##########################################################################
#
# TRIQS: a Toolbox for Research in Interacting Quantum Systems
#
# Copyright (C) 2011 by M. Aichhorn, L. Pourovskii, V. Vildosola
#
# TRIQS is free software: you can redistribute it and/or modify it under the
# terms of the GNU General Public License as published by the Free Software
# Foundation, either version 3 of the License, or (at your option) any later
# version.
#
# TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY
# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
# FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
# details.
#
# You should have received a copy of the GNU General Public License along with
# TRIQS. If not, see .
#
##########################################################################
###
# Wannier90 to HDF5 converter for the SumkDFT class of dfttools/TRIQS;
#
# written by Gabriele Sclauzero (Materials Theory, ETH Zurich), Dec 2015 -- Jan 2016,
# under the supervision of Claude Ederer (Materials Theory).
# Partially based on previous work by K. Dymkovski and the DFT_tools/TRIQS team.
#
# Limitations of the current implementation:
# - the case with SO=1 is not considered at the moment
# - the T rotation matrices are not used in this implementation
# - projectors for uncorrelated shells (proj_mat_all) cannot be set
#
# Things to be improved/checked:
# - the case with SP=1 might work, but was never tested (do we need to define
# rot_mat_time_inv also if symm_op = 0?)
# - the calculation of rot_mat in find_rot_mat() relies on the eigenvalues of H(0);
# this might fail in presence of degenerate eigenvalues (now just prints warning)
# - the FFT is always done in serial mode (because all converters run serially);
# this can become very slow with a large number of R-vectors/k-points
# - make the code more MPI safe (error handling): if we run with more than one process
# and an error occurs on the masternode, the calculation does not abort
###
from types import *
import numpy
import math
from pytriqs.archive import *
from converter_tools import *
from itertools import product
import os.path
class Wannier90Converter(ConverterTools):
"""
Conversion from Wannier90 output to an hdf5 file that can be used as input for the SumkDFT class.
"""
def __init__(self, seedname, hdf_filename=None, dft_subgrp='dft_input',
symmcorr_subgrp='dft_symmcorr_input', repacking=False):
"""
Initialise the class.
Parameters
----------
seedname : string
Base name of Wannier90 files
hdf_filename : string, optional
Name of hdf5 archive to be created
dft_subgrp : string, optional
Name of subgroup storing necessary DFT data
symmcorr_subgrp : string, optional
Name of subgroup storing correlated-shell symmetry data
repacking : boolean, optional
Does the hdf5 archive need to be repacked to save space?
"""
self._name = "Wannier90Converter"
assert type(seedname) == StringType, self._name + \
": Please provide the DFT files' base name as a string."
if hdf_filename is None:
hdf_filename = seedname + '.h5'
self.hdf_file = hdf_filename
# if the w90 output is seedname_hr.dat, the input file for the
# converter must be called seedname.inp
self.inp_file = seedname + '.inp'
self.w90_seed = seedname
self.dft_subgrp = dft_subgrp
self.symmcorr_subgrp = symmcorr_subgrp
self.fortran_to_replace = {'D': 'E'}
# threshold below which matrix elements from wannier90 should be
# considered equal
self._w90zero = 2.e-6
# Checks if h5 file is there and repacks it if wanted:
if (os.path.exists(self.hdf_file) and repacking):
ConverterTools.repack(self)
def convert_dft_input(self):
"""
Reads the appropriate files and stores the data for the
- dft_subgrp
- symmcorr_subgrp
in the hdf5 archive.
"""
# Read and write only on the master node
if not (mpi.is_master_node()):
return
mpi.report("Reading input from %s..." % self.inp_file)
# R is a generator : each R.Next() will return the next number in the
# file
R = ConverterTools.read_fortran_file(
self, self.inp_file, self.fortran_to_replace)
shell_entries = ['atom', 'sort', 'l', 'dim']
corr_shell_entries = ['atom', 'sort', 'l', 'dim', 'SO', 'irep']
# First, let's read the input file with the parameters needed for the
# conversion
try:
# read k - point mesh generation option
kmesh_mode = int(R.next())
if kmesh_mode >= 0:
# read k-point mesh size from input
nki = [int(R.next()) for idir in range(3)]
else:
# some default grid, if everything else fails...
nki = [8, 8, 8]
# read the total number of electrons per cell
density_required = float(R.next())
# we do not read shells, because we have no additional shells beyond correlated ones,
# and the data will be copied from corr_shells into shells (see below)
# number of corr. shells (e.g. Fe d, Ce f) in the unit cell,
n_corr_shells = int(R.next())
# now read the information about the correlated shells (atom, sort,
# l, dim, SO flag, irep):
corr_shells = [{name: int(val) for name, val in zip(
corr_shell_entries, R)} for icrsh in range(n_corr_shells)]
try:
self.fermi_energy = R.next()
except:
self.fermi_energy = 0.
