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-rw-r--r--packages/Makefile38
-rw-r--r--packages/base/CHANGELOG7
-rw-r--r--packages/base/hmatrix.cabal42
-rw-r--r--packages/base/src/Data/Packed/IO.hs1
-rw-r--r--packages/base/src/Data/Packed/Internal/Numeric.hs1
-rw-r--r--packages/base/src/Data/Packed/Internal/Vector.hs1
-rw-r--r--packages/base/src/Data/Packed/Numeric.hs8
-rw-r--r--packages/base/src/Numeric/Chain.hs2
-rw-r--r--packages/base/src/Numeric/LinearAlgebra.hs231
-rw-r--r--packages/base/src/Numeric/LinearAlgebra/Algorithms.hs18
-rw-r--r--packages/base/src/Numeric/LinearAlgebra/HMatrix.hs228
-rw-r--r--packages/base/src/Numeric/LinearAlgebra/LAPACK.hs6
-rw-r--r--packages/base/src/Numeric/LinearAlgebra/Static.hs32
-rw-r--r--packages/base/src/Numeric/LinearAlgebra/Static/Internal.hs4
-rw-r--r--packages/base/src/Numeric/LinearAlgebra/Util.hs58
-rw-r--r--packages/base/src/Numeric/LinearAlgebra/Util/CG.hs6
-rw-r--r--packages/base/src/Numeric/Vectorized.hs1
-rw-r--r--packages/glpk/hmatrix-glpk.cabal4
-rw-r--r--packages/glpk/src/Numeric/LinearProgramming.hs21
-rw-r--r--packages/glpk/src/Numeric/LinearProgramming/L1.hs2
-rw-r--r--packages/gsl/CHANGELOG10
-rw-r--r--packages/gsl/THANKS.md4
-rw-r--r--packages/gsl/hmatrix-gsl.cabal4
-rw-r--r--packages/gsl/src/Graphics/Plot.hs4
-rw-r--r--packages/gsl/src/Numeric/GSL/Fitting.hs16
-rw-r--r--packages/gsl/src/Numeric/GSL/Fourier.hs5
-rw-r--r--packages/gsl/src/Numeric/GSL/IO.hs2
-rw-r--r--packages/gsl/src/Numeric/GSL/Internal.hs7
-rw-r--r--packages/gsl/src/Numeric/GSL/LinearAlgebra.hs2
-rw-r--r--packages/gsl/src/Numeric/GSL/Minimization.hs17
-rw-r--r--packages/gsl/src/Numeric/GSL/ODE.hs16
-rw-r--r--packages/gsl/src/Numeric/GSL/Polynomials.hs7
-rw-r--r--packages/gsl/src/Numeric/GSL/Random.hs16
-rw-r--r--packages/gsl/src/Numeric/GSL/Root.hs18
-rw-r--r--packages/gsl/src/Numeric/GSL/Vector.hs3
-rw-r--r--packages/sparse/src/Numeric/LinearAlgebra/Sparse.hs7
-rw-r--r--packages/special/hmatrix-special.cabal4
-rw-r--r--packages/special/lib/Numeric/GSL/Special/Internal.hsc2
-rw-r--r--packages/tests/hmatrix-tests.cabal6
-rw-r--r--packages/tests/src/Numeric/GSL/Tests.hs4
-rw-r--r--packages/tests/src/Numeric/LinearAlgebra/Tests.hs202
-rw-r--r--packages/tests/src/Numeric/LinearAlgebra/Tests/Instances.hs91
-rw-r--r--packages/tests/src/Numeric/LinearAlgebra/Tests/Properties.hs153
43 files changed, 594 insertions, 717 deletions
diff --git a/packages/Makefile b/packages/Makefile
index e9d8586..b00d71f 100644
--- a/packages/Makefile
+++ b/packages/Makefile
@@ -1,22 +1,26 @@
1pkgs=base gsl special glpk tests ../../hTensor ../../easyVision/packages/base 1pkgs=base gsl special glpk tests ../../hTensor ../../easyVision/packages/tools ../../easyVision/packages/base
2
3mkl=--extra-include-dirs=$(MKL) --extra-lib-dirs=$(MKL)
4
5cabalcmd = \
6 for p in $(1); do \
7 if [ -e $$p ]; then \
8 cd $$p; cabal $(2) ; cd -; \
9 fi; \
10 done; \
11 cd sparse; \
12 cabal $(3) $(2); cd -;
13
2 14
3all: 15all:
4 for p in $(pkgs); do \ 16 $(call cabalcmd, $(pkgs), install --force-reinstall --enable-documentation, $(mkl))
5 if [ -e $$p ]; then \
6 cd $$p; cabal install --force-reinstall --enable-documentation ; cd -; \
7 fi; \
8 done
9 cd sparse; \
10 cabal install --extra-include-dirs=$(MKL) --extra-lib-dirs=$(MKL) \
11 --force-reinstall --enable-documentation ; cd -;
12 17
13fast: 18fast:
14 for p in $(pkgs); do \ 19 $(call cabalcmd, $(pkgs), install --force-reinstall, $(mkl))
15 if [ -e $$p ]; then \ 20
16 cd $$p; cabal install --force-reinstall ; cd -; \ 21clean:
17 fi; \ 22 $(call cabalcmd, $(pkgs), clean)
18 done 23
19 cd sparse; \ 24prof:
20 cabal install --extra-include-dirs=$(MKL) --extra-lib-dirs=$(MKL) \ 25 $(call cabalcmd, $(pkgs), install --force-reinstall --enable-library-profiling, $(mkl))
21 --force-reinstall; cd -;
22 26
diff --git a/packages/base/CHANGELOG b/packages/base/CHANGELOG
index c137285..ce19c97 100644
--- a/packages/base/CHANGELOG
+++ b/packages/base/CHANGELOG
@@ -1,3 +1,10 @@
10.17.0.0
2--------
3
4 * old compatibility modules removed
5
6 * added "unitary" and "pairwiseD2"
7
10.16.1.0 80.16.1.0
2-------- 9--------
3 10
diff --git a/packages/base/hmatrix.cabal b/packages/base/hmatrix.cabal
index 3895dc1..7bfc762 100644
--- a/packages/base/hmatrix.cabal
+++ b/packages/base/hmatrix.cabal
@@ -1,5 +1,5 @@
1Name: hmatrix 1Name: hmatrix
2Version: 0.16.1.5 2Version: 0.17.0.0
3License: BSD3 3License: BSD3
4License-file: LICENSE 4License-file: LICENSE
5Author: Alberto Ruiz 5Author: Alberto Ruiz
@@ -9,16 +9,6 @@ Homepage: https://github.com/albertoruiz/hmatrix
9Synopsis: Numeric Linear Algebra 9Synopsis: Numeric Linear Algebra
10Description: Linear algebra based on BLAS and LAPACK. 10Description: Linear algebra based on BLAS and LAPACK.
11 . 11 .
12 The package is organized as follows:
13 .
14 ["Numeric.LinearAlgebra.HMatrix"] Starting point and recommended import module for most applications.
15 .
16 ["Numeric.LinearAlgebra.Static"] Experimental alternative interface.
17 .
18 ["Numeric.LinearAlgebra.Devel"] Tools for extending the library.
19 .
20 (Other modules are exposed with hidden documentation for backwards compatibility.)
21 .
22 Code examples: <http://dis.um.es/~alberto/hmatrix/hmatrix.html> 12 Code examples: <http://dis.um.es/~alberto/hmatrix/hmatrix.html>
23 13
24Category: Math 14Category: Math
@@ -39,7 +29,7 @@ flag openblas
39 29
40library 30library
41 31
42 Build-Depends: base >= 4 && < 5, 32 Build-Depends: base >= 4.8 && < 5,
43 binary, 33 binary,
44 array, 34 array,
45 deepseq, 35 deepseq,
@@ -51,27 +41,19 @@ library
51 41
52 hs-source-dirs: src 42 hs-source-dirs: src
53 43
54 exposed-modules: Data.Packed, 44 exposed-modules: Numeric.LinearAlgebra
55 Data.Packed.Vector,
56 Data.Packed.Matrix,
57 Data.Packed.Foreign,
58 Data.Packed.ST,
59 Data.Packed.Development,
60
61 Numeric.LinearAlgebra
62 Numeric.LinearAlgebra.LAPACK
63 Numeric.LinearAlgebra.Algorithms
64 Numeric.Container
65 Numeric.LinearAlgebra.Util
66
67 Numeric.LinearAlgebra.Devel 45 Numeric.LinearAlgebra.Devel
68 Numeric.LinearAlgebra.Data 46 Numeric.LinearAlgebra.Data
69 Numeric.LinearAlgebra.HMatrix 47 Numeric.LinearAlgebra.HMatrix
70 Numeric.LinearAlgebra.Static 48 Numeric.LinearAlgebra.Static
71
72
73 49
74 other-modules: Data.Packed.Internal, 50 other-modules: Data.Packed,
51 Data.Packed.Vector
52 Data.Packed.Matrix
53 Data.Packed.Foreign
54 Data.Packed.ST
55 Data.Packed.Development
56 Data.Packed.Internal
75 Data.Packed.Internal.Common 57 Data.Packed.Internal.Common
76 Data.Packed.Internal.Signatures 58 Data.Packed.Internal.Signatures
77 Data.Packed.Internal.Vector 59 Data.Packed.Internal.Vector
@@ -83,12 +65,16 @@ library
83 Numeric.Matrix 65 Numeric.Matrix
84 Data.Packed.Internal.Numeric 66 Data.Packed.Internal.Numeric
85 Data.Packed.Numeric 67 Data.Packed.Numeric
68 Numeric.LinearAlgebra.LAPACK
69 Numeric.LinearAlgebra.Algorithms
70 Numeric.Container
86 Numeric.LinearAlgebra.Util.Convolution 71 Numeric.LinearAlgebra.Util.Convolution
87 Numeric.LinearAlgebra.Util.CG 72 Numeric.LinearAlgebra.Util.CG
88 Numeric.LinearAlgebra.Random 73 Numeric.LinearAlgebra.Random
89 Numeric.Conversion 74 Numeric.Conversion
90 Numeric.Sparse 75 Numeric.Sparse
91 Numeric.LinearAlgebra.Static.Internal 76 Numeric.LinearAlgebra.Static.Internal
77 Numeric.LinearAlgebra.Util
92 78
93 C-sources: src/C/lapack-aux.c 79 C-sources: src/C/lapack-aux.c
94 src/C/vector-aux.c 80 src/C/vector-aux.c
diff --git a/packages/base/src/Data/Packed/IO.hs b/packages/base/src/Data/Packed/IO.hs
index 85f1b37..b0999a8 100644
--- a/packages/base/src/Data/Packed/IO.hs
+++ b/packages/base/src/Data/Packed/IO.hs
@@ -22,7 +22,6 @@ import Text.Printf(printf)
22import Data.List(intersperse) 22import Data.List(intersperse)
23import Data.Complex 23import Data.Complex
24import Numeric.Vectorized(vectorScan,saveMatrix) 24import Numeric.Vectorized(vectorScan,saveMatrix)
25import Control.Applicative((<$>))
26import Data.Packed.Internal 25import Data.Packed.Internal
27 26
28{- | Creates a string from a matrix given a separator and a function to show each entry. Using 27{- | Creates a string from a matrix given a separator and a function to show each entry. Using
diff --git a/packages/base/src/Data/Packed/Internal/Numeric.hs b/packages/base/src/Data/Packed/Internal/Numeric.hs
index 257ad73..7a4dd29 100644
--- a/packages/base/src/Data/Packed/Internal/Numeric.hs
+++ b/packages/base/src/Data/Packed/Internal/Numeric.hs
@@ -48,7 +48,6 @@ import Numeric.Conversion
48import Data.Packed.Development 48import Data.Packed.Development
49import Numeric.Vectorized 49import Numeric.Vectorized
50import Data.Complex 50import Data.Complex
51import Control.Applicative((<*>))
52 51
53import Numeric.LinearAlgebra.LAPACK(multiplyR,multiplyC,multiplyF,multiplyQ) 52import Numeric.LinearAlgebra.LAPACK(multiplyR,multiplyC,multiplyF,multiplyQ)
54import Data.Packed.Internal 53import Data.Packed.Internal
diff --git a/packages/base/src/Data/Packed/Internal/Vector.hs b/packages/base/src/Data/Packed/Internal/Vector.hs
index d0bc143..b49f379 100644
--- a/packages/base/src/Data/Packed/Internal/Vector.hs
+++ b/packages/base/src/Data/Packed/Internal/Vector.hs
@@ -35,7 +35,6 @@ import Foreign.Ptr(Ptr)
35import Foreign.Storable(Storable, peekElemOff, pokeElemOff, sizeOf) 35import Foreign.Storable(Storable, peekElemOff, pokeElemOff, sizeOf)
36import Foreign.C.Types 36import Foreign.C.Types
37import Data.Complex 37import Data.Complex
38import Control.Monad(when)
39import System.IO.Unsafe(unsafePerformIO) 38import System.IO.Unsafe(unsafePerformIO)
40 39
41#if __GLASGOW_HASKELL__ >= 605 40#if __GLASGOW_HASKELL__ >= 605
diff --git a/packages/base/src/Data/Packed/Numeric.hs b/packages/base/src/Data/Packed/Numeric.hs
index 6027f43..6d62f22 100644
--- a/packages/base/src/Data/Packed/Numeric.hs
+++ b/packages/base/src/Data/Packed/Numeric.hs
@@ -39,7 +39,7 @@ module Data.Packed.Numeric (
39 step, cond, find, assoc, accum, 39 step, cond, find, assoc, accum,
40 Transposable(..), Linear(..), 40 Transposable(..), Linear(..),
41 -- * Matrix product 41 -- * Matrix product
42 Product(..), udot, dot, (<·>), (#>), app, 42 Product(..), udot, dot, (<·>), (#>), (<#), app,
43 Mul(..), 43 Mul(..),
44 (<.>), 44 (<.>),
45 optimiseMult, 45 optimiseMult,
@@ -71,7 +71,6 @@ import Data.Packed
71import Data.Packed.Internal.Numeric 71import Data.Packed.Internal.Numeric
72import Data.Complex 72import Data.Complex
73import Numeric.LinearAlgebra.Algorithms(Field,linearSolveSVD) 73import Numeric.LinearAlgebra.Algorithms(Field,linearSolveSVD)
74import Data.Monoid(Monoid(mconcat))
75import Data.Packed.IO 74import Data.Packed.IO
76import Numeric.LinearAlgebra.Random 75import Numeric.LinearAlgebra.Random
77 76
@@ -142,6 +141,11 @@ fromList [140.0,320.0]
142app :: Numeric t => Matrix t -> Vector t -> Vector t 141app :: Numeric t => Matrix t -> Vector t -> Vector t
143app = (#>) 142app = (#>)
144 143
144infixl 8 <#
145-- | dense vector-matrix product
146(<#) :: Numeric t => Vector t -> Matrix t -> Vector t
147(<#) = vXm
148
145-------------------------------------------------------------------------------- 149--------------------------------------------------------------------------------
146 150
147class Mul a b c | a b -> c where 151class Mul a b c | a b -> c where
diff --git a/packages/base/src/Numeric/Chain.hs b/packages/base/src/Numeric/Chain.hs
index 443bd28..64c09c0 100644
--- a/packages/base/src/Numeric/Chain.hs
+++ b/packages/base/src/Numeric/Chain.hs
@@ -1,3 +1,5 @@
1{-# LANGUAGE FlexibleContexts #-}
2
1----------------------------------------------------------------------------- 3-----------------------------------------------------------------------------
2-- | 4-- |
3-- Module : Numeric.Chain 5-- Module : Numeric.Chain
diff --git a/packages/base/src/Numeric/LinearAlgebra.hs b/packages/base/src/Numeric/LinearAlgebra.hs
index ad315e4..4ba0c98 100644
--- a/packages/base/src/Numeric/LinearAlgebra.hs
+++ b/packages/base/src/Numeric/LinearAlgebra.hs
@@ -1,22 +1,235 @@
1-------------------------------------------------------------------------------- 1-----------------------------------------------------------------------------
2{- | 2{- |
3Module : Numeric.LinearAlgebra 3Module : Numeric.LinearAlgebra
4Copyright : (c) Alberto Ruiz 2006-14 4Copyright : (c) Alberto Ruiz 2006-15
5License : BSD3 5License : BSD3
6Maintainer : Alberto Ruiz 6Maintainer : Alberto Ruiz
7Stability : provisional 7Stability : provisional
8 8
9-} 9-}
10-------------------------------------------------------------------------------- 10-----------------------------------------------------------------------------
11{-# OPTIONS_HADDOCK hide #-}
12
13module Numeric.LinearAlgebra ( 11module Numeric.LinearAlgebra (
14 module Numeric.Container, 12
15 module Numeric.LinearAlgebra.Algorithms 13 -- * Basic types and data processing
14 module Numeric.LinearAlgebra.Data,
15
16 -- * Arithmetic and numeric classes
17 -- |
18 -- The standard numeric classes are defined elementwise:
19 --
20 -- >>> vector [1,2,3] * vector [3,0,-2]
21 -- fromList [3.0,0.0,-6.0]
22 --
23 -- >>> matrix 3 [1..9] * ident 3
24 -- (3><3)
25 -- [ 1.0, 0.0, 0.0
26 -- , 0.0, 5.0, 0.0
27 -- , 0.0, 0.0, 9.0 ]
28 --
29 -- In arithmetic operations single-element vectors and matrices
30 -- (created from numeric literals or using 'scalar') automatically
31 -- expand to match the dimensions of the other operand:
32 --
33 -- >>> 5 + 2*ident 3 :: Matrix Double
34 -- (3><3)
35 -- [ 7.0, 5.0, 5.0
36 -- , 5.0, 7.0, 5.0
37 -- , 5.0, 5.0, 7.0 ]
38 --
39 -- >>> matrix 3 [1..9] + matrix 1 [10,20,30]
40 -- (3><3)
41 -- [ 11.0, 12.0, 13.0
42 -- , 24.0, 25.0, 26.0
43 -- , 37.0, 38.0, 39.0 ]
44 --
45
46 -- * Products
47 -- ** dot
48 dot, (<·>),
49 -- ** matrix-vector
50 app, (#>), (<#), (!#>),
51 -- ** matrix-matrix
52 mul, (<>),
53 -- | The matrix product is also implemented in the "Data.Monoid" instance, where
54 -- single-element matrices (created from numeric literals or using 'scalar')
55 -- are used for scaling.
