# This Source Code Form is subject to the terms of the Mozilla Public
# License, v. 2.0. If a copy of the MPL was not distributed with this
# file, You can obtain one at https://mozilla.org/MPL/2.0/.
from __future__ import annotations
import functools as ftool
import warnings
from collections import namedtuple
from numbers import Integral
from typing import Optional
import numpy as np
from numpy import (
allclose,
argsort,
concatenate,
delete,
diff,
insert,
int32,
intersect1d,
lexsort,
repeat,
searchsorted,
tile,
unique,
)
from numpy.lib.mixins import NDArrayOperatorsMixin
from scipy.sparse import csr_matrix
from sisl import _array as _a
from sisl._array import array_arange
from sisl._core import Atom, Geometry, Orbital
from sisl._internal import set_module
from sisl.messages import SislError, SislWarning, deprecate_argument, progressbar, warn
from sisl.typing import AtomsIndex, CellAxes, Coord, SeqOrScalarFloat
from sisl.utils.misc import direction
from sisl.utils.ranges import list2str
from .sparse import SparseCSR, _ncol_to_indptr, issparse
__all__ = ["SparseAtom", "SparseOrbital"]
class _SparseGeometry(NDArrayOperatorsMixin):
"""Sparse object containing sparse elements for a given geometry.
This is a base class intended to be sub-classed because the sparsity information
needs to be extracted from the ``_size`` attribute.
The sub-classed object _must_ implement the ``_size`` attribute.
The sub-classed object may re-implement the ``_cls_kwargs`` routine
to pass down keyword arguments when a new class is instantiated.
This object contains information regarding the
- geometry
"""
def __init__(
self,
geometry: Geometry,
dim: int = 1,
dtype=None,
nnzpr: Optional[int] = None,
**kwargs,
):
"""Create sparse object with element between orbitals"""
self._geometry = geometry
# Initialize the sparsity pattern
self.reset(dim, dtype, nnzpr)
@property
def geometry(self):
"""Associated geometry"""
return self._geometry
@property
def _size(self):
"""The size of the sparse object"""
return self.geometry.na
def __len__(self):
"""Number of rows in the basis"""
return self._size
def _cls_kwargs(self):
"""Custom keyword arguments when creating a new instance"""
return {}
def reset(
self, dim: Optional[int] = None, dtype=np.float64, nnzpr: Optional[int] = None
):
"""The sparsity pattern has all elements removed and everything is reset.
The object will be the same as if it had been
initialized with the same geometry as it were
created with.
Parameters
----------
dim :
number of dimensions per element, default to the current number of
elements per matrix element.
dtype : numpy.dtype, optional
the datatype of the sparse elements
nnzpr :
number of non-zero elements per row
"""
# I know that this is not the most efficient way to
# access a C-array, however, for constructing a
# sparse pattern, it should be faster if memory elements
# are closer...
if dim is None:
dim = self.dim
# We check the first atom and its neighbors, we then
# select max(5,len(nc) * 4)
if nnzpr is None:
nnzpr = self.geometry.close(0)
if nnzpr is None:
nnzpr = 8
else:
nnzpr = max(5, len(nnzpr) * 4)
# query dimension of sparse matrix
s = self._size
self._csr = SparseCSR((s, s * self.geometry.n_s, dim), nnzpr=nnzpr, dtype=dtype)
# Denote that one *must* specify all details of the elements
self._def_dim = -1
def empty(self, keep_nnz: bool = False):
"""See :meth:`~sparse.SparseCSR.empty` for details"""
self._csr.empty(keep_nnz)
@property
def dim(self):
"""Number of components per element"""
return self._csr.shape[-1]
@property
def shape(self):
"""Shape of sparse matrix"""
return self._csr.shape
@property
def dtype(self):
"""Data type of sparse elements"""
return self._csr.dtype
@property
def dkind(self):
"""Data type of sparse elements (in str)"""
return self._csr.dkind
@property
def nnz(self):
"""Number of non-zero elements"""
return self._csr.nnz
def translate2uc(self, atoms: AtomsIndex = None, axes: Optional[CellAxes] = None):
"""Translates all primary atoms to the unit cell.
With this, the coordinates of the geometry are translated to the unit cell
and the supercell connections in the matrix are updated accordingly.
Parameters
----------
atoms :
only translate the specified atoms. If not specified, all
atoms will be translated.
axes :
only translate certain lattice directions, `None` specifies
only the periodic directions
Returns
--------
SparseOrbital or SparseAtom
A new sparse matrix with the updated connections and a new associated geometry.
"""
# Sanitize the axes argument
if axes is None:
axes = (self.lattice.nsc > 1).nonzero()[0]
elif isinstance(axes, bool):
if axes:
axes = (0, 1, 2)
else:
raise ValueError(
"translate2uc with a bool argument can only be True to signal all axes"
)
else:
axes = list(map(direction, axes))
# Sanitize also the atoms argument
if atoms is None:
ats = slice(None)
else:
ats = self.geometry._sanitize_atoms(atoms).ravel()
# Get the fractional coordinates of the associated geometry
fxyz = self.geometry.fxyz
# Get the cell where each atom resides. In fractional coordinates, atoms in the unit cell
# are between 0 and 1. Anything else means that the atom resides in a periodic image. For
# atoms and axes that the user doesn't desire the translation, we are going to set the supercell
# offset as if it was 0, which will result in them not getting translated.
current_sc = np.zeros([self.na, 3], dtype=np.int32)
current_sc[ats, axes] = np.floor(fxyz[ats, axes]).astype(np.int32)
# Simply translate the atoms to move all atoms to the unit cell. That is, all atoms
# should be moved to supercell (0,0,0).
return self._translate_atoms_sc(-current_sc)
def _translate_atoms_sc(self, sc_translations):
"""Translates atoms across supercells.
This operation results in new coordinates of the associated geometry
and new indices for the matrix elements.
Parameters
----------
sc_translations : array of int of shape (na, 3)
For each atom, the displacement in number of supercells along each direction.
Returns
--------
SparseOrbital or SparseAtom
A new sparse matrix with the updated connections and a new associated geometry.
"""
# Make sure that supercell translations is an array of integers
sc_translations = np.asarray(sc_translations, dtype=int)
# Get the row and column of every element in the matrix
rows, cols = self.nonzero()
n_rows = len(self)
is_atom = n_rows == self.na
# Find out the unit cell indices for the columns, and the index of the supercell
# where they are currently located. This is done by dividing into the number of
# columns in the unit cell.
# We will do the conversion back to supercell indices when we know their
# new location after translation, and also the size of the new auxiliary supercell.
sc_idx, uc_col = np.divmod(cols, n_rows)
# We need the unit cell indices of the column atoms. If this is a SparseAtom object, then
# we have already computed them in the previous line. Otherwise, compute them.
if is_atom:
# atomic indices
at_row = rows
at_col = uc_col
else:
# orbital indices
at_row = self.o2a(rows)
at_col = self.o2a(cols) % self.na
# Get the supercell indices of the original positions.
isc = self.sc_off[sc_idx]
# We are going to now displace the supercell index of the connections
# according to how the two orbitals involved have moved. We store the
# result in the same array just to avoid using more memory.
isc += sc_translations[at_row] - sc_translations[at_col]
# It is possible that once we discover the new locations of the connections
# we find out that we need a bigger or smaller auxiliary supercell. Find out
# the size of the new auxiliary supercell.
new_nsc = np.max(abs(isc), axis=0) * 2 + 1
# Create a new geometry object with the new auxiliary supercell size.
new_geometry = self.geometry.copy()
new_geometry.set_nsc(new_nsc)
# Update the coordinates of the geometry, according to the cell
# displacements.
new_geometry.xyz = new_geometry.xyz + sc_translations @ new_geometry.cell
# Find out supercell indices in this new auxiliary supercell
new_sc = new_geometry.isc_off[isc[:, 0], isc[:, 1], isc[:, 2]]
# With this, we can compute the new columns
new_cols = uc_col + new_sc * n_rows
# Build the new csr matrix, which will just be a copy of the current one
# but updating the column indices. It is possible that there are column
# indices that are -1, which are the placeholders for new elements. We make sure
# that we update only the indices that are not -1.
# We also need to make sure that the shape of the matrix is appropiate
# for the size of the new auxiliary cell.
new_csr = self._csr.copy()
new_csr.col[new_csr.col >= 0] = new_cols
new_csr._shape = (n_rows, n_rows * new_geometry.n_s, new_csr.shape[-1])
# Create the new SparseGeometry matrix and associate to it the csr matrix that we have built.
new_matrix = self.__class__(new_geometry)
new_matrix._csr = new_csr
return new_matrix
def _translate_cells(self, old, new):
"""Translates all columns in the `old` cell indices to the `new` cell indices
Since the physical matrices are stored in a CSR form, with shape ``(no, no * n_s)`` each
block of ``(no, no)`` refers to supercell matrices with an offset according to the internal
supercell index.
This routine may be used to translate from one sorting of the columns to another sorting of the columns.
Parameters
----------
old : list of int
integer list of supercell indices (all smaller than `n_s`) that the current blocks of matrices
belong to.
new : list of int
integer list of supercell indices (all smaller than `n_s`) that the current blocks of matrices
are being transferred to. Must have same length as `old`.
"""
old = _a.asarrayi(old).ravel()
new = _a.asarrayi(new).ravel()
if len(old) != len(new):
raise ValueError(
self.__class__.__name__
+ ".translate_cells requires input and output indices with "
"equal length"
)
no = self.no
# Number of elements per matrix
n = _a.emptyi(len(old))
n.fill(no)
old = array_arange(old * no, n=n)
new = array_arange(new * no, n=n)
self._csr.translate_columns(old, new)
def edges(self, atoms: AtomsIndex, exclude: AtomsIndex = None):
"""Retrieve edges (connections) for all `atoms`
The returned edges are unique and sorted (see `numpy.unique`) and are returned
in supercell indices (i.e. ``0 <= edge < self.geometry.na_s``).
Parameters
----------
atoms :
the edges are returned only for the given atom
exclude :
remove edges which are in the `exclude` list.
See Also
--------
SparseCSR.edges: the underlying routine used for extracting the edges
"""
atoms = self.geometry._sanitize_atoms(atoms)
if exclude is not None:
exclude = self.geometry._sanitize_atoms(exclude)
return self._csr.edges(atoms, exclude)
def __str__(self):
"""Representation of the sparse model"""
s = f"{self.__class__.__name__}{{dim: {self.dim}, non-zero: {self.nnz}, kind={self.dkind}\n "
return s + str(self.geometry).replace("\n", "\n ") + "\n}"
def __repr__(self):
return f"<{self.__module__}.{self.__class__.__name__} shape={self._csr.shape[:-1]}, dim={self.dim}, nnz={self.nnz}, kind={self.dkind}>"
def __getattr__(self, attr):
"""Overload attributes from the hosting geometry
Any attribute not found in the sparse class will
be looked up in the hosting geometry.
"""
return getattr(self.geometry, attr)
# Make the indicis behave on the contained sparse matrix
def __delitem__(self, key):
"""Delete elements of the sparse elements"""
del self._csr[key]
def __contains__(self, key):
"""Check whether a sparse index is non-zero"""
return key in self._csr
def set_nsc(self, base_size, *args, **kwargs):
"""Reset the number of allowed supercells in the sparse geometry
If one reduces the number of supercells, *any* sparse element
that references the supercell will be deleted.
See `Lattice.set_nsc` for allowed parameters.
