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)
class WaveFunctions:
"""Class for wave-function related stuff (e.g. projectors)."""
def __init__(self, nbands, kpt_u, setups, kd, gd, dtype=float):
"""Store and initialize required attributes.
Parameters
----------
nbands: int
Number of occupied bands.
kpt_u: list of KPoints
List of KPoint instances from a ground-state calculation (i.e. the
attribute ``calc.wfs.kpt_u``).
setups: Setups
LocalizedFunctionsCollection setups.
kd: KPointDescriptor
K-point and symmetry related stuff.
gd: GridDescriptor
Descriptor for the coarse grid.
dtype: dtype
This is the ``dtype`` for the wave-function derivatives (same as
the ``dtype`` for the ground-state wave-functions).
"""
self.dtype = dtype
# K-point related attributes
self.kd = kd
# Number of occupied bands
self.nbands = nbands
# Projectors
self.pt = LFC(gd, [setup.pt_j for setup in setups], dtype=self.dtype)
# Store grid
self.gd = gd
# Unfold the irreducible BZ to the full BZ
# List of KPointContainers for the k-points in the full BZ
self.kpt_u = []
# No symmetries or only time-reversal symmetry used
if kd.symmetry is None:
# For now, time-reversal symmetry not allowed
assert len(kpt_u) == kd.nbzkpts
for k in range(kd.nbzkpts):
kpt_ = kpt_u[k]
psit_nG = gd.empty(nbands, dtype=self.dtype)
for n, psit_G in enumerate(psit_nG):
psit_G[:] = kpt_.psit_nG[n]
# psit_0 = psit_G[0, 0, 0]
# psit_G *= psit_0.conj() / (abs(psit_0))
# Strip off KPoint attributes and store in the KPointContainer
# Note, only the occupied GS wave-functions are retained here !
kpt = KPointContainer(weight=kpt_.weight,
k=kpt_.k,
s=kpt_.s,
phase_cd=kpt_.phase_cd,
eps_n=kpt_.eps_n[:nbands],
psit_nG=psit_nG,
psit1_nG=None,
P_ani=None,
dP_aniv=None)
# q=kpt.q,
# f_n=kpt.f_n[:nbands])
self.kpt_u.append(kpt)
else:
assert len(kpt_u) == kd.nibzkpts
for k, k_c in enumerate(kd.bzk_kc):
# Index of symmetry related point in the irreducible BZ
ik = kd.kibz_k[k]
# Index of point group operation
s = kd.sym_k[k]
# Time-reversal symmetry used
time_reversal = kd.time_reversal_k[k]
# Coordinates of symmetry related point in the irreducible BZ
ik_c = kd.ibzk_kc[ik]
# Point group operation
op_cc = kd.symmetry.op_scc[s]
# KPoint from ground-state calculation
kpt_ = kpt_u[ik]
weight = 1. / kd.nbzkpts * (2 - kpt_.s)
phase_cd = np.exp(2j * pi * gd.sdisp_cd * k_c[:, np.newaxis])
psit_nG = gd.empty(nbands, dtype=self.dtype)
for n, psit_G in enumerate(psit_nG):
#XXX Seems to corrupt my memory somehow ???
psit_G[:] = kd.symmetry.symmetrize_wavefunction(
kpt_.psit_nG[n], ik_c, k_c, op_cc, time_reversal)
# Choose gauge
# psit_0 = psit_G[0, 0, 0]
# psit_G *= psit_0.conj() / (abs(psit_0))
kpt = KPointContainer(weight=weight,
k=k,
s=kpt_.s,
phase_cd=phase_cd,
eps_n=kpt_.eps_n[:nbands],
psit_nG=psit_nG,
psit1_nG=None,
P_ani=None,
dP_aniv=None)
self.kpt_u.append(kpt)
def initialize(self, spos_ac):
"""Initialize projectors according to the ``gamma`` attribute."""
# Set positions on LFC's
self.pt.set_positions(spos_ac)
if not self.kd.gamma:
# Set k-vectors and update
self.pt.set_k_points(self.kd.ibzk_kc)
self.pt._update(spos_ac)
# Calculate projector coefficients for the GS wave-functions
self.calculate_projector_coef()
def reset(self):
"""Make fresh arrays for wave-function derivatives."""
for kpt in self.kpt_u:
kpt.psit1_nG = self.gd.zeros(n=self.nbands, dtype=self.dtype)
def calculate_projector_coef(self):
"""Coefficients for the derivative of the non-local part of the PP.
Parameters
----------
k: int
Index of the k-point of the Bloch state on which the non-local
potential operates on.
The calculated coefficients are the following (except for an overall
sign of -1; see ``derivative`` member function of class ``LFC``):
1. Coefficients from the projector functions::
/ a
P_ani = | dG p (G) Psi (G) ,
/ i n
2. Coefficients from the derivative of the projector functions::
/ a
dP_aniv = | dG dp (G) Psi (G) ,
/ iv n
where::
a d a
dp (G) = --- Phi (G) .
iv a i
dR
"""
n = self.nbands
for kpt in self.kpt_u:
# K-point index and wave-functions
k = kpt.k
psit_nG = kpt.psit_nG
# Integration dicts
P_ani = self.pt.dict(shape=n)
dP_aniv = self.pt.dict(shape=n, derivative=True)
# 1) Integrate with projectors
self.pt.integrate(psit_nG, P_ani, q=k)
kpt.P_ani = P_ani
# 2) Integrate with derivative of projectors
self.pt.derivative(psit_nG, dP_aniv, q=k)
kpt.dP_aniv = dP_aniv
import numpy as np
from gpaw.lfc import LocalizedFunctionsCollection as LFC
from gpaw.grid_descriptor import GridDescriptor
from gpaw.spline import Spline
a = 4.0
gd = GridDescriptor(N_c=[16, 20, 20], cell_cv=[a, a + 1, a + 2],
pbc_c=(0, 1, 1))
spos_ac = np.array([[0.25, 0.15, 0.35], [0.5, 0.5, 0.5]])
kpts_kc = None
s = Spline(l=0, rmax=2.0, f_g=np.array([1, 0.9, 0.1, 0.0]))
p = Spline(l=1, rmax=2.0, f_g=np.array([1, 0.9, 0.1, 0.0]))
spline_aj = [[s], [s, p]]
c = LFC(gd, spline_aj, cut=True, forces=True)
c.set_positions(spos_ac)
C_ani = c.dict(3, zero=True)
if 1 in C_ani:
C_ani[1][:, 1:] = np.eye(3)
psi = gd.zeros(3)
c.add(psi, C_ani)
c.integrate(psi, C_ani)
if 1 in C_ani:
d = C_ani[1][:, 1:].diagonal()
assert d.ptp() < 4e-6
C_ani[1][:, 1:] -= np.diag(d)
assert abs(C_ani[1]).max() < 5e-17
d_aniv = c.dict(3, derivative=True)
c.derivative(psi, d_aniv)
if 1 in d_aniv:
for v in range(3):
assert abs(d_aniv[1][v - 1, 0, v] + 0.2144) < 5e-5
d_aniv[1][v - 1, 0, v] = 0
class FDWaveFunctions(FDPWWaveFunctions):
mode = 'fd'
def __init__(self,
stencil,
diagksl,
orthoksl,
initksl,
gd,
nvalence,
setups,
bd,
dtype,
world,
kd,
kptband_comm,
timer=None):
FDPWWaveFunctions.__init__(self, diagksl, orthoksl, initksl, gd,
nvalence, setups, bd, dtype, world, kd,
kptband_comm, timer)
# Kinetic energy operator:
self.kin = Laplace(self.gd, -0.5, stencil, self.dtype)
self.matrixoperator = MatrixOperator(self.orthoksl)
self.taugrad_v = None # initialized by MGGA functional
def empty(self, n=(), global_array=False, realspace=False, q=-1):
return self.gd.empty(n, self.dtype, global_array)
def integrate(self, a_xg, b_yg=None, global_integral=True):
return self.gd.integrate(a_xg, b_yg, global_integral)
def bytes_per_wave_function(self):
return self.gd.bytecount(self.dtype)
