc.density.gd
self.finegd = calc.density.finegd
# dtype for ground-state wave-functions
self.gs_dtype = calc.wfs.dtype
# dtype for the perturbing potential and density
self.dtype = dtype
# Grid transformer -- convert array from coarse to fine grid
self.interpolator = Transformer(self.gd, self.finegd, nn=3,
dtype=self.dtype, allocate=False)
# Grid transformer -- convert array from fine to coarse grid
self.restrictor = Transformer(self.finegd, self.gd, nn=3,
dtype=self.dtype, allocate=False)
# Sternheimer operator
self.sternheimer_operator = None
# Krylov solver
self.linear_solver = None
# Phases for transformer objects - since the perturbation determines
# the form of the density response this is obtained from the
# perturbation in the ``__call__`` member function below.
self.phase_cd = None
# Array attributes
self.nt1_G = None
self.vHXC1_G = None
self.nt1_g = None
self.vH1_g = None
# Perturbation
self.perturbation = None
# Number of occupied bands
nvalence = calc.wfs.nvalence
self.nbands = nvalence/2 + nvalence%2
assert self.nbands <= calc.wfs.nbands
self.initialized = False
self.parameters = {}
self.set(**kwargs)
class ResponseCalculator:
"""This class is a calculator for the sc density variation.
From the given perturbation, the set of coupled equations for the
first-order density response is solved self-consistently.
Parameters
----------
max_iter: int
Maximum number of iterations in the self-consistent evaluation of
the density variation.
tolerance_sc: float
Tolerance for the self-consistent loop measured in terms of
integrated absolute change of the density derivative between two
iterations.
tolerance_sternheimer: float
Tolerance for the solution of the Sternheimer equation -- passed to
the ``LinearSolver``.
beta: float (0 < beta < 1)
Mixing coefficient.
nmaxold: int
Length of history for the mixer.
weight: int
Weight for the mixer metric (=1 -> no metric used).
"""
parameters = {'verbose': False,
'max_iter': 100,
'max_iter_krylov': 1000,
'krylov_solver': 'cg',
'tolerance_sc': 1.0e-5,
'tolerance_sternheimer': 1.0e-4,
'use_pc': True,
'beta': 0.1,
'nmaxold': 6,
'weight': 50
}
def __init__(self, calc, wfs, poisson_solver=None, dtype=float, **kwargs):
"""Store calculator etc.
Parameters
----------
calc: Calculator
Calculator instance containing a ground-state calculation
(calc.set_positions must have been called before this point!).
wfs: WaveFunctions
Class taking care of wave-functions, projectors, k-point related
quantities and symmetries.
poisson_solver: PoissonSolver
Multigrid or FFT poisson solver (not required if the
``Perturbation`` to be solved for has a ``solve_poisson`` member
function).
dtype: ...
dtype of the density response.
"""
# Store ground-state quantities
self.hamiltonian = calc.hamiltonian
self.density = calc.density
self.wfs = wfs
# Get list of k-point containers
self.kpt_u = wfs.kpt_u
# Poisson solver
if poisson_solver is None:
# Solver must be provided by the perturbation
self.poisson = None
self.solve_poisson = None
else:
self.poisson = poisson_solver
self.solve_poisson = self.poisson.solve_neutral
# Store grid-descriptors
self.gd = calc.density.gd
self.finegd = calc.density.finegd
# dtype for ground-state wave-functions
self.gs_dtype = calc.wfs.dtype
# dtype for the perturbing potential and density
self.dtype = dtype
# Grid transformer -- convert array from coarse to fine grid
self.interpolator = Transformer(self.gd, self.finegd, nn=3,
dtype=self.dtype, allocate=False)
# Grid transformer -- convert array from fine to coarse grid
self.restrictor = Transformer(self.finegd, self.gd, nn=3,
dtype=self.dtype, allocate=False)
# Sternheimer operator
self.sternheimer_operator = None
# Krylov solver
self.linear_solver = None
# Phases for transformer objects - since the perturbation determines
# the form of the density response this is obtained from the
# perturbation in the ``__call__`` member function below.
self.phase_cd = None
# Array attributes
self.nt1_G = None
self.vHXC1_G = None
self.nt1_g = None
self.vH1_g = None
# Perturbation
self.perturbation = None
# Number of occupied bands
nvalence = calc.wfs.nvalence
self.nbands = nvalence/2 + nvalence%2
assert self.nbands <= calc.wfs.nbands
self.initialized = False
self.parameters = {}
self.set(**kwargs)
def clean(self):
"""Cleanup before call to ``__call__``."""
self.perturbation = None
self.solve_poisson = None
self.nt1_G = None
self.vHXC1_G = None
self.nt1_g = None
self.vH1_g = None
def __call__(self, perturbation):
"""Calculate density response (derivative) to perturbation.
Parameters
----------
perturbation: Perturbation
Class implementing the perturbing potential. Must provide an
``apply`` member function implementing the multiplication of the
perturbing potential to a (set of) state vector(s).
"""
assert self.initialized, ("Linear response calculator "
"not initizalized.")
self.clean()
if self.poisson is None:
assert hasattr(perturbation, 'solve_poisson')
self.solve_poisson = perturbation.solve_poisson
# Store perturbation - used in other member functions
self.perturbation = perturbation
# Reset mixer
self.mixer.reset()
# Reset wave-functions
self.wfs.reset()
# Set phase attribute for Transformer objects
self.phase_cd = self.perturbation.get_phase_cd()
# Parameters for the SC-loop
p = self.parameters
max_iter = p['max_iter']
tolerance = p['tolerance_sc']
for iter in range(max_iter):
if iter == 0:
self.first_iteration()
else:
print "iter:%3i\t" % iter,
norm = self.iteration()
print "abs-norm: %6.3e\t" % norm,
print ("integrated density response (abs): % 5.2e (%5.2e) "
% (self.gd.integrate(self.nt1_G.real),
self.gd.integrate(np.absolute(self.nt1_G))))
if norm < tolerance:
print ("self-consistent loop converged in %i iterations"
% iter)
break
if iter == max_iter:
raise RuntimeError, ("self-consistent loop did not converge "
"in %i iterations" % iter)
def set(self, **kwargs):
"""Set parameters for calculation."""
# Check for legal input parameters
for key, value in kwargs.items():
if not key in ResponseCalculator.parameters:
raise TypeError("Unknown keyword argument: '%s'" % key)
# Insert default values if not given
for key, value in ResponseCalculator.parameters.items():
if key not in kwargs:
kwargs[key] = value
self.parameters.update(kwargs)
def initialize(self, spos_ac):
"""Make the object ready for a calculation."""
# Parameters
p = self.parameters
beta = p['beta']
nmaxold = p['nmaxold']
weight = p['weight']
use_pc = p['use_pc']
tolerance_sternheimer = p['tolerance_sternheimer']
max_iter_krylov = p['max_iter_krylov']
krylov_solver = p['krylov_solver']
# Initialize WaveFunctions attribute
self.wfs.initialize(spos_ac)
# Initialize interpolator and restrictor
self.interpolator.allocate()
self.restrictor.allocate()
# Initialize mixer
# weight = 1 -> no metric is used
self.mixer = BaseMixer(beta=beta, nmaxold=nmaxold,
weight=weight, dtype=self.dtype)
self.mixer.initialize_metric(self.gd)
# Linear operator in the Sternheimer equation
self.sternheimer_operator = \
SternheimerOperator(self.hamiltonian, self.wfs, self.gd,
dtype=self.gs_dtype)
# Preconditioner for the Sternheimer equation
if p['use_pc']:
pc = ScipyPreconditioner(self.gd,
self.sternheimer_operator.project,
dtype=self.gs_dtype)
else:
pc = None
#XXX K-point of the pc must be set in the k-point loop -> store a ref.
self.pc = pc
# Linear solver for the solution of Sternheimer equation
self.linear_solver = ScipyLinearSolver(method=krylov_solver,
preconditioner=pc,
tolerance=tolerance_sternheimer,
max_iter=max_iter_krylov)
self.initialized = True
def first_iteration(self):
"""Perform first iteration of sc-loop."""
self.wave_function_variations()
self.density_response()
self.mixer.mix(self.nt1_G, [], phase_cd=self.phase_cd)
self.interpolate_density()
def iteration(self):
"""Perform iteration."""
# Update variation in the effective potential
self.effective_potential_variation()
# Update wave function variations
self.wave_function_variations()
# Update density
self.density_response()
# Mix - supply phase_cd here for metric inside the mixer
self.mixer.mix(self.nt1_G, [], phase_cd=self.phase_cd)
norm = self.mixer.get_charge_sloshing()
self.interpolate_density()
return norm
def interpolate_density(self):
"""Interpolate density derivative onto the fine grid."""
self.nt1_g = self.finegd.zeros(dtype=self.dtype)
self.interpolator.apply(self.nt1_G, self.nt1_g, phases=self.phase_cd)
def effective_potential_variation(self):
"""Calculate derivative of the effective potential (Hartree + XC)."""
# Hartree part
vHXC1_g = self.finegd.zeros(dtype=self.dtype)
self.solve_poisson(vHXC1_g, self.nt1_g)
# Store for evaluation of second order derivative
self.vH1_g = vHXC1_g.copy()
# XC part
nt_sg = self.density.nt_sg
fxct_sg = np.zeros_like(nt_sg)
self.hamiltonian.xc.calculate_fxc(self.finegd, nt_sg, fxct_sg)
vHXC1_g += fxct_sg[0] * self.nt1_g
# Transfer to coarse grid
self.vHXC1_G = self.gd.zeros(dtype=self.dtype)
self.restrictor.apply(vHXC1_g, self.vHXC1_G, phases=self.phase_cd)
def wave_function_variations(self):
"""Calculate variation in the wave-functions.
Parameters
----------
v1_G: ndarray
Variation of the local effective potential (Hartree + XC).
"""
verbose = self.parameters['verbose']
if verbose:
print "Calculating wave function variations"
if self.perturbation.has_q():
q_c = self.perturbation.get_q()
kplusq_k = self.wfs.kd.find_k_plus_q(q_c)
else:
kplusq_k = None
# Calculate wave-function variations for all k-points.
for kpt in self.kpt_u:
k = kpt.k
if verbose:
print "k-point %2.1i" % k
# Index of k+q vector
if kplusq_k is None:
kplusq = k
kplusqpt = kpt
else:
kplusq = kplusq_k[k]
kplusqpt = self.kpt_u[kplusq]
# Ground-state and first-order wave-functions
psit_nG = kpt.psit_nG
psit1_nG = kpt.psit1_nG
# Update the SternheimerOperator
self.sternheimer_operator.set_k(k)
self.sternheimer_operator.set_kplusq(kplusq)
# Update preconditioner
if self.pc is not None:
# k+q
self.pc.set_kpt(kplusqpt)
# Right-hand side of Sternheimer equations
# k and k+q
# XXX should only be done once for all k-points but maybe too cheap
# to bother ??
rhs_nG = self.gd.zeros(n=self.nbands, dtype=self.gs_dtype)
self.perturbation.apply(psit_nG, rhs_nG, self.wfs, k, kplusq)
if self.vHXC1_G is not None:
rhs_nG += self.vHXC1_G * psit_nG
# Project out occupied subspace
self.sternheimer_operator.project(rhs_nG)
# Loop over occupied bands
for n in range(self.nbands):
# Update band index in SternheimerOperator
self.sternheimer_operator.set_band(n)
# Get view of the Bloch function derivative
psit1_G = psit1_nG[n]
# Rhs of Sternheimer equation
rhs_G = -1 * rhs_nG[n]
# Solve Sternheimer equation
iter, info = self.linear_solver.solve(self.sternheimer_operator,
psit1_G, rhs_G)
if verbose:
print "\tBand %2.1i -" % n,
if info == 0:
if verbose:
print "linear solver converged in %i iterations" % iter
elif info > 0:
assert False, ("linear solver did not converge in maximum "
"number (=%i) of iterations for "
"k-point number %d" % (iter, k))
else:
assert False, ("linear solver failed to converge")
def density_response(self):
"""Calculate density response from variation in the wave-functions."""