See Also
--------
Lattice.set_nsc : the underlying called method
"""
lattice = self.lattice.copy()
# Try first in the new one, then we figure out what to do
lattice.set_nsc(*args, **kwargs)
if allclose(lattice.nsc, self.lattice.nsc):
return
# Create an array of all things that should be translated
old = []
new = []
deleted = np.empty(self.n_s, np.bool_)
deleted[:] = True
for i, sc_off in lattice:
try:
# Luckily there are *only* one time wrap-arounds
j = self.lattice.sc_index(sc_off)
# Now do translation
old.append(j)
new.append(i)
deleted[j] = False
except ValueError:
# Not found, i.e. new, so no need to translate
pass
# 1. Ensure that any one of the *old* supercells that
# are now deleted are put in the end
for i, j in enumerate(deleted.nonzero()[0]):
# Old index (j)
old.append(j)
# Move to the end (*HAS* to be higher than the number of
# cells in the new supercell structure)
new.append(max(self.n_s, lattice.n_s) + i)
# Check that we will translate all indices in the old
# sparsity pattern to the new one
if len(old) not in (self.n_s, lattice.n_s):
raise SislError("Not all supercells are accounted for")
old = _a.arrayi(old)
new = _a.arrayi(new)
# Assert that there are only unique values
if len(unique(old)) != len(old):
raise SislError("non-unique values in old set_nsc")
if len(unique(new)) != len(new):
raise SislError("non-unique values in new set_nsc")
if self.n_s != len(old):
raise SislError("non-valid size of in old set_nsc")
# Figure out if we need to do any work
keep = (old != new).nonzero()[0]
if len(keep) > 0:
# Reduce pivoting work
old = old[keep]
new = new[keep]
# Create the translation tables
n = tile([base_size], len(old))
old = array_arange(old * base_size, n=n)
new = array_arange(new * base_size, n=n)
# Move data to new positions
self._csr.translate_columns(old, new, clean=False)
max_n = new.max() + 1
else:
max_n = 0
# Make sure we delete all column values where we have put fake values
delete = _a.arangei(lattice.n_s * base_size, max(max_n, self.shape[1]))
if len(delete) > 0:
self._csr.delete_columns(delete, keep_shape=True)
# Ensure the shape is correct
shape = list(self._csr.shape)
shape[1] = base_size * lattice.n_s
self._csr._shape = tuple(shape)
self._csr._clean_columns()
self.geometry.set_nsc(*args, **kwargs)
def transpose(self, sort: bool = True):
"""Create the transposed sparse geometry by interchanging supercell indices
Sparse geometries are (typically) relying on symmetry in the supercell picture.
Thus when one transposes a sparse geometry one should *ideally* get the same
matrix. This is true for the Hamiltonian, density matrix, etc.
This routine transposes all rows and columns such that any interaction between
row, `r`, and column `c` in a given supercell `(i,j,k)` will be transposed
into row `c`, column `r` in the supercell `(-i,-j,-k)`.
Parameters
----------
sort :
the returned columns for the transposed structure will be sorted
if this is true, default
Notes
-----
The components for each sparse element are not changed in this method.
Examples
--------
Force a sparse geometry to be Hermitian:
>>> sp = SparseOrbital(...)
>>> sp = (sp + sp.transpose()) / 2
Returns
-------
object
an equivalent sparse geometry with transposed matrix elements
"""
# Create a temporary copy to put data into
T = self.copy()
# clean memory to not crowd memory too much
T._csr.ptr = None
T._csr.col = None
T._csr.ncol = None
T._csr._D = None
# Short-links
lattice = self.geometry.lattice
# Create "DOK" format indices
csr = self._csr
# Number of rows (used for converting to supercell indices)
# With this we don't need to figure out if we are dealing with
# atoms or orbitals
size = csr.shape[0]
# First extract the actual data
ncol = csr.ncol.view()
if csr.finalized:
# ptr = csr.ptr.view()
col = csr.col.copy()
D = csr._D.copy()
else:
idx = array_arange(csr.ptr[:-1], n=ncol, dtype=int32)
# ptr = _ncol_to_indptr(ncol)
col = csr.col[idx]
D = csr._D[idx, :].copy()
del idx
# figure out rows where ncol is > 0
# we skip the first column
row_nonzero = (ncol > 0).nonzero()[0]
row = repeat(row_nonzero.astype(np.int32, copy=False), ncol[row_nonzero])
# Now we have the DOK format
# row, col, _D
# Retrieve all sc-indices in the new transposed array
new_sc_off = lattice.sc_index(-lattice.sc_off)
# Calculate the row-offsets in the new sparse geometry
row += new_sc_off[lattice.sc_index(lattice.sc_off[col // size, :])] * size
# Now convert columns into unit-cell
col %= size
# Now we can re-create the sparse matrix
# All we need is to count the number of non-zeros per column.
rows, nrow = unique(col, return_counts=True)
T._csr.ncol = _a.zerosi(size)
T._csr.ncol[rows] = nrow
del rows
if sort:
# also sort individual rows for each column
idx = lexsort((row, col))
else:
# sort columns to get transposed values.
# This will randomize the rows
idx = argsort(col)
# Our new data will then be
T._csr.col = row[idx]
del row
T._csr._D = D[idx]
del D
T._csr.ptr = _ncol_to_indptr(T._csr.ncol)
# If `sort` we have everything sorted, otherwise it
# is not ensured
T._csr._finalized = sort
return T
def spalign(self, other):
"""See :meth:`~sisl.sparse.SparseCSR.align` for details"""
if isinstance(other, SparseCSR):
self._csr.align(other)
else:
self._csr.align(other._csr)
def eliminate_zeros(self, *args, **kwargs):
"""Removes all zero elements from the sparse matrix
This is an *in-place* operation.
See Also
--------
SparseCSR.eliminate_zeros : method called, see there for parameters
"""
self._csr.eliminate_zeros(*args, **kwargs)
# Create iterations on the non-zero elements
def iter_nnz(self):
"""Iterations of the non-zero elements
An iterator on the sparse matrix with, row and column
Examples
--------
>>> for i, j in self.iter_nnz():
... self[i, j] # is then the non-zero value
"""
yield from self._csr
__iter__ = iter_nnz
def create_construct(self, R, params):
"""Create a simple function for passing to the `construct` function.
This is simply to leviate the creation of simplistic
functions needed for setting up the sparse elements.
Basically this returns a function:
>>> def func(self, ia, atoms, atoms_xyz=None):
... idx = self.geometry.close(ia, R=R, atoms=atoms, atoms_xyz=atoms_xyz)
... for ix, p in zip(idx, params):
... self[ia, ix] = p
Notes
-----
This function only works for geometry sparse matrices (i.e. one
element per atom). If you have more than one element per atom
you have to implement the function your-self.
Parameters
----------
R : array_like
radii parameters for different shells.
Must have same length as `params` or one less.
If one less it will be extended with ``R[0]/100``
params : array_like
coupling constants corresponding to the `R`
ranges. ``params[0, :]`` are the elements
for the all atoms within ``R[0]`` of each atom.
See Also
--------
construct : routine to create the sparse matrix from a generic function (as returned from `create_construct`)
"""
if len(R) != len(params):
raise ValueError(
f"{self.__class__.__name__}.create_construct got different lengths of `R` and `param`"
)
def func(self, ia, atoms, atoms_xyz=None):
idx = self.geometry.close(ia, R=R, atoms=atoms, atoms_xyz=atoms_xyz)
for ix, p in zip(idx, params):
self[ia, ix] = p
func.R = R
func.params = params
return func
def construct(self, func, na_iR: int = 1000, method: str = "rand", eta=None):
"""Automatically construct the sparse model based on a function that does the setting up of the elements
This may be called in two variants.
1. Pass a function (`func`), see e.g. ``create_construct``
which does the setting up.
2. Pass a tuple/list in `func` which consists of two
elements, one is ``R`` the radii parameters for
the corresponding parameters.
The second is the parameters
corresponding to the ``R[i]`` elements.
In this second case all atoms must only have
one orbital.
Parameters
----------
func : callable or array_like
this function *must* take 4 arguments.
1. Is this object (``self``)
2. Is the currently examined atom (``ia``)
3. Is the currently bounded indices (``idxs``)
4. Is the currently bounded indices atomic coordinates (``idxs_xyz``)
An example `func` could be:
>>> def func(self, ia, atoms, atoms_xyz=None):
... idx = self.geometry.close(ia, R=[0.1, 1.44], atoms=atoms, atoms_xyz=atoms_xyz)
... self[ia, idx[0]] = 0
... self[ia, idx[1]] = -2.7
na_iR : int, optional
number of atoms within the sphere for speeding
up the `iter_block` loop.
method : {'rand', str}
method used in `Geometry.iter_block`, see there for details
eta : bool, optional
whether an ETA will be printed
See Also
--------
create_construct : a generic function used to create a generic function which this routine requires
tile : tiling *after* construct is much faster for very large systems
repeat : repeating *after* construct is much faster for very large systems
"""
if not callable(func):
if not isinstance(func, (tuple, list)):
raise ValueError(
"Passed `func` which is not a function, nor tuple/list of `R, param`"
)
if np.any(diff(self.geometry.lasto) > 1):
raise ValueError(
"Automatically setting a sparse model "
"for systems with atoms having more than 1 "
"orbital *must* be done by your-self. You have to define a corresponding `func`."
)
# Convert to a proper function
func = self.create_construct(func[0], func[1])
try:
# if the function was created through `create_construct`, then
# we have access to the radii used.
R = func.R
try:
if len(R) > 0:
R = R[-1]
except TypeError:
pass
except AttributeError:
R = None
iR = self.geometry.iR(na_iR, R=R)
# Create eta-object
eta = progressbar(self.na, f"{self.__class__.__name__ }.construct", "atom", eta)
# Do the loop
for ias, idxs in self.geometry.iter_block(iR=iR, method=method, R=R):
# Get all the indexed atoms...
# This speeds up the searching for coordinates...
idxs_xyz = self.geometry[idxs]
# Loop the atoms inside
for ia in ias:
func(self, ia, idxs, idxs_xyz)
eta.update(len(ias))
eta.close()
@property
def finalized(self):
"""Whether the contained data is finalized and non-used elements have been removed"""
return self._csr.finalized
def untile(
self,
prefix: str,
reps: int,
axis: int,
segment: int = 0,
*args,
sym: bool = True,
**kwargs,
):
"""Untiles a sparse model into a minimum segment, reverse of `tile`
Parameters
----------
prefix : {a, o}
which quantity to request for the size of the matrix
reps :
number of untiles that needs to be performed
axis :
which axis we need to untile (length with be ``1/reps`` along this axis)
segment :
which segment to return, default to the first segment. For a fully symmetric
system there should not be a difference, requesting different segments can
be used to assert this is the case.
sym :
whether to symmetrize before returning
"""
# Create new geometry
with warnings.catch_warnings(record=True) as w:
# Cause all warnings to always be triggered.
warnings.simplefilter("always")
# Create new untiled geometry
geom = self.geometry.untile(reps, axis, segment, *args, **kwargs)
# Check whether the warning exists
if len(w) > 0:
if issubclass(w[-1].category, SislWarning):
warn(
f"{str(w[-1].message)}\n---\n"
"The sparse matrix cannot be untiled as the structure "
"cannot be tiled accordingly. ANY use of the model has been "
"relieved from sisl."
)
# Now we need to re-create number of supercells
no = getattr(self, f"n{prefix}")
geom_no = getattr(geom, f"n{prefix}")
# orig-orbs
orig_orbs = _a.arangei(segment * geom_no, (segment + 1) * geom_no)
# create correct linear offset due to the segment.
# Further below we will take out the linear indices by modulo and integer
# division operations.
lsc = tile(self.geometry.lattice.sc_off, (1, reps)).reshape(-1, reps, 3)
lsc[:, :, axis] = lsc[:, :, axis] * reps + _a.arangei(reps) - segment
lsc.shape = (-1, 3)
# now we have the *correct* lsc that corresponds to the
# sc_off in the cut structure.
# We will later down correct the *wrong* indices
# since we may have nsc == 1 and cut it X times.
# In this case we may find [0, 1, 2, 3, ..., X-1]
# which is clearly wrong. In stead we should determine
# the correct nsc for the output geometry and convert it to
# [-X//2, ..., 0, ... , X//2] (or close to this)
# First we need to figure out how long the interaction range is
# in the cut-direction
# We initialize to be the same as the parent direction
nsc = self.nsc.copy()
# get unique couplings for the orbitals we are cutting out
# we ensure the *onsite* columns are also there
# create sample sparse pattern so we can figure out the columns
# they connect to
S = self.tocsr(0)
sub = np.union1d(unique(S[orig_orbs, :].indices), orig_orbs)
del S
if len(sub) == 0:
raise ValueError(
f"{self.__class__.__name__}.untile couples to no "
"matrix elements, an empty sparse model cannot be split."
