mirror of https://github.com/triqs/dft_tools
1166 lines
46 KiB
Python
1166 lines
46 KiB
Python
|
|
##########################################################################
|
|
#
|
|
# TRIQS: a Toolbox for Research in Interacting Quantum Systems
|
|
#
|
|
# Copyright (C) 2018 by G. J. Kraberger
|
|
# Copyright (C) 2018 by Simons Foundation
|
|
# Authors: G. J. Kraberger, O. Parcollet
|
|
#
|
|
# TRIQS is free software: you can redistribute it and/or modify it under the
|
|
# terms of the GNU General Public License as published by the Free Software
|
|
# Foundation, either version 3 of the License, or (at your option) any later
|
|
# version.
|
|
#
|
|
# TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY
|
|
# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
|
|
# FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
|
|
# details.
|
|
#
|
|
# You should have received a copy of the GNU General Public License along with
|
|
# TRIQS. If not, see <http://www.gnu.org/licenses/>.
|
|
#
|
|
##########################################################################
|
|
|
|
|
|
import copy
|
|
import numpy as np
|
|
from triqs.gf import GfImFreq, BlockGf
|
|
from ast import literal_eval
|
|
import triqs.utility.mpi as mpi
|
|
from warnings import warn
|
|
from collections import defaultdict
|
|
|
|
|
|
class BlockStructure(object):
|
|
""" Contains information about the Green function structure.
|
|
|
|
This class contains information about the structure of the solver
|
|
and sumk Green functions and the mapping between them.
|
|
|
|
Parameters
|
|
----------
|
|
gf_struct_sumk : list of list of tuple
|
|
gf_struct_sumk[ish][idx] = (block_name,list of indices in block)
|
|
|
|
for correlated shell ish; idx is just a counter in the list
|
|
gf_struct_solver : list of dict
|
|
gf_struct_solver[ish][block] = list of indices in that block
|
|
|
|
for *inequivalent* correlated shell ish
|
|
solver_to_sumk : list of dict
|
|
solver_to_sumk[ish][(from_block,from_idx)] = (to_block,to_idx)
|
|
|
|
maps from the solver block and index to the sumk block and index
|
|
for *inequivalent* correlated shell ish
|
|
sumk_to_solver : list of dict
|
|
sumk_to_solver[ish][(from_block,from_idx)] = (to_block,to_idx)
|
|
|
|
maps from the sumk block and index to the solver block and index
|
|
for *inequivalent* correlated shell ish
|
|
solver_to_sumk_block : list of dict
|
|
solver_to_sumk_block[ish][from_block] = to_block
|
|
|
|
maps from the solver block to the sumk block
|
|
for *inequivalent* correlated shell ish
|
|
deg_shells : list of lists of lists OR list of lists of dicts
|
|
In the simple format, ``deg_shells[ish][grp]`` is a list of
|
|
block names; ``ish`` is the index of the inequivalent correlated shell,
|
|
``grp`` is the index of the group of symmetry-related blocks.
|
|
When the name of two blocks is in the same group, that means that
|
|
these two blocks are the same by symmetry.
|
|
|
|
In the more general format, ``deg_shells[ish][grp]`` is a
|
|
dictionary whose keys are the block names that are part of the
|
|
group. The values of the dict for each key are tuples ``(v, conj)``,
|
|
where ``v`` is a transformation matrix with the same matrix dimensions
|
|
as the block and ``conj`` is a bool (whether or not to conjugate).
|
|
Two blocks with ``v_1, conj_1`` and ``v_2, conj_2`` being in the same
|
|
symmetry group means that
|
|
|
|
.. math::
|
|
|
|
C_1(v_1^\dagger G_1 v_1) = C_2(v_2^\dagger G_2 v_2),
|
|
|
|
where the :math:`G_i` are the Green's functions of the block,
|
|
and the functions :math:`C_i` conjugate their argument if the bool
|
|
``conj_i`` is ``True``.
