mirror of
https://github.com/triqs/dft_tools
synced 2025-01-10 21:18:22 +01:00
db8a7e543e
In the (rare) case that one has multiple shells with different number of orbitals (e.g. p-d-systems) the old code crashed when converting GFs from the second shell as matrix dimensions were not fitting (the tmp matrix was always created for the first shell).
1202 lines
47 KiB
Python
1202 lines
47 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) 2018 by G. J. Kraberger
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# Copyright (C) 2018 by Simons Foundation
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# Authors: G. J. Kraberger, O. Parcollet
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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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import copy
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import numpy as np
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from triqs.gf import GfImFreq, BlockGf
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from ast import literal_eval
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import triqs.utility.mpi as mpi
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from warnings import warn
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from collections import defaultdict
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class BlockStructure(object):
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""" Contains information about the Green function structure.
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This class contains information about the structure of the solver
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and sumk Green functions and the mapping between them.
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Parameters
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----------
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gf_struct_sumk : list of list of tuple
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gf_struct_sumk[ish][idx] = (block_name,list of indices in block)
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for correlated shell ish; idx is just a counter in the list
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gf_struct_solver : list of dict
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gf_struct_solver[ish][block] = list of indices in that block
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for *inequivalent* correlated shell ish
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solver_to_sumk : list of dict
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solver_to_sumk[ish][(from_block,from_idx)] = (to_block,to_idx)
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maps from the solver block and index to the sumk block and index
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for *inequivalent* correlated shell ish
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sumk_to_solver : list of dict
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sumk_to_solver[ish][(from_block,from_idx)] = (to_block,to_idx)
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maps from the sumk block and index to the solver block and index
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for *inequivalent* correlated shell ish
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solver_to_sumk_block : list of dict
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solver_to_sumk_block[ish][from_block] = to_block
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maps from the solver block to the sumk block
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for *inequivalent* correlated shell ish
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deg_shells : list of lists of lists OR list of lists of dicts
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In the simple format, ``deg_shells[ish][grp]`` is a list of
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block names; ``ish`` is the index of the inequivalent correlated shell,
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``grp`` is the index of the group of symmetry-related blocks.
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When the name of two blocks is in the same group, that means that
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these two blocks are the same by symmetry.
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In the more general format, ``deg_shells[ish][grp]`` is a
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dictionary whose keys are the block names that are part of the
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group. The values of the dict for each key are tuples ``(v, conj)``,
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where ``v`` is a transformation matrix with the same matrix dimensions
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as the block and ``conj`` is a bool (whether or not to conjugate).
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Two blocks with ``v_1, conj_1`` and ``v_2, conj_2`` being in the same
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symmetry group means that
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.. math::
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C_1(v_1^\dagger G_1 v_1) = C_2(v_2^\dagger G_2 v_2),
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where the :math:`G_i` are the Green's functions of the block,
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and the functions :math:`C_i` conjugate their argument if the bool
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``conj_i`` is ``True``.
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corr_to_inequiv : list
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a list where, for each correlated shell, the index of the corresponding
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inequivalent correlated shell is given
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transformation : list of numpy.array or list of dict
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a list with entries for each ``ish`` giving transformation matrices
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that are used on the Green's function in ``sumk`` space before
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converting to the ``solver`` space
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Up to the change in block structure,
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.. math::
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G_{solver} = T G_{sumk} T^\dagger
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if :math:`T` is the ``transformation`` of that particular shell.
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Note that for each shell this can either be a numpy array which
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applies to all blocks or a dict with a transformation matrix for
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each block.
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"""
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def __init__(self, gf_struct_sumk=None,
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gf_struct_solver=None,
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solver_to_sumk=None,
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sumk_to_solver=None,
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solver_to_sumk_block=None,
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deg_shells=None,
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corr_to_inequiv = None,
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transformation=None):
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self.gf_struct_sumk = gf_struct_sumk
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self.gf_struct_solver = gf_struct_solver
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self.solver_to_sumk = solver_to_sumk
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self.sumk_to_solver = sumk_to_solver
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self.solver_to_sumk_block = solver_to_sumk_block
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self.deg_shells = deg_shells
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self.corr_to_inequiv = corr_to_inequiv
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self.transformation = transformation
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@property
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def gf_struct_solver_list(self):
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""" The structure of the solver Green's function
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This is returned as a
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list (for each shell)
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of lists (for each block)
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of tuples (block_name, block_indices).
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That is,
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``gf_struct_solver_list[ish][b][0]``
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is the name of the block number ``b`` of shell ``ish``, and
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``gf_struct_solver_list[ish][b][1]``
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is a list of its indices.
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The list for each shell is sorted alphabetically by block name.
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"""
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if self.gf_struct_solver is None:
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return None
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# we sort by block name in order to get a reproducible result
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return [sorted([(k, v) for k, v in list(gfs.items())], key=lambda x: x[0])
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for gfs in self.gf_struct_solver]
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@property
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def gf_struct_sumk_list(self):
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""" The structure of the sumk Green's function
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This is returned as a
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list (for each shell)
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of lists (for each block)
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of tuples (block_name, block_indices)
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That is,
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``gf_struct_sumk_list[ish][b][0]``
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is the name of the block number ``b`` of shell ``ish``, and
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``gf_struct_sumk_list[ish][b][1]``
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is a list of its indices.
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"""
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return self.gf_struct_sumk
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@property
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def gf_struct_solver_dict(self):
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""" The structure of the solver Green's function
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This is returned as a
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list (for each shell)
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of dictionaries.
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That is,
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``gf_struct_solver_dict[ish][bname]``
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is a list of the indices of block ``bname`` of shell ``ish``.
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"""
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return self.gf_struct_solver
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@property
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def gf_struct_sumk_dict(self):
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""" The structure of the sumk Green's function
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This is returned as a
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list (for each shell)
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of dictionaries.
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That is,
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``gf_struct_sumk_dict[ish][bname]``
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is a list of the indices of block ``bname`` of shell ``ish``.