def set_setups(self, setups):
self.pt = LFC(self.gd, [setup.pt_j for setup in setups],
self.kd,
dtype=self.dtype,
forces=True)
FDPWWaveFunctions.set_setups(self, setups)
def set_positions(self, spos_ac):
FDPWWaveFunctions.set_positions(self, spos_ac)
def summary(self, fd):
fd.write('Wave functions: Uniform real-space grid\n')
fd.write('Kinetic energy operator: %s\n' % self.kin.description)
def make_preconditioner(self, block=1):
return Preconditioner(self.gd, self.kin, self.dtype, block)
def apply_pseudo_hamiltonian(self, kpt, hamiltonian, psit_xG, Htpsit_xG):
self.timer.start('Apply hamiltonian')
self.kin.apply(psit_xG, Htpsit_xG, kpt.phase_cd)
hamiltonian.apply_local_potential(psit_xG, Htpsit_xG, kpt.s)
self.timer.stop('Apply hamiltonian')
def add_orbital_density(self, nt_G, kpt, n):
if self.dtype == float:
axpy(1.0, kpt.psit_nG[n]**2, nt_G)
else:
axpy(1.0, kpt.psit_nG[n].real**2, nt_G)
axpy(1.0, kpt.psit_nG[n].imag**2, nt_G)
def add_to_density_from_k_point_with_occupation(self, nt_sG, kpt, f_n):
# Used in calculation of response part of GLLB-potential
nt_G = nt_sG[kpt.s]
if self.dtype == float:
for f, psit_G in zip(f_n, kpt.psit_nG):
axpy(f, psit_G**2, nt_G)
else:
for f, psit_G in zip(f_n, kpt.psit_nG):
axpy(f, psit_G.real**2, nt_G)
axpy(f, psit_G.imag**2, nt_G)
# Hack used in delta-scf calculations:
if hasattr(kpt, 'c_on'):
assert self.bd.comm.size == 1
d_nn = np.zeros((self.bd.mynbands, self.bd.mynbands),
dtype=complex)
for ne, c_n in zip(kpt.ne_o, kpt.c_on):
d_nn += ne * np.outer(c_n.conj(), c_n)
for d_n, psi0_G in zip(d_nn, kpt.psit_nG):
for d, psi_G in zip(d_n, kpt.psit_nG):
if abs(d) > 1.e-12:
nt_G += (psi0_G.conj() * d * psi_G).real
def calculate_kinetic_energy_density(self):
if self.taugrad_v is None:
self.taugrad_v = [
Gradient(self.gd, v, n=3, dtype=self.dtype).apply
for v in range(3)
]
assert not hasattr(self.kpt_u[0], 'c_on')
if self.kpt_u[0].psit_nG is None:
raise RuntimeError('No wavefunctions yet')
if isinstance(self.kpt_u[0].psit_nG, FileReference):
# XXX initialize
raise RuntimeError('Wavefunctions have not been initialized.')
taut_sG = self.gd.zeros(self.nspins)
dpsit_G = self.gd.empty(dtype=self.dtype)
for kpt in self.kpt_u:
for f, psit_G in zip(kpt.f_n, kpt.psit_nG):
for v in range(3):
self.taugrad_v[v](psit_G, dpsit_G, kpt.phase_cd)
axpy(0.5 * f, abs(dpsit_G)**2, taut_sG[kpt.s])
self.kd.comm.sum(taut_sG)
self.band_comm.sum(taut_sG)
return taut_sG
def apply_mgga_orbital_dependent_hamiltonian(self, kpt, psit_xG, Htpsit_xG,
dH_asp, dedtaut_G):
a_G = self.gd.empty(dtype=psit_xG.dtype)
for psit_G, Htpsit_G in zip(psit_xG, Htpsit_xG):
for v in range(3):
self.taugrad_v[v](psit_G, a_G, kpt.phase_cd)
self.taugrad_v[v](dedtaut_G * a_G, a_G, kpt.phase_cd)
axpy(-0.5, a_G, Htpsit_G)
def ibz2bz(self, atoms):
"""Transform wave functions in IBZ to the full BZ."""
assert self.kd.comm.size == 1
# New k-point descriptor for full BZ:
kd = KPointDescriptor(self.kd.bzk_kc, nspins=self.nspins)
#kd.set_symmetry(atoms, self.setups, enabled=False)
kd.set_communicator(serial_comm)
self.pt = LFC(self.gd, [setup.pt_j for setup in self.setups],
kd,
dtype=self.dtype)
self.pt.set_positions(atoms.get_scaled_positions())
self.initialize_wave_functions_from_restart_file()
weight = 2.0 / kd.nspins / kd.nbzkpts
# Build new list of k-points:
kpt_u = []
for s in range(self.nspins):
for k in range(kd.nbzkpts):
# Index of symmetry related point in the IBZ
ik = self.kd.bz2ibz_k[k]
r, u = self.kd.get_rank_and_index(s, ik)
assert r == 0
kpt = self.kpt_u[u]
phase_cd = np.exp(2j * np.pi * self.gd.sdisp_cd *
kd.bzk_kc[k, :, np.newaxis])
# New k-point:
kpt2 = KPoint(weight, s, k, k, phase_cd)
kpt2.f_n = kpt.f_n / kpt.weight / kd.nbzkpts * 2 / self.nspins
kpt2.eps_n = kpt.eps_n.copy()
# Transform wave functions using symmetry operation:
Psit_nG = self.gd.collect(kpt.psit_nG)
if Psit_nG is not None:
Psit_nG = Psit_nG.copy()
for Psit_G in Psit_nG:
Psit_G[:] = self.kd.transform_wave_function(Psit_G, k)
kpt2.psit_nG = self.gd.empty(self.bd.nbands, dtype=self.dtype)
self.gd.distribute(Psit_nG, kpt2.psit_nG)
# Calculate PAW projections:
kpt2.P_ani = self.pt.dict(len(kpt.psit_nG))
self.pt.integrate(kpt2.psit_nG, kpt2.P_ani, k)
kpt_u.append(kpt2)
self.kd = kd
self.kpt_u = kpt_u
def write(self, writer, write_wave_functions=False):
writer['Mode'] = 'fd'
if not write_wave_functions:
return
writer.add(
'PseudoWaveFunctions',
('nspins', 'nibzkpts', 'nbands', 'ngptsx', 'ngptsy', 'ngptsz'),
dtype=self.dtype)
if hasattr(writer, 'hdf5'):
parallel = (self.world.size > 1)
for kpt in self.kpt_u:
indices = [kpt.s, kpt.k]
indices.append(self.bd.get_slice())
indices += self.gd.get_slice()
writer.fill(kpt.psit_nG, parallel=parallel, *indices)
else:
for s in range(self.nspins):
for k in range(self.kd.nibzkpts):
for n in range(self.bd.nbands):
psit_G = self.get_wave_function_array(n, k, s)
writer.fill(psit_G, s, k, n)
def read(self, reader, hdf5):
if ((not hdf5 and self.bd.comm.size == 1)
or (hdf5 and self.world.size == 1)):
# We may not be able to keep all the wave
# functions in memory - so psit_nG will be a special type of
# array that is really just a reference to a file:
for kpt in self.kpt_u:
kpt.psit_nG = reader.get_reference('PseudoWaveFunctions',
(kpt.s, kpt.k))
else:
for kpt in self.kpt_u:
kpt.psit_nG = self.empty(self.bd.mynbands)
if hdf5:
indices = [kpt.s, kpt.k]
indices.append(self.bd.get_slice())
indices += self.gd.get_slice()
reader.get('PseudoWaveFunctions',
out=kpt.psit_nG,
parallel=(self.world.size > 1),
*indices)
else:
# Read band by band to save memory
for myn, psit_G in enumerate(kpt.psit_nG):
n = self.bd.global_index(myn)
if self.gd.comm.rank == 0:
big_psit_G = np.array(
reader.get('PseudoWaveFunctions', kpt.s, kpt.k,
n), self.dtype)
else:
big_psit_G = None
self.gd.distribute(big_psit_G, psit_G)
def initialize_from_lcao_coefficients(self, basis_functions, mynbands):
for kpt in self.kpt_u:
kpt.psit_nG = self.gd.zeros(self.bd.mynbands, self.dtype)
basis_functions.lcao_to_grid(kpt.C_nM, kpt.psit_nG[:mynbands],
kpt.q)
kpt.C_nM = None
if use_mic:
kpt.psit_nG_mic = stream.bind(kpt.psit_nG)
stream.sync()
def random_wave_functions(self, nao):
"""Generate random wave functions."""
