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authorAlberto Ruiz <aruiz@um.es>2015-07-16 20:16:59 +0200
committerAlberto Ruiz <aruiz@um.es>2015-07-16 20:16:59 +0200
commita273fdb74b04db6d57d5c9b15e676d83357e71fd (patch)
tree99189532f2a37129a7ec3696f681ff3fd3314950 /packages/base/src/Numeric/LinearAlgebra.hs
parentd9c99a670a393fb232641183623a7fa5921ccff2 (diff)
Her, LU, LDL, Linear, Additive
Diffstat (limited to 'packages/base/src/Numeric/LinearAlgebra.hs')
-rw-r--r--packages/base/src/Numeric/LinearAlgebra.hs47
1 files changed, 25 insertions, 22 deletions
diff --git a/packages/base/src/Numeric/LinearAlgebra.hs b/packages/base/src/Numeric/LinearAlgebra.hs
index 9a924e0..7be2600 100644
--- a/packages/base/src/Numeric/LinearAlgebra.hs
+++ b/packages/base/src/Numeric/LinearAlgebra.hs
@@ -53,11 +53,11 @@ module Numeric.LinearAlgebra (
53 -- 53 --
54 54
55 -- * Products 55 -- * Products
56 -- ** dot 56 -- ** Dot
57 dot, (<.>), 57 dot, (<.>),
58 -- ** matrix-vector 58 -- ** Matrix-vector
59 (#>), (<#), (!#>), 59 (#>), (<#), (!#>),
60 -- ** matrix-matrix 60 -- ** Matrix-matrix
61 (<>), 61 (<>),
62 -- | The matrix product is also implemented in the "Data.Monoid" instance, where 62 -- | The matrix product is also implemented in the "Data.Monoid" instance, where
63 -- single-element matrices (created from numeric literals or using 'scalar') 63 -- single-element matrices (created from numeric literals or using 'scalar')
@@ -73,20 +73,25 @@ module Numeric.LinearAlgebra (
73 -- 'mconcat' uses 'optimiseMult' to get the optimal association order. 73 -- 'mconcat' uses 'optimiseMult' to get the optimal association order.
74 74
75 75
76 -- ** other 76 -- ** Other
77 outer, kronecker, cross, 77 outer, kronecker, cross,
78 scale, 78 scale, add,
79 sumElements, prodElements, 79 sumElements, prodElements,
80 80
81 -- * Linear systems 81 -- * Linear systems
82 -- ** General
82 (<\>), 83 (<\>),
83 linearSolve,
84 linearSolveLS, 84 linearSolveLS,
85 linearSolveSVD, 85 linearSolveSVD,
86 luSolve, 86 -- ** Determined
87 luSolve', 87 linearSolve,
88 luSolve, luPacked,
89 luSolve', luPacked',
90 -- ** Symmetric indefinite
91 ldlSolve, ldlPacked,
92 -- ** Positive definite
88 cholSolve, 93 cholSolve,
89 ldlSolve, 94 -- ** Sparse
90 cgSolve, 95 cgSolve,
91 cgSolve', 96 cgSolve',
92 97
@@ -113,21 +118,18 @@ module Numeric.LinearAlgebra (
113 leftSV, rightSV, 118 leftSV, rightSV,
114 119
115 -- * Eigendecomposition 120 -- * Eigendecomposition
116 eig, eigSH, eigSH', 121 eig, eigSH,
117 eigenvalues, eigenvaluesSH, eigenvaluesSH', 122 eigenvalues, eigenvaluesSH,
118 geigSH', 123 geigSH,
119 124
120 -- * QR 125 -- * QR
121 qr, rq, qrRaw, qrgr, 126 qr, rq, qrRaw, qrgr,
122 127
123 -- * Cholesky 128 -- * Cholesky
124 chol, cholSH, mbCholSH, 129 chol, mbChol,
125 130
126 -- * LU 131 -- * LU
127 lu, luPacked, luPacked', luFact, 132 lu, luFact,
128
129 -- * LDL
130 ldlPacked, ldlPackedSH,
131 133
132 -- * Hessenberg 134 -- * Hessenberg
133 hess, 135 hess,
@@ -150,14 +152,16 @@ module Numeric.LinearAlgebra (
150 -- * Misc 152 -- * Misc
151 meanCov, rowOuters, pairwiseD2, unitary, peps, relativeError, magnit, 153 meanCov, rowOuters, pairwiseD2, unitary, peps, relativeError, magnit,
152 haussholder, optimiseMult, udot, nullspaceSVD, orthSVD, ranksv, 154 haussholder, optimiseMult, udot, nullspaceSVD, orthSVD, ranksv,
153 iC, 155 iC, sym, xTx, trustSym, her,
154 -- * Auxiliary classes 156 -- * Auxiliary classes
155 Element, Container, Product, Numeric, LSDiv, 157 Element, Container, Product, Numeric, LSDiv, Her,
156 Complexable, RealElement, 158 Complexable, RealElement,
157 RealOf, ComplexOf, SingleOf, DoubleOf, 159 RealOf, ComplexOf, SingleOf, DoubleOf,
158 IndexOf, 160 IndexOf,
159 Field, 161 Field, Linear(), Additive(),
160 Transposable, 162 Transposable,
163 LU(..),
164 LDL(..),
161 CGState(..), 165 CGState(..),
162 Testable(..) 166 Testable(..)
163) where 167) where
@@ -169,7 +173,7 @@ import Numeric.Vector()
169import Internal.Matrix 173import Internal.Matrix
170import Internal.Container hiding ((<>)) 174import Internal.Container hiding ((<>))
171import Internal.Numeric hiding (mul) 175import Internal.Numeric hiding (mul)
172import Internal.Algorithms hiding (linearSolve,Normed,orth,luPacked',linearSolve',luSolve') 176import Internal.Algorithms hiding (linearSolve,Normed,orth,luPacked',linearSolve',luSolve',ldlPacked')
173import qualified Internal.Algorithms as A 177import qualified Internal.Algorithms as A
174import Internal.Util 178import Internal.Util
175import Internal.Random 179import Internal.Random
@@ -246,4 +250,3 @@ nullspace m = nullspaceSVD (Left (1*eps)) m (rightSV m)
246-- | return an orthonormal basis of the range space of a matrix. See also 'orthSVD'. 250-- | return an orthonormal basis of the range space of a matrix. See also 'orthSVD'.
247orth m = orthSVD (Left (1*eps)) m (leftSV m) 251orth m = orthSVD (Left (1*eps)) m (leftSV m)
248 252
249