)
# Figure out the supercell indices of sub
sub_sc = getattr(self.geometry, f"{prefix}2isc")(sub)
# convert the sub_sc[axis] into the linear index to figure out the
# actual number of required nsc
sub_lsc = (sub % no + sub_sc[:, axis] * no) // geom_no - segment
# calculate (sorted) unique linear cells
# This is just to figure out how many we are connecting too
sub_lsc = unique(sub_lsc)
# determine the cut placement
if nsc[axis] == 1:
# no initial supercell, special handling
dsub_lsc = np.diff(sub_lsc)
if np.all(dsub_lsc == 1) and len(sub_lsc) == reps:
# the full cut region is touched
nsc[axis] = (reps // 2) * 2 + 1
# here the couplings *touches* each others segments
# We have to figure out if the couplings are *for* real
# or whether we can easily cut them.
if reps % 2 == 1:
# an un-even number of couplings in total
# this means that the same couplings will be duplicated
# to the right and left.
# Example:
# [-1 0 1 2] or [0 1 2 3]
# [0] -> [2] positive direction
# [0] <- [2] negative direction
if sym:
msg = f"The elements connecting from the primary unit-cell to the {nsc[axis]//2} unit-cell will be halved, sym={sym}."
else:
msg = f"The returned matrix will not have symmetric couplings due to sym={sym} argument."
warn(
f"{self.__class__.__name__}.untile matrix has connections crossing "
"the entire unit cell. "
f"This may result in wrong behavior due to non-unique matrix elements. {msg}"
)
else:
# even case
# [-1 0 1]
# [0] -> [1] positive direction
# [0] <- [-1] negative direction
# or [0 1 2]
# [0] -> [1] positive direction
# [0] <- [2] negative direction
warn(
f"{self.__class__.__name__}.untile may have connections crossing "
"the entire unit cell. "
"This may result in wrong behavior due to non-unique matrix elements."
)
else:
# we have something like
# [0 1 - 3]
# meaning that there is a gab in the couplings
# remove duplicate neighboring values
single_sel = np.ones(len(sub_lsc), dtype=bool)
single_sel[1:] = sub_lsc[1:] != sub_lsc[:-1]
single_sub_lsc = sub_lsc[single_sel]
axis0 = (single_sub_lsc == 0).nonzero()[0][0]
# initialize
pos_nsc = 0
found = True
while found:
try:
if single_sub_lsc[axis0 + pos_nsc + 1] == pos_nsc + 1:
pos_nsc += 1
else:
found = False
except Exception:
found = False
neg_nsc = 0
found = True
while found:
try:
if single_sub_lsc[axis0 + neg_nsc - 1] == neg_nsc - 1:
neg_nsc -= 1
else:
found = False
except Exception:
found = False
nsc[axis] = max(pos_nsc, -neg_nsc) * 2 + 1
# correct the linear indices that are *too* high
hnsc = nsc[axis] // 2
lsc[lsc[:, axis] > hnsc, axis] -= reps
lsc[lsc[:, axis] < -hnsc, axis] += reps
# this will still leave some supercell indices *wrong*
# But the algorithm should detect that they are not coupled and
# thus should not be queried.
else:
# *easy* case, we always have supercells so we can't cut too short
# Simply track off the biggest one
nsc[axis] = np.abs(sub_lsc).max() * 2 + 1
# Create the to-columns
if sub_lsc.max() != -sub_lsc.min():
raise ValueError(
f"{self.__class__.__name__}.untile found inconsistent supercell matrix. "
f"The untiled sparse matrix couples to {sub_lsc} supercells but expected a symmetric set of couplings. "
"This may happen if doing multiple cuts along the same direction, or if the matrix is not correctly constructed."
)
# Update number of super-cells
geom.set_nsc(nsc)
# Now we have the following items:
# 1. sub_sc, the supercell offsets for the connecting orbitals
# 2. lsc, containing the linear indices of sub_sc that are directly related
# to the cut structure
# 3. geom, which is the cut structure
def conv(dim):
nonlocal lsc
csr = self.tocsr(dim)[orig_orbs, :]
cols = csr.indices
# now convert cols
cols_lsc = lsc[cols // geom_no]
cols = cols % geom_no + geom.sc_index(cols_lsc) * geom_no
return csr_matrix(
(csr.data, cols, csr.indptr),
shape=(geom_no, geom_no * geom.n_s),
dtype=self.dtype,
)
Ps = [conv(dim) for dim in range(self.dim)]
S = self.fromsp(geom, Ps, **self._cls_kwargs())
if sym:
S *= 0.5
return S + S.transpose()
return S
def unrepeat(
self, reps: int, axis: int, segment: int = 0, *args, sym: bool = True, **kwargs
):
"""Unrepeats the sparse model into different parts (retaining couplings)
Please see `untile` for details, the algorithm and arguments are the same however,
this is the opposite of `repeat`.
"""
atoms = np.arange(self.geometry.na).reshape(-1, reps).T.ravel()
return self.sub(atoms).untile(reps, axis, segment, *args, sym=sym, **kwargs)
def finalize(self):
"""Finalizes the model
Finalizes the model so that all non-used elements are removed. I.e. this simply reduces the memory requirement for the sparse matrix.
Note that adding more elements to the sparse matrix is more time-consuming than for a non-finalized sparse matrix due to the
internal data-representation.
"""
self._csr.finalize()
def tocsr(self, dim: int = 0, isc=None, **kwargs):
"""Return a :class:`~scipy.sparse.csr_matrix` for the specified dimension
Parameters
----------
dim :
the dimension in the sparse matrix (for non-orthogonal cases the last
dimension is the overlap matrix)
isc : int, optional
the supercell index, or all (if ``isc=None``)
"""
if isc is not None:
raise NotImplementedError(
"Requesting sub-sparse has not been implemented yet"
)
return self._csr.tocsr(dim, **kwargs)
def spsame(self, other):
"""Compare two sparse objects and check whether they have the same entries.
This does not necessarily mean that the elements are the same
"""
return self._csr.spsame(other._csr)
@classmethod
def fromsp(cls, geometry: Geometry, P, **kwargs):
r"""Create a sparse model from a preset `Geometry` and a list of sparse matrices
The passed sparse matrices are in one of `scipy.sparse` formats.
Parameters
----------
geometry : Geometry
geometry to describe the new sparse geometry
P : list of scipy.sparse or scipy.sparse
the new sparse matrices that are to be populated in the sparse
matrix
**kwargs : optional
any arguments that are directly passed to the ``__init__`` method
of the class.
Returns
-------
SparseGeometry
a new sparse matrix that holds the passed geometry and the elements of `P`
"""
# Ensure list of * format (to get dimensions)
if issparse(P):
P = [P]
if isinstance(P, tuple):
P = list(P)
p = cls(geometry, len(P), P[0].dtype, 1, **kwargs)
p._csr = p._csr.fromsp(*P, dtype=kwargs.get("dtype"))
if p._size != P[0].shape[0]:
raise ValueError(
f"{cls.__name__}.fromsp cannot create a new class, the geometry "
"and sparse matrices does not have coinciding dimensions size != P[0].shape[0]"
)
return p
# numpy dispatch methods (same priority as SparseCSR!)
__array_priority__ = 14
def __array_ufunc__(self, ufunc, method, *inputs, **kwargs):
# grab the inputs and convert to the respective csr matrices
# such that we can defer the call to that function
# while converting, also grab the first _SparseGeometry
# object such that we may create the output matrix
sp_inputs = []
obj = None
for inp in inputs:
if isinstance(inp, _SparseGeometry):
if obj is None:
# simply store a reference to the first argument that is a sparsegeometry
obj = inp
sp_inputs.append(inp._csr)
else:
sp_inputs.append(inp)
# determine if the user requested output into
# a specific container
out = kwargs.pop("out", None)
if out is not None:
(out,) = out
# ensure the output returns in this field
kwargs["out"] = (out._csr,)
result = self._csr.__array_ufunc__(ufunc, method, *sp_inputs, **kwargs)
if out is not None:
# check that the resulting variable is indeed a sparsecsr
assert isinstance(
result, SparseCSR
), f"{self.__class__.__name__} ({ufunc.__name__}) requires out= to match the resulting operator"
if isinstance(result, SparseCSR):
# return a copy with the sparse result into the output sparse
# matrix. If out was not None, the result should already
# be stored in it.
if out is None:
out = obj.copy()
out._csr = result
else:
# likely reductions etc.
out = result
return out
def __getstate__(self):
"""Return dictionary with the current state"""
return {
"geometry": self.geometry.__getstate__(),
"csr": self._csr.__getstate__(),
}
def __setstate__(self, state):
"""Return dictionary with the current state"""
geom = Geometry([0] * 3, Atom(1))
geom.__setstate__(state["geometry"])
self._geometry = geom
csr = SparseCSR((2, 2, 2))
csr.__setstate__(state["csr"])
self._csr = csr
self._def_dim = -1
@set_module("sisl")
class SparseAtom(_SparseGeometry):
"""Sparse object with number of rows equal to the total number of atoms in the `Geometry`"""
def __getitem__(self, key):
"""Elements for the index(s)"""
dd = self._def_dim
if len(key) > 2:
# This may be a specification of supercell indices
if isinstance(key[-1], tuple):
# We guess it is the supercell index
off = self.geometry.sc_index(key[-1]) * self.na
key = [el for el in key[:-1]]
key[1] = self.geometry.sc2uc(key[1]) + off
if dd >= 0:
key = tuple(key) + (dd,)
self._def_dim = -1
d = self._csr[key]
return d
def __setitem__(self, key, val):
"""Set or create elements in the sparse data
Override set item for slicing operations and enables easy
setting of parameters in a sparse matrix
"""
if len(key) > 2:
# This may be a specification of supercell indices
if isinstance(key[-1], tuple):
# We guess it is the supercell index
off = self.geometry.sc_index(key[-1]) * self.na
key = [el for el in key[:-1]]
key[1] = self.geometry.sc2uc(key[1]) + off
key = tuple(
self.geometry._sanitize_atoms(k) if i < 2 else k for i, k in enumerate(key)
)
dd = self._def_dim
if dd >= 0:
key = tuple(key) + (dd,)
self._def_dim = -1
self._csr[key] = val
@property
def _size(self):
return self.geometry.na
[docs]
def nonzero(self, atoms: AtomsIndex = None, only_cols: bool = False):
"""Indices row and column indices where non-zero elements exists
Parameters
----------
atoms :
only return the tuples for the requested atoms, default is all atoms
only_cols :
only return the non-zero columns
See Also
--------
SparseCSR.nonzero : the equivalent function call
"""
atoms = self.geometry._sanitize_atoms(atoms)
return self._csr.nonzero(rows=atoms, only_cols=only_cols)
[docs]
def iter_nnz(self, atoms: AtomsIndex = None):
"""Iterations of the non-zero elements
An iterator on the sparse matrix with, row and column
Examples
--------
>>> for i, j in self.iter_nnz():
... self[i, j] # is then the non-zero value
Parameters
----------
atoms :
only loop on the non-zero elements coinciding with the atoms
"""
if atoms is None:
yield from self._csr
else:
atoms = self.geometry._sanitize_atoms(atoms)
yield from self._csr.iter_nnz(atoms)
[docs]
def set_nsc(self, *args, **kwargs):
"""Reset the number of allowed supercells in the sparse atom
If one reduces the number of supercells *any* sparse element
that references the supercell will be deleted.
