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 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)
if self.finegrid:
self.poissonsolver = hamiltonian.poisson
self.ghat = density.ghat
self.interpolator = density.interpolator
self.restrictor = hamiltonian.restrictor
else:
self.poissonsolver = PoissonSolver(eps=1e-11)
self.poissonsolver.set_grid_descriptor(density.gd)
self.poissonsolver.initialize()
self.ghat = LFC(density.gd,
[setup.ghat_l for setup in density.setups],
integral=np.sqrt(4 * np.pi),
forces=True)
self.gd = density.gd
self.finegd = self.ghat.gd
def initialize(self, density, hamiltonian, wfs, occ=None):
assert wfs.kd.gamma
assert not wfs.gd.pbc_c.any()
self.wfs = wfs
self.dtype = float
self.xc.initialize(density, hamiltonian, wfs, occ)
self.kpt_comm = wfs.kd.comm
self.nspins = wfs.nspins
self.nbands = wfs.bd.nbands
if self.finegrid:
self.finegd = density.finegd
self.ghat = density.ghat
else:
self.finegd = density.gd
self.ghat = LFC(self.finegd,
[setup.ghat_l for setup in density.setups],
integral=sqrt(4 * pi),
forces=True)
poissonsolver = PoissonSolver(eps=1e-14)
poissonsolver.set_grid_descriptor(self.finegd)
poissonsolver.initialize()
self.spin_s = {}
for kpt in wfs.kpt_u:
self.spin_s[kpt.s] = SICSpin(kpt, self.xc, density, hamiltonian,
wfs, poissonsolver, self.ghat,
self.finegd, **self.parameters)
def initialize(self, density, hamiltonian, wfs, occupations):
self.xc.initialize(density, hamiltonian, wfs, occupations)
self.nspins = wfs.nspins
self.setups = wfs.setups
self.density = density
self.kpt_u = wfs.kpt_u
self.gd = density.gd
self.kd = wfs.kd
self.bd = wfs.bd
if self.bd.comm.size > 1:
raise ValueError('Band parallelization not supported by hybridk')
self.wfs = wfs
self.world = wfs.world
self.fd = logfile(self.fd, self.world.rank)
N = self.gd.N_c.prod()
vol = self.gd.dv * N
if self.alpha is None:
# XXX ?
self.alpha = 6 * vol**(2 / 3.0) / pi**2
if self.ecut is None:
self.ecut = 0.5 * pi**2 / (self.gd.h_cv**2).sum(1).max() * 0.9999
self.bzq_qc = self.kd.get_bz_q_points()
qd = KPointDescriptor(self.bzq_qc)
q0 = self.kd.where_is_q(np.zeros(3), self.bzq_qc)
self.pwd = PWDescriptor(self.ecut, self.gd, complex, kd=qd)
G2_qG = self.pwd.G2_qG
G2_qG[q0][0] = 117.0
self.iG2_qG = [1.0 / G2_G for G2_G in G2_qG]
G2_qG[q0][0] = 0.0
self.iG2_qG[q0][0] = 0.0
self.gamma = (vol / (2 * pi)**2 * sqrt(pi / self.alpha) *
self.kd.nbzkpts)
for q in range(self.kd.nbzkpts):
self.gamma -= np.dot(np.exp(-self.alpha * G2_qG[q]),
self.iG2_qG[q])
self.iG2_qG[q0][0] = self.gamma
self.ghat = LFC(self.gd, [setup.ghat_l for setup in density.setups],
qd,
dtype=complex)
self.log('Value of alpha parameter:', self.alpha)
self.log('Value of gamma parameter:', self.gamma)
self.log('Cutoff energy:', self.ecut, 'Hartree')
self.log('%d x %d x %d k-points' % tuple(self.kd.N_c))
def setUp(self):
UTBandParallelSetup.setUp(self)
for virtvar in ['dtype', 'blocking', 'async']:
assert getattr(self,
virtvar) is not None, 'Virtual "%s"!' % virtvar
# Create randomized atoms
self.atoms = create_random_atoms(self.gd)
# Do we agree on the atomic positions?
pos_ac = self.atoms.get_positions()
pos_rac = np.empty((world.size, ) + pos_ac.shape, pos_ac.dtype)
world.all_gather(pos_ac, pos_rac)
if (pos_rac - pos_rac[world.rank, ...][np.newaxis, ...]).any():
raise RuntimeError('Discrepancy in atomic positions detected.')
# Create setups for atoms
self.Z_a = self.atoms.get_atomic_numbers()
self.setups = Setups(self.Z_a, p.setups, p.basis, p.lmax, xc)
# Create atomic projector overlaps
spos_ac = self.atoms.get_scaled_positions() % 1.0
self.rank_a = self.gd.get_ranks_from_positions(spos_ac)
self.pt = LFC(self.gd, [setup.pt_j for setup in self.setups],
self.kpt_comm,
dtype=self.dtype)
self.pt.set_positions(spos_ac)
if memstats:
# Hack to scramble heap usage into steady-state level
HEAPSIZE = 25 * 1024**2
for i in range(100):
data = np.empty(np.random.uniform(0, HEAPSIZE // 8), float)
del data
self.mem_pre = record_memory()
self.mem_alloc = None
self.mem_test = None
# Stuff for pseudo wave functions and projections
if self.dtype == complex:
self.gamma = 1j**(1.0 / self.nbands)
else:
self.gamma = 1.0
self.psit_nG = None
self.P_ani = None
self.Qeff_a = None
self.Qtotal = None
self.allocate()
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 initialize(self, density, hamiltonian, wfs, occupations):
assert wfs.gamma
self.xc.initialize(density, hamiltonian, wfs, occupations)
self.kpt_comm = wfs.kpt_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)
if self.finegrid:
self.poissonsolver = hamiltonian.poisson
self.ghat = density.ghat
self.interpolator = density.interpolator
self.restrictor = hamiltonian.restrictor
else:
self.poissonsolver = PoissonSolver(eps=1e-11)
self.poissonsolver.set_grid_descriptor(density.gd)
self.poissonsolver.initialize()
self.ghat = LFC(density.gd,
[setup.ghat_l for setup in density.setups],
integral=np.sqrt(4 * np.pi), forces=True)
self.gd = density.gd
self.finegd = self.ghat.gd
def with_compensation_charges(self, finegrid=False):
"""Get pair densisty including the compensation charges"""
rhot = self.get(finegrid)
# Determine the compensation charges for each nucleus
Q_aL = {}
for a, P_ni in self.P_ani.items():
# Generate density matrix
Pi_i = P_ni[self.i]
Pj_i = P_ni[self.j]
D_ii = np.outer(Pi_i, Pj_i)
# allowed to pack as used in the scalar product with
# the symmetric array Delta_pL
D_p = pack(D_ii)
# Determine compensation charge coefficients:
Q_aL[a] = np.dot(D_p, self.setups[a].Delta_pL)
# Add compensation charges
if finegrid:
self.density.ghat.add(rhot, Q_aL)
else:
if not hasattr(self.density, 'Ghat'):
self.density.Ghat = LFC(
self.density.gd, [setup.ghat_l for setup in self.setups],
integral=sqrt(4 * pi))
self.density.Ghat.set_positions(self.spos_ac)
self.density.Ghat.add(rhot, Q_aL)
return rhot
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 initialize(self, density, hamiltonian, wfs, occ=None):
assert wfs.gamma
assert not wfs.gd.pbc_c.any()
self.wfs = wfs
self.dtype = float
self.xc.initialize(density, hamiltonian, wfs, occ)
self.kpt_comm = wfs.kpt_comm
self.nspins = wfs.nspins
self.nbands = wfs.bd.nbands
if self.finegrid:
self.finegd = density.finegd
self.ghat = density.ghat
else:
self.finegd = density.gd
self.ghat = LFC(self.finegd,
[setup.ghat_l for setup in density.setups],
integral=sqrt(4 * pi), forces=True)
poissonsolver = PoissonSolver(eps=1e-14)
poissonsolver.set_grid_descriptor(self.finegd)
poissonsolver.initialize()
self.spin_s = {}
for kpt in wfs.kpt_u:
self.spin_s[kpt.s] = SICSpin(kpt, self.xc,
density, hamiltonian, wfs,
poissonsolver, self.ghat,
self.finegd, **self.parameters)
def get_grid_dP_aMix(spos_ac, wfs, q, timer=nulltimer): # XXXXXX q
nao = wfs.setups.nao
C_MM = np.identity(nao, dtype=wfs.dtype)
# XXX In the future use the New Two-Center integrals
# to evaluate this
dP_aMix = {}
for a, setup in enumerate(wfs.setups):
ni = 0
dP_Mix = np.zeros((nao, setup.ni, 3))
pt = LFC(wfs.gd, [setup.pt_j],
wfs.kd.comm,
dtype=wfs.dtype,
forces=True)
spos1_ac = [spos_ac[a]]
pt.set_k_points(wfs.ibzk_qc)
pt.set_positions(spos1_ac)
for b, setup_b in enumerate(wfs.setups):
nao = setup_b.nao
phi_MG = wfs.gd.zeros(nao, wfs.dtype)
phi_MG = wfs.gd.collect(phi_MG, broadcast=False)
wfs.basis_functions.lcao_to_grid(C_MM[ni:ni + nao], phi_MG, q)
dP_bMix = pt.dict(len(phi_MG), derivative=True)
pt.derivative(phi_MG, dP_bMix, q=q)
dP_Mix[ni:ni + nao] = dP_bMix[0]
ni += nao
timer.write_now('projector grad. doing atoms (%s, %s) ' % (a, b))
dP_aMix[a] = dP_Mix
return dP_aMix
def initialize(self, density, hamiltonian, wfs, occupations):
self.wfs = wfs
self.tauct = LFC(wfs.gd, [[setup.tauct] for setup in wfs.setups], forces=True, cut=True)
self.tauct_G = None
self.dedtaut_sG = None
self.restrict = hamiltonian.restrictor.apply
self.interpolate = density.interpolator.apply
self.taugrad_v = [Gradient(wfs.gd, v, n=self.nn, dtype=wfs.dtype, allocate=True).apply for v in range(3)]
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, 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 __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 set_setups(self, setups):
self.pd = PWDescriptor(self.ecut, self.gd, self.kd.ibzk_qc)
pt = LFC(self.gd, [setup.pt_j for setup in setups],
self.kpt_comm,
dtype=self.dtype,
forces=True)
self.pt = PWLFC(pt, self.pd)
FDPWWaveFunctions.set_setups(self, setups)
def set_grid_descriptor(self, gd):
GGA.set_grid_descriptor(self, gd)
self.dedmu_g = gd.zeros()
self.dedbeta_g = gd.zeros()
# Create gaussian LFC
l_lim = 1.0e-30
rcut = 12
points = 200
r_i = np.linspace(0, rcut, points + 1)
rcgauss = 1.2
g_g = (2 / rcgauss**3 / np.pi *
np.exp(-((r_i / rcgauss)**2)**self.alpha))
# Values too close to zero can cause numerical problems especially with
# forces (some parts of the mu and beta field can become negative)
g_g[np.where(g_g < l_lim)] = l_lim
spline = Spline(l=0, rmax=rcut, f_g=g_g)
spline_j = [[spline]] * len(self.atoms)
self.Pa = LFC(gd, spline_j)
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 __init__(self, density, atoms, finegrid):
"""Initialization needs a paw instance, and whether the compensated
pair density should be on the fine grid (boolean)"""
self.density = density
self.finegrid = finegrid
if not finegrid:
density.Ghat = LFC(density.gd,
[setup.ghat_l for setup in density.setups],
integral=sqrt(4 * pi))
density.Ghat.set_positions(atoms.get_scaled_positions() % 1.0)
def add_potential_correction(self, v_R, alpha):
dens = self.calc.density
dens.D_asp.redistribute(dens.atom_partition.as_serial())
dens.Q_aL.redistribute(dens.atom_partition.as_serial())
dv_a1 = []
for a, D_sp in dens.D_asp.items():
setup = dens.setups[a]
c = setup.xc_correction
rgd = c.rgd
ghat_g = gauss(rgd, 1 / setup.rcgauss**2)
Z_g = gauss(rgd, alpha) * setup.Z
D_q = np.dot(D_sp.sum(0), c.B_pqL[:, :, 0])
dn_g = np.dot(D_q, (c.n_qg - c.nt_qg)) * sqrt(4 * pi)
dn_g += 4 * pi * (c.nc_g - c.nct_g)
dn_g -= Z_g
dn_g -= dens.Q_aL[a][0] * ghat_g * sqrt(4 * pi)
dv_g = rgd.poisson(dn_g) / sqrt(4 * pi)
dv_g[1:] /= rgd.r_g[1:]
dv_g[0] = dv_g[1]
dv_g[-1] = 0.0
dv_a1.append([rgd.spline(dv_g, points=POINTS)])
dens.D_asp.redistribute(dens.atom_partition)
dens.Q_aL.redistribute(dens.atom_partition)
if dv_a1:
dv = LFC(self.gd, dv_a1)
dv.set_positions(self.calc.spos_ac)
dv.add(v_R)
dens.gd.comm.broadcast(v_R, 0)
def _initialize_corrections(self):
if self.dphi is not None:
return
splines = {}
dphi_aj = []
for setup in self.calc.wfs.setups:
dphi_j = splines.get(setup)
if dphi_j is None:
rcut = max(setup.rcut_j) * 1.1
gcut = setup.rgd.ceil(rcut)
dphi_j = []
for l, phi_g, phit_g in zip(setup.l_j,
setup.data.phi_jg,
setup.data.phit_jg):
dphi_g = (phi_g - phit_g)[:gcut]
dphi_j.append(setup.rgd.spline(dphi_g, rcut, l,
points=200))
dphi_aj.append(dphi_j)
self.dphi = LFC(self.gd, dphi_aj, kd=self.calc.wfs.kd.copy(),
dtype=self.calc.wfs.dtype)
self.dphi.set_positions(self.calc.atoms.get_scaled_positions())
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 setUp(self):
UTBandParallelSetup.setUp(self)
for virtvar in ['dtype','blocking','async']:
assert getattr(self,virtvar) is not None, 'Virtual "%s"!' % virtvar
# Create randomized atoms
self.atoms = create_random_atoms(self.gd)