# Density might be complex
self.nt1_G = self.gd.zeros(dtype=self.dtype)
for kpt in self.kpt_u:
# The weight of the k-points includes spin-degeneracy
w = kpt.weight
# Wave functions
psit_nG = kpt.psit_nG
psit1_nG = kpt.psit1_nG
for psit_G, psit1_G in zip(psit_nG, psit1_nG):
# NOTICE: this relies on the automatic down-cast of the complex
# array on the rhs to a real array when the lhs is real !!
# Factor 2 for time-reversal symmetry
self.nt1_G += 2 * w * psit_G.conj() * psit1_G
class RealSpaceDensity(Density):
def __init__(self, gd, finegd, nspins, charge, collinear=True,
stencil=3):
Density.__init__(self, gd, finegd, nspins, charge, collinear)
self.stencil = stencil
def initialize(self, setups, timer, magmom_av, hund):
Density.initialize(self, setups, timer, magmom_av, hund)
# Interpolation function for the density:
self.interpolator = Transformer(self.gd, self.finegd, self.stencil)
spline_aj = []
for setup in setups:
if setup.nct is None:
spline_aj.append([])
else:
spline_aj.append([setup.nct])
self.nct = LFC(self.gd, spline_aj,
integral=[setup.Nct for setup in setups],
forces=True, cut=True)
self.ghat = LFC(self.finegd, [setup.ghat_l for setup in setups],
integral=sqrt(4 * pi), forces=True)
def set_positions(self, spos_ac, rank_a=None):
Density.set_positions(self, spos_ac, rank_a)
self.nct_G = self.gd.zeros()
self.nct.add(self.nct_G, 1.0 / self.nspins)
def interpolate_pseudo_density(self, comp_charge=None):
"""Interpolate pseudo density to fine grid."""
if comp_charge is None:
comp_charge = self.calculate_multipole_moments()
self.nt_sg = self.interpolate(self.nt_sG, self.nt_sg)
# With periodic boundary conditions, the interpolation will
# conserve the number of electrons.
if not self.gd.pbc_c.all():
# With zero-boundary conditions in one or more directions,
# this is not the case.
pseudo_charge = -(self.charge + comp_charge)
if abs(pseudo_charge) > 1.0e-14:
x = (pseudo_charge /
self.finegd.integrate(self.nt_sg[:self.nspins]).sum())
self.nt_sg *= x
def interpolate(self, in_xR, out_xR=None):
"""Interpolate array(s)."""
# ndim will be 3 in finite-difference mode and 1 when working
# with the AtomPAW class (spherical atoms and 1d grids)
ndim = self.gd.ndim
if out_xR is None:
out_xR = self.finegd.empty(in_xR.shape[:-ndim])
a_xR = in_xR.reshape((-1,) + in_xR.shape[-ndim:])
b_xR = out_xR.reshape((-1,) + out_xR.shape[-ndim:])
for in_R, out_R in zip(a_xR, b_xR):
self.interpolator.apply(in_R, out_R)
return out_xR
def calculate_pseudo_charge(self):
self.nt_g = self.nt_sg[:self.nspins].sum(axis=0)
self.rhot_g = self.nt_g.copy()
self.ghat.add(self.rhot_g, self.Q_aL)
if debug:
charge = self.finegd.integrate(self.rhot_g) + self.charge
if abs(charge) > self.charge_eps:
raise RuntimeError('Charge not conserved: excess=%.9f' %
charge)
def get_pseudo_core_kinetic_energy_density_lfc(self):
return LFC(self.gd,
[[setup.tauct] for setup in self.setups],
forces=True, cut=True)
def calculate_dipole_moment(self):
return self.finegd.calculate_dipole_moment(self.rhot_g)
def get_combined_data(self, qmdata=None, cldata=None, spacing=None,
qmgd=None, clgd=None):
if qmdata is None:
qmdata = self.density.rhot_g
if cldata is None:
cldata = (self.classical_material.charge_density *
self.classical_material.sign)
if qmgd is None:
qmgd = self.qm.gd
if clgd is None:
clgd = self.cl.gd
if spacing is None:
spacing = clgd.h_cv[0, 0]
spacing_au = spacing / Bohr # from Angstroms to a.u.
# Refine classical part
clgd = clgd.new_descriptor()
cl_g = cldata.copy()
while clgd.h_cv[0, 0] > spacing_au * 1.50: # 45:
clgd2 = clgd.refine()
cl_g = Transformer(clgd, clgd2).apply(cl_g)
clgd = clgd2
# Coarse quantum part
qmgd = qmgd.new_descriptor()
qm_g = qmdata.copy()
while qmgd.h_cv[0, 0] < clgd.h_cv[0, 0] * 0.95:
qmgd2 = qmgd.coarsen()
qm_g = Transformer(qmgd, qmgd2).apply(qm_g)
qmgd = qmgd2
assert np.all(np.absolute(qmgd.h_cv - clgd.h_cv) < 1e-12), \
" Spacings %.8f (qm) and %.8f (cl) Angstroms" \
% (qmgd.h_cv[0][0] * Bohr, clgd.h_cv[0][0] * Bohr)
# Do distribution on master
big_cl_g = clgd.collect(cl_g)
big_qm_g = qmgd.collect(qm_g, broadcast=True)
if clgd.comm.rank == 0:
# now find the corners
# r_gv_cl = \
# clgd.get_grid_point_coordinates().transpose((1, 2, 3, 0))
cind = (self.qm.corner1 / np.diag(clgd.h_cv) - 1).astype(int)
n = big_qm_g.shape
# print 'Corner points: ', self.qm.corner1*Bohr, \
# ' - ', self.qm.corner2*Bohr
# print 'Calculated points: ', r_gv_cl[tuple(cind)]*Bohr, \
# ' - ', r_gv_cl[tuple(cind+n+1)]*Bohr
big_cl_g[cind[0] + 1:cind[0] + n[0] + 1,
cind[1] + 1:cind[1] + n[1] + 1,
cind[2] + 1:cind[2] + n[2] + 1] += big_qm_g
clgd.distribute(big_cl_g, cl_g)
return cl_g, clgd
def create_subsystems(self, atoms_in):
# Create new Atoms object
atoms_out = atoms_in.copy()
# New quantum grid
self.qm.cell = \
np.diag([(self.shift_indices_2[w] - self.shift_indices_1[w]) *
self.cl.spacing[w] for w in range(3)])
self.qm.spacing = self.cl.spacing / self.hratios
N_c = get_number_of_grid_points(self.qm.cell, self.qm.spacing)
atoms_out.set_cell(np.diag(self.qm.cell) * Bohr)
atoms_out.positions = atoms_in.get_positions() - self.qm.corner1 * Bohr
msg = self.messages.append
msg("Quantum box readjustment:")
msg(" Given cell: [%10.5f %10.5f %10.5f]" %
tuple(np.diag(atoms_in.get_cell())))
msg(" Given atomic coordinates:")
for s, c in zip(atoms_in.get_chemical_symbols(),
atoms_in.get_positions()):
msg(" %s %10.5f %10.5f %10.5f" %
(s, c[0], c[1], c[2]))
msg(" Readjusted cell: [%10.5f %10.5f %10.5f]" %
tuple(np.diag(atoms_out.get_cell())))
msg(" Readjusted atomic coordinates:")
for s, c in zip(atoms_out.get_chemical_symbols(),
atoms_out.get_positions()):
msg(" %s %10.5f %10.5f %10.5f" %
(s, c[0], c[1], c[2]))
msg(" Given corner points: " +
"(%10.5f %10.5f %10.5f) - (%10.5f %10.5f %10.5f)"
% (tuple(np.concatenate((self.given_corner_v1,
self.given_corner_v2)))))
msg(" Readjusted corner points: " +
"(%10.5f %10.5f %10.5f) - (%10.5f %10.5f %10.5f)"
% (tuple(np.concatenate((self.qm.corner1,
self.qm.corner2)) * Bohr)))
msg(" Indices in classical grid: " +
"(%10i %10i %10i) - (%10i %10i %10i)"
% (tuple(np.concatenate((self.shift_indices_1,
self.shift_indices_2)))))
msg(" Grid points in classical grid: " +
"(%10i %10i %10i)"
% (tuple(self.cl.gd.N_c)))
msg(" Grid points in quantum grid: " +
"(%10i %10i %10i)"
% (tuple(N_c)))
msg(" Spacings in quantum grid: " +
"(%10.5f %10.5f %10.5f)"
% (tuple(np.diag(self.qm.cell) * Bohr / N_c)))
msg(" Spacings in classical grid: " +
"(%10.5f %10.5f %10.5f)"
% (tuple(np.diag(self.cl.cell) *
Bohr / get_number_of_grid_points(self.cl.cell,
self.cl.spacing))))
# msg(" Ratios of cl/qm spacings: " +
# "(%10i %10i %10i)" % (tuple(self.hratios)))
# msg(" = (%10.2f %10.2f %10.2f)" %
# (tuple((np.diag(self.cl.cell) * Bohr / \
# get_number_of_grid_points(self.cl.cell,
# self.cl.spacing)) / \
# (np.diag(self.qm.cell) * Bohr / N_c))))
msg(" Needed number of refinements: %10i"
% self.num_refinements)
# First, create the quantum grid equivalent GridDescriptor
# self.cl.subgd. Then coarsen it until its h_cv equals
# that of self.cl.gd. Finally, map the points between
# clgd and coarsened subgrid.
subcell_cv = np.diag(self.qm.corner2 - self.qm.corner1)
N_c = get_number_of_grid_points(subcell_cv, self.cl.spacing)
N_c = self.shift_indices_2 - self.shift_indices_1
self.cl.subgds = []
self.cl.subgds.append(GridDescriptor(N_c, subcell_cv, False,
serial_comm, self.cl.dparsize))
# msg(" N_c/spacing of the subgrid: " +
# "%3i %3i %3i / %.4f %.4f %.4f" %
# (self.cl.subgds[0].N_c[0],
# self.cl.subgds[0].N_c[1],
# self.cl.subgds[0].N_c[2],
# self.cl.subgds[0].h_cv[0][0] * Bohr,
# self.cl.subgds[0].h_cv[1][1] * Bohr,
# self.cl.subgds[0].h_cv[2][2] * Bohr))
# msg(" shape from the subgrid: " +
# "%3i %3i %3i" % (tuple(self.cl.subgds[0].empty().shape)))
self.cl.coarseners = []
self.cl.refiners = []
for n in range(self.num_refinements):
self.cl.subgds.append(self.cl.subgds[n].refine())
self.cl.refiners.append(Transformer(self.cl.subgds[n],
self.cl.subgds[n + 1]))
# msg(" refiners[%i] can perform the transformation " +
# "(%3i %3i %3i) -> (%3i %3i %3i)" % (\
# n,
# self.cl.subgds[n].empty().shape[0],
# self.cl.subgds[n].empty().shape[1],
# self.cl.subgds[n].empty().shape[2],
# self.cl.subgds[n + 1].empty().shape[0],
# self.cl.subgds[n + 1].empty().shape[1],
# self.cl.subgds[n + 1].empty().shape[2]))
self.cl.coarseners.append(Transformer(self.cl.subgds[n + 1],
self.cl.subgds[n]))
self.cl.coarseners[:] = self.cl.coarseners[::-1]
# Now extend the grid in order to handle
# the zero boundary conditions that the refiner assumes
# The default interpolation order
self.extend_nn = \
Transformer(GridDescriptor([8, 8, 8], [1, 1, 1],
False, serial_comm, None),
GridDescriptor([8, 8, 8], [1, 1, 1],
False, serial_comm, None).coarsen()).nn
self.extended_num_indices = self.num_indices + [2, 2, 2]
# Center, left, and right points of the suggested quantum grid
extended_cp = 0.5 * (np.array(self.given_corner_v1 / Bohr) +
np.array(self.given_corner_v2 / Bohr))
extended_lp = extended_cp - 0.5 * (self.extended_num_indices *
self.cl.spacing)
# extended_rp = extended_cp + 0.5 * (self.extended_num_indices *
# self.cl.spacing)
# Indices in the classical grid restricting the quantum grid
self.extended_shift_indices_1 = \
np.round(extended_lp / self.cl.spacing).astype(int)
self.extended_shift_indices_2 = \
self.extended_shift_indices_1 + self.extended_num_indices
# msg(' extended_shift_indices_1: %i %i %i'
# % (self.extended_shift_indices_1[0],
# self.extended_shift_indices_1[1],
# self.extended_shift_indices_1[2]))
# msg(' extended_shift_indices_2: %i %i %i'
# % (self.extended_shift_indices_2[0],
# self.extended_shift_indices_2[1],
# self.extended_shift_indices_2[2]))
# msg(' cl.gd.N_c: %i %i %i'
# % (self.cl.gd.N_c[0], self.cl.gd.N_c[1], self.cl.gd.N_c[2]))
# Sanity checks
assert(all([self.extended_shift_indices_1[w] >= 0 and
self.extended_shift_indices_2[w] <= self.cl.gd.N_c[w]
for w in range(3)])), \
"Could not find appropriate quantum grid. " + \
"Move it further away from the boundary."
