sisl.physics.sparse_physics module

Class implementation for an orbital system with, and without spin

class sisl.physics.sparse_physics.SparseOrbitalBZ(geom, dim=1, dtype=None, nnzpr=None, **kwargs)

Bases: sisl.sparse_geometry.SparseOrbital

Sparse object containing the orbital connections in a Brillouin zone

It contains an intrinsic sparse matrix of the physical elements.

Assigning or changing elements is as easy as with standard numpy assignments:

>>> S = SparseOrbitalBZ(...)
>>> S[1,2] = 0.1

which assigns 0.1 as the element between orbital 2 and 3. (remember that Python is 0-based elements).

Attributes

S
dim	Number of components per element
dkind	Data type of sparse elements (in str)
dtype	Data type of sparse elements
finalized	Whether the contained data is finalized and non-used elements have been removed
geom	Associated geometry
geometry	Associated geometry
nnz	Number of non-zero elements
orthogonal	True if the object is using an orthogonal basis
shape	Shape of sparse matrix

Methods

Sk([k, dtype, gauge, format])	Setup the overlap matrix for a given k-point
align(other)	See SparseCSR.align for details
construct(func[, na_iR, method, eta])	Automatically construct the sparse model based on a function that does the setting up of the elements
copy([dtype])	A copy of this object
create_construct(R, param)	Create a simple function for passing to the construct function.
cut(seps, axis, *args, **kwargs)	Cuts the sparse orbital model into different parts.
eigh([k, atoms, gauge, eigvals_only, ...])	Returns the eigenvalues of the physical quantity
eigsh([k, n, atoms, gauge, eigvals_only])	Calculates a subset of eigenvalues of the physical quantity (default 10)
eliminate_zeros()	Removes all zero elements from the sparse matrix
empty([keep])	See SparseCSR.empty for details
finalize()	Finalizes the model
fromsp(geom, P[, S])	Read and return the object with possible overlap
iter([local])	Iterations of the orbital space in the geometry, two indices from loop
iter_nnz([atom, orbital])	Iterations of the non-zero elements
repeat(reps, axis)	Create a repeated sparse orbital object, equivalent to Geometry.repeat
reset([dim, dtype, nnzpr])	The sparsity pattern is cleaned and every thing is reset.
spsame(other)	Compare two sparse objects and check whether they have the same entries.
sub(atom)	Create a subset of this sparse matrix by only retaining the elements corresponding to the atom
tile(reps, axis)	Create a tiled sparse orbital object, equivalent to Geometry.tile
tocsr(index[, isc])	Return a scipy.sparse.csr_matrix of the specified index

Create SparseOrbitalB model from geometry

Initializes an object using the geom object as the underlying geometry for the parameters that connects orbital elements.

Attributes

S
dim	Number of components per element
dkind	Data type of sparse elements (in str)
dtype	Data type of sparse elements
finalized	Whether the contained data is finalized and non-used elements have been removed
geom	Associated geometry
geometry	Associated geometry
nnz	Number of non-zero elements
orthogonal	True if the object is using an orthogonal basis
shape	Shape of sparse matrix

Methods

Sk([k, dtype, gauge, format])	Setup the overlap matrix for a given k-point
align(other)	See SparseCSR.align for details
construct(func[, na_iR, method, eta])	Automatically construct the sparse model based on a function that does the setting up of the elements
copy([dtype])	A copy of this object
create_construct(R, param)	Create a simple function for passing to the construct function.
cut(seps, axis, *args, **kwargs)	Cuts the sparse orbital model into different parts.
eigh([k, atoms, gauge, eigvals_only, ...])	Returns the eigenvalues of the physical quantity
eigsh([k, n, atoms, gauge, eigvals_only])	Calculates a subset of eigenvalues of the physical quantity (default 10)
eliminate_zeros()	Removes all zero elements from the sparse matrix
empty([keep])	See SparseCSR.empty for details
finalize()	Finalizes the model
fromsp(geom, P[, S])	Read and return the object with possible overlap
iter([local])	Iterations of the orbital space in the geometry, two indices from loop
iter_nnz([atom, orbital])	Iterations of the non-zero elements
repeat(reps, axis)	Create a repeated sparse orbital object, equivalent to Geometry.repeat
reset([dim, dtype, nnzpr])	The sparsity pattern is cleaned and every thing is reset.
spsame(other)	Compare two sparse objects and check whether they have the same entries.
sub(atom)	Create a subset of this sparse matrix by only retaining the elements corresponding to the atom
tile(reps, axis)	Create a tiled sparse orbital object, equivalent to Geometry.tile
tocsr(index[, isc])	Return a scipy.sparse.csr_matrix of the specified index

S

Sk(k=(0, 0, 0), dtype=None, gauge='R', format='csr', *args, **kwargs)

Setup the overlap matrix for a given k-point

Creation and return of the overlap matrix for a given k-point (default to Gamma).