See `Lattice.set_nsc` for allowed parameters.
See Also
--------
Lattice.set_nsc : the underlying called method
"""
super().set_nsc(self.na, *args, **kwargs)
[docs]
def untile(
self, reps: int, axis: int, segment: int = 0, *args, sym: bool = True, **kwargs
):
"""Untiles the sparse model into different parts (retaining couplings)
Recreates a new sparse object with only the cutted
atoms in the structure. This will preserve matrix elements in the supercell.
Parameters
----------
reps :
number of repetitions the tiling function created (opposite meaning as in `untile`)
axis :
which axis to untile along
segment :
which segment to retain. Generally each segment should be equivalent, however
requesting individiual segments can help uncover inconsistencies in the sparse matrix
*args :
arguments passed directly to `Geometry.untile`
sym :
if True, the algorithm will ensure the returned matrix is symmetrized (i.e.
return ``(M + M.transpose())/2``, else return data as is.
False should generally only be used for debugging precision of the matrix elements,
or if one wishes to check the warnings.
**kwargs :
keyword arguments passed directly to `Geometry.untile`
Notes
-----
Untiling structures with ``nsc == 1`` along `axis` are assumed to have periodic boundary
conditions.
When untiling structures with ``nsc == 1`` along `axis` it is important to
untile *as much as possible*. This is because otherwise the algorithm cannot determine
the correct couplings. Therefore to create a geometry of 3 times a unit-cell, one should
untile to the unit-cell, and subsequently tile 3 times.
Consider for example a system of 4 atoms, each atom connects to its 2 neighbors.
Due to the PBC atom 0 will connect to 1 and 3. Untiling this structure in 2 will
group couplings of atoms 0 and 1. As it will only see one coupling to the right
it will halve the coupling and use the same coupling to the left, which is clearly wrong.
In the following the latter is the correct way to do it.
>>> SPM.untile(2, 0) != SPM.untile(4, 0).tile(2, 0)
Raises
------
ValueError :
in case the matrix elements are not conseuctive when determining the
new supercell structure. This may often happen if untiling a matrix
too few times, and then untiling it again.
See Also
--------
tile : opposite of this method
Geometry.untile : same as this method, see details about parameters here
"""
return super().untile("a", reps, axis, segment, *args, sym=sym, **kwargs)
[docs]
def rij(self, dtype=np.float64):
r"""Create a sparse matrix with the distance between atoms
Parameters
----------
dtype : numpy.dtype, optional
the data-type of the sparse matrix.
Notes
-----
The returned sparse matrix with distances are taken from the current sparse pattern.
I.e. a subsequent addition of sparse elements will make them inequivalent.
It is thus important to *only* create the sparse distance when the sparse
structure is completed.
"""
R = self.Rij(dtype)
R._csr = np.sum(R._csr**2, axis=-1) ** 0.5
return R
[docs]
def Rij(self, dtype=np.float64):
r"""Create a sparse matrix with vectors between atoms
Parameters
----------
dtype : numpy.dtype, optional
the data-type of the sparse matrix.
Notes
-----
The returned sparse matrix with vectors are taken from the current sparse pattern.
I.e. a subsequent addition of sparse elements will make them inequivalent.
It is thus important to *only* create the sparse vector matrix when the sparse
structure is completed.
"""
geom = self.geometry
Rij = geom.Rij
# Pointers
ncol = self._csr.ncol
ptr = self._csr.ptr
col = self._csr.col
# Create the output class
R = SparseAtom(geom, 3, dtype, nnzpr=1)
# Re-create the sparse matrix data
R._csr.ptr = ptr.copy()
R._csr.ncol = ncol.copy()
R._csr.col = col.copy()
R._csr._nnz = self._csr.nnz
R._csr._D = np.zeros([self._csr._D.shape[0], 3], dtype=dtype)
R._csr._finalized = self.finalized
for ia in range(self.shape[0]):
sl = slice(ptr[ia], ptr[ia] + ncol[ia])
R._csr._D[sl, :] = Rij(ia, col[sl])
return R
@set_module("sisl")
class SparseOrbital(_SparseGeometry):
"""Sparse object with number of rows equal to the total number of orbitals in the `Geometry`"""
def __getitem__(self, key):
"""Elements for the index(s)"""
dd = self._def_dim
if len(key) > 2:
# This may be a specification of supercell indices
if isinstance(key[-1], tuple):
# We guess it is the supercell index
off = self.geometry.sc_index(key[-1]) * self.no
key = [el for el in key[:-1]]
key[1] = self.geometry.osc2uc(key[1]) + off
if dd >= 0:
key = tuple(key) + (dd,)
self._def_dim = -1
d = self._csr[key]
return d
def __setitem__(self, key, val):
"""Set or create elements in the sparse data
Override set item for slicing operations and enables easy
setting of parameters in a sparse matrix
"""
if len(key) > 2:
# This may be a specification of supercell indices
if isinstance(key[-1], tuple):
# We guess it is the supercell index
off = self.geometry.sc_index(key[-1]) * self.no
key = [el for el in key[:-1]]
key[1] = self.geometry.osc2uc(key[1]) + off
key = tuple(
self.geometry._sanitize_orbs(k) if i < 2 else k for i, k in enumerate(key)
)
dd = self._def_dim
if dd >= 0:
key = tuple(key) + (dd,)
self._def_dim = -1
self._csr[key] = val
@property
def _size(self):
return self.geometry.no
[docs]
def edges(
self,
atoms: AtomsIndex = None,
exclude: AtomsIndex = None,
orbitals=None,
):
"""Retrieve edges (connections) for all `atoms`
The returned edges are unique and sorted (see `numpy.unique`) and are returned
in supercell indices (i.e. ``0 <= edge < self.geometry.no_s``).
Parameters
----------
atoms :
the edges are returned only for the given atom (but by using all orbitals of the
requested atom). The returned edges are also atoms.
exclude :
remove edges which are in the `exclude` list, this list refers to orbitals.
orbitals : int or list of int
the edges are returned only for the given orbital. The returned edges are orbitals.
See Also
--------
SparseCSR.edges: the underlying routine used for extracting the edges
"""
if exclude is not None:
exclude = self.geometry._sanitize_atoms(exclude)
if atoms is None and orbitals is None:
raise ValueError(
f"{self.__class__.__name__}.edges must have either 'atoms' or 'orbitals' keyword defined."
)
if orbitals is None:
return unique(
self.geometry.o2a(
self._csr.edges(self.geometry.a2o(atoms, True), exclude)
)
)
orbitals = self.geometry._sanitize_orbs(orbitals)
return self._csr.edges(orbitals, exclude)
[docs]
def nonzero(self, atoms: AtomsIndex = None, only_cols: bool = False):
"""Indices row and column indices where non-zero elements exists
Parameters
----------
atoms :
only return the tuples for the requested atoms, default is all atoms
But for *all* orbitals.
only_cols :
only return then non-zero columns
See Also
--------
SparseCSR.nonzero : the equivalent function call
"""
if atoms is None:
return self._csr.nonzero(only_cols=only_cols)
rows = self.geometry.a2o(atoms, all=True)
return self._csr.nonzero(rows=rows, only_cols=only_cols)
[docs]
def iter_nnz(self, atoms: AtomsIndex = None, orbitals=None):
"""Iterations of the non-zero elements
An iterator on the sparse matrix with, row and column
Examples
--------
>>> for i, j in self.iter_nnz():
... self[i, j] # is then the non-zero value
Parameters
----------
atoms :
only loop on the non-zero elements coinciding with the orbitals
on these atoms (not compatible with the `orbitals` keyword)
orbitals : int or array_like
only loop on the non-zero elements coinciding with the orbital
(not compatible with the `atoms` keyword)
"""
if atoms is not None:
orbitals = self.geometry.a2o(atoms, True)
elif not orbitals is None:
orbitals = _a.asarrayi(orbitals)
if orbitals is None:
yield from self._csr
else:
yield from self._csr.iter_nnz(orbitals)
[docs]
def set_nsc(self, *args, **kwargs):
"""Reset the number of allowed supercells in the sparse orbital
If one reduces the number of supercells *any* sparse element
that references the supercell will be deleted.
See `Lattice.set_nsc` for allowed parameters.
See Also
--------
Lattice.set_nsc : the underlying called method
"""
super().set_nsc(self.no, *args, **kwargs)
[docs]
def remove_orbital(self, atoms: AtomsIndex, orbitals):
"""Remove a subset of orbitals on `atoms` according to `orbitals`
For more detailed examples, please see the equivalent (but opposite) method
`sub_orbital`.
Parameters
----------
atoms :
indices of atoms or `Atom` that will be reduced in size according to `orbitals`
orbitals : array_like of int or Orbital
indices of the orbitals on `atoms` that are removed from the sparse matrix.
See Also
--------
sub_orbital : retaining a set of orbitals (see here for examples)
"""
# Get specie index of the atom (convert to list of indices)
atoms = self.geometry._sanitize_atoms(atoms).ravel()
# Figure out if all atoms have the same species
species = self.geometry.atoms.species[atoms]
uniq_species, indices = unique(species, return_inverse=True)
if len(uniq_species) > 1:
# In case there are multiple different species but one wishes to
# retain the same orbital index, then we loop on the unique species
new = self
for i in range(uniq_species.size):
idx = (indices == i).nonzero()[0]
# now determine whether it is the whole atom
# or only part of the geometry
new = new.remove_orbital(atoms[idx], orbitals)
return new
# Get the atom object we wish to reduce
# We know np.all(geom.atoms[atom] == old_atom)
old_atom = self.geometry.atoms[atoms[0]]
if isinstance(orbitals, (Orbital, Integral)):
orbitals = [orbitals]
if isinstance(orbitals[0], Orbital):
orbitals = [old_atom.index(orb) for orb in orbitals]
orbitals = delete(_a.arangei(len(old_atom)), np.asarray(orbitals).ravel())
# now call sub_orbital
return self.sub_orbital(atoms, orbitals)
[docs]
def sub_orbital(self, atoms: AtomsIndex, orbitals):
r"""Retain only a subset of the orbitals on `atoms` according to `orbitals`
This allows one to retain only a given subset of the sparse matrix elements.
Parameters
----------
atoms :
indices of atoms or `Atom` that will be reduced in size according to `orbitals`
orbitals : array_like of int or Orbital
indices of the orbitals on `atoms` that are retained in the sparse matrix, the list of
orbitals will be sorted. One cannot re-arrange matrix elements currently.
Notes
-----
Future implementations may allow one to re-arange orbitals using this method.
When using this method the internal species list will be populated by another species
that is named after the orbitals removed. This is to distinguish different atoms.
Examples
--------
>>> # a Carbon atom with 2 orbitals
>>> C = sisl.Atom('C', [1., 2.])
>>> # an oxygen atom with 3 orbitals
>>> O = sisl.Atom('O', [1., 2., 2.4])
>>> geometry = sisl.Geometry([[0] * 3, [1] * 3]], 2, [C, O])
>>> obj = SparseOrbital(geometry).tile(3, 0)
>>> # fill in obj data...
Now ``obj`` is a sparse geometry with 2 different species and 6 atoms (3 of each).
They are ordered ``[C, O, C, O, C, O]``. In the following we
will note species that are different from the original by a ``'`` in the list.