gpts = self.gd.N_c[0] * self.gd.N_c[1] * self.gd.N_c[2]
if self.bd.nbands < gpts / 64:
gd1 = self.gd.coarsen()
gd2 = gd1.coarsen()
psit_G1 = gd1.empty(dtype=self.dtype)
psit_G2 = gd2.empty(dtype=self.dtype)
interpolate2 = Transformer(gd2, gd1, 1, self.dtype).apply
interpolate1 = Transformer(gd1, self.gd, 1, self.dtype).apply
shape = tuple(gd2.n_c)
scale = np.sqrt(12 / abs(np.linalg.det(gd2.cell_cv)))
old_state = np.random.get_state()
np.random.seed(4 + self.world.rank)
for kpt in self.kpt_u:
for psit_G in kpt.psit_nG[nao:]:
if self.dtype == float:
psit_G2[:] = (np.random.random(shape) - 0.5) * scale
else:
psit_G2.real = (np.random.random(shape) - 0.5) * scale
psit_G2.imag = (np.random.random(shape) - 0.5) * scale
interpolate2(psit_G2, psit_G1, kpt.phase_cd)
interpolate1(psit_G1, psit_G, kpt.phase_cd)
np.random.set_state(old_state)
elif gpts / 64 <= self.bd.nbands < gpts / 8:
gd1 = self.gd.coarsen()
psit_G1 = gd1.empty(dtype=self.dtype)
interpolate1 = Transformer(gd1, self.gd, 1, self.dtype).apply
shape = tuple(gd1.n_c)
scale = np.sqrt(12 / abs(np.linalg.det(gd1.cell_cv)))
old_state = np.random.get_state()
np.random.seed(4 + self.world.rank)
for kpt in self.kpt_u:
for psit_G in kpt.psit_nG[nao:]:
if self.dtype == float:
psit_G1[:] = (np.random.random(shape) - 0.5) * scale
else:
psit_G1.real = (np.random.random(shape) - 0.5) * scale
psit_G1.imag = (np.random.random(shape) - 0.5) * scale
interpolate1(psit_G1, psit_G, kpt.phase_cd)
np.random.set_state(old_state)
else:
shape = tuple(self.gd.n_c)
scale = np.sqrt(12 / abs(np.linalg.det(self.gd.cell_cv)))
old_state = np.random.get_state()
np.random.seed(4 + self.world.rank)
for kpt in self.kpt_u:
for psit_G in kpt.psit_nG[nao:]:
if self.dtype == float:
psit_G[:] = (np.random.random(shape) - 0.5) * scale
else:
psit_G.real = (np.random.random(shape) - 0.5) * scale
psit_G.imag = (np.random.random(shape) - 0.5) * scale
np.random.set_state(old_state)
def estimate_memory(self, mem):
FDPWWaveFunctions.estimate_memory(self, mem)
class WaveFunctions:
"""Class for wave-function related stuff (e.g. projectors)."""
def __init__(self, nbands, kpt_u, setups, kd, gd, dtype=float):
"""Store and initialize required attributes.
Parameters
----------
nbands: int
Number of occupied bands.
kpt_u: list of KPoints
List of KPoint instances from a ground-state calculation (i.e. the
attribute ``calc.wfs.kpt_u``).
setups: Setups
LocalizedFunctionsCollection setups.
kd: KPointDescriptor
K-point and symmetry related stuff.
gd: GridDescriptor
Descriptor for the coarse grid.
dtype: dtype
This is the ``dtype`` for the wave-function derivatives (same as
the ``dtype`` for the ground-state wave-functions).
"""
self.dtype = dtype
# K-point related attributes
self.kd = kd
# Number of occupied bands
self.nbands = nbands
# Projectors
self.pt = LFC(gd, [setup.pt_j for setup in setups], kd,
dtype=self.dtype)
# Store grid
self.gd = gd
# Unfold the irreducible BZ to the full BZ
# List of KPointContainers for the k-points in the full BZ
self.kpt_u = []
# No symmetries or only time-reversal symmetry used
assert kd.symmetry.point_group == False
if kd.symmetry.time_reversal == False:
# For now, time-reversal symmetry not allowed
assert len(kpt_u) == kd.nbzkpts
for k in range(kd.nbzkpts):
kpt_ = kpt_u[k]
psit_nG = gd.empty(nbands, dtype=self.dtype)
for n, psit_G in enumerate(psit_nG):
psit_G[:] = kpt_.psit_nG[n]
# psit_0 = psit_G[0, 0, 0]
# psit_G *= psit_0.conj() / (abs(psit_0))
# Strip off KPoint attributes and store in the KPointContainer
# Note, only the occupied GS wave-functions are retained here !
kpt = KPointContainer(weight=kpt_.weight,
k=kpt_.k,
s=kpt_.s,
phase_cd=kpt_.phase_cd,
eps_n=kpt_.eps_n[:nbands],
psit_nG=psit_nG,
psit1_nG=None,
P_ani=None,
dP_aniv=None)
# q=kpt.q,
# f_n=kpt.f_n[:nbands])
self.kpt_u.append(kpt)
else:
assert len(kpt_u) == kd.nibzkpts
for k, k_c in enumerate(kd.bzk_kc):
# Index of symmetry related point in the irreducible BZ
ik = kd.bz2ibz_k[k]
# Index of point group operation
s = kd.sym_k[k]
# Time-reversal symmetry used
time_reversal = kd.time_reversal_k[k]
# Coordinates of symmetry related point in the irreducible BZ
ik_c = kd.ibzk_kc[ik]
# Point group operation
op_cc = kd.symmetry.op_scc[s]
# KPoint from ground-state calculation
kpt_ = kpt_u[ik]
weight = 1. / kd.nbzkpts * (2 - kpt_.s)
phase_cd = np.exp(2j * pi * gd.sdisp_cd * k_c[:, np.newaxis])
psit_nG = gd.empty(nbands, dtype=self.dtype)
for n, psit_G in enumerate(psit_nG):
#XXX Seems to corrupt my memory somehow ???
psit_G[:] = kd.symmetry.symmetrize_wavefunction(
kpt_.psit_nG[n], ik_c, k_c, op_cc, time_reversal)
# Choose gauge
# psit_0 = psit_G[0, 0, 0]
# psit_G *= psit_0.conj() / (abs(psit_0))
kpt = KPointContainer(weight=weight,
k=k,
s=kpt_.s,
phase_cd=phase_cd,
eps_n=kpt_.eps_n[:nbands],
psit_nG=psit_nG,
psit1_nG=None,
P_ani=None,
dP_aniv=None)
self.kpt_u.append(kpt)
def initialize(self, spos_ac):
"""Initialize projectors according to the ``gamma`` attribute."""
# Set positions on LFC's
self.pt.set_positions(spos_ac)
# Calculate projector coefficients for the GS wave-functions
self.calculate_projector_coef()
def reset(self):
"""Make fresh arrays for wave-function derivatives."""
for kpt in self.kpt_u:
kpt.psit1_nG = self.gd.zeros(n=self.nbands, dtype=self.dtype)
def calculate_projector_coef(self):
"""Coefficients for the derivative of the non-local part of the PP.
Parameters
----------
k: int
Index of the k-point of the Bloch state on which the non-local
potential operates on.
