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""" |
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==================================== |
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Linear algebra (:mod:`scipy.linalg`) |
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==================================== |
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.. currentmodule:: scipy.linalg |
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.. toctree:: |
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:hidden: |
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linalg.blas |
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linalg.cython_blas |
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linalg.cython_lapack |
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linalg.interpolative |
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linalg.lapack |
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Linear algebra functions. |
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.. eventually, we should replace the numpy.linalg HTML link with just `numpy.linalg` |
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.. seealso:: |
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`numpy.linalg <https://www.numpy.org/devdocs/reference/routines.linalg.html>`__ |
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for more linear algebra functions. Note that |
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although `scipy.linalg` imports most of them, identically named |
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functions from `scipy.linalg` may offer more or slightly differing |
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functionality. |
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Basics |
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====== |
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.. autosummary:: |
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:toctree: generated/ |
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inv - Find the inverse of a square matrix |
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solve - Solve a linear system of equations |
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solve_banded - Solve a banded linear system |
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solveh_banded - Solve a Hermitian or symmetric banded system |
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solve_circulant - Solve a circulant system |
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solve_triangular - Solve a triangular matrix |
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solve_toeplitz - Solve a toeplitz matrix |
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matmul_toeplitz - Multiply a Toeplitz matrix with an array. |
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det - Find the determinant of a square matrix |
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norm - Matrix and vector norm |
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lstsq - Solve a linear least-squares problem |
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pinv - Pseudo-inverse (Moore-Penrose) using lstsq |
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pinvh - Pseudo-inverse of hermitian matrix |
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kron - Kronecker product of two arrays |
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khatri_rao - Khatri-Rao product of two arrays |
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orthogonal_procrustes - Solve an orthogonal Procrustes problem |
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matrix_balance - Balance matrix entries with a similarity transformation |
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subspace_angles - Compute the subspace angles between two matrices |
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bandwidth - Return the lower and upper bandwidth of an array |
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issymmetric - Check if a square 2D array is symmetric |
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ishermitian - Check if a square 2D array is Hermitian |
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LinAlgError |
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LinAlgWarning |
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Eigenvalue Problems |
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=================== |
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.. autosummary:: |
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:toctree: generated/ |
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eig - Find the eigenvalues and eigenvectors of a square matrix |
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eigvals - Find just the eigenvalues of a square matrix |
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eigh - Find the e-vals and e-vectors of a Hermitian or symmetric matrix |
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eigvalsh - Find just the eigenvalues of a Hermitian or symmetric matrix |
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eig_banded - Find the eigenvalues and eigenvectors of a banded matrix |
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eigvals_banded - Find just the eigenvalues of a banded matrix |
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eigh_tridiagonal - Find the eigenvalues and eigenvectors of a tridiagonal matrix |
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eigvalsh_tridiagonal - Find just the eigenvalues of a tridiagonal matrix |
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Decompositions |
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============== |
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.. autosummary:: |
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:toctree: generated/ |
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lu - LU decomposition of a matrix |
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lu_factor - LU decomposition returning unordered matrix and pivots |
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lu_solve - Solve Ax=b using back substitution with output of lu_factor |
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svd - Singular value decomposition of a matrix |
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svdvals - Singular values of a matrix |
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diagsvd - Construct matrix of singular values from output of svd |
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orth - Construct orthonormal basis for the range of A using svd |
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null_space - Construct orthonormal basis for the null space of A using svd |
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ldl - LDL.T decomposition of a Hermitian or a symmetric matrix. |
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cholesky - Cholesky decomposition of a matrix |
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cholesky_banded - Cholesky decomp. of a sym. or Hermitian banded matrix |
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cho_factor - Cholesky decomposition for use in solving a linear system |
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cho_solve - Solve previously factored linear system |
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cho_solve_banded - Solve previously factored banded linear system |
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polar - Compute the polar decomposition. |
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qr - QR decomposition of a matrix |
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qr_multiply - QR decomposition and multiplication by Q |
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qr_update - Rank k QR update |
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qr_delete - QR downdate on row or column deletion |
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qr_insert - QR update on row or column insertion |
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rq - RQ decomposition of a matrix |
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qz - QZ decomposition of a pair of matrices |
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ordqz - QZ decomposition of a pair of matrices with reordering |
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schur - Schur decomposition of a matrix |
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rsf2csf - Real to complex Schur form |
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hessenberg - Hessenberg form of a matrix |