Retain 2nd orbital on the 2nd atom: ``[C, O', C, O, C, O]``
>>> new_obj = obj.sub_orbital(1, 1)
Retain 2nd orbital on 1st and 2nd atom: ``[C', O', C, O, C, O]``
>>> new_obj = obj.sub_orbital([0, 1], 1)
Retain 2nd orbital on the 1st atom and 3rd orbital on 4th atom: ``[C', O, C, O', C, O]``
>>> new_obj = obj.sub_orbital(0, 1).sub_orbital(3, 2)
Retain 2nd orbital on all atoms equivalent to the first atom: ``[C', O, C', O, C', O]``
>>> new_obj = obj.sub_orbital(obj.geometry.atoms[0], 1)
Retain 1st orbital on 1st atom, and 2nd orbital on 3rd and 5th atom: ``[C', O, C'', O, C'', O]``
>>> new_obj = obj.sub_orbital(0, 0).sub_orbital([2, 4], 1)
See Also
--------
remove_orbital : removing a set of orbitals (opposite of this)
"""
atoms = self.geometry._sanitize_atoms(atoms).ravel()
# Figure out if all atoms have the same species
species = self.geometry.atoms.species[atoms]
uniq_species, indices = unique(species, return_inverse=True)
if len(uniq_species) > 1:
# In case there are multiple different species but one wishes to
# retain the same orbital index, then we loop on the unique species
new = self
for i in range(uniq_species.size):
idx = (indices == i).nonzero()[0]
# now determine whether it is the whole atom
# or only part of the geometry
new = new.sub_orbital(atoms[idx], orbitals)
return new
# Get the atom object we wish to reduce
old_atom = self.geometry.atoms[atoms[0]]
if isinstance(orbitals, (Orbital, Integral)):
orbitals = [orbitals]
if isinstance(orbitals[0], Orbital):
orbitals = [old_atom.index(orb) for orb in orbitals]
orbitals = np.sort(orbitals)
# At this point we are sure that uniq_species is *only* one species!
geom = self.geometry.sub_orbital(atoms, orbitals)
# Now create the new sparse orbital class
SG = self.__class__(geom, self.dim, self.dtype, 1, **self._cls_kwargs())
rem_orbs = delete(_a.arangei(old_atom.no), orbitals)
# Find orbitals to remove (note this HAS to be from the original array)
rem_orbs = np.add.outer(self.geometry.a2o(atoms), rem_orbs).ravel()
# Generate a list of orbitals to retain
sub_idx = delete(_a.arangei(self.no), rem_orbs)
# Generate full supercell indices
n_s = self.geometry.n_s
sc_off = _a.arangei(n_s) * self.no
sub_idx = tile(sub_idx, n_s).reshape(n_s, -1) + sc_off.reshape(-1, 1)
SG._csr = self._csr.sub(sub_idx)
# just ensure we are doing the correct thing
assert SG._csr.shape[0] == SG.geometry.no
return SG
[docs]
def untile(
self, reps: int, axis: int, segment: int = 0, *args, sym: bool = True, **kwargs
):
"""Untiles the sparse model into different parts (retaining couplings)
Recreates a new sparse object with only the cutted
atoms in the structure. This will preserve matrix elements in the supercell.
Parameters
----------
reps :
number of repetitions the tiling function created (opposite meaning as in `untile`)
axis :
which axis to untile along
segment :
which segment to retain. Generally each segment should be equivalent, however
requesting individiual segments can help uncover inconsistencies in the sparse matrix
*args :
arguments passed directly to `Geometry.untile`
sym :
if True, the algorithm will ensure the returned matrix is symmetrized (i.e.
return ``(M + M.transpose())/2``, else return data as is.
False should generally only be used for debugging precision of the matrix elements,
or if one wishes to check the warnings.
**kwargs :
keyword arguments passed directly to `Geometry.untile`
Notes
-----
Untiling structures with ``nsc == 1`` along `axis` are assumed to have periodic boundary
conditions.
When untiling structures with ``nsc == 1`` along `axis` it is important to
untile *as much as possible*. This is because otherwise the algorithm cannot determine
the correct couplings. Therefore to create a geometry of 3 times a unit-cell, one should
untile to the unit-cell, and subsequently tile 3 times.
Consider for example a system of 4 atoms, each atom connects to its 2 neighbors.
Due to the PBC atom 0 will connect to 1 and 3. Untiling this structure in 2 will
group couplings of atoms 0 and 1. As it will only see one coupling to the right
it will halve the coupling and use the same coupling to the left, which is clearly wrong.
In the following the latter is the correct way to do it.
>>> SPM.untile(2, 0) != SPM.untile(4, 0).tile(2, 0)
Raises
------
ValueError :
in case the matrix elements are not conseuctive when determining the
new supercell structure. This may often happen if untiling a matrix
too few times, and then untiling it again.
See Also
--------
tile : opposite of this method
Geometry.untile : same as this method, see details about parameters here
"""
return super().untile("o", reps, axis, segment, *args, sym=sym, **kwargs)
[docs]
def rij(self, what: str = "orbital", dtype=np.float64):
r"""Create a sparse matrix with the distance between atoms/orbitals
Parameters
----------
what : {'orbital', 'atom'}
which kind of sparse distance matrix to return, either an atomic distance matrix
or an orbital distance matrix. The orbital matrix is equivalent to the atomic
one with the same distance repeated for the same atomic orbitals.
The default is the same type as the parent class.
dtype : numpy.dtype, optional
the data-type of the sparse matrix.
Notes
-----
The returned sparse matrix with distances are taken from the current sparse pattern.
I.e. a subsequent addition of sparse elements will make them inequivalent.
It is thus important to *only* create the sparse distance when the sparse
structure is completed.
"""
R = self.Rij(what, dtype)
R._csr = np.sum(R._csr**2, axis=-1) ** 0.5
return R
[docs]
def Rij(self, what: str = "orbital", dtype=np.float64):
r"""Create a sparse matrix with the vectors between atoms/orbitals
Parameters
----------
what : {'orbital', 'atom'}
which kind of sparse vector matrix to return, either an atomic vector matrix
or an orbital vector matrix. The orbital matrix is equivalent to the atomic
one with the same vectors repeated for the same atomic orbitals.
The default is the same type as the parent class.
dtype : numpy.dtype, optional
the data-type of the sparse matrix.
Notes
-----
The returned sparse matrix with vectors are taken from the current sparse pattern.
I.e. a subsequent addition of sparse elements will make them inequivalent.
It is thus important to *only* create the sparse vector matrix when the sparse
structure is completed.
"""
geom = self.geometry
# Pointers
ncol = self._csr.ncol
ptr = self._csr.ptr
col = self._csr.col
if what == "atom":
R = SparseAtom(geom, 3, dtype, nnzpr=np.amax(ncol))
Rij = geom.Rij
o2a = geom.o2a
# Orbitals
orow = _a.arangei(self.shape[0])
# Loop on orbitals and atoms
for io, ia in zip(orow, o2a(orow)):
coln = unique(o2a(col[ptr[io] : ptr[io] + ncol[io]]))
R[ia, coln] = Rij(ia, coln)
elif what in ("orbital", "orb"):
# We create an *exact* copy of the Rij
R = SparseOrbital(geom, 3, dtype, nnzpr=1)
Rij = geom.oRij
# Re-create the sparse matrix data
R._csr.ptr = ptr.copy()
R._csr.ncol = ncol.copy()
R._csr.col = col.copy()
R._csr._nnz = self._csr.nnz
R._csr._D = np.zeros([self._csr._D.shape[0], 3], dtype=dtype)
R._csr._finalized = self.finalized
for io in range(self.shape[0]):
sl = slice(ptr[io], ptr[io] + ncol[io])
R._csr._D[sl, :] = Rij(io, col[sl])
else:
raise ValueError(
self.__class__.__name__ + '.Rij "what" is not one of [atom, orbital].'
)
return R
[docs]
def add(self, other, axis: Optional[int] = None, offset: Coord = (0, 0, 0)):
r"""Add two sparse matrices by adding the parameters to one set. The final matrix will have no couplings between `self` and `other`
The final sparse matrix will not have any couplings between `self` and `other`. Not even if they
have commensurate overlapping regions. If you want to create couplings you have to use `append` but that
requires the structures are commensurate in the coupling region.
Parameters
----------
other : SparseGeometry
the other sparse matrix to be added, all atoms will be appended
axis :
whether a specific axis of the cell will be added to the final geometry.
For ``None`` the final cell will be that of `self`, otherwise the lattice
vector corresponding to `axis` will be appended.
offset :
offset in geometry of `other` when adding the atoms.
See Also
--------
append : append two matrices by also adding overlap couplings
prepend : see `append`
"""
# Check that the sparse matrices are compatible
if not (type(self) is type(other)):
raise ValueError(
self.__class__.__name__
+ f".add requires other to be of same type: {other.__class__.__name__}"
)
if self.dtype != other.dtype:
raise ValueError(
self.__class__.__name__
+ ".add requires the same datatypes in the two matrices."
)
if self.dim != other.dim:
raise ValueError(
self.__class__.__name__
+ ".add requires the same number of dimensions in the matrix."
)
if axis is None:
geom = self.geometry.add(other.geometry, offset=offset)
else:
# Same effect but also adds the lattice vectors
geom = self.geometry.append(other.geometry, axis, offset=offset)
# Now we have the correct geometry, then create the correct
# class
# New indices and data (the constructor for SparseCSR copies)
full = self.__class__(geom, self.dim, self.dtype, 1, **self._cls_kwargs())
full._csr.ptr = concatenate((self._csr.ptr[:-1], other._csr.ptr))
full._csr.ptr[self.no :] += self._csr.ptr[-1]
full._csr.ncol = concatenate((self._csr.ncol, other._csr.ncol))
full._csr._D = concatenate((self._csr._D, other._csr._D))
full._csr._nnz = full._csr.ncol.sum()
full._csr._finalized = False
# Retrieve the maximum number of orbitals (in the supercell)
# This may be used to remove couplings
full_no_s = geom.no_s
# Now we have to transfer the indices to the new sparse pattern
# First create a local copy of the columns, then we transfer, and then we collect.
s_col = self._csr.col.copy()
transfer_idx = _a.arangei(self.geometry.no_s).reshape(-1, self.geometry.no)
transfer_idx += _a.arangei(self.geometry.n_s).reshape(-1, 1) * other.geometry.no
# Remove couplings along axis
if not axis is None:
idx = (self.geometry.lattice.sc_off[:, axis] != 0).nonzero()[0]
# Tell the routine to delete these indices
transfer_idx[idx, :] = full_no_s + 1
idx = array_arange(self._csr.ptr[:-1], n=self._csr.ncol)
s_col[idx] = transfer_idx.ravel()[s_col[idx]]
# Same for the other, but correct for deleted supercells and supercells along
# disconnected auxiliary cells.
o_col = other._csr.col.copy()
transfer_idx = _a.arangei(other.geometry.no_s).reshape(-1, other.geometry.no)
# Transfer the correct supercells
o_idx = []
s_idx = []
idx_delete = []
for isc, sc in enumerate(other.geometry.lattice.sc_off):
try:
s_idx.append(self.geometry.lattice.sc_index(sc))
o_idx.append(isc)
except ValueError:
idx_delete.append(isc)
# o_idx are transferred to s_idx
transfer_idx[o_idx, :] += (
_a.arangei(1, other.geometry.n_s + 1)[s_idx].reshape(-1, 1)
* self.geometry.no
)
# Remove some columns
transfer_idx[idx_delete, :] = full_no_s + 1
# Clean-up to not confuse the rest of the algorithm
del o_idx, s_idx, idx_delete
# Now figure out if the supercells can be kept, at all...
# find SC indices in other corresponding to self
# o_idx_uc = other.geometry.lattice.sc_index([0] * 3)
# o_idx_sc = _a.arangei(other.geometry.lattice.n_s)
# Remove couplings along axis
for i in range(3):
if i == axis:
idx = (other.geometry.lattice.sc_off[:, axis] != 0).nonzero()[0]
elif not allclose(geom.cell[i, :], other.cell[i, :]):
# This will happen in case `axis` is None
idx = (other.geometry.lattice.sc_off[:, i] != 0).nonzero()[0]
else:
# When axis is not specified and cell parameters
# are commensurate, then we will not change couplings
continue
# Tell the routine to delete these indices
transfer_idx[idx, :] = full_no_s + 1
idx = array_arange(other._csr.ptr[:-1], n=other._csr.ncol)
o_col[idx] = transfer_idx.ravel()[o_col[idx]]
# Now we need to decide whether the
del transfer_idx, idx
full._csr.col = concatenate([s_col, o_col])
# Clean up (they could potentially be very large arrays)
del s_col, o_col
# Ensure we remove the elements
full._csr._clean_columns()
return full
[docs]
@deprecate_argument(
"eps",
"atol",
"argument eps has been deprecated in favor of atol.",
"0.15",
"0.16",
)
def prepend(
self, other, axis: int, atol: float = 0.005, scale: SeqOrScalarFloat = 1
):
r"""See `append` for details
This is currently equivalent to:
>>> other.append(self, axis, atol, scale)
"""
return other.append(self, axis, atol, scale)
[docs]
@deprecate_argument(
"eps",
"atol",
"argument eps has been deprecated in favor of atol.",
"0.15",
"0.16",
)
def append(
self, other, axis: int, atol: float = 0.005, scale: SeqOrScalarFloat = 1
):
r"""Append `other` along `axis` to construct a new connected sparse matrix
This method tries to append two sparse geometry objects together by
the following these steps:
1. Create the new extended geometry
2. Use neighbor cell couplings from `self` as the couplings to `other`
This *may* cause problems if the coupling atoms are not exactly equi-positioned.