# Do we agree on the atomic positions?
pos_ac = self.atoms.get_positions()
pos_rac = np.empty((world.size,)+pos_ac.shape, pos_ac.dtype)
world.all_gather(pos_ac, pos_rac)
if (pos_rac-pos_rac[world.rank,...][np.newaxis,...]).any():
raise RuntimeError('Discrepancy in atomic positions detected.')
# Create setups for atoms
self.Z_a = self.atoms.get_atomic_numbers()
self.setups = Setups(self.Z_a, p.setups, p.basis,
p.lmax, xc)
# Create atomic projector overlaps
spos_ac = self.atoms.get_scaled_positions() % 1.0
self.rank_a = self.gd.get_ranks_from_positions(spos_ac)
self.pt = LFC(self.gd, [setup.pt_j for setup in self.setups],
dtype=self.dtype)
self.pt.set_positions(spos_ac)
if memstats:
# Hack to scramble heap usage into steady-state level
HEAPSIZE = 25 * 1024**2
for i in range(100):
data = np.empty(np.random.uniform(0, HEAPSIZE // 8), float)
del data
self.mem_pre = record_memory()
self.mem_alloc = None
self.mem_test = None
# Stuff for pseudo wave functions and projections
if self.dtype == complex:
self.gamma = 1j**(1.0/self.nbands)
else:
self.gamma = 1.0
self.psit_nG = None
self.P_ani = None
self.Qeff_a = None
self.Qtotal = None
self.allocate()
def initialize(self, paw):
if not paw.initialized:
raise RuntimeError('PAW instance is not initialized')
paw.converge_wave_functions()
self.tauct = LFC(self.gd,
[[setup.tauct] for setup in self.density.setups],
forces=True,
cut=True)
self.tauct.set_positions(paw.spos_ac)
self.taut_sg = None
self.nt_grad2_sG = self.gd.empty(self.nspins)
self.nt_grad2_sg = None
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 __init__(self, gd, spline_j, spos_c, index=None):
rcut = max([spline.get_cutoff() for spline in spline_j])
corner_c = np.ceil(spos_c * gd.N_c - rcut / gd.h_c).astype(int)
size_c = np.ceil(spos_c * gd.N_c + rcut / gd.h_c).astype(int) - corner_c
smallgd = GridDescriptor(N_c=size_c + 1,
cell_cv=gd.h_c * (size_c + 1),
pbc_c=False,
comm=mpi.serial_comm)
lfc = LFC(smallgd, [spline_j])
lfc.set_positions((spos_c[np.newaxis, :] * gd.N_c - corner_c + 1) /
smallgd.N_c)
ni = lfc.Mmax
f_iG = smallgd.zeros(ni)
lfc.add(f_iG, {0: np.eye(ni)})
LocalizedFunctions.__init__(self, gd, f_iG, corner_c,
index=index)
def get_grid2_dP_aMix(spos_ac, wfs, q, *args, **kwargs): # XXXXXX q
nao = wfs.setups.nao
C_MM = np.identity(nao, dtype=wfs.dtype)
bfs = wfs.basis_functions
phi_MG = wfs.gd.zeros(nao, wfs.dtype)
bfs.lcao_to_grid(C_MM, phi_MG, q)
setups = wfs.setups
pt = LFC(wfs.gd, [setup.pt_j for setup in setups],
wfs.kd.comm,
dtype=wfs.dtype,
forces=True)
pt.set_k_points(wfs.ibzk_qc)
pt.set_positions(spos_ac)
dP_aMix = pt.dict(len(phi_MG), derivative=True)
pt.derivative(phi_MG, dP_aMix, q=q)
return dP_aMix
def initialize(self, paw):
if not paw.initialized:
raise RuntimeError('PAW instance is not initialized')
self.tauct = LFC(self.gd,
[[setup.tauct] for setup in self.density.setups],
forces=True,
cut=True)
spos_ac = paw.atoms.get_scaled_positions() % 1.0
self.tauct.set_positions(spos_ac)
self.taut_sG = self.gd.empty(self.nspins)
self.taut_sg = None
self.nt_grad2_sG = self.gd.empty(self.nspins)
self.nt_grad2_sg = None
def __init__(self, gd, setups, spos_ac, fft=False):
assert gd.comm.size == 1
self.rhot1_G = gd.empty()
self.rhot2_G = gd.empty()
self.pot_G = gd.empty()
self.dv = gd.dv
if fft:
self.poisson = FFTPoissonSolver()
else:
self.poisson = PoissonSolver(name='fd', nn=3)
self.poisson.set_grid_descriptor(gd)
self.setups = setups
# Set coarse ghat
self.Ghat = LFC(gd, [setup.ghat_l for setup in setups],
integral=sqrt(4 * pi))
self.Ghat.set_positions(spos_ac)
def f(n, p):
N = 2 * n
gd = GridDescriptor((N, N, N), (L, L, L))
a = gd.zeros()
print(a.shape)
#p = PoissonSolver(nn=1, relax=relax)
p.set_grid_descriptor(gd)
cut = N / 2.0 * 0.9
s = Spline(l=0, rmax=cut, f_g=np.array([1, 0.5, 0.0]))
c = LFC(gd, [[s], [s]])
c.set_positions([(0, 0, 0), (0.5, 0.5, 0.5)])
c.add(a)
I0 = gd.integrate(a)
a -= I0 / L**3
b = gd.zeros()
p.solve(b, a, charge=0, eps=1e-20)
return gd.collect(b, broadcast=1)
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 initialize(self, density, hamiltonian, wfs, occupations):
self.xc.initialize(density, hamiltonian, wfs, occupations)
self.nspins = wfs.nspins
self.setups = wfs.setups
self.density = density
self.kpt_u = wfs.kpt_u
self.gd = density.gd
self.kd = wfs.kd
self.bd = wfs.bd
N_c = self.gd.N_c
N = self.gd.N_c.prod()
vol = self.gd.dv * N
if self.alpha is None:
self.alpha = 6 * vol**(2 / 3.0) / pi**2
self.gamma = (vol / (2 * pi)**2 * sqrt(pi / self.alpha) *
self.kd.nbzkpts)
ecut = 0.5 * pi**2 / (self.gd.h_cv**2).sum(1).max()
if self.kd.N_c is None:
self.bzk_kc = np.zeros((1, 3))
dfghdfgh
else:
n = self.kd.N_c * 2 - 1
bzk_kc = np.indices(n).transpose((1, 2, 3, 0))
bzk_kc.shape = (-1, 3)
bzk_kc -= self.kd.N_c - 1
self.bzk_kc = bzk_kc.astype(float) / self.kd.N_c
self.pwd = PWDescriptor(ecut, self.gd, self.bzk_kc)
n = 0
for k_c, Gpk2_G in zip(self.bzk_kc[:], self.pwd.G2_qG):
if (k_c > -0.5).all() and (k_c <= 0.5).all(): #XXX???
if k_c.any():
self.gamma -= np.dot(np.exp(-self.alpha * Gpk2_G),
Gpk2_G**-1)
else:
self.gamma -= np.dot(np.exp(-self.alpha * Gpk2_G[1:]),
Gpk2_G[1:]**-1)
n += 1
assert n == self.kd.N_c.prod()
self.ghat = LFC(self.gd,
[setup.ghat_l for setup in density.setups],
dtype=complex
)
self.ghat.set_k_points(self.bzk_kc)
self.fullkd = KPointDescriptor(self.kd.bzk_kc, nspins=1)
class S:
id_a = []
def set_symmetry(self, s): pass
self.fullkd.set_symmetry(Atoms(pbc=True), S(), False)
self.fullkd.set_communicator(world)
self.pt = LFC(self.gd, [setup.pt_j for setup in density.setups],
dtype=complex)
self.pt.set_k_points(self.fullkd.ibzk_kc)
self.interpolator = density.interpolator
class HybridXC(XCFunctional):
orbital_dependent = True
def __init__(self, name, hybrid=None, xc=None, finegrid=False,
alpha=None):
"""Mix standard functionals with exact exchange.
name: str
Name of hybrid functional.
hybrid: float
Fraction of exact exchange.
xc: str or XCFunctional object
Standard DFT functional with scaled down exchange.
finegrid: boolean
Use fine grid for energy functional evaluations?