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"""
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if self.gf_struct_sumk is None:
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return None
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return [{block: indices for block, indices in gfs}
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for gfs in self.gf_struct_sumk]
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@property
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def inequiv_to_corr(self):
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""" A list mapping an inequivalent correlated shell to a correlated shell
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"""
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if self.corr_to_inequiv is None:
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return None
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N_solver = len(np.unique(self.corr_to_inequiv))
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if self.gf_struct_solver is not None:
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assert N_solver == len(self.gf_struct_solver)
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assert sorted(np.unique(self.corr_to_inequiv)) == list(range(N_solver)),\
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"an inequivalent shell is missing in corr_to_inequiv"
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return [self.corr_to_inequiv.index(icrsh)
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for icrsh in list(range(N_solver))]
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@inequiv_to_corr.setter
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def inequiv_to_corr(self, value):
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# a check for backward compatibility
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if value is None:
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return
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assert self.inequiv_to_corr == value, "Trying to set incompatible inequiv_to_corr"
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@property
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def sumk_to_solver_block(self):
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if self.inequiv_to_corr is None:
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return None
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ret = []
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for ish, icrsh in enumerate(self.inequiv_to_corr):
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d = defaultdict(list)
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for block_solver, block_sumk in list(self.solver_to_sumk_block[ish].items()):
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d[block_sumk].append(block_solver)
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ret.append(d)
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return ret
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@property
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def effective_transformation_sumk(self):
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""" Return the effective transformation matrix
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A list of dicts, one for every correlated shell. In the dict,
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there is a transformation matrix (as numpy array) for each
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block in sumk space, that is used to transform the block.
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"""
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trans = copy.deepcopy(self.transformation)
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if self.gf_struct_sumk is None:
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raise Exception('gf_struct_sumk not set.')
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if self.gf_struct_solver is None:
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raise Exception('gf_struct_solver not set.')
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if trans is None:
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trans = [{block: np.eye(len(indices)) for block, indices in gfs}
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for gfs in self.gf_struct_sumk]
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assert isinstance(trans, list),\
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"transformation has to be a list"
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assert len(trans) == len(self.gf_struct_sumk),\
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"give one transformation per correlated shell"
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for icrsh in list(range(len(trans))):
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ish = self.corr_to_inequiv[icrsh]
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if trans[icrsh] is None:
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trans[icrsh] = {block: np.eye(len(indices))
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for block, indices in self.gf_struct_sumk[icrsh]}
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if not isinstance(trans[icrsh], dict):
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trans[icrsh] = {block: copy.deepcopy(trans[icrsh])
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for block, indices in self.gf_struct_sumk[icrsh]}
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assert list(trans[icrsh].keys()) == list(self.gf_struct_sumk_dict[icrsh].keys()),\
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"wrong block names used in transformation (icrsh = {})".format(icrsh)
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for block in trans[icrsh]:
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assert trans[icrsh][block].shape[0] == trans[icrsh][block].shape[1],\
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"Transformation has to be quadratic; throwing away orbitals can be achieved on the level of the mapping. (icrsh = {}, block = {})".format(icrsh, block)
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assert trans[icrsh][block].shape[0] == len(self.gf_struct_sumk_dict[icrsh][block]),\
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"Transformation block shape does not match gf_struct_sumk. (icrsh = {}, block = {})".format(icrsh, block)
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# zero out all the lines of the transformation that are
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# not included in gf_struct_solver
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for iorb, norb in enumerate(self.gf_struct_sumk_dict[icrsh][block]):
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if self.sumk_to_solver[ish][(block, norb)][0] is None:
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trans[icrsh][block][iorb, :] = 0.0
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return trans
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@property
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def effective_transformation_solver(self):
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""" Return the effective transformation matrix
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A list of dicts, one for every inequivalent correlated shell.
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In the dict, there is a transformation matrix (as numpy array)
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for each block in solver space, that is used to transform from
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the sumk block (see :py:meth:`.solver_to_sumk_block`) to the
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solver block.
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For a solver block ``b`` for inequivalent correlated shell ``ish``,
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the corresponding block of the solver Green's function is::
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# the effective transformation matrix for the block
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T = block_structure.effective_transformation_solver[ish][b]
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# the index of the correlated shell
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icrsh = block_structure.inequiv_to_corr[ish]
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# the name of the corresponding sumk block
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block_sumk = block_structure.solver_to_sumk_block[icrsh][b]
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# transform the Green's function
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G_solver[ish][b].from_L_G_R(T, G_sumk[icrsh][block_sumk], T.conjugate().transpose())
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The functionality of that code block is implemented in
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:py:meth:`.convert_gf` (i.e., you don't need to use this directly).
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"""
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eff_trans_sumk = self.effective_transformation_sumk
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ets = []
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for ish in range(len(self.gf_struct_solver)):
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icrsh = self.inequiv_to_corr[ish]
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ets.append(dict())
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for block in self.gf_struct_solver[ish]:
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block_sumk = self.solver_to_sumk_block[ish][block]
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T = eff_trans_sumk[icrsh][block_sumk]
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ets[ish][block] = np.zeros((len(self.gf_struct_solver[ish][block]),
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len(T)),
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dtype=T.dtype)
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for i in self.gf_struct_solver[ish][block]:
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i_sumk = self.solver_to_sumk[ish][block, i]
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assert i_sumk[0] == block_sumk,\
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"Wrong block in solver_to_sumk"
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i_sumk = i_sumk[1]
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ets[ish][block][i, :] = T[i_sumk, :]
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return ets
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@classmethod
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def full_structure(cls,gf_struct,corr_to_inequiv):
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""" Construct structure that maps to itself.
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This has the same structure for sumk and solver, and the
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mapping solver_to_sumk and sumk_to_solver is one-to-one.
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Parameters
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----------
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gf_struct : list of dict
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gf_struct[ish][block] = list of indices in that block
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for (inequivalent) correlated shell ish
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corr_to_inequiv : list
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gives the mapping from correlated shell csh to inequivalent
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correlated shell icsh, so that corr_to_inequiv[csh]=icsh
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e.g. SumkDFT.corr_to_inequiv
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if None, each inequivalent correlated shell is supposed to
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be correspond to just one correlated shell with the same
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index; there is not default, None has to be set explicitly!
