def spilu(A, drop_tol=None, fill_factor=None, drop_rule=None, permc_spec=None,
diag_pivot_thresh=None, relax=None, panel_size=None, options=None):
"""
Compute an incomplete LU decomposition for a sparse, square matrix A.
The resulting object is an approximation to the inverse of A.
Parameters
----------
A
Sparse matrix to factorize
drop_tol : float, optional
Drop tolerance (0 <= tol <= 1) for an incomplete LU decomposition.
(default: 1e-4)
fill_factor : float, optional
Specifies the fill ratio upper bound (>= 1.0) for ILU. (default: 10)
drop_rule : str, optional
Comma-separated string of drop rules to use.
Available rules: ``basic``, ``prows``, ``column``, ``area``,
``secondary``, ``dynamic``, ``interp``. (Default: ``basic,area``)
See SuperLU documentation for details.
milu : str, optional
Which version of modified ILU to use. (Choices: ``silu``,
``smilu_1``, ``smilu_2`` (default), ``smilu_3``.)
Remaining other options
Same as for `splu`
Returns
-------
invA_approx : scipy.sparse.linalg.dsolve._superlu.SciPyLUType
Object, which has a ``solve`` method.
See also
--------
splu : complete LU decomposition
Notes
-----
To improve the better approximation to the inverse, you may need to
increase ``fill_factor`` AND decrease ``drop_tol``.
This function uses the SuperLU library.
"""
if not isspmatrix_csc(A):
A = csc_matrix(A)
warn('splu requires CSC matrix format', SparseEfficiencyWarning)
A.sort_indices()
A = A.asfptype() #upcast to a floating point format
M, N = A.shape
if (M != N):
raise ValueError("can only factor square matrices") #is this true?
_options = dict(ILU_DropRule=drop_rule, ILU_DropTol=drop_tol,
ILU_FillFactor=fill_factor,
DiagPivotThresh=diag_pivot_thresh, ColPerm=permc_spec,
PanelSize=panel_size, Relax=relax)
if options is not None:
_options.update(options)
return _superlu.gstrf(N, A.nnz, A.data, A.indices, A.indptr,
ilu=True, options=_options)
def spilu(A,
drop_tol=None,
fill_factor=None,
drop_rule=None,
permc_spec=None,
diag_pivot_thresh=None,
relax=None,
panel_size=None,
options=None):
"""
Compute an incomplete LU decomposition for a sparse, square matrix A.
The resulting object is an approximation to the inverse of A.
Parameters
----------
A
Sparse matrix to factorize
drop_tol : float, optional
Drop tolerance (0 <= tol <= 1) for an incomplete LU decomposition.
(default: 1e-4)
fill_factor : float, optional
Specifies the fill ratio upper bound (>= 1.0) for ILU. (default: 10)
drop_rule : str, optional
Comma-separated string of drop rules to use.
Available rules: ``basic``, ``prows``, ``column``, ``area``,
``secondary``, ``dynamic``, ``interp``. (Default: ``basic,area``)
See SuperLU documentation for details.
milu : str, optional
Which version of modified ILU to use. (Choices: ``silu``,
``smilu_1``, ``smilu_2`` (default), ``smilu_3``.)
Remaining other options
Same as for `splu`
Returns
-------
invA_approx : scipy.sparse.linalg.dsolve._superlu.SciPyLUType
Object, which has a ``solve`` method.
See also
--------
splu : complete LU decomposition
Notes
-----
To improve the better approximation to the inverse, you may need to
increase ``fill_factor`` AND decrease ``drop_tol``.
This function uses the SuperLU library.
"""
if not isspmatrix_csc(A):
A = csc_matrix(A)
warn('splu requires CSC matrix format', SparseEfficiencyWarning)
A.sort_indices()
A = A.asfptype() #upcast to a floating point format
M, N = A.shape
if (M != N):
raise ValueError("can only factor square matrices") #is this true?
_options = dict(ILU_DropRule=drop_rule,
ILU_DropTol=drop_tol,
ILU_FillFactor=fill_factor,
DiagPivotThresh=diag_pivot_thresh,
ColPerm=permc_spec,
PanelSize=panel_size,
Relax=relax)
if options is not None:
_options.update(options)
return _superlu.gstrf(N,
A.nnz,
A.data,
A.indices,
A.indptr,
ilu=True,
options=_options)
def splu(A, permc_spec=None, diag_pivot_thresh=None,
drop_tol=None, relax=None, panel_size=None, options=dict()):
"""
Compute the LU decomposition of a sparse, square matrix.
