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authorAlberto Ruiz <aruiz@um.es>2014-05-16 14:13:49 +0200
committerAlberto Ruiz <aruiz@um.es>2014-05-16 14:13:49 +0200
commit51f4cc7b4b301142b8df73568ffaa448f9e6dd50 (patch)
tree7f9b9a26344a23a0d1e3fb6e4105fe968465cd2a /packages/hmatrix/src/Numeric
parent1838c4248679b7476bb8716a76171712dc3cd335 (diff)
license changes, reexport modules
Diffstat (limited to 'packages/hmatrix/src/Numeric')
-rw-r--r--packages/hmatrix/src/Numeric/Container.hs241
-rw-r--r--packages/hmatrix/src/Numeric/HMatrix.hs139
-rw-r--r--packages/hmatrix/src/Numeric/HMatrix/Data.hs70
-rw-r--r--packages/hmatrix/src/Numeric/HMatrix/Devel.hs69
4 files changed, 241 insertions, 278 deletions
diff --git a/packages/hmatrix/src/Numeric/Container.hs b/packages/hmatrix/src/Numeric/Container.hs
new file mode 100644
index 0000000..146780d
--- /dev/null
+++ b/packages/hmatrix/src/Numeric/Container.hs
@@ -0,0 +1,241 @@
1{-# LANGUAGE TypeFamilies #-}
2{-# LANGUAGE FlexibleContexts #-}
3{-# LANGUAGE FlexibleInstances #-}
4{-# LANGUAGE MultiParamTypeClasses #-}
5{-# LANGUAGE FunctionalDependencies #-}
6{-# LANGUAGE UndecidableInstances #-}
7
8-----------------------------------------------------------------------------
9-- |
10-- Module : Numeric.Container
11-- Copyright : (c) Alberto Ruiz 2010-14
12-- License : BSD3
13-- Maintainer : Alberto Ruiz
14-- Stability : provisional
15-- Portability : portable
16--
17-- Basic numeric operations on 'Vector' and 'Matrix', including conversion routines.
18--
19-- The 'Container' class is used to define optimized generic functions which work
20-- on 'Vector' and 'Matrix' with real or complex elements.
21--
22-- Some of these functions are also available in the instances of the standard
23-- numeric Haskell classes provided by "Numeric.LinearAlgebra".
24--
25-----------------------------------------------------------------------------
26{-# OPTIONS_HADDOCK hide #-}
27
28module Numeric.Container (
29 -- * Basic functions
30 module Data.Packed,
31 konst, build,
32 linspace,
33 diag, ident,
34 ctrans,
35 -- * Generic operations
36 Container(..),
37 -- * Matrix product
38 Product(..), udot, dot, (◇),
39 Mul(..),
40 Contraction(..),
41 optimiseMult,
42 mXm,mXv,vXm,LSDiv(..),
43 outer, kronecker,
44 -- * Element conversion
45 Convert(..),
46 Complexable(),
47 RealElement(),
48
49 RealOf, ComplexOf, SingleOf, DoubleOf,
50
51 IndexOf,
52 module Data.Complex
53) where
54
55import Data.Packed hiding (stepD, stepF, condD, condF, conjugateC, conjugateQ)
56import Data.Packed.Numeric
57import Data.Complex
58import Numeric.LinearAlgebra.Algorithms(Field,linearSolveSVD)
59import Data.Monoid(Monoid(mconcat))
60
61------------------------------------------------------------------
62
63{- | Creates a real vector containing a range of values:
64
65>>> linspace 5 (-3,7::Double)
66fromList [-3.0,-0.5,2.0,4.5,7.0]@
67
68>>> linspace 5 (8,2+i) :: Vector (Complex Double)
