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
|
-----------------------------------------------------------------------------
{- |
Module : Numeric.HMatrix
Copyright : (c) Alberto Ruiz 2006-14
License : GPL
Maintainer : Alberto Ruiz
Stability : provisional
This module reexports the most common Linear Algebra functions.
-}
-----------------------------------------------------------------------------
module Numeric.HMatrix (
-- * Basic types and data processing
module Numeric.HMatrix.Data,
-- | The standard numeric classes are defined elementwise.
--
-- >>> fromList [1,2,3] * fromList [3,0,-2 :: Double]
-- fromList [3.0,0.0,-6.0]
--
-- In arithmetic operations single-element vectors and matrices automatically
-- expand to match the dimensions of the other operand.
--
-- >>> 2 * ident 3
-- 2 * ident 3 :: Matrix Double
-- (3><3)
-- [ 2.0, 0.0, 0.0
-- , 0.0, 2.0, 0.0
-- , 0.0, 0.0, 2.0 ]
--
-- * Products
(<>), (·), outer, kronecker, cross,
optimiseMult, scale,
sumElements, prodElements, absSum,
-- * Linear Systems
(<\>),
linearSolve,
linearSolveLS,
linearSolveSVD,
luSolve,
cholSolve,
-- * Inverse and pseudoinverse
inv, pinv, pinvTol,
-- * Determinant and rank
rcond, rank, ranksv,
det, invlndet,
-- * Singular value decomposition
svd,
fullSVD,
thinSVD,
compactSVD,
singularValues,
leftSV, rightSV,
-- * Eigensystems
eig, eigSH, eigSH',
eigenvalues, eigenvaluesSH, eigenvaluesSH',
geigSH',
-- * QR
qr, rq,
-- * Cholesky
chol, cholSH, mbCholSH,
-- * Hessenberg
hess,
-- * Schur
schur,
-- * LU
lu, luPacked,
-- * Matrix functions
expm,
sqrtm,
matFunc,
-- * Nullspace
nullspacePrec,
nullVector,
nullspaceSVD,
null1, null1sym,
orth,
-- * Norms
norm1, norm2, normInf,
-- * Correlation and Convolution
corr, conv, corrMin, corr2, conv2,
-- * Random arrays
rand, randn, RandDist(..), randomVector, gaussianSample, uniformSample,
-- * Misc
meanCov, peps, relativeError, haussholder
) where
import Numeric.HMatrix.Data
import Numeric.Matrix()
import Numeric.Vector()
import Numeric.Container
import Numeric.LinearAlgebra.Algorithms
import Numeric.LinearAlgebra.Util
|