Parameters:

k : array_like

the k-point to setup the overlap at

dtype : numpy.dtype , optional

the data type of the returned matrix. Do NOT request non-complex data-type for non-Gamma k. The default data-type is ‘numpy.complex128`

gauge : {‘R’, ‘r’}

the chosen gauge, R for cell vector gauge, and r for orbital distance gauge.

format : {‘csr’, ‘array’, ‘dense’, ‘coo’, ...}

the returned format of the matrix, defaulting to the scipy.sparse.csr_matrix, however if one always requires operations on dense matrices, one can always return in numpy.ndarray ('array') or numpy.matrix ('dense').

Notes

Currently the implemented gauge for the k-point is the cell vector gauge:

\[S(k) = S_{ij} e^{i k R}\]

where \(R\) is an integer times the cell vector and \(i\), \(j\) are orbital indices.

Another possible gauge is the orbital distance which can be written as

\[S(k) = S_{ij} e^{i k r}\]

where \(r\) is the distance between the orbitals \(i\) and \(j\). Currently the second gauge is not implemented (yet).

eigh(k=(0, 0, 0), atoms=None, gauge='R', eigvals_only=True, overwrite_a=True, overwrite_b=True, *args, **kwargs)

Returns the eigenvalues of the physical quantity

Setup the system and overlap matrix with respect to the given k-point, then reduce the space to the specified atoms and calculate the eigenvalues.

All subsequent arguments gets passed directly to scipy.linalg.eigh

eigsh(k=(0, 0, 0), n=10, atoms=None, gauge='R', eigvals_only=True, *args, **kwargs)

Calculates a subset of eigenvalues of the physical quantity (default 10)

Setup the quantity and overlap matrix with respect to the given k-point, then reduce the space to the specified atoms and calculate a subset of the eigenvalues using the sparse algorithms.

All subsequent arguments gets passed directly to scipy.linalg.eigsh

classmethod fromsp(geom, P, S=None)

Read and return the object with possible overlap

iter(local=False)

Iterations of the orbital space in the geometry, two indices from loop

An iterator returning the current atomic index and the corresponding orbital index.

>>> for ia, io in self:

In the above case io always belongs to atom ia and ia may be repeated according to the number of orbitals associated with the atom ia.

Parameters:

local : bool=False

whether the orbital index is the global index, or the local index relative to the atom it resides on.

orthogonal

True if the object is using an orthogonal basis

class sisl.physics.sparse_physics.SparseOrbitalBZSpin(geom, dim=1, dtype=None, nnzpr=None, **kwargs)

Bases: sisl.physics.sparse_physics.SparseOrbitalBZ

Sparse object containing the orbital connections in a Brillouin zone with possible spin-components

It contains an intrinsic sparse matrix of the physical elements.

Assigning or changing elements is as easy as with standard numpy assignments:

>>> S = SparseOrbitalBZSpin(...)
>>> S[1,2] = 0.1

which assigns 0.1 as the element between orbital 2 and 3. (remember that Python is 0-based elements).

Attributes

S
dim	Number of components per element
dkind	Data type of sparse elements (in str)
dtype	Data type of sparse elements
finalized	Whether the contained data is finalized and non-used elements have been removed
geom	Associated geometry
geometry	Associated geometry
nnz	Number of non-zero elements
orthogonal	True if the object is using an orthogonal basis
shape	Shape of sparse matrix
spin	Spin class