"""
if name == 'EXX':
assert hybrid is None and xc is None
hybrid = 1.0
xc = XC(XCNull())
elif name == 'PBE0':
assert hybrid is None and xc is None
hybrid = 0.25
xc = XC('HYB_GGA_XC_PBEH')
elif name == 'B3LYP':
assert hybrid is None and xc is None
hybrid = 0.2
xc = XC('HYB_GGA_XC_B3LYP')
if isinstance(xc, str):
xc = XC(xc)
self.hybrid = hybrid
self.xc = xc
self.type = xc.type
self.alpha = alpha
self.exx = 0.0
XCFunctional.__init__(self, name)
def get_setup_name(self):
return 'PBE'
def calculate_radial(self, rgd, n_sLg, Y_L, v_sg,
dndr_sLg=None, rnablaY_Lv=None,
tau_sg=None, dedtau_sg=None):
return self.xc.calculate_radial(rgd, n_sLg, Y_L, v_sg,
dndr_sLg, rnablaY_Lv)
def initialize(self, density, hamiltonian, wfs, occupations):
self.xc.initialize(density, hamiltonian, wfs, occupations)
self.nspins = wfs.nspins
self.setups = wfs.setups
self.density = density
self.kpt_u = wfs.kpt_u
self.gd = density.gd
self.kd = wfs.kd
self.bd = wfs.bd
N_c = self.gd.N_c
N = self.gd.N_c.prod()
vol = self.gd.dv * N
if self.alpha is None:
self.alpha = 6 * vol**(2 / 3.0) / pi**2
self.gamma = (vol / (2 * pi)**2 * sqrt(pi / self.alpha) *
self.kd.nbzkpts)
ecut = 0.5 * pi**2 / (self.gd.h_cv**2).sum(1).max()
if self.kd.N_c is None:
self.bzk_kc = np.zeros((1, 3))
dfghdfgh
else:
n = self.kd.N_c * 2 - 1
bzk_kc = np.indices(n).transpose((1, 2, 3, 0))
bzk_kc.shape = (-1, 3)
bzk_kc -= self.kd.N_c - 1
self.bzk_kc = bzk_kc.astype(float) / self.kd.N_c
self.pwd = PWDescriptor(ecut, self.gd, self.bzk_kc)
n = 0
for k_c, Gpk2_G in zip(self.bzk_kc[:], self.pwd.G2_qG):
if (k_c > -0.5).all() and (k_c <= 0.5).all(): #XXX???
if k_c.any():
self.gamma -= np.dot(np.exp(-self.alpha * Gpk2_G),
Gpk2_G**-1)
else:
self.gamma -= np.dot(np.exp(-self.alpha * Gpk2_G[1:]),
Gpk2_G[1:]**-1)
n += 1
assert n == self.kd.N_c.prod()
self.ghat = LFC(self.gd,
[setup.ghat_l for setup in density.setups],
dtype=complex
)
self.ghat.set_k_points(self.bzk_kc)
self.fullkd = KPointDescriptor(self.kd.bzk_kc, nspins=1)
class S:
id_a = []
def set_symmetry(self, s): pass
self.fullkd.set_symmetry(Atoms(pbc=True), S(), False)
self.fullkd.set_communicator(world)
self.pt = LFC(self.gd, [setup.pt_j for setup in density.setups],
dtype=complex)
self.pt.set_k_points(self.fullkd.ibzk_kc)
self.interpolator = density.interpolator
def set_positions(self, spos_ac):
self.ghat.set_positions(spos_ac)
self.pt.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)
# Add EXX contribution:
return exc + self.exx
def calculate_exx(self):
"""Non-selfconsistent calculation."""
kd = self.kd
K = self.fullkd.nibzkpts
assert self.nspins == 1
Q = K // world.size
assert Q * world.size == K
parallel = (world.size > self.nspins)
self.exx = 0.0
self.exx_skn = np.zeros((self.nspins, K, self.bd.nbands))
kpt_u = []
for k in range(world.rank * Q, (world.rank + 1) * Q):
k_c = self.fullkd.ibzk_kc[k]
for k1, k1_c in enumerate(kd.bzk_kc):
if abs(k1_c - k_c).max() < 1e-10:
break
# Index of symmetry related point in the irreducible BZ
ik = kd.kibz_k[k1]
kpt = self.kpt_u[ik]
# KPoint from ground-state calculation
phase_cd = np.exp(2j * pi * self.gd.sdisp_cd * k_c[:, np.newaxis])
kpt2 = KPoint0(kpt.weight, kpt.s, k, None, phase_cd)
kpt2.psit_nG = np.empty_like(kpt.psit_nG)
kpt2.f_n = kpt.f_n / kpt.weight / K * 2
for n, psit_G in enumerate(kpt2.psit_nG):
psit_G[:] = kd.transform_wave_function(kpt.psit_nG[n], k1)
kpt2.P_ani = self.pt.dict(len(kpt.psit_nG))
self.pt.integrate(kpt2.psit_nG, kpt2.P_ani, k)
kpt_u.append(kpt2)
for s in range(self.nspins):
kpt1_q = [KPoint(self.fullkd, kpt) for kpt in kpt_u if kpt.s == s]
kpt2_q = kpt1_q[:]
if len(kpt1_q) == 0:
# No s-spins on this CPU:
continue
# Send rank:
srank = self.fullkd.get_rank_and_index(s, (kpt1_q[0].k - 1) % K)[0]
# Receive rank:
rrank = self.fullkd.get_rank_and_index(s, (kpt1_q[-1].k + 1) % K)[0]
# Shift k-points K // 2 times:
for i in range(K // 2 + 1):
if i < K // 2:
if parallel:
kpt = kpt2_q[-1].next()
kpt.start_receiving(rrank)
kpt2_q[0].start_sending(srank)
else:
kpt = kpt2_q[0]
for kpt1, kpt2 in zip(kpt1_q, kpt2_q):
if 2 * i == K:
self.apply(kpt1, kpt2, invert=(kpt1.k > kpt2.k))
else:
self.apply(kpt1, kpt2)
self.apply(kpt1, kpt2, invert=True)
if i < K // 2:
if parallel:
kpt.wait()
kpt2_q[0].wait()
kpt2_q.pop(0)
kpt2_q.append(kpt)
self.exx = world.sum(self.exx)
world.sum(self.exx_skn)
self.exx += self.calculate_paw_correction()
def apply(self, kpt1, kpt2, invert=False):
#print world.rank,kpt1.k,kpt2.k,invert
k1_c = self.fullkd.ibzk_kc[kpt1.k]
k2_c = self.fullkd.ibzk_kc[kpt2.k]
if invert:
k2_c = -k2_c
k12_c = k1_c - k2_c
N_c = self.gd.N_c
eikr_R = np.exp(2j * pi * np.dot(np.indices(N_c).T, k12_c / N_c).T)
for q, k_c in enumerate(self.bzk_kc):
if abs(k_c + k12_c).max() < 1e-9:
q0 = q
break
for q, k_c in enumerate(self.bzk_kc):
if abs(k_c - k12_c).max() < 1e-9:
q00 = q
break
Gpk2_G = self.pwd.G2_qG[q0]
if Gpk2_G[0] == 0:
Gpk2_G = Gpk2_G.copy()
Gpk2_G[0] = 1.0 / self.gamma
N = N_c.prod()
vol = self.gd.dv * N
nspins = self.nspins
same = (kpt1.k == kpt2.k)
for n1, psit1_R in enumerate(kpt1.psit_nG):
f1 = kpt1.f_n[n1]
for n2, psit2_R in enumerate(kpt2.psit_nG):
if same and n2 > n1:
continue
f2 = kpt2.f_n[n2]
nt_R = self.calculate_pair_density(n1, n2, kpt1, kpt2, q0,
invert)
nt_G = self.pwd.fft(nt_R * eikr_R) / N
vt_G = nt_G.copy()
vt_G *= -pi * vol / Gpk2_G
e = np.vdot(nt_G, vt_G).real * nspins * self.hybrid
if same and n1 == n2:
e /= 2
self.exx += e * f1 * f2
self.ekin -= 2 * e * f1 * f2
self.exx_skn[kpt1.s, kpt1.k, n1] += f2 * e
self.exx_skn[kpt2.s, kpt2.k, n2] += f1 * e
calculate_potential = not True
if calculate_potential:
vt_R = self.pwd.ifft(vt_G).conj() * eikr_R * N / vol
if kpt1 is kpt2 and not invert and n1 == n2:
kpt1.vt_nG[n1] = 0.5 * f1 * vt_R
if invert:
kpt1.Htpsit_nG[n1] += \
f2 * nspins * psit2_R.conj() * vt_R
else:
kpt1.Htpsit_nG[n1] += f2 * nspins * psit2_R * vt_R
if kpt1 is not kpt2:
if invert:
kpt2.Htpsit_nG[n2] += (f1 * nspins *
psit1_R.conj() * vt_R)
else:
kpt2.Htpsit_nG[n2] += (f1 * nspins *
psit1_R * vt_R.conj())
def calculate_paw_correction(self):
exx = 0
deg = 2 // self.nspins # spin degeneracy
for a, D_sp in self.density.D_asp.items():
setup = self.setups[a]
for D_p in D_sp:
D_ii = unpack2(D_p)
ni = len(D_ii)
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 += setup.M_pp[p13, p24] * D_ii[i3, i4]
p12 = packed_index(i1, i2, ni)
exx -= self.hybrid / deg * D_ii[i1, i2] * A
if setup.X_p is not None:
exx -= self.hybrid * np.dot(D_p, setup.X_p)
exx += self.hybrid * setup.ExxC
return exx
def calculate_pair_density(self, n1, n2, kpt1, kpt2, q, invert):
if invert:
nt_G = kpt1.psit_nG[n1].conj() * kpt2.psit_nG[n2].conj()
else:
nt_G = kpt1.psit_nG[n1].conj() * kpt2.psit_nG[n2]
Q_aL = {}
for a, P1_ni in kpt1.P_ani.items():
P1_i = P1_ni[n1]
P2_i = kpt2.P_ani[a][n2]
if invert:
D_ii = np.outer(P1_i.conj(), P2_i.conj())
else:
D_ii = np.outer(P1_i.conj(), P2_i)
D_p = pack(D_ii)
Q_aL[a] = np.dot(D_p, self.setups[a].Delta_pL)
self.ghat.add(nt_G, Q_aL, q)
return nt_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)
class SIC(XCFunctional):
orbital_dependent = True
unitary_invariant = False
def __init__(self, xc='LDA', finegrid=False, **parameters):
"""Self-Interaction Corrected Functionals (PZ-SIC).
finegrid: boolean
Use fine grid for energy functional evaluations?