|
|
corr_to_inequiv : list
|
|
a list where, for each correlated shell, the index of the corresponding
|
|
inequivalent correlated shell is given
|
|
transformation : list of numpy.array or list of dict
|
|
a list with entries for each ``ish`` giving transformation matrices
|
|
that are used on the Green's function in ``sumk`` space before
|
|
converting to the ``solver`` space
|
|
Up to the change in block structure,
|
|
|
|
.. math::
|
|
|
|
G_{solver} = T G_{sumk} T^\dagger
|
|
|
|
if :math:`T` is the ``transformation`` of that particular shell.
|
|
|
|
Note that for each shell this can either be a numpy array which
|
|
applies to all blocks or a dict with a transformation matrix for
|
|
each block.
|
|
"""
|
|
|
|
def __init__(self, gf_struct_sumk=None,
|
|
gf_struct_solver=None,
|
|
solver_to_sumk=None,
|
|
sumk_to_solver=None,
|
|
solver_to_sumk_block=None,
|
|
deg_shells=None,
|
|
corr_to_inequiv = None,
|
|
transformation=None):
|
|
self.gf_struct_sumk = gf_struct_sumk
|
|
self.gf_struct_solver = gf_struct_solver
|
|
self.solver_to_sumk = solver_to_sumk
|
|
self.sumk_to_solver = sumk_to_solver
|
|
self.solver_to_sumk_block = solver_to_sumk_block
|
|
self.deg_shells = deg_shells
|
|
self.corr_to_inequiv = corr_to_inequiv
|
|
self.transformation = transformation
|
|
|
|
@property
|
|
def gf_struct_solver_list(self):
|
|
""" The structure of the solver Green's function
|
|
|
|
This is returned as a
|
|
list (for each shell)
|
|
of lists (for each block)
|
|
of tuples (block_name, block_indices).
|
|
|
|
That is,
|
|
``gf_struct_solver_list[ish][b][0]``
|
|
is the name of the block number ``b`` of shell ``ish``, and
|
|
``gf_struct_solver_list[ish][b][1]``
|
|
is a list of its indices.
|
|
|
|
The list for each shell is sorted alphabetically by block name.
|
|
"""
|
|
if self.gf_struct_solver is None:
|
|
return None
|
|
# we sort by block name in order to get a reproducible result
|
|
return [sorted([(k, v) for k, v in list(gfs.items())], key=lambda x: x[0])
|
|
for gfs in self.gf_struct_solver]
|
|
|
|
@property
|
|
def gf_struct_sumk_list(self):
|
|
""" The structure of the sumk Green's function
|
|
|
|
This is returned as a
|
|
list (for each shell)
|
|
of lists (for each block)
|
|
of tuples (block_name, block_indices)
|
|
|
|
That is,
|
|
``gf_struct_sumk_list[ish][b][0]``
|
|
is the name of the block number ``b`` of shell ``ish``, and
|
|
``gf_struct_sumk_list[ish][b][1]``
|
|
is a list of its indices.
|
|
"""
|
|
return self.gf_struct_sumk
|
|
|
|
@property
|
|
def gf_struct_solver_dict(self):
|
|
""" The structure of the solver Green's function
|
|
|
|
This is returned as a
|
|
list (for each shell)
|
|
of dictionaries.
|
|
|
|
That is,
|
|
``gf_struct_solver_dict[ish][bname]``
|
|
is a list of the indices of block ``bname`` of shell ``ish``.
|
|
"""
|
|
return self.gf_struct_solver
|
|
|
|
@property
|
|
def gf_struct_sumk_dict(self):
|
|
""" The structure of the sumk Green's function
|
|
|
|
This is returned as a
|
|
list (for each shell)
|
|
of dictionaries.
|
|
|
|
That is,
|
|
``gf_struct_sumk_dict[ish][bname]``
|
|
is a list of the indices of block ``bname`` of shell ``ish``.