69fromList [8.0 :+ 0.0,6.5 :+ 0.25,5.0 :+ 0.5,3.5 :+ 0.75,2.0 :+ 1.0]
70
71Logarithmic spacing can be defined as follows:
72
73@logspace n (a,b) = 10 ** linspace n (a,b)@
74-}
75linspace :: (Container Vector e) => Int -> (e, e) -> Vector e
76linspace 0 (a,b) = fromList[(a+b)/2]
77linspace n (a,b) = addConstant a $ scale s $ fromList $ map fromIntegral [0 .. n-1]
78 where s = (b-a)/fromIntegral (n-1)
79
80--------------------------------------------------------
81
82class Contraction a b c | a b -> c
83 where
84 infixl 7 <.>
85 {- | Matrix product, matrix vector product, and dot product
86
87Examples:
88
89>>> let a = (3><4) [1..] :: Matrix Double
90>>> let v = fromList [1,0,2,-1] :: Vector Double
91>>> let u = fromList [1,2,3] :: Vector Double
92
93>>> a
94(3><4)
95 [ 1.0, 2.0, 3.0, 4.0
96 , 5.0, 6.0, 7.0, 8.0
97 , 9.0, 10.0, 11.0, 12.0 ]
98
99matrix × matrix:
100
101>>> disp 2 (a <.> trans a)
1023x3
103 30 70 110
104 70 174 278
105110 278 446
106
107matrix × vector:
108
109>>> a <.> v
110fromList [3.0,11.0,19.0]
111
112dot product:
113
114>>> u <.> fromList[3,2,1::Double]
11510
116
117For complex vectors the first argument is conjugated:
118
119>>> fromList [1,i] <.> fromList[2*i+1,3]
1201.0 :+ (-1.0)
121
122>>> fromList [1,i,1-i] <.> complex a
123fromList [10.0 :+ 4.0,12.0 :+ 4.0,14.0 :+ 4.0,16.0 :+ 4.0]
124
125-}
126 (<.>) :: a -> b -> c
127
128
129instance (Product t, Container Vector t) => Contraction (Vector t) (Vector t) t where
130 u <.> v = conj u `udot` v
131
132instance Product t => Contraction (Matrix t) (Vector t) (Vector t) where
133 (<.>) = mXv
134
135instance (Container Vector t, Product t) => Contraction (Vector t) (Matrix t) (Vector t) where
136 (<.>) v m = (conj v) `vXm` m
137
138instance Product t => Contraction (Matrix t) (Matrix t) (Matrix t) where
139 (<.>) = mXm
140
141
142--------------------------------------------------------------------------------
143
144class Mul a b c | a b -> c where
145 infixl 7 <>
146 -- | Matrix-matrix, matrix-vector, and vector-matrix products.
147 (<>) :: Product t => a t -> b t -> c t
148
149instance Mul Matrix Matrix Matrix where
150 (<>) = mXm
151
152instance Mul Matrix Vector Vector where
153 (<>) m v = flatten $ m <> asColumn v
154
155instance Mul Vector Matrix Vector where
156 (<>) v m = flatten $ asRow v <> m
157
158--------------------------------------------------------------------------------
159
160class LSDiv c where
161 infixl 7 <\>
162 -- | least squares solution of a linear system, similar to the \\ operator of Matlab\/Octave (based on linearSolveSVD)
163 (<\>) :: Field t => Matrix t -> c t -> c t
164
165instance LSDiv Vector where
166 m <\> v = flatten (linearSolveSVD m (reshape 1 v))
167
168instance LSDiv Matrix where
169 (<\>) = linearSolveSVD
170
171--------------------------------------------------------------------------------
172
173class Konst e d c | d -> c, c -> d
174 where
175 -- |
176 -- >>> konst 7 3 :: Vector Float
177 -- fromList [7.0,7.0,7.0]
178 --
