Coverage for /pythoncovmergedfiles/medio/medio/usr/local/lib/python3.8/site-packages/scipy/linalg/__init__.py: 100%
26 statements
« prev ^ index » next coverage.py v7.3.2, created at 2023-12-12 06:31 +0000
1"""
2====================================
3Linear algebra (:mod:`scipy.linalg`)
4====================================
6.. currentmodule:: scipy.linalg
8Linear algebra functions.
10.. eventually, we should replace the numpy.linalg HTML link with just `numpy.linalg`
12.. seealso::
14 `numpy.linalg <https://www.numpy.org/devdocs/reference/routines.linalg.html>`__
15 for more linear algebra functions. Note that
16 although `scipy.linalg` imports most of them, identically named
17 functions from `scipy.linalg` may offer more or slightly differing
18 functionality.
21Basics
22======
24.. autosummary::
25 :toctree: generated/
27 inv - Find the inverse of a square matrix
28 solve - Solve a linear system of equations
29 solve_banded - Solve a banded linear system
30 solveh_banded - Solve a Hermitian or symmetric banded system
31 solve_circulant - Solve a circulant system
32 solve_triangular - Solve a triangular matrix
33 solve_toeplitz - Solve a toeplitz matrix
34 matmul_toeplitz - Multiply a Toeplitz matrix with an array.
35 det - Find the determinant of a square matrix
36 norm - Matrix and vector norm
37 lstsq - Solve a linear least-squares problem
38 pinv - Pseudo-inverse (Moore-Penrose) using lstsq
39 pinvh - Pseudo-inverse of hermitian matrix
40 kron - Kronecker product of two arrays
41 khatri_rao - Khatri-Rao product of two arrays
42 tril - Construct a lower-triangular matrix from a given matrix
43 triu - Construct an upper-triangular matrix from a given matrix
44 orthogonal_procrustes - Solve an orthogonal Procrustes problem
45 matrix_balance - Balance matrix entries with a similarity transformation
46 subspace_angles - Compute the subspace angles between two matrices
47 bandwidth - Return the lower and upper bandwidth of an array
48 issymmetric - Check if a square 2D array is symmetric
49 ishermitian - Check if a square 2D array is Hermitian
50 LinAlgError
51 LinAlgWarning
53Eigenvalue Problems
54===================
56.. autosummary::
57 :toctree: generated/
59 eig - Find the eigenvalues and eigenvectors of a square matrix
60 eigvals - Find just the eigenvalues of a square matrix
61 eigh - Find the e-vals and e-vectors of a Hermitian or symmetric matrix
62 eigvalsh - Find just the eigenvalues of a Hermitian or symmetric matrix
63 eig_banded - Find the eigenvalues and eigenvectors of a banded matrix
64 eigvals_banded - Find just the eigenvalues of a banded matrix
65 eigh_tridiagonal - Find the eigenvalues and eigenvectors of a tridiagonal matrix
66 eigvalsh_tridiagonal - Find just the eigenvalues of a tridiagonal matrix
68Decompositions
69==============
71.. autosummary::
72 :toctree: generated/
74 lu - LU decomposition of a matrix
75 lu_factor - LU decomposition returning unordered matrix and pivots
76 lu_solve - Solve Ax=b using back substitution with output of lu_factor
77 svd - Singular value decomposition of a matrix
78 svdvals - Singular values of a matrix
79 diagsvd - Construct matrix of singular values from output of svd
80 orth - Construct orthonormal basis for the range of A using svd
81 null_space - Construct orthonormal basis for the null space of A using svd
82 ldl - LDL.T decomposition of a Hermitian or a symmetric matrix.
83 cholesky - Cholesky decomposition of a matrix
84 cholesky_banded - Cholesky decomp. of a sym. or Hermitian banded matrix
85 cho_factor - Cholesky decomposition for use in solving a linear system
86 cho_solve - Solve previously factored linear system
87 cho_solve_banded - Solve previously factored banded linear system
88 polar - Compute the polar decomposition.