The calculated coefficients are the following (except for an overall
sign of -1; see ``derivative`` member function of class ``LFC``):
1. Coefficients from the projector functions::
/ a
P_ani = | dG p (G) Psi (G) ,
/ i n
2. Coefficients from the derivative of the projector functions::
/ a
dP_aniv = | dG dp (G) Psi (G) ,
/ iv n
where::
a d a
dp (G) = --- Phi (G) .
iv a i
dR
"""
n = self.nbands
for kpt in self.kpt_u:
# K-point index and wave-functions
k = kpt.k
psit_nG = kpt.psit_nG
# Integration dicts
P_ani = self.pt.dict(shape=n)
dP_aniv = self.pt.dict(shape=n, derivative=True)
# 1) Integrate with projectors
self.pt.integrate(psit_nG, P_ani, q=k)
kpt.P_ani = P_ani
# 2) Integrate with derivative of projectors
self.pt.derivative(psit_nG, dP_aniv, q=k)
kpt.dP_aniv = dP_aniv
from gpaw.setup import Setup
rc = 2.0
a = 2.5 * rc
n = 64
lmax = 2
b = 8.0
m = (lmax + 1)**2
gd = GridDescriptor([n, n, n], [a, a, a])
r = np.linspace(0, rc, 200)
g = np.exp(-(r / rc * b)**2)
splines = [Spline(l=l, rmax=rc, f_g=g) for l in range(lmax + 1)]
c = LFC(gd, [splines])
c.set_positions([(0, 0, 0)])
psi = gd.zeros(m)
d0 = c.dict(m)
if 0 in d0:
d0[0] = np.identity(m)
c.add(psi, d0)
d1 = c.dict(m, derivative=True)
c.derivative(psi, d1)
class TestSetup(Setup):
l_j = range(lmax + 1)
nj = lmax + 1
ni = m
def __init__(self):
pass
rgd = EquidistantRadialGridDescriptor(r[1], len(r))
g = [np.exp(-(r / rc * b)**2) * r**l for l in range(lmax + 1)]
d2 = TestSetup().get_derivative_integrals(rgd, g, np.zeros_like(g))
if 0 in d1:
# Initialize s, p, d (9 in total) wave and put them on grid
rc = 2.0
a = 2.5 * rc
n = 64
lmax = 2
b = 8.0
m = (lmax + 1)**2
gd = GridDescriptor([n, n, n], [a, a, a])
r = np.linspace(0, rc, 200)
g = np.exp(-(r / rc * b)**2)
splines = [Spline(l=l, rmax=rc, f_g=g) for l in range(lmax + 1)]
c = LFC(gd, [splines])
c.set_positions([(0.5, 0.5, 0.5)])
psi = gd.zeros(m)
d0 = c.dict(m)
if 0 in d0:
d0[0] = np.identity(m)
c.add(psi, d0)
# Calculate on 3d-grid < phi_i | e**(-ik.r) | phi_j >
R_a = np.array([a / 2, a / 2, a / 2])
rr = gd.get_grid_point_coordinates()
for dim in range(3):
rr[dim] -= R_a[dim]
k_G = np.array([[11., 0.2, 0.1], [10., 0., 10.]])
nkpt = k_G.shape[0]
d0 = np.zeros((nkpt, m, m), dtype=complex)
for i in range(m):
from __future__ import print_function
import numpy as np
from gpaw.lfc import LocalizedFunctionsCollection as LFC
from gpaw.grid_descriptor import GridDescriptor
from gpaw.spline import Spline
gd = GridDescriptor([20, 16, 16], [(4, 2, 0), (0, 4, 0), (0, 0, 4)])
spos_ac = np.array([[0.252, 0.15, 0.35], [0.503, 0.5, 0.5]])
s = Spline(l=0, rmax=2.0, f_g=np.array([1, 0.9, 0.1, 0.0]))
spline_aj = [[s], [s]]
c = LFC(gd, spline_aj)
c.set_positions(spos_ac)
c_ai = c.dict(zero=True)
if 1 in c_ai:
c_ai[1][0] = 2.0
psi = gd.zeros()
c.add(psi, c_ai)
d_avv = dict([(a, np.zeros((3, 3))) for a in c.my_atom_indices])
c.second_derivative(psi, d_avv)
if 0 in d_avv:
print(d_avv[0])
eps = 0.000001
d_aiv = c.dict(derivative=True)
pos_av = np.dot(spos_ac, gd.cell_cv)
for v in range(3):
pos_av[0, v] += eps
c.set_positions(np.dot(pos_av, gd.icell_cv.T))
c.derivative(psi, d_aiv)
if 0 in d_aiv:
from gpaw.setup import Setup
rc = 2.0
a = 2.5 * rc
n = 64
lmax = 2
b = 8.0
m = (lmax + 1)**2
gd = GridDescriptor([n, n, n], [a, a, a])
r = np.linspace(0, rc, 200)
g = np.exp(-(r / rc * b)**2)
splines = [Spline(l=l, rmax=rc, f_g=g) for l in range(lmax + 1)]
c = LFC(gd, [splines])
c.set_positions([(0, 0, 0)])
psi = gd.zeros(m)
d0 = c.dict(m)
if 0 in d0:
d0[0] = np.identity(m)
c.add(psi, d0)
d1 = c.dict(m, derivative=True)
c.derivative(psi, d1)
class TestSetup(Setup):
l_j = range(lmax + 1)
nj = lmax + 1
ni = m
def __init__(self):
pass
import numpy as np
from gpaw.lfc import LocalizedFunctionsCollection as LFC
from gpaw.grid_descriptor import GridDescriptor
from gpaw.spline import Spline
a = 4.0
gd = GridDescriptor(N_c=[16, 20, 20],
cell_cv=[a, a + 1, a + 2],
pbc_c=(0, 1, 1))
spos_ac = np.array([[0.25, 0.15, 0.35], [0.5, 0.5, 0.5]])
kpts_kc = None
s = Spline(l=0, rmax=2.0, f_g=np.array([1, 0.9, 0.1, 0.0]))
p = Spline(l=1, rmax=2.0, f_g=np.array([1, 0.9, 0.1, 0.0]))
spline_aj = [[s], [s, p]]
c = LFC(gd, spline_aj, cut=True, forces=True)
c.set_positions(spos_ac)
C_ani = c.dict(3, zero=True)
if 1 in C_ani:
C_ani[1][:, 1:] = np.eye(3)
psi = gd.zeros(3)
c.add(psi, C_ani)
c.integrate(psi, C_ani)
if 1 in C_ani:
d = C_ani[1][:, 1:].diagonal()
assert d.ptp() < 4e-6
C_ani[1][:, 1:] -= np.diag(d)
assert abs(C_ani[1]).max() < 5e-17
d_aniv = c.dict(3, derivative=True)
c.derivative(psi, d_aniv)
if 1 in d_aniv:
for v in range(3):
assert abs(d_aniv[1][v - 1, 0, v] + 0.2144) < 5e-5
class FDWaveFunctions(FDPWWaveFunctions):
def __init__(self,
stencil,
diagksl,
orthoksl,
initksl,
gd,
nvalence,
setups,
bd,
dtype,
world,
kd,
timer=None):
FDPWWaveFunctions.__init__(self, diagksl, orthoksl, initksl, gd,
nvalence, setups, bd, dtype, world, kd,
timer)
self.wd = self.gd # wave function descriptor
# Kinetic energy operator:
self.kin = Laplace(self.gd, -0.5, stencil, self.dtype, allocate=False)
self.matrixoperator = MatrixOperator(orthoksl)
def set_setups(self, setups):
self.pt = LFC(self.gd, [setup.pt_j for setup in setups],
self.kpt_comm,
dtype=self.dtype,
forces=True)
FDPWWaveFunctions.set_setups(self, setups)
def set_positions(self, spos_ac):
if not self.kin.is_allocated():
self.kin.allocate()
FDPWWaveFunctions.set_positions(self, spos_ac)
def summary(self, fd):
fd.write('Mode: Finite-difference\n')
def make_preconditioner(self, block=1):
return Preconditioner(self.gd, self.kin, self.dtype, block)
def apply_pseudo_hamiltonian(self, kpt, hamiltonian, psit_xG, Htpsit_xG):
self.kin.apply(psit_xG, Htpsit_xG, kpt.phase_cd)
hamiltonian.apply_local_potential(psit_xG, Htpsit_xG, kpt.s)
def add_orbital_density(self, nt_G, kpt, n):
if self.dtype == float:
axpy(1.0, kpt.psit_nG[n]**2, nt_G)
else:
axpy(1.0, kpt.psit_nG[n].real**2, nt_G)
axpy(1.0, kpt.psit_nG[n].imag**2, nt_G)
def add_to_density_from_k_point_with_occupation(self, nt_sG, kpt, f_n):
# Used in calculation of response part of GLLB-potential
nt_G = nt_sG[kpt.s]
if self.dtype == float:
for f, psit_G in zip(f_n, kpt.psit_nG):
axpy(f, psit_G**2, nt_G)
else:
for f, psit_G in zip(f_n, kpt.psit_nG):
axpy(f, psit_G.real**2, nt_G)
axpy(f, psit_G.imag**2, nt_G)
# Hack used in delta-scf calculations:
if hasattr(kpt, 'c_on'):
assert self.bd.comm.size == 1
d_nn = np.zeros((self.bd.mynbands, self.bd.mynbands),
dtype=complex)
for ne, c_n in zip(kpt.ne_o, kpt.c_on):
d_nn += ne * np.outer(c_n.conj(), c_n)
for d_n, psi0_G in zip(d_nn, kpt.psit_nG):
for d, psi_G in zip(d_n, kpt.psit_nG):
if abs(d) > 1.e-12:
nt_G += (psi0_G.conj() * d * psi_G).real
def calculate_kinetic_energy_density(self, tauct, grad_v):
assert not hasattr(self.kpt_u[0], 'c_on')
if isinstance(self.kpt_u[0].psit_nG, TarFileReference):
raise RuntimeError('Wavefunctions have not been initialized.')