56 --
57 -- >>> import Data.Monoid as M
58 -- >>> let m = matrix 3 [1..6]
59 -- >>> m M.<> 2 M.<> diagl[0.5,1,0]
60 -- (2><3)
61 -- [ 1.0, 4.0, 0.0
62 -- , 4.0, 10.0, 0.0 ]
63 --
64 -- 'mconcat' uses 'optimiseMult' to get the optimal association order.
65
66
67 -- ** other
68 outer, kronecker, cross,
69 scale,
70 sumElements, prodElements,
71
72 -- * Linear Systems
73 (<\>),
74 linearSolve,
75 linearSolveLS,
76 linearSolveSVD,
77 luSolve,
78 cholSolve,
79 cgSolve,
80 cgSolve',
81
82 -- * Inverse and pseudoinverse
83 inv, pinv, pinvTol,
84
85 -- * Determinant and rank
86 rcond, rank,
87 det, invlndet,
88
89 -- * Norms
90 Normed(..),
91 norm_Frob, norm_nuclear,
92
93 -- * Nullspace and range
94 orth,
95 nullspace, null1, null1sym,
96
97 -- * SVD
98 svd,
99 thinSVD,
100 compactSVD,
101 singularValues,
102 leftSV, rightSV,
103
104 -- * Eigensystems
105 eig, eigSH, eigSH',
106 eigenvalues, eigenvaluesSH, eigenvaluesSH',
107 geigSH',
108
109 -- * QR
110 qr, rq, qrRaw, qrgr,
111
112 -- * Cholesky
113 chol, cholSH, mbCholSH,
114
115 -- * Hessenberg
116 hess,
117
118 -- * Schur
119 schur,
120
121 -- * LU
122 lu, luPacked,
123
124 -- * Matrix functions
125 expm,
126 sqrtm,
127 matFunc,
128
129 -- * Correlation and convolution
130 corr, conv, corrMin, corr2, conv2,
131
132 -- * Random arrays
133
134 Seed, RandDist(..), randomVector, rand, randn, gaussianSample, uniformSample,
135
136 -- * Misc
137 meanCov, rowOuters, pairwiseD2, unitary, peps, relativeError, haussholder, optimiseMult, udot, nullspaceSVD, orthSVD, ranksv,
138 ℝ,ℂ,iC,
139 -- * Auxiliary classes
140 Element, Container, Product, Numeric, LSDiv,
141 Complexable, RealElement,
142 RealOf, ComplexOf, SingleOf, DoubleOf,
143 IndexOf,
144 Field,
145-- Normed,
146 Transposable,
147 CGState(..),
148 Testable(..)
16) where 149) where
17 150
18import Numeric.Container 151import Numeric.LinearAlgebra.Data
19import Numeric.LinearAlgebra.Algorithms 152
20import Numeric.Matrix() 153import Numeric.Matrix()
21import Numeric.Vector() 154import Numeric.Vector()
155import Data.Packed.Numeric hiding ((<>), mul)
156import Numeric.LinearAlgebra.Algorithms hiding (linearSolve,Normed,orth)
157import qualified Numeric.LinearAlgebra.Algorithms as A
158import Numeric.LinearAlgebra.Util
159import Numeric.LinearAlgebra.Random
160import Numeric.Sparse((!#>))
161import Numeric.LinearAlgebra.Util.CG
162
163{- | infix synonym of 'mul'
164
165>>> let a = (3><5) [1..]
166>>> a
167(3><5)
168 [ 1.0, 2.0, 3.0, 4.0, 5.0
169 , 6.0, 7.0, 8.0, 9.0, 10.0
170 , 11.0, 12.0, 13.0, 14.0, 15.0 ]
171
172>>> let b = (5><2) [1,3, 0,2, -1,5, 7,7, 6,0]
173>>> b
174(5><2)
175 [ 1.0, 3.0
176 , 0.0, 2.0
177 , -1.0, 5.0
178 , 7.0, 7.0
179 , 6.0, 0.0 ]
180
181>>> a <> b
182(3><2)
183 [ 56.0, 50.0
184 , 121.0, 135.0
185 , 186.0, 220.0 ]
186
187-}
188(<>) :: Numeric t => Matrix t -> Matrix t -> Matrix t
189(<>) = mXm
190infixr 8 <>
191
192-- | dense matrix product
193mul :: Numeric t => Matrix t -> Matrix t -> Matrix t
194mul = mXm
195
196
197{- | Solve a linear system (for square coefficient matrix and several right-hand sides) using the LU decomposition, returning Nothing for a singular system. For underconstrained or overconstrained systems use 'linearSolveLS' or 'linearSolveSVD'.
198
199@
200a = (2><2)
201 [ 1.0, 2.0
202 , 3.0, 5.0 ]
203@
204
205@
206b = (2><3)
207 [ 6.0, 1.0, 10.0
208 , 15.0, 3.0, 26.0 ]
209@
210
211>>> linearSolve a b
212Just (2><3)
213 [ -1.4802973661668753e-15, 0.9999999999999997, 1.999999999999997
214 , 3.000000000000001, 1.6653345369377348e-16, 4.000000000000002 ]
215
216>>> let Just x = it
217>>> disp 5 x
2182x3
219-0.00000 1.00000 2.00000
220 3.00000 0.00000 4.00000
221
222>>> a <> x
223(2><3)
224 [ 6.0, 1.0, 10.0
225 , 15.0, 3.0, 26.0 ]
226
227-}
228linearSolve m b = A.mbLinearSolve m b
229
230-- | return an orthonormal basis of the null space of a matrix. See also 'nullspaceSVD'.
231nullspace m = nullspaceSVD (Left (1*eps)) m (rightSV m)
232
233-- | return an orthonormal basis of the range space of a matrix. See also 'orthSVD'.
234orth m = orthSVD (Left (1*eps)) m (leftSV m)
22 235
diff --git a/packages/base/src/Numeric/LinearAlgebra/Algorithms.hs b/packages/base/src/Numeric/LinearAlgebra/Algorithms.hs
index 02ac6a0..0e085c1 100644
--- a/packages/base/src/Numeric/LinearAlgebra/Algorithms.hs
+++ b/packages/base/src/Numeric/LinearAlgebra/Algorithms.hs
@@ -228,7 +228,9 @@ fromList [35.18264833189422,1.4769076999800903,1.089145439970417e-15]
228 228
229-} 229-}
230svd :: Field t => Matrix t -> (Matrix t, Vector Double, Matrix t) 230svd :: Field t => Matrix t -> (Matrix t, Vector Double, Matrix t)
231svd = {-# SCC "svd" #-} svd' 231svd = {-# SCC "svd" #-} g . svd'
232 where
233 g (u,s,v) = (u,s,tr v)
232 234
233{- | A version of 'svd' which returns only the @min (rows m) (cols m)@ singular vectors of @m@. 235{- | A version of 'svd' which returns only the @min (rows m) (cols m)@ singular vectors of @m@.
234 236
@@ -272,7 +274,10 @@ fromList [35.18264833189422,1.4769076999800903,1.089145439970417e-15]
272 274
273-} 275-}
274thinSVD :: Field t => Matrix t -> (Matrix t, Vector Double, Matrix t) 276thinSVD :: Field t => Matrix t -> (Matrix t, Vector Double, Matrix t)
275thinSVD = {-# SCC "thinSVD" #-} thinSVD' 277thinSVD = {-# SCC "thinSVD" #-} g . thinSVD'
278 where
279 g (u,s,v) = (u,s,tr v)
280
276 281
277-- | Singular values only. 282-- | Singular values only.
278singularValues :: Field t => Matrix t -> Vector Double 283singularValues :: Field t => Matrix t -> Vector Double
@@ -587,7 +592,7 @@ m = (3><3) [ 1, 0, 0
587-} 592-}
588 593
589pinvTol :: Field t => Double -> Matrix t -> Matrix t 594pinvTol :: Field t => Double -> Matrix t -> Matrix t
590pinvTol t m = conj v' `mXm` diag s' `mXm` ctrans u' where 595pinvTol t m = v' `mXm` diag s' `mXm` ctrans u' where
591 (u,s,v) = thinSVD m 596 (u,s,v) = thinSVD m
592 sl@(g:_) = toList s 597 sl@(g:_) = toList s
593 s' = real . fromList . map rec $ sl 598 s' = real . fromList . map rec $ sl
@@ -649,7 +654,7 @@ nullspaceSVD hint a (s,v) = vs where
649 k = case hint of 654 k = case hint of
650 Right t -> t 655 Right t -> t
651 _ -> rankSVD tol a s 656 _ -> rankSVD tol a s
652 vs = conj (dropColumns k v) 657 vs = dropColumns k v
653 658
654 659
655-- | The nullspace of a matrix. See also 'nullspaceSVD'. 660-- | The nullspace of a matrix. See also 'nullspaceSVD'.
@@ -935,10 +940,9 @@ relativeError' x y = dig (norm (x `sub` y) / norm x)
935 dig r = round $ -logBase 10 (realToFrac r :: Double) 940 dig r = round $ -logBase 10 (realToFrac r :: Double)
936 941
937 942
938relativeError :: (Normed c t, Num (c t)) => NormType -> c t -> c t -> Double 943relativeError :: Num a => (a -> Double) -> a -> a -> Double
939relativeError t a b = realToFrac r 944relativeError norm a b = r
940 where 945 where
941 norm = pnorm t
942 na = norm a 946 na = norm a
943 nb = norm b 947 nb = norm b
944 nab = norm (a-b) 948 nab = norm (a-b)
diff --git a/packages/base/src/Numeric/LinearAlgebra/HMatrix.hs b/packages/base/src/Numeric/LinearAlgebra/HMatrix.hs
index 677f9ee..8e67eb4 100644
--- a/packages/base/src/Numeric/LinearAlgebra/HMatrix.hs
+++ b/packages/base/src/Numeric/LinearAlgebra/HMatrix.hs
@@ -1,4 +1,4 @@
1----------------------------------------------------------------------------- 1--------------------------------------------------------------------------------
2{- | 2{- |
3Module : Numeric.LinearAlgebra.HMatrix 3Module : Numeric.LinearAlgebra.HMatrix
4Copyright : (c) Alberto Ruiz 2006-14 4Copyright : (c) Alberto Ruiz 2006-14
@@ -7,229 +7,11 @@ Maintainer : Alberto Ruiz
7Stability : provisional 7Stability : provisional
8 8
9-} 9-}
10----------------------------------------------------------------------------- 10--------------------------------------------------------------------------------
11module Numeric.LinearAlgebra.HMatrix (
12
13 -- * Basic types and data processing
14 module Numeric.LinearAlgebra.Data,
15
16 -- * Arithmetic and numeric classes
17 -- |
18 -- The standard numeric classes are defined elementwise:
19 --
20 -- >>> vector [1,2,3] * vector [3,0,-2]
21 -- fromList [3.0,0.0,-6.0]
22 --
23 -- >>> matrix 3 [1..9] * ident 3
24 -- (3><3)
25 -- [ 1.0, 0.0, 0.0
26 -- , 0.0, 5.0, 0.0
27 -- , 0.0, 0.0, 9.0 ]
28 --
29 -- In arithmetic operations single-element vectors and matrices
30 -- (created from numeric literals or using 'scalar') automatically
31 -- expand to match the dimensions of the other operand:
32 --
33 -- >>> 5 + 2*ident 3 :: Matrix Double
34 -- (3><3)
35 -- [ 7.0, 5.0, 5.0
36 -- , 5.0, 7.0, 5.0
37 -- , 5.0, 5.0, 7.0 ]
38 --
39 -- >>> matrix 3 [1..9] + matrix 1 [10,20,30]
40 -- (3><3)
41 -- [ 11.0, 12.0, 13.0
42 -- , 24.0, 25.0, 26.0
43 -- , 37.0, 38.0, 39.0 ]
44 --
45
46 -- * Products
47 -- ** dot
48 dot, (<·>),
49 -- ** matrix-vector
50 app, (#>), (!#>),
51 -- ** matrix-matrix
52 mul, (<>),
53 -- | The matrix product is also implemented in the "Data.Monoid" instance, where
54 -- single-element matrices (created from numeric literals or using 'scalar')
55 -- are used for scaling.
56 --
57 -- >>> import Data.Monoid as M
58 -- >>> let m = matrix 3 [1..6]
59 -- >>> m M.<> 2 M.<> diagl[0.5,1,0]
60 -- (2><3)
61 -- [ 1.0, 4.0, 0.0
62 -- , 4.0, 10.0, 0.0 ]
63 --
64 -- 'mconcat' uses 'optimiseMult' to get the optimal association order.
65
66
67 -- ** other
68 outer, kronecker, cross,
69 scale,
70 sumElements, prodElements,
71
72 -- * Linear Systems
73 (<\>),
74 linearSolve,
75 linearSolveLS,
76 linearSolveSVD,
77 luSolve,
78 cholSolve,
79 cgSolve,
80 cgSolve',
81
82 -- * Inverse and pseudoinverse
83 inv, pinv, pinvTol,
84
85 -- * Determinant and rank
86 rcond, rank,
87 det, invlndet,
88
89 -- * Norms
90 Normed(..),
91 norm_Frob, norm_nuclear,
92
93 -- * Nullspace and range
94 orth,
95 nullspace, null1, null1sym,
96
97 -- * SVD
98 svd,
99 thinSVD,
100 compactSVD,
101 singularValues,
102 leftSV, rightSV,
103
104 -- * Eigensystems
105 eig, eigSH, eigSH',
106 eigenvalues, eigenvaluesSH, eigenvaluesSH',
107 geigSH',
108
109 -- * QR
110 qr, rq, qrRaw, qrgr,
111
112 -- * Cholesky
113 chol, cholSH, mbCholSH,
114
115 -- * Hessenberg
116 hess,
117
118 -- * Schur
119 schur,
120
121 -- * LU
122 lu, luPacked,
123
124 -- * Matrix functions
125 expm,
126 sqrtm,
127 matFunc,
128
129 -- * Correlation and convolution
130 corr, conv, corrMin, corr2, conv2,
131
132 -- * Random arrays
133 11
134 Seed, RandDist(..), randomVector, rand, randn, gaussianSample, uniformSample, 12module Numeric.LinearAlgebra.HMatrix (
135 13 module Numeric.LinearAlgebra
136 -- * Misc
137 meanCov, rowOuters, peps, relativeError, haussholder, optimiseMult, udot, nullspaceSVD, orthSVD, ranksv,
138 ℝ,ℂ,iC,
139 -- * Auxiliary classes
140 Element, Container, Product, Numeric, LSDiv,
141 Complexable, RealElement,
142 RealOf, ComplexOf, SingleOf, DoubleOf,
143 IndexOf,
144 Field,
145-- Normed,
146 Transposable,
147 CGState(..),
148 Testable(..)
149) where 14) where
150 15
151import Numeric.LinearAlgebra.Data 16import Numeric.LinearAlgebra
152
153import Numeric.Matrix()
154import Numeric.Vector()
155import Data.Packed.Numeric hiding ((<>), mul)
156import Numeric.LinearAlgebra.Algorithms hiding (linearSolve,Normed,orth)
157import qualified Numeric.LinearAlgebra.Algorithms as A
158import Numeric.LinearAlgebra.Util
159import Numeric.LinearAlgebra.Random
160import Numeric.Sparse((!#>))
161import Numeric.LinearAlgebra.Util.CG
162
163{- | infix synonym of 'mul'
164
165>>> let a = (3><5) [1..]