"""
if isinstance(xc, str):
xc = XC(xc)
self.xc = xc
self.type = xc.type
XCFunctional.__init__(self, xc.name + '-PZ-SIC')
self.finegrid = finegrid
self.parameters = parameters
def initialize(self, density, hamiltonian, wfs, occ=None):
assert wfs.gamma
assert not wfs.gd.pbc_c.any()
self.wfs = wfs
self.dtype = float
self.xc.initialize(density, hamiltonian, wfs, occ)
self.kpt_comm = wfs.kpt_comm
self.nspins = wfs.nspins
self.nbands = wfs.bd.nbands
if self.finegrid:
self.finegd = density.finegd
self.ghat = density.ghat
else:
self.finegd = density.gd
self.ghat = LFC(self.finegd,
[setup.ghat_l for setup in density.setups],
integral=sqrt(4 * pi), forces=True)
poissonsolver = PoissonSolver(eps=1e-14)
poissonsolver.set_grid_descriptor(self.finegd)
poissonsolver.initialize()
self.spin_s = {}
for kpt in wfs.kpt_u:
self.spin_s[kpt.s] = SICSpin(kpt, self.xc,
density, hamiltonian, wfs,
poissonsolver, self.ghat,
self.finegd, **self.parameters)
def get_setup_name(self):
return self.xc.get_setup_name()
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 set_positions(self, spos_ac):
if not self.finegrid:
self.ghat.set_positions(spos_ac)
def calculate(self, gd, n_sg, v_sg=None, e_g=None):
self.gd = gd
# Normal XC contribution:
exc = self.xc.calculate(gd, n_sg, v_sg, e_g)
# SIC:
self.esic = 0.0
self.ekin = 0.0
for spin in self.spin_s.values():
if spin.kpt.psit_nG is not None:
desic, dekin = spin.calculate()
self.esic += desic
self.ekin += dekin
self.esic = self.kpt_comm.sum(self.esic)
self.ekin = self.kpt_comm.sum(self.ekin)
return exc + self.esic
def apply_orbital_dependent_hamiltonian(self, kpt, psit_nG,
Htpsit_nG=None, dH_asp=None):
spin = self.spin_s[kpt.s]
if spin.W_mn is None:
return
spin.apply_orbital_dependent_hamiltonian(psit_nG)
def correct_hamiltonian_matrix(self, kpt, H_nn):
spin = self.spin_s[kpt.s]
if spin.W_mn is None:
return
spin.correct_hamiltonian_matrix(H_nn)
def add_correction(self, kpt, psit_xG, Htpsit_xG, P_axi, c_axi, n_x,
calculate_change=False):
spin = self.spin_s[kpt.s]
if spin.W_mn is None:
return
if calculate_change:
spin.calculate_residual_change(psit_xG, Htpsit_xG, P_axi,
c_axi, n_x)
else:
spin.calculate_residual(psit_xG, Htpsit_xG, P_axi, c_axi)
def rotate(self, kpt, U_nn):
self.spin_s[kpt.s].rotate(U_nn)
def setup_force_corrections(self, F_av):
self.dF_av = np.zeros_like(F_av)
for spin in self.spin_s.values():
spin.add_forces(self.dF_av)
self.wfs.kpt_comm.sum(self.dF_av)
def add_forces(self, F_av):
F_av += self.dF_av
def summary(self, out=sys.stdout):
for s in range(self.nspins):
if s in self.spin_s:
stabpot = self.spin_s[s].stabpot
spin = self.spin_s[s]
pos_mv = spin.get_centers()
exc_m = spin.exc_m
ecoulomb_m = spin.ecoulomb_m
if self.kpt_comm.rank == 1 and self.gd.comm.rank == 0:
nocc = self.kpt_comm.sum(spin.nocc)
self.kpt_comm.send(pos_mv, 0)
self.kpt_comm.send(exc_m, 0)
self.kpt_comm.send(ecoulomb_m, 0)
else:
if self.kpt_comm.rank == 0 and self.gd.comm.rank == 0:
nocc = self.kpt_comm.sum(0)
pos_mv = np.zeros((nocc, 3))
exc_m = np.zeros(nocc)
ecoulomb_m = np.zeros(nocc)
self.kpt_comm.receive(pos_mv, 1)
self.kpt_comm.receive(exc_m, 1)
self.kpt_comm.receive(ecoulomb_m, 1)
if self.kpt_comm.rank == 0 and self.gd.comm.rank == 0:
out.write('\nSIC orbital centers and energies:\n')
out.write(' %5.2fx %5.2fx\n' %
(self.spin_s[0].xc_factor,
self.spin_s[0].coulomb_factor))
out.write(' x y z XC Coulomb\n')
out.write('--------------------------------------------------\n')
m = 0
for pos_v, exc, ecoulomb in zip(pos_mv, exc_m, ecoulomb_m):
out.write('%3d (%7.3f,%7.3f,%7.3f): %8.3f %8.3f\n' %
((m,) + tuple(pos_v) +
(exc * Hartree, ecoulomb * Hartree)))
m += 1
out.write('--------------------------------------------------\n')
out.write('\nTotal SIC energy : %12.5f\n' % (self.esic * Hartree))
out.write('Stabilizing potential: %12.5f\n' % (stabpot * Hartree))
def read(self, reader):
xc_factor = reader['SIC_xc_factor']
coulomb_factor = reader['SIC_coulomb_factor']
#
for s in range(self.nspins):
#
try:
npart = reader.dimension('npart'+str(s))
except KeyError:
npart = 0
#
if npart>0:
W_mn = reader.get('UnitaryTransformation'+str(s))
else:
W_mn = None
#
if s in self.spin_s.keys():
self.spin_s[s].initial_W_mn = W_mn
self.spin_s[s].xc_factor = xc_factor
self.spin_s[s].coulomb_factor = coulomb_factor
def write(self, writer, natoms=None):
#
for s in self.spin_s.keys():
spin = self.spin_s[s]
if self.wfs.world.rank==0:
writer['SIC_xc_factor'] = spin.xc_factor
writer['SIC_coulomb_factor'] = spin.coulomb_factor
break
#
for s in range(self.nspins):
#
W_mn = self.get_unitary_transformation(s)
#
if self.wfs.world.rank == 0:
if W_mn!=None:
writer.dimension('npart'+str(s), W_mn.shape[0])
writer.add('UnitaryTransformation'+str(s),
('npart'+str(s),'npart'+str(s)),
dtype=self.dtype)
writer.fill(W_mn)
def get_unitary_transformation(self, s):
#
if s in self.spin_s.keys():
spin = self.spin_s[s]
#
if spin.W_mn==None or spin.finegd.rank!=0:
n = 0
else:
n = spin.W_mn.shape[0]
#
else:
n=0
#
n = self.wfs.world.sum(n)
#
if n>0:
W_mn = np.zeros((n,n), dtype=self.dtype)
else:
W_mn = None
return W_mn
#
if s in self.spin_s.keys():
spin = self.spin_s[s]
#
if spin.W_mn==None or spin.finegd.rank!=0:
W_mn[:] = 0.0
else:
W_mn[:] = spin.W_mn[:]
#
else:
W_mn[:] = 0.0
#
self.wfs.world.sum(W_mn)
return W_mn
def initialize(self, density, hamiltonian, wfs, occupations):
self.xc.initialize(density, hamiltonian, wfs, occupations)
self.nspins = wfs.nspins
self.setups = wfs.setups
self.density = density
self.kpt_u = wfs.kpt_u
self.wfs = wfs
self.gd = density.gd
self.kd = wfs.kd
self.bd = wfs.bd
N_c = self.gd.N_c
N = self.gd.N_c.prod()
vol = self.gd.dv * N
if self.alpha is None:
# XXX ?
self.alpha = 6 * vol ** (2 / 3.0) / pi ** 2
self.gamma = vol / (2 * pi) ** 2 * sqrt(pi / self.alpha) * self.kd.nbzkpts
if self.ecut is None:
self.ecut = 0.5 * pi ** 2 / (self.gd.h_cv ** 2).sum(1).max() * 0.9999
assert self.kd.N_c is not None
n = self.kd.N_c * 2 - 1
bzk_kc = np.indices(n).transpose((1, 2, 3, 0))
bzk_kc.shape = (-1, 3)
bzk_kc -= self.kd.N_c - 1
self.bzk_kc = bzk_kc.astype(float) / self.kd.N_c
self.bzq_qc = self.kd.get_bz_q_points()
if self.qsym:
op_scc = self.kd.symmetry.op_scc
self.ibzq_qc = self.kd.get_ibz_q_points(self.bzq_qc, op_scc)[0]
self.q_weights = self.kd.q_weights * len(self.bzq_qc)
else:
self.ibzq_qc = self.bzq_qc
self.q_weights = np.ones(len(self.bzq_qc))
self.pwd = PWDescriptor(self.ecut, self.gd, complex)
self.G2_qG = self.pwd.g2(self.bzk_kc)
n = 0
for k_c, Gpk2_G in zip(self.bzk_kc[:], self.G2_qG):
if (k_c > -0.5).all() and (k_c <= 0.5).all(): # XXX???
if k_c.any():
self.gamma -= np.dot(np.exp(-self.alpha * Gpk2_G), Gpk2_G ** -1)
else:
self.gamma -= np.dot(np.exp(-self.alpha * Gpk2_G[1:]), Gpk2_G[1:] ** -1)
n += 1
assert n == self.kd.N_c.prod()
self.pwd = PWDescriptor(self.ecut, self.gd, complex)
self.G2_qG = self.pwd.g2(self.ibzq_qc)
self.ghat = LFC(
self.gd, [setup.ghat_l for setup in density.setups], KPointDescriptor(self.bzq_qc), dtype=complex
)
# self.interpolator = density.interpolator
self.print_initialization(hamiltonian.xc.name)
class RealSpaceHamiltonian(Hamiltonian):
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 summary(self, fd):
Hamiltonian.summary(self, fd)
degree = self.restrictor.nn * 2 - 1
name = ["linear", "cubic", "quintic", "heptic"][degree // 2]
fd.write("Interpolation: tri-%s " % name + "(%d. degree polynomial)\n" % degree)
fd.write("Poisson solver: %s\n" % self.poisson.get_description())
def set_positions(self, spos_ac, rank_a):
Hamiltonian.set_positions(self, spos_ac, rank_a)
if self.vbar_g is None:
self.vbar_g = self.finegd.empty()
self.vbar_g[:] = 0.0
self.vbar.add(self.vbar_g)
def update_pseudo_potential(self, density):
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 is not None:
assert self.collinear
vt_g += self.vext.get_potential(self.finegd)
Eext = self.finegd.integrate(vt_g, density.nt_g, global_integral=False) - Ebar
self.vt_sg[1 : self.nspins] = vt_g
self.vt_sg[self.nspins :] = 0.0
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
s = 0
for s, (vt_g, vt_G, nt_G) in enumerate(zip(self.vt_sg, self.vt_sG, density.nt_sG)):
if s < self.nspins:
vt_g += self.vHt_g
self.restrict(vt_g, vt_G)
if self.ref_vt_sG is not None:
vt_G += self.ref_vt_sG[s]
if s < self.nspins:
Ekin -= self.gd.integrate(vt_G, nt_G - density.nct_G, global_integral=False)
else:
Ekin -= self.gd.integrate(vt_G, nt_G, global_integral=False)
s += 1
self.timer.stop("Hartree integrate/restrict")
# Calculate atomic hamiltonians:
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)
return Ekin, Epot, Ebar, Eext, Exc, W_aL
def calculate_forces2(self, dens, ghat_aLv, nct_av, vbar_av):
if self.nspins == 2:
vt_G = self.vt_sG.mean(0)
else:
vt_G = self.vt_sG[0]
dens.ghat.derivative(self.vHt_g, ghat_aLv)
dens.nct.derivative(vt_G, nct_av)
self.vbar.derivative(dens.nt_g, vbar_av)
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)
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 update(self):
if self.ranges is None: # First time
self.ranges = []
self.nbands = self.lcao.wfs.bd.nbands
start = 0
if self.ranges_str != "full":
for rng in self.ranges_str.split(","):
print("rng", rng)
rng = eval(rng)
self.ranges.append(range(start, rng))
start = rng
self.ranges.append(range(start, self.nbands))
print(self.ranges)
self.ghat = LFC(
self.lcao.wfs.gd,
[setup.ghat_l for setup in self.lcao.density.setups],
integral=sqrt(4 * pi),
forces=False,
)
spos_ac = self.lcao.atoms.get_scaled_positions() % 1.0
self.ghat.set_positions(spos_ac)
# Clear files
for rid, rng in enumerate(self.ranges):
f = open(self.filename + "." + str(rid) + ".density", "w")
print("# Density file", file=f)
N_c = self.lcao.wfs.gd.N_c
print(N_c[0], N_c[1], N_c[2], file=f)
print("# This header is 10 lines long, then double precision binary data starts.", file=f)
for i in range(7):
print("#", file=f)
f.close()
# self.lcao.timer.start('Dump density')
for rid, rng in enumerate(self.ranges):
assert len(self.lcao.wfs.kpt_u) == 1
f_un = [self.lcao.wfs.kpt_u[0].f_n.copy()]
for n in range(self.lcao.wfs.bd.nbands):
band_rank, myn = self.lcao.wfs.bd.who_has(n)
if self.lcao.wfs.bd.rank == band_rank:
if not n in rng:
f_un[0][myn] = 0.0
n_sG = self.lcao.wfs.gd.zeros(1)
self.lcao.wfs.add_to_density_from_k_point_with_occupation(n_sG, self.lcao.wfs.kpt_u[0], f_un[0])
self.lcao.wfs.kptband_comm.sum(n_sG)
D_asp = {}
for a in self.lcao.density.D_asp:
ni = self.lcao.density.setups[a].ni
D_asp[a] = np.zeros((1, ni * (ni + 1) // 2))
self.lcao.wfs.calculate_atomic_density_matrices_with_occupation(D_asp, f_un)
Q_aL = {}
for a, D_sp in D_asp.items():
Q_aL[a] = np.dot(D_sp.sum(0), self.lcao.density.setups[a].Delta_pL)
self.ghat.add(n_sG, Q_aL)
n_sg = self.lcao.wfs.gd.collect(n_sG, broadcast=False)
if world.rank == 0:
f = open(self.filename + "." + str(rid) + ".density", "a+")
# n_sg.astype(np.float32).tofile(f)
# print "max", np.max(n_sg), np.min(n_sg)
n_sg.tofile(f)
f.close()
s = n_sg.shape
f = open(self.filename + ".info", "w")
print(s[0], s[1], s[2], file=f)
f.close()
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):
"""Mix standard functionals with exact exchange.