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cdf2rdf - Complex diagonal form to real diagonal block form |
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cossin - Cosine sine decomposition of a unitary or orthogonal matrix |
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.. seealso:: |
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`scipy.linalg.interpolative` -- Interpolative matrix decompositions |
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Matrix Functions |
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================ |
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.. autosummary:: |
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:toctree: generated/ |
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expm - Matrix exponential |
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logm - Matrix logarithm |
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cosm - Matrix cosine |
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sinm - Matrix sine |
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tanm - Matrix tangent |
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coshm - Matrix hyperbolic cosine |
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sinhm - Matrix hyperbolic sine |
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tanhm - Matrix hyperbolic tangent |
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signm - Matrix sign |
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sqrtm - Matrix square root |
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funm - Evaluating an arbitrary matrix function |
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expm_frechet - Frechet derivative of the matrix exponential |
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expm_cond - Relative condition number of expm in the Frobenius norm |
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fractional_matrix_power - Fractional matrix power |
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Matrix Equation Solvers |
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======================= |
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.. autosummary:: |
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:toctree: generated/ |
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solve_sylvester - Solve the Sylvester matrix equation |
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solve_continuous_are - Solve the continuous-time algebraic Riccati equation |
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solve_discrete_are - Solve the discrete-time algebraic Riccati equation |
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solve_continuous_lyapunov - Solve the continuous-time Lyapunov equation |
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solve_discrete_lyapunov - Solve the discrete-time Lyapunov equation |
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Sketches and Random Projections |
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=============================== |
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.. autosummary:: |
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:toctree: generated/ |
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clarkson_woodruff_transform - Applies the Clarkson Woodruff Sketch (a.k.a CountMin Sketch) |
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Special Matrices |
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================ |
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.. autosummary:: |
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:toctree: generated/ |
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block_diag - Construct a block diagonal matrix from submatrices |
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circulant - Circulant matrix |
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companion - Companion matrix |
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convolution_matrix - Convolution matrix |
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dft - Discrete Fourier transform matrix |
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fiedler - Fiedler matrix |
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fiedler_companion - Fiedler companion matrix |
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hadamard - Hadamard matrix of order 2**n |
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hankel - Hankel matrix |
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helmert - Helmert matrix |
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hilbert - Hilbert matrix |
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invhilbert - Inverse Hilbert matrix |
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leslie - Leslie matrix |
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pascal - Pascal matrix |
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invpascal - Inverse Pascal matrix |
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toeplitz - Toeplitz matrix |
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Low-level routines |
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================== |
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.. autosummary:: |
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:toctree: generated/ |
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get_blas_funcs |
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get_lapack_funcs |
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find_best_blas_type |
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.. seealso:: |
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`scipy.linalg.blas` -- Low-level BLAS functions |
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`scipy.linalg.lapack` -- Low-level LAPACK functions |
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`scipy.linalg.cython_blas` -- Low-level BLAS functions for Cython |
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`scipy.linalg.cython_lapack` -- Low-level LAPACK functions for Cython |
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""" |
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from ._misc import * |
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from ._cythonized_array_utils import * |
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from ._basic import * |
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from ._decomp import * |
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from ._decomp_lu import * |
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from ._decomp_ldl import * |
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from ._decomp_cholesky import * |
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from ._decomp_qr import * |
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from ._decomp_qz import * |
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from ._decomp_svd import * |
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from ._decomp_schur import * |
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from ._decomp_polar import * |
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from ._matfuncs import * |
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from .blas import * |
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from .lapack import * |
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from ._special_matrices import * |
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from ._solvers import * |
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from ._procrustes import * |
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from ._decomp_update import * |
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from ._sketches import * |
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from ._decomp_cossin import * |
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from . import ( |
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decomp, decomp_cholesky, decomp_lu, decomp_qr, decomp_svd, decomp_schur, |
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basic, misc, special_matrices, matfuncs, |
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) |
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__all__ = [s for s in dir() if not s.startswith('_')] |
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from scipy._lib._testutils import PytestTester |
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test = PytestTester(__name__) |
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del PytestTester |
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