_MhdZddlTddlTddlTddlTddlTddlTddlTddlTddl Tddl m Z m Z m Z mZmZdeDZddlmZeeZ[dS)a Sparse linear algebra (:mod:`scipy.sparse.linalg`) ================================================== .. currentmodule:: scipy.sparse.linalg Abstract linear operators ------------------------- .. autosummary:: :toctree: generated/ LinearOperator -- abstract representation of a linear operator aslinearoperator -- convert an object to an abstract linear operator Matrix Operations ----------------- .. autosummary:: :toctree: generated/ inv -- compute the sparse matrix inverse expm -- compute the sparse matrix exponential expm_multiply -- compute the product of a matrix exponential and a matrix matrix_power -- compute the matrix power by raising a matrix to an exponent Matrix norms ------------ .. autosummary:: :toctree: generated/ norm -- Norm of a sparse matrix onenormest -- Estimate the 1-norm of a sparse matrix Solving linear problems ----------------------- Direct methods for linear equation systems: .. autosummary:: :toctree: generated/ spsolve -- Solve the sparse linear system Ax=b spsolve_triangular -- Solve sparse linear system Ax=b for a triangular A. is_sptriangular -- Check if sparse A is triangular. spbandwidth -- Find the bandwidth of a sparse matrix. factorized -- Pre-factorize matrix to a function solving a linear system MatrixRankWarning -- Warning on exactly singular matrices use_solver -- Select direct solver to use Iterative methods for linear equation systems: .. autosummary:: :toctree: generated/ bicg -- Use BIConjugate Gradient iteration to solve Ax = b bicgstab -- Use BIConjugate Gradient STABilized iteration to solve Ax = b cg -- Use Conjugate Gradient iteration to solve Ax = b cgs -- Use Conjugate Gradient Squared iteration to solve Ax = b gmres -- Use Generalized Minimal RESidual iteration to solve Ax = b lgmres -- Solve a matrix equation using the LGMRES algorithm minres -- Use MINimum RESidual iteration to solve Ax = b qmr -- Use Quasi-Minimal Residual iteration to solve Ax = b gcrotmk -- Solve a matrix equation using the GCROT(m,k) algorithm tfqmr -- Use Transpose-Free Quasi-Minimal Residual iteration to solve Ax = b Iterative methods for least-squares problems: .. autosummary:: :toctree: generated/ lsqr -- Find the least-squares solution to a sparse linear equation system lsmr -- Find the least-squares solution to a sparse linear equation system Matrix factorizations --------------------- Eigenvalue problems: .. autosummary:: :toctree: generated/ eigs -- Find k eigenvalues and eigenvectors of the square matrix A eigsh -- Find k eigenvalues and eigenvectors of a symmetric matrix lobpcg -- Solve symmetric partial eigenproblems with optional preconditioning Singular values problems: .. autosummary:: :toctree: generated/ svds -- Compute k singular values/vectors for a sparse matrix The `svds` function supports the following solvers: .. toctree:: sparse.linalg.svds-arpack sparse.linalg.svds-lobpcg sparse.linalg.svds-propack Complete or incomplete LU factorizations .. autosummary:: :toctree: generated/ splu -- Compute a LU decomposition for a sparse matrix spilu -- Compute an incomplete LU decomposition for a sparse matrix SuperLU -- Object representing an LU factorization Sparse arrays with structure ---------------------------- .. autosummary:: :toctree: generated/ LaplacianNd -- Laplacian on a uniform rectangular grid in ``N`` dimensions Exceptions ---------- .. autosummary:: :toctree: generated/ ArpackNoConvergence ArpackError )*)isolvedsolve interfaceeigenmatfuncsc<g|]}|d|S)_) startswith).0ss \/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/scipy/sparse/linalg/__init__.py rs) 5 5 51<<#4#4 51 5 5 5) PytestTesterN)__doc___isolve_dsolve _interface_eigen _matfuncs _onenormest_norm_expm_multiply_special_sparse_arraysrrrrrdir__all__scipy._lib._testutilsr__name__testrrr$s@@D%%%%98888888888888 5 5ccee 5 5 5......|HLLr