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. factorized(A) 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, ...]) 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, 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)