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dft_tools/python/vasp/plotools.py
Oleg E. Peil be21838e30 Modified ProjectedShell to conform to new projectors
The new projector input requires a different approach of selecting
the projectors for each shell. Specifically, for each site/orbital
index defined for a given shell one has to look for the corresponding
input projector (from PROJCAR).

Also, small fixes were required to make 'ferw' array index order
consistent with what is expected in ProjectorShell. This order might
eventually be modified.
2015-10-15 13:26:48 +02:00

638 lines
22 KiB
Python

import itertools as it
import numpy as np
# 'simplejson' is supposed to be faster than 'json' in stdlib.
try:
import simplejson as json
except ImportError:
import json
class Projector:
"""
Class describing a local-orbital projector.
"""
def __init__(self, matrix, ib1=1, ib2=None, nion=1):
self.p_matrix = matrix.astype(np.complex128)
self.norb, self.nb = matrix.shape
self.nion = nion
self.ib1 = ib1 - 1
if not ib2 is None:
self.ib2 = ib2 - 1
else:
self.ib2 = self.nb - 1
def project_up(self, mat):
return np.dot(self.p_matrix.conj().T, np.dot(mat, self.p_matrix))
def project_down(self, mat):
assert mat.shape == (self.nb, self.nb), " Matrix must match projector in size"
return np.dot(self.p_matrix, np.dot(mat, self.p_matrix.conj().T))
def orthogonalize(self):
"""
Orthogonalizes a projector.
Returns an overlap matrix and its eigenvalues for initial projectors.
"""
self.p_matrix, overlap, over_eig = orthogonalize_projector(self.p_matrix)
return (overlap, over_eig)
################################################################################
#
# orthogonalize_projector_matrix()
#
################################################################################
def orthogonalize_projector_matrix(p_matrix):
"""
Orthogonalizes a projector defined by a rectangular matrix `p_matrix`.
Parameters
----------
p_matrix (numpy.array[complex]) : matrix `Nm x Nb`, where `Nm` is
the number of orbitals, `Nb` number of bands
Returns
-------
Orthogonalized projector matrix, initial overlap matrix and its eigenvalues.
"""
# Overlap matrix O_{m m'} = \sum_{v} P_{m v} P^{*}_{v m'}
overlap = np.dot(p_matrix, p_matrix.conj().T)
# Calculate [O^{-1/2}]_{m m'}
eig, eigv = np.linalg.eigh(overlap)
assert np.all(eig > 0.0), ("Negative eigenvalues of the overlap matrix:"
"projectors are ill-defined")
sqrt_eig = np.diag(1.0 / np.sqrt(eig))
shalf = np.dot(eigv, np.dot(sqrt_eig, eigv.conj().T))
# Apply \tilde{P}_{m v} = \sum_{m'} [O^{-1/2}]_{m m'} P_{m' v}
p_ortho = np.dot(shalf, p_matrix)
return (p_ortho, overlap, eig)
################################################################################
# check_data_consistency()
################################################################################
def check_data_consistency(pars, el_struct):
"""
Check the consistency of the VASP data.
"""
# Check that ions inside each shell are of the same sort
for sh in pars.shells:
assert max(sh['ion_list']) <= el_struct.natom, "Site index in the projected shell exceeds the number of ions in the structure"
sorts = set([el_struct.type_of_ion[io] for io in sh['ion_list']])
assert len(sorts) == 1, "Each projected shell must contain only ions of the same sort"
# Check that ion and orbital lists in shells match those of projectors
ion_list = sh['ion_list']
lshell = sh['lshell']
for ion in ion_list:
for par in el_struct.proj_params:
if par['isite'] - 1 == ion and par['l'] == lshell:
break
else:
errmsg = "Projector for isite = %s, l = %s does not match PROJCAR"%(ion + 1, lshell)
raise Exception(errmsg)
################################################################################
# select_bands()
################################################################################
def select_bands(eigvals, emin, emax):
"""
Select a subset of bands lying within a given energy window.
The band energies are assumed to be sorted in an ascending order.
