### Table Of Contents

- Sparse linear algebra (`scipy.sparse.linalg`)
  - Abstract linear operators
  - Matrix Operations
  - Matrix norms
  - Solving linear problems
  - Matrix factorizations
  - Exceptions

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

## Abstract linear operators

`LinearOperator`(dtype, shape) | Common interface for performing matrix vector products Many iterative methods (e.g.
`aslinearoperator`(A) | Return A as a LinearOperator.

## Matrix Operations

`inv`(A) | Compute the inverse of a sparse matrix :Parameters: A : (M,M) ndarray or sparse matrix square matrix to be inverted :Returns: Ainv : (M,M) ndarray or sparse matrix inverse of A ..
`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

`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.
`factorized`(A) | Return a fuction for solving a sparse linear system, with A pre-factorized.

Iterative methods for linear equation systems:

`bicg`(A, b[, x0, tol, maxiter, xtype, M, ...]) | Use BIConjugate Gradient iteration to solve A x = b :Parameters: A : {sparse matrix, dense matrix, LinearOperator} The real or complex N-by-N matrix of the linear system It is required that the linear operator can produce `Ax` and `A^T x`.
`bicgstab`(A, b[, x0, tol, maxiter, xtype, M, ...]) | Use BIConjugate Gradient STABilized iteration to solve A x = b :Parameters: A : {sparse matrix, dense matrix, LinearOperator} The real or complex N-by-N matrix of the linear system `A` must represent a hermitian, positive definite matrix b : {array, matrix} Right hand side of the linear system.
`cg`(A, b[, x0, tol, maxiter, xtype, M, callback]) | Use Conjugate Gradient iteration to solve A x = b :Parameters: A : {sparse matrix, dense matrix, LinearOperator} The real or complex N-by-N matrix of the linear system `A` must represent a hermitian, positive definite matrix b : {array, matrix} Right hand side of the linear system.
`cgs`(A, b[, x0, tol, maxiter, xtype, M, callback]) | Use Conjugate Gradient Squared iteration to solve A x = b :Parameters: A : {sparse matrix, dense matrix, LinearOperator} The real-valued N-by-N matrix of the linear system b : {array, matrix} Right hand side of the linear system.
`gmres`(A, b[, x0, tol, restart, maxiter, ...]) | Use Generalized Minimal RESidual iteration to solve A x = b.
`lgmres`(A, b[, x0, tol, maxiter, M, ...]) | Solve a matrix equation using the LGMRES algorithm.
`minres`(A, b[, x0, shift, tol, maxiter, ...]) | Use MINimum RESidual iteration to solve Ax=b MINRES minimizes norm(A*x - b) for a real symmetric matrix A.
`qmr`(A, b[, x0, tol, maxiter, xtype, M1, M2, ...]) | Use Quasi-Minimal Residual iteration to solve A x = b :Parameters: A : {sparse matrix, dense matrix, LinearOperator} The real-valued N-by-N matrix of the linear system.

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) LOBPCG is a preconditioned eigensolver for large symmetric positive definite (SPD) generalized eigenproblems.

Singular values problems:

`svds`(A[, k, ncv, tol, which, v0, maxiter, ...]) | Compute the largest 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