taut_sG = self.gd.zeros(self.nspins)
dpsit_G = self.gd.empty(dtype=self.dtype)
for kpt in self.kpt_u:
for f, psit_G in zip(kpt.f_n, kpt.psit_nG):
for v in range(3):
grad_v[v](psit_G, dpsit_G, kpt.phase_cd)
axpy(0.5 * f, abs(dpsit_G)**2, taut_sG[kpt.s])
self.kpt_comm.sum(taut_sG)
self.band_comm.sum(taut_sG)
return taut_sG
def calculate_forces(self, hamiltonian, F_av):
# Calculate force-contribution from k-points:
F_av.fill(0.0)
F_aniv = self.pt.dict(self.bd.mynbands, derivative=True)
for kpt in self.kpt_u:
self.pt.derivative(kpt.psit_nG, F_aniv, kpt.q)
for a, F_niv in F_aniv.items():
F_niv = F_niv.conj()
F_niv *= kpt.f_n[:, np.newaxis, np.newaxis]
dH_ii = unpack(hamiltonian.dH_asp[a][kpt.s])
P_ni = kpt.P_ani[a]
F_vii = np.dot(np.dot(F_niv.transpose(), P_ni), dH_ii)
F_niv *= kpt.eps_n[:, np.newaxis, np.newaxis]
dO_ii = hamiltonian.setups[a].dO_ii
F_vii -= np.dot(np.dot(F_niv.transpose(), P_ni), dO_ii)
F_av[a] += 2 * F_vii.real.trace(0, 1, 2)
# Hack used in delta-scf calculations:
if hasattr(kpt, 'c_on'):
assert self.bd.comm.size == 1
self.pt.derivative(kpt.psit_nG, F_aniv, kpt.q) #XXX again
d_nn = np.zeros((self.bd.mynbands, self.bd.mynbands),
dtype=complex)
for ne, c_n in zip(kpt.ne_o, kpt.c_on):
d_nn += ne * np.outer(c_n.conj(), c_n)
for a, F_niv in F_aniv.items():
F_niv = F_niv.conj()
dH_ii = unpack(hamiltonian.dH_asp[a][kpt.s])
Q_ni = np.dot(d_nn, kpt.P_ani[a])
F_vii = np.dot(np.dot(F_niv.transpose(), Q_ni), dH_ii)
F_niv *= kpt.eps_n[:, np.newaxis, np.newaxis]
dO_ii = hamiltonian.setups[a].dO_ii
F_vii -= np.dot(np.dot(F_niv.transpose(), Q_ni), dO_ii)
F_av[a] += 2 * F_vii.real.trace(0, 1, 2)
self.bd.comm.sum(F_av, 0)
if self.bd.comm.rank == 0:
self.kpt_comm.sum(F_av, 0)
def estimate_memory(self, mem):
FDPWWaveFunctions.estimate_memory(self, mem)
self.kin.estimate_memory(mem.subnode('Kinetic operator'))
class FDWaveFunctions(FDPWWaveFunctions):
def __init__(self, stencil, diagksl, orthoksl, initksl,
gd, nvalence, setups, bd,
dtype, world, kd, timer=None):
FDPWWaveFunctions.__init__(self, diagksl, orthoksl, initksl,
gd, nvalence, setups, bd,
dtype, world, kd, timer)
self.wd = self.gd # wave function descriptor
# Kinetic energy operator:
self.kin = Laplace(self.gd, -0.5, stencil, self.dtype, allocate=False)
self.matrixoperator = MatrixOperator(orthoksl)
def set_setups(self, setups):
self.pt = LFC(self.gd, [setup.pt_j for setup in setups],
self.kpt_comm, dtype=self.dtype, forces=True)
FDPWWaveFunctions.set_setups(self, setups)
def set_positions(self, spos_ac):
if not self.kin.is_allocated():
self.kin.allocate()
FDPWWaveFunctions.set_positions(self, spos_ac)
def summary(self, fd):
fd.write('Mode: Finite-difference\n')
def make_preconditioner(self, block=1):
return Preconditioner(self.gd, self.kin, self.dtype, block)
def apply_pseudo_hamiltonian(self, kpt, hamiltonian, psit_xG, Htpsit_xG):
self.kin.apply(psit_xG, Htpsit_xG, kpt.phase_cd)
hamiltonian.apply_local_potential(psit_xG, Htpsit_xG, kpt.s)
def add_orbital_density(self, nt_G, kpt, n):
if self.dtype == float:
axpy(1.0, kpt.psit_nG[n]**2, nt_G)
else:
axpy(1.0, kpt.psit_nG[n].real**2, nt_G)
axpy(1.0, kpt.psit_nG[n].imag**2, nt_G)
def add_to_density_from_k_point_with_occupation(self, nt_sG, kpt, f_n):
# Used in calculation of response part of GLLB-potential
nt_G = nt_sG[kpt.s]
if self.dtype == float:
for f, psit_G in zip(f_n, kpt.psit_nG):
axpy(f, psit_G**2, nt_G)
else:
for f, psit_G in zip(f_n, kpt.psit_nG):
axpy(f, psit_G.real**2, nt_G)
axpy(f, psit_G.imag**2, nt_G)
# Hack used in delta-scf calculations:
if hasattr(kpt, 'c_on'):
assert self.bd.comm.size == 1
d_nn = np.zeros((self.bd.mynbands, self.bd.mynbands),
dtype=complex)
for ne, c_n in zip(kpt.ne_o, kpt.c_on):
d_nn += ne * np.outer(c_n.conj(), c_n)
for d_n, psi0_G in zip(d_nn, kpt.psit_nG):
for d, psi_G in zip(d_n, kpt.psit_nG):
if abs(d) > 1.e-12:
nt_G += (psi0_G.conj() * d * psi_G).real
def calculate_kinetic_energy_density(self, tauct, grad_v):
assert not hasattr(self.kpt_u[0], 'c_on')
if isinstance(self.kpt_u[0].psit_nG, TarFileReference):
raise RuntimeError('Wavefunctions have not been initialized.')