If the coupling coordinates and the coordinates in `other` differ by more than
0.01 Ang, a warning will be issued.
If this difference is above `atol` the couplings will be removed.
When appending sparse matrices made up of atoms, this method assumes that
the orbitals on the overlapping atoms have the same orbitals, as well as the
same orbital ordering.
Examples
--------
>>> sporb = SparseOrbital(....)
>>> sporb2 = sporb.append(sporb, 0)
>>> sporbt = sporb.tile(2, 0)
>>> sporb2.spsame(sporbt)
True
To retain couplings only from the *left* sparse matrix, do:
>>> sporb = left.append(right, 0, scale=(2, 0))
>>> sporb = (sporb + sporb.transpose()) / 2
To retain couplings only from the *right* sparse matrix, do:
>>> sporb = left.append(right, 0, scale=(0, 2.))
>>> sporb = (sporb + sporb.transpose()) / 2
Notes
-----
The current implementation does not preserve the hermiticity of the matrix.
If you want to preserve hermiticity of the matrix you have to do the
following:
>>> sm = (sm + sm.transpose()) / 2
Parameters
----------
other : object
must be an object of the same type as `self`
axis :
axis to append the two sparse geometries along
atol :
tolerance that all coordinates *must* be within to allow an append.
It is important that this value is smaller than half the distance between
the two closests atoms such that there is no ambiguity in selecting
equivalent atoms. An internal stricter tolerance is used as a baseline, see above.
scale : float or array_like, optional
the scale used for the overlapping region. For scalar values it corresponds
to passing: ``(scale, scale)``.
For array-like input ``scale[0]`` refers to the scale of the matrix elements
coupling from `self`, while ``scale[1]`` is the scale of the matrix elements
in `other`.
See Also
--------
prepend : equivalent scheme as this method
add : merge two matrices without considering overlap or commensurability
transpose : ensure hermiticity by using this routine
replace : replace a sub-set of atoms with another sparse matrix
Geometry.append
Geometry.prepend
SparseCSR.scale_columns : method used to scale the two matrix elements values
Raises
------
ValueError
if the two geometries are not compatible for either coordinate, orbital or supercell errors
Returns
-------
object
a new instance with two sparse matrices joined and appended together
"""
if not (type(self) is type(other)):
raise ValueError(
f"{self.__class__.__name__}.append requires other to be of same type: {other.__class__.__name__}"
)
if self.geometry.nsc[axis] > 3 or other.geometry.nsc[axis] > 3:
raise ValueError(
f"{self.__class__.__name__}.append requires sparse-geometries to maximally "
"have 3 supercells along appending axis."
)
if not allclose(self.geometry.nsc, other.geometry.nsc):
raise ValueError(
f"{self.__class__.__name__}.append requires sparse-geometries to have the same "
"number of supercells along all directions."
)
if not allclose(
self.geometry.lattice._isc_off, other.geometry.lattice._isc_off
):
raise ValueError(
f"{self.__class__.__name__}.append requires supercell offsets to be the same."
)
if self.dtype != other.dtype:
raise ValueError(
f"{self.__class__.__name__}.append requires the same datatypes in the two matrices."
)
if self.dim != other.dim:
raise ValueError(
f"{self.__class__.__name__}.append requires the same number of dimensions in the matrix."
)
if np.asarray(scale).size == 1:
scale = np.array([scale, scale])
scale = np.asarray(scale)
# Our procedure will be to separate the sparsity patterns into separate chunks
# First generate the full geometry
geom = self.geometry.append(other.geometry, axis)
# create the new sparsity patterns with offset
# New indices and data (the constructor for SparseCSR copies)
full = self.__class__(geom, self.dim, self.dtype, 1, **self._cls_kwargs())
full._csr.ptr = concatenate((self._csr.ptr[:-1], other._csr.ptr))
full._csr.ptr[self.no :] += self._csr.ptr[-1]
full._csr.ncol = concatenate((self._csr.ncol, other._csr.ncol))
full._csr._D = concatenate((self._csr._D, other._csr._D))
full._csr._nnz = full._csr.ncol.sum()
full._csr._finalized = False
# First create a local copy of the columns, then we transfer, and then we collect.
s_col = self._csr.col.copy()
# transfer
transfer_idx = _a.arangei(self.geometry.no_s).reshape(-1, self.geometry.no)
transfer_idx += _a.arangei(self.geometry.n_s).reshape(-1, 1) * other.geometry.no
idx = array_arange(self._csr.ptr[:-1], n=self._csr.ncol)
s_col[idx] = transfer_idx.ravel()[s_col[idx]]
o_col = other._csr.col.copy()
# transfer
transfer_idx = _a.arangei(other.geometry.no_s).reshape(-1, other.geometry.no)
transfer_idx += (
_a.arangei(1, other.geometry.n_s + 1).reshape(-1, 1) * self.geometry.no
)
idx = array_arange(other._csr.ptr[:-1], n=other._csr.ncol)
o_col[idx] = transfer_idx.ravel()[o_col[idx]]
# Store all column indices
del transfer_idx, idx
full._csr.col = concatenate((s_col, o_col))
# Clean up (they could potentially be very large arrays)
del s_col, o_col
# Now everything is contained in 1 sparse matrix.
# All matrix elements are as though they are in their own
# What needs to be done is to find the overlapping atoms and transfer indices in
# both these sparsity patterns to the correct elements.
# 1. find overlapping atoms along axis
idx_s_first, idx_o_first = self.geometry.overlap(other.geometry, atol=atol)
idx_s_last, idx_o_last = self.geometry.overlap(
other.geometry,
atol=atol,
offset=-self.geometry.lattice.cell[axis, :],
offset_other=-other.geometry.lattice.cell[axis, :],
)
# IFF idx_s_* contains duplicates, then we have multiple overlapping atoms which is not
# allowed
def _test(diff):
if diff.size != diff.nonzero()[0].size:
raise ValueError(
f"{self.__class__.__name__}.append requires that there is maximally one "
"atom overlapping one other atom in the other structure."
)
_test(diff(idx_s_first))
_test(diff(idx_s_last))
# Also ensure that atoms have the same number of orbitals in the two cases
if (
not allclose(
self.geometry.orbitals[idx_s_first],
other.geometry.orbitals[idx_o_first],
)
) or (
not allclose(
self.geometry.orbitals[idx_s_last], other.geometry.orbitals[idx_o_last]
)
):
raise ValueError(
f"{self.__class__.__name__}.append requires the overlapping geometries "
"to have the same number of orbitals per atom that is to be replaced."
)
def _check_edges_and_coordinates(spgeom, atoms, isc, err_help):
# Figure out if we have found all couplings
geom = spgeom.geometry
# Find orbitals that we wish to exclude from the orbital connections
# This ensures that we only find couplings crossing the supercell boundaries
irrelevant_sc = delete(
_a.arangei(geom.lattice.n_s), geom.lattice.sc_index(isc)
)
sc_orbitals = _a.arangei(geom.no_s).reshape(geom.lattice.n_s, -1)
exclude = sc_orbitals[irrelevant_sc, :].ravel()
# get connections and transfer them to the unit-cell
edges_sc = geom.o2a(
spgeom.edges(orbitals=_a.arangei(geom.no), exclude=exclude), True
)
edges_uc = geom.sc2uc(edges_sc, True)
edges_valid = np.isin(edges_uc, atoms, assume_unique=True)
if not np.all(edges_valid):
edges_uc = edges_sc % geom.na
# Reduce edges to those that are faulty
edges_valid = np.isin(edges_uc, atoms, assume_unique=False)
errors = edges_sc[~edges_valid]
# Get supercell offset and unit-cell atom
isc_off, uca = np.divmod(errors, geom.na)
# group atoms for each supercell index
# find unique supercell offsets
sc_off_atoms = []
# This will be much faster
for isc in unique(isc_off):
idx = (isc_off == isc).nonzero()[0]
sc_off_atoms.append(
"{k}: {v}".format(
k=str(geom.lattice.sc_off[isc]),
v=list2str(np.sort(uca[idx])),
)
)
sc_off_atoms = "\n ".join(sc_off_atoms)
raise ValueError(
f"{self.__class__.__name__}.append requires matching coupling elements.\n\n"
f"The following atoms in a {err_help[1]} connection of `{err_help[0]}` super-cell "
"are connected from the unit cell, but are not found in matches:\n\n"
f"[sc-offset]: atoms\n {sc_off_atoms}"
)
# setup supercells to look up
isc_inplace = [None] * 3
isc_inplace[axis] = 0
isc_forward = isc_inplace.copy()
isc_forward[axis] = 1
isc_back = isc_inplace.copy()
isc_back[axis] = -1
# Check that edges and overlapping atoms are the same (or at least that the
# edges are all in the overlapping region)
# [self|other]: self sc-connections forward must be on left-aligned matching atoms
_check_edges_and_coordinates(
self, idx_s_first, isc_forward, err_help=("self", "forward")
)
# [other|self]: other sc-connections forward must be on left-aligned matching atoms
_check_edges_and_coordinates(
other, idx_o_first, isc_forward, err_help=("other", "forward")
)
# [other|self]: self sc-connections backward must be on right-aligned matching atoms
_check_edges_and_coordinates(
self, idx_s_last, isc_back, err_help=("self", "backward")
)
# [self|other]: other sc-connections backward must be on right-aligned matching atoms
_check_edges_and_coordinates(
other, idx_o_last, isc_back, err_help=("other", "backward")
)
# Now we have ensured that the overlapping coordinates and the connectivity graph
# co-incide and that we can actually perform the merge.
idx = _a.arangei(geom.n_s).reshape(-1, 1) * geom.no
def _sc_index_sort(isc):
idx = geom.lattice.sc_index(isc)