finegrid: boolean
Use fine grid for energy functional evaluations ?
unocc: boolean
Apply vxx also to unoccupied states ?
"""
self.finegrid = finegrid
self.unocc = unocc
HybridXCBase.__init__(self, name, hybrid, xc)
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.gamma
self.xc.initialize(density, hamiltonian, wfs, occupations)
self.kpt_comm = wfs.kpt_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)
if self.finegrid:
self.poissonsolver = hamiltonian.poisson
self.ghat = density.ghat
self.interpolator = density.interpolator
self.restrictor = hamiltonian.restrictor
else:
self.poissonsolver = PoissonSolver(eps=1e-11)
self.poissonsolver.set_grid_descriptor(density.gd)
self.poissonsolver.initialize()
self.ghat = LFC(density.gd,
[setup.ghat_l for setup in density.setups],
integral=np.sqrt(4 * np.pi), forces=True)
self.gd = density.gd
self.finegd = self.ghat.gd
def set_positions(self, spos_ac):
if not self.finegrid:
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)
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
vt_g = self.finegd.empty()
if self.gd is not self.finegd:
vt_G = self.gd.empty()
nocc = int(kpt.f_n.sum()) // (3 - self.nspins)
if self.unocc:
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
# 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
# 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
iter = self.poissonsolver.solve(vt_g, -rhot_g,
charge=-float(n1 == n2),
eps=1e-12,
zero_initial_phi=True)
vt_g *= hybrid
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
else:
Htpsit_nG[n2] += f1 * 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:
v_ni[n2] += f1 * np.dot(v_ii, P_ni[n1])
else:
# XXX Check this:
v_nii[n1] = f1 * v_ii
# 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
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 += setup.M_pp[p13, p24] * D_ii[i3, i4]
p12 = packed_index(i1, i2, ni)
if Htpsit_nG is not None:
dH_p[p12] -= 2 * hybrid / deg * A / ((i1 != i2) + 1)
ekin += 2 * hybrid / deg * D_ii[i1, i2] * A
exx -= hybrid / deg * D_ii[i1, i2] * A
# 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)
# Add core-core exchange energy
if kpt.s == 0:
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)
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
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
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)
class MGGA(GGA):
orbital_dependent = True
def __init__(self, kernel, nn=1):
"""Meta GGA functional.
nn: int
Number of neighbor grid points to use for FD stencil for
wave function gradient.
"""
self.nn = nn
GGA.__init__(self, kernel)
def set_grid_descriptor(self, gd):
GGA.set_grid_descriptor(self, gd)
def get_setup_name(self):
return "PBE"
def initialize(self, density, hamiltonian, wfs, occupations):
self.wfs = wfs
self.tauct = LFC(wfs.gd, [[setup.tauct] for setup in wfs.setups], forces=True, cut=True)
self.tauct_G = None
self.dedtaut_sG = None
self.restrict = hamiltonian.restrictor.apply
self.interpolate = density.interpolator.apply
self.taugrad_v = [Gradient(wfs.gd, v, n=self.nn, dtype=wfs.dtype, allocate=True).apply for v in range(3)]
def set_positions(self, spos_ac):
self.tauct.set_positions(spos_ac)
if self.tauct_G is None:
self.tauct_G = self.wfs.gd.empty()
self.tauct_G[:] = 0.0
self.tauct.add(self.tauct_G)
def calculate_gga(self, e_g, nt_sg, v_sg, sigma_xg, dedsigma_xg):
taut_sG = self.wfs.calculate_kinetic_energy_density(self.tauct, self.taugrad_v)
taut_sg = np.empty_like(nt_sg)
for taut_G, taut_g in zip(taut_sG, taut_sg):
taut_G += 1.0 / self.wfs.nspins * self.tauct_G
self.interpolate(taut_G, taut_g)
dedtaut_sg = np.empty_like(nt_sg)
self.kernel.calculate(e_g, nt_sg, v_sg, sigma_xg, dedsigma_xg, taut_sg, dedtaut_sg)
self.dedtaut_sG = self.wfs.gd.empty(self.wfs.nspins)
self.ekin = 0.0
for s in range(self.wfs.nspins):
self.restrict(dedtaut_sg[s], self.dedtaut_sG[s])
self.ekin -= self.wfs.gd.integrate(self.dedtaut_sG[s] * (taut_sG[s] - self.tauct_G / self.wfs.nspins))
def apply_orbital_dependent_hamiltonian(self, kpt, psit_xG, Htpsit_xG, dH_asp):
a_G = self.wfs.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](self.dedtaut_sG[kpt.s] * a_G, a_G, kpt.phase_cd)
axpy(-0.5, a_G, Htpsit_G)
def add_forces(self, F_av):
dF_av = self.tauct.dict(derivative=True)
self.tauct.derivative(self.dedtaut_sG.sum(0), dF_av)
for a, dF_v in dF_av.items():
F_av[a] += dF_v[0]
def estimate_memory(self, mem):
bytecount = self.wfs.gd.bytecount()
mem.subnode("MGGA arrays", (1 + self.wfs.nspins) * bytecount)
def initialize_kinetic(self, xccorr):
nii = xccorr.nii
nn = len(xccorr.rnablaY_nLv)
ng = len(xccorr.phi_jg[0])
tau_npg = np.zeros((nn, nii, ng))
taut_npg = np.zeros((nn, nii, ng))
self.create_kinetic(xccorr, nn, xccorr.phi_jg, tau_npg)
self.create_kinetic(xccorr, nn, xccorr.phit_jg, taut_npg)
return tau_npg, taut_npg
def create_kinetic(self, x, ny, phi_jg, tau_ypg):
"""Short title here.
kinetic expression is::
__ __
tau_s = 1/2 Sum_{i1,i2} D(s,i1,i2) \/phi_i1 . \/phi_i2 +tauc_s
here the orbital dependent part is calculated::
__ __
\/phi_i1 . \/phi_i2 =
__ __
\/YL1.\/YL2 phi_j1 phi_j2 +YL1 YL2 dphi_j1 dphi_j2
------ ------
dr dr
__ __
\/YL1.\/YL2 [y] = Sum_c A[L1,c,y] A[L2,c,y] / r**2
"""
nj = len(phi_jg)
ni = len(x.jlL)
nii = ni * (ni + 1) // 2
dphidr_jg = np.zeros(np.shape(phi_jg))
for j in range(nj):
phi_g = phi_jg[j]
x.rgd.derivative(phi_g, dphidr_jg[j])
# Second term:
for y in range(ny):
i1 = 0
p = 0
Y_L = x.Y_nL[y]
for j1, l1, L1 in x.jlL:
for j2, l2, L2 in x.jlL[i1:]:
c = Y_L[L1] * Y_L[L2]
temp = c * dphidr_jg[j1] * dphidr_jg[j2]
tau_ypg[y, p, :] += temp
p += 1
i1 += 1
##first term
for y in range(ny):
i1 = 0
p = 0
rnablaY_Lv = x.rnablaY_nLv[y, : x.Lmax]
Ax_L = rnablaY_Lv[:, 0]
Ay_L = rnablaY_Lv[:, 1]
Az_L = rnablaY_Lv[:, 2]
for j1, l1, L1 in x.jlL:
for j2, l2, L2 in x.jlL[i1:]:
temp = Ax_L[L1] * Ax_L[L2] + Ay_L[L1] * Ay_L[L2] + Az_L[L1] * Az_L[L2]
temp *= phi_jg[j1] * phi_jg[j2]
temp[1:] /= x.rgd.r_g[1:] ** 2
temp[0] = temp[1]
tau_ypg[y, p, :] += temp
p += 1
i1 += 1
tau_ypg *= 0.5
return
class UTConstantWavefunctionSetup(UTBandParallelSetup):
__doc__ = UTBandParallelSetup.__doc__ + """
The pseudo wavefunctions are constants normalized to their band index."""
allocated = False
blocking = None
async = None
def setUp(self):
UTBandParallelSetup.setUp(self)
for virtvar in ['dtype','blocking','async']:
assert getattr(self,virtvar) is not None, 'Virtual "%s"!' % virtvar
# Create randomized atoms
self.atoms = create_random_atoms(self.gd)
# Do we agree on the atomic positions?
pos_ac = self.atoms.get_positions()
pos_rac = np.empty((world.size,)+pos_ac.shape, pos_ac.dtype)
world.all_gather(pos_ac, pos_rac)
if (pos_rac-pos_rac[world.rank,...][np.newaxis,...]).any():
raise RuntimeError('Discrepancy in atomic positions detected.')
