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scipy.sparse.linalg¶
Sparse linear algebra (scipy.sparse.linalg)¶
Abstract linear operators¶
LinearOperator(dtype, shape) |
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, endpoint]) |
Compute the action of the matrix exponential of A on B. |
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, xtype, M, ...]) |
Use BIConjugate Gradient iteration to solve Ax = b. |
bicgstab(A, b[, x0, tol, maxiter, xtype, M, ...]) |
Use BIConjugate Gradient STABilized iteration to solve Ax = b. |
cg(A, b[, x0, tol, maxiter, xtype, M, callback]) |
Use Conjugate Gradient iteration to solve Ax = b. |
cgs(A, b[, x0, tol, maxiter, xtype, M, callback]) |
Use Conjugate Gradient Squared iteration to solve Ax = b. |
gmres(A, b[, x0, tol, restart, maxiter, ...]) |
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, ...]) |
Use MINimum RESidual iteration to solve Ax=b |
qmr(A, b[, x0, tol, maxiter, xtype, M1, M2, ...]) |
Use 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, ...]) |
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 Ax = b. |
bicgstab(A, b[, x0, tol, maxiter, xtype, M, ...]) |
Use BIConjugate Gradient STABilized iteration to solve Ax = b. |
cg(A, b[, x0, tol, maxiter, xtype, M, callback]) |
Use Conjugate Gradient iteration to solve Ax = b. |
cgs(A, b[, x0, tol, maxiter, xtype, M, callback]) |
Use Conjugate Gradient Squared iteration to solve Ax = b. |
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 function for solving a sparse linear system, with A pre-factorized. |
gmres(A, b[, x0, tol, restart, maxiter, ...]) |
Use Generalized Minimal RESidual iteration to solve Ax = b. |
inv(A) |
Compute the inverse of a sparse matrix |
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) |
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 |
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. |
qmr(A, b[, x0, tol, maxiter, xtype, M1, M2, ...]) |
Use Quasi-Minimal Residual iteration to solve Ax = b. |
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. |
spsolve_triangular(A, b[, lower, ...]) |
Solve the equation A x = b for x, assuming A is a triangular 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 |
SuperLU |
LU factorization of a sparse matrix. |
Tester |
alias of NoseTester |
Exceptions
ArpackError(info[, infodict]) |
ARPACK error |
ArpackNoConvergence(msg, eigenvalues, ...) |
ARPACK iteration did not converge |
MatrixRankWarning |