mirror of https://github.com/triqs/dft_tools
507 lines
20 KiB
Python
507 lines
20 KiB
Python
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################################################################################
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#
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# TRIQS: a Toolbox for Research in Interacting Quantum Systems
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#
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# Copyright (C) 2011 by M. Ferrero, O. Parcollet
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#
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# DFT tools: Copyright (C) 2011 by M. Aichhorn, L. Pourovskii, V. Vildosola
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#
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# PLOVasp: Copyright (C) 2015 by O. E. Peil
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#
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# TRIQS is free software: you can redistribute it and/or modify it under the
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# terms of the GNU General Public License as published by the Free Software
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# Foundation, either version 3 of the License, or (at your option) any later
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# version.
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#
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# TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY
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# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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# FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
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# details.
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#
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# You should have received a copy of the GNU General Public License along with
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# TRIQS. If not, see <http://www.gnu.org/licenses/>.
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#
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################################################################################
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r"""
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plovasp.proj_shell
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==================
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Storage and manipulation on projector shells.
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"""
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def issue_warning(message):
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"""
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Issues a warning.
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"""
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print()
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print(" !!! WARNING !!!: " + message)
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print()
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import itertools as it
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import numpy as np
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from . import atm
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np.set_printoptions(suppress=True)
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################################################################################
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################################################################################
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#
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# class ProjectorShell
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#
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################################################################################
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################################################################################
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class ProjectorShell:
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"""
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Container of projectors related to a specific shell.
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The constructor pre-selects a subset of projectors according to
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the shell parameters passed from the config-file.
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Parameters:
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- sh_pars (dict) : shell parameters from the config-file
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- proj_raw (numpy.array) : array of raw projectors
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"""
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def __init__(self, sh_pars, proj_raw, proj_params, kmesh, structure, nc_flag):
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self.lorb = sh_pars['lshell']
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self.ions = sh_pars['ions']
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self.user_index = sh_pars['user_index']
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self.corr = sh_pars['corr']
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self.ion_sort = [sh_pars['ion_sort']]
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self.nc_flag = nc_flag
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# try:
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# self.tmatrix = sh_pars['tmatrix']
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# except KeyError:
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# self.tmatrix = None
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self.lm1 = self.lorb**2
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self.lm2 = (self.lorb+1)**2
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self.nion = self.ions['nion']
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# Extract ion list and equivalence classes (ion sorts)
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self.ion_list = sorted(it.chain(*self.ions['ion_list']))
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if self.ion_sort[0] is None:
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self.ion_sort = []
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for ion in self.ion_list:
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for icl, eq_cl in enumerate(self.ions['ion_list']):
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if ion in eq_cl:
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self.ion_sort.append(icl + 1) # Enumerate classes starting from 1
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break
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self.ndim = self.extract_tmatrices(sh_pars)
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self.extract_projectors(proj_raw, proj_params, kmesh, structure)
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################################################################################
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#
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# extract_tmatrices
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#
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################################################################################
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def extract_tmatrices(self, sh_pars):
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"""
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Extracts and interprets transformation matrices provided by the
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config-parser.
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There are two relevant options in 'sh_pars':
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'tmatrix' : a transformation matrix applied to all ions in the shell
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'tmatrices': interpreted as a set of transformation matrices for each ion.
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If both of the options are present a warning is issued and 'tmatrices'
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supersedes 'tmatrix'.
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Flag 'self.do_transform' is introduced for the optimization purposes
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to avoid superfluous matrix multiplications.
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"""
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nion = self.nion
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nm = self.lm2 - self.lm1
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if 'tmatrices' in sh_pars:
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self.do_transform = True
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if 'tmatrix' in sh_pars:
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mess = "Both TRANSFORM and TRANSFILE are specified, TRANSFORM will be ignored."