# Corner coordinates
self.qm.extended_corner1 = \
self.extended_shift_indices_1 * self.cl.spacing
self.qm.extended_corner2 = \
self.extended_shift_indices_2 * self.cl.spacing
N_c = self.extended_shift_indices_2 - self.extended_shift_indices_1
self.cl.extended_subgds = []
self.cl.extended_refiners = []
extended_subcell_cv = np.diag(self.qm.extended_corner2 -
self.qm.extended_corner1)
self.cl.extended_subgds.append(GridDescriptor(
N_c, extended_subcell_cv, False, serial_comm, None))
for n in range(self.num_refinements):
self.cl.extended_subgds.append(self.cl.extended_subgds[n].refine())
self.cl.extended_refiners.append(Transformer(
self.cl.extended_subgds[n], self.cl.extended_subgds[n + 1]))
# msg(" extended_refiners[%i] can perform the transformation " +
# "(%3i %3i %3i) -> (%3i %3i %3i)"
# % (n,
# self.cl.extended_subgds[n].empty().shape[0],
# self.cl.extended_subgds[n].empty().shape[1],
# self.cl.extended_subgds[n].empty().shape[2],
# self.cl.extended_subgds[n + 1].empty().shape[0],
# self.cl.extended_subgds[n + 1].empty().shape[1],
# self.cl.extended_subgds[n + 1].empty().shape[2]))
# msg(" N_c/spacing of the refined subgrid: " +
# "%3i %3i %3i / %.4f %.4f %.4f"
# % (self.cl.subgds[-1].N_c[0],
# self.cl.subgds[-1].N_c[1],
# self.cl.subgds[-1].N_c[2],
# self.cl.subgds[-1].h_cv[0][0] * Bohr,
# self.cl.subgds[-1].h_cv[1][1] * Bohr,
# self.cl.subgds[-1].h_cv[2][2] * Bohr))
# msg(" shape from the refined subgrid: %3i %3i %3i"
# % (tuple(self.cl.subgds[-1].empty().shape)))
self.extended_deltaIndex = 2**(self.num_refinements) * self.extend_nn
# msg(" self.extended_deltaIndex = %i" % self.extended_deltaIndex)
qgpts = self.cl.subgds[-1].coarsen().N_c
# Assure that one returns to the original shape
dmygd = self.cl.subgds[-1].coarsen()
for n in range(self.num_refinements - 1):
dmygd = dmygd.coarsen()
# msg(" N_c/spacing of the coarsened subgrid: " +
# "%3i %3i %3i / %.4f %.4f %.4f"
# % (dmygd.N_c[0], dmygd.N_c[1], dmygd.N_c[2],
# dmygd.h_cv[0][0] * Bohr,
# dmygd.h_cv[1][1] * Bohr,
# dmygd.h_cv[2][2] * Bohr))
self.has_subsystems = True
return atoms_out, self.qm.spacing[0] * Bohr, qgpts
class Hamiltonian:
"""Hamiltonian object.
Attributes:
=============== =====================================================
``xc`` ``XC3DGrid`` object.
``poisson`` ``PoissonSolver``.
``gd`` Grid descriptor for coarse grids.
``finegd`` Grid descriptor for fine grids.
``restrict`` Function for restricting the effective potential.
=============== =====================================================
Soft and smooth pseudo functions on uniform 3D grids:
========== =========================================
``vHt_g`` Hartree potential on the fine grid.
``vt_sG`` Effective potential on the coarse grid.
``vt_sg`` Effective potential on the fine grid.
========== =========================================
Energy contributions and forces:
=========== ==========================================
Description
=========== ==========================================
``Ekin`` Kinetic energy.
``Epot`` Potential energy.
``Etot`` Total energy.
``Exc`` Exchange-Correlation energy.
``Eext`` Energy of external potential
``Eref`` Reference energy for all-electron atoms.
``S`` Entropy.
``Ebar`` Should be close to zero!
=========== ==========================================
"""
def __init__(self, gd, finegd, nspins, setups, stencil, timer, xc,
psolver, vext_g):
"""Create the Hamiltonian."""
self.gd = gd
self.finegd = finegd
self.nspins = nspins
self.setups = setups
self.timer = timer
self.xc = xc
# Solver for the Poisson equation:
if psolver is None:
psolver = PoissonSolver(nn=3, relax='J')
self.poisson = psolver
self.poisson.set_grid_descriptor(finegd)
self.dH_asp = None
# The external potential
self.vext_g = vext_g
self.vt_sG = None
self.vHt_g = None
self.vt_sg = None
self.vbar_g = None
self.rank_a = None
# Restrictor function for the potential:
self.restrictor = Transformer(self.finegd, self.gd, stencil,
allocate=False)
self.restrict = self.restrictor.apply
self.vbar = LFC(self.finegd, [[setup.vbar] for setup in setups],
forces=True)
self.Ekin0 = None
self.Ekin = None
self.Epot = None
self.Ebar = None
self.Eext = None
self.Exc = None
self.Etot = None
self.S = None
self.allocated = False
def allocate(self):
# TODO We should move most of the gd.empty() calls here
assert not self.allocated
self.restrictor.allocate()
self.allocated = True
def set_positions(self, spos_ac, rank_a=None):
self.spos_ac = spos_ac
if not self.allocated:
self.allocate()
self.vbar.set_positions(spos_ac)
if self.vbar_g is None:
self.vbar_g = self.finegd.empty()
self.vbar_g[:] = 0.0
self.vbar.add(self.vbar_g)
self.xc.set_positions(spos_ac)
# If both old and new atomic ranks are present, start a blank dict if
# it previously didn't exist but it will needed for the new atoms.
if (self.rank_a is not None and rank_a is not None and
self.dH_asp is None and (rank_a == self.gd.comm.rank).any()):
self.dH_asp = {}
if self.rank_a is not None and self.dH_asp is not None:
self.timer.start('Redistribute')
requests = []
flags = (self.rank_a != rank_a)
my_incoming_atom_indices = np.argwhere(np.bitwise_and(flags, \
rank_a == self.gd.comm.rank)).ravel()
my_outgoing_atom_indices = np.argwhere(np.bitwise_and(flags, \
self.rank_a == self.gd.comm.rank)).ravel()
for a in my_incoming_atom_indices:
# Get matrix from old domain:
ni = self.setups[a].ni
dH_sp = np.empty((self.nspins, ni * (ni + 1) // 2))
requests.append(self.gd.comm.receive(dH_sp, self.rank_a[a],
tag=a, block=False))
assert a not in self.dH_asp
self.dH_asp[a] = dH_sp
for a in my_outgoing_atom_indices:
# Send matrix to new domain:
dH_sp = self.dH_asp.pop(a)
requests.append(self.gd.comm.send(dH_sp, rank_a[a],
tag=a, block=False))
self.gd.comm.waitall(requests)
self.timer.stop('Redistribute')
self.rank_a = rank_a
def aoom(self, DM, a, l, scale=1):
"""Atomic Orbital Occupation Matrix.
Determine the Atomic Orbital Occupation Matrix (aoom) for a
given l-quantum number.
This operation, takes the density matrix (DM), which for
example is given by unpack2(D_asq[i][spin]), and corrects for
the overlap between the selected orbitals (l) upon which the
the density is expanded (ex <p|p*>,<p|p>,<p*|p*> ).
Returned is only the "corrected" part of the density matrix,
which represents the orbital occupation matrix for l=2 this is
a 5x5 matrix.
"""
S=self.setups[a]
l_j = S.l_j
n_j = S.n_j
lq = S.lq
nl = np.where(np.equal(l_j, l))[0]
V = np.zeros(np.shape(DM))
if len(nl) == 2:
aa = (nl[0])*len(l_j)-((nl[0]-1)*(nl[0])/2)
bb = (nl[1])*len(l_j)-((nl[1]-1)*(nl[1])/2)
ab = aa+nl[1]-nl[0]
if(scale==0 or scale=='False' or scale =='false'):
lq_a = lq[aa]
lq_ab = lq[ab]
lq_b = lq[bb]
else:
lq_a = 1
lq_ab = lq[ab]/lq[aa]
lq_b = lq[bb]/lq[aa]
# and the correct entrances in the DM
nn = (2*np.array(l_j)+1)[0:nl[0]].sum()
mm = (2*np.array(l_j)+1)[0:nl[1]].sum()
# finally correct and add the four submatrices of NC_DM
A = DM[nn:nn+2*l+1,nn:nn+2*l+1]*(lq_a)
B = DM[nn:nn+2*l+1,mm:mm+2*l+1]*(lq_ab)
C = DM[mm:mm+2*l+1,nn:nn+2*l+1]*(lq_ab)
D = DM[mm:mm+2*l+1,mm:mm+2*l+1]*(lq_b)
V[nn:nn+2*l+1,nn:nn+2*l+1]=+(lq_a)
V[nn:nn+2*l+1,mm:mm+2*l+1]=+(lq_ab)
V[mm:mm+2*l+1,nn:nn+2*l+1]=+(lq_ab)
V[mm:mm+2*l+1,mm:mm+2*l+1]=+(lq_b)
return A+B+C+D, V
else:
nn =(2*np.array(l_j)+1)[0:nl[0]].sum()
A=DM[nn:nn+2*l+1,nn:nn+2*l+1]*lq[-1]
V[nn:nn+2*l+1,nn:nn+2*l+1]=+lq[-1]
return A,V
def update(self, density):
"""Calculate effective potential.
The XC-potential and the Hartree potential are evaluated on
the fine grid, and the sum is then restricted to the coarse
grid."""