Parameters
----------
eigvals (numpy.array) : all eigenvalues
emin, emax (float) : energy window
Returns
-------
ib_win, nb_min, nb_max :
"""
# Sanity check
if emin > eigvals.max() or emax < eigvals.min():
raise Exception("Energy window does not overlap with the band structure")
nk, nband, ns_band = eigvals.shape
ib_win = np.zeros((nk, ns_band, 2), dtype=np.int32)
nb_min = 10000000
nb_max = 0
for isp in xrange(ns_band):
for ik in xrange(nk):
for ib in xrange(nband):
en = eigvals[ik, ib, isp]
if en >= emin:
break
ib1 = ib
for ib in xrange(ib1, nband):
en = eigvals[ik, ib, isp]
if en > emax:
break
else:
# If we reached the last band add 1 to get the correct bound
ib += 1
ib2 = ib - 1
ib_win[ik, isp, 0] = ib1
ib_win[ik, isp, 1] = ib2
nb_min = min(nb_min, ib1)
nb_max = max(nb_max, ib2)
return ib_win, nb_min, nb_max
################################################################################
################################################################################
#
# class ProjectorGroup
#
################################################################################
################################################################################
class ProjectorGroup:
"""
Container of projectors defined within a certain energy window.
The constructor selects a subset of projectors according to
the parameters from the config-file (passed in `pars`).
Parameters:
- gr_pars (dict) : group parameters from the config-file
- shells ([ProjectorShell]) : array of ProjectorShell objects
- eigvals (numpy.array) : array of KS eigenvalues
"""
def __init__(self, gr_pars, shells, eigvals, ferw):
"""
Constructor
"""
self.emin = gr_pars['emin']
self.emax = gr_pars['emax']
self.ishells = gr_pars['shells']
self.ortho = gr_pars['normalize']
self.normion = gr_pars['normion']
self.shells = shells
# Determine the minimum and maximum band numbers
ib_win, nb_min, nb_max = select_bands(eigvals, self.emin, self.emax)
self.ib_win = ib_win
self.nb_min = nb_min
self.nb_max = nb_max
# Select projectors within the energy window
for ish in self.ishells:
shell = self.shells[ish]
shell.select_projectors(ib_win, nb_min, nb_max)
################################################################################
#
# nelect_window
#
################################################################################
def nelect_window(self, el_struct):
"""
Determines the total number of electrons within the window.
"""
self.nelect = 0
nk, ns_band, _ = self.ib_win.shape
rspin = 2.0 if ns_band == 1 else 1.0
for isp in xrange(ns_band):
for ik in xrange(nk):
ib1 = self.ib_win[ik, isp, 0]
ib2 = self.ib_win[ik, isp, 1]
occ = el_struct.ferw[isp, ik, ib1:ib2]
kwght = el_struct.kmesh['kweights'][ik]
self.nelect += occ.sum() * kwght * rspin
return self.nelect
################################################################################
#
# orthogonalize
#
################################################################################
def orthogonalize(self):
"""
Orthogonalize a group of projectors.
"""
# Quick exit if no normalization is requested
if not self.ortho:
return
# TODO: add the case of 'normion = True'
assert not self.normion, "'NORMION = True' is not yet implemented"
# Determine the dimension of the projector matrix
# and map the blocks to the big matrix
i1_bl = 0
bl_map = [{} for ish in self.ishells]
for ish in self.ishells:
_shell = self.shells[ish]
nion, ns, nk, nlm, nb_max = _shell.proj_win.shape
bmat_bl = [] # indices corresponding to a big block matrix
for ion in xrange(nion):
i2_bl = i1_bl + nlm
bmat_bl.append((i1_bl, i2_bl))
i1_bl = i2_bl
bl_map[ish]['bmat_blocks'] = bmat_bl
ndim = i2_bl
p_mat = np.zeros((ndim, nb_max), dtype=np.complex128)
for isp in xrange(ns):
for ik in xrange(nk):
nb = self.ib_win[ik, isp, 1] - self.ib_win[ik, isp, 0] + 1
# Combine all projectors of the group to one block projector
for ish in self.ishells:
shell = self.shells[ish]
blocks = bl_map[ish]['bmat_blocks']
for ion in xrange(nion):
i1, i2 = blocks[ion]
p_mat[i1:i2, :nb] = shell.proj_win[ion, isp, ik, :nlm, :nb]
# Now orthogonalize the obtained block projector
p_orth, overl, eig = orthogonalize_projector_matrix(p_mat)
# Distribute back projectors in the same order
for ish in self.ishells:
shell = self.shells[ish]
blocks = bl_map[ish]['bmat_blocks']
for ion in xrange(nion):
i1, i2 = blocks[ion]
shell.proj_win[ion, isp, ik, :nlm, :nb] = p_mat[i1:i2, :nb]
################################################################################
################################################################################
#
# class ProjectorShell
#
################################################################################
################################################################################
class ProjectorShell:
"""
Container of projectors related to a specific shell.