except StopIteration: # a more explicit error if the file is corrupted.
mpi.report(self._name + ": reading input file %s failed!" %
self.inp_file)
# close the input file
R.close()
# Set or derive some quantities
# Wannier90 does not use symmetries to reduce the k-points
# the following might change in future versions
symm_op = 0
# copy corr_shells into shells (see above)
n_shells = n_corr_shells
shells = []
for ish in range(n_shells):
shells.append({key: corr_shells[ish].get(
key, None) for key in shell_entries})
###
SP = 0 # NO spin-polarised calculations for now
SO = 0 # NO spin-orbit calculation for now
charge_below = 0 # total charge below energy window NOT used for now
energy_unit = 1.0 # should be understood as eV units
###
# this is more general
n_spin = SP + 1 - SO
dim_corr_shells = sum([sh['dim'] for sh in corr_shells])
mpi.report(
"Total number of WFs expected in the correlated shells: %d" % dim_corr_shells)
# determine the number of inequivalent correlated shells and maps,
# needed for further processing
n_inequiv_shells, corr_to_inequiv, inequiv_to_corr = ConverterTools.det_shell_equivalence(
self, corr_shells)
mpi.report("Number of inequivalent shells: %d" % n_inequiv_shells)
mpi.report("Shell representatives: " + format(inequiv_to_corr))
shells_map = [inequiv_to_corr[corr_to_inequiv[ish]]
for ish in range(n_corr_shells)]
mpi.report("Mapping: " + format(shells_map))
# build the k-point mesh, if its size was given on input (kmesh_mode >= 0),
# otherwise it is built according to the data in the hr file (see
# below)
if kmesh_mode >= 0:
n_k, k_mesh, bz_weights = self.kmesh_build(nki, kmesh_mode)
self.n_k = n_k
self.k_mesh = k_mesh
# not used in this version: reset to dummy values?
n_reps = [1 for i in range(n_inequiv_shells)]
dim_reps = [0 for i in range(n_inequiv_shells)]
T = []
for ish in range(n_inequiv_shells):
ll = 2 * corr_shells[inequiv_to_corr[ish]]['l'] + 1
lmax = ll * (corr_shells[inequiv_to_corr[ish]]['SO'] + 1)
T.append(numpy.zeros([lmax, lmax], numpy.complex_))
spin_w90name = ['_up', '_down']
hamr_full = []
# TODO: generalise to SP=1 (only partially done)
rot_mat_time_inv = [0 for i in range(n_corr_shells)]
# Second, let's read the file containing the Hamiltonian in WF basis
# produced by Wannier90
for isp in range(n_spin):
# begin loop on isp
# build filename according to wannier90 conventions
if SP == 1:
mpi.report(
"Reading information for spin component n. %d" % isp)
hr_file = self.w90_seed + spin_w90name[isp] + '_hr.dat'
else:
hr_file = self.w90_seed + '_hr.dat'
# now grab the data from the H(R) file
mpi.report(
"The Hamiltonian in MLWF basis is extracted from %s ..." % hr_file)
nr, rvec, rdeg, nw, hamr = self.read_wannier90hr(hr_file)
# number of R vectors, their indices, their degeneracy, number of
# WFs, H(R)
mpi.report("... done: %d R vectors, %d WFs found" % (nr, nw))
if isp == 0:
# set or check some quantities that must be the same for both
# spins
self.nrpt = nr
# k-point grid: (if not defined before)
if kmesh_mode == -1:
# the size of the k-point mesh is determined from the
# largest R vector
nki = [2 * rvec[:, idir].max() + 1 for idir in range(3)]
# it will be the same as in the win only when nki is odd, because of the
# wannier90 convention: if we have nki k-points along the i-th direction,
# then we should get 2*(nki/2)+nki%2 R points along that
# direction
n_k, k_mesh, bz_weights = self.kmesh_build(nki)
self.n_k = n_k
self.k_mesh = k_mesh
# set the R vectors and their degeneracy
self.rvec = rvec
self.rdeg = rdeg
self.nwfs = nw
# check that the total number of WFs makes sense
if self.nwfs < dim_corr_shells:
mpi.report(
"ERROR: number of WFs in the file smaller than number of correlated orbitals!")
