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1-----------------------------------------------------------------------------
2{- |
3Module : Numeric.HMatrix
4Copyright : (c) Alberto Ruiz 2006-14
5License : GPL
6
7Maintainer : Alberto Ruiz
8Stability : provisional
9
10This module reexports the most common Linear Algebra functions.
11
12-}
13-----------------------------------------------------------------------------
14module Numeric.HMatrix (
15
16 -- * Basic types and data processing
17 module Numeric.HMatrix.Data,
18
19 -- | The standard numeric classes are defined elementwise.
20 --
21 -- >>> fromList [1,2,3] * fromList [3,0,-2 :: Double]
22 -- fromList [3.0,0.0,-6.0]
23 --
24 -- In arithmetic operations single-element vectors and matrices automatically
25 -- expand to match the dimensions of the other operand.
26 --
27 -- >>> 2 * ident 3
28 -- 2 * ident 3 :: Matrix Double
29 -- (3><3)
30 -- [ 2.0, 0.0, 0.0
31 -- , 0.0, 2.0, 0.0
32 -- , 0.0, 0.0, 2.0 ]
33 --
34
35 -- * Products
36 (<>), (ยท), outer, kronecker, cross,
37 optimiseMult, scale,
38 sumElements, prodElements, absSum,
39
40 -- * Linear Systems
41 (<\>),
42 linearSolve,
43 linearSolveLS,
44 linearSolveSVD,
45 luSolve,
46 cholSolve,
47
48 -- * Inverse and pseudoinverse
49 inv, pinv, pinvTol,
50
51 -- * Determinant and rank
52 rcond, rank, ranksv,
53 det, invlndet,
54
55 -- * Singular value decomposition
56 svd,
57 fullSVD,
58 thinSVD,
59 compactSVD,
60 singularValues,
61 leftSV, rightSV,
62
63 -- * Eigensystems
64 eig, eigSH, eigSH',
65 eigenvalues, eigenvaluesSH, eigenvaluesSH',
66 geigSH',
67
68 -- * QR
69 qr, rq,
70
71 -- * Cholesky
72 chol, cholSH, mbCholSH,
73
74 -- * Hessenberg
75 hess,
76
77 -- * Schur
78 schur,
79
80 -- * LU
81 lu, luPacked,
82
83 -- * Matrix functions
84 expm,
85 sqrtm,
86 matFunc,
87
88 -- * Nullspace
89 nullspacePrec,
90 nullVector,
91 nullspaceSVD,
92 null1, null1sym,
93
94 orth,
95
96 -- * Norms
97 norm1, norm2, normInf,
98
99 -- * Correlation and Convolution
100 corr, conv, corrMin, corr2, conv2,
101
102 -- * Random arrays
103 rand, randn, RandDist(..), randomVector, gaussianSample, uniformSample,
104
105 -- * Misc
106 meanCov, peps, relativeError, haussholder
107) where
108
109import Numeric.HMatrix.Data
110
111import Numeric.Matrix()
112import Numeric.Vector()
113import Numeric.Container
114import Numeric.LinearAlgebra.Algorithms
115import Numeric.LinearAlgebra.Util
116
117