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
assert abs(d_aniv[1]).max() < 3e-16
eps = 0.0001
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.integrate(psi, C_ani)
if 0 in d_aniv:
C0_n = C_ani[0][:, 0].copy()
pos_av[0, v] -= 2 * eps
c.set_positions(np.dot(pos_av, gd.icell_cv.T))
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
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
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 = RadialGridDescriptor(r, np.ones_like(r) * r[1])
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:
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()
pos_av[0, v] -= 2 * 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]
d0_v /= -2 * eps
print(d0_v)
d_avv[0][v] -= d0_v
pos_av[0, v] += eps
if 0 in d_avv:
assert np.abs(d_avv[0]).max() < 1e-10
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'))
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:
print abs(d1[0] - d2).max()
assert abs(d1[0] - d2).max() < 2e-6