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"""
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solver_to_sumk = []
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s2sblock = []
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gs_sumk = []
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for ish in range(len(gf_struct)):
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so2su = {}
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so2sublock = {}
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gss = []
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for block in gf_struct[ish]:
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so2sublock[block]=block
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for ind in gf_struct[ish][block]:
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so2su[(block,ind)]=(block,ind)
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gss.append((block,gf_struct[ish][block]))
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solver_to_sumk.append(so2su)
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s2sblock.append(so2sublock)
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gs_sumk.append(gss)
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# gf_struct_sumk is not given for each inequivalent correlated
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# shell, but for every correlated shell!
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if corr_to_inequiv is not None:
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gs_sumk_all = [None]*len(corr_to_inequiv)
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for i in range(len(corr_to_inequiv)):
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gs_sumk_all[i] = gs_sumk[corr_to_inequiv[i]]
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else:
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gs_sumk_all = gs_sumk
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return cls(gf_struct_solver=copy.deepcopy(gf_struct),
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gf_struct_sumk = gs_sumk_all,
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solver_to_sumk = copy.deepcopy(solver_to_sumk),
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sumk_to_solver = solver_to_sumk,
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solver_to_sumk_block = s2sblock,
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deg_shells = [[] for ish in range(len(gf_struct))],
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corr_to_inequiv = corr_to_inequiv)
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def pick_gf_struct_solver(self, new_gf_struct):
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""" Pick selected orbitals within blocks.
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This throws away parts of the Green's function that (for some
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reason - be sure that you know what you're doing) shouldn't be
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included in the calculation.
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To drop an entire block, just don't include it.
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To drop a certain index within a block, just don't include it.
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If it was before:
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[{'up':[0,1],'down':[0,1],'left':[0,1]}]
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to choose the 0th index of the up block and the 1st index of
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the down block and drop the left block, the new_gf_struct would
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have to be
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[{'up':[0],'down':[1]}]
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Note that the indices will be renamed to be a 0-based
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sequence of integers, i.e. the new structure will actually
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be [{'up':[0],'down':[0]}].
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For dropped indices, sumk_to_solver will map to (None,None).
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Parameters
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----------
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new_gf_struct : list of dict
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formatted the same as gf_struct_solver:
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new_gf_struct[ish][block]=list of indices in that block.
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"""
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for ish in range(len(self.gf_struct_solver)):
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gf_struct = new_gf_struct[ish]
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# create new solver_to_sumk
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so2su = {}
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so2su_block = {}
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for blk,idxs in list(gf_struct.items()):
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for i in range(len(idxs)):
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so2su[(blk, i)] = self.solver_to_sumk[ish][(blk, idxs[i])]
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so2su_block[blk] = so2su[(blk, i)][0]
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self.solver_to_sumk[ish] = so2su
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self.solver_to_sumk_block[ish] = so2su_block
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# create new sumk_to_solver
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for k,v in list(self.sumk_to_solver[ish].items()):
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blk,ind=v
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if blk in gf_struct and ind in gf_struct[blk]:
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new_ind = gf_struct[blk].index(ind)
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self.sumk_to_solver[ish][k] = (blk, new_ind)
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else:
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self.sumk_to_solver[ish][k] = (None, None)
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# adapt deg_shells
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self.adapt_deg_shells(gf_struct, ish)
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# reindexing gf_struct so that it starts with 0
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for k in gf_struct:
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gf_struct[k]=list(range(len(gf_struct[k])))
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self.gf_struct_solver[ish]=gf_struct
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def adapt_deg_shells(self, gf_struct, ish=0):
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""" Adapts the deg_shells to a new gf_struct
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Internally called when using pick_gf_struct and map_gf_struct
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"""
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if self.deg_shells is not None:
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for degsh in self.deg_shells[ish]:
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if isinstance(degsh, dict):
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for key in list(degsh.keys()):
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if not key in gf_struct:
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del degsh[key]
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continue
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|
if gf_struct[key] != self.gf_struct_solver[ish][key]:
|
|
v, C = degsh[key]
|
|
degsh[key][0] = \
|
|
v[gf_struct[key], :][:, gf_struct[key]]
|
|
warn(
|
|
'Removing shells from degenerate shell {}. Cannot guarantee that they continue to be equivalent.')
|
|
else: # degshell is list
|
|
degsh1 = copy.deepcopy(degsh) # in order to not remove a key while iterating
|
|
for key in degsh1:
|
|
if not key in gf_struct:
|
|
warn('Removing shells from degenerate shell {}.')
|
|
degsh.remove(key)
|
|
|
|
def pick_gf_struct_sumk(self, new_gf_struct):
|
|
""" Pick selected orbitals within blocks.
|
|
|
|
This throws away parts of the Green's function that (for some
|
|
reason - be sure that you know what you're doing) shouldn't be
|
|
included in the calculation.
|
|
|
|
To drop an entire block, just don't include it.
|
|
To drop a certain index within a block, just don't include it.
|
|
|
|
If it was before:
|
|
|
|
[{'up':[0,1],'down':[0,1],'left':[0,1]}]
|
|
|
|
to choose the 0th index of the up block and the 1st index of
|
|
the down block and drop the left block, the new_gf_struct would
|
|
have to be
|
|
|
|
[{'up':[0],'down':[1]}]
|
|
|
|
Note that the indices will be renamed to be a 0-based
|
|
sequence of integers.
|
|
|
|
For dropped indices, sumk_to_solver will map to (None,None).
|
|
|
|
Parameters
|
|
----------
|
|
new_gf_struct : list of dict
|
|
formatted the same as gf_struct_solver:
|
|
|
|
new_gf_struct[ish][block]=list of indices in that block.
|
|
|
|
However, the indices are not according to the solver Gf
|
|
but the sumk Gf.
