scipy.sparse.linalg¶
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¶
| norm(x[, ord, axis]) | Norm of a sparse matrix This function is able to return one of seven different matrix norms, depending on the value of the ord parameter. |
| 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. |
| MatrixRankWarning | |
| use_solver(**kwargs) | Select default sparse direct solver to be used. |
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 |
Functions
| aslinearoperator(A) | Return A as a LinearOperator. |
| 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. |
| 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. |
| 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. |
| factorized(A) | Return a fuction for solving a sparse linear system, with A pre-factorized. |
| gmres(A, b[, x0, tol, restart, maxiter, ...]) | Use Generalized Minimal RESidual iteration to solve A x = b. |
| 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 .. |
| lgmres(A, b[, x0, tol, maxiter, M, ...]) | Solve a matrix equation using the LGMRES algorithm. |
| 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. |
| lsmr(A, b[, damp, atol, btol, conlim, ...]) | Iterative solver for least-squares problems. |
| lsqr(A, b[, damp, atol, btol, conlim, ...]) | Find the least-squares solution to a large, sparse, linear system of equations. |
| 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. |
| norm(x[, ord, axis]) | Norm of a sparse matrix This function is able to return one of seven different matrix norms, depending on the value of the ord parameter. |
| onenormest(A[, t, itmax, compute_v, compute_w]) | Compute a lower bound of the 1-norm of a sparse matrix. |
| 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. |
| spilu(A[, drop_tol, fill_factor, drop_rule, ...]) | Compute an incomplete LU decomposition for a sparse, square matrix. |
| splu(A[, permc_spec, diag_pivot_thresh, ...]) | Compute the LU decomposition of a sparse, square matrix. |
| spsolve(A, b[, permc_spec, use_umfpack]) | Solve the sparse linear system Ax=b, where b may be a vector or a matrix. |
| svds(A[, k, ncv, tol, which, v0, maxiter, ...]) | Compute the largest k singular values/vectors for a sparse matrix. |
| use_solver(**kwargs) | Select default sparse direct solver to be used. |
Classes
| LinearOperator(dtype, shape) | Common interface for performing matrix vector products Many iterative methods (e.g. |
| SuperLU | LU factorization of a sparse matrix. |
| Tester | Nose test runner. |
Exceptions
| ArpackError(info[, infodict]) | ARPACK error |
| ArpackNoConvergence(msg, eigenvalues, ...) | ARPACK iteration did not converge .. |
| MatrixRankWarning |