self.timer.start('Hamiltonian')
if self.vt_sg is None:
self.timer.start('Initialize Hamiltonian')
self.vt_sg = self.finegd.empty(self.nspins)
self.vHt_g = self.finegd.zeros()
self.vt_sG = self.gd.empty(self.nspins)
self.poisson.initialize()
self.timer.stop('Initialize Hamiltonian')
self.timer.start('vbar')
Ebar = self.finegd.integrate(self.vbar_g, density.nt_g,
global_integral=False)
vt_g = self.vt_sg[0]
vt_g[:] = self.vbar_g
self.timer.stop('vbar')
Eext = 0.0
if self.vext_g is not None:
vt_g += self.vext_g.get_potential(self.finegd)
Eext = self.finegd.integrate(vt_g, density.nt_g,
global_integral=False) - Ebar
if self.nspins == 2:
self.vt_sg[1] = vt_g
self.timer.start('XC 3D grid')
Exc = self.xc.calculate(self.finegd, density.nt_sg, self.vt_sg)
Exc /= self.gd.comm.size
self.timer.stop('XC 3D grid')
self.timer.start('Poisson')
# npoisson is the number of iterations:
self.npoisson = self.poisson.solve(self.vHt_g, density.rhot_g,
charge=-density.charge)
self.timer.stop('Poisson')
self.timer.start('Hartree integrate/restrict')
Epot = 0.5 * self.finegd.integrate(self.vHt_g, density.rhot_g,
global_integral=False)
Ekin = 0.0
for vt_g, vt_G, nt_G in zip(self.vt_sg, self.vt_sG, density.nt_sG):
vt_g += self.vHt_g
self.restrict(vt_g, vt_G)
Ekin -= self.gd.integrate(vt_G, nt_G - density.nct_G,
global_integral=False)
self.timer.stop('Hartree integrate/restrict')
# Calculate atomic hamiltonians:
self.timer.start('Atomic')
W_aL = {}
for a in density.D_asp:
W_aL[a] = np.empty((self.setups[a].lmax + 1)**2)
density.ghat.integrate(self.vHt_g, W_aL)
self.dH_asp = {}
for a, D_sp in density.D_asp.items():
W_L = W_aL[a]
setup = self.setups[a]
D_p = D_sp.sum(0)
dH_p = (setup.K_p + setup.M_p +
setup.MB_p + 2.0 * np.dot(setup.M_pp, D_p) +
np.dot(setup.Delta_pL, W_L))
Ekin += np.dot(setup.K_p, D_p) + setup.Kc
Ebar += setup.MB + np.dot(setup.MB_p, D_p)
Epot += setup.M + np.dot(D_p, (setup.M_p +
np.dot(setup.M_pp, D_p)))
if self.vext_g is not None:
vext = self.vext_g.get_taylor(spos_c=self.spos_ac[a, :])
# Tailor expansion to the zeroth order
Eext += vext[0][0] * (sqrt(4 * pi) * density.Q_aL[a][0]
+ setup.Z)
dH_p += vext[0][0] * sqrt(4 * pi) * setup.Delta_pL[:, 0]
if len(vext) > 1:
# Tailor expansion to the first order
Eext += sqrt(4 * pi / 3) * np.dot(vext[1],
density.Q_aL[a][1:4])
# there must be a better way XXXX
Delta_p1 = np.array([setup.Delta_pL[:, 1],
setup.Delta_pL[:, 2],
setup.Delta_pL[:, 3]])
dH_p += sqrt(4 * pi / 3) * np.dot(vext[1], Delta_p1)
self.dH_asp[a] = dH_sp = np.zeros_like(D_sp)
self.timer.start('XC Correction')
Exc += setup.xc_correction.calculate(self.xc, D_sp, dH_sp, a)
self.timer.stop('XC Correction')
if setup.HubU is not None:
nspins = len(D_sp)
l_j = setup.l_j
l = setup.Hubl
nl = np.where(np.equal(l_j,l))[0]
nn = (2*np.array(l_j)+1)[0:nl[0]].sum()
for D_p, H_p in zip(D_sp, self.dH_asp[a]):
[N_mm,V] =self.aoom(unpack2(D_p),a,l)
N_mm = N_mm / 2 * nspins
Eorb = setup.HubU / 2. * (N_mm - np.dot(N_mm,N_mm)).trace()
Vorb = setup.HubU * (0.5 * np.eye(2*l+1) - N_mm)
Exc += Eorb
if nspins == 1:
# add contribution of other spin manyfold
Exc += Eorb
if len(nl)==2:
mm = (2*np.array(l_j)+1)[0:nl[1]].sum()
V[nn:nn+2*l+1,nn:nn+2*l+1] *= Vorb
V[mm:mm+2*l+1,nn:nn+2*l+1] *= Vorb
V[nn:nn+2*l+1,mm:mm+2*l+1] *= Vorb
V[mm:mm+2*l+1,mm:mm+2*l+1] *= Vorb
else:
V[nn:nn+2*l+1,nn:nn+2*l+1] *= Vorb
Htemp = unpack(H_p)
Htemp += V
H_p[:] = pack2(Htemp)
dH_sp += dH_p
Ekin -= (D_sp * dH_sp).sum()
self.timer.stop('Atomic')
# Make corrections due to non-local xc:
#xcfunc = self.xc.xcfunc
self.Enlxc = 0.0#XXXxcfunc.get_non_local_energy()
Ekin += self.xc.get_kinetic_energy_correction() / self.gd.comm.size
energies = np.array([Ekin, Epot, Ebar, Eext, Exc])
self.timer.start('Communicate energies')
self.gd.comm.sum(energies)
self.timer.stop('Communicate energies')
(self.Ekin0, self.Epot, self.Ebar, self.Eext, self.Exc) = energies
#self.Exc += self.Enlxc
#self.Ekin0 += self.Enlkin
self.timer.stop('Hamiltonian')
def get_energy(self, occupations):
self.Ekin = self.Ekin0 + occupations.e_band
self.S = occupations.e_entropy
# Total free energy:
self.Etot = (self.Ekin + self.Epot + self.Eext +
self.Ebar + self.Exc - self.S)
return self.Etot
def apply_local_potential(self, psit_nG, Htpsit_nG, s):
"""Apply the Hamiltonian operator to a set of vectors.
XXX Parameter description is deprecated!
Parameters:
a_nG: ndarray
Set of vectors to which the overlap operator is applied.
b_nG: ndarray, output
Resulting H times a_nG vectors.
kpt: KPoint object
k-point object defined in kpoint.py.
calculate_projections: bool
When True, the integrals of projector times vectors
P_ni = <p_i | a_nG> are calculated.
When False, existing P_uni are used
local_part_only: bool
When True, the non-local atomic parts of the Hamiltonian
are not applied and calculate_projections is ignored.
"""
vt_G = self.vt_sG[s]
if psit_nG.ndim == 3:
Htpsit_nG += psit_nG * vt_G
else:
for psit_G, Htpsit_G in zip(psit_nG, Htpsit_nG):
Htpsit_G += psit_G * vt_G
def apply(self, a_xG, b_xG, wfs, kpt, calculate_P_ani=True):
"""Apply the Hamiltonian operator to a set of vectors.
Parameters:
a_nG: ndarray
Set of vectors to which the overlap operator is applied.
b_nG: ndarray, output
Resulting S times a_nG vectors.
wfs: WaveFunctions
Wave-function object defined in wavefunctions.py
kpt: KPoint object
k-point object defined in kpoint.py.
calculate_P_ani: bool
When True, the integrals of projector times vectors
P_ni = <p_i | a_nG> are calculated.
When False, existing P_ani are used
"""
wfs.kin.apply(a_xG, b_xG, kpt.phase_cd)
self.apply_local_potential(a_xG, b_xG, kpt.s)
shape = a_xG.shape[:-3]
P_axi = wfs.pt.dict(shape)
if calculate_P_ani: #TODO calculate_P_ani=False is experimental
wfs.pt.integrate(a_xG, P_axi, kpt.q)
else:
for a, P_ni in kpt.P_ani.items():
P_axi[a][:] = P_ni
for a, P_xi in P_axi.items():
dH_ii = unpack(self.dH_asp[a][kpt.s])
P_axi[a] = np.dot(P_xi, dH_ii)
wfs.pt.add(b_xG, P_axi, kpt.q)
def get_xc_difference(self, xc, density):
"""Calculate non-selfconsistent XC-energy difference."""
if density.nt_sg is None:
density.interpolate()
nt_sg = density.nt_sg
if hasattr(xc, 'hybrid'):
xc.calculate_exx()
Exc = xc.calculate(density.finegd, nt_sg) / self.gd.comm.size
for a, D_sp in density.D_asp.items():
setup = self.setups[a]
Exc += setup.xc_correction.calculate(xc, D_sp)
Exc = self.gd.comm.sum(Exc)
return Exc - self.Exc
def get_vxc(self, density, wfs):
"""Calculate matrix elements of the xc-potential."""
dtype = wfs.dtype
nbands = wfs.nbands
nu = len(wfs.kpt_u)
if density.nt_sg is None:
density.interpolate()
# Allocate space for result matrix
Vxc_unn = np.empty((nu, nbands, nbands), dtype=dtype)
# Get pseudo xc potential on the coarse grid
Vxct_sG = self.gd.empty(self.nspins)
Vxct_sg = self.finegd.zeros(self.nspins)
if nspins == 1:
self.xc.get_energy_and_potential(density.nt_sg[0], Vxct_sg[0])
else:
self.xc.get_energy_and_potential(density.nt_sg[0], Vxct_sg[0],
density.nt_sg[1], Vxct_sg[1])
for Vxct_G, Vxct_g in zip(Vxct_sG, Vxct_sg):
self.restrict(Vxct_g, Vxct_G)
del Vxct_sg
# Get atomic corrections to the xc potential
Vxc_asp = {}
for a, D_sp in density.D_asp.items():
Vxc_asp[a] = np.zeros_like(D_sp)
self.setups[a].xc_correction.calculate_energy_and_derivatives(
D_sp, Vxc_asp[a])
# Project potential onto the eigenstates
for kpt, Vxc_nn in xip(wfs.kpt_u, Vxc_unn):
s, q = kpt.s, kpt.q
psit_nG = kpt.psit_nG
# Project pseudo part
r2k(.5 * self.gd.dv, psit_nG, Vxct_sG[s] * psit_nG, 0.0, Vxc_nn)
tri2full(Vxc_nn, 'L')
self.gd.comm.sum(Vxc_nn)
# Add atomic corrections
# H_ij = \int dr phi_i(r) Ĥ phi_j^*(r)
# P_ni = \int dr psi_n(r) pt_i^*(r)
# Vxc_nm = \int dr phi_n(r) vxc(r) phi_m^*(r)
# + sum_ij P_ni H_ij P_mj^*
for a, P_ni in kpt.P_ani.items():
Vxc_ii = unpack(Vxc_asp[a][s])
Vxc_nn += np.dot(P_ni, np.inner(H_ii, P_ni).conj())
return Vxc_unn
def estimate_memory(self, mem):
nbytes = self.gd.bytecount()
nfinebytes = self.finegd.bytecount()
arrays = mem.subnode('Arrays', 0)
arrays.subnode('vHt_g', nfinebytes)
arrays.subnode('vt_sG', self.nspins * nbytes)
arrays.subnode('vt_sg', self.nspins * nfinebytes)
self.restrictor.estimate_memory(mem.subnode('Restrictor'))
self.xc.estimate_memory(mem.subnode('XC'))
self.poisson.estimate_memory(mem.subnode('Poisson'))
self.vbar.estimate_memory(mem.subnode('vbar'))
def __init__(self, calc):
#initialization
self.calc = calc
self.wfs = calc.wfs
self.ham = calc.hamiltonian
self.den = calc.density
self.occ = calc.occupations
#initialization plane and grid descriptors from GPAW calculation
self.pd = calc.wfs.pd
self.gd = calc.wfs.gd
self.volume = np.abs(np.linalg.det(self.gd.cell_cv))
#number of k-points
self.nq = len(calc.wfs.kpt_u)
#number of bands
self.nbands = calc.get_number_of_bands()
#number of electrons
self.nelectrons = calc.get_number_of_electrons()
#kinetic operator
self.kinetic = np.zeros((self.nq, self.nbands, self.nbands),
dtype=complex)
#overlap operator
self.overlap = np.zeros((self.nq, self.nbands, self.nbands),
dtype=complex)
#local momentum operator
self.local_moment = np.zeros((3, self.nq, self.nbands, self.nbands),
dtype=complex)
#nonlocal momentum operator
self.nonlocal_moment = np.zeros((3, self.nq, self.nbands, self.nbands),
dtype=complex)
#Fermi-Dirac occupation
self.f_n = np.zeros((self.nq, self.nbands), dtype=float)
#ground state Kohn-Sham orbitals wavefunctions
psi_gs = []
#ground state Kohn-Sham orbitals density
den_gs = []
for kpt in self.wfs.kpt_u:
self.overlap[kpt.q] = np.eye(self.nbands)
self.f_n[kpt.q] = kpt.f_n
kinetic = 0.5 * self.pd.G2_qG[kpt.q] # |G+q|^2/2
gradient = self.pd.get_reciprocal_vectors(kpt.q)
psi = []
den = []
for n in range(self.nbands):
psi.append(self.pd.ifft(kpt.psit_nG[n], kpt.q))
den.append(np.abs(psi[-1])**2)
for m in range(self.nbands):
self.kinetic[kpt.q, n, m] = self.pd.integrate(
kpt.psit_nG[n], kinetic * kpt.psit_nG[m])
#calculation local momentum
#<psi_qn|\nabla|psi_qm>
for i in range(3):
self.local_moment[i, kpt.q, n, m] = self.pd.integrate(
kpt.psit_nG[n], gradient[:, i] * kpt.psit_nG[m])
psi_gs.append(psi)
den_gs.append(den)
self.psi_gs = np.array(psi_gs)
self.den_gs = np.array(den_gs, dtype=float)
#real space grid points
self.r = self.gd.get_grid_point_coordinates()
#initialization local and nonlocal part of pseudopotential
self.init_potential()
self.proj = np.zeros((self.nq, self.nbands, self.norb), dtype=complex)
self.proj_r = np.zeros((3, self.nq, self.nbands, self.norb),
dtype=complex)
self.density = self.den.nt_sG.copy()
#initialization charge density (ion+electrons) for Hartree potential
self.ion_density = calc.hamiltonian.poisson.pd.ifft(
calc.density.rhot_q) - calc.density.nt_sg[0]
#plane wave descriptor for Hartree potential
self.pd0 = self.ham.poisson.pd
#reciprocal |G|^2 vectors for Hartree potential V(G)=4pi/|G|^2
self.G2 = self.ham.poisson.G2_q
self.G = self.pd0.get_reciprocal_vectors()
#fine to coarse and coarse to fine grids transformers (for correct calculation local potential)
self.fine_to_coarse = Transformer(calc.density.finegd, calc.density.gd,
3)
self.coarse_to_fine = Transformer(calc.density.gd, calc.density.finegd,
3)
#initialization local potenital from ground state density
self.update_local_potential()
self.update_gauge([0, 0, 0])
class DensityFourierTransform(Observer):
def __init__(self, timestep, frequencies, width=None, interval=1):
"""
Parameters
----------
timestep: float
Time step in attoseconds (10^-18 s), e.g., 4.0 or 8.0
frequencies: NumPy array or list of floats
Frequencies in eV for Fourier transforms
width: float or None
Width of Gaussian envelope in eV, otherwise no envelope
interval: int
Number of timesteps between calls (used when attaching)
"""
Observer.__init__(self, interval)
self.timestep = interval * timestep * attosec_to_autime # autime
self.omega_w = np.asarray(frequencies) * eV_to_aufrequency # autime^(-1)
if width is None:
self.sigma = None
else:
self.sigma = width * eV_to_aufrequency # autime^(-1)
self.nw = len(self.omega_w)
self.dtype = complex # np.complex128 really, but hey...
self.Fnt_wsG = None
self.Fnt_wsg = None
self.Ant_sG = None
self.Ant_sg = None
def initialize(self, paw, allocate=True):
self.allocated = False
assert hasattr(paw, 'time') and hasattr(paw, 'niter'), 'Use TDDFT!'
self.time = paw.time
self.niter = paw.niter
self.world = paw.wfs.world
self.gd = paw.density.gd
self.finegd = paw.density.finegd
self.nspins = paw.density.nspins
self.stencil = paw.input_parameters.stencils[1] # i.e. tar['InterpolationStencil']
self.interpolator = paw.density.interpolator
self.cinterpolator = Transformer(self.gd, self.finegd, self.stencil, \
dtype=self.dtype, allocate=False)
self.phase_cd = np.ones((3, 2), dtype=complex)
self.Ant_sG = paw.density.nt_sG.copy() # TODO in allocate instead?