179 -- >>> konst i (3::Int,4::Int)
180 -- (3><4)
181 -- [ 0.0 :+ 1.0, 0.0 :+ 1.0, 0.0 :+ 1.0, 0.0 :+ 1.0
182 -- , 0.0 :+ 1.0, 0.0 :+ 1.0, 0.0 :+ 1.0, 0.0 :+ 1.0
183 -- , 0.0 :+ 1.0, 0.0 :+ 1.0, 0.0 :+ 1.0, 0.0 :+ 1.0 ]
184 --
185 konst :: e -> d -> c e
186
187instance Container Vector e => Konst e Int Vector
188 where
189 konst = konst'
190
191instance Container Vector e => Konst e (Int,Int) Matrix
192 where
193 konst = konst'
194
195--------------------------------------------------------------------------------
196
197class Build d f c e | d -> c, c -> d, f -> e, f -> d, f -> c, c e -> f, d e -> f
198 where
199 -- |
200 -- >>> build 5 (**2) :: Vector Double
201 -- fromList [0.0,1.0,4.0,9.0,16.0]
202 --
203 -- Hilbert matrix of order N:
204 --
205 -- >>> let hilb n = build (n,n) (\i j -> 1/(i+j+1)) :: Matrix Double
206 -- >>> putStr . dispf 2 $ hilb 3
207 -- 3x3
208 -- 1.00 0.50 0.33
209 -- 0.50 0.33 0.25
210 -- 0.33 0.25 0.20
211 --
212 build :: d -> f -> c e
213
214instance Container Vector e => Build Int (e -> e) Vector e
215 where
216 build = build'
217
218instance Container Matrix e => Build (Int,Int) (e -> e -> e) Matrix e
219 where
220 build = build'
221
222--------------------------------------------------------------------------------
223
224{- | alternative operator for '(\<.\>)'
225
226x25c7, white diamond
227
228-}
229(◇) :: Contraction a b c => a -> b -> c
230infixl 7 ◇
231(◇) = (<.>)
232
233-- | dot product: @cdot u v = 'udot' ('conj' u) v@
234dot :: (Container Vector t, Product t) => Vector t -> Vector t -> t
235dot u v = udot (conj u) v
236
237--------------------------------------------------------------------------------
238
239optimiseMult :: Monoid (Matrix t) => [Matrix t] -> Matrix t
240optimiseMult = mconcat
241
diff --git a/packages/hmatrix/src/Numeric/HMatrix.hs b/packages/hmatrix/src/Numeric/HMatrix.hs
deleted file mode 100644
index fcd3e02..0000000
--- a/packages/hmatrix/src/Numeric/HMatrix.hs
+++ /dev/null
@@ -1,139 +0,0 @@
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 -- >>> (3><3) [1..9] * ident 3 :: Matrix Double
25 -- (3><3)
26 -- [ 1.0, 0.0, 0.0
27 -- , 0.0, 5.0, 0.0
28 -- , 0.0, 0.0, 9.0 ]
29 --
30 -- In arithmetic operations single-element vectors and matrices
31 -- (created from numeric literals or using 'scalar') automatically
32 -- expand to match the dimensions of the other operand:
33 --
34 -- >>> 5 + 2*ident 3 :: Matrix Double
35 -- (3><3)
36 -- [ 7.0, 5.0, 5.0
37 -- , 5.0, 7.0, 5.0
38 -- , 5.0, 5.0, 7.0 ]
39 --
40
41 -- * Products
42 (<.>),
43
44 -- | The matrix product is also implemented in the "Data.Monoid" instance for Matrix, where
45 -- single-element matrices (created from numeric literals or using 'scalar')
46 -- are used for scaling.
47 --
48 -- >>> let m = (2><3)[1..] :: Matrix Double
49 -- >>> m <> 2 <> diagl[0.5,1,0]
50 -- (2><3)
51 -- [ 1.0, 4.0, 0.0
52 -- , 4.0, 10.0, 0.0 ]
53 --
54 -- mconcat uses 'optimiseMult' to get the optimal association order.
