def compute_dos(self, fixmu, mu=None, totdens=None):
#AV: as the gloc method is written for the Matsubara representation,
# we pass an ad-hoc frequency to get the retarded Green's function
fake_iw = -1j * self.w + self.deltino
# the effective leads' self-energy is given by the sum over nleads
# we also need to subtract the crystal fields, already included in Delta
# at the moment we subtract H(k) or should we rather subtract just the diagonal elements epsilon_d?
# this depends on the definition of the Delta obtained from the DFT calculation
sw_leads = self.leadsw.sum(1) - self.hk.mean(0)
# get the retarded Green's function and extract the dos from the diagonal elements
gloc_w = KspaceHamiltonian.gloc(self, fake_iw, 0, sw_leads)
self.dos = -1 / np.pi * orbspin.extract_diagonal(gloc_w.imag)
siw_leads = self.leadsiw.sum(1)
def get_totdens_for_mu(mu):
gloc_iw = KspaceHamiltonian.gloc(self, self.iwleads, mu, siw_leads)
#np.savetxt("hk_test", self.hk[0,:,0,:,0])
gloc_model = self.eye * 1 / (1j * self.iwleads + mu)[:, None, None,
None, None]
dens_model = fermi(-mu, self.beta) * self.eye
dens_matrix = (gloc_iw -
gloc_model).sum(0) / self.beta + dens_model
self.densities = orbspin.extract_diagonal(dens_matrix)
return self.densities.sum()
if fixmu:
self.mu = scipy.optimize.brentq(
lambda mu: get_totdens_for_mu(mu) - totdens, self.w.min(),
self.w.max())
else:
self.mu = mu
get_totdens_for_mu(mu)
def write_to_node(node, part, pshape=None):
if pshape is None:
try:
pshape = part.shape
except AttributeError:
pshape = ()
pslice = qtty_slice
if band_dims == 0:
pass
elif band_dims == 1:
# extract the diagonal because that is what should go into HDF5
part = orbspin.extract_diagonal(part)
axes_list = [-2, -1] + range(part.ndim - 2)
part = part.transpose(axes_list)
pshape = pshape[-2:] + pshape[:-4]
if pslice is not None:
pslice = (slice(None), ) * 2 + (qtty_slice, )
elif band_dims == 2:
axes_list = [-4, -3, -2, -1] + range(part.ndim - 4)
part = part.transpose(axes_list)
pshape = pshape[-4:] + pshape[:-4]
if pslice is not None:
pslice = (slice(None), ) * 4 + (qtty_slice, )
else:
warn("Unclear how to deal with > 2 band dims", UserWarning, 3)
if write_everything:
node.create_dataset(qtty_name + "/value", data=part)
else:
#print "SETTING", qtty_slice, "OF", qtty_name, "SHAPE", pshape
dataset = node.require_dataset(qtty_name + "/value",
shape=pshape,
dtype=part.dtype,
exact=True)
dataset[pslice] = part
def gloc(self, iw, mu, siw, siw_gw=None):
ziw = (1j * iw + mu)[:, None, None, None, None] * self.eye - siw
orbspin.warn_offdiagonal(siw)
zeta = orbspin.extract_diagonal(ziw - self.hloc)
d2 = self.d[np.newaxis]**2
glociw = 2 * zeta / d2 * (1 - np.sqrt(1 - d2 / zeta**2))
glociw = orbspin.promote_diagonal(glociw)
return glociw
def get(self, siws=None, smoms=None, giws=None, occs=None):
if giws is None:
# initializing with FLL double counting... better than 0
dc_fll = FullyLocalisedLimit(self.shell_av['densities'],
self.shell_av['atom_list'],
self.shell_av['u_full'])
self.dc_value = dc_fll.get()
return self.dc_value
for ineq, giw, occ, occ0 in zip(self.ineq_list, giws, occs,
self.d_dens_sum):
# DOS as "approximated" by first Matsubara frequency
iw0 = giw.shape[0] // 2
dos_fermi_level = -1 / np.pi * orbspin.trace(giw[iw0].imag)
# impurity density from double occupations.
# TODO: this is tied to diagonal hybr
dens_impurity = orbspin.promote_diagonal(
orbspin.extract_diagonal(occ))
dens_impurity = np.array(dens_impurity).astype(np.float)
dens_impurity = np.sum(dens_impurity)