elif self.nwfs > dim_corr_shells:
# NOTE: correlated shells must appear before uncorrelated
# ones inside the file
mpi.report("Number of WFs larger than correlated orbitals:\n" +
"WFs from %d to %d treated as uncorrelated" % (dim_corr_shells + 1, self.nwfs))
else:
mpi.report(
"Number of WFs equal to number of correlated orbitals")
# we assume spin up and spin down always have same total number
# of WFs
n_orbitals = numpy.ones(
[self.n_k, n_spin], numpy.int) * self.nwfs
else:
# consistency check between the _up and _down file contents
if nr != self.nrpt:
mpi.report(
"Different number of R vectors for spin-up/spin-down!")
if nw != self.nwfs:
mpi.report(
"Different number of WFs for spin-up/spin-down!")
hamr_full.append(hamr)
# FIXME: when do we actually need deepcopy()?
# hamr_full.append(deepcopy(hamr))
for ir in range(nr):
# checks if the Hamiltonian is real (it should, if
# wannierisation worked fine)
if numpy.abs((hamr[ir].imag.max()).max()) > self._w90zero:
mpi.report(
"H(R) has large complex components at R %d" % ir)
# copy the R=0 block corresponding to the correlated shells
# into another variable (needed later for finding rot_mat)
if rvec[ir, 0] == 0 and rvec[ir, 1] == 0 and rvec[ir, 2] == 0:
ham_corr0 = hamr[ir][0:dim_corr_shells, 0:dim_corr_shells]
# checks if ham0 is Hermitian
if not numpy.allclose(ham_corr0.transpose().conjugate(), ham_corr0, atol=self._w90zero, rtol=1.e-9):
raise ValueError("H(R=0) matrix is not Hermitian!")
# find rot_mat symmetries by diagonalising the on-site Hamiltonian
# of the first spin
if isp == 0:
use_rotations, rot_mat = self.find_rot_mat(
n_corr_shells, corr_shells, shells_map, ham_corr0)
else:
# consistency check
use_rotations_, rot_mat_ = self.find_rot_mat(
n_corr_shells, corr_shells, shells_map, ham_corr0)
if (use_rotations and not use_rotations_):
mpi.report(
"Rotations cannot be used for spin component n. %d" % isp)
for icrsh in range(n_corr_shells):
if not numpy.allclose(rot_mat_[icrsh], rot_mat[icrsh], atol=self._w90zero, rtol=1.e-15):
mpi.report(
"Rotations for spin component n. %d do not match!" % isp)
# end loop on isp
mpi.report("The k-point grid has dimensions: %d, %d, %d" % tuple(nki))
# if calculations are spin-polarized, then renormalize k-point weights
if SP == 1:
bz_weights = 0.5 * bz_weights
# Third, compute the hoppings in reciprocal space
hopping = numpy.zeros([self.n_k, n_spin, numpy.max(
n_orbitals), numpy.max(n_orbitals)], numpy.complex_)
for isp in range(n_spin):
# make Fourier transform H(R) -> H(k) : it can be done one spin at
# a time
hamk = self.fourier_ham(self.nwfs, hamr_full[isp])
# copy the H(k) in the right place of hoppings... is there a better
# way to do this??
for ik in range(self.n_k):
#hopping[ik,isp,:,:] = deepcopy(hamk[ik][:,:])*energy_unit
hopping[ik, isp, :, :] = hamk[ik][:, :] * energy_unit
# Then, initialise the projectors
k_dep_projection = 0 # we always have the same number of WFs at each k-point
proj_mat = numpy.zeros([self.n_k, n_spin, n_corr_shells, max(
[crsh['dim'] for crsh in corr_shells]), numpy.max(n_orbitals)], numpy.complex_)
iorb = 0
# Projectors simply consist in identity matrix blocks selecting those MLWFs that
# correspond to the specific correlated shell indexed by icrsh.
# NOTE: we assume that the correlated orbitals appear at the beginning of the H(R)
# file and that the ordering of MLWFs matches the corr_shell info from
# the input.
for icrsh in range(n_corr_shells):
norb = corr_shells[icrsh]['dim']
proj_mat[:, :, icrsh, 0:norb, iorb:iorb +
norb] = numpy.identity(norb, numpy.complex_)
iorb += norb
# Finally, save all required data into the HDF archive:
with HDFArchive(self.hdf_file, 'a') as ar:
if not (self.dft_subgrp in ar):
ar.create_group(self.dft_subgrp)
