1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
|
"""
====================================
Linear algebra (:mod:`scipy.linalg`)
====================================
.. currentmodule:: scipy.linalg
Linear algebra functions.
.. seealso::
`numpy.linalg` for more linear algebra functions. Note that
although `scipy.linalg` imports most of them, identically named
functions from `scipy.linalg` may offer more or slightly differing
functionality.
Basics
======
.. autosummary::
:toctree: generated/
inv - Find the inverse of a square matrix
solve - Solve a linear system of equations
solve_banded - Solve a banded linear system
solveh_banded - Solve a Hermitian or symmetric banded system
solve_triangular - Solve a triangular matrix
det - Find the determinant of a square matrix
norm - Matrix and vector norm
lstsq - Solve a linear least-squares problem
pinv - Pseudo-inverse (Moore-Penrose) using lstsq
pinv2 - Pseudo-inverse using svd
kron - Kronecker product of two arrays
tril - Construct a lower-triangular matrix from a given matrix
triu - Construct an upper-triangular matrix from a given matrix
Eigenvalue Problems
===================
.. autosummary::
:toctree: generated/
eig - Find the eigenvalues and eigenvectors of a square matrix
eigvals - Find just the eigenvalues of a square matrix
eigh - Find the e-vals and e-vectors of a Hermitian or symmetric matrix
eigvalsh - Find just the eigenvalues of a Hermitian or symmetric matrix
eig_banded - Find the eigenvalues and eigenvectors of a banded matrix
eigvals_banded - Find just the eigenvalues of a banded matrix
Decompositions
==============
.. autosummary::
:toctree: generated/
lu - LU decomposition of a matrix
lu_factor - LU decomposition returning unordered matrix and pivots
lu_solve - Solve Ax=b using back substitution with output of lu_factor
svd - Singular value decomposition of a matrix
svdvals - Singular values of a matrix
diagsvd - Construct matrix of singular values from output of svd
orth - Construct orthonormal basis for the range of A using svd
cholesky - Cholesky decomposition of a matrix
cholesky_banded - Cholesky decomp. of a sym. or Hermitian banded matrix
cho_factor - Cholesky decomposition for use in solving a linear system
cho_solve - Solve previously factored linear system
cho_solve_banded - Solve previously factored banded linear system
qr - QR decomposition of a matrix
schur - Schur decomposition of a matrix
rsf2csf - Real to complex Schur form
hessenberg - Hessenberg form of a matrix
Matrix Functions
================
.. autosummary::
:toctree: generated/
expm - Matrix exponential using Pade approximation
expm2 - Matrix exponential using eigenvalue decomposition
expm3 - Matrix exponential using Taylor-series expansion
logm - Matrix logarithm
cosm - Matrix cosine
sinm - Matrix sine
tanm - Matrix tangent
coshm - Matrix hyperbolic cosine
sinhm - Matrix hyperbolic sine
tanhm - Matrix hyperbolic tangent
signm - Matrix sign
sqrtm - Matrix square root
funm - Evaluating an arbitrary matrix function
Special Matrices
================
.. autosummary::
:toctree: generated/
block_diag - Construct a block diagonal matrix from submatrices
circulant - Circulant matrix
companion - Companion matrix
hadamard - Hadamard matrix of order 2**n
hankel - Hankel matrix
hilbert - Hilbert matrix
invhilbert - Inverse Hilbert matrix
leslie - Leslie matrix
toeplitz - Toeplitz matrix
tri - Construct a matrix filled with ones at and below a given diagonal
"""
from linalg_version import linalg_version as __version__
from misc import *
from basic import *
from decomp import *
from decomp_lu import *
from decomp_cholesky import *
from decomp_qr import *
from decomp_svd import *
from decomp_schur import *
from matfuncs import *
from blas import *
from special_matrices import *
__all__ = filter(lambda s: not s.startswith('_'), dir())
from numpy.dual import register_func
for k in ['norm', 'inv', 'svd', 'solve', 'det', 'eig', 'eigh', 'eigvals',
'eigvalsh', 'lstsq', 'cholesky']:
try:
register_func(k, eval(k))
except ValueError:
pass
try:
register_func('pinv', pinv2)
except ValueError:
pass
del k, register_func
from numpy.testing import Tester
test = Tester().test
bench = Tester().bench
|