Methods

Sk([k, dtype, gauge, format])	Setup the overlap matrix for a given k-point
align(other)	See SparseCSR.align for details
construct(func[, na_iR, method, eta])	Automatically construct the sparse model based on a function that does the setting up of the elements
copy([dtype])	A copy of this object
create_construct(R, param)	Create a simple function for passing to the construct function.
cut(seps, axis, *args, **kwargs)	Cuts the sparse orbital model into different parts.
eigh([k, atoms, gauge, eigvals_only, ...])	Returns the eigenvalues of the physical quantity
eigsh([k, n, atoms, gauge, eigvals_only])	Calculates a subset of eigenvalues of the physical quantity (default 10)
eliminate_zeros()	Removes all zero elements from the sparse matrix
empty([keep])	See SparseCSR.empty for details
finalize()	Finalizes the model
fromsp(geom, P[, S])	Read and return the object with possible overlap
iter([local])	Iterations of the orbital space in the geometry, two indices from loop
iter_nnz([atom, orbital])	Iterations of the non-zero elements
repeat(reps, axis)	Create a repeated sparse orbital object, equivalent to Geometry.repeat
reset([dim, dtype, nnzpr])	The sparsity pattern is cleaned and every thing is reset.
spsame(other)	Compare two sparse objects and check whether they have the same entries.
sub(atom)	Create a subset of this sparse matrix by only retaining the elements corresponding to the atom
tile(reps, axis)	Create a tiled sparse orbital object, equivalent to Geometry.tile
tocsr(index[, isc])	Return a scipy.sparse.csr_matrix of the specified index

Create SparseOrbitalBZSpin model from geometry

Initializes an object using the geom object as the underlying geometry for the parameters that connects orbital elements.

Attributes

S
dim	Number of components per element
dkind	Data type of sparse elements (in str)
dtype	Data type of sparse elements
finalized	Whether the contained data is finalized and non-used elements have been removed
geom	Associated geometry
geometry	Associated geometry
nnz	Number of non-zero elements
orthogonal	True if the object is using an orthogonal basis
shape	Shape of sparse matrix
spin	Spin class

Methods

Sk([k, dtype, gauge, format])	Setup the overlap matrix for a given k-point
align(other)	See SparseCSR.align for details
construct(func[, na_iR, method, eta])	Automatically construct the sparse model based on a function that does the setting up of the elements
copy([dtype])	A copy of this object
create_construct(R, param)	Create a simple function for passing to the construct function.
cut(seps, axis, *args, **kwargs)	Cuts the sparse orbital model into different parts.
eigh([k, atoms, gauge, eigvals_only, ...])	Returns the eigenvalues of the physical quantity
eigsh([k, n, atoms, gauge, eigvals_only])	Calculates a subset of eigenvalues of the physical quantity (default 10)
eliminate_zeros()	Removes all zero elements from the sparse matrix
empty([keep])	See SparseCSR.empty for details
finalize()	Finalizes the model
fromsp(geom, P[, S])	Read and return the object with possible overlap
iter([local])	Iterations of the orbital space in the geometry, two indices from loop
iter_nnz([atom, orbital])	Iterations of the non-zero elements
repeat(reps, axis)	Create a repeated sparse orbital object, equivalent to Geometry.repeat
reset([dim, dtype, nnzpr])	The sparsity pattern is cleaned and every thing is reset.
spsame(other)	Compare two sparse objects and check whether they have the same entries.
sub(atom)	Create a subset of this sparse matrix by only retaining the elements corresponding to the atom
tile(reps, axis)	Create a tiled sparse orbital object, equivalent to Geometry.tile
tocsr(index[, isc])	Return a scipy.sparse.csr_matrix of the specified index

eigh(k=(0, 0, 0), atoms=None, gauge='R', eigvals_only=True, overwrite_a=True, overwrite_b=True, *args, **kwargs)

Returns the eigenvalues of the physical quantity

Setup the system and overlap matrix with respect to the given k-point, then reduce the space to the specified atoms and calculate the eigenvalues.

All subsequent arguments gets passed directly to scipy.linalg.eigh

eigsh(k=(0, 0, 0), n=10, atoms=None, gauge='R', eigvals_only=True, *args, **kwargs)

Calculates a subset of eigenvalues of the physical quantity (default 10)

Setup the quantity and overlap matrix with respect to the given k-point, then reduce the space to the specified atoms and calculate a subset of the eigenvalues using the sparse algorithms.

All subsequent arguments gets passed directly to scipy.linalg.eigsh

classmethod fromsp(geom, P, S=None)

Read and return the object with possible overlap

spin

Spin class