taut_sG = self.gd.zeros(self.nspins)
dpsit_G = self.gd.empty(dtype=self.dtype)
for kpt in self.kpt_u:
for f, psit_G in zip(kpt.f_n, kpt.psit_nG):
for v in range(3):
grad_v[v](psit_G, dpsit_G, kpt.phase_cd)
axpy(0.5 * f, abs(dpsit_G)**2, taut_sG[kpt.s])
self.kpt_comm.sum(taut_sG)
self.band_comm.sum(taut_sG)
return taut_sG
def calculate_forces(self, hamiltonian, F_av):
# Calculate force-contribution from k-points:
F_av.fill(0.0)
F_aniv = self.pt.dict(self.bd.mynbands, derivative=True)
for kpt in self.kpt_u:
self.pt.derivative(kpt.psit_nG, F_aniv, kpt.q)
for a, F_niv in F_aniv.items():
F_niv = F_niv.conj()
F_niv *= kpt.f_n[:, np.newaxis, np.newaxis]
dH_ii = unpack(hamiltonian.dH_asp[a][kpt.s])
P_ni = kpt.P_ani[a]
F_vii = np.dot(np.dot(F_niv.transpose(), P_ni), dH_ii)
F_niv *= kpt.eps_n[:, np.newaxis, np.newaxis]
dO_ii = hamiltonian.setups[a].dO_ii
F_vii -= np.dot(np.dot(F_niv.transpose(), P_ni), dO_ii)
F_av[a] += 2 * F_vii.real.trace(0, 1, 2)
# Hack used in delta-scf calculations:
if hasattr(kpt, 'c_on'):
assert self.bd.comm.size == 1
self.pt.derivative(kpt.psit_nG, F_aniv, kpt.q) #XXX again
d_nn = np.zeros((self.bd.mynbands, self.bd.mynbands),
dtype=complex)
for ne, c_n in zip(kpt.ne_o, kpt.c_on):
d_nn += ne * np.outer(c_n.conj(), c_n)
for a, F_niv in F_aniv.items():
F_niv = F_niv.conj()
dH_ii = unpack(hamiltonian.dH_asp[a][kpt.s])
Q_ni = np.dot(d_nn, kpt.P_ani[a])
F_vii = np.dot(np.dot(F_niv.transpose(), Q_ni), dH_ii)
F_niv *= kpt.eps_n[:, np.newaxis, np.newaxis]
dO_ii = hamiltonian.setups[a].dO_ii
F_vii -= np.dot(np.dot(F_niv.transpose(), Q_ni), dO_ii)
F_av[a] += 2 * F_vii.real.trace(0, 1, 2)
self.bd.comm.sum(F_av, 0)
if self.bd.comm.rank == 0:
self.kpt_comm.sum(F_av, 0)
def estimate_memory(self, mem):
FDPWWaveFunctions.estimate_memory(self, mem)
self.kin.estimate_memory(mem.subnode('Kinetic operator'))
df = DF(calc)
df.spos_ac = spos_ac
if mode == 'fd':
pt = LFC(gd, [setup.pt_j for setup in setups],
KPointDescriptor(bzk_kc),
dtype=calc.wfs.dtype)
pt.set_positions(spos_ac)
for spin in range(nspins):
for k in range(len(bzk_kc)):
ibzk = k # since no symmetry
u = kd.get_rank_and_index(spin, ibzk)[1]
kpt = calc.wfs.kpt_u[u]
for n in range(nbands):
P_ai = pt.dict()
psit_G = calc.wfs.get_wave_function_array(n, ibzk,
spin)
pt.integrate(psit_G, P_ai, ibzk)
for a in range(len(P_ai)):
assert np.abs(
P_ai[a] -
calc.wfs.kpt_u[u].P_ani[a][n]).sum() < 1e-8
assert np.abs(
P_ai[a] -
df.get_P_ai(k, n, spin)[a]).sum() < 1e-8
else:
pt = PWLFC([setup.pt_j for setup in setups], calc.wfs.pd)
pt.set_positions(spos_ac)
# Initialize s, p, d (9 in total) wave and put them on grid
rc = 2.0
a = 2.5 * rc
n = 64
lmax = 2
b = 8.0
m = (lmax + 1)**2
gd = GridDescriptor([n, n, n], [a, a, a])
r = np.linspace(0, rc, 200)
g = np.exp(-(r / rc * b)**2)
splines = [Spline(l=l, rmax=rc, f_g=g) for l in range(lmax + 1)]
c = LFC(gd, [splines])
c.set_positions([(0.5, 0.5, 0.5)])
psi = gd.zeros(m)
d0 = c.dict(m)
if 0 in d0:
d0[0] = np.identity(m)
c.add(psi, d0)
# Calculate on 3d-grid < phi_i | e**(-ik.r) | phi_j >
R_a = np.array([a/2,a/2,a/2])
rr = gd.get_grid_point_coordinates()
for dim in range(3):
rr[dim] -= R_a[dim]
k_G = np.array([[11.,0.2,0.1],[10., 0., 10.]])
nkpt = k_G.shape[0]
d0 = np.zeros((nkpt,m,m), dtype=complex)
for i in range(m):
def get_projections(self, locfun, spin=0):
"""Project wave functions onto localized functions
Determine the projections of the Kohn-Sham eigenstates
onto specified localized functions of the format::
locfun = [[spos_c, l, sigma], [...]]
spos_c can be an atom index, or a scaled position vector. l is
the angular momentum, and sigma is the (half-) width of the
radial gaussian.
Return format is::
f_kni = <psi_kn | f_i>
where psi_kn are the wave functions, and f_i are the specified
localized functions.
As a special case, locfun can be the string 'projectors', in which
case the bound state projectors are used as localized functions.
"""
wfs = self.wfs
if locfun == 'projectors':
f_kin = []
for kpt in wfs.kpt_u:
if kpt.s == spin:
f_in = []
for a, P_ni in kpt.P_ani.items():
i = 0
setup = wfs.setups[a]
for l, n in zip(setup.l_j, setup.n_j):
if n >= 0:
for j in range(i, i + 2 * l + 1):
f_in.append(P_ni[:, j])
i += 2 * l + 1
f_kin.append(f_in)
f_kni = np.array(f_kin).transpose(0, 2, 1)
return f_kni.conj()
from gpaw.lfc import LocalizedFunctionsCollection as LFC
from gpaw.spline import Spline
from gpaw.utilities import _fact
nkpts = len(wfs.ibzk_kc)
nbf = np.sum([2 * l + 1 for pos, l, a in locfun])
f_kni = np.zeros((nkpts, wfs.nbands, nbf), wfs.dtype)
spos_ac = self.atoms.get_scaled_positions() % 1.0
spos_xc = []
splines_x = []
for spos_c, l, sigma in locfun:
if isinstance(spos_c, int):
spos_c = spos_ac[spos_c]
spos_xc.append(spos_c)
alpha = .5 * Bohr**2 / sigma**2
r = np.linspace(0, 6. * sigma, 500)
f_g = (_fact[l] * (4 * alpha)**(l + 3 / 2.) *
np.exp(-alpha * r**2) /
(np.sqrt(4 * np.pi) * _fact[2 * l + 1]))
splines_x.append([Spline(l, rmax=r[-1], f_g=f_g, points=61)])
lf = LFC(wfs.gd, splines_x, wfs.kpt_comm, dtype=wfs.dtype)
if not wfs.gamma:
lf.set_k_points(wfs.ibzk_qc)
lf.set_positions(spos_xc)
k = 0
f_ani = lf.dict(wfs.nbands)
for kpt in wfs.kpt_u:
if kpt.s != spin:
continue
lf.integrate(kpt.psit_nG[:], f_ani, kpt.q)
i1 = 0
for x, f_ni in f_ani.items():
i2 = i1 + f_ni.shape[1]
f_kni[k, :, i1:i2] = f_ni
i1 = i2
k += 1
return f_kni.conj()
def get_projections(self, locfun, spin=0):
"""Project wave functions onto localized functions
Determine the projections of the Kohn-Sham eigenstates
onto specified localized functions of the format::
locfun = [[spos_c, l, sigma], [...]]
spos_c can be an atom index, or a scaled position vector. l is
the angular momentum, and sigma is the (half-) width of the
radial gaussian.