166>>> a
167(3><5)
168 [ 1.0, 2.0, 3.0, 4.0, 5.0
169 , 6.0, 7.0, 8.0, 9.0, 10.0
170 , 11.0, 12.0, 13.0, 14.0, 15.0 ]
171
172>>> let b = (5><2) [1,3, 0,2, -1,5, 7,7, 6,0]
173>>> b
174(5><2)
175 [ 1.0, 3.0
176 , 0.0, 2.0
177 , -1.0, 5.0
178 , 7.0, 7.0
179 , 6.0, 0.0 ]
180
181>>> a <> b
182(3><2)
183 [ 56.0, 50.0
184 , 121.0, 135.0
185 , 186.0, 220.0 ]
186
187-}
188(<>) :: Numeric t => Matrix t -> Matrix t -> Matrix t
189(<>) = mXm
190infixr 8 <>
191
192-- | dense matrix product
193mul :: Numeric t => Matrix t -> Matrix t -> Matrix t
194mul = mXm
195
196
197{- | Solve a linear system (for square coefficient matrix and several right-hand sides) using the LU decomposition, returning Nothing for a singular system. For underconstrained or overconstrained systems use 'linearSolveLS' or 'linearSolveSVD'.
198
199@
200a = (2><2)
201 [ 1.0, 2.0
202 , 3.0, 5.0 ]
203@
204
205@
206b = (2><3)
207 [ 6.0, 1.0, 10.0
208 , 15.0, 3.0, 26.0 ]
209@
210
211>>> linearSolve a b
212Just (2><3)
213 [ -1.4802973661668753e-15, 0.9999999999999997, 1.999999999999997
214 , 3.000000000000001, 1.6653345369377348e-16, 4.000000000000002 ]
215
216>>> let Just x = it
217>>> disp 5 x
2182x3
219-0.00000 1.00000 2.00000
220 3.00000 0.00000 4.00000
221
222>>> a <> x
223(2><3)
224 [ 6.0, 1.0, 10.0
225 , 15.0, 3.0, 26.0 ]
226
227-}
228linearSolve m b = A.mbLinearSolve m b
229
230-- | return an orthonormal basis of the null space of a matrix. See also 'nullspaceSVD'.
231nullspace m = nullspaceSVD (Left (1*eps)) m (rightSV m)
232
233-- | return an orthonormal basis of the range space of a matrix. See also 'orthSVD'.
234orth m = orthSVD (Left (1*eps)) m (leftSV m)
235 17
diff --git a/packages/base/src/Numeric/LinearAlgebra/LAPACK.hs b/packages/base/src/Numeric/LinearAlgebra/LAPACK.hs
index e088fdc..d96e14f 100644
--- a/packages/base/src/Numeric/LinearAlgebra/LAPACK.hs
+++ b/packages/base/src/Numeric/LinearAlgebra/LAPACK.hs
@@ -115,7 +115,7 @@ svdAux f st x = unsafePerformIO $ do
115 s <- createVector (min r c) 115 s <- createVector (min r c)
116 v <- createMatrix ColumnMajor c c 116 v <- createMatrix ColumnMajor c c
117 app4 f mat x mat u vec s mat v st 117 app4 f mat x mat u vec s mat v st
118 return (u,s,trans v) 118 return (u,s,v)
119 where r = rows x 119 where r = rows x
120 c = cols x 120 c = cols x
121 121
@@ -141,7 +141,7 @@ thinSVDAux f st x = unsafePerformIO $ do
141 s <- createVector q 141 s <- createVector q
142 v <- createMatrix ColumnMajor q c 142 v <- createMatrix ColumnMajor q c
143 app4 f mat x mat u vec s mat v st 143 app4 f mat x mat u vec s mat v st
144 return (u,s,trans v) 144 return (u,s,v)
145 where r = rows x 145 where r = rows x
146 c = cols x 146 c = cols x
147 q = min r c 147 q = min r c
@@ -185,7 +185,7 @@ rightSVAux f st x = unsafePerformIO $ do
185 s <- createVector q 185 s <- createVector q
186 v <- createMatrix ColumnMajor c c 186 v <- createMatrix ColumnMajor c c
187 app3 g mat x vec s mat v st 187 app3 g mat x vec s mat v st
188 return (s,trans v) 188 return (s,v)
189 where r = rows x 189 where r = rows x
190 c = cols x 190 c = cols x
191 q = min r c 191 q = min r c
diff --git a/packages/base/src/Numeric/LinearAlgebra/Static.hs b/packages/base/src/Numeric/LinearAlgebra/Static.hs
index 3398e6a..25b10b4 100644
--- a/packages/base/src/Numeric/LinearAlgebra/Static.hs
+++ b/packages/base/src/Numeric/LinearAlgebra/Static.hs
@@ -1,5 +1,3 @@
1#if __GLASGOW_HASKELL__ >= 708
2
3{-# LANGUAGE DataKinds #-} 1{-# LANGUAGE DataKinds #-}
4{-# LANGUAGE KindSignatures #-} 2{-# LANGUAGE KindSignatures #-}
5{-# LANGUAGE GeneralizedNewtypeDeriving #-} 3{-# LANGUAGE GeneralizedNewtypeDeriving #-}
@@ -13,7 +11,6 @@
13{-# LANGUAGE TypeOperators #-} 11{-# LANGUAGE TypeOperators #-}
14{-# LANGUAGE ViewPatterns #-} 12{-# LANGUAGE ViewPatterns #-}
15{-# LANGUAGE GADTs #-} 13{-# LANGUAGE GADTs #-}
16{-# LANGUAGE OverlappingInstances #-}
17{-# LANGUAGE TypeFamilies #-} 14{-# LANGUAGE TypeFamilies #-}
18 15
19 16
@@ -63,13 +60,13 @@ module Numeric.LinearAlgebra.Static(
63 60
64 61
65import GHC.TypeLits 62import GHC.TypeLits
66import Numeric.LinearAlgebra.HMatrix hiding ( 63import Numeric.LinearAlgebra hiding (
67 (<>),(#>),(<·>),Konst(..),diag, disp,(¦),(——), 64 (<>),(#>),(<·>),Konst(..),diag, disp,(¦),(——),
68 row,col,vector,matrix,linspace,toRows,toColumns, 65 row,col,vector,matrix,linspace,toRows,toColumns,
69 (<\>),fromList,takeDiag,svd,eig,eigSH,eigSH', 66 (<\>),fromList,takeDiag,svd,eig,eigSH,eigSH',
70 eigenvalues,eigenvaluesSH,eigenvaluesSH',build, 67 eigenvalues,eigenvaluesSH,eigenvaluesSH',build,
71 qr,size,app,mul,dot,chol) 68 qr,size,app,mul,dot,chol)
72import qualified Numeric.LinearAlgebra.HMatrix as LA 69import qualified Numeric.LinearAlgebra as LA
73import Data.Proxy(Proxy) 70import Data.Proxy(Proxy)
74import Numeric.LinearAlgebra.Static.Internal 71import Numeric.LinearAlgebra.Static.Internal
75import Control.Arrow((***)) 72import Control.Arrow((***))
@@ -184,8 +181,9 @@ a ¦ b = tr (tr a —— tr b)
184type Sq n = L n n 181type Sq n = L n n
185--type CSq n = CL n n 182--type CSq n = CL n n
186 183
187type GL = forall n m. (KnownNat n, KnownNat m) => L m n 184
188type GSq = forall n. KnownNat n => Sq n 185type GL = forall n m . (KnownNat n, KnownNat m) => L m n
186type GSq = forall n . KnownNat n => Sq n
189 187
190isKonst :: forall m n . (KnownNat m, KnownNat n) => L m n -> Maybe (ℝ,(Int,Int)) 188isKonst :: forall m n . (KnownNat m, KnownNat n) => L m n -> Maybe (ℝ,(Int,Int))
191isKonst s@(unwrap -> x) 189isKonst s@(unwrap -> x)
@@ -618,23 +616,3 @@ instance (KnownNat n', KnownNat m') => Testable (L n' m')
618 where 616 where
619 checkT _ = test 617 checkT _ = test
620 618
621#else
622
623{- |
624Module : Numeric.LinearAlgebra.Static
625Copyright : (c) Alberto Ruiz 2014
626License : BSD3
627Stability : experimental
628
629Experimental interface with statically checked dimensions.
630
631This module requires GHC >= 7.8
632
633-}
634
635module Numeric.LinearAlgebra.Static
636{-# WARNING "This module requires GHC >= 7.8" #-}
637where
638
639#endif
640
diff --git a/packages/base/src/Numeric/LinearAlgebra/Static/Internal.hs b/packages/base/src/Numeric/LinearAlgebra/Static/Internal.hs
index ec02cf6..a5fc29b 100644
--- a/packages/base/src/Numeric/LinearAlgebra/Static/Internal.hs
+++ b/packages/base/src/Numeric/LinearAlgebra/Static/Internal.hs
@@ -24,8 +24,8 @@ module Numeric.LinearAlgebra.Static.Internal where
24 24
25 25
26import GHC.TypeLits 26import GHC.TypeLits
27import qualified Numeric.LinearAlgebra.HMatrix as LA 27import qualified Numeric.LinearAlgebra as LA
28import Numeric.LinearAlgebra.HMatrix hiding (konst,size) 28import Numeric.LinearAlgebra hiding (konst,size)
29import Data.Packed as D 29import Data.Packed as D
30import Data.Packed.ST 30import Data.Packed.ST
31import Data.Proxy(Proxy) 31import Data.Proxy(Proxy)
diff --git a/packages/base/src/Numeric/LinearAlgebra/Util.hs b/packages/base/src/Numeric/LinearAlgebra/Util.hs
index 043aa21..370ca27 100644
--- a/packages/base/src/Numeric/LinearAlgebra/Util.hs
+++ b/packages/base/src/Numeric/LinearAlgebra/Util.hs
@@ -16,7 +16,6 @@ Stability : provisional
16 16
17-} 17-}
18----------------------------------------------------------------------------- 18-----------------------------------------------------------------------------
19{-# OPTIONS_HADDOCK hide #-}
20 19
21module Numeric.LinearAlgebra.Util( 20module Numeric.LinearAlgebra.Util(
22 21
@@ -53,18 +52,7 @@ module Numeric.LinearAlgebra.Util(
53 -- ** 1D 52 -- ** 1D
54 corr, conv, corrMin, 53 corr, conv, corrMin,
55 -- ** 2D 54 -- ** 2D
56 corr2, conv2, separable, 55 corr2, conv2, separable
57 -- * Tools for the Kronecker product
58 --
59 -- | (see A. Fusiello, A matter of notation: Several uses of the Kronecker product in
60 -- 3d computer vision, Pattern Recognition Letters 28 (15) (2007) 2127-2132)
61
62 --
63 -- | @`vec` (a \<> x \<> b) == ('trans' b ` 'kronecker' ` a) \<> 'vec' x@
64 vec,
65 vech,
66 dup,
67 vtrans
68) where 56) where
69 57
70import Data.Packed.Numeric 58import Data.Packed.Numeric
@@ -227,10 +215,11 @@ infixl 9 ¿
227(¿)= flip extractColumns 215(¿)= flip extractColumns
228 216
229 217
230cross :: Vector Double -> Vector Double -> Vector Double 218cross :: Product t => Vector t -> Vector t -> Vector t
231-- ^ cross product (for three-element real vectors) 219-- ^ cross product (for three-element vectors)
232cross x y | dim x == 3 && dim y == 3 = fromList [z1,z2,z3] 220cross x y | dim x == 3 && dim y == 3 = fromList [z1,z2,z3]
233 | otherwise = error $ "cross ("++show x++") ("++show y++")" 221 | otherwise = error $ "the cross product requires 3-element vectors (sizes given: "
222 ++show (dim x)++" and "++show (dim y)++")"
234 where 223 where
235 [x1,x2,x3] = toList x 224 [x1,x2,x3] = toList x
236 [y1,y2,y3] = toList y 225 [y1,y2,y3] = toList y
@@ -238,6 +227,9 @@ cross x y | dim x == 3 && dim y == 3 = fromList [z1,z2,z3]
238 z2 = x3*y1-x1*y3 227 z2 = x3*y1-x1*y3
239 z3 = x1*y2-x2*y1 228 z3 = x1*y2-x2*y1
240 229
230{-# SPECIALIZE cross :: Vector Double -> Vector Double -> Vector Double #-}
231{-# SPECIALIZE cross :: Vector (Complex Double) -> Vector (Complex Double) -> Vector (Complex Double) #-}
232
241norm :: Vector Double -> Double 233norm :: Vector Double -> Double
242-- ^ 2-norm of real vector 234-- ^ 2-norm of real vector
243norm = pnorm PNorm2 235norm = pnorm PNorm2
@@ -403,40 +395,6 @@ null1sym = last . toColumns . snd . eigSH'
403 395
404-------------------------------------------------------------------------------- 396--------------------------------------------------------------------------------
405 397
406vec :: Element t => Matrix t -> Vector t
407-- ^ stacking of columns
408vec = flatten . trans
409
410
411vech :: Element t => Matrix t -> Vector t
412-- ^ half-vectorization (of the lower triangular part)
413vech m = vjoin . zipWith f [0..] . toColumns $ m
414 where
415 f k v = subVector k (dim v - k) v
416
417
418dup :: (Num t, Num (Vector t), Element t) => Int -> Matrix t
419-- ^ duplication matrix (@'dup' k \<> 'vech' m == 'vec' m@, for symmetric m of 'dim' k)
420dup k = trans $ fromRows $ map f es
421 where
422 rs = zip [0..] (toRows (ident (k^(2::Int))))
423 es = [(i,j) | j <- [0..k-1], i <- [0..k-1], i>=j ]
424 f (i,j) | i == j = g (k*j + i)
425 | otherwise = g (k*j + i) + g (k*i + j)
426 g j = v
427 where
428 Just v = lookup j rs
429
430
431vtrans :: Element t => Int -> Matrix t -> Matrix t
432-- ^ generalized \"vector\" transposition: @'vtrans' 1 == 'trans'@, and @'vtrans' ('rows' m) m == 'asColumn' ('vec' m)@
433vtrans p m | r == 0 = fromBlocks . map (map asColumn . takesV (replicate q p)) . toColumns $ m
434 | otherwise = error $ "vtrans " ++ show p ++ " of matrix with " ++ show (rows m) ++ " rows"
435 where
436 (q,r) = divMod (rows m) p
437
438--------------------------------------------------------------------------------
439
440infixl 0 ~!~ 398infixl 0 ~!~
441c ~!~ msg = when c (error msg) 399c ~!~ msg = when c (error msg)
442 400
diff --git a/packages/base/src/Numeric/LinearAlgebra/Util/CG.hs b/packages/base/src/Numeric/LinearAlgebra/Util/CG.hs
index b82c74f..899a5bf 100644
--- a/packages/base/src/Numeric/LinearAlgebra/Util/CG.hs
+++ b/packages/base/src/Numeric/LinearAlgebra/Util/CG.hs
@@ -9,7 +9,7 @@ module Numeric.LinearAlgebra.Util.CG(
9import Data.Packed.Numeric 9import Data.Packed.Numeric
10import Numeric.Sparse 10import Numeric.Sparse
11import Numeric.Vector() 11import Numeric.Vector()
12import Numeric.LinearAlgebra.Algorithms(linearSolveLS, relativeError, NormType(..)) 12import Numeric.LinearAlgebra.Algorithms(linearSolveLS, relativeError, pnorm, NormType(..))
