Sparse linear algebra (scipy.sparse.linalg
)#
Abstract linear operators#
|
Common interface for performing matrix vector products |
Return A as a LinearOperator. |
Matrix Operations#
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Compute the inverse of a sparse matrix |
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Compute the matrix exponential using Pade approximation. |
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Compute the action of the matrix exponential of A on B. |
Matrix norms#
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Norm of a sparse matrix |
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Compute a lower bound of the 1-norm of a sparse matrix. |
Solving linear problems#
Direct methods for linear equation systems:
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Solve the sparse linear system Ax=b, where b may be a vector or a matrix. |
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Solve the equation |
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Return a function for solving a sparse linear system, with A pre-factorized. |
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Select default sparse direct solver to be used. |
Iterative methods for linear equation systems:
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Use BIConjugate Gradient iteration to solve |
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Use BIConjugate Gradient STABilized iteration to solve |
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Use Conjugate Gradient iteration to solve |
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Use Conjugate Gradient Squared iteration to solve |
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Use Generalized Minimal RESidual iteration to solve |
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Solve a matrix equation using the LGMRES algorithm. |
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Use MINimum RESidual iteration to solve Ax=b |
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Use Quasi-Minimal Residual iteration to solve |
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Solve a matrix equation using flexible GCROT(m,k) algorithm. |
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Use Transpose-Free Quasi-Minimal Residual iteration to solve |
Iterative methods for least-squares problems:
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Find the least-squares solution to a large, sparse, linear system of equations. |
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Iterative solver for least-squares problems. |
Matrix factorizations#
Eigenvalue problems:
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Find k eigenvalues and eigenvectors of the square matrix A. |
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Find k eigenvalues and eigenvectors of the real symmetric square matrix or complex Hermitian matrix A. |
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Locally Optimal Block Preconditioned Conjugate Gradient Method (LOBPCG) |
Singular values problems:
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Partial singular value decomposition of a sparse matrix. |
The svds
function supports the following solvers:
Complete or incomplete LU factorizations
|
Compute the LU decomposition of a sparse, square matrix. |
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Compute an incomplete LU decomposition for a sparse, square matrix. |
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LU factorization of a sparse matrix. |
Exceptions#
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ARPACK iteration did not converge |
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ARPACK error |