55
56 (◇),
57 outer, kronecker, cross,
58 scale,
59 sumElements, prodElements, absSum,
60
61 -- * Linear Systems
62 (<\>),
63 linearSolve,
64 linearSolveLS,
65 linearSolveSVD,
66 luSolve,
67 cholSolve,
68
69 -- * Inverse and pseudoinverse
70 inv, pinv, pinvTol,
71
72 -- * Determinant and rank
73 rcond, rank, ranksv,
74 det, invlndet,
75
76 -- * Singular value decomposition
77 svd,
78 fullSVD,
79 thinSVD,
80 compactSVD,
81 singularValues,
82 leftSV, rightSV,
83
84 -- * Eigensystems
85 eig, eigSH, eigSH',
86 eigenvalues, eigenvaluesSH, eigenvaluesSH',
87 geigSH',
88
89 -- * QR
90 qr, rq, qrRaw, qrgr,
91
92 -- * Cholesky
93 chol, cholSH, mbCholSH,
94
95 -- * Hessenberg
96 hess,
97
98 -- * Schur
99 schur,
100
101 -- * LU
102 lu, luPacked,
103
104 -- * Matrix functions
105 expm,
106 sqrtm,
107 matFunc,
108
109 -- * Nullspace
110 nullspacePrec,
111 nullVector,
112 nullspaceSVD,
113 null1, null1sym,
114
115 orth,
116
117 -- * Norms
118 norm1, norm2, normInf, pnorm, NormType(..),
119
120 -- * Correlation and Convolution
121 corr, conv, corrMin, corr2, conv2,
122
123 -- * Random arrays
124 rand, randn, RandDist(..), randomVector, gaussianSample, uniformSample,
125
126 -- * Misc
127 meanCov, peps, relativeError, haussholder, optimiseMult, udot
128) where
129
130import Numeric.HMatrix.Data
131
132--import Numeric.Matrix()
133--import Numeric.Vector()
134import Numeric.Container
135import Numeric.LinearAlgebra.Algorithms
136import Numeric.LinearAlgebra.Util
137import Numeric.Random
138
139
diff --git a/packages/hmatrix/src/Numeric/HMatrix/Data.hs b/packages/hmatrix/src/Numeric/HMatrix/Data.hs
deleted file mode 100644
index 5d7ce4f..0000000
--- a/packages/hmatrix/src/Numeric/HMatrix/Data.hs
+++ /dev/null
@@ -1,70 +0,0 @@
1--------------------------------------------------------------------------------
2{- |
3Module : Numeric.HMatrix.Data
4Copyright : (c) Alberto Ruiz 2014
5License : GPL
6
7Maintainer : Alberto Ruiz
8Stability : provisional
9
10Basic data processing.
11
12-}
13--------------------------------------------------------------------------------
14
15module Numeric.HMatrix.Data(
16
17 -- * Vector
18 -- | 1D arrays are storable vectors from the vector package.