# we do not use the non interacting density from Weiss field
# but that from the DFT Hamiltonian.
# that is a lot more stable
# impurity non-interacting density (from Weiss field)
#iw = tf.matfreq(beta, 'fermi', imp_result.problem.niwf)
#eye = np.eye(imp_result.problem.norbitals * imp_result.problem.nspins) \
# .reshape(imp_result.problem.norbitals, imp_result.problem.nspins,
# imp_result.problem.norbitals, imp_result.problem.nspins)
#g0iw = orbspin.invert(imp_result.problem.g0iwinv)
#g0iw_model = orbspin.invert(1j * iw * eye + imp_result.problem.muimp)
#dens_model = lattice.fermi(-imp_result.problem.muimp) # FIXME offdiag
#dens0_impurity = (g0iw - g0iw_model).real.sum(0) / imp_result.problem.beta \
# + dens_model
if ineq.occ_dc_number is not None:
dens0_impurity = ineq.occ_dc_number
else:
dens0_impurity = occ0
# If the DOS at the Fermi level is large, we do not want to adjust
# too much for stability reasons (fudging)
if dos_fermi_level > 1.:
delta_dc = (dens0_impurity - dens_impurity) / dos_fermi_level
else:
delta_dc = dens0_impurity - dens_impurity
# Fudging factor
delta_dc *= 0.2
delta_dc = delta_dc * np.eye(ineq.nd * self.nspins).reshape(
ineq.nd, self.nspins, ineq.nd, self.nspins)
ineq.d_setpart(self.dc_value,
ineq.d_downfold(self.dc_value) - delta_dc)
return self.dc_value
def prepare_input(cls, qtty):
orbspin.warn_offdiagonal(qtty)
qtty = orbspin.extract_diagonal(qtty)
if (np.abs(qtty.imag) > 1e-10).any():
warn("Quantity has non-vanishing imaginary part", UserWarning, 2)
qtty = qtty.real
if qtty.ndim > 2:
axes_list = [-2, -1] + range(qtty.ndim - 2)
qtty = qtty.transpose(axes_list)
return qtty
def get_totdens_for_mu(mu):
gloc_iw = KspaceHamiltonian.gloc(self, self.iwleads, mu, siw_leads)
#np.savetxt("hk_test", self.hk[0,:,0,:,0])
gloc_model = self.eye * 1 / (1j * self.iwleads + mu)[:, None, None,
None, None]
dens_model = fermi(-mu, self.beta) * self.eye
dens_matrix = (gloc_iw -
gloc_model).sum(0) / self.beta + dens_model
self.densities = orbspin.extract_diagonal(dens_matrix)
return self.densities.sum()
def gloc(self, iw, mu, siw, siw_gw=None):
orbspin.warn_offdiagonal(siw)
siw = orbspin.extract_diagonal(siw)
zeta = (1j * iw + mu)[:, None, None] - siw
# compute integral de N(e)/(zeta - e)
glociw = self.integrator(
self.dos.transpose(1, 2, 0)[None, :, :, :] /
(zeta[:, :, :, None] - self.w[None, None, None, :]))
glociw = orbspin.promote_diagonal(glociw)
return glociw
def get_gsigmaiw(cls, config, problem, result):
gsigmaiw = None
if config["QMC"]["MeasGSigmaiw"] == 1:
gsigmaiw = result["gsigmaiw"]
if config["QMC"]["WormMeasGSigmaiw"] == 1:
if gsigmaiw is not None:
warn("Worm GSigmaiw overwriting Z GSigmaiw", UserWarning, 2)
gsigmaiw = result["gsigmaiw-worm"]
gsigmaiw = orbspin.extract_diagonal(gsigmaiw.transpose(4,0,1,2,3)) \
.transpose(1,2,0)
return gsigmaiw
def siw2gloc(self):
self.glociw = self.lattice.gloc(self.my_iwf, self.mu, self.siw_full,
self.siw_gw)
self.gmodeliw, dmatrix = self.lattice.gmodel(self.my_iwf, self.mu,
self.siw_moments,
self.smom_gw)
self.densmatrix = (self.glociw - self.gmodeliw).sum(0) / self.beta
if self.mpi_comm is not None:
self.densmatrix = self.mpi_comm.allreduce(self.densmatrix)
self.densmatrix += dmatrix
self.densities = orbspin.extract_diagonal(self.densmatrix)
# Destroy large GW siw for MC cycle
self.siw_GW_dyn = None
nat = len(cfg["Atoms"])
nneq = len(
[ineq for ineq in args.hf['start'].keys() if ineq[0:4] == u'ineq'])
nw = len(w)
Siw = np.zeros((0, 2, nw))
DC = np.zeros((0, 2))
istart = 0
for i in xrange(1, nneq + 1):
ineq = "ineq-%03d" % i
s = iter[ineq]['siw/value'].value
nds = args.hf['.config'].attrs['atoms.' + str(i) + '.nd']
nps = args.hf['.config'].attrs['atoms.' + str(i) + '.np']
d = iter['dc-latt/value'].value[istart:nds + nps]
d = orbspin.extract_diagonal(d)