# Attach to PAW-type object
paw.attach(self, self.interval, density=paw.density)
if allocate:
self.allocate()
def allocate(self):
if not self.allocated:
self.Fnt_wsG = self.gd.zeros((self.nw, self.nspins), \
dtype=self.dtype)
self.Fnt_wsg = None
#self.Ant_sG = ...
self.Ant_sg = None
self.gamma_w = np.ones(self.nw, dtype=complex) * self.timestep
self.cinterpolator.allocate()
self.allocated = True
if debug:
assert is_contiguous(self.Fnt_wsG, self.dtype)
def interpolate_fourier_transform(self):
if self.Fnt_wsg is None:
self.Fnt_wsg = self.finegd.empty((self.nw, self.nspins), \
dtype=self.dtype)
if self.dtype == float:
intapply = self.interpolator.apply
else:
intapply = lambda Fnt_G, Fnt_g: self.cinterpolator.apply(Fnt_G, \
Fnt_g, self.phase_cd)
for w in range(self.nw):
for s in range(self.nspins):
intapply(self.Fnt_wsG[w,s], self.Fnt_wsg[w,s])
def interpolate_average(self):
if self.Ant_sg is None:
self.Ant_sg = self.finegd.empty(self.nspins, dtype=float)
for s in range(self.nspins):
self.interpolator.apply(self.Ant_sG[s], self.Ant_sg[s])
def update(self, density):
# Update time
# t[N] = t[N-1] + dt[N-1] #TODO better time-convention?
self.time += self.timestep
# Complex exponential with/without finite-width envelope
f_w = np.exp(1.0j*self.omega_w*self.time)
if self.sigma is not None:
f_w *= np.exp(-self.time**2*self.sigma**2/2.0)
# Update Fourier transformed density components
# Fnt_wG[N] = Fnt_wG[N-1] + 1/sqrt(pi) * (nt_G[N]-avg_nt_G[N-1]) \
# * (f[N]*t[N] - gamma[N-1]) * dt[N]/(t[N]+dt[N])
for w in range(self.nw):
self.Fnt_wsG[w] += 1/np.pi**0.5 * (density.nt_sG - self.Ant_sG) \
* (f_w[w]*self.time - self.gamma_w[w]) * self.timestep \
/ (self.time + self.timestep)
# Update the cumulative phase factors
# gamma[N] = gamma[N-1] + f[N]*dt[N]
self.gamma_w += f_w * self.timestep
# If dt[N] = dt for all N and sigma = 0, then this simplifies to:
# gamma[N] = Sum_{n=0}^N exp(i*omega*n*dt) * dt
# = (1 - exp(i*omega*(N+1)*dt)) / (1 - exp(i*omega*dt)) * dt
# Update average density
# Ant_G[N] = (t[N]*Ant_G[N-1] + nt_G[N]*dt[N])/(t[N]+dt[N])
self.Ant_sG = (self.time*self.Ant_sG + density.nt_sG*self.timestep) \
/ (self.time + self.timestep)
def get_fourier_transform(self, frequency=0, spin=0, gridrefinement=1):
if gridrefinement == 1:
return self.Fnt_wsG[frequency, spin]
elif gridrefinement == 2:
if self.Fnt_wsg is None:
self.interpolate_fourier_transform()
return self.Fnt_wsg[frequency, spin]
else:
raise NotImplementedError('Arbitrary refinement not implemented')
def get_average(self, spin=0, gridrefinement=1):
if gridrefinement == 1:
return self.Ant_sG[spin]
elif gridrefinement == 2:
if self.Ant_sg is None:
self.interpolate_average()
return self.Ant_sg[spin]
else:
raise NotImplementedError('Arbitrary refinement not implemented')
def read(self, filename, idiotproof=True):
if idiotproof and not filename.endswith('.ftd'):
raise IOError('Filename must end with `.ftd`.')
tar = Reader(filename)
# Test data type
dtype = {'Float':float, 'Complex':complex}[tar['DataType']]
if dtype != self.dtype:
raise IOError('Data is an incompatible type.')
# Test time
time = tar['Time']
if idiotproof and abs(time-self.time) >= 1e-9:
raise IOError('Timestamp is incompatible with calculator.')
# Test timestep (non-critical)
timestep = tar['TimeStep']
if abs(timestep - self.timestep) > 1e-12:
print 'Warning: Time-step has been altered. (%lf -> %lf)' \
% (self.timestep, timestep)
self.timestep = timestep
# Test dimensions
nw = tar.dimension('nw')
nspins = tar.dimension('nspins')
ng = (tar.dimension('ngptsx'), tar.dimension('ngptsy'), \
tar.dimension('ngptsz'),)
if (nw != self.nw or nspins != self.nspins or
(ng != self.gd.get_size_of_global_array()).any()):
raise IOError('Data has incompatible shapes.')
# Test width (non-critical)
sigma = tar['Width']
if ((sigma is None)!=(self.sigma is None) or # float <-> None
(sigma is not None and self.sigma is not None and \
abs(sigma - self.sigma) > 1e-12)): # float -> float
print 'Warning: Width has been altered. (%s -> %s)' \
% (self.sigma, sigma)
self.sigma = sigma
# Read frequencies
self.omega_w[:] = tar.get('Frequency')
# Read cumulative phase factors
self.gamma_w[:] = tar.get('PhaseFactor')
# Read average densities on master and distribute
for s in range(self.nspins):
all_Ant_G = tar.get('Average', s)
self.gd.distribute(all_Ant_G, self.Ant_sG[s])
# Read fourier transforms on master and distribute
for w in range(self.nw):
for s in range(self.nspins):
all_Fnt_G = tar.get('FourierTransform', w, s)
self.gd.distribute(all_Fnt_G, self.Fnt_wsG[w,s])
# Close for good measure
tar.close()
def write(self, filename, idiotproof=True):
if idiotproof and not filename.endswith('.ftd'):
raise IOError('Filename must end with `.ftd`.')
master = self.world.rank == 0
# Open writer on master and set parameters/dimensions
if master:
tar = Writer(filename)
tar['DataType'] = {float:'Float', complex:'Complex'}[self.dtype]
tar['Time'] = self.time
tar['TimeStep'] = self.timestep #non-essential
tar['Width'] = self.sigma
tar.dimension('nw', self.nw)
tar.dimension('nspins', self.nspins)
# Create dimensions for varioius netCDF variables:
ng = self.gd.get_size_of_global_array()
tar.dimension('ngptsx', ng[0])
tar.dimension('ngptsy', ng[1])
tar.dimension('ngptsz', ng[2])
# Write frequencies
tar.add('Frequency', ('nw',), self.omega_w, dtype=float)
# Write cumulative phase factors
tar.add('PhaseFactor', ('nw',), self.gamma_w, dtype=self.dtype)
# Collect average densities on master and write
if master:
tar.add('Average', ('nspins', 'ngptsx', 'ngptsy',
'ngptsz', ), dtype=float)
for s in range(self.nspins):
big_Ant_G = self.gd.collect(self.Ant_sG[s])
if master:
tar.fill(big_Ant_G)
# Collect fourier transforms on master and write
if master:
tar.add('FourierTransform', ('nw', 'nspins', 'ngptsx', 'ngptsy', \
'ngptsz', ), dtype=self.dtype)
for w in range(self.nw):
for s in range(self.nspins):
big_Fnt_G = self.gd.collect(self.Fnt_wsG[w,s])
if master:
tar.fill(big_Fnt_G)
# Close to flush changes
if master:
tar.close()
# Make sure slaves don't return before master is done
self.world.barrier()
def dump(self, filename):
if debug:
assert is_contiguous(self.Fnt_wsG, self.dtype)
assert is_contiguous(self.Ant_sG, float)
all_Fnt_wsG = self.gd.collect(self.Fnt_wsG)
all_Ant_sG = self.gd.collect(self.Ant_sG)
if self.world.rank == 0:
all_Fnt_wsG.dump(filename)
all_Ant_sG.dump(filename+'_avg') # crude but easy
self.omega_w.dump(filename+'_omega') # crude but easy
self.gamma_w.dump(filename+'_gamma') # crude but easy
def load(self, filename):
if self.world.rank == 0:
all_Fnt_wsG = np.load(filename)
all_Ant_sG = np.load(filename+'_avg') # crude but easy
else:
all_Fnt_wsG = None
all_Ant_sG = None
if debug:
assert all_Fnt_wsG is None or is_contiguous(all_Fnt_wsG, self.dtype)
assert all_Ant_sG is None or is_contiguous(all_Ant_sG, float)
if not self.allocated:
self.allocate()
self.gd.distribute(all_Fnt_wsG, self.Fnt_wsG)
self.gd.distribute(all_Ant_sG, self.Ant_sG)
self.omega_w = np.load(filename+'_omega') # crude but easy
self.gamma_w = np.load(filename+'_gamma') # crude but easy
def __init__(self, calc, kd, poisson_solver, dtype=float, **kwargs):
"""Store useful objects, e.g. lfc's for the various atomic functions.
Depending on whether the system is periodic or finite, Poisson's equation
is solved with FFT or multigrid techniques, respectively.
Parameters
----------
calc: Calculator
Ground-state calculation.
kd: KPointDescriptor
Descriptor for the q-vectors of the dynamical matrix.
"""
self.kd = kd
self.dtype = dtype
self.poisson = poisson_solver
# Gamma wrt q-vector
if self.kd.gamma:
self.phase_cd = None
else:
assert self.kd.mynks == len(self.kd.ibzk_qc)
self.phase_qcd = []
sdisp_cd = calc.wfs.gd.sdisp_cd
for q in range(self.kd.mynks):
phase_cd = np.exp(2j * np.pi * \
sdisp_cd * self.kd.ibzk_qc[q, :, np.newaxis])
self.phase_qcd.append(phase_cd)
# Store grid-descriptors
self.gd = calc.density.gd
self.finegd = calc.density.finegd
# Steal setups for the lfc's
setups = calc.wfs.setups
# Store projector coefficients
self.dH_asp = calc.hamiltonian.dH_asp.copy()
# Localized functions:
# core corections
self.nct = LFC(self.gd, [[setup.nct] for setup in setups],
integral=[setup.Nct for setup in setups], dtype=self.dtype)
# compensation charges
#XXX what is the consequence of numerical errors in the integral ??
self.ghat = LFC(self.finegd, [setup.ghat_l for setup in setups],
dtype=self.dtype)
## self.ghat = LFC(self.finegd, [setup.ghat_l for setup in setups],
## integral=sqrt(4 * pi), dtype=self.dtype)
# vbar potential
self.vbar = LFC(self.finegd, [[setup.vbar] for setup in setups],
dtype=self.dtype)
# Expansion coefficients for the compensation charges
self.Q_aL = calc.density.Q_aL.copy()
# Grid transformer -- convert array from fine to coarse grid
self.restrictor = Transformer(self.finegd, self.gd, nn=3,
dtype=self.dtype, allocate=False)
# Atom, cartesian coordinate and q-vector of the perturbation
self.a = None
self.v = None
# Local q-vector index of the perturbation
if self.kd.gamma:
self.q = -1
else:
self.q = None
def new_get_all_electron_density(self, atoms, gridrefinement=2):
"""Return real all-electron density array."""