|
|
"""
|
|
if self.gf_struct_sumk is None:
|
|
return None
|
|
return [{block: indices for block, indices in gfs}
|
|
for gfs in self.gf_struct_sumk]
|
|
|
|
@property
|
|
def inequiv_to_corr(self):
|
|
""" A list mapping an inequivalent correlated shell to a correlated shell
|
|
"""
|
|
|
|
if self.corr_to_inequiv is None:
|
|
return None
|
|
N_solver = len(np.unique(self.corr_to_inequiv))
|
|
if self.gf_struct_solver is not None:
|
|
assert N_solver == len(self.gf_struct_solver)
|
|
assert sorted(np.unique(self.corr_to_inequiv)) == list(range(N_solver)),\
|
|
"an inequivalent shell is missing in corr_to_inequiv"
|
|
return [self.corr_to_inequiv.index(icrsh)
|
|
for icrsh in list(range(N_solver))]
|
|
|
|
@inequiv_to_corr.setter
|
|
def inequiv_to_corr(self, value):
|
|
# a check for backward compatibility
|
|
if value is None:
|
|
return
|
|
assert self.inequiv_to_corr == value, "Trying to set incompatible inequiv_to_corr"
|
|
|
|
@property
|
|
def sumk_to_solver_block(self):
|
|
if self.inequiv_to_corr is None:
|
|
return None
|
|
ret = []
|
|
for ish, icrsh in enumerate(self.inequiv_to_corr):
|
|
d = defaultdict(list)
|
|
for block_solver, block_sumk in list(self.solver_to_sumk_block[ish].items()):
|
|
d[block_sumk].append(block_solver)
|
|
ret.append(d)
|
|
return ret
|
|
|
|
@property
|
|
def effective_transformation_sumk(self):
|
|
""" Return the effective transformation matrix
|
|
|
|
A list of dicts, one for every correlated shell. In the dict,
|
|
there is a transformation matrix (as numpy array) for each
|
|
block in sumk space, that is used to transform the block.
|
|
"""
|
|
trans = copy.deepcopy(self.transformation)
|
|
if self.gf_struct_sumk is None:
|
|
raise Exception('gf_struct_sumk not set.')
|
|
if self.gf_struct_solver is None:
|
|
raise Exception('gf_struct_solver not set.')
|
|
|
|
if trans is None:
|
|
trans = [{block: np.eye(len(indices)) for block, indices in gfs}
|
|
for gfs in self.gf_struct_sumk]
|
|
|
|
assert isinstance(trans, list),\
|
|
"transformation has to be a list"
|
|
|
|
assert len(trans) == len(self.gf_struct_sumk),\
|
|
"give one transformation per correlated shell"
|
|
|
|
for icrsh in list(range(len(trans))):
|
|
ish = self.corr_to_inequiv[icrsh]
|
|
if trans[icrsh] is None:
|
|
trans[icrsh] = {block: np.eye(len(indices))
|
|
for block, indices in self.gf_struct_sumk[icrsh]}
|
|
|
|
if not isinstance(trans[icrsh], dict):
|
|
trans[icrsh] = {block: copy.deepcopy(trans[icrsh])
|
|
for block, indices in self.gf_struct_sumk[icrsh]}
|
|
|
|
assert list(trans[icrsh].keys()) == list(self.gf_struct_sumk_dict[icrsh].keys()),\
|
|
"wrong block names used in transformation (icrsh = {})".format(icrsh)
|
|
|
|
for block in trans[icrsh]:
|
|
assert trans[icrsh][block].shape[0] == trans[icrsh][block].shape[1],\
|
|
"Transformation has to be quadratic; throwing away orbitals can be achieved on the level of the mapping. (icrsh = {}, block = {})".format(icrsh, block)
|
|
|
|
assert trans[icrsh][block].shape[0] == len(self.gf_struct_sumk_dict[icrsh][block]),\
|
|
"Transformation block shape does not match gf_struct_sumk. (icrsh = {}, block = {})".format(icrsh, block)
|
|
|
|
# zero out all the lines of the transformation that are
|
|
# not included in gf_struct_solver
|
|
for iorb, norb in enumerate(self.gf_struct_sumk_dict[icrsh][block]):
|
|
if self.sumk_to_solver[ish][(block, norb)][0] is None:
|
|
trans[icrsh][block][iorb, :] = 0.0
|
|
return trans
|
|
|
|
@property
|
|
def effective_transformation_solver(self):
|
|
""" Return the effective transformation matrix
|
|
|
|
A list of dicts, one for every inequivalent correlated shell.
