def ibz2bz(self, atoms):
"""Transform wave functions in IBZ to the full BZ."""
assert self.kd.comm.size == 1
# New k-point descriptor for full BZ:
kd = KPointDescriptor(self.kd.bzk_kc, nspins=self.nspins)
kd.set_symmetry(atoms, self.setups, usesymm=None)
kd.set_communicator(serial_comm)
self.pt = LFC(self.gd, [setup.pt_j for setup in self.setups],
kd, dtype=self.dtype)
self.pt.set_positions(atoms.get_scaled_positions())
self.initialize_wave_functions_from_restart_file()
weight = 2.0 / kd.nspins / kd.nbzkpts
# Build new list of k-points:
kpt_u = []
for s in range(self.nspins):
for k in range(kd.nbzkpts):
# Index of symmetry related point in the IBZ
ik = self.kd.bz2ibz_k[k]
r, u = self.kd.get_rank_and_index(s, ik)
assert r == 0
kpt = self.kpt_u[u]
phase_cd = np.exp(2j * np.pi * self.gd.sdisp_cd *
kd.bzk_kc[k, :, np.newaxis])
# New k-point:
kpt2 = KPoint(weight, s, k, k, phase_cd)
kpt2.f_n = kpt.f_n / kpt.weight / kd.nbzkpts * 2 / self.nspins
kpt2.eps_n = kpt.eps_n.copy()
# Transform wave functions using symmetry operation:
Psit_nG = self.gd.collect(kpt.psit_nG)
if Psit_nG is not None:
Psit_nG = Psit_nG.copy()
for Psit_G in Psit_nG:
Psit_G[:] = self.kd.transform_wave_function(Psit_G, k)
kpt2.psit_nG = self.gd.empty(self.bd.nbands, dtype=self.dtype)
self.gd.distribute(Psit_nG, kpt2.psit_nG)
# Calculate PAW projections:
kpt2.P_ani = self.pt.dict(len(kpt.psit_nG))
self.pt.integrate(kpt2.psit_nG, kpt2.P_ani, k)
kpt_u.append(kpt2)
self.kd = kd
self.kpt_u = kpt_u
def dummy_test(lmax=4, rcut=6., lmin=0): # fix args
"""Run a test using a Gaussian reference function."""
dtype = complex
generator = PolarizationOrbitalGenerator(rcut, gaussians=4)
r = np.arange(0., rcut, .01)
alpha_ref = 1. / (rcut / 4.)**2.
import pylab
for l in range(lmin, lmax + 1):
g = QuasiGaussian(alpha_ref, rcut)
norm = get_norm(r, g(r), l)
g.renormalize(norm)
gd, psit_k, center, ref = make_dummy_reference(l, g, rcut, dtype=dtype)
k_kc = ((0., 0., 0.), (.5, .5, .5))
kpt_u = [
KPoint([], gd, 1., 0, i, i, k_c, dtype=dtype)
for i, k_c in enumerate(k_kc)
]
for kpt in kpt_u:
kpt.allocate(1)
kpt.f_n = np.array([2.])