# Refinement of coarse grid, for representation of the AE-density
if gridrefinement == 1:
gd = self.gd
n_sg = self.nt_sG.copy()
elif gridrefinement == 2:
gd = self.finegd
if self.nt_sg is None:
self.interpolate()
n_sg = self.nt_sg.copy()
elif gridrefinement == 4:
# Extra fine grid
gd = self.finegd.refine()
# Interpolation function for the density:
interpolator = Transformer(self.finegd, gd, 3)
# Transfer the pseudo-density to the fine grid:
n_sg = gd.empty(self.nspins)
if self.nt_sg is None:
self.interpolate()
for s in range(self.nspins):
interpolator.apply(self.nt_sg[s], n_sg[s])
else:
raise NotImplementedError
# Add corrections to pseudo-density to get the AE-density
splines = {}
phi_aj = []
phit_aj = []
nc_a = []
nct_a = []
for a, id in enumerate(self.setups.id_a):
if id in splines:
phi_j, phit_j, nc, nct = splines[id]
else:
# Load splines:
phi_j, phit_j, nc, nct = self.setups[a].get_partial_waves()[:4]
splines[id] = (phi_j, phit_j, nc, nct)
phi_aj.append(phi_j)
phit_aj.append(phit_j)
nc_a.append([nc])
nct_a.append([nct])
# Create localized functions from splines
phi = BasisFunctions(gd, phi_aj)
phit = BasisFunctions(gd, phit_aj)
nc = LFC(gd, nc_a)
nct = LFC(gd, nct_a)
spos_ac = atoms.get_scaled_positions() % 1.0
phi.set_positions(spos_ac)
phit.set_positions(spos_ac)
nc.set_positions(spos_ac)
nct.set_positions(spos_ac)
I_sa = np.zeros((self.nspins, len(atoms)))
a_W = np.empty(len(phi.M_W), np.int32)
W = 0
for a in phi.atom_indices:
nw = len(phi.sphere_a[a].M_w)
a_W[W:W + nw] = a
W += nw
rho_MM = np.zeros((phi.Mmax, phi.Mmax))
for s, I_a in enumerate(I_sa):
M1 = 0
for a, setup in enumerate(self.setups):
ni = setup.ni
D_sp = self.D_asp.get(a)
if D_sp is None:
D_sp = np.empty((self.nspins, ni * (ni + 1) // 2))
else:
I_a[a] = ((setup.Nct - setup.Nc) / self.nspins -
sqrt(4 * pi) *
np.dot(D_sp[s], setup.Delta_pL[:, 0]))
if gd.comm.size > 1:
gd.comm.broadcast(D_sp, self.rank_a[a])
M2 = M1 + ni
rho_MM[M1:M2, M1:M2] = unpack2(D_sp[s])
M1 = M2
phi.lfc.ae_valence_density_correction(rho_MM, n_sg[s], a_W, I_a)
phit.lfc.ae_valence_density_correction(-rho_MM, n_sg[s], a_W, I_a)
a_W = np.empty(len(nc.M_W), np.int32)
W = 0
for a in nc.atom_indices:
nw = len(nc.sphere_a[a].M_w)
a_W[W:W + nw] = a
W += nw
scale = 1.0 / self.nspins
for s, I_a in enumerate(I_sa):
nc.lfc.ae_core_density_correction(scale, n_sg[s], a_W, I_a)
nct.lfc.ae_core_density_correction(-scale, n_sg[s], a_W, I_a)
gd.comm.sum(I_a)
N_c = gd.N_c
g_ac = np.around(N_c * spos_ac).astype(int) % N_c - gd.beg_c
for I, g_c in zip(I_a, g_ac):
if (g_c >= 0).all() and (g_c < gd.n_c).all():
n_sg[s][tuple(g_c)] -= I / gd.dv
return n_sg, gd
class HybridXC(HybridXCBase):
def __init__(self,
name,
hybrid=None,
xc=None,
finegrid=False,
unocc=False,
omega=None,
excitation=None,
excited=0,
stencil=2):
"""Mix standard functionals with exact exchange.
finegrid: boolean
Use fine grid for energy functional evaluations ?
unocc: boolean
Apply vxx also to unoccupied states ?
omega: float
RSF mixing parameter
excitation: string:
Apply operator for improved virtual orbitals
to unocc states? Possible modes:
singlet: excitations to singlets
triplet: excitations to triplets
average: average between singlets and tripletts
see f.e. http://dx.doi.org/10.1021/acs.jctc.8b00238
excited: number
Band to excite from - counted from H**O downwards
"""
self.finegrid = finegrid
self.unocc = unocc
self.excitation = excitation
self.excited = excited
HybridXCBase.__init__(self,
name,
hybrid=hybrid,
xc=xc,
omega=omega,
stencil=stencil)
def calculate_paw_correction(self,
setup,
D_sp,
dEdD_sp=None,
addcoredensity=True,
a=None):
return self.xc.calculate_paw_correction(setup, D_sp, dEdD_sp,
addcoredensity, a)
def initialize(self, density, hamiltonian, wfs, occupations):
assert wfs.kd.gamma
self.xc.initialize(density, hamiltonian, wfs, occupations)
self.kpt_comm = wfs.kd.comm
self.nspins = wfs.nspins
self.setups = wfs.setups
self.density = density
self.kpt_u = wfs.kpt_u
self.exx_s = np.zeros(self.nspins)
self.ekin_s = np.zeros(self.nspins)
self.nocc_s = np.empty(self.nspins, int)
self.gd = density.gd
self.redistributor = density.redistributor
use_charge_center = hamiltonian.poisson.use_charge_center
# XXX How do we construct a copy of the Poisson solver of the
# Hamiltonian? We don't know what class it is, etc., but gd
# may differ.
# XXX One might consider using a charged centered compensation
# charge for the PoissonSolver in the case of EXX as standard
self.poissonsolver = PoissonSolver('fd',
eps=1e-11,
use_charge_center=use_charge_center)
# self.poissonsolver = hamiltonian.poisson
if self.finegrid:
self.finegd = self.gd.refine()
# XXX Taking restrictor from Hamiltonian will not work in PW mode,
# will it? I think this supports only real-space mode.
# self.restrictor = hamiltonian.restrictor
self.restrictor = Transformer(self.finegd, self.gd, 3)
self.interpolator = Transformer(self.gd, self.finegd, 3)
else:
self.finegd = self.gd
self.ghat = LFC(self.finegd,
[setup.ghat_l for setup in density.setups],
integral=np.sqrt(4 * np.pi),
forces=True)
self.poissonsolver.set_grid_descriptor(self.finegd)
if self.rsf == 'Yukawa':
omega2 = self.omega**2
self.screened_poissonsolver = HelmholtzSolver(
k2=-omega2,
eps=1e-11,
nn=3,
use_charge_center=use_charge_center)
self.screened_poissonsolver.set_grid_descriptor(self.finegd)
def set_positions(self, spos_ac):
self.ghat.set_positions(spos_ac)
def calculate(self, gd, n_sg, v_sg=None, e_g=None):
# Normal XC contribution:
exc = self.xc.calculate(gd, n_sg, v_sg, e_g)
# Note that the quantities passed are on the
# density/Hamiltonian grids!
# They may be distributed differently from own quantities.
self.ekin = self.kpt_comm.sum(self.ekin_s.sum())
return exc + self.kpt_comm.sum(self.exx_s.sum())
def calculate_exx(self):
for kpt in self.kpt_u:
self.apply_orbital_dependent_hamiltonian(kpt, kpt.psit_nG)
def apply_orbital_dependent_hamiltonian(self,
kpt,
psit_nG,
Htpsit_nG=None,
dH_asp=None):
if kpt.f_n is None:
return
deg = 2 // self.nspins # Spin degeneracy
hybrid = self.hybrid
P_ani = kpt.P_ani
setups = self.setups
is_cam = self.is_cam
vt_g = self.finegd.empty()
if self.gd is not self.finegd:
vt_G = self.gd.empty()
if self.rsf == 'Yukawa':
y_vt_g = self.finegd.empty()
# if self.gd is not self.finegd:
# y_vt_G = self.gd.empty()
nocc = int(ceil(kpt.f_n.sum())) // (3 - self.nspins)
if self.excitation is not None:
ex_band = nocc - self.excited - 1
if self.excitation == 'singlet':
ex_weight = -1
elif self.excitation == 'triplet':
ex_weight = +1
else:
ex_weight = 0
if self.unocc or self.excitation is not None:
nbands = len(kpt.f_n)
else:
nbands = nocc
self.nocc_s[kpt.s] = nocc
if Htpsit_nG is not None:
kpt.vt_nG = self.gd.empty(nbands)
kpt.vxx_ani = {}
kpt.vxx_anii = {}
for a, P_ni in P_ani.items():
I = P_ni.shape[1]
kpt.vxx_ani[a] = np.zeros((nbands, I))
kpt.vxx_anii[a] = np.zeros((nbands, I, I))
exx = 0.0
ekin = 0.0
# XXXX nbands can be different numbers on different cpus!
# That means some will execute the loop and others not.
# And deadlocks with augment-grids.
# Determine pseudo-exchange
for n1 in range(nbands):
psit1_G = psit_nG[n1]
f1 = kpt.f_n[n1] / deg
for n2 in range(n1, nbands):
psit2_G = psit_nG[n2]
f2 = kpt.f_n[n2] / deg
if n1 != n2 and f1 == 0 and f1 == f2:
continue # Don't work on double unocc. bands
# Double count factor:
dc = (1 + (n1 != n2)) * deg
nt_G, rhot_g = self.calculate_pair_density(
n1, n2, psit_nG, P_ani)
vt_g[:] = 0.0
# XXXXX This will go wrong because we are solving the
# Poisson equation on the distribution of gd, not finegd
# Or maybe it's fixed now
self.poissonsolver.solve(vt_g,
-rhot_g,
charge=-float(n1 == n2),
eps=1e-12,
zero_initial_phi=True)
vt_g *= hybrid
if self.rsf == 'Yukawa':
y_vt_g[:] = 0.0
self.screened_poissonsolver.solve(y_vt_g,
-rhot_g,
charge=-float(n1 == n2),
eps=1e-12,
zero_initial_phi=True)
if is_cam: # Cam like correction
y_vt_g *= self.cam_beta
else:
y_vt_g *= hybrid
vt_g -= y_vt_g
if self.gd is self.finegd:
vt_G = vt_g
else:
self.restrictor.apply(vt_g, vt_G)
# Integrate the potential on fine and coarse grids
int_fine = self.finegd.integrate(vt_g * rhot_g)
int_coarse = self.gd.integrate(vt_G * nt_G)
if self.gd.comm.rank == 0: # only add to energy on master CPU
exx += 0.5 * dc * f1 * f2 * int_fine
ekin -= dc * f1 * f2 * int_coarse
if Htpsit_nG is not None:
Htpsit_nG[n1] += f2 * vt_G * psit2_G
if n1 == n2:
kpt.vt_nG[n1] = f1 * vt_G
if self.excitation is not None and n1 == ex_band:
Htpsit_nG[nocc:] += f1 * vt_G * psit_nG[nocc:]
else:
if self.excitation is None or n1 != ex_band \
or n2 < nocc:
Htpsit_nG[n2] += f1 * vt_G * psit1_G
else:
Htpsit_nG[n2] += f1 * ex_weight * vt_G * psit1_G
# Update the vxx_uni and vxx_unii vectors of the nuclei,
# used to determine the atomic hamiltonian, and the
# residuals
v_aL = self.ghat.dict()
self.ghat.integrate(vt_g, v_aL)
for a, v_L in v_aL.items():
v_ii = unpack(np.dot(setups[a].Delta_pL, v_L))
v_ni = kpt.vxx_ani[a]
v_nii = kpt.vxx_anii[a]
P_ni = P_ani[a]
v_ni[n1] += f2 * np.dot(v_ii, P_ni[n2])
if n1 != n2:
if self.excitation is None or n1 != ex_band or \
n2 < nocc:
v_ni[n2] += f1 * np.dot(v_ii, P_ni[n1])
else:
v_ni[n2] += f1 * ex_weight * \
np.dot(v_ii, P_ni[n1])
else:
# XXX Check this:
v_nii[n1] = f1 * v_ii
if self.excitation is not None and n1 == ex_band:
for nuoc in range(nocc, nbands):
v_ni[nuoc] += f1 * \
np.dot(v_ii, P_ni[nuoc])
def calculate_vv(ni, D_ii, M_pp, weight, addme=False):
"""Calculate the local corrections depending on Mpp."""