19
20 Vector, (|>), dim, (@>),
21
22 -- * Matrix
23 Matrix, (><), size, (@@>), trans, ctrans,
24
25 -- * Construction
26 scalar, konst, build, assoc, accum, linspace, -- ones, zeros,
27
28 -- * Diagonal
29 ident, diag, diagl, diagRect, takeDiag,
30
31 -- * Data manipulation
32 fromList, toList, subVector, takesV, vjoin,
33 flatten, reshape, asRow, asColumn, row, col,
34 fromRows, toRows, fromColumns, toColumns, fromLists, toLists, fromArray2D,
35 takeRows, dropRows, takeColumns, dropColumns, subMatrix, (?), (¿), fliprl, flipud,
36
37 -- * Block matrix
38 fromBlocks, (¦), (——), diagBlock, repmat, toBlocks, toBlocksEvery,
39
40 -- * Mapping functions
41 conj, cmap, step, cond,
42
43 -- * Find elements
44 find, maxIndex, minIndex, maxElement, minElement, atIndex,
45
46 -- * IO
47 disp, dispf, disps, dispcf, latexFormat, format,
48 loadMatrix, saveMatrix, fromFile, fileDimensions,
49 readMatrix,
50 fscanfVector, fprintfVector, freadVector, fwriteVector,
51
52-- * Conversion
53 Convert(..),
54
55 -- * Misc
56 arctan2,
57 rows, cols,
58 separable,
59
60 module Data.Complex
61
62) where
63
64import Data.Packed.Vector
65import Data.Packed.Matrix
66import Numeric.Container
67import Numeric.IO
68import Numeric.LinearAlgebra.Util
69import Data.Complex
70
diff --git a/packages/hmatrix/src/Numeric/HMatrix/Devel.hs b/packages/hmatrix/src/Numeric/HMatrix/Devel.hs
deleted file mode 100644
index b921f44..0000000
--- a/packages/hmatrix/src/Numeric/HMatrix/Devel.hs
+++ /dev/null
@@ -1,69 +0,0 @@
1--------------------------------------------------------------------------------
2{- |
3Module : Numeric.HMatrix.Devel
4Copyright : (c) Alberto Ruiz 2014
5License : GPL
6
7Maintainer : Alberto Ruiz
8Stability : provisional
9
10The library can be easily extended using the tools in this module.
11
12-}
13--------------------------------------------------------------------------------
14
15module Numeric.HMatrix.Devel(
16 -- * FFI helpers
17 -- | Sample usage, to upload a perspective matrix to a shader.
18 --
19 -- @ glUniformMatrix4fv 0 1 (fromIntegral gl_TRUE) \`appMatrix\` perspective 0.01 100 (pi\/2) (4\/3)
20 -- @
21 module Data.Packed.Foreign,
22
23 -- * FFI tools
24 -- | Illustrative usage examples can be found
25 -- in the @examples\/devel@ folder included in the package.
26 module Data.Packed.Development,
27
28 -- * ST
29 -- | In-place manipulation inside the ST monad.
30 -- See examples\/inplace.hs in the distribution.
31
32 -- ** Mutable Vectors
33 STVector, newVector, thawVector, freezeVector, runSTVector,
34 readVector, writeVector, modifyVector, liftSTVector,
35 -- ** Mutable Matrices
36 STMatrix, newMatrix, thawMatrix, freezeMatrix, runSTMatrix,
37 readMatrix, writeMatrix, modifyMatrix, liftSTMatrix,
38 -- ** Unsafe functions
39 newUndefinedVector,
40 unsafeReadVector, unsafeWriteVector,
41 unsafeThawVector, unsafeFreezeVector,
42 newUndefinedMatrix,
43 unsafeReadMatrix, unsafeWriteMatrix,
44 unsafeThawMatrix, unsafeFreezeMatrix,
45
46 -- * Special maps and zips
47 mapVectorWithIndex, zipVector, zipVectorWith, unzipVector, unzipVectorWith,
48 mapVectorM, mapVectorM_, mapVectorWithIndexM, mapVectorWithIndexM_,
49 foldLoop, foldVector, foldVectorG, foldVectorWithIndex,
50 mapMatrixWithIndex, mapMatrixWithIndexM, mapMatrixWithIndexM_,
51 liftMatrix, liftMatrix2, liftMatrix2Auto,
52
53 -- * Auxiliary classes
54 Element, Container, Product, Contraction, LSDiv,
55 Complexable(), RealElement(),
56 RealOf, ComplexOf, SingleOf, DoubleOf,
57 IndexOf,
58 Field, Normed
59) where
60
61import Data.Packed.Foreign
62import Data.Packed.Development
63import Data.Packed.ST
64import Numeric.Container(Container,Contraction,LSDiv,Product,
65 Complexable(),RealElement(),
66 RealOf, ComplexOf, SingleOf, DoubleOf, IndexOf)
67import Data.Packed
68import Numeric.LinearAlgebra.Algorithms(Field,Normed)
69
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-11 10:00:59 +0000