# Create setups for atoms
self.Z_a = self.atoms.get_atomic_numbers()
self.setups = Setups(self.Z_a, p.setups, p.basis,
p.lmax, xc)
# Create atomic projector overlaps
spos_ac = self.atoms.get_scaled_positions() % 1.0
self.rank_a = self.gd.get_ranks_from_positions(spos_ac)
self.pt = LFC(self.gd, [setup.pt_j for setup in self.setups],
dtype=self.dtype)
self.pt.set_positions(spos_ac)
if memstats:
# Hack to scramble heap usage into steady-state level
HEAPSIZE = 25 * 1024**2
for i in range(100):
data = np.empty(np.random.uniform(0, HEAPSIZE // 8), float)
del data
self.mem_pre = record_memory()
self.mem_alloc = None
self.mem_test = None
# Stuff for pseudo wave functions and projections
if self.dtype == complex:
self.gamma = 1j**(1.0/self.nbands)
else:
self.gamma = 1.0
self.psit_nG = None
self.P_ani = None
self.Qeff_a = None
self.Qtotal = None
self.allocate()
def tearDown(self):
UTBandParallelSetup.tearDown(self)
del self.P_ani, self.psit_nG
del self.pt, self.setups, self.atoms
if memstats:
self.print_memory_summary()
del self.mem_pre, self.mem_alloc, self.mem_test
self.allocated = False
def print_memory_summary(self):
if not memstats:
raise RuntimeError('No memory statistics were recorded!')
if world.rank == 0:
sys.stdout.write('\n')
sys.stdout.flush()
dm_r, dminfo = create_memory_info(MemorySingleton(), self.mem_pre)
if world.rank == 0:
print('overhead: %s -> %8.4f MB' % (dminfo, dm_r.sum()/1024**2.))
dm_r, dminfo = create_memory_info(self.mem_pre, self.mem_alloc)
if world.rank == 0:
print('allocate: %s -> %8.4f MB' % (dminfo, dm_r.sum()/1024**2.))
dm_r, dminfo = create_memory_info(self.mem_alloc, self.mem_test)
if world.rank == 0:
print('test-use: %s -> %8.4f MB' % (dminfo, dm_r.sum()/1024**2.))
def allocate(self):
"""
Allocate constant wavefunctions and their projections according to::
/ \ _____ i*phase*(n-m)
<psi |psi > = ( 1 + Q ) * V m*n * e
n n' \ total/
"""
if self.allocated:
raise RuntimeError('Already allocated!')
self.allocate_wavefunctions()
self.allocate_projections()
# XXX DEBUG disables projection contributions
if False:
for a,P_ni in self.P_ani.items():
P_ni[:] = 0.
self.Qeff_a[a] = 0.
self.Qtotal = 0.
self.Z_a[:] = 2**63-1
# XXX DEBUG
self.Qtotal = np.empty(1, dtype=float)
self.Qtotal[:] = np.sum([Qeff for Qeff in self.Qeff_a.values()])
self.gd.comm.sum(self.Qtotal)
band_indices = np.arange(self.nbands).astype(self.dtype)
z = self.gamma**band_indices * band_indices**0.5
self.S0_nn = (1. + self.Qtotal) * np.outer(z.conj(), z)
self.allocated = True
if memstats:
self.mem_alloc = record_memory()
def allocate_wavefunctions(self):
"""
Allocate constant pseudo wavefunctions according to::
~ ~ _____ i*phase*(n-m)
<psi |psi > = V m*n * e
n n'
"""
if self.allocated:
raise RuntimeError('Already allocated!')
# Fill in wave functions
gpts_c = self.gd.get_size_of_global_array()
self.psit_nG = self.gd.empty(self.bd.mynbands, self.dtype)
for myn, psit_G in enumerate(self.psit_nG):
n = self.bd.global_index(myn)
# Fill psit_nG: | psit_n > = exp(i*phase*n) * sqrt(n) / sqrt(V)
psit_G[:] = self.gamma**n * n**0.5 / (self.gd.dv * gpts_c.prod())**0.5
def allocate_projections(self):
"""
Construct dummy projection of pseudo wavefunction according to::
___
\ ~ ~a a ~a ~ 1 _____ i*phase*(n-m)
) <psi |p > dO <p |psi > = +/- --- * V m*n * e
/___ n i ii' i' n' Z
ii' a
"""
if self.allocated:
raise RuntimeError('Already allocated!')
# Fill in projector overlaps
my_band_indices = self.bd.get_band_indices()
my_atom_indices = np.argwhere(self.gd.comm.rank == self.rank_a).ravel()
# Holm-Nielsen check:
natoms = len(self.atoms)
assert (self.gd.comm.sum(float(sum(my_atom_indices))) ==
natoms * (natoms - 1) // 2)
# Check that LFC agrees with us:
self.assertEqual(len(my_atom_indices), len(self.pt.my_atom_indices))
for a1, a2 in zip(my_atom_indices, self.pt.my_atom_indices):
self.assertEqual(a1, a2)
self.Qeff_a = {}
self.P_ani = self.pt.dict(self.bd.mynbands)
for a in my_atom_indices:
ni = self.setups[a].ni
# Fill P_ni: <p_i | psit_n > = beta_i * exp(i*phase*n) * sqrt(n)
#
# | ____ |
# | \ * a | 1
# | ) beta dO beta | = ----
# | /___ i ij j | Z
# | ij | a
#
# Substitution by linear transformation: beta_i -> dO_ij alpha_j,
# where we start out with some initial non-constant vector:
alpha_i = np.exp(-np.arange(ni).astype(self.dtype)/ni)
try:
# Try Cholesky decomposition dO_ii = L_ii * L_ii^dag
L_ii = np.linalg.cholesky(self.setups[a].dO_ii)
alpha_i /= np.vdot(alpha_i, alpha_i)**0.5
beta_i = np.linalg.solve(L_ii.T.conj(), alpha_i)
except np.linalg.LinAlgError:
# Eigenvector decomposition dO_ii = V_ii * W_ii * V_ii^dag
W_i, V_ii = np.linalg.eigh(self.setups[a].dO_ii)
alpha_i /= np.abs(np.vdot(alpha_i,
np.dot(np.diag(W_i), alpha_i)))**0.5
beta_i = np.linalg.solve(V_ii.T.conj(), alpha_i)
# Normalize according to plus/minus charge
beta_i /= self.Z_a[a]**0.5
self.Qeff_a[a] = np.vdot(beta_i, np.dot(self.setups[a].dO_ii, \
beta_i)).real
self.P_ani[a][:] = np.outer(self.gamma**my_band_indices \
* my_band_indices**0.5, beta_i)
def check_and_plot(self, A_nn, A0_nn, digits, keywords=''):
# Construct fingerprint of input matrices for comparison
fingerprint = np.array([md5_array(A_nn, numeric=True),
md5_array(A0_nn, numeric=True)])
# Compare fingerprints across all processors
fingerprints = np.empty((world.size, 2), np.int64)
world.all_gather(fingerprint, fingerprints)
if fingerprints.ptp(0).any():
raise RuntimeError('Distributed matrices are not identical!')
# If assertion fails, catch temporarily while plotting, then re-raise
try:
self.assertAlmostEqual(np.abs(A_nn-A0_nn).max(), 0, digits)
except AssertionError:
if world.rank == 0 and mpl is not None:
from matplotlib.figure import Figure
fig = Figure()
ax = fig.add_axes([0.0, 0.1, 1.0, 0.83])
ax.set_title(self.__class__.__name__)
im = ax.imshow(np.abs(A_nn-A0_nn), interpolation='nearest')
fig.colorbar(im)
fig.text(0.5, 0.05, 'Keywords: ' + keywords, \
horizontalalignment='center', verticalalignment='top')
from matplotlib.backends.backend_agg import FigureCanvasAgg
img = 'ut_hsops_%s_%s.png' % (self.__class__.__name__, \
'_'.join(keywords.split(',')))
FigureCanvasAgg(fig).print_figure(img.lower(), dpi=90)
raise
def get_optimal_number_of_blocks(self, blocking='fast'):
"""Estimate the optimal number of blocks for band parallelization.
The number of blocks determines how many parallel send/receive
operations are performed, as well as the added memory footprint
of the required send/receive buffers.
``blocking`` ``nblocks`` Description
============ ============= ========================================
'fast' ``1`` Heavy on memory, more accurate and fast.
'light' ``mynbands`` Light on memory, less accurate and slow.
'intdiv' ``...`` First integer divisible value
'nonintdiv' ``...`` Some non-integer divisible cases
"""
#if self.bd.comm.size == 1:
# return 1
if blocking == 'fast':
return 1
elif blocking == 'light':
return self.bd.mynbands
elif blocking == 'intdiv':
# Find first value of nblocks that leads to integer
# divisible mybands / nblock. This is very like to be
# 2 but coded here for the general case
nblocks = 2
while self.bd.mynbands % nblocks != 0:
nblocks +=1
return nblocks
elif blocking == 'nonintdiv1':
# Find first value of nblocks that leads to non-integer
# divisible mynbands / nblock that is less than M
nblocks = 2
M = self.bd.mynbands // nblocks
while self.bd.mynbands % nblocks < M:
nblocks += 1
M = self.bd.mynbands // nblocks
return nblocks
elif blocking == 'nonintdiv2':
# Find first value of nblocks that leads to non-integer
# divisible mynbands / nblock that is less than M
nblocks = 2
M = self.bd.mynbands // nblocks
while self.bd.mynbands % nblocks > M:
nblocks += 1
M = self.mynbands // nblocks
return nblocks
else:
nblocks = blocking
assert self.bd.mynbands // nblocks > 0
return nblocks
# =================================
def test_contents_wavefunction(self):
# Integrate diagonal brakets of pseudo wavefunctions
gpts_c = self.gd.get_size_of_global_array()
intpsit_myn = self.bd.empty(dtype=self.dtype)
for myn, psit_G in enumerate(self.psit_nG):
n = self.bd.global_index(myn)
intpsit_myn[myn] = np.vdot(psit_G, psit_G) * self.gd.dv
self.gd.comm.sum(intpsit_myn)
if memstats:
self.mem_test = record_memory()
my_band_indices = self.bd.get_band_indices()
self.assertAlmostEqual(np.abs(intpsit_myn-my_band_indices).max(), 0, 9)
intpsit_n = self.bd.collect(intpsit_myn, broadcast=True)
self.assertAlmostEqual(np.abs(intpsit_n-np.arange(self.nbands)).max(), 0, 9)
def test_contents_projection(self):
# Distribute inverse effective charges to everybody in domain
all_Qeff_a = np.empty(len(self.atoms), dtype=float)
for a,rank in enumerate(self.rank_a):
if rank == self.gd.comm.rank:
Qeff = np.array([self.Qeff_a[a]])
else:
Qeff = np.empty(1, dtype=float)
self.gd.comm.broadcast(Qeff, rank)
all_Qeff_a[a] = Qeff
# Check absolute values consistency of inverse effective charges
self.assertAlmostEqual(np.abs(1./self.Z_a-np.abs(all_Qeff_a)).max(), 0, 9)
# Check sum of inverse effective charges against total
self.assertAlmostEqual(all_Qeff_a.sum(), self.Qtotal, 9)
# Make sure that we all agree on inverse effective charges
fingerprint = np.array([md5_array(all_Qeff_a, numeric=True)])
all_fingerprints = np.empty(world.size, fingerprint.dtype)
world.all_gather(fingerprint, all_fingerprints)
if all_fingerprints.ptp(0).any():
raise RuntimeError('Distributed eff. charges are not identical!')
def test_overlaps_hermitian(self):
# Set up Hermitian overlap operator:
S = lambda x: x
dS = lambda a, P_ni: np.dot(P_ni, self.setups[a].dO_ii)
nblocks = self.get_optimal_number_of_blocks(self.blocking)
overlap = MatrixOperator(self.ksl, nblocks, self.async, True)
S_nn = overlap.calculate_matrix_elements(self.psit_nG, \
self.P_ani, S, dS).T.copy() # transpose to get <psit_m|A|psit_n>
tri2full(S_nn, 'U') # upper to lower...