|
|
"""
|
|
eff_trans_sumk = self.effective_transformation_sumk
|
|
|
|
assert len(eff_trans_sumk) == len(new_gf_struct),\
|
|
"new_gf_struct has the wrong length"
|
|
|
|
new_gf_struct_transformed = copy.deepcopy(new_gf_struct)
|
|
|
|
# when there is a transformation matrix, this first zeroes out
|
|
# the corresponding rows of (a copy of) T and then applies
|
|
# pick_gf_struct_solver for all lines of T that have at least
|
|
# one non-zero entry
|
|
|
|
for icrsh in range(len(new_gf_struct)):
|
|
for block, indices in self.gf_struct_sumk[icrsh]:
|
|
if not block in new_gf_struct[icrsh]:
|
|
#del new_gf_struct_transformed[block] # this MUST be wrong, as new_gf_struct_transformed needs to have a integer index for icrsh... # error when index is not kept at all
|
|
continue
|
|
T = eff_trans_sumk[icrsh][block]
|
|
for index in indices:
|
|
if not index in new_gf_struct[icrsh][block]:
|
|
T[:, index] = 0.0
|
|
new_indices = []
|
|
for index in indices:
|
|
if np.any(np.abs(T[index, :]) > 1.e-15):
|
|
new_indices.append(index)
|
|
new_gf_struct_transformed[icrsh][block] = new_indices
|
|
|
|
gfs = []
|
|
# construct gfs, which is the equivalent of new_gf_struct
|
|
# but according to the solver Gf, by using the sumk_to_solver
|
|
# mapping
|
|
for icrsh in range(len(new_gf_struct_transformed)):
|
|
ish = self.corr_to_inequiv[icrsh]
|
|
gfs.append({})
|
|
for block in list(new_gf_struct_transformed[icrsh].keys()):
|
|
for ind in new_gf_struct_transformed[icrsh][block]:
|
|
ind_sol = self.sumk_to_solver[ish][(block,ind)]
|
|
if not ind_sol[0] in gfs[icrsh]:
|
|
gfs[icrsh][ind_sol[0]]=[]
|
|
gfs[icrsh][ind_sol[0]].append(ind_sol[1])
|
|
self.pick_gf_struct_solver(gfs)
|
|
|
|
def map_gf_struct_solver(self, mapping):
|
|
r""" Map the Green function structure from one struct to another.
|
|
|
|
Parameters
|
|
----------
|
|
mapping : list of dict
|
|
the dict consists of elements
|
|
(from_block,from_index) : (to_block,to_index)
|
|
that maps from one structure to the other
|
|
(one for each shell; use a mapping ``None`` for a shell
|
|
you want to leave unchanged)
|
|
|
|
Examples
|
|
--------
|
|
|
|
Consider a `gf_struct_solver` consisting of two :math:`1 \times 1`
|
|
blocks, `block_1` and `block_2`. Say you want to have a new block
|
|
structure where you merge them into one block because you want to
|
|
introduce an off-diagonal element. You could perform the mapping
|
|
via::
|
|
|
|
map_gf_struct_solver([{('block_1',0) : ('block', 0)
|
|
('block_2',0) : ('block', 1)}])
|
|
"""
|
|
|
|
for ish in range(len(mapping)):
|
|
if mapping[ish] is None:
|
|
continue
|
|
gf_struct = {}
|
|
so2su = {}
|
|
su2so = {}
|
|
so2su_block = {}
|
|
for frm,to in list(mapping[ish].items()):
|
|
if not to[0] in gf_struct:
|
|
gf_struct[to[0]] = []
|
|
gf_struct[to[0]].append(to[1])
|
|
|
|
so2su[to] = self.solver_to_sumk[ish][frm]
|
|
su2so[self.solver_to_sumk[ish][frm]] = to
|
|
if to[0] in so2su_block:
|
|
if so2su_block[to[0]] != \
|
|
self.solver_to_sumk_block[ish][frm[0]]:
|
|
warn("solver block '{}' maps to more than one sumk block: '{}', '{}'".format(
|
|
to[0], so2su_block[to[0]], self.solver_to_sumk_block[ish][frm[0]]))
|
|
else:
|
|
so2su_block[to[0]] =\
|
|
self.solver_to_sumk_block[ish][frm[0]]
|
|
for k in list(self.sumk_to_solver[ish].keys()):
|
|
if not k in su2so:
|
|
su2so[k] = (None, None)
|
|
|
|
self.adapt_deg_shells(gf_struct, ish)
|
|
|
|
self.gf_struct_solver[ish] = gf_struct
|
|
self.solver_to_sumk[ish] = so2su
|
|
self.sumk_to_solver[ish] = su2so
|
|
self.solver_to_sumk_block[ish] = so2su_block
|
|
self.deg_shells[ish] = []
|
|
|
|
def create_gf(self, ish=0, gf_function=GfImFreq, space='solver', **kwargs):
|
|
""" Create a zero BlockGf having the correct structure.
|
|
|
|
For ``space='solver'``, the structure is according to
|
|
``gf_struct_solver``, else according to ``gf_struct_sumk``.
|
|
|
|
When using GfImFreq as gf_function, typically you have to
|
|
supply beta as keyword argument.
|
|
|
|
Parameters
|
|
----------
|
|
ish : int
|
|
shell index
|
|
If ``space='solver'``, the index of the of the inequivalent correlated shell,
|
|
if ``space='sumk'``, the index of the correlated shell
|
|
gf_function : constructor
|
|
function used to construct the Gf objects constituting the
|
|
individual blocks; default: GfImFreq
|
|
space : 'solver' or 'sumk'
|
|
which space the structure should correspond to
|
|
**kwargs :
|
|
options passed on to the Gf constructor for the individual
|
|
blocks
|
|
"""
|
|
|
|
return self._create_gf_or_matrix(ish, gf_function, BlockGf, space, **kwargs)
|
|
|
|
def create_matrix(self, ish=0, space='solver', dtype=np.complex_):
|
|
""" Create a zero matrix having the correct structure.
