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

## Abstract linear operators¶

 `LinearOperator`(shape, matvec[, rmatvec, …]) Common interface for performing matrix vector products Return A as a LinearOperator.

## Matrix norms¶

 `norm`(x[, ord, axis]) Norm of a cupy.scipy.spmatrix

## Solving linear problems¶

Direct methods for linear equation systems:

 `spsolve`(A, b) Solves a sparse linear system `A x = b` `spsolve_triangular`(A, b[, lower, …]) Solves a sparse triangular system `A x = b`. Return a function for solving a sparse linear system, with A pre-factorized.

Iterative methods for linear equation systems:

 `cg`(A, b[, x0, tol, maxiter, M, callback, atol]) Uses Conjugate Gradient iteration to solve `Ax = b`. `gmres`(A, b[, x0, tol, restart, maxiter, M, …]) Uses Generalized Minimal RESidual iteration to solve `Ax = b`. `cgs`(A, b[, x0, tol, maxiter, M, callback, atol]) Use Conjugate Gradient Squared iteration to solve `Ax = b`. `minres`(A, b[, x0, shift, tol, maxiter, M, …]) Uses MINimum RESidual iteration to solve `Ax = b`.

Iterative methods for least-squares problems:

 `lsqr`(A, b) Solves linear system with QR decomposition. `lsmr`(A, b[, x0, damp, atol, btol, conlim, …]) Iterative solver for least-squares problems.

## Matrix factorizations¶

Eigenvalue problems:

 `eigsh`(a[, k, which, ncv, maxiter, tol, …]) Finds `k` eigenvalues and eigenvectors of the real symmetric matrix. `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, maxiter, …]) Finds the largest `k` singular values/vectors for a sparse matrix.

Complete or incomplete LU factorizations:

 `splu`(A[, permc_spec, diag_pivot_thresh, …]) Computes the LU decomposition of a sparse square matrix. `spilu`(A[, drop_tol, fill_factor, drop_rule, …]) Computes the incomplete LU decomposition of a sparse square matrix. `SuperLU`(obj)