if self.bd.comm.rank == 0:
self.gd.comm.broadcast(S_nn, 0)
self.bd.comm.broadcast(S_nn, 0)
if memstats:
self.mem_test = record_memory()
self.check_and_plot(S_nn, self.S0_nn, 9, 'overlaps,hermitian')
def test_overlaps_nonhermitian(self):
alpha = np.random.normal(size=1).astype(self.dtype)
if self.dtype == complex:
alpha += 1j*np.random.normal(size=1)
world.broadcast(alpha, 0)
# Set up non-Hermitian overlap operator:
S = lambda x: alpha*x
dS = lambda a, P_ni: np.dot(alpha*P_ni, self.setups[a].dO_ii)
nblocks = self.get_optimal_number_of_blocks(self.blocking)
overlap = MatrixOperator(self.ksl, nblocks, self.async, False)
S_nn = overlap.calculate_matrix_elements(self.psit_nG, \
self.P_ani, S, dS).T.copy() # transpose to get <psit_m|A|psit_n>
if self.bd.comm.rank == 0:
self.gd.comm.broadcast(S_nn, 0)
self.bd.comm.broadcast(S_nn, 0)
if memstats:
self.mem_test = record_memory()
self.check_and_plot(S_nn, alpha*self.S0_nn, 9, 'overlaps,nonhermitian')
def test_trivial_cholesky(self):
# Known starting point of SI_nn = <psit_m|S+alpha*I|psit_n>
I_nn = np.eye(*self.S0_nn.shape)
alpha = 1e-3 # shift eigenvalues away from zero
SI_nn = self.S0_nn + alpha * I_nn
# Try Cholesky decomposition SI_nn = L_nn * L_nn^dag
L_nn = np.linalg.cholesky(SI_nn)
# |psit_n> -> C_nn |psit_n> , C_nn^(-1) = L_nn^dag
# <psit_m|SI|psit_n> -> <psit_m|C_nn^dag SI C_nn|psit_n> = diag(W_n)
C_nn = np.linalg.inv(L_nn.T.conj())
# Set up Hermitian overlap operator:
S = lambda x: x
dS = lambda a, P_ni: np.dot(P_ni, self.setups[a].dO_ii)
nblocks = self.get_optimal_number_of_blocks(self.blocking)
overlap = MatrixOperator(self.ksl, nblocks, self.async, True)
self.psit_nG = overlap.matrix_multiply(C_nn.T.copy(), self.psit_nG, self.P_ani)
D_nn = overlap.calculate_matrix_elements(self.psit_nG, \
self.P_ani, S, dS).T.copy() # transpose to get <psit_m|A|psit_n>
tri2full(D_nn, 'U') # upper to lower...
if self.bd.comm.rank == 0:
self.gd.comm.broadcast(D_nn, 0)
self.bd.comm.broadcast(D_nn, 0)
if memstats:
self.mem_test = record_memory()
# D_nn = C_nn^dag * S_nn * C_nn = I_nn - alpha * C_nn^dag * C_nn
D0_nn = I_nn - alpha * np.dot(C_nn.T.conj(), C_nn)
self.check_and_plot(D_nn, D0_nn, 6, 'trivial,cholesky') #XXX precision
def test_trivial_diagonalize(self):
# Known starting point of S_nn = <psit_m|S|psit_n>
S_nn = self.S0_nn
# Eigenvector decomposition S_nn = V_nn * W_nn * V_nn^dag
# Utilize the fact that they are analytically known (cf. Maple)
band_indices = np.arange(self.nbands)
V_nn = np.eye(self.nbands).astype(self.dtype)
if self.dtype == complex:
V_nn[1:,1] = np.conj(self.gamma)**band_indices[1:] * band_indices[1:]**0.5
V_nn[1,2:] = -self.gamma**band_indices[1:-1] * band_indices[2:]**0.5
else:
V_nn[2:,1] = band_indices[2:]**0.5
V_nn[1,2:] = -band_indices[2:]**0.5
W_n = np.zeros(self.nbands).astype(self.dtype)
W_n[1] = (1. + self.Qtotal) * self.nbands * (self.nbands - 1) / 2.
# Find the inverse basis
Vinv_nn = np.linalg.inv(V_nn)
# Test analytical eigenvectors for consistency against analytical S_nn
D_nn = np.dot(Vinv_nn, np.dot(S_nn, V_nn))
self.assertAlmostEqual(np.abs(D_nn.diagonal()-W_n).max(), 0, 8)
self.assertAlmostEqual(np.abs(np.tril(D_nn, -1)).max(), 0, 4)
self.assertAlmostEqual(np.abs(np.triu(D_nn, 1)).max(), 0, 4)
del Vinv_nn, D_nn
# Perform Gram Schmidt orthonormalization for diagonalization
# |psit_n> -> C_nn |psit_n>, using orthonormalized basis Q_nn
# <psit_m|S|psit_n> -> <psit_m|C_nn^dag S C_nn|psit_n> = diag(W_n)
# using S_nn = V_nn * W_nn * V_nn^(-1) = Q_nn * W_nn * Q_nn^dag
C_nn = V_nn.copy()
gram_schmidt(C_nn)
self.assertAlmostEqual(np.abs(np.dot(C_nn.T.conj(), C_nn) \
- np.eye(self.nbands)).max(), 0, 6)
# Set up Hermitian overlap operator:
S = lambda x: x
dS = lambda a, P_ni: np.dot(P_ni, self.setups[a].dO_ii)
nblocks = self.get_optimal_number_of_blocks(self.blocking)
overlap = MatrixOperator(self.ksl, nblocks, self.async, True)
self.psit_nG = overlap.matrix_multiply(C_nn.T.copy(), self.psit_nG, self.P_ani)
D_nn = overlap.calculate_matrix_elements(self.psit_nG, \
self.P_ani, S, dS).T.copy() # transpose to get <psit_m|A|psit_n>
tri2full(D_nn, 'U') # upper to lower...
if self.bd.comm.rank == 0:
self.gd.comm.broadcast(D_nn, 0)
self.bd.comm.broadcast(D_nn, 0)
if memstats:
self.mem_test = record_memory()
# D_nn = C_nn^dag * S_nn * C_nn = W_n since Q_nn^dag = Q_nn^(-1)
D0_nn = np.dot(C_nn.T.conj(), np.dot(S_nn, C_nn))
self.assertAlmostEqual(np.abs(D0_nn-np.diag(W_n)).max(), 0, 9)
self.check_and_plot(D_nn, D0_nn, 9, 'trivial,diagonalize')
def test_multiply_randomized(self):
# Known starting point of S_nn = <psit_m|S|psit_n>
S_nn = self.S0_nn
if self.dtype == complex:
C_nn = np.random.uniform(size=self.nbands**2) * \
np.exp(1j*np.random.uniform(0,2*np.pi,size=self.nbands**2))
else:
C_nn = np.random.normal(size=self.nbands**2)
C_nn = C_nn.reshape((self.nbands,self.nbands)) / np.linalg.norm(C_nn,2)
world.broadcast(C_nn, 0)
# Set up Hermitian overlap operator:
S = lambda x: x
dS = lambda a, P_ni: np.dot(P_ni, self.setups[a].dO_ii)
nblocks = self.get_optimal_number_of_blocks(self.blocking)
overlap = MatrixOperator(self.ksl, nblocks, self.async, True)
self.psit_nG = overlap.matrix_multiply(C_nn.T.copy(), self.psit_nG, self.P_ani)
D_nn = overlap.calculate_matrix_elements(self.psit_nG, \
self.P_ani, S, dS).T.copy() # transpose to get <psit_m|A|psit_n>
tri2full(D_nn, 'U') # upper to lower...
if self.bd.comm.rank == 0:
self.gd.comm.broadcast(D_nn, 0)
self.bd.comm.broadcast(D_nn, 0)
if memstats:
self.mem_test = record_memory()
# D_nn = C_nn^dag * S_nn * C_nn
D0_nn = np.dot(C_nn.T.conj(), np.dot(S_nn, C_nn))
self.check_and_plot(D_nn, D0_nn, 9, 'multiply,randomized')
def test_multiply_nonhermitian(self):
alpha = np.random.normal(size=1).astype(self.dtype)
if self.dtype == complex:
alpha += 1j*np.random.normal(size=1)
world.broadcast(alpha, 0)
# Known starting point of S_nn = <psit_m|S|psit_n>
S_nn = alpha*self.S0_nn
if self.dtype == complex:
C_nn = np.random.uniform(size=self.nbands**2) * \
np.exp(1j*np.random.uniform(0,2*np.pi,size=self.nbands**2))
else:
C_nn = np.random.normal(size=self.nbands**2)
C_nn = C_nn.reshape((self.nbands,self.nbands)) / np.linalg.norm(C_nn,2)
world.broadcast(C_nn, 0)
# Set up non-Hermitian overlap operator:
S = lambda x: alpha*x
dS = lambda a, P_ni: np.dot(alpha*P_ni, self.setups[a].dO_ii)
nblocks = self.get_optimal_number_of_blocks(self.blocking)
overlap = MatrixOperator(self.ksl, nblocks, self.async, False)
self.psit_nG = overlap.matrix_multiply(C_nn.T.copy(), self.psit_nG, self.P_ani)
D_nn = overlap.calculate_matrix_elements(self.psit_nG, \
self.P_ani, S, dS).T.copy() # transpose to get <psit_m|A|psit_n>
if self.bd.comm.rank == 0:
self.gd.comm.broadcast(D_nn, 0)
self.bd.comm.broadcast(D_nn, 0)
if memstats:
self.mem_test = record_memory()
# D_nn = C_nn^dag * S_nn * C_nn
D0_nn = np.dot(C_nn.T.conj(), np.dot(S_nn, C_nn))
self.check_and_plot(D_nn, D0_nn, 9, 'multiply,nonhermitian')
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 HybridXC(XCFunctional):
orbital_dependent = True
def __init__(
self,
name,
hybrid=None,
xc=None,
finegrid=False,
alpha=None,
skip_gamma=False,
gygi=False,
acdf=True,
qsym=True,
txt=None,
ecut=None,
):
"""Mix standard functionals with exact exchange.
name: str
Name of hybrid functional.
hybrid: float
Fraction of exact exchange.
xc: str or XCFunctional object
Standard DFT functional with scaled down exchange.
finegrid: boolean
Use fine grid for energy functional evaluations?