Return format is::
f_kni = <psi_kn | f_i>
where psi_kn are the wave functions, and f_i are the specified
localized functions.
As a special case, locfun can be the string 'projectors', in which
case the bound state projectors are used as localized functions.
"""
wfs = self.wfs
if locfun == 'projectors':
f_kin = []
for kpt in wfs.kpt_u:
if kpt.s == spin:
f_in = []
for a, P_ni in kpt.P_ani.items():
i = 0
setup = wfs.setups[a]
for l, n in zip(setup.l_j, setup.n_j):
if n >= 0:
for j in range(i, i + 2 * l + 1):
f_in.append(P_ni[:, j])
i += 2 * l + 1
f_kin.append(f_in)
f_kni = np.array(f_kin).transpose(0, 2, 1)
return f_kni.conj()
from gpaw.lfc import LocalizedFunctionsCollection as LFC
from gpaw.spline import Spline
from gpaw.utilities import _fact
nkpts = len(wfs.ibzk_kc)
nbf = np.sum([2 * l + 1 for pos, l, a in locfun])
f_kni = np.zeros((nkpts, wfs.nbands, nbf), wfs.dtype)
spos_ac = self.atoms.get_scaled_positions() % 1.0
spos_xc = []
splines_x = []
for spos_c, l, sigma in locfun:
if isinstance(spos_c, int):
spos_c = spos_ac[spos_c]
spos_xc.append(spos_c)
alpha = .5 * Bohr**2 / sigma**2
r = np.linspace(0, 6. * sigma, 500)
f_g = (_fact[l] * (4 * alpha)**(l + 3 / 2.) *
np.exp(-alpha * r**2) /
(np.sqrt(4 * np.pi) * _fact[2 * l + 1]))
splines_x.append([Spline(l, rmax=r[-1], f_g=f_g, points=61)])
lf = LFC(wfs.gd, splines_x, wfs.kpt_comm, dtype=wfs.dtype)
if not wfs.gamma:
lf.set_k_points(wfs.ibzk_qc)
lf.set_positions(spos_xc)
k = 0
f_ani = lf.dict(wfs.nbands)
for kpt in wfs.kpt_u:
if kpt.s != spin:
continue
lf.integrate(kpt.psit_nG[:], f_ani, kpt.q)
i1 = 0
for x, f_ni in f_ani.items():
i2 = i1 + f_ni.shape[1]
f_kni[k, :, i1:i2] = f_ni
i1 = i2
k += 1
return f_kni.conj()
class FDWaveFunctions(FDPWWaveFunctions):
def __init__(self, stencil, diagksl, orthoksl, initksl,
gd, nvalence, setups, bd,
dtype, world, kd, timer=None):
FDPWWaveFunctions.__init__(self, diagksl, orthoksl, initksl,
gd, nvalence, setups, bd,
dtype, world, kd, timer)
# Kinetic energy operator:
self.kin = Laplace(self.gd, -0.5, stencil, self.dtype)
self.matrixoperator = MatrixOperator(self.orthoksl)
self.taugrad_v = None # initialized by MGGA functional
def empty(self, n=(), global_array=False, realspace=False, q=-1):
return self.gd.empty(n, self.dtype, global_array)
def integrate(self, a_xg, b_yg=None, global_integral=True):
return self.gd.integrate(a_xg, b_yg, global_integral)
def bytes_per_wave_function(self):
return self.gd.bytecount(self.dtype)
def set_setups(self, setups):
self.pt = LFC(self.gd, [setup.pt_j for setup in setups],
self.kd, dtype=self.dtype, forces=True)
FDPWWaveFunctions.set_setups(self, setups)
def set_positions(self, spos_ac):
FDPWWaveFunctions.set_positions(self, spos_ac)
def summary(self, fd):
fd.write('Wave functions: Uniform real-space grid\n')
fd.write('Kinetic energy operator: %s\n' % self.kin.description)
def make_preconditioner(self, block=1):
return Preconditioner(self.gd, self.kin, self.dtype, block)
def apply_pseudo_hamiltonian(self, kpt, hamiltonian, psit_xG, Htpsit_xG):
self.timer.start('Apply hamiltonian')
self.kin.apply(psit_xG, Htpsit_xG, kpt.phase_cd)
hamiltonian.apply_local_potential(psit_xG, Htpsit_xG, kpt.s)
self.timer.stop('Apply hamiltonian')
def add_orbital_density(self, nt_G, kpt, n):
if self.dtype == float:
axpy(1.0, kpt.psit_nG[n]**2, nt_G)
else:
axpy(1.0, kpt.psit_nG[n].real**2, nt_G)
axpy(1.0, kpt.psit_nG[n].imag**2, nt_G)
def add_to_density_from_k_point_with_occupation(self, nt_sG, kpt, f_n):
# Used in calculation of response part of GLLB-potential
nt_G = nt_sG[kpt.s]
if self.dtype == float:
for f, psit_G in zip(f_n, kpt.psit_nG):
axpy(f, psit_G**2, nt_G)
else:
for f, psit_G in zip(f_n, kpt.psit_nG):
axpy(f, psit_G.real**2, nt_G)
axpy(f, psit_G.imag**2, nt_G)
# Hack used in delta-scf calculations:
if hasattr(kpt, 'c_on'):
assert self.bd.comm.size == 1
d_nn = np.zeros((self.bd.mynbands, self.bd.mynbands),
dtype=complex)
for ne, c_n in zip(kpt.ne_o, kpt.c_on):
d_nn += ne * np.outer(c_n.conj(), c_n)
for d_n, psi0_G in zip(d_nn, kpt.psit_nG):
for d, psi_G in zip(d_n, kpt.psit_nG):
if abs(d) > 1.e-12:
nt_G += (psi0_G.conj() * d * psi_G).real
def calculate_kinetic_energy_density(self):
if self.taugrad_v is None:
self.taugrad_v = [
Gradient(self.gd, v, n=3, dtype=self.dtype).apply
for v in range(3)]
assert not hasattr(self.kpt_u[0], 'c_on')
if self.kpt_u[0].psit_nG is None:
raise RuntimeError('No wavefunctions yet')
if isinstance(self.kpt_u[0].psit_nG, FileReference):
# XXX initialize
raise RuntimeError('Wavefunctions have not been initialized.')
taut_sG = self.gd.zeros(self.nspins)
dpsit_G = self.gd.empty(dtype=self.dtype)
for kpt in self.kpt_u:
for f, psit_G in zip(kpt.f_n, kpt.psit_nG):
for v in range(3):
self.taugrad_v[v](psit_G, dpsit_G, kpt.phase_cd)
axpy(0.5 * f, abs(dpsit_G)**2, taut_sG[kpt.s])
self.kpt_comm.sum(taut_sG)
self.band_comm.sum(taut_sG)
return taut_sG
def apply_mgga_orbital_dependent_hamiltonian(self, kpt, psit_xG,
Htpsit_xG, dH_asp,
dedtaut_G):
a_G = self.gd.empty(dtype=psit_xG.dtype)
for psit_G, Htpsit_G in zip(psit_xG, Htpsit_xG):
for v in range(3):
self.taugrad_v[v](psit_G, a_G, kpt.phase_cd)
self.taugrad_v[v](dedtaut_G * a_G, a_G, kpt.phase_cd)
axpy(-0.5, a_G, Htpsit_G)
def ibz2bz(self, atoms):
"""Transform wave functions in IBZ to the full BZ."""