kpt.psit_nG = psit_k
phi = generator.generate(l, gd, kpt_u, [center], dtype=dtype)
pylab.figure(l)
#pylab.plot(r, ref(r)*r**l, 'g', label='ref')
pylab.plot(r, g(r) * r**l, 'b', label='g')
pylab.plot(r, phi(r) * r**l, 'r--', label='pol')
pylab.title('l=%d' % l)
pylab.legend()
pylab.show()
def make_dummy_kpt_reference(l, function, k_c,
rcut=6., a=10., n=60, dtype=complex):
r = np.linspace(0., rcut, 300)
mcount = 2*l + 1
fcount = 1
kcount = 1
gd = GridDescriptor((n, n, n), (a, a, a), (True, True, True))
kpt = KPoint([], gd, 1., 0, 0, 0, k_c, dtype)
spline = Spline(l, r[-1], function(r))
center = (.5, .5, .5)
lf = create_localized_functions([spline], gd, center, dtype=dtype)
lf.set_phase_factors([kpt.k_c])
psit_nG = gd.zeros(mcount, dtype=dtype)
coef_xi = np.identity(mcount * fcount, dtype=dtype)
lf.add(psit_nG, coef_xi, k=0)
kpt.psit_nG = psit_nG
print 'Number of boxes', len(lf.box_b)
print 'Phase kb factors shape', lf.phase_kb.shape
return gd, kpt, center
def make_dummy_kpt_reference(l,
function,
k_c,
rcut=6.,
a=10.,
n=60,
dtype=complex):
r = np.linspace(0., rcut, 300)
mcount = 2 * l + 1
fcount = 1
kcount = 1
gd = GridDescriptor((n, n, n), (a, a, a), (True, True, True))
kpt = KPoint([], gd, 1., 0, 0, 0, k_c, dtype)
spline = Spline(l, r[-1], function(r))
center = (.5, .5, .5)
lf = create_localized_functions([spline], gd, center, dtype=dtype)
lf.set_phase_factors([kpt.k_c])
psit_nG = gd.zeros(mcount, dtype=dtype)
coef_xi = np.identity(mcount * fcount, dtype=dtype)
lf.add(psit_nG, coef_xi, k=0)
kpt.psit_nG = psit_nG
print 'Number of boxes', len(lf.box_b)
print 'Phase kb factors shape', lf.phase_kb.shape
return gd, kpt, center
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 create_k_points(self, gd):
"""Return a list of KPoints."""
sdisp_cd = gd.sdisp_cd
kpt_u = []
for ks in range(self.ks0, self.ks0 + self.mynks):
s, k = divmod(ks, self.nibzkpts)
q = (ks - self.ks0) % self.nibzkpts
weight = self.weight_k[k] * 2 / self.nspins
if self.gamma:
phase_cd = np.ones((3, 2), complex)
else:
phase_cd = np.exp(2j * np.pi * sdisp_cd *
self.ibzk_kc[k, :, np.newaxis])
kpt_u.append(KPoint(weight, s, k, q, phase_cd))
return kpt_u
def create_k_points(self, gd, collinear):
"""Return a list of KPoints."""
sdisp_cd = gd.sdisp_cd # Maybe pass gd.sdisp_cd instead of gd??
# We do not in fact use any other property of gd.
kpt_u = []
for ks in range(self.ks0, self.ks0 + self.mynks):
s, k = divmod(ks, self.nibzkpts)
q = (ks - self.ks0) % self.nibzkpts
weight = self.weight_k[k] * 2 / self.nspins
if self.gamma:
phase_cd = np.ones((3, 2), complex)
else:
phase_cd = np.exp(2j * np.pi *
sdisp_cd * self.ibzk_kc[k, :, np.newaxis])
if not collinear:
s = None
weight *= 0.5
kpt_u.append(KPoint(weight, s, k, q, phase_cd))
return kpt_u
def dummy_kpt_test():
l = 0
rcut = 6.
a = 5.
k_kc = [(.5, .5, .5)] #[(0., 0., 0.), (0.5, 0.5, 0.5)]
kcount = len(k_kc)
dtype = complex
r = np.arange(0., rcut, .01)
spos_ac_ref = [(0., 0., 0.)] #, (.2, .2, .2)]
spos_ac = [(0., 0., 0.), (.2, .2, .2)]
ngaussians = 4
realgaussindex = (ngaussians - 1) / 2
rchars = np.linspace(1., rcut, ngaussians)
splines = []
gaussians = [QuasiGaussian(1. / rch**2., rcut) for rch in rchars]
for g in gaussians:
norm = get_norm(r, g(r), l)
g.renormalize(norm)
spline = Spline(l, r[-1], g(r))
splines.append(spline)
refgauss = gaussians[realgaussindex]
refspline = splines[realgaussindex]
gd = GridDescriptor((60, 60, 60), (a, a, a), (1, 1, 1))
reflf_a = [
create_localized_functions([refspline], gd, spos_c, dtype=dtype)
for spos_c in spos_ac_ref
]
for reflf in reflf_a:
reflf.set_phase_factors(k_kc)
kpt_u = [
KPoint([], gd, 1., 0, k, k, k_c, dtype) for k, k_c in enumerate(k_kc)
]
for kpt in kpt_u:
kpt.allocate(1)
kpt.f_n[0] = 1.
