Coverage for /pythoncovmergedfiles/medio/medio/usr/local/lib/python3.9/dist-packages/scipy/linalg/__init__.py: 100%
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1"""
2====================================
3Linear algebra (:mod:`scipy.linalg`)
4====================================
6.. currentmodule:: scipy.linalg
8.. toctree::
9 :hidden:
11 linalg.blas
12 linalg.cython_blas
13 linalg.cython_lapack
14 linalg.interpolative
15 linalg.lapack
17Linear algebra functions.
19.. eventually, we should replace the numpy.linalg HTML link with just `numpy.linalg`
21.. seealso::
23 `numpy.linalg <https://www.numpy.org/devdocs/reference/routines.linalg.html>`__
24 for more linear algebra functions. Note that
25 although `scipy.linalg` imports most of them, identically named
26 functions from `scipy.linalg` may offer more or slightly differing
27 functionality.
30Basics
31======
33.. autosummary::
34 :toctree: generated/
36 inv - Find the inverse of a square matrix
37 solve - Solve a linear system of equations
38 solve_banded - Solve a banded linear system
39 solveh_banded - Solve a Hermitian or symmetric banded system
40 solve_circulant - Solve a circulant system
41 solve_triangular - Solve a triangular matrix
42 solve_toeplitz - Solve a toeplitz matrix
43 matmul_toeplitz - Multiply a Toeplitz matrix with an array.
44 det - Find the determinant of a square matrix
45 norm - Matrix and vector norm
46 lstsq - Solve a linear least-squares problem
47 pinv - Pseudo-inverse (Moore-Penrose) using lstsq
48 pinvh - Pseudo-inverse of hermitian matrix
49 kron - Kronecker product of two arrays
50 khatri_rao - Khatri-Rao product of two arrays
51 orthogonal_procrustes - Solve an orthogonal Procrustes problem
52 matrix_balance - Balance matrix entries with a similarity transformation
53 subspace_angles - Compute the subspace angles between two matrices
54 bandwidth - Return the lower and upper bandwidth of an array
55 issymmetric - Check if a square 2D array is symmetric
56 ishermitian - Check if a square 2D array is Hermitian
57 LinAlgError
58 LinAlgWarning
60Eigenvalue Problems
61===================
63.. autosummary::
64 :toctree: generated/
66 eig - Find the eigenvalues and eigenvectors of a square matrix
67 eigvals - Find just the eigenvalues of a square matrix
68 eigh - Find the e-vals and e-vectors of a Hermitian or symmetric matrix
69 eigvalsh - Find just the eigenvalues of a Hermitian or symmetric matrix
70 eig_banded - Find the eigenvalues and eigenvectors of a banded matrix
71 eigvals_banded - Find just the eigenvalues of a banded matrix
72 eigh_tridiagonal - Find the eigenvalues and eigenvectors of a tridiagonal matrix
73 eigvalsh_tridiagonal - Find just the eigenvalues of a tridiagonal matrix
75Decompositions
76==============
78.. autosummary::
79 :toctree: generated/
81 lu - LU decomposition of a matrix
82 lu_factor - LU decomposition returning unordered matrix and pivots
83 lu_solve - Solve Ax=b using back substitution with output of lu_factor
84 svd - Singular value decomposition of a matrix
85 svdvals - Singular values of a matrix
86 diagsvd - Construct matrix of singular values from output of svd
87 orth - Construct orthonormal basis for the range of A using svd
88 null_space - Construct orthonormal basis for the null space of A using svd
89 ldl - LDL.T decomposition of a Hermitian or a symmetric matrix.
90 cholesky - Cholesky decomposition of a matrix
91 cholesky_banded - Cholesky decomp. of a sym. or Hermitian banded matrix
92 cho_factor - Cholesky decomposition for use in solving a linear system
93 cho_solve - Solve previously factored linear system
94 cho_solve_banded - Solve previously factored banded linear system
95 polar - Compute the polar decomposition.
