# Sparse linear algebra (`scipy.sparse.linalg`)

## Abstract linear operators

`LinearOperator`(*args, **kwargs) | Common interface for performing matrix vector products
`aslinearoperator`(A) | Return A as a LinearOperator.

## Matrix Operations

`inv`(A) | Compute the inverse of a sparse matrix
`expm`(A) | Compute the matrix exponential using Pade approximation.
`expm_multiply`(A, B[, start, stop, num, endpoint]) | Compute the action of the matrix exponential of A on B.

## Matrix norms

`norm`(x[, ord, axis]) | Norm of a sparse matrix
`onenormest`(A[, t, itmax, compute_v, compute_w]) | Compute a lower bound of the 1-norm of a sparse matrix.

## Solving linear problems

Direct methods for linear equation systems:

`spsolve`(A, b[, permc_spec, use_umfpack]) | Solve the sparse linear system Ax=b, where b may be a vector or a matrix.
`spsolve_triangular`(A, b[, lower, …]) | Solve the equation `A x = b` for x, assuming A is a triangular matrix.
`factorized`(A) | Return a function for solving a sparse linear system, with A pre-factorized.
`MatrixRankWarning` |
`use_solver`(**kwargs) | Select default sparse direct solver to be used.

Iterative methods for linear equation systems:

`bicg`(A, b[, x0, tol, maxiter, M, callback, atol]) | Use BIConjugate Gradient iteration to solve `Ax = b`.
`bicgstab`(A, b[, x0, tol, maxiter, M, …]) | Use BIConjugate Gradient STABilized iteration to solve `Ax = b`.
`cg`(A, b[, x0, tol, maxiter, M, callback, atol]) | Use Conjugate Gradient iteration to solve `Ax = b`.
`cgs`(A, b[, x0, tol, maxiter, M, callback, atol]) | Use Conjugate Gradient Squared iteration to solve `Ax = b`.
`gmres`(A, b[, x0, tol, restart, maxiter, M, …]) | Use Generalized Minimal RESidual iteration to solve `Ax = b`.
`lgmres`(A, b[, x0, tol, maxiter, M, …]) | Solve a matrix equation using the LGMRES algorithm.
`minres`(A, b[, x0, shift, tol, maxiter, M, …]) | Use MINimum RESidual iteration to solve Ax=b
`qmr`(A, b[, x0, tol, maxiter, M1, M2, …]) | Use Quasi-Minimal Residual iteration to solve `Ax = b`.
`gcrotmk`(A, b[, x0, tol, maxiter, M, …]) | Solve a matrix equation using flexible GCROT(m,k) algorithm.

Iterative methods for least-squares problems:

`lsqr`(A, b[, damp, atol, btol, conlim, …]) | Find the least-squares solution to a large, sparse, linear system of equations.
`lsmr`(A, b[, damp, atol, btol, conlim, …]) | Iterative solver for least-squares problems.

## Matrix factorizations

Eigenvalue problems:

`eigs`(A[, k, M, sigma, which, v0, ncv, …]) | Find k eigenvalues and eigenvectors of the square matrix A.
`eigsh`(A[, k, M, sigma, which, v0, ncv, …]) | Find k eigenvalues and eigenvectors of the real symmetric square matrix or complex Hermitian matrix A.
`lobpcg`(A, X[, B, M, Y, tol, maxiter, …]) | Locally Optimal Block Preconditioned Conjugate Gradient Method (LOBPCG)

Singular values problems:

`svds`(A[, k, ncv, tol, which, v0, maxiter, …]) | Compute the largest or smallest k singular values/vectors for a sparse matrix.

Complete or incomplete LU factorizations

`splu`(A[, permc_spec, diag_pivot_thresh, …]) | Compute the LU decomposition of a sparse, square matrix.
`spilu`(A[, drop_tol, fill_factor, drop_rule, …]) | Compute an incomplete LU decomposition for a sparse, square matrix.
`SuperLU`() | LU factorization of a sparse matrix.

## Exceptions

`ArpackNoConvergence`(msg, eigenvalues, …) | ARPACK iteration did not converge
`ArpackError`(info[, infodict]) | ARPACK error

scipy.sparse.SparseWarning scipy.sparse.linalg.LinearOperator