# The subgroup containing the data. If it does not exist, it is
# created. If it exists, the data is overwritten!
things_to_save = ['energy_unit', 'n_k', 'k_dep_projection', 'SP', 'SO', 'charge_below', 'density_required',
'symm_op', 'n_shells', 'shells', 'n_corr_shells', 'corr_shells', 'use_rotations', 'rot_mat',
'rot_mat_time_inv', 'n_reps', 'dim_reps', 'T', 'n_orbitals', 'proj_mat', 'bz_weights', 'hopping',
'n_inequiv_shells', 'corr_to_inequiv', 'inequiv_to_corr']
for it in things_to_save:
ar[self.dft_subgrp][it] = locals()[it]
def read_wannier90hr(self, hr_filename="wannier_hr.dat"):
"""
Method for reading the seedname_hr.dat file produced by Wannier90 (http://wannier.org)
Parameters
----------
hr_filename : string
full name of the H(R) file produced by Wannier90 (usually seedname_hr.dat)
Returns
-------
nrpt : integer
number of R vectors found in the file
rvec_idx : numpy.array of integers
Miller indices of the R vectors
rvec_deg : numpy.array of floats
weight of the R vectors
num_wf : integer
number of Wannier functions found
h_of_r : list of numpy.array
= Hamilonian matrix elements in the Wannier basis
"""
# Read only from the master node
if not (mpi.is_master_node()):
return
try:
with open(hr_filename, "r") as hr_filedesc:
hr_data = hr_filedesc.readlines()
hr_filedesc.close()
except IOError:
mpi.report("The file %s could not be read!" % hr_filename)
mpi.report("Reading %s..." % hr_filename + hr_data[0])
try:
# reads number of Wannier functions per spin
num_wf = int(hr_data[1])
nrpt = int(hr_data[2])
except ValueError:
mpi.report("Could not read number of WFs or R vectors")
# allocate arrays to save the R vector indexes and degeneracies and the
# Hamiltonian
rvec_idx = numpy.zeros((nrpt, 3), dtype=int)
rvec_deg = numpy.zeros(nrpt, dtype=int)
h_of_r = [numpy.zeros((num_wf, num_wf), dtype=numpy.complex_)
for n in range(nrpt)]
# variable currpos points to the current line in the file
currpos = 2
try:
ir = 0
# read the degeneracy of the R vectors (needed for the Fourier
# transform)
while ir < nrpt:
currpos += 1
for x in hr_data[currpos].split():
if ir >= nrpt:
raise IndexError("wrong number of R vectors??")
rvec_deg[ir] = int(x)
ir += 1
# for each direct lattice vector R read the block of the
# Hamiltonian H(R)
for ir, jj, ii in product(range(nrpt), range(num_wf), range(num_wf)):
# advance one line, split the line into tokens
currpos += 1
cline = hr_data[currpos].split()
# check if the orbital indexes in the file make sense
if int(cline[3]) != ii + 1 or int(cline[4]) != jj + 1:
mpi.report(
"Inconsistent indices at %s%s of R n. %s" % (ii, jj, ir))
rcurr = numpy.array(
[int(cline[0]), int(cline[1]), int(cline[2])])
if ii == 0 and jj == 0:
rvec_idx[ir] = rcurr
rprec = rcurr
else:
# check if the vector indices are consistent
if not numpy.array_equal(rcurr, rprec):
mpi.report(
"Inconsistent indices for R vector n. %s" % ir)
# fill h_of_r with the matrix elements of the Hamiltonian
if not numpy.any(rcurr) and ii == jj:
h_of_r[ir][ii, jj] = complex(float(cline[5]) - self.fermi_energy, float(cline[6]))
else:
h_of_r[ir][ii, jj] = complex(float(cline[5]), float(cline[6]))
except ValueError:
mpi.report("Wrong data or structure in file %s" % hr_filename)
# return the data into variables
return nrpt, rvec_idx, rvec_deg, num_wf, h_of_r
def find_rot_mat(self, n_sh, sh_lst, sh_map, ham0):
"""
Method for finding the matrices that bring from local to global coordinate systems
(and viceversa), based on the eigenvalues of H(R=0)
Parameters
----------
n_sh : integer
number of shells
sh_lst : list of shells-type dictionaries
contains the shells (could be correlated or not)
sh_map : list of integers
mapping between shells
ham0 : numpy.array of floats
local Hamiltonian matrix elements
Returns
-------
istatus : integer
if 0, something failed in the construction of the matrices
rot_mat : list of numpy.array
rotation matrix for each of the shell
"""
# initialize the rotation matrices to identities
rot_mat = [numpy.identity(sh_lst[ish]['dim'], dtype=complex)
for ish in range(n_sh)]
istatus = 0
hs = ham0.shape
if hs[0] != hs[1] or hs[0] != sum([sh['dim'] for sh in sh_lst]):
mpi.report(
"find_rot_mat: wrong block structure of input Hamiltonian!")