"""
if name == "EXX":
assert hybrid is None and xc is None
hybrid = 1.0
xc = XC(XCNull())
elif name == "PBE0":
assert hybrid is None and xc is None
hybrid = 0.25
xc = XC("HYB_GGA_XC_PBEH")
elif name == "B3LYP":
assert hybrid is None and xc is None
hybrid = 0.2
xc = XC("HYB_GGA_XC_B3LYP")
if isinstance(xc, str):
xc = XC(xc)
self.hybrid = hybrid
self.xc = xc
self.type = xc.type
self.alpha = alpha
self.qsym = qsym
self.skip_gamma = skip_gamma
self.gygi = gygi
self.acdf = acdf
self.exx = None
self.ecut = ecut
if txt is None:
if rank == 0:
# self.txt = devnull
self.txt = sys.stdout
else:
sys.stdout = devnull
self.txt = devnull
else:
assert type(txt) is str
from ase.parallel import paropen
self.txt = paropen(txt, "w")
XCFunctional.__init__(self, name)
def get_setup_name(self):
return "PBE"
def calculate_radial(self, rgd, n_sLg, Y_L, v_sg, dndr_sLg=None, rnablaY_Lv=None, tau_sg=None, dedtau_sg=None):
return self.xc.calculate_radial(rgd, n_sLg, Y_L, v_sg, dndr_sLg, rnablaY_Lv)
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):
self.xc.initialize(density, hamiltonian, wfs, occupations)
self.nspins = wfs.nspins
self.setups = wfs.setups
self.density = density
self.kpt_u = wfs.kpt_u
self.wfs = wfs
self.gd = density.gd
self.kd = wfs.kd
self.bd = wfs.bd
N_c = self.gd.N_c
N = self.gd.N_c.prod()
vol = self.gd.dv * N
if self.alpha is None:
# XXX ?
self.alpha = 6 * vol ** (2 / 3.0) / pi ** 2
self.gamma = vol / (2 * pi) ** 2 * sqrt(pi / self.alpha) * self.kd.nbzkpts
if self.ecut is None:
self.ecut = 0.5 * pi ** 2 / (self.gd.h_cv ** 2).sum(1).max() * 0.9999
assert self.kd.N_c is not None
n = self.kd.N_c * 2 - 1
bzk_kc = np.indices(n).transpose((1, 2, 3, 0))
bzk_kc.shape = (-1, 3)
bzk_kc -= self.kd.N_c - 1
self.bzk_kc = bzk_kc.astype(float) / self.kd.N_c
self.bzq_qc = self.kd.get_bz_q_points()
if self.qsym:
op_scc = self.kd.symmetry.op_scc
self.ibzq_qc = self.kd.get_ibz_q_points(self.bzq_qc, op_scc)[0]
self.q_weights = self.kd.q_weights * len(self.bzq_qc)
else:
self.ibzq_qc = self.bzq_qc
self.q_weights = np.ones(len(self.bzq_qc))
self.pwd = PWDescriptor(self.ecut, self.gd, complex)
self.G2_qG = self.pwd.g2(self.bzk_kc)
n = 0
for k_c, Gpk2_G in zip(self.bzk_kc[:], self.G2_qG):
if (k_c > -0.5).all() and (k_c <= 0.5).all(): # XXX???
if k_c.any():
self.gamma -= np.dot(np.exp(-self.alpha * Gpk2_G), Gpk2_G ** -1)
else:
self.gamma -= np.dot(np.exp(-self.alpha * Gpk2_G[1:]), Gpk2_G[1:] ** -1)
n += 1
assert n == self.kd.N_c.prod()
self.pwd = PWDescriptor(self.ecut, self.gd, complex)
self.G2_qG = self.pwd.g2(self.ibzq_qc)
self.ghat = LFC(
self.gd, [setup.ghat_l for setup in density.setups], KPointDescriptor(self.bzq_qc), dtype=complex
)
# self.interpolator = density.interpolator
self.print_initialization(hamiltonian.xc.name)
def set_positions(self, spos_ac):
self.ghat.set_positions(spos_ac)
self.spos_ac = 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)
# Add EXX contribution:
return exc + self.exx
def calculate_exx(self):
"""Non-selfconsistent calculation."""
kd = self.kd
K = len(kd.bzk_kc)
W = world.size // self.nspins
parallel = W > 1
self.exx = 0.0
self.exx_kq = np.zeros((K, len(self.ibzq_qc)), float)
for s in range(self.nspins):
ibz_kpts = [KPoint(kd, kpt) for kpt in self.kpt_u if kpt.s == s]
for ik, kpt in enumerate(kd.bzk_kc):
print >>self.txt, "K %s %s ..." % (ik, kpt)
for iq, q in enumerate(self.ibzq_qc):
kpq = kd.find_k_plus_q(q, kpts_k=[ik])
self.apply(ibz_kpts[kd.bz2ibz_k[ik]], ibz_kpts[kd.bz2ibz_k[kpq[0]]], ik, kpq[0], iq)
self.exx = world.sum(self.exx)
self.exx += self.calculate_exx_paw_correction()
exx_q = np.sum(self.exx_kq, 0)
print >>self.txt
print >>self.txt, "------------------------------------------------------"
print >>self.txt
print >>self.txt, "Contributions: q w E_q (eV)"
for q in range(len(exx_q)):
print >>self.txt, "[%1.3f %1.3f %1.3f] %1.3f %s" % (
self.ibzq_qc[q][0],
self.ibzq_qc[q][1],
self.ibzq_qc[q][2],
self.q_weights[q] / len(self.bzq_qc),
exx_q[q] / self.q_weights[q] * len(self.bzq_qc) * Ha,
)
print >>self.txt, "E_EXX = %s eV" % (self.exx * Ha)
print >>self.txt
print >>self.txt, "Calculation completed at: ", ctime()
print >>self.txt
print >>self.txt, "------------------------------------------------------"
print >>self.txt
def apply(self, kpt1, kpt2, ik1, ik2, iq):
k1_c = self.kd.bzk_kc[ik1]
k2_c = self.kd.bzk_kc[ik2]
q = self.ibzq_qc[iq]
if self.qsym:
for i, q in enumerate(self.bzq_qc):
if abs(q - self.ibzq_qc[iq]).max() < 1e-9:
bzq_index = i
break
else:
bzq_index = iq
N_c = self.gd.N_c
eikr_R = np.exp(-2j * pi * np.dot(np.indices(N_c).T, q / N_c).T)
Gamma = abs(q).max() < 1e-9
if Gamma and self.skip_gamma:
return
Gpk2_G = self.G2_qG[iq]
if Gamma:
Gpk2_G = Gpk2_G.copy()
Gpk2_G[0] = 1.0 / self.gamma
N = N_c.prod()
vol = self.gd.dv * N
nspins = self.nspins
fcut = 1e-10
for n1, psit1_R in enumerate(kpt1.psit_nG):
f1 = kpt1.f_n[n1]
for n2, psit2_R in enumerate(kpt2.psit_nG):
if self.acdf:
if self.gygi and Gamma:
# print n2, kpt2.f_n[n2]/kpt2.weight
f2 = self.q_weights[iq] * kpt2.weight
else:
f2 = self.q_weights[iq] * kpt2.weight * (1 - np.sign(kpt2.eps_n[n2] - kpt1.eps_n[n1]))
else:
f2 = kpt2.f_n[n2] * self.q_weights[iq]
if abs(f1) < fcut or abs(f2) < fcut:
continue
nt_R = self.calculate_pair_density(n1, n2, kpt1, kpt2, ik1, ik2, bzq_index)
nt_G = self.pwd.fft(nt_R * eikr_R) / N
vt_G = nt_G.copy()
vt_G *= -pi * vol / Gpk2_G
e = np.vdot(nt_G, vt_G).real * nspins * self.hybrid
self.exx += f1 * f2 * e
self.exx_kq[ik1, iq] += f1 * f2 * e
def calculate_pair_density(self, n1, n2, kpt1, kpt2, ik1, ik2, bzq_index):
psit1_G = self.kd.transform_wave_function(kpt1.psit_nG[n1], ik1)
psit2_G = self.kd.transform_wave_function(kpt2.psit_nG[n2], ik2)
nt_G = psit1_G.conj() * psit2_G
s1 = self.kd.sym_k[ik1]
s2 = self.kd.sym_k[ik2]
t1 = self.kd.time_reversal_k[ik1]
t2 = self.kd.time_reversal_k[ik2]
k1_c = self.kd.ibzk_kc[kpt1.k]
k2_c = self.kd.ibzk_kc[kpt2.k]
Q_aL = {}
for a in kpt1.P_ani.keys():
b1 = self.kd.symmetry.a_sa[s1, a]
b2 = self.kd.symmetry.a_sa[s2, a]
S1_c = np.dot(self.spos_ac[a], self.kd.symmetry.op_scc[s1]) - self.spos_ac[b1]
S2_c = np.dot(self.spos_ac[a], self.kd.symmetry.op_scc[s2]) - self.spos_ac[b2]
assert abs(S1_c.round() - S1_c).max() < 1e-13
assert abs(S2_c.round() - S2_c).max() < 1e-13
x1 = np.exp(2j * pi * np.dot(k1_c, S1_c))
x2 = np.exp(2j * pi * np.dot(k2_c, S2_c))
P1_i = np.dot(self.setups[a].R_sii[s1], kpt1.P_ani[b1][n1]) * x1
P2_i = np.dot(self.setups[a].R_sii[s2], kpt2.P_ani[b2][n2]) * x2
if t1:
P1_i = P1_i.conj()
if t2:
P2_i = P2_i.conj()
D_ii = np.outer(P1_i.conj(), P2_i)
D_p = pack(D_ii)
Q_aL[a] = np.dot(D_p, self.setups[a].Delta_pL)
self.ghat.add(nt_G, Q_aL, bzq_index)
return nt_G
def calculate_exx_paw_correction(self):
exx = 0
deg = 2 // self.nspins # spin degeneracy
for a, D_sp in self.density.D_asp.items():
setup = self.setups[a]
for D_p in D_sp:
D_ii = unpack2(D_p)
ni = len(D_ii)
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 += setup.M_pp[p13, p24] * D_ii[i3, i4]
p12 = packed_index(i1, i2, ni)
exx -= self.hybrid / deg * D_ii[i1, i2] * A
if setup.X_p is not None:
exx -= self.hybrid * np.dot(D_p, setup.X_p)
exx += self.hybrid * setup.ExxC
return exx
def print_initialization(self, xc):
print >>self.txt, "------------------------------------------------------"
print >>self.txt, "Non-self-consistent HF correlation energy"
print >>self.txt, "------------------------------------------------------"
print >>self.txt, "Started at: ", ctime()
print >>self.txt
print >>self.txt, "Ground state XC functional : %s" % xc
print >>self.txt, "Valence electrons : %s" % self.setups.nvalence
print >>self.txt, "Number of Spins : %s" % self.nspins
print >>self.txt, "Plane wave cutoff energy : %4.1f eV" % (self.ecut * Ha)
print >>self.txt, "Gamma q-point excluded : %s" % self.skip_gamma
if not self.skip_gamma:
print >>self.txt, "Alpha parameter : %s" % self.alpha
print >>self.txt, "Gamma parameter : %3.3f" % self.gamma
print >>self.txt, "ACDF method : %s" % self.acdf
print >>self.txt, "Number of k-points : %s" % len(self.kd.bzk_kc)
print >>self.txt, "Number of Irreducible k-points : %s" % len(self.kd.ibzk_kc)
print >>self.txt, "Number of q-points : %s" % len(self.bzq_qc)
if not self.qsym:
print >>self.txt, "q-point symmetry : %s" % self.qsym
else:
print >>self.txt, "Number of Irreducible q-points : %s" % len(self.ibzq_qc)
print >>self.txt
for q, weight in zip(self.ibzq_qc, self.q_weights):
print >>self.txt, "q: [%1.3f %1.3f %1.3f] - weight: %1.3f" % (q[0], q[1], q[2], weight / len(self.bzq_qc))
print >>self.txt
print >>self.txt, "------------------------------------------------------"
print >>self.txt, "------------------------------------------------------"
print >>self.txt
print >>self.txt, "Looping over k-points in the full Brillouin zone"
print >>self.txt
def get_pseudo_core_kinetic_energy_density_lfc(self):
return LFC(self.gd, [[setup.tauct] for setup in self.setups],
forces=True,
cut=True)
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'))