89 qr - QR decomposition of a matrix
90 qr_multiply - QR decomposition and multiplication by Q
91 qr_update - Rank k QR update
92 qr_delete - QR downdate on row or column deletion
93 qr_insert - QR update on row or column insertion
94 rq - RQ decomposition of a matrix
95 qz - QZ decomposition of a pair of matrices
96 ordqz - QZ decomposition of a pair of matrices with reordering
97 schur - Schur decomposition of a matrix
98 rsf2csf - Real to complex Schur form
99 hessenberg - Hessenberg form of a matrix
100 cdf2rdf - Complex diagonal form to real diagonal block form
101 cossin - Cosine sine decomposition of a unitary or orthogonal matrix
103.. seealso::
105 `scipy.linalg.interpolative` -- Interpolative matrix decompositions
108Matrix Functions
109================
111.. autosummary::
112 :toctree: generated/
114 expm - Matrix exponential
115 logm - Matrix logarithm
116 cosm - Matrix cosine
117 sinm - Matrix sine
118 tanm - Matrix tangent
119 coshm - Matrix hyperbolic cosine
120 sinhm - Matrix hyperbolic sine
121 tanhm - Matrix hyperbolic tangent
122 signm - Matrix sign
123 sqrtm - Matrix square root
124 funm - Evaluating an arbitrary matrix function
125 expm_frechet - Frechet derivative of the matrix exponential
126 expm_cond - Relative condition number of expm in the Frobenius norm
127 fractional_matrix_power - Fractional matrix power
130Matrix Equation Solvers
131=======================
133.. autosummary::
134 :toctree: generated/
136 solve_sylvester - Solve the Sylvester matrix equation
137 solve_continuous_are - Solve the continuous-time algebraic Riccati equation
138 solve_discrete_are - Solve the discrete-time algebraic Riccati equation
139 solve_continuous_lyapunov - Solve the continuous-time Lyapunov equation
140 solve_discrete_lyapunov - Solve the discrete-time Lyapunov equation
143Sketches and Random Projections
144===============================
146.. autosummary::
147 :toctree: generated/
149 clarkson_woodruff_transform - Applies the Clarkson Woodruff Sketch (a.k.a CountMin Sketch)
151Special Matrices
152================
154.. autosummary::
155 :toctree: generated/
157 block_diag - Construct a block diagonal matrix from submatrices
158 circulant - Circulant matrix
159 companion - Companion matrix
160 convolution_matrix - Convolution matrix
161 dft - Discrete Fourier transform matrix
162 fiedler - Fiedler matrix
163 fiedler_companion - Fiedler companion matrix
164 hadamard - Hadamard matrix of order 2**n
165 hankel - Hankel matrix
166 helmert - Helmert matrix
167 hilbert - Hilbert matrix
168 invhilbert - Inverse Hilbert matrix
169 leslie - Leslie matrix
170 pascal - Pascal matrix
171 invpascal - Inverse Pascal matrix
172 toeplitz - Toeplitz matrix
173 tri - Construct a matrix filled with ones at and below a given diagonal
175Low-level routines
176==================
178.. autosummary::
179 :toctree: generated/
181 get_blas_funcs
182 get_lapack_funcs
183 find_best_blas_type
185.. seealso::
187 `scipy.linalg.blas` -- Low-level BLAS functions
189 `scipy.linalg.lapack` -- Low-level LAPACK functions
191 `scipy.linalg.cython_blas` -- Low-level BLAS functions for Cython
193 `scipy.linalg.cython_lapack` -- Low-level LAPACK functions for Cython
195""" # noqa: E501
197from ._misc import *
198from ._cythonized_array_utils import *
199from ._basic import *
200from ._decomp import *
201from ._decomp_lu import *
202from ._decomp_ldl import *
203from ._decomp_cholesky import *
204from ._decomp_qr import *
205from ._decomp_qz import *
206from ._decomp_svd import *
207from ._decomp_schur import *
208from ._decomp_polar import *
209from ._matfuncs import *
210from .blas import *
211from .lapack import *
212from ._special_matrices import *
213from ._solvers import *
214from ._procrustes import *
215from ._decomp_update import *
216from ._sketches import *
217from ._decomp_cossin import *
219# Deprecated namespaces, to be removed in v2.0.0
220from . import (
221 decomp, decomp_cholesky, decomp_lu, decomp_qr, decomp_svd, decomp_schur,
222 basic, misc, special_matrices, flinalg, matfuncs
223)
225__all__ = [s for s in dir() if not s.startswith('_')]
228from scipy._lib._testutils import PytestTester
229test = PytestTester(__name__)
230del PytestTester