# Now sort so that all indices are corresponding one2one
# This is important since two different supercell indices
# need not be sorted in the same manner.
# This ensures that there is a correspondance between
# two different sparse elements
off = delete(geom.lattice.sc_off[idx].T, axis, axis=0)
return idx[np.lexsort(off)]
idx_iscP = idx[_sc_index_sort(isc_forward)]
idx_isc0 = idx[_sc_index_sort(isc_inplace)]
idx_iscM = idx[_sc_index_sort(isc_back)]
# Clean (for me to know what to do in this code)
del idx, _sc_index_sort
# First scale all values
idx_s_first = self.geometry.a2o(idx_s_first, all=True).reshape(1, -1)
idx_s_last = self.geometry.a2o(idx_s_last, all=True).reshape(1, -1)
col = concatenate(
((idx_s_first + idx_iscP).ravel(), (idx_s_last + idx_iscM).ravel())
)
full._csr.scale_columns(col, scale[0])
idx_o_first = (
other.geometry.a2o(idx_o_first, all=True).reshape(1, -1) + self.geometry.no
)
idx_o_last = (
other.geometry.a2o(idx_o_last, all=True).reshape(1, -1) + self.geometry.no
)
col = concatenate(
((idx_o_first + idx_iscP).ravel(), (idx_o_last + idx_iscM).ravel())
)
full._csr.scale_columns(col, scale[1])
# Clean up (they may be very large)
del col
# Now we can easily build from->to arrays
# other[0] -> other[1] changes to other[0] -> full_G[1] | self[1]
# self[0] -> self[1] changes to self[0] -> full_G[0] | other[0]
# self[0] -> self[-1] changes to self[0] -> full_G[-1] | other[-1]
# other[0] -> other[-1] changes to other[0] -> full_G[0] | self[0]
col_from = concatenate(
(
(idx_o_first + idx_iscP).ravel(),
(idx_s_first + idx_iscP).ravel(),
(idx_s_last + idx_iscM).ravel(),
(idx_o_last + idx_iscM).ravel(),
)
)
col_to = concatenate(
(
(idx_s_first + idx_iscP).ravel(),
(idx_o_first + idx_isc0).ravel(),
(idx_o_last + idx_iscM).ravel(),
(idx_s_last + idx_isc0).ravel(),
)
)
full._csr.translate_columns(col_from, col_to)
return full
[docs]
@deprecate_argument(
"eps",
"atol",
"argument eps has been deprecated in favor of atol",
"0.15",
"0.16",
)
def replace(
self,
atoms: AtomsIndex,
other,
other_atoms: AtomsIndex = None,
atol: float = 0.005,
scale: SeqOrScalarFloat = 1.0,
):
r"""Replace `atoms` in `self` with `other_atoms` in `other` and retain couplings between them
This method replaces a subset of atoms in `self` with
another sparse geometry retaining any couplings between them.
The algorithm checks whether the coupling atoms have the same number of
orbitals. Meaning that atoms in the overlapping region should have the same
connections and number of orbitals per atom.
It will _not_ check whether the orbitals or atoms _are_ the same, nor the order
of the orbitals.
The replacement algorithm takes the couplings from ``self -> other`` on atoms
belonging to ``self`` and ``other -> self`` from ``other``. This will in some
cases mean that the matrix becomes non-symmetric. See in Notes for details on
symmetrizing the matrices.
Examples
--------
>>> minimal = SparseOrbital(....)
>>> big = minimal.tile(2, 0)
>>> big2 = big.replace(np.arange(big.na), minimal)
>>> big.spsame(big2)
True
To ensure hermiticity and using the average of the couplings from ``big`` and
``minimal`` one can do:
>>> big2 = big.replace(np.arange(big.na), minimal)
>>> big2 = (big2 + big2.transpose()) / 2
To retain couplings only from the ``big`` sparse matrix, one should
do the following (note the subsequent transposing which ensures hermiticy
and is effectively copying couplings from ``big`` to the replaced region.
>>> big2 = big.replace(np.arange(big.na), minimal, scale=(2, 0))
>>> big2 = (big2 + big2.transpose()) / 2
To only retain couplings from the ``minimal`` sparse matrix:
>>> big2 = big.replace(np.arange(big.na), minimal, scale=(0, 2))
>>> big2 = (big2 + big2.transpose()) / 2
Notes
-----
The current implementation does not preserve the hermiticity of the matrix.
If you want to preserve hermiticity of the matrix you have to do the
following:
>>> sm = (sm + sm.transpose()) / 2
Also note that the ordering of the atoms will be ``range(atoms.min()), range(len(other_atoms)), <rest>``.
Algorithms that utilizes atomic indices should be careful.
When the tolerance `atol` is high, the elements may be more prone to differences in the
symmetry elements. A good idea would be to check the difference between the couplings.
The below variable ``diff`` will contain the difference ``(self -> other) - (other -> self)``
>>> diff = sm - sm.transpose()
Parameters
----------
atoms :
which atoms in `self` that are removed and replaced with ``other.sub(other_atoms)``
other : object
must be an object of the same type as `self`, a subset is taken from this
sparse matrix and combined with `self` to create a new sparse matrix
other_atoms :
to select a subset of atoms in `other` that are taken out.
Defaults to all atoms in `other`.
atol :
coordinate tolerance for allowing replacement.
It is important that this value is at least smaller than half the distance between
the two closests atoms such that there is no ambiguity in selecting
equivalent atoms.
scale :
the scale used for the overlapping region. For scalar values it corresponds
to passing: ``(scale, scale)``.
For array-like input ``scale[0]`` refers to the scale of the matrix elements
coupling from `self`, while ``scale[1]`` is the scale of the matrix elements
in `other`.
See Also
--------
prepend : prepend two sparse matrices, see `append` for details
add : merge two matrices without considering overlap or commensurability
transpose : may be used to ensure hermiticity (symmetrization of the matrix elements)
append : append two sparse matrices
Geometry.append
Geometry.prepend
SparseCSR.scale_columns : method used to scale the two matrix elements values
Raises
------
ValueError
if the two geometries are not compatible for either coordinate, orbital or supercell errors
AssertionError
if the two geometries are not compatible for either coordinate, orbital or supercell errors
Warns
-----
SislWarning
in case the overlapping atoms are not comprising the same atomic specie. In some cases this may not be a problem. However, care must be taken by the user if this warning is issued.
Returns
-------
object
a new instance with two sparse matrices merged together by replacing some atoms
"""
if np.asarray(scale).size == 1:
scale = np.array([scale, scale])
scale = np.asarray(scale)
# here our connection is defined as what is connected to "in"
# and what is connected to "out"
# Say 0 -> 1
# And `atoms` is [0].
# Then in = [0], out = [1]
# since atoms connect out to [1]
# figure out the atoms that needs replacement
def get_reduced_system(sp, atoms):
"""convert the geometry in `sp` to only atoms `atoms` and return the following:
1. atoms (sanitized and no order change)
2. orbitals (ordered as `atoms`
3. the atoms that are connected to OUT and IN
4. the orbitals that are connected to OUT and IN
"""
geom = sp.geometry
atoms = _a.asarrayi(geom._sanitize_atoms(atoms)).ravel()
if unique(atoms).size != atoms.size:
raise ValueError(
f"{self.__class__.__name__}.replace requires a unique set of atoms"
)
orbs = geom.a2o(atoms, all=True)
# other_orbs = geom.ouc2sc(np.delete(_a.arangei(geom.no), orbs))
# Find the orbitals that these atoms connect to such that we can compare
# atomic coordinates
out_connect_orb_sc = sp.edges(orbitals=orbs, exclude=orbs)
out_connect_orb = geom.osc2uc(out_connect_orb_sc, True)
out_connect_atom_sc = geom.o2a(out_connect_orb_sc, True)
out_connect_atom = geom.asc2uc(out_connect_atom_sc, True)
# figure out connecting back
atoms_orbs = list(
map(_a.arangei, geom.firsto[atoms], geom.firsto[atoms + 1])
)
in_connect_atom = []
in_connect_orb = []
for atom, atom_orbs in zip(atoms, atoms_orbs):
edges = sp.edges(orbitals=atom_orbs, exclude=orbs)
if len(intersect1d(edges, out_connect_orb_sc)) > 0:
in_connect_atom.append(atom)
in_connect_orb.append(atom_orbs)
in_connect_atom = _a.arrayi(in_connect_atom)
in_connect_orb = concatenate(in_connect_orb)
# create the connection tables
atom_uc = Connect(in_connect_atom, out_connect_atom)
atom_sc = Connect(in_connect_atom, out_connect_atom_sc)
orb_uc = Connect(in_connect_orb, out_connect_orb)
orb_sc = Connect(in_connect_orb, out_connect_orb_sc)
atom_connect = UCSC(atom_uc, atom_sc)
orb_connect = UCSC(orb_uc, orb_sc)
return Info(atoms, orbs, atom_connect, orb_connect)
UCSC = namedtuple("UCSC", ["uc", "sc"])
Connect = namedtuple("Connect", ["IN", "OUT"])
Info = namedtuple("Info", ["atoms", "orbitals", "atom_connect", "orb_connect"])
sgeom = self.geometry
s_info = get_reduced_system(self, atoms)
atoms = s_info.atoms # sanitized (no order change)
ogeom = other.geometry
o_info = get_reduced_system(other, other_atoms)
other_atoms = o_info.atoms # sanitized (no order change)
# Get overlapping atoms by their offset
# We need to get a 1-1 correspondance between the two connecting geometries
# For instance `self` may be ordered differently than `other`.
# So we need to figure out how the atoms are arranged in *both* regions.
# This is where `atol` comes into play since we have to ensure that the
# connecting regions are within some given tolerance.
def create_geometry(geom, atoms):
"""Create the supercell geometry with coordinates as given"""
xyz = geom.axyz(atoms)
uc_atoms = geom.sc2uc(atoms)
return Geometry(xyz, atoms=geom.atoms[uc_atoms])
# We know that the *IN* connections are in the primary unit-cell
# so we don't need to handle supercell information
# Atoms *inside* the replacement region that couples out
sgeom_in = sgeom.sub(s_info.atom_connect.uc.IN)
ogeom_in = ogeom.sub(o_info.atom_connect.uc.IN)
soverlap_in, ooverlap_in = sgeom_in.overlap(
ogeom_in,
atol=atol,
offset=-sgeom_in.xyz.min(0),
offset_other=-ogeom_in.xyz.min(0),
)
# Not replacement region, i.e. the IN (above) atoms are connecting to
# these atoms:
sgeom_out = create_geometry(sgeom, s_info.atom_connect.sc.OUT)
ogeom_out = create_geometry(ogeom, o_info.atom_connect.sc.OUT)
soverlap_out, ooverlap_out = sgeom_out.overlap(
ogeom_out,
atol=atol,
offset=-sgeom_out.xyz.min(0),
offset_other=-ogeom_out.xyz.min(0),
)
# trigger for errors
err_msg = ""
# Now we have the different geometries around to handle how the merging
# process.
# Before proceeding we will check whether the dimensions match.
# I.e. checking that the orbitals connecting in/out are the same is important.
# print("in:")
# print(s_info.atom_connect.uc.IN)
# print(soverlap_in)
# print(o_info.atom_connect.uc.IN)
# print(ooverlap_in)
if not (
len(sgeom_in) == len(soverlap_in) and len(ogeom_in) == len(ooverlap_in)
):
# figure out which atoms are not connecting
s_diff = np.setdiff1d(
np.arange(s_info.atom_connect.uc.IN.size), soverlap_in
)
o_diff = np.setdiff1d(
np.arange(o_info.atom_connect.uc.IN.size), ooverlap_in
)
if len(s_diff) > 0 or len(o_diff) > 0:
err_msg = f"""{err_msg}
The number of atoms in the replacement region that connects to the surrounding
atoms are not the same in 'self' and 'other'.