13import Control.Arrow((***)) 13import Control.Arrow((***))
14 14
15{- 15{-
@@ -142,13 +142,13 @@ instance Testable GMatrix
142 print s3; print d3 142 print s3; print d3
143 print s4; print d4 143 print s4; print d4
144 print s5; print d5 144 print s5; print d5
145 print $ relativeError Infinity s5 d5 145 print $ relativeError (pnorm Infinity) s5 d5
146 146
147 ok = s1==d1 147 ok = s1==d1
148 && s2==d2 148 && s2==d2
149 && s3==d3 149 && s3==d3
150 && s4==d4 150 && s4==d4
151 && relativeError Infinity s5 d5 < 1E-10 151 && relativeError (pnorm Infinity) s5 d5 < 1E-10
152 152
153 disp = putStr . dispf 2 153 disp = putStr . dispf 2
154 154
diff --git a/packages/base/src/Numeric/Vectorized.hs b/packages/base/src/Numeric/Vectorized.hs
index 6f0d240..405ae01 100644
--- a/packages/base/src/Numeric/Vectorized.hs
+++ b/packages/base/src/Numeric/Vectorized.hs
@@ -37,7 +37,6 @@ import Foreign.C.String
37import System.IO.Unsafe(unsafePerformIO) 37import System.IO.Unsafe(unsafePerformIO)
38 38
39import Control.Monad(when) 39import Control.Monad(when)
40import Control.Applicative((<$>))
41 40
42 41
43 42
diff --git a/packages/glpk/hmatrix-glpk.cabal b/packages/glpk/hmatrix-glpk.cabal
index 5a1b59c..8593e0a 100644
--- a/packages/glpk/hmatrix-glpk.cabal
+++ b/packages/glpk/hmatrix-glpk.cabal
@@ -1,5 +1,5 @@
1Name: hmatrix-glpk 1Name: hmatrix-glpk
2Version: 0.4.1.0 2Version: 0.5.0.0
3License: GPL 3License: GPL
4License-file: LICENSE 4License-file: LICENSE
5Author: Alberto Ruiz 5Author: Alberto Ruiz
@@ -23,7 +23,7 @@ extra-source-files: examples/simplex1.hs
23 examples/simplex5.hs 23 examples/simplex5.hs
24 24
25library 25library
26 Build-Depends: base <5, hmatrix >= 0.16, containers >= 0.5.4.0 26 Build-Depends: base <5, hmatrix >= 0.17, containers
27 27
28 hs-source-dirs: src 28 hs-source-dirs: src
29 29
diff --git a/packages/glpk/src/Numeric/LinearProgramming.hs b/packages/glpk/src/Numeric/LinearProgramming.hs
index 6a0c47d..7bf4279 100644
--- a/packages/glpk/src/Numeric/LinearProgramming.hs
+++ b/packages/glpk/src/Numeric/LinearProgramming.hs
@@ -85,8 +85,8 @@ module Numeric.LinearProgramming(
85 Solution(..) 85 Solution(..)
86) where 86) where
87 87
88import Data.Packed 88import Numeric.LinearAlgebra.HMatrix
89import Data.Packed.Development 89import Numeric.LinearAlgebra.Devel hiding (Dense)
90import Foreign(Ptr) 90import Foreign(Ptr)
91import System.IO.Unsafe(unsafePerformIO) 91import System.IO.Unsafe(unsafePerformIO)
92import Foreign.C.Types 92import Foreign.C.Types
@@ -180,16 +180,17 @@ exact opt constr@(General _) bnds = exact opt (sparseOfGeneral constr) bnds
180 180
181adapt :: Optimization -> (Int, Double, [Double]) 181adapt :: Optimization -> (Int, Double, [Double])
182adapt opt = case opt of 182adapt opt = case opt of
183 Maximize x -> (size x, 1 ,x) 183 Maximize x -> (sz x, 1 ,x)
184 Minimize x -> (size x, -1, (map negate x)) 184 Minimize x -> (sz x, -1, (map negate x))
185 where size x | null x = error "simplex: objective function with zero variables" 185 where
186 | otherwise = length x 186 sz x | null x = error "simplex: objective function with zero variables"
187 | otherwise = length x
187 188
188extract :: Double -> Vector Double -> Solution 189extract :: Double -> Vector Double -> Solution
189extract sg sol = r where 190extract sg sol = r where
190 z = sg * (sol@>1) 191 z = sg * (sol!1)
191 v = toList $ subVector 2 (dim sol -2) sol 192 v = toList $ subVector 2 (size sol -2) sol
192 r = case round(sol@>0)::Int of 193 r = case round(sol!0)::Int of
193 1 -> Undefined 194 1 -> Undefined
194 2 -> Feasible (z,v) 195 2 -> Feasible (z,v)
195 3 -> Infeasible (z,v) 196 3 -> Infeasible (z,v)
@@ -261,7 +262,7 @@ mkConstrD n f b1 | ok = fromLists (ob ++ co)
261 ok = all (==n) ls 262 ok = all (==n) ls
262 den = fromLists cs 263 den = fromLists cs
263 ob = map (([0,0]++).return) f 264 ob = map (([0,0]++).return) f
264 co = [[fromIntegral i, fromIntegral j,den@@>(i-1,j-1)]| i<-[1 ..rows den], j<-[1 .. cols den]] 265 co = [[fromIntegral i, fromIntegral j,den `atIndex` (i-1,j-1)]| i<-[1 ..rows den], j<-[1 .. cols den]]
265 266
266mkConstrS :: Int -> [Double] -> [Bound [(Double, Int)]] -> Matrix Double 267mkConstrS :: Int -> [Double] -> [Bound [(Double, Int)]] -> Matrix Double
267mkConstrS n objfun b1 = fromLists (ob ++ co) where 268mkConstrS n objfun b1 = fromLists (ob ++ co) where
diff --git a/packages/glpk/src/Numeric/LinearProgramming/L1.hs b/packages/glpk/src/Numeric/LinearProgramming/L1.hs
index f55c721..d7f1258 100644
--- a/packages/glpk/src/Numeric/LinearProgramming/L1.hs
+++ b/packages/glpk/src/Numeric/LinearProgramming/L1.hs
@@ -14,7 +14,7 @@ module Numeric.LinearProgramming.L1 (
14 l1SolveU, 14 l1SolveU,
15) where 15) where
16 16
17import Numeric.LinearAlgebra 17import Numeric.LinearAlgebra.HMatrix
18import Numeric.LinearProgramming 18import Numeric.LinearProgramming
19 19
20-- | L_inf solution of overconstrained system Ax=b. 20-- | L_inf solution of overconstrained system Ax=b.
diff --git a/packages/gsl/CHANGELOG b/packages/gsl/CHANGELOG
new file mode 100644
index 0000000..b83973a
--- /dev/null
+++ b/packages/gsl/CHANGELOG
@@ -0,0 +1,10 @@
10.17.0.0
2--------
3
4 * Added interpolation modules
5
60.16.0.0
7--------
8
9 * The modules Numeric.GSL.* have been moved from hmatrix to the new package hmatrix-gsl.
10
diff --git a/packages/gsl/THANKS.md b/packages/gsl/THANKS.md
new file mode 100644
index 0000000..b066185
--- /dev/null
+++ b/packages/gsl/THANKS.md
@@ -0,0 +1,4 @@
1Matt Peddie wrote the interpolation interface.
2
3(see also the THANKS file of the hmatrix package)
4
diff --git a/packages/gsl/hmatrix-gsl.cabal b/packages/gsl/hmatrix-gsl.cabal
index 2f6f51b..7028bae 100644
--- a/packages/gsl/hmatrix-gsl.cabal
+++ b/packages/gsl/hmatrix-gsl.cabal
@@ -1,5 +1,5 @@
1Name: hmatrix-gsl 1Name: hmatrix-gsl
2Version: 0.16.0.3 2Version: 0.17.0.0
3License: GPL 3License: GPL
4License-file: LICENSE 4License-file: LICENSE
5Author: Alberto Ruiz 5Author: Alberto Ruiz
@@ -25,7 +25,7 @@ flag onlygsl
25 25
26library 26library
27 27
28 Build-Depends: base<5, hmatrix>=0.16, array, vector, 28 Build-Depends: base<5, hmatrix>=0.17, array, vector,
29 process, random 29 process, random
30 30
31 31
diff --git a/packages/gsl/src/Graphics/Plot.hs b/packages/gsl/src/Graphics/Plot.hs
index 0ea41ac..d2ea192 100644
--- a/packages/gsl/src/Graphics/Plot.hs
+++ b/packages/gsl/src/Graphics/Plot.hs
@@ -27,13 +27,13 @@ module Graphics.Plot(
27 27
28) where 28) where
29 29
30import Numeric.Container 30import Numeric.LinearAlgebra.HMatrix
31import Data.List(intersperse) 31import Data.List(intersperse)
32import System.Process (system) 32import System.Process (system)
33 33
34-- | From vectors x and y, it generates a pair of matrices to be used as x and y arguments for matrix functions. 34-- | From vectors x and y, it generates a pair of matrices to be used as x and y arguments for matrix functions.
35meshdom :: Vector Double -> Vector Double -> (Matrix Double , Matrix Double) 35meshdom :: Vector Double -> Vector Double -> (Matrix Double , Matrix Double)
36meshdom r1 r2 = (outer r1 (constant 1 (dim r2)), outer (constant 1 (dim r1)) r2) 36meshdom r1 r2 = (outer r1 (konst 1 (size r2)), outer (konst 1 (size r1)) r2)
37 37
38 38
39{- | Draws a 3D surface representation of a real matrix. 39{- | Draws a 3D surface representation of a real matrix.
diff --git a/packages/gsl/src/Numeric/GSL/Fitting.hs b/packages/gsl/src/Numeric/GSL/Fitting.hs
index 0a92373..db9d82f 100644
--- a/packages/gsl/src/Numeric/GSL/Fitting.hs
+++ b/packages/gsl/src/Numeric/GSL/Fitting.hs
@@ -1,3 +1,5 @@
1{-# LANGUAGE FlexibleContexts #-}
2
1{- | 3{- |
2Module : Numeric.GSL.Fitting 4Module : Numeric.GSL.Fitting
3Copyright : (c) Alberto Ruiz 2010 5Copyright : (c) Alberto Ruiz 2010
@@ -50,7 +52,7 @@ module Numeric.GSL.Fitting (
50 fitModelScaled, fitModel 52 fitModelScaled, fitModel
51) where 53) where
52 54
53import Numeric.LinearAlgebra 55import Numeric.LinearAlgebra.HMatrix
54import Numeric.GSL.Internal 56import Numeric.GSL.Internal
55 57
56import Foreign.Ptr(FunPtr, freeHaskellFunPtr) 58import Foreign.Ptr(FunPtr, freeHaskellFunPtr)
@@ -80,13 +82,13 @@ nlFitting :: FittingMethod
80nlFitting method epsabs epsrel maxit fun jac xinit = nlFitGen (fi (fromEnum method)) fun jac xinit epsabs epsrel maxit 82nlFitting method epsabs epsrel maxit fun jac xinit = nlFitGen (fi (fromEnum method)) fun jac xinit epsabs epsrel maxit
81 83
82nlFitGen m f jac xiv epsabs epsrel maxit = unsafePerformIO $ do 84nlFitGen m f jac xiv epsabs epsrel maxit = unsafePerformIO $ do
83 let p = dim xiv 85 let p = size xiv
84 n = dim (f xiv) 86 n = size (f xiv)
85 fp <- mkVecVecfun (aux_vTov (checkdim1 n p . f)) 87 fp <- mkVecVecfun (aux_vTov (checkdim1 n p . f))
86 jp <- mkVecMatfun (aux_vTom (checkdim2 n p . jac)) 88 jp <- mkVecMatfun (aux_vTom (checkdim2 n p . jac))
87 rawpath <- createMatrix RowMajor maxit (2+p) 89 rawpath <- createMatrix RowMajor maxit (2+p)
88 app2 (c_nlfit m fp jp epsabs epsrel (fi maxit) (fi n)) vec xiv mat rawpath "c_nlfit" 90 app2 (c_nlfit m fp jp epsabs epsrel (fi maxit) (fi n)) vec xiv mat rawpath "c_nlfit"
89 let it = round (rawpath @@> (maxit-1,0)) 91 let it = round (rawpath `atIndex` (maxit-1,0))
90 path = takeRows it rawpath 92 path = takeRows it rawpath
91 [sol] = toRows $ dropRows (it-1) path 93 [sol] = toRows $ dropRows (it-1) path
92 freeHaskellFunPtr fp 94 freeHaskellFunPtr fp
@@ -99,7 +101,7 @@ foreign import ccall safe "nlfit"
99------------------------------------------------------- 101-------------------------------------------------------
100 102
101checkdim1 n _p v 103checkdim1 n _p v
102 | dim v == n = v 104 | size v == n = v
103 | otherwise = error $ "Error: "++ show n 105 | otherwise = error $ "Error: "++ show n
104 ++ " components expected in the result of the function supplied to nlFitting" 106 ++ " components expected in the result of the function supplied to nlFitting"
105 107
@@ -114,9 +116,9 @@ err (model,deriv) dat vsol = zip sol errs where
114 sol = toList vsol 116 sol = toList vsol
115 c = max 1 (chi/sqrt (fromIntegral dof)) 117 c = max 1 (chi/sqrt (fromIntegral dof))
116 dof = length dat - (rows cov) 118 dof = length dat - (rows cov)
117 chi = norm2 (fromList $ cost (resMs model) dat sol) 119 chi = norm_2 (fromList $ cost (resMs model) dat sol)
118 js = fromLists $ jacobian (resDs deriv) dat sol 120 js = fromLists $ jacobian (resDs deriv) dat sol
119 cov = inv $ trans js <> js 121 cov = inv $ tr js <> js
120 errs = toList $ scalar c * sqrt (takeDiag cov) 122 errs = toList $ scalar c * sqrt (takeDiag cov)
121 123
122 124
diff --git a/packages/gsl/src/Numeric/GSL/Fourier.hs b/packages/gsl/src/Numeric/GSL/Fourier.hs
index 734325b..d824b4f 100644
--- a/packages/gsl/src/Numeric/GSL/Fourier.hs
+++ b/packages/gsl/src/Numeric/GSL/Fourier.hs
@@ -16,14 +16,13 @@ module Numeric.GSL.Fourier (
16 ifft 16 ifft
17) where 17) where
18 18
19import Data.Packed 19import Numeric.LinearAlgebra.HMatrix
20import Numeric.GSL.Internal 20import Numeric.GSL.Internal
21import Data.Complex
22import Foreign.C.Types 21import Foreign.C.Types
23import System.IO.Unsafe (unsafePerformIO) 22import System.IO.Unsafe (unsafePerformIO)
24 23
25genfft code v = unsafePerformIO $ do 24genfft code v = unsafePerformIO $ do
26 r <- createVector (dim v) 25 r <- createVector (size v)
27 app2 (c_fft code) vec v vec r "fft" 26 app2 (c_fft code) vec v vec r "fft"
28 return r 27 return r
29 28
diff --git a/packages/gsl/src/Numeric/GSL/IO.hs b/packages/gsl/src/Numeric/GSL/IO.hs
index 0d6031a..936f6bf 100644
--- a/packages/gsl/src/Numeric/GSL/IO.hs
+++ b/packages/gsl/src/Numeric/GSL/IO.hs
@@ -14,7 +14,7 @@ module Numeric.GSL.IO (
14 fileDimensions, loadMatrix, fromFile 14 fileDimensions, loadMatrix, fromFile
15) where 15) where
16 16
17import Data.Packed 17import Numeric.LinearAlgebra.HMatrix hiding(saveMatrix, loadMatrix)
18import Numeric.GSL.Vector 18import Numeric.GSL.Vector
19import System.Process(readProcess) 19import System.Process(readProcess)
20 20
diff --git a/packages/gsl/src/Numeric/GSL/Internal.hs b/packages/gsl/src/Numeric/GSL/Internal.hs
