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Note that identically named functions from " }, { "__type": "CrossRef", "__tag": 4002, "value": "scipy.linalg", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.linalg" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " may offer more or slightly differing functionality." } ] } ] } ], "title": [ { "__type": "Text", "__tag": 4046, "value": "Linear algebra (" }, { "__type": "InlineRole", "__tag": 4003, "value": "scipy.linalg", "domain": null, "role": "mod", "inventory": null }, { "__type": "Text", "__tag": 4046, "value": ")" } ], "level": 0, "target": null }, { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Code", "__tag": 4050, "value": ".. autosummary:: \n :toctree:generated/\n inv - Find the inverse of a square matrix\n solve - Solve a linear system of equations\n solve_banded - Solve a banded linear system\n solveh_banded - Solve a Hermitian or symmetric banded system\n solve_circulant - Solve a circulant system\n solve_triangular - Solve a triangular matrix\n solve_toeplitz - Solve a toeplitz matrix\n matmul_toeplitz - Multiply a Toeplitz matrix with an array.\n det - Find the determinant of a square matrix\n norm - Matrix and vector norm\n lstsq - Solve a linear least-squares problem\n pinv - Pseudo-inverse (Moore-Penrose) using lstsq\n pinvh - Pseudo-inverse of hermitian matrix\n khatri_rao - Khatri-Rao product of two arrays\n orthogonal_procrustes - Solve an orthogonal Procrustes problem\n matrix_balance - Balance matrix entries with a similarity transformation\n subspace_angles - Compute the subspace angles between two matrices\n bandwidth - Return the lower and upper bandwidth of an array\n issymmetric - Check if a square 2D array is symmetric\n ishermitian - Check if a square 2D array is Hermitian\n LinAlgError\n LinAlgWarning", "execution_status": null } ], "title": [ { "__type": "Text", "__tag": 4046, "value": "Basics" } ], "level": 1, "target": null }, { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Code", "__tag": 4050, "value": ".. autosummary:: \n :toctree:generated/\n eig - Find the eigenvalues and eigenvectors of a square matrix\n eigvals - Find just the eigenvalues of a square matrix\n eigh - Find the e-vals and e-vectors of a Hermitian or symmetric matrix\n eigvalsh - Find just the eigenvalues of a Hermitian or symmetric matrix\n eig_banded - Find the eigenvalues and eigenvectors of a banded matrix\n eigvals_banded - Find just the eigenvalues of a banded matrix\n eigh_tridiagonal - Find the eigenvalues and eigenvectors of a tridiagonal matrix\n eigvalsh_tridiagonal - Find just the eigenvalues of a tridiagonal matrix", "execution_status": null } ], "title": [ { "__type": "Text", "__tag": 4046, "value": "Eigenvalue Problems" } ], "level": 1, "target": null }, { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Code", "__tag": 4050, "value": ".. autosummary:: \n :toctree:generated/\n lu - LU decomposition of a matrix\n lu_factor - LU decomposition returning unordered matrix and pivots\n lu_solve - Solve Ax=b using back substitution with output of lu_factor\n svd - Singular value decomposition of a matrix\n svdvals - Singular values of a matrix\n diagsvd - Construct matrix of singular values from output of svd\n orth - Construct orthonormal basis for the range of A using svd\n null_space - Construct orthonormal basis for the null space of A using svd\n ldl - LDL.T decomposition of a Hermitian or a symmetric matrix.\n cholesky - Cholesky decomposition of a matrix\n cholesky_banded - Cholesky decomp. of a sym. or Hermitian banded matrix\n cho_factor - Cholesky decomposition for use in solving a linear system\n cho_solve - Solve previously factored linear system\n cho_solve_banded - Solve previously factored banded linear system\n polar - Compute the polar decomposition.\n qr - QR decomposition of a matrix\n qr_multiply - QR decomposition and multiplication by Q\n qr_update - Rank k QR update\n qr_delete - QR downdate on row or column deletion\n qr_insert - QR update on row or column insertion\n rq - RQ decomposition of a matrix\n qz - QZ decomposition of a pair of matrices\n ordqz - QZ decomposition of a pair of matrices with reordering\n schur - Schur decomposition of a matrix\n rsf2csf - Real to complex Schur form\n hessenberg - Hessenberg form of a matrix\n cdf2rdf - Complex diagonal form to real diagonal block form\n cossin - Cosine sine decomposition of a unitary or orthogonal matrix", "execution_status": null }, { "__type": "Admonition", "__tag": 4056, "kind": "seealso", "base_type": "note", "children": [ { "__type": "AdmonitionTitle", "__tag": 4055, "children": [ { "__type": "Text", "__tag": 4046, "value": "seealso " } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "CrossRef", "__tag": 4002, "value": "scipy.linalg.interpolative", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.linalg.interpolative" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " -- Interpolative matrix decompositions" } ] } ] } ], "title": [ { "__type": "Text", "__tag": 4046, "value": "Decompositions" } ], "level": 1, "target": null }, { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Code", "__tag": 4050, "value": ".. autosummary:: \n :toctree:generated/\n expm - Matrix exponential\n logm - Matrix logarithm\n cosm - Matrix cosine\n sinm - Matrix sine\n tanm - Matrix tangent\n coshm - Matrix hyperbolic cosine\n sinhm - Matrix hyperbolic sine\n tanhm - Matrix hyperbolic tangent\n signm - Matrix sign\n sqrtm - Matrix square root\n funm - Evaluating an arbitrary matrix function\n expm_frechet - Frechet derivative of the matrix exponential\n expm_cond - Relative condition number of expm in the Frobenius norm\n fractional_matrix_power - Fractional matrix power", "execution_status": null } ], "title": [ { "__type": "Text", "__tag": 4046, "value": "Matrix Functions" } ], "level": 1, "target": null }, { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Code", "__tag": 4050, "value": ".. autosummary:: \n :toctree:generated/\n solve_sylvester - Solve the Sylvester matrix equation\n solve_continuous_are - Solve the continuous-time algebraic Riccati equation\n solve_discrete_are - Solve the discrete-time algebraic Riccati equation\n solve_continuous_lyapunov - Solve the continuous-time Lyapunov equation\n solve_discrete_lyapunov - Solve the discrete-time Lyapunov equation", "execution_status": null } ], "title": [ { "__type": "Text", "__tag": 4046, "value": "Matrix Equation Solvers" } ], "level": 1, "target": null }, { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Code", "__tag": 4050, "value": ".. autosummary:: \n :toctree:generated/\n clarkson_woodruff_transform - Applies the Clarkson Woodruff Sketch (a.k.a CountMin Sketch)", "execution_status": null } ], "title": [ { "__type": "Text", "__tag": 4046, "value": "Sketches and Random Projections" } ], "level": 1, "target": null }, { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Code", "__tag": 4050, "value": ".. autosummary:: \n :toctree:generated/\n block_diag - Construct a block diagonal matrix from submatrices\n circulant - Circulant matrix\n companion - Companion matrix\n convolution_matrix - Convolution matrix\n dft - Discrete Fourier transform matrix\n fiedler - Fiedler matrix\n fiedler_companion - Fiedler companion matrix\n hadamard - Hadamard matrix of order 2**n\n hankel - Hankel matrix\n helmert - Helmert matrix\n hilbert - Hilbert matrix\n invhilbert - Inverse Hilbert matrix\n leslie - Leslie matrix\n pascal - Pascal matrix\n invpascal - Inverse Pascal matrix\n toeplitz - Toeplitz matrix", "execution_status": null } ], "title": [ { "__type": "Text", "__tag": 4046, "value": "Special Matrices" } ], "level": 1, "target": null }, { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Code", "__tag": 4050, "value": ".. autosummary:: \n :toctree:generated/\n get_blas_funcs\n get_lapack_funcs\n find_best_blas_type", "execution_status": null }, { "__type": "Admonition", "__tag": 4056, "kind": "seealso", "base_type": "note", "children": [ { "__type": "AdmonitionTitle", "__tag": 4055, "children": [ { "__type": "Text", "__tag": 4046, "value": "seealso " } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "CrossRef", "__tag": 4002, "value": "scipy.linalg.blas", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.linalg.blas" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " -- Low-level BLAS functions" } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "CrossRef", "__tag": 4002, "value": "scipy.linalg.lapack", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.linalg.lapack" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " -- Low-level LAPACK functions" } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "CrossRef", "__tag": 4002, "value": "scipy.linalg.cython_blas", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.linalg.cython_blas" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " -- Low-level BLAS functions for Cython" } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "CrossRef", "__tag": 4002, "value": "scipy.linalg.cython_lapack", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.linalg.cython_lapack" }, "kind": "module" }, { "__type": "Text", "__tag": 4046, "value": " -- Low-level LAPACK functions for Cython" } ] } ] } ], "title": [ { "__type": "Text", "__tag": 4046, "value": "Low-level routines" } ], "level": 1, "target": null } ], "local_refs": [] }