dexx = 0
dekin = 0
if not addme:
addsign = -2.0
else:
addsign = 2.0
for i1 in range(ni):
for i2 in range(ni):
A = 0.0
for i3 in range(ni):
p13 = packed_index(i1, i3, ni)
for i4 in range(ni):
p24 = packed_index(i2, i4, ni)
A += M_pp[p13, p24] * D_ii[i3, i4]
p12 = packed_index(i1, i2, ni)
if Htpsit_nG is not None:
dH_p[p12] += addsign * weight / \
deg * A / ((i1 != i2) + 1)
dekin += 2 * weight / deg * D_ii[i1, i2] * A
dexx -= weight / deg * D_ii[i1, i2] * A
return (dexx, dekin)
# Apply the atomic corrections to the energy and the Hamiltonian
# matrix
for a, P_ni in P_ani.items():
setup = setups[a]
if Htpsit_nG is not None:
# Add non-trivial corrections the Hamiltonian matrix
h_nn = symmetrize(
np.inner(P_ni[:nbands], kpt.vxx_ani[a][:nbands]))
ekin -= np.dot(kpt.f_n[:nbands], h_nn.diagonal())
dH_p = dH_asp[a][kpt.s]
# Get atomic density and Hamiltonian matrices
D_p = self.density.D_asp[a][kpt.s]
D_ii = unpack2(D_p)
ni = len(D_ii)
# Add atomic corrections to the valence-valence exchange energy
# --
# > D C D
# -- ii iiii ii
(dexx, dekin) = calculate_vv(ni, D_ii, setup.M_pp, hybrid)
ekin += dekin
exx += dexx
if self.rsf is not None:
Mg_pp = setup.calculate_yukawa_interaction(self.omega)
if is_cam:
(dexx, dekin) = calculate_vv(ni,
D_ii,
Mg_pp,
self.cam_beta,
addme=True)
else:
(dexx, dekin) = calculate_vv(ni,
D_ii,
Mg_pp,
hybrid,
addme=True)
ekin -= dekin
exx -= dexx
# Add valence-core exchange energy
# --
# > X D
# -- ii ii
if setup.X_p is not None:
exx -= hybrid * np.dot(D_p, setup.X_p)
if Htpsit_nG is not None:
dH_p -= hybrid * setup.X_p
ekin += hybrid * np.dot(D_p, setup.X_p)
if self.rsf == 'Yukawa' and setup.X_pg is not None:
if is_cam:
thybrid = self.cam_beta # 0th order
else:
thybrid = hybrid
exx += thybrid * np.dot(D_p, setup.X_pg)
if Htpsit_nG is not None:
dH_p += thybrid * setup.X_pg
ekin -= thybrid * np.dot(D_p, setup.X_pg)
elif self.rsf == 'Yukawa' and setup.X_pg is None:
thybrid = exp(-3.62e-2 * self.omega) # educated guess
if is_cam:
thybrid *= self.cam_beta
else:
thybrid *= hybrid
exx += thybrid * np.dot(D_p, setup.X_p)
if Htpsit_nG is not None:
dH_p += thybrid * setup.X_p
ekin -= thybrid * np.dot(D_p, setup.X_p)
# Add core-core exchange energy
if kpt.s == 0:
if self.rsf is None or is_cam:
if is_cam:
exx += self.cam_alpha * setup.ExxC
else:
exx += hybrid * setup.ExxC
self.exx_s[kpt.s] = self.gd.comm.sum(exx)
self.ekin_s[kpt.s] = self.gd.comm.sum(ekin)
def correct_hamiltonian_matrix(self, kpt, H_nn):
if not hasattr(kpt, 'vxx_ani'):
return
# if self.gd.comm.rank > 0:
# H_nn[:] = 0.0
nocc = self.nocc_s[kpt.s]
nbands = len(kpt.vt_nG)
for a, P_ni in kpt.P_ani.items():
H_nn[:nbands, :nbands] += symmetrize(
np.inner(P_ni[:nbands], kpt.vxx_ani[a]))
# self.gd.comm.sum(H_nn)
if not self.unocc or self.excitation is not None:
H_nn[:nocc, nocc:] = 0.0
H_nn[nocc:, :nocc] = 0.0
def calculate_pair_density(self, n1, n2, psit_nG, P_ani):
Q_aL = {}
for a, P_ni in P_ani.items():
P1_i = P_ni[n1]
P2_i = P_ni[n2]
D_ii = np.outer(P1_i, P2_i.conj()).real
D_p = pack(D_ii)
Q_aL[a] = np.dot(D_p, self.setups[a].Delta_pL)
nt_G = psit_nG[n1] * psit_nG[n2]
if self.finegd is self.gd:
nt_g = nt_G
else:
nt_g = self.finegd.empty()
self.interpolator.apply(nt_G, nt_g)
rhot_g = nt_g.copy()
self.ghat.add(rhot_g, Q_aL)
return nt_G, rhot_g
def add_correction(self,
kpt,
psit_xG,
Htpsit_xG,
P_axi,
c_axi,
n_x,
calculate_change=False):
if kpt.f_n is None:
return
if self.unocc or self.excitation is not None:
nocc = len(kpt.vt_nG)
else:
nocc = self.nocc_s[kpt.s]
if calculate_change:
for x, n in enumerate(n_x):
if n < nocc:
Htpsit_xG[x] += kpt.vt_nG[n] * psit_xG[x]
for a, P_xi in P_axi.items():
c_axi[a][x] += np.dot(kpt.vxx_anii[a][n], P_xi[x])
else:
for a, c_xi in c_axi.items():
c_xi[:nocc] += kpt.vxx_ani[a][:nocc]
def rotate(self, kpt, U_nn):
if kpt.f_n is None:
return
U_nn = U_nn.T.copy()
nocc = self.nocc_s[kpt.s]
if len(kpt.vt_nG) == nocc:
U_nn = U_nn[:nocc, :nocc]
gemm(1.0, kpt.vt_nG.copy(), U_nn, 0.0, kpt.vt_nG)
for v_ni in kpt.vxx_ani.values():
gemm(1.0, v_ni.copy(), U_nn, 0.0, v_ni)
for v_nii in kpt.vxx_anii.values():
gemm(1.0, v_nii.copy(), U_nn, 0.0, v_nii)
def get_all_electron_density(self,
atoms=None,
gridrefinement=2,
spos_ac=None,
skip_core=False):
"""Return real all-electron density array.
Usage: Either get_all_electron_density(atoms) or
get_all_electron_density(spos_ac=spos_ac)
skip_core=True theoretically returns the
all-electron valence density (use with
care; will not in general integrate
to valence)
"""
if spos_ac is None:
spos_ac = atoms.get_scaled_positions() % 1.0
# Refinement of coarse grid, for representation of the AE-density
# XXXXXXXXXXXX think about distribution depending on gridrefinement!
if gridrefinement == 1:
gd = self.redistributor.aux_gd
n_sg = self.nt_sG.copy()
# This will get the density with the same distribution
# as finegd:
n_sg = self.redistributor.distribute(n_sg)
elif gridrefinement == 2:
gd = self.finegd
if self.nt_sg is None:
self.interpolate_pseudo_density()
n_sg = self.nt_sg.copy()
elif gridrefinement == 4:
# Extra fine grid
gd = self.finegd.refine()
# Interpolation function for the density:
interpolator = Transformer(self.finegd, gd, 3) # XXX grids!
# Transfer the pseudo-density to the fine grid:
n_sg = gd.empty(self.nspins)
if self.nt_sg is None:
self.interpolate_pseudo_density()
for s in range(self.nspins):
interpolator.apply(self.nt_sg[s], n_sg[s])
else:
raise NotImplementedError
# Add corrections to pseudo-density to get the AE-density
splines = {}
phi_aj = []
phit_aj = []
nc_a = []
nct_a = []
for a, id in enumerate(self.setups.id_a):
if id in splines:
phi_j, phit_j, nc, nct = splines[id]
else:
# Load splines:
phi_j, phit_j, nc, nct = self.setups[a].get_partial_waves()[:4]
splines[id] = (phi_j, phit_j, nc, nct)
phi_aj.append(phi_j)
phit_aj.append(phit_j)
nc_a.append([nc])
nct_a.append([nct])
# Create localized functions from splines
phi = BasisFunctions(gd, phi_aj)
phit = BasisFunctions(gd, phit_aj)
nc = LFC(gd, nc_a)
nct = LFC(gd, nct_a)
phi.set_positions(spos_ac)
phit.set_positions(spos_ac)
nc.set_positions(spos_ac)
nct.set_positions(spos_ac)
I_sa = np.zeros((self.nspins, len(spos_ac)))
a_W = np.empty(len(phi.M_W), np.intc)
W = 0
for a in phi.atom_indices:
nw = len(phi.sphere_a[a].M_w)
a_W[W:W + nw] = a
W += nw
x_W = phi.create_displacement_arrays()[0]
D_asp = self.D_asp # XXX really?
rho_MM = np.zeros((phi.Mmax, phi.Mmax))
for s, I_a in enumerate(I_sa):
M1 = 0
for a, setup in enumerate(self.setups):
ni = setup.ni
D_sp = D_asp.get(a)
if D_sp is None:
D_sp = np.empty((self.nspins, ni * (ni + 1) // 2))
else:
I_a[a] = (
(setup.Nct) / self.nspins -
sqrt(4 * pi) * np.dot(D_sp[s], setup.Delta_pL[:, 0]))
if not skip_core:
I_a[a] -= setup.Nc / self.nspins
if gd.comm.size > 1:
gd.comm.broadcast(D_sp, D_asp.partition.rank_a[a])
M2 = M1 + ni
rho_MM[M1:M2, M1:M2] = unpack2(D_sp[s])
M1 = M2
assert np.all(n_sg[s].shape == phi.gd.n_c)
phi.lfc.ae_valence_density_correction(rho_MM, n_sg[s], a_W, I_a,
x_W)
phit.lfc.ae_valence_density_correction(-rho_MM, n_sg[s], a_W, I_a,
x_W)
a_W = np.empty(len(nc.M_W), np.intc)
W = 0
for a in nc.atom_indices:
nw = len(nc.sphere_a[a].M_w)
a_W[W:W + nw] = a
W += nw
scale = 1.0 / self.nspins
for s, I_a in enumerate(I_sa):
if not skip_core:
nc.lfc.ae_core_density_correction(scale, n_sg[s], a_W, I_a)
nct.lfc.ae_core_density_correction(-scale, n_sg[s], a_W, I_a)
gd.comm.sum(I_a)
N_c = gd.N_c
g_ac = np.around(N_c * spos_ac).astype(int) % N_c - gd.beg_c
if not skip_core:
for I, g_c in zip(I_a, g_ac):
if (g_c >= 0).all() and (g_c < gd.n_c).all():
n_sg[s][tuple(g_c)] -= I / gd.dv
return n_sg, gd
class RealSpaceDensity(Density):
def __init__(self,
gd,
finegd,
nspins,
charge,
redistributor,
stencil=3,
background_charge=None):
Density.__init__(self,
gd,
finegd,
nspins,
charge,
redistributor,
background_charge=background_charge)
self.stencil = stencil
def initialize(self, setups, timer, magmom_a, hund):
Density.initialize(self, setups, timer, magmom_a, hund)
# Interpolation function for the density:
self.interpolator = Transformer(self.redistributor.aux_gd, self.finegd,
self.stencil)
spline_aj = []
for setup in setups:
if setup.nct is None:
spline_aj.append([])
else:
spline_aj.append([setup.nct])
self.nct = LFC(self.gd,
spline_aj,
integral=[setup.Nct for setup in setups],
forces=True,
cut=True)
self.ghat = LFC(self.finegd, [setup.ghat_l for setup in setups],
integral=sqrt(4 * pi),
forces=True)
def set_positions(self, spos_ac, rank_a=None):
Density.set_positions(self, spos_ac, rank_a)
self.nct_G = self.gd.zeros()
self.nct.add(self.nct_G, 1.0 / self.nspins)
def interpolate_pseudo_density(self, comp_charge=None):
"""Interpolate pseudo density to fine grid."""
if comp_charge is None:
comp_charge = self.calculate_multipole_moments()
self.nt_sg = self.distribute_and_interpolate(self.nt_sG, self.nt_sg)
# With periodic boundary conditions, the interpolation will
# conserve the number of electrons.
if not self.gd.pbc_c.all():
# With zero-boundary conditions in one or more directions,
# this is not the case.
pseudo_charge = (self.background_charge.charge - self.charge -
comp_charge)
if abs(pseudo_charge) > 1.0e-14:
x = (pseudo_charge / self.finegd.integrate(self.nt_sg).sum())
self.nt_sg *= x
def interpolate(self, in_xR, out_xR=None):
"""Interpolate array(s)."""