Parameters
----------
A : sparse matrix
Sparse matrix to factorize. Should be in CSR or CSC format.
permc_spec : str, optional
How to permute the columns of the matrix for sparsity preservation.
(default: 'COLAMD')
- ``NATURAL``: natural ordering.
- ``MMD_ATA``: minimum degree ordering on the structure of A^T A.
- ``MMD_AT_PLUS_A``: minimum degree ordering on the structure of A^T+A.
- ``COLAMD``: approximate minimum degree column ordering
diag_pivot_thresh : float, optional
Threshold used for a diagonal entry to be an acceptable pivot.
See SuperLU user's guide for details [SLU]_
drop_tol : float, optional
(deprecated) No effect.
relax : int, optional
Expert option for customizing the degree of relaxing supernodes.
See SuperLU user's guide for details [SLU]_
panel_size : int, optional
Expert option for customizing the panel size.
See SuperLU user's guide for details [SLU]_
options : dict, optional
Dictionary containing additional expert options to SuperLU.
See SuperLU user guide [SLU]_ (section 2.4 on the 'Options' argument)
for more details. For example, you can specify
``options=dict(Equil=False, IterRefine='SINGLE'))``
to turn equilibration off and perform a single iterative refinement.
Returns
-------
invA : scipy.sparse.linalg.dsolve._superlu.SciPyLUType
Object, which has a ``solve`` method.
See also
--------
spilu : incomplete LU decomposition
Notes
-----
This function uses the SuperLU library.
References
----------
.. [SLU] SuperLU http://crd.lbl.gov/~xiaoye/SuperLU/
"""
if not isspmatrix_csc(A):
A = csc_matrix(A)
warn('splu requires CSC matrix format', SparseEfficiencyWarning)
A.sort_indices()
A = A.asfptype() #upcast to a floating point format
M, N = A.shape
if (M != N):
raise ValueError("can only factor square matrices") #is this true?
_options = dict(DiagPivotThresh=diag_pivot_thresh, ColPerm=permc_spec,
PanelSize=panel_size, Relax=relax)
if options is not None:
_options.update(options)
return _superlu.gstrf(N, A.nnz, A.data, A.indices, A.indptr,
ilu=False, options=_options)
def splu(A,
permc_spec=None,
diag_pivot_thresh=None,
drop_tol=None,
relax=None,
panel_size=None,
options=dict()):
"""
Compute the LU decomposition of a sparse, square matrix.
Parameters
----------
A : sparse matrix
Sparse matrix to factorize. Should be in CSR or CSC format.
permc_spec : str, optional
How to permute the columns of the matrix for sparsity preservation.
(default: 'COLAMD')
- ``NATURAL``: natural ordering.
- ``MMD_ATA``: minimum degree ordering on the structure of A^T A.
- ``MMD_AT_PLUS_A``: minimum degree ordering on the structure of A^T+A.
- ``COLAMD``: approximate minimum degree column ordering
diag_pivot_thresh : float, optional
Threshold used for a diagonal entry to be an acceptable pivot.
See SuperLU user's guide for details [SLU]_
drop_tol : float, optional
(deprecated) No effect.
relax : int, optional
Expert option for customizing the degree of relaxing supernodes.
See SuperLU user's guide for details [SLU]_
panel_size : int, optional
Expert option for customizing the panel size.
See SuperLU user's guide for details [SLU]_
options : dict, optional
Dictionary containing additional expert options to SuperLU.
See SuperLU user guide [SLU]_ (section 2.4 on the 'Options' argument)
for more details. For example, you can specify
``options=dict(Equil=False, IterRefine='SINGLE'))``
to turn equilibration off and perform a single iterative refinement.
Returns
-------
invA : scipy.sparse.linalg.dsolve._superlu.SciPyLUType
Object, which has a ``solve`` method.
See also
--------
spilu : incomplete LU decomposition
Notes
-----
This function uses the SuperLU library.
References
----------
.. [SLU] SuperLU http://crd.lbl.gov/~xiaoye/SuperLU/
"""
if not isspmatrix_csc(A):
A = csc_matrix(A)
warn('splu requires CSC matrix format', SparseEfficiencyWarning)
A.sort_indices()
A = A.asfptype() #upcast to a floating point format
M, N = A.shape
if (M != N):
raise ValueError("can only factor square matrices") #is this true?
_options = dict(DiagPivotThresh=diag_pivot_thresh,
ColPerm=permc_spec,
PanelSize=panel_size,
Relax=relax)
if options is not None:
_options.update(options)
return _superlu.gstrf(N,
A.nnz,
A.data,
A.indices,
A.indptr,
ilu=False,
options=_options)