index a1c4e0c..a269224 100644
--- a/packages/gsl/src/Numeric/GSL/Internal.hs
+++ b/packages/gsl/src/Numeric/GSL/Internal.hs
@@ -22,14 +22,13 @@ module Numeric.GSL.Internal(
22 aux_vTom, 22 aux_vTom,
23 createV, 23 createV,
24 createMIO, 24 createMIO,
25 module Data.Packed.Development, 25 module Numeric.LinearAlgebra.Devel,
26 check, 26 check,
27 Res,TV,TM,TCV,TCM 27 Res,TV,TM,TCV,TCM
28) where 28) where
29 29
30import Data.Packed 30import Numeric.LinearAlgebra.HMatrix
31import Data.Packed.Development hiding (check) 31import Numeric.LinearAlgebra.Devel hiding (check)
32import Data.Complex
33 32
34import Foreign.Marshal.Array(copyArray) 33import Foreign.Marshal.Array(copyArray)
35import Foreign.Ptr(Ptr, FunPtr) 34import Foreign.Ptr(Ptr, FunPtr)
diff --git a/packages/gsl/src/Numeric/GSL/LinearAlgebra.hs b/packages/gsl/src/Numeric/GSL/LinearAlgebra.hs
index 17e2258..cb78bf4 100644
--- a/packages/gsl/src/Numeric/GSL/LinearAlgebra.hs
+++ b/packages/gsl/src/Numeric/GSL/LinearAlgebra.hs
@@ -15,7 +15,7 @@ module Numeric.GSL.LinearAlgebra (
15 fileDimensions, loadMatrix, fromFile 15 fileDimensions, loadMatrix, fromFile
16) where 16) where
17 17
18import Data.Packed 18import Numeric.LinearAlgebra.HMatrix hiding (RandDist,randomVector,saveMatrix,loadMatrix)
19import Numeric.GSL.Internal hiding (TV,TM,TCV,TCM) 19import Numeric.GSL.Internal hiding (TV,TM,TCV,TCM)
20 20
21import Foreign.Marshal.Alloc(free) 21import Foreign.Marshal.Alloc(free)
diff --git a/packages/gsl/src/Numeric/GSL/Minimization.hs b/packages/gsl/src/Numeric/GSL/Minimization.hs
index 056d463..00e0619 100644
--- a/packages/gsl/src/Numeric/GSL/Minimization.hs
+++ b/packages/gsl/src/Numeric/GSL/Minimization.hs
@@ -1,3 +1,6 @@
1{-# LANGUAGE FlexibleContexts #-}
2
3
1{- | 4{- |
2Module : Numeric.GSL.Minimization 5Module : Numeric.GSL.Minimization
3Copyright : (c) Alberto Ruiz 2006-9 6Copyright : (c) Alberto Ruiz 2006-9
@@ -56,7 +59,7 @@ module Numeric.GSL.Minimization (
56) where 59) where
57 60
58 61
59import Data.Packed 62import Numeric.LinearAlgebra.HMatrix hiding(step)
60import Numeric.GSL.Internal 63import Numeric.GSL.Internal
61 64
62import Foreign.Ptr(Ptr, FunPtr, freeHaskellFunPtr) 65import Foreign.Ptr(Ptr, FunPtr, freeHaskellFunPtr)
@@ -99,7 +102,7 @@ uniMinimizeGen m f xmin xl xu epsrel maxit = unsafePerformIO $ do
99 rawpath <- createMIO maxit 4 102 rawpath <- createMIO maxit 4
100 (c_uniMinize m fp epsrel (fi maxit) xmin xl xu) 103 (c_uniMinize m fp epsrel (fi maxit) xmin xl xu)
101 "uniMinimize" 104 "uniMinimize"
102 let it = round (rawpath @@> (maxit-1,0)) 105 let it = round (rawpath `atIndex` (maxit-1,0))
103 path = takeRows it rawpath 106 path = takeRows it rawpath
104 [sol] = toLists $ dropRows (it-1) path 107 [sol] = toLists $ dropRows (it-1) path
105 freeHaskellFunPtr fp 108 freeHaskellFunPtr fp
@@ -137,13 +140,13 @@ minimize method eps maxit sz f xi = v2l $ minimizeV method eps maxit (fromList s
137ww2 w1 o1 w2 o2 f = w1 o1 $ \a1 -> w2 o2 $ \a2 -> f a1 a2 140ww2 w1 o1 w2 o2 f = w1 o1 $ \a1 -> w2 o2 $ \a2 -> f a1 a2
138 141
139minimizeV method eps maxit szv f xiv = unsafePerformIO $ do 142minimizeV method eps maxit szv f xiv = unsafePerformIO $ do
140 let n = dim xiv 143 let n = size xiv
141 fp <- mkVecfun (iv f) 144 fp <- mkVecfun (iv f)
142 rawpath <- ww2 vec xiv vec szv $ \xiv' szv' -> 145 rawpath <- ww2 vec xiv vec szv $ \xiv' szv' ->
143 createMIO maxit (n+3) 146 createMIO maxit (n+3)
144 (c_minimize (fi (fromEnum method)) fp eps (fi maxit) // xiv' // szv') 147 (c_minimize (fi (fromEnum method)) fp eps (fi maxit) // xiv' // szv')
145 "minimize" 148 "minimize"
146 let it = round (rawpath @@> (maxit-1,0)) 149 let it = round (rawpath `atIndex` (maxit-1,0))
147 path = takeRows it rawpath 150 path = takeRows it rawpath
148 sol = flatten $ dropColumns 3 $ dropRows (it-1) path 151 sol = flatten $ dropColumns 3 $ dropRows (it-1) path
149 freeHaskellFunPtr fp 152 freeHaskellFunPtr fp
@@ -191,7 +194,7 @@ minimizeD method eps maxit istep tol f df xi = v2l $ minimizeVD
191 194
192 195
193minimizeVD method eps maxit istep tol f df xiv = unsafePerformIO $ do 196minimizeVD method eps maxit istep tol f df xiv = unsafePerformIO $ do
194 let n = dim xiv 197 let n = size xiv
195 f' = f 198 f' = f
196 df' = (checkdim1 n . df) 199 df' = (checkdim1 n . df)
197 fp <- mkVecfun (iv f') 200 fp <- mkVecfun (iv f')
@@ -200,7 +203,7 @@ minimizeVD method eps maxit istep tol f df xiv = unsafePerformIO $ do
200 createMIO maxit (n+2) 203 createMIO maxit (n+2)
201 (c_minimizeD (fi (fromEnum method)) fp dfp istep tol eps (fi maxit) // xiv') 204 (c_minimizeD (fi (fromEnum method)) fp dfp istep tol eps (fi maxit) // xiv')
202 "minimizeD" 205 "minimizeD"
203 let it = round (rawpath @@> (maxit-1,0)) 206 let it = round (rawpath `atIndex` (maxit-1,0))
204 path = takeRows it rawpath 207 path = takeRows it rawpath
205 sol = flatten $ dropColumns 2 $ dropRows (it-1) path 208 sol = flatten $ dropColumns 2 $ dropRows (it-1) path
206 freeHaskellFunPtr fp 209 freeHaskellFunPtr fp
@@ -217,6 +220,6 @@ foreign import ccall safe "gsl-aux.h minimizeD"
217--------------------------------------------------------------------- 220---------------------------------------------------------------------
218 221
219checkdim1 n v 222checkdim1 n v
220 | dim v == n = v 223 | size v == n = v
221 | otherwise = error $ "Error: "++ show n 224 | otherwise = error $ "Error: "++ show n
222 ++ " components expected in the result of the gradient supplied to minimizeD" 225 ++ " components expected in the result of the gradient supplied to minimizeD"
diff --git a/packages/gsl/src/Numeric/GSL/ODE.hs b/packages/gsl/src/Numeric/GSL/ODE.hs
index 7549a65..3258b83 100644
--- a/packages/gsl/src/Numeric/GSL/ODE.hs
+++ b/packages/gsl/src/Numeric/GSL/ODE.hs
@@ -1,3 +1,6 @@
1{-# LANGUAGE FlexibleContexts #-}
2
3
1{- | 4{- |
2Module : Numeric.GSL.ODE 5Module : Numeric.GSL.ODE
3Copyright : (c) Alberto Ruiz 2010 6Copyright : (c) Alberto Ruiz 2010
@@ -32,7 +35,7 @@ module Numeric.GSL.ODE (
32 odeSolve, odeSolveV, ODEMethod(..), Jacobian 35 odeSolve, odeSolveV, ODEMethod(..), Jacobian
33) where 36) where
34 37
35import Data.Packed 38import Numeric.LinearAlgebra.HMatrix
36import Numeric.GSL.Internal 39import Numeric.GSL.Internal
37 40
38import Foreign.Ptr(FunPtr, nullFunPtr, freeHaskellFunPtr) 41import Foreign.Ptr(FunPtr, nullFunPtr, freeHaskellFunPtr)
@@ -68,7 +71,7 @@ odeSolve
68 -> Vector Double -- ^ desired solution times 71 -> Vector Double -- ^ desired solution times
69 -> Matrix Double -- ^ solution 72 -> Matrix Double -- ^ solution
70odeSolve xdot xi ts = odeSolveV RKf45 hi epsAbs epsRel (l2v xdot) (fromList xi) ts 73odeSolve xdot xi ts = odeSolveV RKf45 hi epsAbs epsRel (l2v xdot) (fromList xi) ts
71 where hi = (ts@>1 - ts@>0)/100 74 where hi = (ts!1 - ts!0)/100
72 epsAbs = 1.49012e-08 75 epsAbs = 1.49012e-08
73 epsRel = 1.49012e-08 76 epsRel = 1.49012e-08
74 l2v f = \t -> fromList . f t . toList 77 l2v f = \t -> fromList . f t . toList
@@ -107,14 +110,14 @@ odeSolveV'
107 -> Vector Double -- ^ desired solution times 110 -> Vector Double -- ^ desired solution times
108 -> Matrix Double -- ^ solution 111 -> Matrix Double -- ^ solution
109odeSolveV' method mbjac h epsAbs epsRel f xiv ts = unsafePerformIO $ do 112odeSolveV' method mbjac h epsAbs epsRel f xiv ts = unsafePerformIO $ do
110 let n = dim xiv 113 let n = size xiv
111 fp <- mkDoubleVecVecfun (\t -> aux_vTov (checkdim1 n . f t)) 114 fp <- mkDoubleVecVecfun (\t -> aux_vTov (checkdim1 n . f t))
112 jp <- case mbjac of 115 jp <- case mbjac of
113 Just jac -> mkDoubleVecMatfun (\t -> aux_vTom (checkdim2 n . jac t)) 116 Just jac -> mkDoubleVecMatfun (\t -> aux_vTom (checkdim2 n . jac t))
114 Nothing -> return nullFunPtr 117 Nothing -> return nullFunPtr
115 sol <- vec xiv $ \xiv' -> 118 sol <- vec xiv $ \xiv' ->
116 vec (checkTimes ts) $ \ts' -> 119 vec (checkTimes ts) $ \ts' ->
117 createMIO (dim ts) n 120 createMIO (size ts) n
118 (ode_c (method) h epsAbs epsRel fp jp // xiv' // ts' ) 121 (ode_c (method) h epsAbs epsRel fp jp // xiv' // ts' )
119 "ode" 122 "ode"
120 freeHaskellFunPtr fp 123 freeHaskellFunPtr fp
@@ -126,7 +129,7 @@ foreign import ccall safe "ode"
126------------------------------------------------------- 129-------------------------------------------------------
127 130
128checkdim1 n v 131checkdim1 n v
129 | dim v == n = v 132 | size v == n = v
130 | otherwise = error $ "Error: "++ show n 133 | otherwise = error $ "Error: "++ show n
131 ++ " components expected in the result of the function supplied to odeSolve" 134 ++ " components expected in the result of the function supplied to odeSolve"
132 135
@@ -135,6 +138,7 @@ checkdim2 n m
135 | otherwise = error $ "Error: "++ show n ++ "x" ++ show n 138 | otherwise = error $ "Error: "++ show n ++ "x" ++ show n
136 ++ " Jacobian expected in odeSolve" 139 ++ " Jacobian expected in odeSolve"
137 140
138checkTimes ts | dim ts > 1 && all (>0) (zipWith subtract ts' (tail ts')) = ts 141checkTimes ts | size ts > 1 && all (>0) (zipWith subtract ts' (tail ts')) = ts
139 | otherwise = error "odeSolve requires increasing times" 142 | otherwise = error "odeSolve requires increasing times"
140 where ts' = toList ts 143 where ts' = toList ts
144
diff --git a/packages/gsl/src/Numeric/GSL/Polynomials.hs b/packages/gsl/src/Numeric/GSL/Polynomials.hs
index b1be85d..246e301 100644
--- a/packages/gsl/src/Numeric/GSL/Polynomials.hs
+++ b/packages/gsl/src/Numeric/GSL/Polynomials.hs
@@ -16,9 +16,8 @@ module Numeric.GSL.Polynomials (
16 polySolve 16 polySolve
17) where 17) where
18 18
19import Data.Packed 19import Numeric.LinearAlgebra.HMatrix
20import Numeric.GSL.Internal 20import Numeric.GSL.Internal
21import Data.Complex
22import System.IO.Unsafe (unsafePerformIO) 21import System.IO.Unsafe (unsafePerformIO)
23 22
24#if __GLASGOW_HASKELL__ >= 704 23#if __GLASGOW_HASKELL__ >= 704
@@ -47,8 +46,8 @@ polySolve :: [Double] -> [Complex Double]
47polySolve = toList . polySolve' . fromList 46polySolve = toList . polySolve' . fromList
48 47
49polySolve' :: Vector Double -> Vector (Complex Double) 48polySolve' :: Vector Double -> Vector (Complex Double)
50polySolve' v | dim v > 1 = unsafePerformIO $ do 49polySolve' v | size v > 1 = unsafePerformIO $ do
51 r <- createVector (dim v-1) 50 r <- createVector (size v-1)
52 app2 c_polySolve vec v vec r "polySolve" 51 app2 c_polySolve vec v vec r "polySolve"
53 return r 52 return r
54 | otherwise = error "polySolve on a polynomial of degree zero" 53 | otherwise = error "polySolve on a polynomial of degree zero"
diff --git a/packages/gsl/src/Numeric/GSL/Random.hs b/packages/gsl/src/Numeric/GSL/Random.hs
index f1f49e5..139c921 100644
--- a/packages/gsl/src/Numeric/GSL/Random.hs
+++ b/packages/gsl/src/Numeric/GSL/Random.hs
@@ -21,11 +21,13 @@ module Numeric.GSL.Random (
21) where 21) where
22 22
23import Numeric.GSL.Vector 23import Numeric.GSL.Vector
24import Numeric.LinearAlgebra(cholSH) 24import Numeric.LinearAlgebra.HMatrix hiding (
25import Numeric.Container hiding (
26 randomVector, 25 randomVector,
27 gaussianSample, 26 gaussianSample,
28 uniformSample 27 uniformSample,
28 Seed,
29 rand,
30 randn
29 ) 31 )
30import System.Random(randomIO) 32import System.Random(randomIO)
31 33
@@ -40,10 +42,10 @@ gaussianSample :: Seed
40 -> Matrix Double -- ^ covariance matrix 42 -> Matrix Double -- ^ covariance matrix
41 -> Matrix Double -- ^ result 43 -> Matrix Double -- ^ result
42gaussianSample seed n med cov = m where 44gaussianSample seed n med cov = m where
43 c = dim med 45 c = size med
44 meds = konst 1 n `outer` med 46 meds = konst 1 n `outer` med
45 rs = reshape c $ randomVector seed Gaussian (c * n) 47 rs = reshape c $ randomVector seed Gaussian (c * n)
46 m = rs `mXm` cholSH cov `add` meds 48 m = rs <> cholSH cov + meds
47 49
48-- | Obtains a matrix whose rows are pseudorandom samples from a multivariate 50-- | Obtains a matrix whose rows are pseudorandom samples from a multivariate
49-- uniform distribution. 51-- uniform distribution.