|
|
In the dict, there is a transformation matrix (as numpy array)
|
|
for each block in solver space, that is used to transform from
|
|
the sumk block (see :py:meth:`.solver_to_sumk_block`) to the
|
|
solver block.
|
|
|
|
|
|
For a solver block ``b`` for inequivalent correlated shell ``ish``,
|
|
the corresponding block of the solver Green's function is::
|
|
|
|
# the effective transformation matrix for the block
|
|
T = block_structure.effective_transformation_solver[ish][b]
|
|
# the index of the correlated shell
|
|
icrsh = block_structure.inequiv_to_corr[ish]
|
|
# the name of the corresponding sumk block
|
|
block_sumk = block_structure.solver_to_sumk_block[icrsh][b]
|
|
# transform the Green's function
|
|
G_solver[ish][b].from_L_G_R(T, G_sumk[icrsh][block_sumk], T.conjugate().transpose())
|
|
|
|
The functionality of that code block is implemented in
|
|
:py:meth:`.convert_gf` (i.e., you don't need to use this directly).
|
|
"""
|
|
|
|
eff_trans_sumk = self.effective_transformation_sumk
|
|
|
|
ets = []
|
|
for ish in range(len(self.gf_struct_solver)):
|
|
icrsh = self.inequiv_to_corr[ish]
|
|
ets.append(dict())
|
|
for block in self.gf_struct_solver[ish]:
|
|
block_sumk = self.solver_to_sumk_block[ish][block]
|
|
T = eff_trans_sumk[icrsh][block_sumk]
|
|
ets[ish][block] = np.zeros((len(self.gf_struct_solver[ish][block]),
|
|
len(T)),
|
|
dtype=T.dtype)
|
|
for i in self.gf_struct_solver[ish][block]:
|
|
i_sumk = self.solver_to_sumk[ish][block, i]
|
|
assert i_sumk[0] == block_sumk,\
|
|
"Wrong block in solver_to_sumk"
|
|
i_sumk = i_sumk[1]
|
|
ets[ish][block][i, :] = T[i_sumk, :]
|
|
return ets
|
|
|
|
|
|
@classmethod
|
|
def full_structure(cls,gf_struct,corr_to_inequiv):
|
|
""" Construct structure that maps to itself.
|
|
|
|
This has the same structure for sumk and solver, and the
|
|
mapping solver_to_sumk and sumk_to_solver is one-to-one.
|
|
|
|
Parameters
|
|
----------
|
|
gf_struct : list of dict
|
|
gf_struct[ish][block] = list of indices in that block
|
|
|
|
for (inequivalent) correlated shell ish
|
|
corr_to_inequiv : list
|
|
gives the mapping from correlated shell csh to inequivalent
|
|
correlated shell icsh, so that corr_to_inequiv[csh]=icsh
|
|
e.g. SumkDFT.corr_to_inequiv
|
|
|
|
if None, each inequivalent correlated shell is supposed to
|
|
be correspond to just one correlated shell with the same
|
|
index; there is not default, None has to be set explicitly!