istatus = 0
# this error will lead into troubles later... early return
return istatus, rot_mat
# TODO: better handling of degenerate eigenvalue case
eigval_lst = []
eigvec_lst = []
iwf = 0
# loop over shells
for ish in range(n_sh):
# nw = number of orbitals in this shell
nw = sh_lst[ish]["dim"]
# diagonalize the sub-block of H(0) corresponding to this shell
eigval, eigvec = numpy.linalg.eigh(
ham0[iwf:iwf + nw, iwf:iwf + nw])
# find the indices sorting the eigenvalues in ascending order
eigsrt = eigval[0:nw].argsort()
# order eigenvalues and eigenvectors and save in a list
eigval_lst.append(eigval[eigsrt])
eigvec_lst.append(eigvec[eigsrt])
iwf += nw
# TODO: better handling of degenerate eigenvalue case
if sh_map[ish] != ish: # issue warning only when there are equivalent shells
for i in range(nw):
for j in range(i + 1, nw):
if (abs(eigval[j] - eigval[i]) < self._w90zero):
mpi.report("WARNING: degenerate eigenvalue of H(0) detected for shell %d: " % (ish) +
"global-to-local transformation might not work!")
for ish in range(n_sh):
try:
# build rotation matrices by combining the unitary
# transformations that diagonalize H(0)
rot_mat[ish] = numpy.dot(eigvec_lst[ish], eigvec_lst[
sh_map[ish]].conjugate().transpose())
except ValueError:
mpi.report(
"Global-to-local rotation matrices cannot be constructed!")
istatus = 1
# check that eigenvalues are the same (within accuracy) for
# equivalent shells
if not numpy.allclose(eigval_lst[ish], eigval_lst[sh_map[ish]], atol=self._w90zero, rtol=1.e-15):
mpi.report(
"ERROR: eigenvalue mismatch between equivalent shells! %d" % ish)
eigval_diff = eigval_lst[ish] - eigval_lst[sh_map[ish]]
mpi.report("Eigenvalue difference: " + format(eigval_diff))
istatus = 0
# TODO: add additional consistency check on rot_mat matrices?
return istatus, rot_mat
def kmesh_build(self, msize=None, mmode=0):
"""
Method for the generation of the k-point mesh.
Right now it only supports the option for generating a full grid containing k=0,0,0.
Parameters
----------
msize : list of 3 integers
the dimensions of the mesh
mmode : integer
mesh generation mode (right now, only full grid available)
Returns
-------
nkpt : integer
total number of k-points in the mesh
k_mesh : numpy.array[nkpt,3] of floats
the coordinates of all k-points
wk : numpy.array[nkpt] of floats
the weight of each k-point
"""
if mmode != 0:
raise ValueError("Mesh generation mode not supported: %s" % mmode)
# a regular mesh including Gamma point
# total number of k-points
nkpt = msize[0] * msize[1] * msize[2]
kmesh = numpy.zeros((nkpt, 3), dtype=float)
ii = 0
for ix, iy, iz in product(range(msize[0]), range(msize[1]), range(msize[2])):
kmesh[ii, :] = [float(ix) / msize[0], float(iy) /
msize[1], float(iz) / msize[2]]
ii += 1
# weight is equal for all k-points because wannier90 uses uniform grid on whole BZ
# (normalization is always 1 and takes into account spin degeneracy)
wk = numpy.ones([nkpt], dtype=float) / float(nkpt)
return nkpt, kmesh, wk
def fourier_ham(self, norb, h_of_r):
"""
Method for obtaining H(k) from H(R) via Fourier transform
The R vectors and k-point mesh are read from global module variables
Parameters
----------
norb : integer
number of orbitals
h_of_r : list of numpy.array[norb,norb]
Hamiltonian H(R) in Wannier basis
Returns
-------
h_of_k : list of numpy.array[norb,norb]
transformed Hamiltonian H(k) in Wannier basis
"""
twopi = 2 * numpy.pi
h_of_k = [numpy.zeros((norb, norb), dtype=numpy.complex_)
for ik in range(self.n_k)]
ridx = numpy.array(range(self.nrpt))
for ik, ir in product(range(self.n_k), ridx):
rdotk = twopi * numpy.dot(self.k_mesh[ik], self.rvec[ir])
factor = (math.cos(rdotk) + 1j * math.sin(rdotk)) / \
float(self.rdeg[ir])
h_of_k[ik][:, :] += factor * h_of_r[ir][:, :]
return h_of_k