@@ -55,10 +57,10 @@ uniformSample seed n rgs = m where
55 (as,bs) = unzip rgs 57 (as,bs) = unzip rgs
56 a = fromList as 58 a = fromList as
57 cs = zipWith subtract as bs 59 cs = zipWith subtract as bs
58 d = dim a 60 d = size a
59 dat = toRows $ reshape n $ randomVector seed Uniform (n*d) 61 dat = toRows $ reshape n $ randomVector seed Uniform (n*d)
60 am = konst 1 n `outer` a 62 am = konst 1 n `outer` a
61 m = fromColumns (zipWith scale cs dat) `add` am 63 m = fromColumns (zipWith scale cs dat) + am
62 64
63-- | pseudorandom matrix with uniform elements between 0 and 1 65-- | pseudorandom matrix with uniform elements between 0 and 1
64randm :: RandDist 66randm :: RandDist
diff --git a/packages/gsl/src/Numeric/GSL/Root.hs b/packages/gsl/src/Numeric/GSL/Root.hs
index b9f3b94..724f32f 100644
--- a/packages/gsl/src/Numeric/GSL/Root.hs
+++ b/packages/gsl/src/Numeric/GSL/Root.hs
@@ -1,3 +1,5 @@
1{-# LANGUAGE FlexibleContexts #-}
2
1{- | 3{- |
2Module : Numeric.GSL.Root 4Module : Numeric.GSL.Root
3Copyright : (c) Alberto Ruiz 2009 5Copyright : (c) Alberto Ruiz 2009
@@ -39,7 +41,7 @@ module Numeric.GSL.Root (
39 rootJ, RootMethodJ(..), 41 rootJ, RootMethodJ(..),
40) where 42) where
41 43
42import Data.Packed 44import Numeric.LinearAlgebra.HMatrix
43import Numeric.GSL.Internal 45import Numeric.GSL.Internal
44import Foreign.Ptr(FunPtr, freeHaskellFunPtr) 46import Foreign.Ptr(FunPtr, freeHaskellFunPtr)
45import Foreign.C.Types 47import Foreign.C.Types
@@ -69,7 +71,7 @@ uniRootGen m f xl xu epsrel maxit = unsafePerformIO $ do
69 rawpath <- createMIO maxit 4 71 rawpath <- createMIO maxit 4
70 (c_root m fp epsrel (fi maxit) xl xu) 72 (c_root m fp epsrel (fi maxit) xl xu)
71 "root" 73 "root"
72 let it = round (rawpath @@> (maxit-1,0)) 74 let it = round (rawpath `atIndex` (maxit-1,0))
73 path = takeRows it rawpath 75 path = takeRows it rawpath
74 [sol] = toLists $ dropRows (it-1) path 76 [sol] = toLists $ dropRows (it-1) path
75 freeHaskellFunPtr fp 77 freeHaskellFunPtr fp
@@ -100,7 +102,7 @@ uniRootJGen m f df x epsrel maxit = unsafePerformIO $ do
100 rawpath <- createMIO maxit 2 102 rawpath <- createMIO maxit 2
101 (c_rootj m fp dfp epsrel (fi maxit) x) 103 (c_rootj m fp dfp epsrel (fi maxit) x)
102 "rootj" 104 "rootj"
103 let it = round (rawpath @@> (maxit-1,0)) 105 let it = round (rawpath `atIndex` (maxit-1,0))
104 path = takeRows it rawpath 106 path = takeRows it rawpath
105 [sol] = toLists $ dropRows (it-1) path 107 [sol] = toLists $ dropRows (it-1) path
106 freeHaskellFunPtr fp 108 freeHaskellFunPtr fp
@@ -132,13 +134,13 @@ root method epsabs maxit fun xinit = rootGen (fi (fromEnum method)) fun xinit ep
132 134
133rootGen m f xi epsabs maxit = unsafePerformIO $ do 135rootGen m f xi epsabs maxit = unsafePerformIO $ do
134 let xiv = fromList xi 136 let xiv = fromList xi
135 n = dim xiv 137 n = size xiv
136 fp <- mkVecVecfun (aux_vTov (checkdim1 n . fromList . f . toList)) 138 fp <- mkVecVecfun (aux_vTov (checkdim1 n . fromList . f . toList))
137 rawpath <- vec xiv $ \xiv' -> 139 rawpath <- vec xiv $ \xiv' ->
138 createMIO maxit (2*n+1) 140 createMIO maxit (2*n+1)
139 (c_multiroot m fp epsabs (fi maxit) // xiv') 141 (c_multiroot m fp epsabs (fi maxit) // xiv')
140 "multiroot" 142 "multiroot"
141 let it = round (rawpath @@> (maxit-1,0)) 143 let it = round (rawpath `atIndex` (maxit-1,0))
142 path = takeRows it rawpath 144 path = takeRows it rawpath
143 [sol] = toLists $ dropRows (it-1) path 145 [sol] = toLists $ dropRows (it-1) path
144 freeHaskellFunPtr fp 146 freeHaskellFunPtr fp
@@ -169,14 +171,14 @@ rootJ method epsabs maxit fun jac xinit = rootJGen (fi (fromEnum method)) fun ja
169 171
170rootJGen m f jac xi epsabs maxit = unsafePerformIO $ do 172rootJGen m f jac xi epsabs maxit = unsafePerformIO $ do
171 let xiv = fromList xi 173 let xiv = fromList xi
172 n = dim xiv 174 n = size xiv
173 fp <- mkVecVecfun (aux_vTov (checkdim1 n . fromList . f . toList)) 175 fp <- mkVecVecfun (aux_vTov (checkdim1 n . fromList . f . toList))
174 jp <- mkVecMatfun (aux_vTom (checkdim2 n . fromLists . jac . toList)) 176 jp <- mkVecMatfun (aux_vTom (checkdim2 n . fromLists . jac . toList))
175 rawpath <- vec xiv $ \xiv' -> 177 rawpath <- vec xiv $ \xiv' ->
176 createMIO maxit (2*n+1) 178 createMIO maxit (2*n+1)
177 (c_multirootj m fp jp epsabs (fi maxit) // xiv') 179 (c_multirootj m fp jp epsabs (fi maxit) // xiv')
178 "multiroot" 180 "multiroot"
179 let it = round (rawpath @@> (maxit-1,0)) 181 let it = round (rawpath `atIndex` (maxit-1,0))
180 path = takeRows it rawpath 182 path = takeRows it rawpath
181 [sol] = toLists $ dropRows (it-1) path 183 [sol] = toLists $ dropRows (it-1) path
182 freeHaskellFunPtr fp 184 freeHaskellFunPtr fp
@@ -189,7 +191,7 @@ foreign import ccall safe "multirootj"
189------------------------------------------------------- 191-------------------------------------------------------
190 192
191checkdim1 n v 193checkdim1 n v
192 | dim v == n = v 194 | size v == n = v
193 | otherwise = error $ "Error: "++ show n 195 | otherwise = error $ "Error: "++ show n
194 ++ " components expected in the result of the function supplied to root" 196 ++ " components expected in the result of the function supplied to root"
195 197
diff --git a/packages/gsl/src/Numeric/GSL/Vector.hs b/packages/gsl/src/Numeric/GSL/Vector.hs
index af79f32..0cd99eb 100644
--- a/packages/gsl/src/Numeric/GSL/Vector.hs
+++ b/packages/gsl/src/Numeric/GSL/Vector.hs
@@ -14,8 +14,7 @@ module Numeric.GSL.Vector (
14 fwriteVector, freadVector, fprintfVector, fscanfVector 14 fwriteVector, freadVector, fprintfVector, fscanfVector
15) where 15) where
16 16
17import Data.Packed 17import Numeric.LinearAlgebra.HMatrix hiding(randomVector, saveMatrix)
18import Numeric.LinearAlgebra(RandDist(..))
19import Numeric.GSL.Internal hiding (TV,TM,TCV,TCM) 18import Numeric.GSL.Internal hiding (TV,TM,TCV,TCM)
20 19
21import Foreign.Marshal.Alloc(free) 20import Foreign.Marshal.Alloc(free)
diff --git a/packages/sparse/src/Numeric/LinearAlgebra/Sparse.hs b/packages/sparse/src/Numeric/LinearAlgebra/Sparse.hs
index 8608394..d75fec2 100644
--- a/packages/sparse/src/Numeric/LinearAlgebra/Sparse.hs
+++ b/packages/sparse/src/Numeric/LinearAlgebra/Sparse.hs
@@ -13,8 +13,11 @@ import System.IO.Unsafe(unsafePerformIO)
13import Foreign(Ptr) 13import Foreign(Ptr)
14import Numeric.LinearAlgebra.HMatrix 14import Numeric.LinearAlgebra.HMatrix
15import Text.Printf 15import Text.Printf
16import Numeric.LinearAlgebra.Util((~!~)) 16import Control.Monad(when)
17 17
18(???) :: Bool -> String -> IO ()
19infixl 0 ???
20c ??? msg = when c (error msg)
18 21
19type IV t = CInt -> Ptr CInt -> t 22type IV t = CInt -> Ptr CInt -> t
20type V t = CInt -> Ptr Double -> t 23type V t = CInt -> Ptr Double -> t
@@ -22,7 +25,7 @@ type SMxV = V (IV (IV (V (V (IO CInt)))))
22 25
23dss :: CSR -> Vector Double -> Vector Double 26dss :: CSR -> Vector Double -> Vector Double
24dss CSR{..} b = unsafePerformIO $ do 27dss CSR{..} b = unsafePerformIO $ do
25 size b /= csrNRows ~!~ printf "dss: incorrect sizes: (%d,%d) x %d" csrNRows csrNCols (size b) 28 size b /= csrNRows ??? printf "dss: incorrect sizes: (%d,%d) x %d" csrNRows csrNCols (size b)
26 r <- createVector csrNCols 29 r <- createVector csrNCols
27 app5 c_dss vec csrVals vec csrCols vec csrRows vec b vec r "dss" 30 app5 c_dss vec csrVals vec csrCols vec csrRows vec b vec r "dss"
28 return r 31 return r
diff --git a/packages/special/hmatrix-special.cabal b/packages/special/hmatrix-special.cabal
index 28b294b..3b122c8 100644
--- a/packages/special/hmatrix-special.cabal
+++ b/packages/special/hmatrix-special.cabal
@@ -1,5 +1,5 @@
1Name: hmatrix-special 1Name: hmatrix-special
2Version: 0.3.0.1 2Version: 0.4.0.0
3License: GPL 3License: GPL
4License-file: LICENSE 4License-file: LICENSE
5Author: Alberto Ruiz 5Author: Alberto Ruiz
@@ -27,7 +27,7 @@ flag safe-cheap
27 default: False 27 default: False
28 28
29library 29library
30 Build-Depends: base <5, hmatrix, hmatrix-gsl 30 Build-Depends: base <5, hmatrix>=0.17, hmatrix-gsl
31 31
32 Extensions: ForeignFunctionInterface, 32 Extensions: ForeignFunctionInterface,
33 CPP 33 CPP
diff --git a/packages/special/lib/Numeric/GSL/Special/Internal.hsc b/packages/special/lib/Numeric/GSL/Special/Internal.hsc
index e7c38e8..a9aab9b 100644
--- a/packages/special/lib/Numeric/GSL/Special/Internal.hsc
+++ b/packages/special/lib/Numeric/GSL/Special/Internal.hsc
@@ -33,7 +33,7 @@ import Foreign.Storable
33import Foreign.Ptr 33import Foreign.Ptr
34import Foreign.Marshal 34import Foreign.Marshal
35import System.IO.Unsafe(unsafePerformIO) 35import System.IO.Unsafe(unsafePerformIO)
36import Data.Packed.Development(check,(//)) 36import Numeric.LinearAlgebra.Devel(check,(//))
37import Foreign.C.Types 37import Foreign.C.Types
38 38
39data Precision = PrecDouble | PrecSingle | PrecApprox 39data Precision = PrecDouble | PrecSingle | PrecApprox
diff --git a/packages/tests/hmatrix-tests.cabal b/packages/tests/hmatrix-tests.cabal
index 0514843..de796e8 100644
--- a/packages/tests/hmatrix-tests.cabal
+++ b/packages/tests/hmatrix-tests.cabal
@@ -1,5 +1,5 @@
1Name: hmatrix-tests 1Name: hmatrix-tests
2Version: 0.4.1.0 2Version: 0.5.0.0
3License: BSD3 3License: BSD3
4License-file: LICENSE 4License-file: LICENSE
5Author: Alberto Ruiz 5Author: Alberto Ruiz
@@ -28,9 +28,9 @@ library
28 28
29 Build-Depends: base >= 4 && < 5, 29 Build-Depends: base >= 4 && < 5,
30 QuickCheck >= 2, HUnit, random, 30 QuickCheck >= 2, HUnit, random,
31 hmatrix >= 0.16 31 hmatrix >= 0.17
32 if flag(gsl) 32 if flag(gsl)
33 Build-Depends: hmatrix-gsl >= 0.16 33 Build-Depends: hmatrix-gsl >= 0.17
34 34
35 hs-source-dirs: src 35 hs-source-dirs: src
36 36
diff --git a/packages/tests/src/Numeric/GSL/Tests.hs b/packages/tests/src/Numeric/GSL/Tests.hs
index 9dff6f5..e5d205d 100644
--- a/packages/tests/src/Numeric/GSL/Tests.hs
+++ b/packages/tests/src/Numeric/GSL/Tests.hs
@@ -19,7 +19,7 @@ import System.Exit (exitFailure)
19 19
20import Test.HUnit (runTestTT, failures, Test(..), errors) 20import Test.HUnit (runTestTT, failures, Test(..), errors)
21 21
22import Numeric.LinearAlgebra 22import Numeric.LinearAlgebra.HMatrix
23import Numeric.GSL 23import Numeric.GSL
24import Numeric.LinearAlgebra.Tests (qCheck, utest) 24import Numeric.LinearAlgebra.Tests (qCheck, utest)
25import Numeric.LinearAlgebra.Tests.Properties ((|~|), (~~)) 25import Numeric.LinearAlgebra.Tests.Properties ((|~|), (~~))
@@ -42,7 +42,7 @@ fittingTest = utest "levmar" (ok1 && ok2)
42 sol = fst $ fitModel 1E-4 1E-4 20 (expModel, expModelDer) dat [1,0,0] 42 sol = fst $ fitModel 1E-4 1E-4 20 (expModel, expModelDer) dat [1,0,0]
43 43
44 ok1 = and (zipWith f sols [5,0.1,1]) where f (x,d) r = abs (x-r)<2*d 44 ok1 = and (zipWith f sols [5,0.1,1]) where f (x,d) r = abs (x-r)<2*d
45 ok2 = norm2 (fromList (map fst sols) - fromList sol) < 1E-5 45 ok2 = norm_2 (fromList (map fst sols) - fromList sol) < 1E-5
46 46
47--------------------------------------------------------------------- 47---------------------------------------------------------------------
48 48
diff --git a/packages/tests/src/Numeric/LinearAlgebra/Tests.hs b/packages/tests/src/Numeric/LinearAlgebra/Tests.hs
index 713af79..71c7c16 100644
--- a/packages/tests/src/Numeric/LinearAlgebra/Tests.hs
+++ b/packages/tests/src/Numeric/LinearAlgebra/Tests.hs
@@ -28,12 +28,9 @@ module Numeric.LinearAlgebra.Tests(
28--, runBigTests 28--, runBigTests
29) where 29) where
30 30
31import Numeric.LinearAlgebra 31import Numeric.LinearAlgebra hiding (unitary)
32import Numeric.LinearAlgebra.HMatrix hiding ((<>),linearSolve) 32import Numeric.LinearAlgebra.Devel hiding (vec)
33import Numeric.LinearAlgebra.Static(L) 33import Numeric.LinearAlgebra.Static(L)
34import Numeric.LinearAlgebra.Util(col,row)
35import Data.Packed
36import Numeric.LinearAlgebra.LAPACK
37import Numeric.LinearAlgebra.Tests.Instances 34import Numeric.LinearAlgebra.Tests.Instances
38import Numeric.LinearAlgebra.Tests.Properties 35import Numeric.LinearAlgebra.Tests.Properties
39import Test.HUnit hiding ((~:),test,Testable,State) 36import Test.HUnit hiding ((~:),test,Testable,State)
@@ -44,16 +41,13 @@ import qualified Prelude
44import System.CPUTime 41import System.CPUTime
45import System.Exit 42import System.Exit
46import Text.Printf 43import Text.Printf
47import Data.Packed.Development(unsafeFromForeignPtr,unsafeToForeignPtr) 44import Numeric.LinearAlgebra.Devel(unsafeFromForeignPtr,unsafeToForeignPtr)
48import Control.Arrow((***)) 45import Control.Arrow((***))
49import Debug.Trace 46import Debug.Trace
50import Control.Monad(when) 47import Control.Monad(when)
51import Numeric.LinearAlgebra.Util hiding (ones,row,col)
52import Control.Applicative 48import Control.Applicative
53import Control.Monad(ap) 49import Control.Monad(ap)
54 50
55import Data.Packed.ST
56
57import Test.QuickCheck(Arbitrary,arbitrary,coarbitrary,choose,vector 51import Test.QuickCheck(Arbitrary,arbitrary,coarbitrary,choose,vector
58 ,sized,classify,Testable,Property 52 ,sized,classify,Testable,Property
59 ,quickCheckWithResult,maxSize,stdArgs,shrink) 53 ,quickCheckWithResult,maxSize,stdArgs,shrink)
@@ -89,7 +83,7 @@ detTest1 = det m == 26
89 mc = (3><3) 83 mc = (3><3)
90 [ 1, 2, 3 84 [ 1, 2, 3
91 , 4, 5, 7 85 , 4, 5, 7
92 , 2, 8, i 86 , 2, 8, iC
93 ] 87 ]
94 88
95detTest2 = inv1 |~| inv2 && [det1] ~~ [det2] 89detTest2 = inv1 |~| inv2 && [det1] ~~ [det2]
@@ -140,7 +134,7 @@ randomTestGaussian = c :~1~: snd (meanCov dat) where
140 2,4,0, 134 2,4,0,
141 -2,2,1] 135 -2,2,1]
142 m = 3 |> [1,2,3] 136 m = 3 |> [1,2,3]
143 c = a <> trans a 137 c = a <> tr a
144 dat = gaussianSample 7 (10^6) m c 138 dat = gaussianSample 7 (10^6) m c
145 139
146randomTestUniform = c :~1~: snd (meanCov dat) where 140randomTestUniform = c :~1~: snd (meanCov dat) where
@@ -174,54 +168,54 @@ offsetTest = y == y' where
174 168
175normsVTest = TestList [ 169normsVTest = TestList [
176 utest "normv2CD" $ norm2PropC v 170 utest "normv2CD" $ norm2PropC v
177 , utest "normv2CF" $ norm2PropC (single v) 171-- , utest "normv2CF" $ norm2PropC (single v)
178#ifndef NONORMVTEST 172#ifndef NONORMVTEST
179 , utest "normv2D" $ norm2PropR x 173 , utest "normv2D" $ norm2PropR x
180 , utest "normv2F" $ norm2PropR (single x) 174-- , utest "normv2F" $ norm2PropR (single x)
181#endif 175#endif
182 , utest "normv1CD" $ norm1 v == 8 176 , utest "normv1CD" $ norm_1 v == 8
183 , utest "normv1CF" $ norm1 (single v) == 8 177-- , utest "normv1CF" $ norm_1 (single v) == 8
184 , utest "normv1D" $ norm1 x == 6 178 , utest "normv1D" $ norm_1 x == 6