|
|
"""
|
|
|
|
solver_to_sumk = []
|
|
s2sblock = []
|
|
gs_sumk = []
|
|
for ish in range(len(gf_struct)):
|
|
so2su = {}
|
|
so2sublock = {}
|
|
gss = []
|
|
for block in gf_struct[ish]:
|
|
so2sublock[block]=block
|
|
for ind in gf_struct[ish][block]:
|
|
so2su[(block,ind)]=(block,ind)
|
|
gss.append((block,gf_struct[ish][block]))
|
|
solver_to_sumk.append(so2su)
|
|
s2sblock.append(so2sublock)
|
|
gs_sumk.append(gss)
|
|
|
|
# gf_struct_sumk is not given for each inequivalent correlated
|
|
# shell, but for every correlated shell!
|
|
if corr_to_inequiv is not None:
|
|
gs_sumk_all = [None]*len(corr_to_inequiv)
|
|
for i in range(len(corr_to_inequiv)):
|
|
gs_sumk_all[i] = gs_sumk[corr_to_inequiv[i]]
|
|
else:
|
|
gs_sumk_all = gs_sumk
|
|
|
|
return cls(gf_struct_solver=copy.deepcopy(gf_struct),
|
|
gf_struct_sumk = gs_sumk_all,
|
|
solver_to_sumk = copy.deepcopy(solver_to_sumk),
|
|
sumk_to_solver = solver_to_sumk,
|
|
solver_to_sumk_block = s2sblock,
|
|
deg_shells = [[] for ish in range(len(gf_struct))],
|
|
corr_to_inequiv = corr_to_inequiv)
|
|
|
|
def pick_gf_struct_solver(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, i.e. the new structure will actually
|
|
be [{'up':[0],'down':[0]}].
|
|
|
|
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.
|
|
"""
|
|
|
|
assert len(self.gf_struct_solver) == len(new_gf_struct),\
|
|
"new_gf_struct has the wrong length"
|
|
|
|
|
|
for ish in range(len(self.gf_struct_solver)):
|
|
gf_struct = new_gf_struct[ish].copy()
|
|
|
|
# create new solver_to_sumk
|
|
so2su = {}
|
|
so2su_block = {}
|
|
for blk,idxs in list(gf_struct.items()):
|
|
for i in range(len(idxs)):
|
|
so2su[(blk, i)] = self.solver_to_sumk[ish][(blk, idxs[i])]
|
|
so2su_block[blk] = so2su[(blk, i)][0]
|
|
self.solver_to_sumk[ish] = so2su
|
|
self.solver_to_sumk_block[ish] = so2su_block
|
|
# create new sumk_to_solver
|
|
for k,v in list(self.sumk_to_solver[ish].items()):
|
|
blk,ind=v
|
|
if blk in gf_struct and ind in gf_struct[blk]:
|
|
new_ind = gf_struct[blk].index(ind)
|
|
self.sumk_to_solver[ish][k] = (blk, new_ind)
|
|
else:
|
|
self.sumk_to_solver[ish][k] = (None, None)
|
|
# adapt deg_shells
|
|
|
|
self.adapt_deg_shells(gf_struct, ish)
|
|
|
|
|
|
# reindexing gf_struct so that it starts with 0
|
|
for k in gf_struct:
|
|
gf_struct[k]=list(range(len(gf_struct[k])))
|
|
self.gf_struct_solver[ish]=gf_struct
|
|
|
|
def adapt_deg_shells(self, gf_struct, ish=0):
|
|
""" Adapts the deg_shells to a new gf_struct
|
|
Internally called when using pick_gf_struct and map_gf_struct
|
|
"""
|
|
if self.deg_shells is not None:
|
|
for degsh in self.deg_shells[ish]:
|
|
if isinstance(degsh, dict):
|
|
for key in list(degsh.keys()):
|
|
if not key in gf_struct:
|
|
del degsh[key]
|
|
continue
|
|
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(self.gf_struct_solver) == 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=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
|
|
|
|
from h5.formats import register_class
|
|
register_class(BlockStructure)
|