The constructor pre-selects a subset of projectors according to
the shell parameters passed from the config-file.
Parameters:
- sh_pars (dict) : shell parameters from the config-file
- proj_raw (numpy.array) : array of raw projectors
"""
def __init__(self, sh_pars, proj_raw, proj_params):
self.lorb = sh_pars['lshell']
self.ion_list = sh_pars['ion_list']
self.user_index = sh_pars['user_index']
try:
self.tmatrix = sh_pars['tmatrix']
except KeyError:
self.tmatrix = None
self.lm1 = self.lorb**2
self.lm2 = (self.lorb+1)**2
if self.tmatrix is None:
self.ndim = self.lm2 - self.lm1
else:
# TODO: generalize this to a tmatrix for every ion
self.ndim = self.tmatrix.shape[0]
# Pre-select a subset of projectors (this should be an array view => no memory is wasted)
# !!! This sucks but I have to change the order of 'ib' and 'ilm' indices here
# This should perhaps be done right after the projector array is read from PLOCAR
# self.proj_arr = proj_raw[self.ion_list, :, :, :, self.lm1:self.lm2].transpose((0, 1, 2, 4, 3))
# We want to select projectors from 'proj_raw' and form an array
# self.proj_arr[nion, ns, nk, nlm, nb]
# TODO: think of a smart way of copying the selected projectors
# perhaps, by redesigning slightly the structure of 'proj_arr' and 'proj_win'
# or by storing only a mapping between site/orbitals and indices of 'proj_raw'
# iproj_l = []
nion = len(self.ion_list)
nlm = self.lm2 - self.lm1
_, ns, nk, nb = proj_raw.shape
self.proj_arr = np.zeros((nion, ns, nk, nlm, nb), dtype=np.complex128)
for io, ion in enumerate(self.ion_list):
for m in xrange(nlm):
# Here we search for the index of the projector with the given isite/l/m indices
for ip, par in enumerate(proj_params):
if par['isite'] - 1 == ion and par['l'] == self.lorb and par['m'] == m:
# iproj_l.append(ip)
self.proj_arr[io, :, :, m, :] = proj_raw[ip, :, :, :]
break
# self.proj_arr = proj_raw[iproj_l, :, :, :].transpose((1, 2, 0, 3))
################################################################################
#
# select_projectors
#
################################################################################
def select_projectors(self, ib_win, nb_min, nb_max):
"""
Selects a subset of projectors corresponding to a given energy window.
"""
self.ib_win = ib_win
self.nb_min = nb_min
self.nb_max = nb_max
# Set the dimensions of the array
nb_win = self.nb_max - self.nb_min + 1
nion, ns, nk, nlm, nbtot = self.proj_arr.shape
# !!! Note that the order of the two last indices is different !!!
self.proj_win = np.zeros((nion, ns, nk, nlm, nb_win), dtype=np.complex128)
# Select projectors for a given energy window
ns_band = self.ib_win.shape[1]
for isp in xrange(ns):
for ik in xrange(nk):
# TODO: for non-collinear case something else should be done here
is_b = min(isp, ns_band)
ib1 = self.ib_win[ik, is_b, 0]
ib2 = self.ib_win[ik, is_b, 1] + 1
ib1_win = ib1 - self.nb_min
ib2_win = ib2 - self.nb_min
self.proj_win[:, isp, ik, :, ib1_win:ib2_win] = self.proj_arr[:, isp, ik, :, ib1:ib2]
################################################################################
#
# select_projectors
#
################################################################################
def density_matrix(self, el_struct, site_diag=True, spin_diag=True):
"""
Returns occupation matrix/matrices for the shell.