# We upcast the selfenergy to (nbands x 2 x nw) here. This
# could be optimized by passing Np(i) to delta_N and upcasting
# from Nd(i) to Nbands for each w individually.
Siw = np.vstack((Siw, s, np.zeros((nps, 2, nw))))
DC = np.vstack((DC, d))
istart = nds + nps
wien2k.init(cfg, kpoints, sys.stdout)
if args.debug:
(dnk, g1, g2) = wien2k.delta_N_debug(beta, w, mu_lda, mu_dmft, Hk, Siw,
DC, nat, nneq)
else:
dnk = wien2k.delta_N(beta, w, mu_lda, mu_dmft, Hk, Siw, DC, nat, nneq)
def get_giw(cls, config, problem, result):
#typ = "legendre" # FIXME: QMC config does not contain FTtype
typ = config["General"]["FTType"]
if config["QMC"]["offdiag"] == 1 and typ == "legendre":
typ = "legendre_full"
if typ == "none":
giw = -result["giw-meas"]
elif typ == "none_worm":
giw = result["giw-worm"]
giw = orbspin.extract_diagonal(giw.transpose(4,0,1,2,3)) \
.transpose(1,2,0)
elif typ == "plain":
ntau = config["QMC"]["Ntau"]
tf_matrix = tf.tau2mat(problem.beta, ntau, 'fermi', problem.niw)
giw = tf.transform(tf_matrix, result["gtau"], None)
elif typ == "legendre":
nleg = config["QMC"]["NLegOrder"]
tf_matrix = -tf.leg2mat(nleg, problem.niw)
giw = tf.transform(tf_matrix,
result["gleg"],
None,
onmismatch=tf.Truncate.tofirst,
warn=False)
elif typ == "legendre_full":
nleg = config["QMC"]["NLegOrder"]
tf_matrix = -tf.leg2mat(nleg, problem.niw)
nbands = result["gleg-full"].shape[0]
giw = np.zeros(shape=(nbands, 2, nbands, 2, problem.niw),
dtype=complex)
for b in range(0, nbands):
for s in range(0, 2):
giw[b, s, :, :, :] = tf.transform(
tf_matrix,
result["gleg-full"][b, s, :, :, :],
None,
onmismatch=tf.Truncate.tofirst,
warn=False)
#### the old one
#tmp = tf.transform(tf_matrix, result["gleg-full"][b,s,:,:,:], None,
#onmismatch=tf.Truncate.tofirst, warn=False)
#for b2 in range(0,nbands):
#for s2 in range(0,2):
#for w in range(0,problem.niw):
#print "w", w
#giw[b,s,b2,s2,w] = tmp[b2,s2,w]
giw = giw.reshape(nbands * 2, nbands * 2, problem.niw)
giw_new = np.zeros_like(giw, dtype=complex)
for i in range(0, problem.niw):
tmp = giw[:, :, i]
giw_new[:, :, i] = 0.5 * (tmp.transpose(1, 0) + tmp)
giw = giw_new
else:
raise RuntimeError("Invalid transform type: `%s'" % typ)
return giw # copy not necessary here.
def set_problem(self, problem, compute_fourpoint=0):
# problem
self.problem = problem
problem_params = self.config_to_pstring({
"Hamiltonian":
problem.interaction.name,
"beta":
problem.beta,
"Nd":
problem.norbitals,
"ParaMag":
int(problem.paramag),
"QuantumNumbers":
" ".join(problem.interaction.quantum_numbers),
"Phonon":
int(problem.use_phonons),
"g_phonon":
" ".join(problem.phonon_g),
"omega0":
" ".join(problem.phonon_omega0),
"Screening":
int(problem.use_screening),
"Uw":
self.Uw,
})
symm_params = self.symm_to_pstring(problem.symmetry_moves)
all_params = self.param_string + problem_params + symm_params
ctqmc.init_paras(all_params)
ctqmc.fourpnt = compute_fourpoint
# prepare parameters
if self.config["QMC"]["offdiag"] == 0:
self.ftau = orbspin.promote_diagonal(
orbspin.extract_diagonal(self.problem.ftau))
self.ftau = self.problem.ftau.transpose(1, 2, 3, 4, 0)
# CT-HYB uses a different convention for muimp
#self.muimp = -self.prepare_input(self.problem.muimp)
self.muimp = -self.problem.muimp
self.umatrix = self.problem.interaction.u_matrix.reshape(
self.problem.nflavours, self.problem.nflavours,
self.problem.nflavours, self.problem.nflavours)
if self.Uw == 0:
self.screening = self.problem.screening.transpose(1, 2, 3, 4,
0).real
# START DYNAMICAL U
if self.Uw == 1:
#print " "
#print " ****************************"
#print " ****** U(w) is active ******"
#print " ****************************"