185 , utest "normv1F" $ norm1 (single x) == 6 179-- , utest "normv1F" $ norm_1 (single x) == 6
186 180
187 , utest "normvInfCD" $ normInf v == 5 181 , utest "normvInfCD" $ norm_Inf v == 5
188 , utest "normvInfCF" $ normInf (single v) == 5 182-- , utest "normvInfCF" $ norm_Inf (single v) == 5
189 , utest "normvInfD" $ normInf x == 3 183 , utest "normvInfD" $ norm_Inf x == 3
190 , utest "normvInfF" $ normInf (single x) == 3 184-- , utest "normvInfF" $ norm_Inf (single x) == 3
191 185
192 ] where v = fromList [1,-2,3:+4] :: Vector (Complex Double) 186 ] where v = fromList [1,-2,3:+4] :: Vector (Complex Double)
193 x = fromList [1,2,-3] :: Vector Double 187 x = fromList [1,2,-3] :: Vector Double
194#ifndef NONORMVTEST 188#ifndef NONORMVTEST
195 norm2PropR a = norm2 a =~= sqrt (udot a a) 189 norm2PropR a = norm_2 a =~= sqrt (udot a a)
196#endif 190#endif
197 norm2PropC a = norm2 a =~= realPart (sqrt (a <.> a)) 191 norm2PropC a = norm_2 a =~= realPart (sqrt (a `dot` a))
198 a =~= b = fromList [a] |~| fromList [b] 192 a =~= b = fromList [a] |~| fromList [b]
199 193
200normsMTest = TestList [ 194normsMTest = TestList [
201 utest "norm2mCD" $ pnorm PNorm2 v =~= 8.86164970498005 195 utest "norm2mCD" $ norm_2 v =~= 8.86164970498005
202 , utest "norm2mCF" $ pnorm PNorm2 (single v) =~= 8.86164970498005 196-- , utest "norm2mCF" $ norm_2 (single v) =~= 8.86164970498005
203 , utest "norm2mD" $ pnorm PNorm2 x =~= 5.96667765076216 197 , utest "norm2mD" $ norm_2 x =~= 5.96667765076216
204 , utest "norm2mF" $ pnorm PNorm2 (single x) =~= 5.96667765076216 198-- , utest "norm2mF" $ norm_2 (single x) =~= 5.96667765076216
205 199
206 , utest "norm1mCD" $ pnorm PNorm1 v == 9 200 , utest "norm1mCD" $ norm_1 v == 9
207 , utest "norm1mCF" $ pnorm PNorm1 (single v) == 9 201-- , utest "norm1mCF" $ norm_1 (single v) == 9
208 , utest "norm1mD" $ pnorm PNorm1 x == 7 202 , utest "norm1mD" $ norm_1 x == 7
209 , utest "norm1mF" $ pnorm PNorm1 (single x) == 7 203-- , utest "norm1mF" $ norm_1 (single x) == 7
210 204
211 , utest "normmInfCD" $ pnorm Infinity v == 12 205 , utest "normmInfCD" $ norm_Inf v == 12
212 , utest "normmInfCF" $ pnorm Infinity (single v) == 12 206-- , utest "normmInfCF" $ norm_Inf (single v) == 12
213 , utest "normmInfD" $ pnorm Infinity x == 8 207 , utest "normmInfD" $ norm_Inf x == 8
214 , utest "normmInfF" $ pnorm Infinity (single x) == 8 208-- , utest "normmInfF" $ norm_Inf (single x) == 8
215 209
216 , utest "normmFroCD" $ pnorm Frobenius v =~= 8.88819441731559 210 , utest "normmFroCD" $ norm_Frob v =~= 8.88819441731559
217 , utest "normmFroCF" $ pnorm Frobenius (single v) =~~= 8.88819441731559 211-- , utest "normmFroCF" $ norm_Frob (single v) =~~= 8.88819441731559
218 , utest "normmFroD" $ pnorm Frobenius x =~= 6.24499799839840 212 , utest "normmFroD" $ norm_Frob x =~= 6.24499799839840
219 , utest "normmFroF" $ pnorm Frobenius (single x) =~~= 6.24499799839840 213-- , utest "normmFroF" $ norm_Frob (single x) =~~= 6.24499799839840
220 214
221 ] where v = (2><2) [1,-2*i,3:+4,7] :: Matrix (Complex Double) 215 ] where v = (2><2) [1,-2*iC,3:+4,7] :: Matrix (Complex Double)
222 x = (2><2) [1,2,-3,5] :: Matrix Double 216 x = (2><2) [1,2,-3,5] :: Matrix Double
223 a =~= b = fromList [a] :~10~: fromList [b] 217 a =~= b = fromList [a] :~10~: fromList [b]
224 a =~~= b = fromList [a] :~5~: fromList [b] 218-- a =~~= b = fromList [a] :~5~: fromList [b]
225 219
226--------------------------------------------------------------------- 220---------------------------------------------------------------------
227 221
@@ -236,7 +230,7 @@ sumprodTest = TestList [
236 , utest "prodD" $ prodProp v 230 , utest "prodD" $ prodProp v
237 , utest "prodF" $ prodProp (single v) 231 , utest "prodF" $ prodProp (single v)
238 ] where v = fromList [1,2,3] :: Vector Double 232 ] where v = fromList [1,2,3] :: Vector Double
239 z = fromList [1,2-i,3+i] 233 z = fromList [1,2-iC,3+iC]
240 prodProp x = prodElements x == product (toList x) 234 prodProp x = prodElements x == product (toList x)
241 235
242--------------------------------------------------------------------- 236---------------------------------------------------------------------
@@ -250,7 +244,7 @@ chainTest = utest "chain" $ foldl1' (<>) ms |~| optimiseMult ms where
250 244
251--------------------------------------------------------------------- 245---------------------------------------------------------------------
252 246
253conjuTest m = mapVector conjugate (flatten (trans m)) == flatten (ctrans m) 247conjuTest m = cmap conjugate (flatten (conj (tr m))) == flatten (tr m)
254 248
255--------------------------------------------------------------------- 249---------------------------------------------------------------------
256 250
@@ -306,7 +300,7 @@ lift_maybe m = MaybeT $ do
306 300
307-- apply a test to successive elements of a vector, evaluates to true iff test passes for all pairs 301-- apply a test to successive elements of a vector, evaluates to true iff test passes for all pairs
308--successive_ :: Storable a => (a -> a -> Bool) -> Vector a -> Bool 302--successive_ :: Storable a => (a -> a -> Bool) -> Vector a -> Bool
309successive_ t v = maybe False (\_ -> True) $ evalState (runMaybeT (mapVectorM_ stp (subVector 1 (dim v - 1) v))) (v @> 0) 303successive_ t v = maybe False (\_ -> True) $ evalState (runMaybeT (mapVectorM_ stp (subVector 1 (size v - 1) v))) (v ! 0)
310 where stp e = do 304 where stp e = do
311 ep <- lift_maybe $ state_get 305 ep <- lift_maybe $ state_get
312 if t e ep 306 if t e ep
@@ -315,7 +309,7 @@ successive_ t v = maybe False (\_ -> True) $ evalState (runMaybeT (mapVectorM_ s
315 309
316-- operate on successive elements of a vector and return the resulting vector, whose length 1 less than that of the input 310-- operate on successive elements of a vector and return the resulting vector, whose length 1 less than that of the input
317--successive :: (Storable a, Storable b) => (a -> a -> b) -> Vector a -> Vector b 311--successive :: (Storable a, Storable b) => (a -> a -> b) -> Vector a -> Vector b
318successive f v = evalState (mapVectorM stp (subVector 1 (dim v - 1) v)) (v @> 0) 312successive f v = evalState (mapVectorM stp (subVector 1 (size v - 1) v)) (v ! 0)
319 where stp e = do 313 where stp e = do
320 ep <- state_get 314 ep <- state_get
321 state_put e 315 state_put e
@@ -377,23 +371,6 @@ convolutionTest = utest "convolution" ok
377 371
378-------------------------------------------------------------------------------- 372--------------------------------------------------------------------------------
379 373
380kroneckerTest = utest "kronecker" ok
381 where
382 a,x,b :: Matrix Double
383 a = (3><4) [1..]
384 x = (4><2) [3,5..]
385 b = (2><5) [0,5..]
386 v1 = vec (a <> x <> b)
387 v2 = (trans b `kronecker` a) <> vec x
388 s = trans b <> b
389 v3 = vec s
390 v4 = (dup 5 :: Matrix Double) <> vech s
391 ok = v1 == v2 && v3 == v4
392 && vtrans 1 a == trans a
393 && vtrans (rows a) a == asColumn (vec a)
394
395--------------------------------------------------------------------------------
396
397sparseTest = utest "sparse" (fst $ checkT (undefined :: GMatrix)) 374sparseTest = utest "sparse" (fst $ checkT (undefined :: GMatrix))
398 375
399-------------------------------------------------------------------------------- 376--------------------------------------------------------------------------------
@@ -435,11 +412,11 @@ runTests n = do
435 test (multProp1 10 . cConsist) 412 test (multProp1 10 . cConsist)
436 test (multProp2 10 . rConsist) 413 test (multProp2 10 . rConsist)
437 test (multProp2 10 . cConsist) 414 test (multProp2 10 . cConsist)
438 putStrLn "------ mult Float" 415-- putStrLn "------ mult Float"
439 test (multProp1 6 . (single *** single) . rConsist) 416-- test (multProp1 6 . (single *** single) . rConsist)
440 test (multProp1 6 . (single *** single) . cConsist) 417-- test (multProp1 6 . (single *** single) . cConsist)
441 test (multProp2 6 . (single *** single) . rConsist) 418-- test (multProp2 6 . (single *** single) . rConsist)
442 test (multProp2 6 . (single *** single) . cConsist) 419-- test (multProp2 6 . (single *** single) . cConsist)
443 putStrLn "------ sub-trans" 420 putStrLn "------ sub-trans"
444 test (subProp . rM) 421 test (subProp . rM)
445 test (subProp . cM) 422 test (subProp . cM)
@@ -472,16 +449,16 @@ runTests n = do
472 putStrLn "------ svd" 449 putStrLn "------ svd"
473 test (svdProp1 . rM) 450 test (svdProp1 . rM)
474 test (svdProp1 . cM) 451 test (svdProp1 . cM)
475 test (svdProp1a svdR) 452 test (svdProp1a svd . rM)
476 test (svdProp1a svdC) 453 test (svdProp1a svd . cM)
477 test (svdProp1a svdRd) 454-- test (svdProp1a svdRd)
478 test (svdProp1b svdR) 455 test (svdProp1b svd . rM)
479 test (svdProp1b svdC) 456 test (svdProp1b svd . cM)
480 test (svdProp1b svdRd) 457-- test (svdProp1b svdRd)
481 test (svdProp2 thinSVDR) 458 test (svdProp2 thinSVD . rM)
482 test (svdProp2 thinSVDC) 459 test (svdProp2 thinSVD . cM)
483 test (svdProp2 thinSVDRd) 460-- test (svdProp2 thinSVDRd)
484 test (svdProp2 thinSVDCd) 461-- test (svdProp2 thinSVDCd)
485 test (svdProp3 . rM) 462 test (svdProp3 . rM)
486 test (svdProp3 . cM) 463 test (svdProp3 . cM)
487 test (svdProp4 . rM) 464 test (svdProp4 . rM)
@@ -492,12 +469,12 @@ runTests n = do
492 test (svdProp6b) 469 test (svdProp6b)
493 test (svdProp7 . rM) 470 test (svdProp7 . rM)
494 test (svdProp7 . cM) 471 test (svdProp7 . cM)
495 putStrLn "------ svdCd" 472-- putStrLn "------ svdCd"
496#ifdef NOZGESDD 473#ifdef NOZGESDD
497 putStrLn "Omitted" 474-- putStrLn "Omitted"
498#else 475#else
499 test (svdProp1a svdCd) 476-- test (svdProp1a svdCd)
500 test (svdProp1b svdCd) 477-- test (svdProp1b svdCd)
501#endif 478#endif
502 putStrLn "------ eig" 479 putStrLn "------ eig"
503 test (eigSHProp . rHer) 480 test (eigSHProp . rHer)
@@ -515,10 +492,10 @@ runTests n = do
515 test (qrProp . rM) 492 test (qrProp . rM)
516 test (qrProp . cM) 493 test (qrProp . cM)
517 test (rqProp . rM) 494 test (rqProp . rM)
518 test (rqProp . cM) 495-- test (rqProp . cM)
519 test (rqProp1 . cM) 496 test (rqProp1 . cM)
520 test (rqProp2 . cM) 497 test (rqProp2 . cM)
521 test (rqProp3 . cM) 498-- test (rqProp3 . cM)
522 putStrLn "------ hess" 499 putStrLn "------ hess"
523 test (hessProp . rSq) 500 test (hessProp . rSq)
524 test (hessProp . cSq) 501 test (hessProp . cSq)
@@ -539,12 +516,12 @@ runTests n = do
539 test (\u -> sin u ** 2 + cos u ** 2 |~| (1::RM)) 516 test (\u -> sin u ** 2 + cos u ** 2 |~| (1::RM))
540 test (\u -> cos u * tan u |~| sin (u::RM)) 517 test (\u -> cos u * tan u |~| sin (u::RM))
541 test $ (\u -> cos u * tan u |~| sin (u::CM)) . liftMatrix makeUnitary 518 test $ (\u -> cos u * tan u |~| sin (u::CM)) . liftMatrix makeUnitary
542 putStrLn "------ vector operations - Float" 519-- putStrLn "------ vector operations - Float"
543 test (\u -> sin u ^ 2 + cos u ^ 2 |~~| (1::FM)) 520-- test (\u -> sin u ^ 2 + cos u ^ 2 |~~| (1::FM))
544 test $ (\u -> sin u ^ 2 + cos u ^ 2 |~~| (1::ZM)) . liftMatrix makeUnitary 521-- test $ (\u -> sin u ^ 2 + cos u ^ 2 |~~| (1::ZM)) . liftMatrix makeUnitary
545 test (\u -> sin u ** 2 + cos u ** 2 |~~| (1::FM)) 522-- test (\u -> sin u ** 2 + cos u ** 2 |~~| (1::FM))
546 test (\u -> cos u * tan u |~~| sin (u::FM)) 523-- test (\u -> cos u * tan u |~~| sin (u::FM))
547 test $ (\u -> cos u * tan u |~~| sin (u::ZM)) . liftMatrix makeUnitary 524-- test $ (\u -> cos u * tan u |~~| sin (u::ZM)) . liftMatrix makeUnitary
548 putStrLn "------ read . show" 525 putStrLn "------ read . show"
549 test (\m -> (m::RM) == read (show m)) 526 test (\m -> (m::RM) == read (show m))
550 test (\m -> (m::CM) == read (show m)) 527 test (\m -> (m::CM) == read (show m))
@@ -562,8 +539,8 @@ runTests n = do
562 , utest "expm1" (expmTest1) 539 , utest "expm1" (expmTest1)
563 , utest "expm2" (expmTest2) 540 , utest "expm2" (expmTest2)
564 , utest "arith1" $ ((ones (100,100) * 5 + 2)/0.5 - 7)**2 |~| (49 :: RM) 541 , utest "arith1" $ ((ones (100,100) * 5 + 2)/0.5 - 7)**2 |~| (49 :: RM)
565 , utest "arith2" $ ((scalar (1+i) * ones (100,100) * 5 + 2)/0.5 - 7)**2 |~| ( scalar (140*i-51) :: CM) 542 , utest "arith2" $ ((scalar (1+iC) * ones (100,100) * 5 + 2)/0.5 - 7)**2 |~| ( scalar (140*iC-51) :: CM)
566 , utest "arith3" $ exp (scalar i * ones(10,10)*pi) + 1 |~| 0 543 , utest "arith3" $ exp (scalar iC * ones(10,10)*pi) + 1 |~| 0
567 , utest "<\\>" $ (3><2) [2,0,0,3,1,1::Double] <\> 3|>[4,9,5] |~| 2|>[2,3] 544 , utest "<\\>" $ (3><2) [2,0,0,3,1,1::Double] <\> 3|>[4,9,5] |~| 2|>[2,3]
568-- , utest "gamma" (gamma 5 == 24.0) 545-- , utest "gamma" (gamma 5 == 24.0)
569-- , besselTest 546-- , besselTest
@@ -571,10 +548,10 @@ runTests n = do
571 , utest "randomGaussian" randomTestGaussian 548 , utest "randomGaussian" randomTestGaussian
572 , utest "randomUniform" randomTestUniform 549 , utest "randomUniform" randomTestUniform
573 , utest "buildVector/Matrix" $ 550 , utest "buildVector/Matrix" $
574 complex (10 |> [0::Double ..]) == buildVector 10 fromIntegral 551 complex (10 |> [0::Double ..]) == build 10 id
575 && ident 5 == buildMatrix 5 5 (\(r,c) -> if r==c then 1::Double else 0) 552 && ident 5 == build (5,5) (\r c -> if r==c then 1::Double else 0)
576 , utest "rank" $ rank ((2><3)[1,0,0,1,5*eps,0]) == 1 553 , utest "rank" $ rank ((2><3)[1,0,0,1,5*peps,0::Double]) == 1
577 && rank ((2><3)[1,0,0,1,7*eps,0]) == 2 554 && rank ((2><3)[1,0,0,1,7*peps,0::Double]) == 2
578 , utest "block" $ fromBlocks [[ident 3,0],[0,ident 4]] == (ident 7 :: CM) 555 , utest "block" $ fromBlocks [[ident 3,0],[0,ident 4]] == (ident 7 :: CM)
579 , mbCholTest 556 , mbCholTest
580 , utest "offset" offsetTest 557 , utest "offset" offsetTest
@@ -588,7 +565,6 @@ runTests n = do
588 , conformTest 565 , conformTest
589 , accumTest 566 , accumTest
590 , convolutionTest 567 , convolutionTest
591 , kroneckerTest
592 , sparseTest 568 , sparseTest
593 , staticTest 569 , staticTest
594 ] 570 ]
@@ -597,12 +573,12 @@ runTests n = do
597 573
598 574
599-- single precision approximate equality 575-- single precision approximate equality
600infixl 4 |~~| 576-- infixl 4 |~~|
601a |~~| b = a :~6~: b 577-- a |~~| b = a :~6~: b
602 578
603makeUnitary v | realPart n > 1 = v / scalar n 579makeUnitary v | realPart n > 1 = v / scalar n
604 | otherwise = v 580 | otherwise = v
605 where n = sqrt (v <.> v) 581 where n = sqrt (v `dot` v)
606 582
607-- -- | Some additional tests on big matrices. They take a few minutes. 583-- -- | Some additional tests on big matrices. They take a few minutes.