|
|
|
|
For ``space='solver'``, the structure is according to
|
|
``gf_struct_solver``, else according to ``gf_struct_sumk``.
|
|
|
|
Parameters
|
|
----------
|
|
ish : int
|
|
shell index
|
|
If ``space='solver'``, the index of the of the inequivalent correlated shell,
|
|
if ``space='sumk'``, the index of the correlated shell
|
|
space : 'solver' or 'sumk'
|
|
which space the structure should correspond to
|
|
"""
|
|
|
|
def gf_function(indices):
|
|
return np.zeros((len(indices), len(indices)), dtype=dtype)
|
|
|
|
def block_function(name_list, block_list):
|
|
d = dict()
|
|
for i in range(len(name_list)):
|
|
d[name_list[i]] = block_list[i]
|
|
return d
|
|
|
|
return self._create_gf_or_matrix(ish, gf_function, block_function, space)
|
|
|
|
def _create_gf_or_matrix(self, ish=0, gf_function=GfImFreq, block_function=BlockGf, space='solver', **kwargs):
|
|
if space == 'solver':
|
|
gf_struct = self.gf_struct_solver
|
|
elif space == 'sumk':
|
|
gf_struct = self.gf_struct_sumk_dict
|
|
else:
|
|
raise Exception(
|
|
"Argument space has to be either 'solver' or 'sumk'.")
|
|
|
|
names = list(gf_struct[ish].keys())
|
|
blocks = []
|
|
for n in names:
|
|
G = gf_function(indices=gf_struct[ish][n], **kwargs)
|
|
blocks.append(G)
|
|
G = block_function(name_list=names, block_list=blocks)
|
|
return G
|
|
|
|
def check_gf(self, G, ish=None, space='solver'):
|
|
""" check whether the Green's function G has the right structure
|
|
|
|
This throws an error if the structure of G is not the same
|
|
as ``gf_struct_solver`` (for ``space=solver``) or
|
|
``gf_struct_sumk`` (for ``space=sumk``)..
|
|
|
|
Parameters
|
|
----------
|
|
G : BlockGf or list of BlockGf
|
|
Green's function to check
|
|
if it is a list, there should be as many entries as there
|
|
are shells, and the check is performed for all shells (unless
|
|
ish is given).
|
|
ish : int
|
|
shell index
|
|
default: 0 if G is just one Green's function is given,
|
|
check all if list of Green's functions is given
|
|
space : 'solver' or 'sumk'
|
|
which space the structure should correspond to
|
|
"""
|
|
|
|
return self._check_gf_or_matrix(G, ish, space)
|
|
|
|
def check_matrix(self, G, ish=None, space='solver'):
|
|
""" check whether the matrix G has the right structure
|
|
|
|
This throws an error if the structure of G is not the same
|
|
as ``gf_struct_solver`` (for ``space=solver``) or
|
|
``gf_struct_sumk`` (for ``space=sumk``)..
|
|
|
|
Parameters
|
|
----------
|
|
G : dict of matrices or list of dict of matrices
|
|
matrix to check
|
|
if it is a list, there should be as many entries as there
|
|
are shells, and the check is performed for all shells (unless
|
|
ish is given).
|
|
ish : int
|
|
shell index
|
|
default: 0 if G is just one matrix is given,
|
|
check all if list of dicts is given
|
|
space : 'solver' or 'sumk'
|
|
which space the structure should correspond to
|
|
"""
|
|
|
|
return self._check_gf_or_matrix(G, ish, space)
|
|
|
|
def _check_gf_or_matrix(self, G, ish=None, space='solver'):
|
|
if space == 'solver':
|
|
gf_struct = self.gf_struct_solver
|
|
elif space == 'sumk':
|
|
gf_struct = self.gf_struct_sumk_dict
|
|
else:
|
|
raise Exception(
|
|
"Argument space has to be either 'solver' or 'sumk'.")
|
|
|
|
if isinstance(G, list):
|
|
assert len(G) == len(gf_struct),\
|
|
"list of G does not have the correct length"
|
|
if ish is None:
|
|
ishs = list(range(len(gf_struct)))
|
|
else:
|
|
ishs = [ish]
|
|
for ish in ishs:
|
|
self.check_gf(G[ish], ish=ish, space=space)
|
|
return
|
|
|
|
if ish is None:
|
|
ish = 0
|
|
|
|
if isinstance(G, BlockGf):
|
|
for block in gf_struct[ish]:
|
|
assert block in G.indices,\
|
|
"block " + block + " not in G (shell {})".format(ish)
|
|
for block, gf in G:
|
|
assert block in gf_struct[ish],\
|
|
"block " + block + " not in struct (shell {})".format(ish)
|
|
assert list(gf.indices) == 2 * [list(map(str, gf_struct[ish][block]))],\
|
|
"block " + block + \
|
|
" has wrong indices (shell {})".format(ish)
|
|
else:
|
|
for block in gf_struct[ish]:
|
|
assert block in G,\
|
|
"block " + block + " not in G (shell {})".format(ish)
|
|
for block, gf in list(G.items()):
|
|
assert block in gf_struct[ish],\
|
|
"block " + block + " not in struct (shell {})".format(ish)
|
|
assert list(range(len(gf))) == 2 * [list(map(str, gf_struct[ish][block]))],\
|
|
"block " + block + \
|
|
" has wrong indices (shell {})".format(ish)
|
|
|
|
def convert_operator(self, O, ish=0):
|
|
""" Converts a second-quantization operator from sumk structure
|
|
to solver structure.