### ===> UPDATE This is now done in the init above.
### ===> UPDATE _Retarded2Shifts = dynamicalU.Replace_Retarded_Interaction_by_a_Shift_of_instantaneous_Potentials(problem.beta, self.umatrix, self.Uw_Mat)
### ===> UPDATE The umatrix shifting is now performed in config.py.
### ===> UPDATE The umatrix shifting is now performed in config.py.
### ===> # This should be executed for all atoms in the first iteration
### ===> try:
### ===> self.iteration_ID # Not defined for first DMFT iteration
### ===> except:
### ===> self.umatrix_original = copy.copy(self.umatrix)
### ===> self.iteration_ID = 1
### ===> if (self.umatrix==self.umatrix_original).all():
### ===> self.umatrix = _Retarded2Shifts.shift_instantaneous_densitydensity_potentials(self.umatrix)
### ===> UPDATE The umatrix shifting is now performed in config.py.
### ===> UPDATE The umatrix shifting is now performed in config.py.
### ===> UPDATE This is now done in the init above.
### ===> UPDATE self.screening = _Retarded2Shifts.create_tau_dependent_UV_screening_function(problem.nftau, problem.beta, self.screening)
# Perform chemical potential shift in each DMFT iteration
if problem.norbitals == 1 and self.epsn == 0:
self.muimp = self._Retarded2Shifts.shift_chemical_potential_for_single_band_case(
self.muimp, self.umatrix)
def postprocessing(self, siw_method="improved", smom_method="estimate"):
# This function is disjoint from the initialisation, because it is a
# "derived" quantity that should be computed after averaging over bins
fallback = False
if siw_method == "dyson":
if self.g_diagonal_only:
# If the solver is only capable of supplying the spin/orbital-
# diagonal terms of the Green's function, we need to make sure
# that also only the diagonal terms of G_0 are taken into
# account in the Dyson equation, otherwise Sigma erroneously
# "counteracts" these terms. As an added performance benefit,
# we can use 1/giw rather than the inversion in this case.
self.siw = orbspin.promote_diagonal(
orbspin.extract_diagonal(self.problem.g0inviw) -
1 / orbspin.extract_diagonal(self.giw))
else:
self.siw = self.problem.g0inviw - orbspin.invert(self.giw)
elif siw_method == "improved":
if self.gsigmaiw is None:
warn(
"Cannot compute improved estimators - GSigmaiw missing\n"
"Falling back to Dyson equation", UserWarning, 2)
siw_method = "dyson"
fallback = True
raise NotImplementedError() # FIXME
elif siw_method == 'improved_worm':
if self.gsigmaiw is None:
warn(
"Cannot compute improved estimators - GSigmaiw missing\n"
"Falling back to Dyson equation", UserWarning, 2)
siw_method = "dyson"
fallback = True
if self.g_diagonal_only:
#TODO: check gsigma sign
self.siw = -orbspin.promote_diagonal(
orbspin.extract_diagonal(self.gsigmaiw) /
orbspin.extract_diagonal(self.giw))
else:
raise NotImplementedError("Offdiagonal worm improved \n"
"estimators not implemented")
else:
raise ValueError("unknown siw_method: %s" % siw_method)
if smom_method == "extract":
warn("Extracting moment of self-energy from the data", UserWarning,
2)
self.smom = self.siw[:1].real.copy()
elif smom_method == "estimate":
if self.smom is None:
warn(
"Cannot compute smom estimate - rho1 and rho2 missing\n"
"Falling back to extraction", UserWarning, 2)
smom_method = "extract"
fallback = True
else:
raise ValueError("unknown smom_method: %s" % smom_method)
if fallback:
self.postprocessing(siw_method, smom_method)