Sparse linear algebra (scipy.sparse.linalg) — SciPy v1.15.3 Manual (original) (raw)
Abstract linear operators#
Matrix Operations#
| inv(A) | Compute the inverse of a sparse arrays |
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| 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 |
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| onenormest(A[, t, itmax, compute_v, compute_w]) | Compute a lower bound of the 1-norm of a sparse array. |
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. |
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| spsolve_triangular(A, b[, lower, ...]) | Solve the equation A x = b for x, assuming A is a triangular matrix. |
| is_sptriangular(A) | Returns 2-tuple indicating lower/upper triangular structure for sparse A |
| spbandwidth(A) | Return the lower and upper bandwidth of a 2D numeric array. |
| 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, rtol, atol, maxiter, M, ...]) | Use BIConjugate Gradient iteration to solve Ax = b. |
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| bicgstab(A, b[, x0, rtol, atol, maxiter, M, ...]) | Use BIConjugate Gradient STABilized iteration to solve Ax = b. |
| cg(A, b[, x0, rtol, atol, maxiter, M, callback]) | Use Conjugate Gradient iteration to solve Ax = b. |
| cgs(A, b[, x0, rtol, atol, maxiter, M, callback]) | Use Conjugate Gradient Squared iteration to solve Ax = b. |
| gmres(A, b[, x0, rtol, atol, restart, ...]) | Use Generalized Minimal RESidual iteration to solve Ax = b. |
| lgmres(A, b[, x0, rtol, atol, maxiter, M, ...]) | Solve a matrix equation using the LGMRES algorithm. |
| minres(A, b[, x0, rtol, shift, maxiter, M, ...]) | Use MINimum RESidual iteration to solve Ax=b |
| qmr(A, b[, x0, rtol, atol, maxiter, M1, M2, ...]) | Use Quasi-Minimal Residual iteration to solve Ax = b. |
| gcrotmk(A, b[, x0, rtol, atol, maxiter, M, ...]) | Solve a matrix equation using flexible GCROT(m,k) algorithm. |
| tfqmr(A, b[, x0, rtol, atol, maxiter, M, ...]) | 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. |
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| 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. |
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| 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. |
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The svds function supports the following solvers:
Complete or incomplete LU factorizations
| splu(A[, permc_spec, diag_pivot_thresh, ...]) | Compute the LU decomposition of a sparse, square matrix. |
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| 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. |
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