|
|
|
|
Parameters
|
|
----------
|
|
O : triqs.operators.Operator
|
|
Operator in sumk structure
|
|
|
|
ish : int
|
|
shell index on which the operator acts
|
|
"""
|
|
|
|
from triqs.operators import Operator, c, c_dag
|
|
|
|
T = self.transformation[ish]
|
|
sk2s = self.sumk_to_solver[ish]
|
|
|
|
O_out = Operator(0)
|
|
|
|
for monomial in O:
|
|
coefficient = monomial[-1]
|
|
new_monomial = Operator(1)
|
|
#if coefficient > 1e-10:
|
|
for single_operator in monomial[0]:
|
|
new_single_operator = Operator(0)
|
|
daggered = single_operator[0]
|
|
|
|
blockname = single_operator[1][0]
|
|
i = single_operator[1][1]
|
|
for j in range(len(T[blockname])):
|
|
if sk2s[(blockname, j)] != (None, None):
|
|
if daggered:
|
|
new_single_operator += (T[blockname][j,i] * c_dag(*sk2s[(blockname, j)]))
|
|
else:
|
|
new_single_operator += (T[blockname][j,i].conjugate() * c(*sk2s[(blockname, j)]))
|
|
|
|
new_monomial *= new_single_operator
|
|
|
|
O_out += new_monomial * coefficient
|
|
return O_out
|
|
|
|
|
|
|
|
def convert_gf(self, G, G_struct=None, ish_from=0, ish_to=None, show_warnings=True,
|
|
G_out=None, space_from='solver', space_to='solver', ish=None, **kwargs):
|
|
""" Convert BlockGf from its structure to this structure.
|
|
|
|
.. warning::
|
|
|
|
Elements that are zero in the new structure due to
|
|
the new block structure will be just ignored, thus
|
|
approximated to zero.
|
|
|
|
Parameters
|
|
----------
|
|
G : BlockGf
|
|
the Gf that should be converted
|
|
G_struct : BlockStructure or str
|
|
the structure of that G or None (then, this structure
|
|
is used)
|
|
ish_from : int
|
|
shell index of the input structure
|
|
ish_to : int
|
|
shell index of the output structure; if None (the default),
|
|
it is the same as ish_from
|
|
show_warnings : bool or float
|
|
whether to show warnings when elements of the Green's
|
|
function get thrown away
|
|
if float, set the threshold for the magnitude of an element
|
|
about to be thrown away to trigger a warning
|
|
(default: 1.e-10)
|
|
G_out : BlockGf
|
|
the output Green's function (if not given, a new one is
|
|
created)
|
|
space_from : 'solver' or 'sumk'
|
|
whether the Green's function ``G`` corresponds to the
|
|
solver or sumk structure of ``G_struct``
|
|
space_to : 'solver' or 'sumk'
|
|
whether the output Green's function should be according to
|
|
the solver of sumk structure of this structure
|
|
**kwargs :
|
|
options passed to the constructor for the new Gf
|
|
"""
|
|
|
|
if ish is not None:
|
|
warn(
|
|
'The parameter ish in convert_gf is deprecated. Use ish_from and ish_to instead.')
|
|
ish_from = ish
|
|
ish_to = ish
|
|
return self._convert_gf_or_matrix(G, G_struct, ish_from, ish_to,
|
|
show_warnings, G_out, space_from, space_to, **kwargs)
|
|
|
|
def convert_matrix(self, G, G_struct=None, ish_from=0, ish_to=None, show_warnings=True,
|
|
G_out=None, space_from='solver', space_to='solver'):
|
|
""" Convert matrix from its structure to this structure.
|
|
|
|
.. warning::
|
|
|
|
Elements that are zero in the new structure due to
|
|
the new block structure will be just ignored, thus
|
|
approximated to zero.
|
|
|
|
Parameters
|
|
----------
|
|
G : dict of numpy array
|
|
the matrix that should be converted
|
|
G_struct : BlockStructure or str
|
|
the structure of that G or None (then, this structure
|
|
is used)
|
|
ish_from : int
|
|
shell index of the input structure
|
|
ish_to : int
|
|
shell index of the output structure; if None (the default),
|
|
it is the same as ish_from
|
|
show_warnings : bool or float
|
|
whether to show warnings when elements of the Green's
|
|
function get thrown away
|
|
if float, set the threshold for the magnitude of an element
|
|
about to be thrown away to trigger a warning
|
|
(default: 1.e-10)
|
|
G_out : dict of numpy array
|
|
the output numpy array (if not given, a new one is
|
|
created)
|
|
space_from : 'solver' or 'sumk'
|
|
whether the matrix ``G`` corresponds to the
|
|
solver or sumk structure of ``G_struct``
|
|
space_to : 'solver' or 'sumk'
|
|
whether the output matrix should be according to
|
|
the solver of sumk structure of this structure
|
|
**kwargs :
|
|
options passed to the constructor for the new Gf
|
|
"""
|
|
|
|
return self._convert_gf_or_matrix(G, G_struct, ish_from, ish_to,
|
|
show_warnings, G_out, space_from, space_to)
|
|
|
|
def _convert_gf_or_matrix(self, G, G_struct=None, ish_from=0, ish_to=None, show_warnings=True,
|
|
G_out=None, space_from='solver', space_to='solver', **kwargs):
|
|
if ish_to is None:
|
|
ish_to = ish_from
|
|
|
|
warning_threshold = 1.e-10
|
|
if isinstance(show_warnings, float):
|
|
warning_threshold = show_warnings
|
|
show_warnings = True
|
|
|
|
if G_struct is None:
|
|
G_struct = self
|
|
|
|
if space_from == 'solver':
|
|
gf_struct_from = G_struct.gf_struct_solver[ish_from]
|
|
eff_trans_from = G_struct.effective_transformation_solver[ish_from]
|
|
block_mapping_from = G_struct.sumk_to_solver_block[ish_from]
|
|
elif space_from == 'sumk':
|
|
gf_struct_from = G_struct.gf_struct_sumk_dict[ish_from]
|
|
eff_trans_from = {block: np.eye(len(indices))
|
|
for block, indices in G_struct.gf_struct_sumk[ish_from]}
|
|
block_mapping_from = {b: [b] for b in gf_struct_from}
|
|
else:
|
|
raise Exception(
|
|
"Argument space_from has to be either 'solver' or 'sumk'.")