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issue_warning(mess)
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raw_matrices = sh_pars['tmatrices']
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nrow, ncol = raw_matrices.shape
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assert nrow%nion == 0, "Number of rows in TRANSFILE must be divisible by the number of ions"
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assert ncol%nm == 0, "Number of columns in TRANSFILE must be divisible by the number of orbitals 2*l + 1"
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nr = nrow // nion
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nsize = ncol // nm
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assert nsize in (1, 2, 4), "Number of columns in TRANSFILE must be divisible by either 1, 2, or 4"
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#
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# Determine the spin-dimension and whether the matrices are real or complex
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#
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# if nsize == 1 or nsize == 2:
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# Matrices (either real or complex) are spin-independent
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# nls_dim = nm
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# if msize == 2:
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# is_complex = True
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# else:
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# is_complex = False
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# elif nsize = 4:
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# Matrices are complex and spin-dependent
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# nls_dim = 2 * nm
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# is_complex = True
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#
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is_complex = nsize > 1
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ns_dim = max(1, nsize // 2)
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# Dimension of the orbital subspace
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assert nr%ns_dim == 0, "Number of rows in TRANSFILE is not compatible with the spin dimension"
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ndim = nr // ns_dim
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self.tmatrices = np.zeros((nion, nr, nm * ns_dim), dtype=complex)
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if is_complex:
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raw_matrices = raw_matrices[:, ::2] + raw_matrices[:, 1::2] * 1j
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for io in range(nion):
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i1 = io * nr
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i2 = (io + 1) * nr
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self.tmatrices[io, :, :] = raw_matrices[i1:i2, :]
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return ndim
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if 'tmatrix' in sh_pars:
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self.do_transform = True
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raw_matrix = sh_pars['tmatrix']
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nrow, ncol = raw_matrix.shape
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assert ncol%nm == 0, "Number of columns in TRANSFORM must be divisible by the number of orbitals 2*l + 1"
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# Only spin-independent matrices are expected here
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nsize = ncol // nm
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assert nsize in (1, 2), "Number of columns in TRANSFORM must be divisible by either 1 or 2"
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is_complex = nsize > 1
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if is_complex:
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matrix = raw_matrix[:, ::2] + raw_matrix[:, 1::2] * 1j
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else:
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matrix = raw_matrix
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ndim = nrow
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self.tmatrices = np.zeros((nion, nrow, nm), dtype=complex)
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for io in range(nion):
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self.tmatrices[io, :, :] = raw_matrix
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return ndim
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# If no transformation matrices are provided define a default one
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self.do_transform = False
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ns_dim = 2 if self.nc_flag else 1
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ndim = nm * ns_dim
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# We still need the matrices for the output
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self.tmatrices = np.zeros((nion, ndim, ndim), dtype=complex)
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for io in range(nion):
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self.tmatrices[io, :, :] = np.identity(ndim, dtype=complex)
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return ndim
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################################################################################
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#
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# extract_projectors
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#
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################################################################################
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def extract_projectors(self, proj_raw, proj_params, kmesh, structure):
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"""
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Extracts projectors for the given shell.
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Projectors are selected from the raw-projector array 'proj_raw'
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according to the shell parameters.
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If necessary the projectors are transformed usin 'self.tmatrices'.
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"""
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assert self.nc_flag == False, "Non-collinear case is not implemented"
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# nion = len(self.ion_list)
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nion = self.nion
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nlm = self.lm2 - self.lm1
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_, ns, nk, nb = proj_raw.shape
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if self.do_transform:
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# TODO: implement a non-collinear case
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# for a non-collinear case 'ndim' is 'ns * nm'
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ndim = self.tmatrices.shape[1]
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self.proj_arr = np.zeros((nion, ns, nk, ndim, nb), dtype=complex)
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for ik in range(nk):
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kp = kmesh['kpoints'][ik]
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for io, ion in enumerate(self.ion_list):
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proj_k = np.zeros((ns, nlm, nb), dtype=complex)
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qcoord = structure['qcoords'][ion]
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# kphase = np.exp(-2.0j * np.pi * np.dot(kp, qcoord))
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# kphase = 1.0
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for m in range(nlm):
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# Here we search for the index of the projector with the given isite/l/m indices
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for ip, par in enumerate(proj_params):
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if par['isite'] - 1 == ion and par['l'] == self.lorb and par['m'] == m:
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proj_k[:, m, :] = proj_raw[ip, :, ik, :] #* kphase
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break
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for isp in range(ns):
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self.proj_arr[io, isp, ik, :, :] = np.dot(self.tmatrices[io, :, :], proj_k[isp, :, :])
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else:
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# No transformation: just copy the projectors as they are
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self.proj_arr = np.zeros((nion, ns, nk, nlm, nb), dtype=complex)
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for io, ion in enumerate(self.ion_list):
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qcoord = structure['qcoords'][ion]
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for m in range(nlm):
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# Here we search for the index of the projector with the given isite/l/m indices
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for ip, par in enumerate(proj_params):
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if par['isite'] - 1 == ion and par['l'] == self.lorb and par['m'] == m:
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self.proj_arr[io, :, :, m, :] = proj_raw[ip, :, :, :]
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# for ik in range(nk):
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# kp = kmesh['kpoints'][ik]
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## kphase = np.exp(-2.0j * np.pi * np.dot(kp, qcoord))
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# kphase = 1.0
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# self.proj_arr[io, :, :, m, :] = proj_raw[ip, :, :, :] # * kphase
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break
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################################################################################
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#
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# select_projectors
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#
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################################################################################
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def select_projectors(self, ib_win, ib_min, ib_max):
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"""
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Selects a subset of projectors corresponding to a given energy window.