"""
nion, ns, nk, nlm, nbtot = self.proj_win.shape
assert site_diag, "site_diag = False is not implemented"
assert spin_diag, "spin_diag = False is not implemented"
occ_mats = np.zeros((ns, nion, nlm, nlm), dtype=np.float64)
kweights = el_struct.kmesh['kweights']
occnums = el_struct.ferw
ib1 = self.nb_min
ib2 = self.nb_max + 1
for isp in xrange(ns):
for ik, weight, occ in it.izip(it.count(), kweights, occnums[isp, :, :]):
for io in xrange(nion):
proj_k = self.proj_win[isp, io, ik, ...]
occ_mats[isp, io, :, :] += np.dot(proj_k * occ[ib1:ib2],
proj_k.conj().T).real * weight
# if not symops is None:
# occ_mats = symmetrize_matrix_set(occ_mats, symops, ions, perm_map)
return occ_mats
################################################################################
#
# generate_plo()
#
################################################################################
def generate_plo(conf_pars, el_struct):
"""
Parameters
----------
conf_pars (dict) : dictionary of input parameters (from conf-file)
el_struct : ElectronicStructure object
"""
check_data_consistency(conf_pars, el_struct)
proj_raw = el_struct.proj_raw
try:
efermi = conf_pars.general['efermi']
except (KeyError, AttributeError):
efermi = el_struct.efermi
# eigvals(nktot, nband, ispin) are defined with respect to the Fermi level
eigvals = el_struct.eigvals - efermi
pshells = []
for sh_par in conf_pars.shells:
pshells.append(ProjectorShell(sh_par, proj_raw, el_struct.proj_params))
pgroups = []
for gr_par in conf_pars.groups:
pgroup = ProjectorGroup(gr_par, pshells, eigvals, el_struct.ferw)
# pgroup.orthogonalize()
pgroups.append(pgroup)
return pshells, pgroups
# TODO: k-points with weights should be stored once and for all
################################################################################
#
# kpoints_output
#
################################################################################
def kpoints_output(basename, el_struct):
"""
Outputs k-point data into a text file.
"""
kmesh = el_struct.kmesh
fname = basename + '.kpoints'
with open(fname, 'wt') as f:
f.write("# Number of k-points: nktot\n")
nktot = kmesh['nktot']
f.write("%i\n"%(nktot))
# TODO: add the output of reciprocal lattice vectors
f.write("# List of k-points with weights\n")
for ik in xrange(nktot):
kx, ky, kz = kmesh['kpoints'][ik, :]
kwght = kmesh['kweights'][ik]
f.write("%15.10f%15.10f%15.10f%20.10f\n"%(kx, ky, kz, kwght))
# Check if there are tetrahedra defined and if they are, output them
try:
ntet = kmesh['ntet']
volt = kmesh['volt']
f.write("\n# Number of tetrahedra and volume: ntet, volt\n")
f.write("%i %s\n"%(ntet, volt))
f.write("# List of tetrahedra: imult, ik1, ..., ik4\n")
for it in xrange(ntet):
f.write(' '.join(map("{0:d}".format, *kmesh['itet'][it, :])) + '\n')
except KeyError:
pass
################################################################################
#
# ctrl_output
#
################################################################################
def ctrl_output(conf_pars, el_struct, ng):
"""
Outputs a ctrl-file.
"""
ctrl_fname = conf_pars.general['basename'] + '.ctrl'
head_dict = {}
# TODO: Add output of tetrahedra
# Construct the header dictionary
head_dict['ngroups'] = ng
head_dict['nk'] = el_struct.kmesh['nktot']
head_dict['ns'] = el_struct.nspin
head_dict['nc_flag'] = 1 if el_struct.nc_flag else 0
# head_dict['efermi'] = conf_pars.general['efermi'] # We probably don't need Efermi
header = json.dumps(head_dict, indent=4, separators=(',', ': '))
print " Storing ctrl-file..."
with open(ctrl_fname, 'wt') as f:
f.write(header + "\n")
f.write("#END OF HEADER\n")
f.write("# k-points and weights\n")
labels = ['kx', 'ky', 'kz', 'kweight']
out = "".join(map(lambda s: s.center(15), labels))
f.write("#" + out + "\n")
for ik, kp in enumerate(el_struct.kmesh['kpoints']):
tmp1 = "".join(map("{0:15.10f}".format, kp))
out = tmp1 + "{0:16.10f}".format(el_struct.kmesh['kweights'][ik])
f.write(out + "\n")
################################################################################
#
# plo_output
#
################################################################################
def plo_output(conf_pars, el_struct, pshells, pgroups):
"""
Outputs PLO groups into text files.