96 qr - QR decomposition of a matrix
97 qr_multiply - QR decomposition and multiplication by Q
98 qr_update - Rank k QR update
99 qr_delete - QR downdate on row or column deletion
100 qr_insert - QR update on row or column insertion
101 rq - RQ decomposition of a matrix
102 qz - QZ decomposition of a pair of matrices
103 ordqz - QZ decomposition of a pair of matrices with reordering
104 schur - Schur decomposition of a matrix
105 rsf2csf - Real to complex Schur form
106 hessenberg - Hessenberg form of a matrix
107 cdf2rdf - Complex diagonal form to real diagonal block form
108 cossin - Cosine sine decomposition of a unitary or orthogonal matrix
110.. seealso::
112 `scipy.linalg.interpolative` -- Interpolative matrix decompositions
115Matrix Functions
116================
118.. autosummary::
119 :toctree: generated/
121 expm - Matrix exponential
122 logm - Matrix logarithm
123 cosm - Matrix cosine
124 sinm - Matrix sine
125 tanm - Matrix tangent
126 coshm - Matrix hyperbolic cosine
127 sinhm - Matrix hyperbolic sine
128 tanhm - Matrix hyperbolic tangent
129 signm - Matrix sign
130 sqrtm - Matrix square root
131 funm - Evaluating an arbitrary matrix function
132 expm_frechet - Frechet derivative of the matrix exponential
133 expm_cond - Relative condition number of expm in the Frobenius norm
134 fractional_matrix_power - Fractional matrix power
137Matrix Equation Solvers
138=======================
140.. autosummary::
141 :toctree: generated/
143 solve_sylvester - Solve the Sylvester matrix equation
144 solve_continuous_are - Solve the continuous-time algebraic Riccati equation
145 solve_discrete_are - Solve the discrete-time algebraic Riccati equation
146 solve_continuous_lyapunov - Solve the continuous-time Lyapunov equation
147 solve_discrete_lyapunov - Solve the discrete-time Lyapunov equation
150Sketches and Random Projections
151===============================
153.. autosummary::
154 :toctree: generated/
156 clarkson_woodruff_transform - Applies the Clarkson Woodruff Sketch (a.k.a CountMin Sketch)
158Special Matrices
159================
161.. autosummary::
162 :toctree: generated/
164 block_diag - Construct a block diagonal matrix from submatrices
165 circulant - Circulant matrix
166 companion - Companion matrix
167 convolution_matrix - Convolution matrix
168 dft - Discrete Fourier transform matrix
169 fiedler - Fiedler matrix
170 fiedler_companion - Fiedler companion matrix
171 hadamard - Hadamard matrix of order 2**n
172 hankel - Hankel matrix
173 helmert - Helmert matrix
174 hilbert - Hilbert matrix
175 invhilbert - Inverse Hilbert matrix
176 leslie - Leslie matrix
177 pascal - Pascal matrix
178 invpascal - Inverse Pascal matrix
179 toeplitz - Toeplitz matrix
181Low-level routines
182==================
184.. autosummary::
185 :toctree: generated/
187 get_blas_funcs
188 get_lapack_funcs
189 find_best_blas_type
191.. seealso::
193 `scipy.linalg.blas` -- Low-level BLAS functions
195 `scipy.linalg.lapack` -- Low-level LAPACK functions
197 `scipy.linalg.cython_blas` -- Low-level BLAS functions for Cython
199 `scipy.linalg.cython_lapack` -- Low-level LAPACK functions for Cython
201""" # noqa: E501
203from ._misc import *
204from ._cythonized_array_utils import *
205from ._basic import *
206from ._decomp import *
207from ._decomp_lu import *
208from ._decomp_ldl import *
209from ._decomp_cholesky import *
210from ._decomp_qr import *
211from ._decomp_qz import *
212from ._decomp_svd import *
213from ._decomp_schur import *
214from ._decomp_polar import *
215from ._matfuncs import *
216from .blas import *
217from .lapack import *
218from ._special_matrices import *
219from ._solvers import *
220from ._procrustes import *
221from ._decomp_update import *
222from ._sketches import *
223from ._decomp_cossin import *
225# Deprecated namespaces, to be removed in v2.0.0
226from . import (
227 decomp, decomp_cholesky, decomp_lu, decomp_qr, decomp_svd, decomp_schur,
228 basic, misc, special_matrices, matfuncs,
229)
231__all__ = [s for s in dir() if not s.startswith('_')]
234from scipy._lib._testutils import PytestTester
235test = PytestTester(__name__)
236del PytestTester