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"""
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self.ib_win = ib_win
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self.ib_min = ib_min
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self.ib_max = ib_max
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nb_max = ib_max - ib_min + 1
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# Set the dimensions of the array
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nion, ns, nk, nlm, nbtot = self.proj_arr.shape
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# !!! Note that the order of the two last indices is different !!!
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self.proj_win = np.zeros((nion, ns, nk, nlm, nb_max), dtype=complex)
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# Select projectors for a given energy window
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ns_band = self.ib_win.shape[1]
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for isp in range(ns):
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for ik in range(nk):
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# TODO: for non-collinear case something else should be done here
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is_b = min(isp, ns_band)
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ib1 = self.ib_win[ik, is_b, 0]
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ib2 = self.ib_win[ik, is_b, 1] + 1
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ib_win = ib2 - ib1
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self.proj_win[:, isp, ik, :, :ib_win] = self.proj_arr[:, isp, ik, :, ib1:ib2]
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################################################################################
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#
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# density_matrix
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#
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################################################################################
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def density_matrix(self, el_struct, site_diag=True, spin_diag=True):
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"""
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Returns occupation matrix/matrices for the shell.
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"""
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nion, ns, nk, nlm, nbtot = self.proj_win.shape
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# assert site_diag, "site_diag = False is not implemented"
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assert spin_diag, "spin_diag = False is not implemented"
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if site_diag:
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occ_mats = np.zeros((ns, nion, nlm, nlm), dtype=float)
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overlaps = np.zeros((ns, nion, nlm, nlm), dtype=float)
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else:
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ndim = nion * nlm
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occ_mats = np.zeros((ns, 1, ndim, ndim), dtype=float)
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overlaps = np.zeros((ns, 1, ndim, ndim), dtype=float)
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# self.proj_win = np.zeros((nion, ns, nk, nlm, nb_max), dtype=complex)
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kweights = el_struct.kmesh['kweights']
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occnums = el_struct.ferw
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ib1 = self.ib_min
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ib2 = self.ib_max + 1
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if site_diag:
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for isp in range(ns):
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for ik, weight, occ in zip(it.count(), kweights, occnums[isp, :, :]):
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for io in range(nion):
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proj_k = self.proj_win[io, isp, ik, ...]
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occ_mats[isp, io, :, :] += np.dot(proj_k * occ[ib1:ib2],
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proj_k.conj().T).real * weight
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overlaps[isp, io, :, :] += np.dot(proj_k,
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proj_k.conj().T).real * weight
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else:
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proj_k = np.zeros((ndim, nbtot), dtype=complex)
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for isp in range(ns):
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for ik, weight, occ in zip(it.count(), kweights, occnums[isp, :, :]):
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for io in range(nion):
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i1 = io * nlm
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i2 = (io + 1) * nlm
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proj_k[i1:i2, :] = self.proj_win[io, isp, ik, ...]
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occ_mats[isp, 0, :, :] += np.dot(proj_k * occ[ib1:ib2],
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proj_k.conj().T).real * weight
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overlaps[isp, 0, :, :] += np.dot(proj_k,
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proj_k.conj().T).real * weight
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# if not symops is None:
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# occ_mats = symmetrize_matrix_set(occ_mats, symops, ions, perm_map)
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return occ_mats, overlaps
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################################################################################
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#
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# local_hamiltonian
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#
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################################################################################
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def local_hamiltonian(self, el_struct, site_diag=True, spin_diag=True):
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"""
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Returns occupation matrix/matrices for the shell.
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"""
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nion, ns, nk, nlm, nbtot = self.proj_win.shape
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assert site_diag, "site_diag = False is not implemented"
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assert spin_diag, "spin_diag = False is not implemented"
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loc_ham = np.zeros((ns, nion, nlm, nlm), dtype=complex)
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# self.proj_win = np.zeros((nion, ns, nk, nlm, nb_max), dtype=complex)
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kweights = el_struct.kmesh['kweights']
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occnums = el_struct.ferw
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ib1 = self.ib_min
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ib2 = self.ib_max + 1
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for isp in range(ns):
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for ik, weight, occ, eigk in zip(it.count(), kweights, occnums[isp, :, :],
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el_struct.eigvals[:, ib1:ib2, isp]):
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for io in range(nion):
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proj_k = self.proj_win[io, isp, ik, ...]
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loc_ham[isp, io, :, :] += np.dot(proj_k * (eigk - el_struct.efermi),
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proj_k.conj().T) * weight
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# if not symops is None:
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# occ_mats = symmetrize_matrix_set(occ_mats, symops, ions, perm_map)
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return loc_ham
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################################################################################
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#
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# density_of_states
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#
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################################################################################
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def density_of_states(self, el_struct, emesh):
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"""
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Returns projected DOS for the shell.