|
|
|
|
if space_to == 'solver':
|
|
gf_struct_to = self.gf_struct_solver[ish_to]
|
|
eff_trans_to = self.effective_transformation_solver[ish_to]
|
|
block_mapping_to = self.solver_to_sumk_block[ish_to]
|
|
elif space_to == 'sumk':
|
|
gf_struct_to = self.gf_struct_sumk_dict[ish_to]
|
|
eff_trans_to = {block: np.eye(len(indices))
|
|
for block, indices in self.gf_struct_sumk_list[ish_to]}
|
|
block_mapping_to = {b: b for b in gf_struct_to}
|
|
else:
|
|
raise Exception(
|
|
"Argument space_to has to be either 'solver' or 'sumk'.")
|
|
|
|
if isinstance(G, BlockGf):
|
|
# create a Green's function to hold the result
|
|
if G_out is None:
|
|
if not 'mesh' in kwargs and not 'beta' in kwargs:
|
|
kwargs['mesh'] = G.mesh
|
|
G_out = self.create_gf(ish=ish_to, space=space_to, **kwargs)
|
|
else:
|
|
self.check_gf(G_out, ish=ish_to, space=space_to)
|
|
elif isinstance(G, dict):
|
|
if G_out is None:
|
|
G_out = self.create_matrix(ish=ish_to, space=space_to)
|
|
else:
|
|
self.check_matrix(G_out, ish=ish_to, space=space_to)
|
|
else:
|
|
raise Exception('G is neither BlockGf nor dict.')
|
|
|
|
for block_to in list(gf_struct_to.keys()):
|
|
if isinstance(G, BlockGf):
|
|
G_out[block_to].zero()
|
|
else:
|
|
G_out[block_to][:] = 0.0
|
|
block_intermediate = block_mapping_to[block_to]
|
|
block_from = block_mapping_from[block_intermediate]
|
|
T_to = eff_trans_to[block_to]
|
|
g_help = G_out[block_to].copy()
|
|
for block in block_from:
|
|
T_from = eff_trans_from[block]
|
|
if isinstance(G, BlockGf):
|
|
g_help.from_L_G_R(np.dot(T_to, np.conjugate(np.transpose(T_from))),
|
|
G[block],
|
|
np.dot(T_from, np.conjugate(np.transpose(T_to))))
|
|
G_out[block_to] << G_out[block_to] + g_help
|
|
else:
|
|
g_help = np.dot(np.dot(T_to, np.conjugate(np.transpose(T_from))),
|
|
np.dot(G[block],
|
|
np.dot(T_from, np.conjugate(np.transpose(T_to)))))
|
|
G_out[block_to] += g_help
|
|
|
|
if show_warnings:
|
|
# we back-transform it
|
|
G_back = G_struct._convert_gf_or_matrix(G_out, self, ish_from=ish_to,
|
|
ish_to=ish_from,
|
|
show_warnings=False, # else we get an endless loop
|
|
space_from=space_to, space_to=space_from, **kwargs)
|
|
for name, gf in (G_back if isinstance(G, BlockGf) else list(G_back.items())):
|
|
if isinstance(G, BlockGf):
|
|
maxdiff = np.max(np.abs(G_back[name].data - G[name].data),
|
|
axis=0)
|
|
else:
|
|
maxdiff = G_back[name] - G[name]
|
|
|
|
if space_to == 'solver' and self == G_struct: # do comparison in solver (ignore diff. in ignored orbitals)
|
|
tmp = self.create_matrix(space='sumk', ish=ish_from)
|
|
tmp[name] = maxdiff
|
|
maxdiff = G_struct._convert_gf_or_matrix(tmp, self, ish_from=ish_from,
|
|
ish_to=ish_to,
|
|
show_warnings=False,
|
|
space_from=space_from, space_to=space_to, **kwargs)
|
|
|
|
for block in maxdiff:
|
|
maxdiff_b = maxdiff[block]
|
|
if np.any(maxdiff_b > warning_threshold):
|
|
warn('Block {} maximum difference:\n'.format(name) + str(maxdiff))
|
|
|
|
|
|
elif np.any(maxdiff > warning_threshold):
|
|
warn('Block {} maximum difference:\n'.format(name)
|
|
+ str(maxdiff))
|
|
|
|
return G_out
|
|
|
|
def approximate_as_diagonal(self):
|
|
""" Create a structure for a GF with zero off-diagonal elements.
|
|
|
|
.. warning::
|
|
|
|
In general, this will throw away non-zero elements of the
|
|
Green's function. Be sure to verify whether this approximation
|
|
is justified.
|
|
"""
|
|
|
|
self.gf_struct_solver=[]
|
|
self.solver_to_sumk=[]
|
|
self.solver_to_sumk_block=[]
|
|
for ish in range(len(self.sumk_to_solver)):
|
|
self.gf_struct_solver.append({})
|
|
self.solver_to_sumk.append({})
|
|
self.solver_to_sumk_block.append({})
|
|
for frm,to in list(self.sumk_to_solver[ish].items()):
|
|
if to[0] is not None:
|
|
self.gf_struct_solver[ish][frm[0]+'_'+str(frm[1])]=[0]
|
|
self.sumk_to_solver[ish][frm]=(frm[0]+'_'+str(frm[1]),0)
|
|
self.solver_to_sumk[ish][(frm[0]+'_'+str(frm[1]),0)]=frm
|
|
self.solver_to_sumk_block[ish][frm[0]+'_'+str(frm[1])]=frm[0]
|
|
|
|
def __eq__(self,other):
|
|
def compare(one,two):
|
|
if type(one)!=type(two):
|
|
if not (isinstance(one, (bool, np.bool_)) and isinstance(two, (bool, np.bool_))):
|
|
return False
|
|
if one is None and two is None:
|
|
return True
|
|
if isinstance(one,list) or isinstance(one,tuple):
|
|
if len(one) != len(two):
|
|
return False
|
|
for x,y in zip(one,two):
|
|
if not compare(x,y):
|
|
return False
|
|
return True
|
|
elif isinstance(one,(int,bool, str, np.bool_)):
|
|
return one==two
|
|
elif isinstance(one,np.ndarray):
|
|
return np.all(one==two)
|
|
elif isinstance(one,dict):
|
|
if set(one.keys()) != set(two.keys()):
|
|
return False
|
|
for k in set(one.keys()).intersection(list(two.keys())):
|
|
if not compare(one[k],two[k]):
|
|
return False
|
|
return True
|
|
warn('Cannot compare {}'.format(type(one)))
|
|
return False
|
|
|
|
for prop in [ "gf_struct_sumk", "gf_struct_solver",
|
|
"solver_to_sumk", "sumk_to_solver", "solver_to_sumk_block",
|
|
"deg_shells","transformation", "corr_to_inequiv"]:
|
|
if not compare(getattr(self,prop),getattr(other,prop)):
|
|
return False
|
|
return True
|
|
|
|
def copy(self):
|
|
return copy.deepcopy(self)
|
|
|
|
def __reduce_to_dict__(self):
|
|
""" Reduce to dict for HDF5 export."""
