137 lines
3.6 KiB
Python
137 lines
3.6 KiB
Python
|
"""
|
||
|
|
Sparse linear algebra (:mod:`scipy.sparse.linalg`)
|
||
|
|
==================================================
|
||
|
|
|
||
|
|
.. currentmodule:: scipy.sparse.linalg
|
||
|
|
|
||
|
|
Abstract linear operators
|
||
|
|
-------------------------
|
||
|
|
|
||
|
|
.. autosummary::
|
||
|
|
:toctree: generated/
|
||
|
|
|
||
|
|
LinearOperator -- abstract representation of a linear operator
|
||
|
|
aslinearoperator -- convert an object to an abstract linear operator
|
||
|
|
|
||
|
|
Matrix Operations
|
||
|
|
-----------------
|
||
|
|
|
||
|
|
.. autosummary::
|
||
|
|
:toctree: generated/
|
||
|
|
|
||
|
|
inv -- compute the sparse matrix inverse
|
||
|
|
expm -- compute the sparse matrix exponential
|
||
|
|
expm_multiply -- compute the product of a matrix exponential and a matrix
|
||
|
|
|
||
|
|
Matrix norms
|
||
|
|
------------
|
||
|
|
|
||
|
|
.. autosummary::
|
||
|
|
:toctree: generated/
|
||
|
|
|
||
|
|
norm -- Norm of a sparse matrix
|
||
|
|
onenormest -- Estimate the 1-norm of a sparse matrix
|
||
|
|
|
||
|
|
Solving linear problems
|
||
|
|
-----------------------
|
||
|
|
|
||
|
|
Direct methods for linear equation systems:
|
||
|
|
|
||
|
|
.. autosummary::
|
||
|
|
:toctree: generated/
|
||
|
|
|
||
|
|
spsolve -- Solve the sparse linear system Ax=b
|
||
|
|
spsolve_triangular -- Solve the sparse linear system Ax=b for a triangular matrix
|
||
|
|
factorized -- Pre-factorize matrix to a function solving a linear system
|
||
|
|
MatrixRankWarning -- Warning on exactly singular matrices
|
||
|
|
use_solver -- Select direct solver to use
|
||
|
|
|
||
|
|
Iterative methods for linear equation systems:
|
||
|
|
|
||
|
|
.. autosummary::
|
||
|
|
:toctree: generated/
|
||
|
|
|
||
|
|
bicg -- Use BIConjugate Gradient iteration to solve A x = b
|
||
|
|
bicgstab -- Use BIConjugate Gradient STABilized iteration to solve A x = b
|
||
|
|
cg -- Use Conjugate Gradient iteration to solve A x = b
|
||
|
|
cgs -- Use Conjugate Gradient Squared iteration to solve A x = b
|
||
|
|
gmres -- Use Generalized Minimal RESidual iteration to solve A x = b
|
||
|
|
lgmres -- Solve a matrix equation using the LGMRES algorithm
|
||
|
|
minres -- Use MINimum RESidual iteration to solve Ax = b
|
||
|
|
qmr -- Use Quasi-Minimal Residual iteration to solve A x = b
|
||
|
|
gcrotmk -- Solve a matrix equation using the GCROT(m,k) algorithm
|
||
|
|
tfqmr -- Use Transpose-Free Quasi-Minimal Residual iteration to solve A x = b
|
||
|
|
|
||
|
|
Iterative methods for least-squares problems:
|
||
|
|
|
||
|
|
.. autosummary::
|
||
|
|
:toctree: generated/
|
||
|
|
|
||
|
|
lsqr -- Find the least-squares solution to a sparse linear equation system
|
||
|
|
lsmr -- Find the least-squares solution to a sparse linear equation system
|
||
|
|
|
||
|
|
Matrix factorizations
|
||
|
|
---------------------
|
||
|
|
|
||
|
|
Eigenvalue problems:
|
||
|
|
|
||
|
|
.. autosummary::
|
||
|
|
:toctree: generated/
|
||
|
|
|
||
|
|
eigs -- Find k eigenvalues and eigenvectors of the square matrix A
|
||
|
|
eigsh -- Find k eigenvalues and eigenvectors of a symmetric matrix
|
||
|
|
lobpcg -- Solve symmetric partial eigenproblems with optional preconditioning
|
||
|
|
|
||
|
|
Singular values problems:
|
||
|
|
|
||
|
|
.. autosummary::
|
||
|
|
:toctree: generated/
|
||
|
|
|
||
|
|
svds -- Compute k singular values/vectors for a sparse matrix
|
||
|
|
|
||
|
|
The `svds` function supports the following solvers:
|
||
|
|
|
||
|
|
.. toctree::
|
||
|
|
|
||
|
|
sparse.linalg.svds-arpack
|
||
|
|
sparse.linalg.svds-lobpcg
|
||
|
|
sparse.linalg.svds-propack
|
||
|
|
|
||
|
|
Complete or incomplete LU factorizations
|
||
|
|
|
||
|
|
.. autosummary::
|
||
|
|
:toctree: generated/
|
||
|
|
|
||
|
|
splu -- Compute a LU decomposition for a sparse matrix
|
||
|
|
spilu -- Compute an incomplete LU decomposition for a sparse matrix
|
||
|
|
SuperLU -- Object representing an LU factorization
|
||
|
|
|
||
|
|
Exceptions
|
||
|
|
----------
|
||
|
|
|
||
|
|
.. autosummary::
|
||
|
|
:toctree: generated/
|
||
|
|
|
||
|
|
ArpackNoConvergence
|
||
|
|
ArpackError
|
||
|
|
|
||
|
|
"""
|
||
|
|
|
||
|
|
from ._isolve import *
|
||
|
|
from ._dsolve import *
|
||
|
|
from ._interface import *
|
||
|
|
from ._eigen import *
|
||
|
|
from ._matfuncs import *
|
||
|
|
from ._onenormest import *
|
||
|
|
from ._norm import *
|
||
|
|
from ._expm_multiply import *
|
||
|
|
|
||
|
|
# Deprecated namespaces, to be removed in v2.0.0
|
||
|
|
from . import isolve, dsolve, interface, eigen, matfuncs
|
||
|
|
|
||
|
|
__all__ = [s for s in dir() if not s.startswith('_')]
|
||
|
|
|
||
|
|
from scipy._lib._testutils import PytestTester
|
||
|
|
test = PytestTester(__name__)
|
||
|
|
del PytestTester
|