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"""
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nion, ns, nk, nlm, nbtot = self.proj_win.shape
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# There is a problem with data storage structure of projectors that will
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# make life more complicated. The problem is that band-indices of projectors
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# for different k-points do not match because we store 'nb_max' values starting
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# from 0.
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nb_max = self.ib_max - self.ib_min + 1
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ns_band = self.ib_win.shape[1]
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ne = len(emesh)
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dos = np.zeros((ne, ns, nion, nlm))
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w_k = np.zeros((nk, nb_max, ns, nion, nlm), dtype=complex)
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for isp in range(ns):
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for ik in range(nk):
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is_b = min(isp, ns_band)
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ib1 = self.ib_win[ik, is_b, 0]
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ib2 = self.ib_win[ik, is_b, 1] + 1
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for ib_g in range(ib1, ib2):
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for io in range(nion):
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# Note the difference between 'ib' and 'ibn':
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# 'ib' counts from 0 to 'nb_k - 1'
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# 'ibn' counts from 'ib1 - ib_min' to 'ib2 - ib_min'
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ib = ib_g - ib1
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ibn = ib_g - self.ib_min
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proj_k = self.proj_win[io, isp, ik, :, ib]
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w_k[ik, ib, isp, io, :] = proj_k * proj_k.conj()
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# eigv_ef = el_struct.eigvals[ik, ib, isp] - el_struct.efermi
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itt = el_struct.kmesh['itet'].T
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# k-indices are starting from 0 in Python
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itt[1:, :] -= 1
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for isp in range(ns):
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for ib, eigk in enumerate(el_struct.eigvals[:, self.ib_min:self.ib_max+1, isp].T):
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for ie, e in enumerate(emesh):
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eigk_ef = eigk - el_struct.efermi
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cti = atm.dos_tetra_weights_3d(eigk_ef, e, itt)
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for im in range(nlm):
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for io in range(nion):
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dos[ie, isp, io, im] += np.sum((cti * w_k[itt[1:, :], ib, isp, io, im].real).sum(0) * itt[0, :])
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dos *= 2 * el_struct.kmesh['volt']
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# for isp in range(ns):
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# for ik, weight, occ in zip(it.count(), kweights, occnums[isp, :, :]):
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# for io in range(nion):
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# proj_k = self.proj_win[isp, io, ik, ...]
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# occ_mats[isp, io, :, :] += np.dot(proj_k * occ[ib1:ib2],
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# proj_k.conj().T).real * weight
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# overlaps[isp, io, :, :] += np.dot(proj_k,
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# proj_k.conj().T).real * weight
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# if not symops is None:
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# occ_mats = symmetrize_matrix_set(occ_mats, symops, ions, perm_map)
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return dos
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################################################################################
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################################################################################
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#
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# class ProjectorShell
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#
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################################################################################
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################################################################################
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class ComplementShell(ProjectorShell):
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"""
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Container of projectors related to a complement shell.
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Parameters:
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- sh_pars (dict) : shell parameters from the config-file
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- proj_compl (numpy.array) : array of complement projectors
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"""
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def __init__(self, sh_pars, proj_compl, nc_flag):
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self.lorb = sh_pars['lshell']
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self.ions = sh_pars['ions']
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self.user_index = sh_pars['user_index']
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self.corr = sh_pars['corr']
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self.nc_flag = nc_flag
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self.ib_min = sh_pars['ib_min']
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self.ib_max = sh_pars['ib_max']
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self.ib_win = sh_pars['ib_win']
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#self.lm1 = self.lorb**2
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#self.lm2 = (self.lorb+1)**2
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self.nion = self.ions['nion']
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# Extract ion list and equivalence classes (ion sorts)
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self.ion_list = sorted(it.chain(*self.ions['ion_list']))
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self.ion_sort = []
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for ion in self.ion_list:
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for icl, eq_cl in enumerate(self.ions['ion_list']):
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if ion in eq_cl:
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self.ion_sort.append(icl + 1) # Enumerate classes starting from 1
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break
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self.ndim = proj_compl.shape[3]
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self.proj_win = proj_compl
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def extract_tmatrices(self, sh_pars):
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raise Exception('not implemented')
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def local_hamiltonian(self, el_struct, site_diag=True, spin_diag=True):
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raise Exception('not implemented')
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def density_matrix(self, el_struct, site_diag=True, spin_diag=True):
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raise Exception('not implemented')
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#def density_of_states(self, el_struct, emesh):
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# raise Exception('not implemented')
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