scipy.sparse.linalg

Sparse linear algebra (scipy.sparse.linalg)

Abstract linear operators

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    LinearOperator -- abstract representation of a linear operator
    aslinearoperator -- convert an object to an abstract linear operator

Matrix Operations

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    inv -- compute the sparse matrix inverse
    expm -- compute the sparse matrix exponential
    expm_multiply -- compute the product of a matrix exponential and a matrix
    funm_multiply_krylov -- use a Krylov method to compute f(A)b for a general f
    matrix_power -- compute the matrix power by raising a matrix to an exponent

Matrix norms

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    norm -- Norm of a sparse matrix
    onenormest -- Estimate the 1-norm of a sparse matrix

Solving linear problems

Direct methods for linear equation systems:

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    spsolve -- Solve the sparse linear system Ax=b
    spsolve_triangular -- Solve sparse linear system Ax=b for a triangular A.
    is_sptriangular -- Check if sparse A is triangular.
    spbandwidth -- Find the bandwidth of a sparse 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:

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    bicg -- Use BIConjugate Gradient iteration to solve Ax = b
    bicgstab -- Use BIConjugate Gradient STABilized iteration to solve Ax = b
    cg -- Use Conjugate Gradient iteration to solve Ax = b
    cgs -- Use Conjugate Gradient Squared iteration to solve Ax = b
    gmres -- Use Generalized Minimal RESidual iteration to solve Ax = 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 Ax = b
    gcrotmk -- Solve a matrix equation using the GCROT(m,k) algorithm
    tfqmr -- Use Transpose-Free Quasi-Minimal Residual iteration to solve Ax = b

Iterative methods for least-squares problems:

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    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:

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    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:

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    svds -- Compute k singular values/vectors for a sparse matrix

The svds function supports the following solvers:

• sparse.linalg.svds-arpack

• sparse.linalg.svds-lobpcg

• sparse.linalg.svds-propack

Complete or incomplete LU factorizations

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    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

Sparse arrays with structure

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    LaplacianNd -- Laplacian on a uniform rectangular grid in ``N`` dimensions

Exceptions

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    ArpackNoConvergence
    ArpackError