psit_nG = gd.zeros(1, dtype=dtype)
coef_xi = np.identity(1, dtype=dtype)
integral = np.zeros((1, 1), dtype=dtype)
for reflf in reflf_a:
reflf.add(psit_nG, coef_xi, k=kpt.k)
reflf.integrate(psit_nG, integral, k=kpt.k)
kpt.psit_nG = psit_nG
print 'ref norm', integral
print 'calculating overlaps'
os_kmii, oS_kmii = overlaps(l, gd, splines, kpt_u, spos_ac=spos_ac_ref)
print 'done'
lf_a = [
create_localized_functions(splines, gd, spos_c, dtype=dtype)
for spos_c in spos_ac
]
for lf in lf_a:
lf.set_phase_factors(k_kc)
s_kii = np.zeros((kcount, ngaussians, ngaussians), dtype=dtype)
S_kii = np.zeros((kcount, ngaussians, ngaussians), dtype=dtype)
for kpt in kpt_u:
k = kpt.k
all_integrals = np.zeros((1, ngaussians), dtype=dtype)
tempgrids = gd.zeros(ngaussians, dtype=dtype)
tempcoef_xi = np.identity(ngaussians, dtype=dtype)
for lf in lf_a:
lf.integrate(kpt.psit_nG, all_integrals, k=k)
lf.add(tempgrids, tempcoef_xi, k=k)
lf.integrate(tempgrids, s_kii[k], k=k)
print 'all <phi|psi>'
print all_integrals
conj_integrals = np.conj(all_integrals)
for i in range(ngaussians):
for j in range(ngaussians):
S_kii[k, i, j] = conj_integrals[0, i] * all_integrals[0, j]
print 'handmade s_kmii'
print s_kii
print 'handmade S_ii'
print S_kii
s_kmii = s_kii.reshape(kcount, 1, ngaussians, ngaussians)
S_kmii = S_kii.reshape(kcount, 1, ngaussians, ngaussians)
print 'matrices from overlap function'
print 's_kmii'
print os_kmii
print 'S_kmii'
print oS_kmii
optimizer = CoefficientOptimizer(s_kmii, S_kmii, ngaussians)
coefficients = optimizer.find_coefficients()
optimizer2 = CoefficientOptimizer(os_kmii, oS_kmii, ngaussians)
coefficients2 = optimizer2.find_coefficients()
print 'coefs'
print coefficients
print 'overlaps() coefs'
print coefficients2
print 'badness'
print optimizer.evaluate(coefficients)
exactsolution = [0.] * ngaussians
exactsolution[realgaussindex] = 1.
print 'badness of exact solution'
print optimizer.evaluate(exactsolution)
orbital = LinearCombination(coefficients, gaussians)
orbital2 = LinearCombination(coefficients2, gaussians)
norm = get_norm(r, orbital(r), l)
norm2 = get_norm(r, orbital2(r), l)
orbital.renormalize(norm)
orbital2.renormalize(norm2)
import pylab
pylab.plot(r, refgauss(r), label='ref')
pylab.plot(r, orbital(r), label='opt')
pylab.plot(r, orbital2(r), '--', label='auto')
pylab.legend()
pylab.show()
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_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.mykpts[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 = UniformGridWaveFunctions(self.bd.nbands,
self.gd,
self.dtype,
kpt=k,
dist=(self.bd.comm,
self.bd.comm.size),
spin=kpt.s,
collinear=True)
self.gd.distribute(Psit_nG, kpt2.psit_nG)
# Calculate PAW projections:
nproj_a = [setup.ni for setup in self.setups]
kpt2.projections = Projections(self.bd.nbands,
nproj_a,
kpt.projections.atom_partition,
self.bd.comm,
collinear=True,
spin=s,
dtype=self.dtype)
kpt2.psit.matrix_elements(self.pt, out=kpt2.projections)
kpt_u.append(kpt2)
self.kd = kd
self.mykpts = kpt_u