Filenames are defined by <basename> that is passed from config-file.
All necessary general parameters are stored in a file '<basename>.ctrl'.
Each group is stored in a '<basename>.plog<Ng>' file. The format is the
following:
# Energy window: emin, emax
ib_min, ib_max
nelect
# Eigenvalues
isp, ik1, kx, ky, kz, kweight
ib1, ib2
eig1
eig2
...
eigN
ik2, kx, ky, kz, kweight
...
# Projected shells
Nshells
# Shells: <shell indices>
# Shell <1>
Shell 1
ndim
# complex arrays: plo(ns, nion, ndim, nb)
...
# Shells: <shell indices>
# Shell <2>
Shell 2
...
"""
for ig, pgroup in enumerate(pgroups):
plo_fname = conf_pars.general['basename'] + '.pg%i'%(ig + 1)
print " Storing PLO-group file '%s'..."%(plo_fname)
head_dict = {}
head_dict['ewindow'] = (pgroup.emin, pgroup.emax)
head_dict['nb_max'] = pgroup.nb_max
# Number of electrons within the window
head_dict['nelect'] = pgroup.nelect_window(el_struct)
print " Density within window:", head_dict['nelect']
head_shells = []
for ish in pgroup.ishells:
shell = pgroup.shells[ish]
sh_dict = {}
sh_dict['shell_index'] = ish
sh_dict['lorb'] = shell.lorb
sh_dict['ndim'] = shell.ndim
# Convert ion indices from the internal representation (starting from 0)
# to conventional VASP representation (starting from 1)
ion_output = [io + 1 for io in shell.ion_list]
sh_dict['ion_list'] = ion_output
sh_dict['ion_sort'] = el_struct.type_of_ion[shell.ion_list[0]]
# TODO: add the output of transformation matrices
head_shells.append(sh_dict)
head_dict['shells'] = head_shells
header = json.dumps(head_dict, indent=4, separators=(',', ': '))
with open(plo_fname, 'wt') as f:
f.write(header + "\n")
f.write("#END OF HEADER\n")
# Eigenvalues within the window
f.write("# Eigenvalues within the energy window: %s, %s\n"%(pgroup.emin, pgroup.emax))
nk, nband, ns_band = el_struct.eigvals.shape
for isp in xrange(ns_band):
f.write("# is = %i\n"%(isp + 1))
for ik in xrange(nk):
ib1, ib2 = pgroup.ib_win[ik, isp, 0], pgroup.ib_win[ik, isp, 1]
f.write(" %i %i\n"%(ib1, ib2))
for ib in xrange(ib1, ib2 + 1):
f.write("%15.7f\n"%(el_struct.eigvals[ik, ib, isp]))
# Projected shells
f.write("# Projected shells\n")
f.write("# Shells: %s\n"%(pgroup.ishells))
for ish in pgroup.ishells:
shell = pgroup.shells[ish]
f.write("# Shell %i\n"%(ish))
nion, ns, nk, nlm, nb = shell.proj_win.shape
for isp in xrange(ns):
f.write("# is = %i\n"%(isp + 1))
for ik in xrange(nk):
f.write("# ik = %i\n"%(ik + 1))
for ion in xrange(nion):
for ilm in xrange(nlm):
ib1, ib2 = pgroup.ib_win[ik, isp, 0], pgroup.ib_win[ik, isp, 1]
ib1_win = ib1 - shell.nb_min
ib2_win = ib2 - shell.nb_min
for ib in xrange(ib1_win, ib2_win + 1):
p = shell.proj_win[ion, isp, ik, ilm, ib]
f.write("{0:16.10f}{1:16.10f}\n".format(p.real, p.imag))
f.write("\n")
################################################################################
#
# output_as_text
#
################################################################################
def output_as_text(pars, el_struct, pshells, pgroups):
"""
Output all information necessary for the converter as text files.
"""
ctrl_output(pars, el_struct, len(pgroups))
plo_output(pars, el_struct, pshells, pgroups)