assert self.kd.comm.size == 1
# New k-point descriptor for full BZ:
kd = KPointDescriptor(self.kd.bzk_kc, nspins=self.nspins)
kd.set_symmetry(atoms, self.setups, usesymm=None)
kd.set_communicator(serial_comm)
self.pt = LFC(self.gd, [setup.pt_j for setup in self.setups],
kd, dtype=self.dtype)
self.pt.set_positions(atoms.get_scaled_positions())
self.initialize_wave_functions_from_restart_file()
weight = 2.0 / kd.nspins / kd.nbzkpts
# Build new list of k-points:
kpt_u = []
for s in range(self.nspins):
for k in range(kd.nbzkpts):
# Index of symmetry related point in the IBZ
ik = self.kd.bz2ibz_k[k]
r, u = self.kd.get_rank_and_index(s, ik)
assert r == 0
kpt = self.kpt_u[u]
phase_cd = np.exp(2j * np.pi * self.gd.sdisp_cd *
kd.bzk_kc[k, :, np.newaxis])
# New k-point:
kpt2 = KPoint(weight, s, k, k, phase_cd)
kpt2.f_n = kpt.f_n / kpt.weight / kd.nbzkpts * 2 / self.nspins
kpt2.eps_n = kpt.eps_n.copy()
# Transform wave functions using symmetry operation:
Psit_nG = self.gd.collect(kpt.psit_nG)
if Psit_nG is not None:
Psit_nG = Psit_nG.copy()
for Psit_G in Psit_nG:
Psit_G[:] = self.kd.transform_wave_function(Psit_G, k)
kpt2.psit_nG = self.gd.empty(self.bd.nbands, dtype=self.dtype)
self.gd.distribute(Psit_nG, kpt2.psit_nG)
# Calculate PAW projections:
kpt2.P_ani = self.pt.dict(len(kpt.psit_nG))
self.pt.integrate(kpt2.psit_nG, kpt2.P_ani, k)
kpt_u.append(kpt2)
self.kd = kd
self.kpt_u = kpt_u
def write(self, writer, write_wave_functions=False):
writer['Mode'] = 'fd'
if not write_wave_functions:
return
writer.add('PseudoWaveFunctions',
('nspins', 'nibzkpts', 'nbands',
'ngptsx', 'ngptsy', 'ngptsz'),
dtype=self.dtype)
if hasattr(writer, 'hdf5'):
parallel = (self.world.size > 1)
for kpt in self.kpt_u:
indices = [kpt.s, kpt.k]
indices.append(self.bd.get_slice())
indices += self.gd.get_slice()
writer.fill(kpt.psit_nG, parallel=parallel, *indices)
else:
for s in range(self.nspins):
for k in range(self.nibzkpts):
for n in range(self.bd.nbands):
psit_G = self.get_wave_function_array(n, k, s)
writer.fill(psit_G, s, k, n)
def read(self, reader, hdf5):
if ((not hdf5 and self.bd.comm.size == 1) or
(hdf5 and self.world.size == 1)):
# We may not be able to keep all the wave
# functions in memory - so psit_nG will be a special type of
# array that is really just a reference to a file:
for kpt in self.kpt_u:
kpt.psit_nG = reader.get_reference('PseudoWaveFunctions',
(kpt.s, kpt.k))
else:
for kpt in self.kpt_u:
kpt.psit_nG = self.empty(self.bd.mynbands)
if hdf5:
indices = [kpt.s, kpt.k]
indices.append(self.bd.get_slice())
indices += self.gd.get_slice()
reader.get('PseudoWaveFunctions', out=kpt.psit_nG,
parallel=(self.world.size > 1), *indices)
else:
# Read band by band to save memory
for myn, psit_G in enumerate(kpt.psit_nG):
n = self.bd.global_index(myn)
if self.gd.comm.rank == 0:
big_psit_G = np.array(
reader.get('PseudoWaveFunctions',
kpt.s, kpt.k, n),
self.dtype)
else:
big_psit_G = None
self.gd.distribute(big_psit_G, psit_G)
def initialize_from_lcao_coefficients(self, basis_functions, mynbands):
for kpt in self.kpt_u:
kpt.psit_nG = self.gd.zeros(self.bd.mynbands, self.dtype)
basis_functions.lcao_to_grid(kpt.C_nM,
kpt.psit_nG[:mynbands], kpt.q)
kpt.C_nM = None
def random_wave_functions(self, nao):
"""Generate random wave functions."""
gpts = self.gd.N_c[0] * self.gd.N_c[1] * self.gd.N_c[2]
if self.bd.nbands < gpts / 64:
gd1 = self.gd.coarsen()
gd2 = gd1.coarsen()
psit_G1 = gd1.empty(dtype=self.dtype)
psit_G2 = gd2.empty(dtype=self.dtype)
interpolate2 = Transformer(gd2, gd1, 1, self.dtype).apply
interpolate1 = Transformer(gd1, self.gd, 1, self.dtype).apply
shape = tuple(gd2.n_c)
scale = np.sqrt(12 / abs(np.linalg.det(gd2.cell_cv)))
old_state = np.random.get_state()
np.random.seed(4 + self.world.rank)
for kpt in self.kpt_u:
for psit_G in kpt.psit_nG[nao:]:
if self.dtype == float:
psit_G2[:] = (np.random.random(shape) - 0.5) * scale
else:
psit_G2.real = (np.random.random(shape) - 0.5) * scale
psit_G2.imag = (np.random.random(shape) - 0.5) * scale
interpolate2(psit_G2, psit_G1, kpt.phase_cd)
interpolate1(psit_G1, psit_G, kpt.phase_cd)
np.random.set_state(old_state)
elif gpts / 64 <= self.bd.nbands < gpts / 8:
gd1 = self.gd.coarsen()
psit_G1 = gd1.empty(dtype=self.dtype)
interpolate1 = Transformer(gd1, self.gd, 1, self.dtype).apply
shape = tuple(gd1.n_c)
scale = np.sqrt(12 / abs(np.linalg.det(gd1.cell_cv)))
old_state = np.random.get_state()
np.random.seed(4 + self.world.rank)
for kpt in self.kpt_u:
for psit_G in kpt.psit_nG[nao:]:
if self.dtype == float:
psit_G1[:] = (np.random.random(shape) - 0.5) * scale
else:
psit_G1.real = (np.random.random(shape) - 0.5) * scale
psit_G1.imag = (np.random.random(shape) - 0.5) * scale
interpolate1(psit_G1, psit_G, kpt.phase_cd)
np.random.set_state(old_state)
else:
shape = tuple(self.gd.n_c)
scale = np.sqrt(12 / abs(np.linalg.det(self.gd.cell_cv)))
old_state = np.random.get_state()
np.random.seed(4 + self.world.rank)
for kpt in self.kpt_u:
for psit_G in kpt.psit_nG[nao:]:
if self.dtype == float:
psit_G[:] = (np.random.random(shape) - 0.5) * scale
else:
psit_G.real = (np.random.random(shape) - 0.5) * scale
psit_G.imag = (np.random.random(shape) - 0.5) * scale
np.random.set_state(old_state)
def estimate_memory(self, mem):
FDPWWaveFunctions.estimate_memory(self, mem)
import numpy as np
from gpaw.lfc import LocalizedFunctionsCollection as LFC
from gpaw.grid_descriptor import GridDescriptor
from gpaw.spline import Spline
gd = GridDescriptor([20, 16, 16], [(4, 2, 0), (0, 4, 0), (0, 0, 4)])
spos_ac = np.array([[0.252, 0.15, 0.35], [0.503, 0.5, 0.5]])
s = Spline(l=0, rmax=2.0, f_g=np.array([1, 0.9, 0.1, 0.0]))
spline_aj = [[s], [s]]
c = LFC(gd, spline_aj)
c.set_positions(spos_ac)
c_ai = c.dict(zero=True)
if 1 in c_ai:
c_ai[1][0] = 2.0
psi = gd.zeros()
c.add(psi, c_ai)
d_avv = dict([(a, np.zeros((3, 3))) for a in c.my_atom_indices])
c.second_derivative(psi, d_avv)
if 0 in d_avv:
print d_avv[0]
eps = 0.000001
d_aiv = c.dict(derivative=True)
pos_av = np.dot(spos_ac, gd.cell_cv)
for v in range(3):
pos_av[0, v] += eps
c.set_positions(np.dot(pos_av, gd.icell_cv.T))
c.derivative(psi, d_aiv)
if 0 in d_aiv:
d0_v = d_aiv[0][0].copy()