This means that the number of connections is not the same. Please ensure this."""
if len(s_diff) > 0:
err_msg = f"""{err_msg}
self: atoms not matched in 'other': {s_info.atom_connect.uc.IN[s_diff]}."""
if len(o_diff) > 0:
err_msg = f"""{err_msg}
other: atoms not matched in 'self': {o_info.atom_connect.uc.IN[o_diff]}."""
elif not np.allclose(
sgeom_in.orbitals[soverlap_in], ogeom_in.orbitals[ooverlap_in]
):
err_msg = f"""{err_msg}
Atoms in the replacement region have different number of orbitals on the atoms
that lie at the border.
self orbitals:
{sgeom_in.orbitals[soverlap_in]}
other orbitals:
{ogeom_in.orbitals[ooverlap_in]}"""
# print("out:")
# print(s_info.atom_connect.uc.OUT)
# print(soverlap_out)
# print(o_info.atom_connect.uc.OUT)
# print(ooverlap_out)
# [so]overlap_out are now in the order of [so]_info.atom_connect.out
# so we still have to convert them to proper indices if used
# We cannot really check the soverlap_out == len(sgeom_out)
# in case we have a replaced sparse matrix in the middle of another bigger
# sparse matrix.
if not (
len(sgeom_out) == len(soverlap_out) and len(ogeom_out) == len(ooverlap_out)
):
# figure out which atoms are not connecting
s_diff = np.setdiff1d(
np.arange(s_info.atom_connect.sc.OUT.size), soverlap_out
)
o_diff = np.setdiff1d(
np.arange(o_info.atom_connect.sc.OUT.size), ooverlap_out
)
if len(s_diff) > 0 or len(o_diff) > 0:
err_msg = f"""{err_msg}
Number of atoms connecting to the replacement region are not the same in 'self' and 'other'.
Please ensure this."""
if len(s_diff) > 0:
err_msg = f"""{err_msg}
self: atoms (in supercell) connecting to 'atoms' not matched in 'other': {s_info.atom_connect.sc.OUT[s_diff]}."""
if len(o_diff) > 0:
err_msg = f"""{err_msg}
other: atoms (in supercell) connecting to 'other_atoms' not matched in 'self': {o_info.atom_connect.sc.OUT[o_diff]}."""
elif not np.allclose(
sgeom_out.orbitals[soverlap_out], ogeom_out.orbitals[ooverlap_out]
):
err_msg = f"""{err_msg}
Atoms in the connection region have different number of orbitals on the atoms.
self orbitals:
{sgeom_out.orbitals[soverlap_out]}
other orbitals:
{ogeom_out.orbitals[ooverlap_out]}"""
# we can only ensure the orbitals that connect *out* have the same count
# For supercell connections hopping *IN* might be different due to the supercell
if (
len(s_info.orb_connect.sc.OUT) != len(o_info.orb_connect.sc.OUT)
and not err_msg
):
err_msg = f"""{err_msg}
Number of orbitals connecting to replacement region is not consistent
between 'self' and 'other'."""
if err_msg:
raise ValueError(err_msg[1:])
warn_msg = ""
S_ = s_info.atom_connect.uc.IN
O_ = o_info.atom_connect.uc.IN
for s_, o_ in zip(soverlap_in, ooverlap_in):
if sgeom_in.atoms[s_] != ogeom_in.atoms[o_]:
warn_msg = f"""{warn_msg}
Atom 'self[{S_[s_]}]' is not equivalent to 'other[{O_[o_]}]':
{sgeom_in.atoms[s_]} != {ogeom_in.atoms[o_]}"""
if warn_msg:
warn(
f"""Inequivalent atoms found in replacement region, this may or may not be a problem
depending on your use case. Please be careful though.{warn_msg}"""
)
warn_msg = ""
S_ = s_info.atom_connect.sc.OUT
O_ = o_info.atom_connect.sc.OUT
checked1d = _a.zerosi([self.geometry.na])
for s_, o_ in zip(soverlap_out, ooverlap_out):
uc_s_ = S_[s_] % self.geometry.na
if sgeom_out.atoms[s_] != ogeom_out.atoms[o_] and checked1d[uc_s_] == 0:
checked1d[uc_s_] = 1
warn_msg = f"""{warn_msg}
Atom 'self[{S_[s_]}]' is not equivalent to 'other[{O_[o_]}]':
{sgeom_out.atoms[s_]} != {ogeom_out.atoms[o_]}"""
if warn_msg:
warn(
f"""Inequivalent atoms found in connection region, this may or may not be a problem
depending on your use case. Note indices in the following are supercell indices. Please be careful though.{warn_msg}"""
)
# clean-up to make it clear that we are not going to use them.
del sgeom_out, ogeom_out
# this is where other.sub(other_atoms) gets inserted
ainsert_idx = atoms.min()
oinsert_idx = sgeom.a2o(ainsert_idx)
# this is the indices of the new atoms in the new geometry
# self_other_atoms = _a.arangei(ainsert_idx, ainsert_idx + len(other_atoms))
# We need to do the replacement in two steps
# A. the geometry
# This will insert other at ainsert_idx
# Note that sub(other_atoms) re-arranges the atoms correctly
idx = np.argmin((sgeom_in.xyz[soverlap_in] ** 2).sum(1))
offset = sgeom_in.xyz[soverlap_in[idx]] - ogeom_in.xyz[ooverlap_in[idx]]
# this will perhaps re-order atoms from other_atoms
geom = sgeom.replace(atoms, other.geometry.sub(other_atoms), offset=offset)
del sgeom_in, ogeom_in
# A. DONE
# B. Merge the two sparse patterns
scsr = self._csr
ncol = scsr.ncol
col = scsr.col
D = scsr._D
# helper function
def a2o(geom, atoms, sc=True):
if sc:
return geom.ouc2sc(geom.a2o(atoms, all=True))
return geom.a2o(atoms, all=True)
# Our first task is to merge the two sparse patterns.
# Delete the *old* values
# To ensure that inserting will not leave *empty* values
# we first reduce arrays so that the ptr array is not needed
ncol = delete(ncol, s_info.orbitals)
ptr = delete(scsr.ptr, s_info.orbitals)
idx = array_arange(ptr[:-1], n=ncol)
col = col[idx]
D = D[idx]
# Do the same reduction for the inserted values
ocsr = other._csr
idx = array_arange(ocsr.ptr[o_info.orbitals], n=ocsr.ncol[o_info.orbitals])
# we offset the new columns by self.shape[1], in this way we know
# which couplings belong to the inserted and the original csr
col = insert(col, ncol[:oinsert_idx].sum(), ocsr.col[idx] + self.shape[1])
D = insert(D, ncol[:oinsert_idx].sum(), ocsr._D[idx], axis=0)
ncol = insert(ncol, oinsert_idx, ocsr.ncol[o_info.orbitals])
# Create the sparse pattern
csr = SparseCSR(
(D, col, _ncol_to_indptr(ncol)),
shape=(geom.no, sgeom.no_s + ogeom.no_s, D.shape[1]),
)
del D, col, ncol
# Now we have merged the two sparse patterns
# But we need to correct the orbital couplings
# : *outside* refers to the original sparse pattern (without `atoms`)
# : *inside* refers to the inserted sparse pattern (other.sub(other_atoms))
# We have to do 1 and 2 simultaneously.
# We have to do 3 and 4 simultaneously.
# This is because they may have overlapping columns
# 1: couplings from *outside* to *outside* (no scale)
# 2: couplings from *outside* to *inside* (scaled)
# 3: couplings from *inside* to *inside* (no scale)
# 4: couplings from *inside* to *outside* (scaled)
convert = [[], []]
conc = np.concatenate
def assert_unique(old, new):
old = conc(old)
new = conc(new)
assert len(unique(old)) == len(old)
assert len(unique(new)) == len(new)
return old, new
# 1:
# print("1:")
old = delete(_a.arangei(len(sgeom)), atoms)
new = _a.arangei(len(old))
new[ainsert_idx:] += len(other_atoms)
old = a2o(sgeom, old)
convert[0].append(old)
new = a2o(geom, new)
convert[1].append(new)
rows = geom.osc2uc(new, unique=True)
# 2:
# print("2:")
old = s_info.atom_connect.uc.IN[soverlap_in]
# algorithm to get indices in other_atoms
new = o_info.atom_connect.uc.IN[ooverlap_in]
tmp = argsort(other_atoms)
new = tmp[searchsorted(other_atoms, new, sorter=tmp)] + ainsert_idx
old = a2o(sgeom, old)
convert[0].append(old)
new = a2o(geom, new)
convert[1].append(new)
# translate columns
csr.translate_columns(*assert_unique(convert[0], convert[1]), rows=rows)
# scale columns that connects inside
csr.scale_columns(convert[1][1], scale=scale[0], rows=rows)
# on to the *inside* 3, 4
convert = [[], []]
# 3:
# print("3:")
# we have all the *inside* column indices offset by self.shape[1]
old = a2o(ogeom, other_atoms, False) + self.shape[1]
new = ainsert_idx + _a.arangei(len(other_atoms))
# print("old: ", old)
# print("new: ", new)
new = a2o(geom, new, False)
convert[0].append(old)
convert[1].append(new)
rows = geom.osc2uc(new, unique=True)
# 4:
# print("4:")
old = o_info.atom_connect.sc.OUT
new = _a.emptyi(len(old))
for i, atom in enumerate(old):
idx = geom.close(ogeom.axyz(atom) + offset, R=atol)
assert (
len(idx) == 1
), f"More than 1 atom {idx} for atom {atom} = {ogeom.axyz(atom)}, {geom.axyz(idx)}"
new[i] = idx[0]
# print("old: ", old)
# print("new: ", new)
old = a2o(ogeom, old, False) + self.shape[1]
new = a2o(geom, new, False)
convert[0].append(old)
convert[1].append(new)
# translate columns
csr.translate_columns(*assert_unique(convert[0], convert[1]), rows=rows)
# scale columns that connects inside
csr.scale_columns(convert[1][1], scale=scale[1], rows=rows)
# ensure we have translated all columns correctly
assert len((csr.col >= geom.no_s).nonzero()[0]) == 0
# correct shape of column matrix
csr._shape = (csr.shape[0], geom.no_s, csr.shape[2])
out = self.copy()
out._csr = csr
out._geometry = geom
return out
[docs]
def toSparseAtom(self, dim: int = None, dtype=None):
"""Convert the sparse object (without data) to a new sparse object with equivalent but reduced sparse pattern
This converts the orbital sparse pattern to an atomic sparse pattern.
Parameters
----------
dim :
number of dimensions allocated in the SparseAtom object, default to the same
dtype : numpy.dtype, optional
used data-type for the sparse object. Defaults to the same.
"""
if dim is None:
dim = self.shape[-1]
if dtype is None:
dtype = self.dtype
geom = self.geometry
# Create a conversion vector
orb2atom = tile(geom.o2a(_a.arangei(geom.no)), geom.n_s)
orb2atom.shape = (-1, geom.no)
orb2atom += _a.arangei(geom.n_s).reshape(-1, 1) * geom.na
orb2atom.shape = (-1,)
# First convert all rows to the same
csr = self._csr
# Now build the new sparse pattern
ptr = _a.emptyi(geom.na + 1)
ptr[0] = 0
col = [None] * geom.na
for ia in range(geom.na):
o1, o2 = geom.a2o([ia, ia + 1])
# Get current atomic elements
idx = array_arange(csr.ptr[o1:o2], n=csr.ncol[o1:o2])
# These are now the atomic columns
# Immediately reduce to unique elements
acol = unique(orb2atom[csr.col[idx]])
# Step counters
col[ia] = acol
ptr[ia + 1] = ptr[ia] + len(acol)
# Now we can create the sparse atomic
col = np.concatenate(col, axis=0).astype(int32, copy=False)
spAtom = SparseAtom(geom, dim=dim, dtype=dtype, nnzpr=0)
spAtom._csr.ptr[:] = ptr[:]
spAtom._csr.ncol[:] = diff(ptr)
spAtom._csr.col = col
spAtom._csr._D = np.zeros([len(col), dim], dtype=dtype)
spAtom._csr._nnz = len(col)
spAtom._csr._finalized = True # unique returns sorted elements
return spAtom