# ndim will be 3 in finite-difference mode and 1 when working
# with the AtomPAW class (spherical atoms and 1d grids)
ndim = self.gd.ndim
if out_xR is None:
out_xR = self.finegd.empty(in_xR.shape[:-ndim])
a_xR = in_xR.reshape((-1, ) + in_xR.shape[-ndim:])
b_xR = out_xR.reshape((-1, ) + out_xR.shape[-ndim:])
for in_R, out_R in zip(a_xR, b_xR):
self.interpolator.apply(in_R, out_R)
return out_xR
def distribute_and_interpolate(self, in_xR, out_xR=None):
in_xR = self.redistributor.distribute(in_xR)
return self.interpolate(in_xR, out_xR)
def calculate_pseudo_charge(self):
self.nt_g = self.nt_sg.sum(axis=0)
self.rhot_g = self.nt_g.copy()
self.ghat.add(self.rhot_g, self.Q_aL)
self.background_charge.add_charge_to(self.rhot_g)
if debug:
charge = self.finegd.integrate(self.rhot_g) + self.charge
if abs(charge) > self.charge_eps:
raise RuntimeError('Charge not conserved: excess=%.9f' %
charge)
def get_pseudo_core_kinetic_energy_density_lfc(self):
return LFC(self.gd, [[setup.tauct] for setup in self.setups],
forces=True,
cut=True)
def calculate_dipole_moment(self):
return self.finegd.calculate_dipole_moment(self.rhot_g)
class PhononPerturbation(Perturbation):
"""Implementation of a phonon perturbation.
This class implements the change in the effective potential due to a
displacement of an atom ``a`` in direction ``v`` with wave-vector ``q``.
The action of the perturbing potential on a state vector is implemented in
the ``apply`` member function.
"""
def __init__(self, calc, kd, poisson_solver, dtype=float, **kwargs):
"""Store useful objects, e.g. lfc's for the various atomic functions.
Depending on whether the system is periodic or finite, Poisson's equation
is solved with FFT or multigrid techniques, respectively.
Parameters
----------
calc: Calculator
Ground-state calculation.
kd: KPointDescriptor
Descriptor for the q-vectors of the dynamical matrix.
"""
self.kd = kd
self.dtype = dtype
self.poisson = poisson_solver
# Gamma wrt q-vector
if self.kd.gamma:
self.phase_cd = None
else:
assert self.kd.mynks == len(self.kd.ibzk_qc)
self.phase_qcd = []
sdisp_cd = calc.wfs.gd.sdisp_cd
for q in range(self.kd.mynks):
phase_cd = np.exp(2j * np.pi * \
sdisp_cd * self.kd.ibzk_qc[q, :, np.newaxis])
self.phase_qcd.append(phase_cd)
# Store grid-descriptors
self.gd = calc.density.gd
self.finegd = calc.density.finegd
# Steal setups for the lfc's
setups = calc.wfs.setups
# Store projector coefficients
self.dH_asp = calc.hamiltonian.dH_asp.copy()
# Localized functions:
# core corections
self.nct = LFC(self.gd, [[setup.nct] for setup in setups],
integral=[setup.Nct for setup in setups], dtype=self.dtype)
# compensation charges
#XXX what is the consequence of numerical errors in the integral ??
self.ghat = LFC(self.finegd, [setup.ghat_l for setup in setups],
dtype=self.dtype)
## self.ghat = LFC(self.finegd, [setup.ghat_l for setup in setups],
## integral=sqrt(4 * pi), dtype=self.dtype)
# vbar potential
self.vbar = LFC(self.finegd, [[setup.vbar] for setup in setups],
dtype=self.dtype)
# Expansion coefficients for the compensation charges
self.Q_aL = calc.density.Q_aL.copy()
# Grid transformer -- convert array from fine to coarse grid
self.restrictor = Transformer(self.finegd, self.gd, nn=3,
dtype=self.dtype, allocate=False)
# Atom, cartesian coordinate and q-vector of the perturbation
self.a = None
self.v = None
# Local q-vector index of the perturbation
if self.kd.gamma:
self.q = -1
else:
self.q = None
def initialize(self, spos_ac):
"""Prepare the various attributes for a calculation."""
# Set positions on LFC's
self.nct.set_positions(spos_ac)
self.ghat.set_positions(spos_ac)
self.vbar.set_positions(spos_ac)
if not self.kd.gamma:
# Set q-vectors and update
self.ghat.set_k_points(self.kd.ibzk_qc)
self.ghat._update(spos_ac)
# Set q-vectors and update
self.vbar.set_k_points(self.kd.ibzk_qc)
self.vbar._update(spos_ac)
# Phase factor exp(iq.r) needed to obtian the periodic part of lfcs
coor_vg = self.finegd.get_grid_point_coordinates()
cell_cv = self.finegd.cell_cv
# Convert to scaled coordinates
scoor_cg = np.dot(la.inv(cell_cv), coor_vg.swapaxes(0, -2))
scoor_cg = scoor_cg.swapaxes(1,-2)
# Phase factor
phase_qg = np.exp(2j * pi *
np.dot(self.kd.ibzk_qc, scoor_cg.swapaxes(0,-2)))
self.phase_qg = phase_qg.swapaxes(1, -2)
#XXX To be removed from this class !!
# Setup the Poisson solver -- to be used on the fine grid
self.poisson.set_grid_descriptor(self.finegd)
self.poisson.initialize()
# Grid transformer
self.restrictor.allocate()
def set_q(self, q):
"""Set the index of the q-vector of the perturbation."""
assert not self.kd.gamma, "Gamma-point calculation"
self.q = q
# Update phases and Poisson solver
self.phase_cd = self.phase_qcd[q]
self.poisson.set_q(self.kd.ibzk_qc[q])
# Invalidate calculated quantities
# - local part of perturbing potential
self.v1_G = None
def set_av(self, a, v):
"""Set atom and cartesian component of the perturbation.
Parameters
----------
a: int
Index of the atom.
v: int
Cartesian component (0, 1 or 2) of the atomic displacement.
"""
assert self.q is not None
self.a = a
self.v = v
# Update derivative of local potential
self.calculate_local_potential()
def get_phase_cd(self):
"""Overwrite base class member function."""
return self.phase_cd
def has_q(self):
"""Overwrite base class member function."""
return (not self.kd.gamma)
def get_q(self):
"""Return q-vector."""
assert not self.kd.gamma, "Gamma-point calculation."
return self.kd.ibzk_qc[self.q]
def solve_poisson(self, phi_g, rho_g):
"""Solve Poisson's equation for a Bloch-type charge distribution.
More to come here ...
Parameters
----------
phi_g: GridDescriptor
Grid for the solution of Poissons's equation.
rho_g: GridDescriptor
Grid with the charge distribution.
"""
#assert phi_g.shape == rho_g.shape == self.phase_qg.shape[-3:], \
# ("Arrays have incompatible shapes.")
assert self.q is not None, ("q-vector not set")
# Gamma point calculation wrt the q-vector -> rho_g periodic
if self.kd.gamma:
#XXX NOTICE: solve_neutral
self.poisson.solve_neutral(phi_g, rho_g)
else:
# Divide out the phase factor to get the periodic part
rhot_g = rho_g/self.phase_qg[self.q]
# Solve Poisson's equation for the periodic part of the potential
#XXX NOTICE: solve_neutral
self.poisson.solve_neutral(phi_g, rhot_g)
# Return to Bloch form
phi_g *= self.phase_qg[self.q]
def calculate_local_potential(self):
"""Derivate of the local potential wrt an atomic displacements.
The local part of the PAW potential has contributions from the
compensation charges (``ghat``) and a spherical symmetric atomic
potential (``vbar``).
"""
assert self.a is not None
assert self.v is not None
assert self.q is not None
a = self.a
v = self.v
# Expansion coefficients for the ghat functions
Q_aL = self.ghat.dict(zero=True)
# Remember sign convention for add_derivative method
# And be sure not to change the dtype of the arrays by assigning values
# to array elements.
Q_aL[a][:] = -1 * self.Q_aL[a]
# Grid for derivative of compensation charges
ghat1_g = self.finegd.zeros(dtype=self.dtype)
self.ghat.add_derivative(a, v, ghat1_g, c_axi=Q_aL, q=self.q)
# Solve Poisson's eq. for the potential from the periodic part of the
# compensation charge derivative
v1_g = self.finegd.zeros(dtype=self.dtype)
self.solve_poisson(v1_g, ghat1_g)
# Store potential from the compensation charge
self.vghat1_g = v1_g.copy()
# Add derivative of vbar - sign convention in add_derivative method
c_ai = self.vbar.dict(zero=True)
c_ai[a][0] = -1.
self.vbar.add_derivative(a, v, v1_g, c_axi=c_ai, q=self.q)
# Store potential for the evaluation of the energy derivative
self.v1_g = v1_g.copy()
# Transfer to coarse grid
v1_G = self.gd.zeros(dtype=self.dtype)
self.restrictor.apply(v1_g, v1_G, phases=self.phase_cd)
self.v1_G = v1_G
def apply(self, psi_nG, y_nG, wfs, k, kplusq):
"""Apply perturbation to unperturbed wave-functions.
Parameters
----------
psi_nG: ndarray
Set of grid vectors to which the perturbation is applied.
y_nG: ndarray
Output vectors.
wfs: WaveFunctions
Instance of class ``WaveFunctions``.
k: int
Index of the k-point for the vectors.
kplusq: int
Index of the k+q vector.
"""
assert self.a is not None
assert self.v is not None
assert self.q is not None
assert psi_nG.ndim in (3, 4)
assert tuple(self.gd.n_c) == psi_nG.shape[-3:]
if psi_nG.ndim == 3:
y_nG += self.v1_G * psi_nG
else:
y_nG += self.v1_G[np.newaxis, :] * psi_nG
self.apply_nonlocal_potential(psi_nG, y_nG, wfs, k, kplusq)
def apply_nonlocal_potential(self, psi_nG, y_nG, wfs, k, kplusq):
"""Derivate of the non-local PAW potential wrt an atomic displacement.
Parameters
----------
k: int
Index of the k-point being operated on.
kplusq: int
Index of the k+q vector.
"""
assert self.a is not None
assert self.v is not None
assert psi_nG.ndim in (3, 4)
assert tuple(self.gd.n_c) == psi_nG.shape[-3:]
if psi_nG.ndim == 3:
n = 1
else:
n = psi_nG.shape[0]
a = self.a
v = self.v
P_ani = wfs.kpt_u[k].P_ani
dP_aniv = wfs.kpt_u[k].dP_aniv
pt = wfs.pt
# < p_a^i | Psi_nk >
P_ni = P_ani[a]
# < dp_av^i | Psi_nk > - remember the sign convention of the derivative
dP_ni = -1 * dP_aniv[a][...,v]
# Expansion coefficients for the projectors on atom a
dH_ii = unpack(self.dH_asp[a][0])
# The derivative of the non-local PAW potential has two contributions
# 1) Sum over projectors
c_ni = np.dot(dP_ni, dH_ii)
c_ani = pt.dict(shape=n, zero=True)
c_ani[a] = c_ni
# k+q !!
pt.add(y_nG, c_ani, q=kplusq)
# 2) Sum over derivatives of the projectors
dc_ni = np.dot(P_ni, dH_ii)
dc_ani = pt.dict(shape=n, zero=True)
# Take care of sign of derivative in the coefficients
dc_ani[a] = -1 * dc_ni
# k+q !!
pt.add_derivative(a, v, y_nG, dc_ani, q=kplusq)