|
|
|
|
ret = {}
|
|
for element in [ "gf_struct_sumk", "gf_struct_solver",
|
|
"solver_to_sumk_block","deg_shells",
|
|
"transformation", "corr_to_inequiv"]:
|
|
ret[element] = getattr(self,element)
|
|
if ret[element] is None:
|
|
ret[element] = 'None'
|
|
|
|
if ret["transformation"] is None:
|
|
ret["transformation"] = "None"
|
|
|
|
def construct_mapping(mapping):
|
|
d = []
|
|
for ish in range(len(mapping)):
|
|
d.append({})
|
|
for k,v in list(mapping[ish].items()):
|
|
d[ish][repr(k)] = repr(v)
|
|
return d
|
|
|
|
ret['solver_to_sumk']=construct_mapping(self.solver_to_sumk)
|
|
ret['sumk_to_solver']=construct_mapping(self.sumk_to_solver)
|
|
return ret
|
|
|
|
@classmethod
|
|
def __factory_from_dict__(cls,name,D) :
|
|
""" Create from dict for HDF5 import."""
|
|
|
|
def reconstruct_mapping(mapping):
|
|
d = []
|
|
for ish in range(len(mapping)):
|
|
d.append({})
|
|
for k,v in list(mapping[ish].items()):
|
|
# literal_eval is a saje alternative to eval
|
|
d[ish][literal_eval(k)] = literal_eval(v)
|
|
return d
|
|
|
|
for elem in D:
|
|
if D[elem]=="None":
|
|
D[elem] = None
|
|
|
|
D['solver_to_sumk']=reconstruct_mapping(D['solver_to_sumk'])
|
|
D['sumk_to_solver']=reconstruct_mapping(D['sumk_to_solver'])
|
|
return cls(**D)
|
|
|
|
def __str__(self):
|
|
s=''
|
|
s+= "corr_to_inequiv "+str(self.corr_to_inequiv)+'\n'
|
|
s+= "gf_struct_sumk "+str(self.gf_struct_sumk)+'\n'
|
|
s+= "gf_struct_solver "+str(self.gf_struct_solver)+'\n'
|
|
s+= "solver_to_sumk_block "+str(self.solver_to_sumk_block)+'\n'
|
|
for el in ['solver_to_sumk','sumk_to_solver']:
|
|
s+=el+'\n'
|
|
element=getattr(self,el)
|
|
for ish in range(len(element)):
|
|
s+=' shell '+str(ish)+'\n'
|
|
def keyfun(el):
|
|
return '{}_{:05d}'.format(el[0],el[1])
|
|
keys = sorted(list(element[ish].keys()),key=keyfun)
|
|
for k in keys:
|
|
s+=' '+str(k)+str(element[ish][k])+'\n'
|
|
s += "deg_shells\n"
|
|
for ish in range(len(self.deg_shells)):
|
|
s+=' shell '+str(ish)+'\n'
|
|
for l in range(len(self.deg_shells[ish])):
|
|
s+=' equivalent group '+str(l)+'\n'
|
|
if isinstance(self.deg_shells[ish][l],dict):
|
|
for key, val in list(self.deg_shells[ish][l].items()):
|
|
s+=' '+key+('*' if val[1] else '')+':\n'
|
|
s+=' '+str(val[0]).replace('\n','\n ')+'\n'
|
|
else:
|
|
for key in self.deg_shells[ish][l]:
|
|
s+=' '+key+'\n'
|
|
s += "transformation\n"
|
|
s += str(self.transformation)
|
|
return s
|
|
|
|
def gf_struct_flatten(gf_struct):
|
|
'''
|
|
flattens gf_struct objecti
|
|
|
|
input gf_struct can looks like this:
|
|
|
|
[('up', [0, 1, 2]), ('down', [0, 1, 2])]
|
|
|
|
and will be returned as
|
|
|
|
[('up', 3), ('down', 3)]
|
|
|
|
Same for dict but replacing the values. This is for compatibility with the upcoming triqs releases.
|
|
|
|
Parameters
|
|
----------
|
|
gf_struct: list of tuple or dict representing the Gf structure
|
|
__Returns:__
|
|
gf_struct_flat: flattens the values of the dict or the tuple representing the Gf indices by replacing them with the len of the list of indices
|
|
|
|
'''
|
|
|
|
if isinstance(gf_struct, list):
|
|
# create a copy of the original list
|
|
gf_struct_flat = gf_struct.copy()
|
|
for idx, block in enumerate(gf_struct_flat):
|
|
# exchange list of indices with length of list
|
|
gf_struct_flat[idx] = (block[0], len(block[1]))
|
|
elif isinstance(gf_struct, dict):
|
|
# create a copy of the original dict
|
|
gf_struct_flat = dict(gf_struct)
|
|
for key, value in gf_struct_flat.items():
|
|
# exchange list of indices with length of list
|
|
gf_struct_flat[key] = len(value)
|
|
else:
|
|
raise Exception('gf_struct input needs to be list or dict')
|
|
|
|
|
|
return gf_struct_flat
|
|
|
|
from h5.formats import register_class
|
|
register_class(BlockStructure)
|