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""" 

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 

 

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 

 

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 __future__ import division, print_function, absolute_import 

 

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 * 

 

__all__ = [s for s in dir() if not s.startswith('_')] 

 

from scipy._lib._testutils import PytestTester 

test = PytestTester(__name__) 

del PytestTester