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

Examples

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.sparse.linalg._eigen.lobpcg.lobpcg.lobpcg scipy.sparse.linalg._dsolve.linsolve.spsolve scipy.optimize._nonlin.KrylovJacobian scipy.sparse.linalg._eigen.arpack.arpack.eigsh scipy.sparse.linalg._isolve.iterative.gmres scipy.optimize._nonlin.newton_krylov scipy.sparse.linalg._dsolve.linsolve.spilu scipy.sparse.linalg._onenormest.onenormest scipy.sparse.linalg._matfuncs.inv scipy.sparse.linalg._eigen._svds.svds scipy.sparse.linalg._expm_multiply.expm_multiply scipy.sparse.linalg._isolve.lsqr.lsqr scipy.sparse.linalg._dsolve.linsolve.splu scipy.sparse.linalg._isolve.tfqmr.tfqmr scipy.sparse.linalg._norm.norm scipy.sparse.linalg._interface.LinearOperator scipy.sparse.linalg._interface.aslinearoperator scipy.sparse.linalg._dsolve.linsolve.factorized scipy.sparse.linalg._isolve.minres.minres scipy.sparse.linalg._matfuncs.expm scipy.sparse.linalg._dsolve.linsolve.spsolve_triangular scipy.sparse.linalg._isolve.lsmr.lsmr scipy.sparse.linalg._eigen.arpack.arpack.eigs scipy.sparse.linalg._isolve.iterative.qmr scipy.sparse.linalg._isolve.lgmres.lgmres

Local connectivity graph

Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.

Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them

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