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, ...])	Compute the action of the matrix exponential of A on B.
matrix_power(A, power)	Raise a square matrix to the integer power, power.

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, ...])	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, ...])	Use Conjugate Gradient iteration to solve Ax = b.
cgs(A, b[, x0, tol, maxiter, M, callback, ...])	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.
tfqmr(A, b[, x0, tol, maxiter, M, callback, ...])	Use Transpose-Free Quasi-Minimal Residual iteration to solve Ax = b.

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, ...])

Partial singular value decomposition of a sparse matrix.

The svds function supports the following solvers:

• svds(solver=’arpack’)
• svds(solver=’lobpcg’)
• svds(solver=’propack’)

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.

Sparse arrays with structure

LaplacianNd(*args, **kwargs)

The grid Laplacian in N dimensions and its eigenvalues/eigenvectors.

Exceptions

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