608-- runBigTests :: IO () 584-- runBigTests :: IO ()
@@ -668,9 +644,9 @@ manyvec5 xs = sumElements $ fromRows $ map (\x -> vec3 x (x**2) (x**3)) xs
668 644
669 645
670manyvec2 xs = sum $ map (\x -> sqrt(x^2 + (x**2)^2 +(x**3)^2)) xs 646manyvec2 xs = sum $ map (\x -> sqrt(x^2 + (x**2)^2 +(x**3)^2)) xs
671manyvec3 xs = sum $ map (pnorm PNorm2 . (\x -> fromList [x,x**2,x**3])) xs 647manyvec3 xs = sum $ map (norm_2 . (\x -> fromList [x,x**2,x**3])) xs
672 648
673manyvec4 xs = sum $ map (pnorm PNorm2 . (\x -> vec3 x (x**2) (x**3))) xs 649manyvec4 xs = sum $ map (norm_2 . (\x -> vec3 x (x**2) (x**3))) xs
674 650
675vec3 :: Double -> Double -> Double -> Vector Double 651vec3 :: Double -> Double -> Double -> Vector Double
676vec3 a b c = runSTVector $ do 652vec3 a b c = runSTVector $ do
@@ -695,11 +671,11 @@ mkVecBench = do
695 671
696subBench = do 672subBench = do
697 putStrLn "" 673 putStrLn ""
698 let g = foldl1' (.) (replicate (10^5) (\v -> subVector 1 (dim v -1) v)) 674 let g = foldl1' (.) (replicate (10^5) (\v -> subVector 1 (size v -1) v))
699 time "0.1M subVector " (g (konst 1 (1+10^5) :: Vector Double) @> 0) 675 time "0.1M subVector " (g (konst 1 (1+10^5) :: Vector Double) ! 0)
700 let f = foldl1' (.) (replicate (10^5) (fromRows.toRows)) 676 let f = foldl1' (.) (replicate (10^5) (fromRows.toRows))
701 time "subVector-join 3" (f (ident 3 :: Matrix Double) @@>(0,0)) 677 time "subVector-join 3" (f (ident 3 :: Matrix Double) `atIndex` (0,0))
702 time "subVector-join 10" (f (ident 10 :: Matrix Double) @@>(0,0)) 678 time "subVector-join 10" (f (ident 10 :: Matrix Double) `atIndex` (0,0))
703 679
704-------------------------------- 680--------------------------------
705 681
@@ -724,7 +700,7 @@ multBench = do
724 700
725eigBench = do 701eigBench = do
726 let m = reshape 1000 (randomVector 777 Uniform (1000*1000)) 702 let m = reshape 1000 (randomVector 777 Uniform (1000*1000))
727 s = m + trans m 703 s = m + tr m
728 m `seq` s `seq` putStrLn "" 704 m `seq` s `seq` putStrLn ""
729 time "eigenvalues symmetric 1000x1000" (eigenvaluesSH' m) 705 time "eigenvalues symmetric 1000x1000" (eigenvaluesSH' m)
730 time "eigenvectors symmetric 1000x1000" (snd $ eigSH' m) 706 time "eigenvectors symmetric 1000x1000" (snd $ eigSH' m)
@@ -736,7 +712,7 @@ eigBench = do
736svdBench = do 712svdBench = do
737 let a = reshape 500 (randomVector 777 Uniform (3000*500)) 713 let a = reshape 500 (randomVector 777 Uniform (3000*500))
738 b = reshape 1000 (randomVector 777 Uniform (1000*1000)) 714 b = reshape 1000 (randomVector 777 Uniform (1000*1000))
739 fv (_,_,v) = v@@>(0,0) 715 fv (_,_,v) = v `atIndex` (0,0)
740 a `seq` b `seq` putStrLn "" 716 a `seq` b `seq` putStrLn ""
741 time "singular values 3000x500" (singularValues a) 717 time "singular values 3000x500" (singularValues a)
742 time "thin svd 3000x500" (fv $ thinSVD a) 718 time "thin svd 3000x500" (fv $ thinSVD a)
@@ -748,7 +724,7 @@ svdBench = do
748 724
749solveBenchN n = do 725solveBenchN n = do
750 let x = uniformSample 777 (2*n) (replicate n (-1,1)) 726 let x = uniformSample 777 (2*n) (replicate n (-1,1))
751 a = trans x <> x 727 a = tr x <> x
752 b = asColumn $ randomVector 666 Uniform n 728 b = asColumn $ randomVector 666 Uniform n
753 a `seq` b `seq` putStrLn "" 729 a `seq` b `seq` putStrLn ""
754 time ("svd solve " ++ show n) (linearSolveSVD a b) 730 time ("svd solve " ++ show n) (linearSolveSVD a b)
@@ -765,7 +741,7 @@ solveBench = do
765 741
766cholBenchN n = do 742cholBenchN n = do
767 let x = uniformSample 777 (2*n) (replicate n (-1,1)) 743 let x = uniformSample 777 (2*n) (replicate n (-1,1))
768 a = trans x <> x 744 a = tr x <> x
769 a `seq` putStr "" 745 a `seq` putStr ""
770 time ("chol " ++ show n) (chol a) 746 time ("chol " ++ show n) (chol a)
771 747
diff --git a/packages/tests/src/Numeric/LinearAlgebra/Tests/Instances.hs b/packages/tests/src/Numeric/LinearAlgebra/Tests/Instances.hs
index 53fc4d2..904ae05 100644
--- a/packages/tests/src/Numeric/LinearAlgebra/Tests/Instances.hs
+++ b/packages/tests/src/Numeric/LinearAlgebra/Tests/Instances.hs
@@ -1,5 +1,4 @@
1{-# LANGUAGE FlexibleContexts, UndecidableInstances, CPP, FlexibleInstances #-} 1{-# LANGUAGE FlexibleContexts, UndecidableInstances, FlexibleInstances #-}
2{-# OPTIONS_GHC -fno-warn-unused-imports #-}
3----------------------------------------------------------------------------- 2-----------------------------------------------------------------------------
4{- | 3{- |
5Module : Numeric.LinearAlgebra.Tests.Instances 4Module : Numeric.LinearAlgebra.Tests.Instances
@@ -26,15 +25,11 @@ module Numeric.LinearAlgebra.Tests.Instances(
26 25
27import System.Random 26import System.Random
28 27
29import Numeric.LinearAlgebra 28import Numeric.LinearAlgebra.HMatrix hiding (vector)
30import Numeric.LinearAlgebra.Devel
31import Numeric.Container
32import Control.Monad(replicateM) 29import Control.Monad(replicateM)
33import Test.QuickCheck(Arbitrary,arbitrary,coarbitrary,choose,vector 30import Test.QuickCheck(Arbitrary,arbitrary,choose,vector,sized,shrink)
34 ,sized,classify,Testable,Property 31
35 ,quickCheckWith,maxSize,stdArgs,shrink)
36 32
37#if MIN_VERSION_QuickCheck(2,0,0)
38shrinkListElementwise :: (Arbitrary a) => [a] -> [[a]] 33shrinkListElementwise :: (Arbitrary a) => [a] -> [[a]]
39shrinkListElementwise [] = [] 34shrinkListElementwise [] = []
40shrinkListElementwise (x:xs) = [ y:xs | y <- shrink x ] 35shrinkListElementwise (x:xs) = [ y:xs | y <- shrink x ]
@@ -42,25 +37,6 @@ shrinkListElementwise (x:xs) = [ y:xs | y <- shrink x ]
42 37
43shrinkPair :: (Arbitrary a, Arbitrary b) => (a,b) -> [(a,b)] 38shrinkPair :: (Arbitrary a, Arbitrary b) => (a,b) -> [(a,b)]
44shrinkPair (a,b) = [ (a,x) | x <- shrink b ] ++ [ (x,b) | x <- shrink a ] 39shrinkPair (a,b) = [ (a,x) | x <- shrink b ] ++ [ (x,b) | x <- shrink a ]
45#endif
46
47#if MIN_VERSION_QuickCheck(2,1,1)
48#else
49instance (Arbitrary a, RealFloat a) => Arbitrary (Complex a) where
50 arbitrary = do
51 re <- arbitrary
52 im <- arbitrary
53 return (re :+ im)
54
55#if MIN_VERSION_QuickCheck(2,0,0)
56 shrink (re :+ im) =
57 [ u :+ v | (u,v) <- shrinkPair (re,im) ]
58#else
59 -- this has been moved to the 'Coarbitrary' class in QuickCheck 2
60 coarbitrary = undefined
61#endif
62
63#endif
64 40
65chooseDim = sized $ \m -> choose (1,max 1 m) 41chooseDim = sized $ \m -> choose (1,max 1 m)
66 42
@@ -68,15 +44,9 @@ instance (Field a, Arbitrary a) => Arbitrary (Vector a) where
68 arbitrary = do m <- chooseDim 44 arbitrary = do m <- chooseDim
69 l <- vector m 45 l <- vector m
70 return $ fromList l 46 return $ fromList l
71
72#if MIN_VERSION_QuickCheck(2,0,0)
73 -- shrink any one of the components 47 -- shrink any one of the components
74 shrink = map fromList . shrinkListElementwise . toList 48 shrink = map fromList . shrinkListElementwise . toList
75 49
76#else
77 coarbitrary = undefined
78#endif
79
80instance (Element a, Arbitrary a) => Arbitrary (Matrix a) where 50instance (Element a, Arbitrary a) => Arbitrary (Matrix a) where
81 arbitrary = do 51 arbitrary = do
82 m <- chooseDim 52 m <- chooseDim
@@ -84,16 +54,11 @@ instance (Element a, Arbitrary a) => Arbitrary (Matrix a) where
84 l <- vector (m*n) 54 l <- vector (m*n)
85 return $ (m><n) l 55 return $ (m><n) l
86 56
87#if MIN_VERSION_QuickCheck(2,0,0)
88 -- shrink any one of the components 57 -- shrink any one of the components
89 shrink a = map (rows a >< cols a) 58 shrink a = map (rows a >< cols a)
90 . shrinkListElementwise 59 . shrinkListElementwise
91 . concat . toLists 60 . concat . toLists
92 $ a 61 $ a
93#else
94 coarbitrary = undefined
95#endif
96
97 62
98-- a square matrix 63-- a square matrix
99newtype (Sq a) = Sq (Matrix a) deriving Show 64newtype (Sq a) = Sq (Matrix a) deriving Show
@@ -103,11 +68,7 @@ instance (Element a, Arbitrary a) => Arbitrary (Sq a) where
103 l <- vector (n*n) 68 l <- vector (n*n)
104 return $ Sq $ (n><n) l 69 return $ Sq $ (n><n) l
105 70
106#if MIN_VERSION_QuickCheck(2,0,0)
107 shrink (Sq a) = [ Sq b | b <- shrink a ] 71 shrink (Sq a) = [ Sq b | b <- shrink a ]
108#else
109 coarbitrary = undefined
110#endif
111 72
112 73
113-- a unitary matrix 74-- a unitary matrix
@@ -118,11 +79,6 @@ instance (Field a, Arbitrary a) => Arbitrary (Rot a) where
118 let (q,_) = qr m 79 let (q,_) = qr m
119 return (Rot q) 80 return (Rot q)
120 81
121#if MIN_VERSION_QuickCheck(2,0,0)
122#else
123 coarbitrary = undefined
124#endif
125
126 82
127-- a complex hermitian or real symmetric matrix 83-- a complex hermitian or real symmetric matrix
128newtype (Her a) = Her (Matrix a) deriving Show 84newtype (Her a) = Her (Matrix a) deriving Show
@@ -130,12 +86,8 @@ instance (Field a, Arbitrary a, Num (Vector a)) => Arbitrary (Her a) where
130 arbitrary = do 86 arbitrary = do
131 Sq m <- arbitrary 87 Sq m <- arbitrary
132 let m' = m/2 88 let m' = m/2
133 return $ Her (m' + ctrans m') 89 return $ Her (m' + tr m')
134 90
135#if MIN_VERSION_QuickCheck(2,0,0)
136#else
137 coarbitrary = undefined
138#endif
139 91
140class (Field a, Arbitrary a, Element (RealOf a), Random (RealOf a)) => ArbitraryField a 92class (Field a, Arbitrary a, Element (RealOf a), Random (RealOf a)) => ArbitraryField a
141instance ArbitraryField Double 93instance ArbitraryField Double
@@ -144,7 +96,7 @@ instance ArbitraryField (Complex Double)
144 96
145-- a well-conditioned general matrix (the singular values are between 1 and 100) 97-- a well-conditioned general matrix (the singular values are between 1 and 100)
146newtype (WC a) = WC (Matrix a) deriving Show 98newtype (WC a) = WC (Matrix a) deriving Show
147instance (ArbitraryField a) => Arbitrary (WC a) where 99instance (Numeric a, ArbitraryField a) => Arbitrary (WC a) where
148 arbitrary = do 100 arbitrary = do
149 m <- arbitrary 101 m <- arbitrary
150 let (u,_,v) = svd m 102 let (u,_,v) = svd m
@@ -153,34 +105,24 @@ instance (ArbitraryField a) => Arbitrary (WC a) where
153 n = min r c 105 n = min r c
154 sv' <- replicateM n (choose (1,100)) 106 sv' <- replicateM n (choose (1,100))
155 let s = diagRect 0 (fromList sv') r c 107 let s = diagRect 0 (fromList sv') r c
156 return $ WC (u `mXm` real s `mXm` trans v) 108 return $ WC (u <> real s <> tr v)
157
158#if MIN_VERSION_QuickCheck(2,0,0)
159#else
160 coarbitrary = undefined
161#endif
162 109
163 110
164-- a well-conditioned square matrix (the singular values are between 1 and 100) 111-- a well-conditioned square matrix (the singular values are between 1 and 100)
165newtype (SqWC a) = SqWC (Matrix a) deriving Show 112newtype (SqWC a) = SqWC (Matrix a) deriving Show
166instance (ArbitraryField a) => Arbitrary (SqWC a) where 113instance (ArbitraryField a, Numeric a) => Arbitrary (SqWC a) where
167 arbitrary = do 114 arbitrary = do
168 Sq m <- arbitrary 115 Sq m <- arbitrary
169 let (u,_,v) = svd m 116 let (u,_,v) = svd m
170 n = rows m 117 n = rows m
171 sv' <- replicateM n (choose (1,100)) 118 sv' <- replicateM n (choose (1,100))
172 let s = diag (fromList sv') 119 let s = diag (fromList sv')
173 return $ SqWC (u `mXm` real s `mXm` trans v) 120 return $ SqWC (u <> real s <> tr v)
174
175#if MIN_VERSION_QuickCheck(2,0,0)
176#else
177 coarbitrary = undefined
178#endif
179 121
180 122
181-- a positive definite square matrix (the eigenvalues are between 0 and 100) 123-- a positive definite square matrix (the eigenvalues are between 0 and 100)
182newtype (PosDef a) = PosDef (Matrix a) deriving Show 124newtype (PosDef a) = PosDef (Matrix a) deriving Show
183instance (ArbitraryField a, Num (Vector a)) 125instance (Numeric a, ArbitraryField a, Num (Vector a))
184 => Arbitrary (PosDef a) where 126 => Arbitrary (PosDef a) where
185 arbitrary = do 127 arbitrary = do
186 Her m <- arbitrary 128 Her m <- arbitrary
@@ -188,13 +130,8 @@ instance (ArbitraryField a, Num (Vector a))
188 n = rows m 130 n = rows m
189 l <- replicateM n (choose (0,100)) 131 l <- replicateM n (choose (0,100))
190 let s = diag (fromList l) 132 let s = diag (fromList l)
191 p = v `mXm` real s `mXm` ctrans v 133 p = v <> real s <> tr v
192 return $ PosDef (0.5 * p + 0.5 * ctrans p) 134 return $ PosDef (0.5 * p + 0.5 * tr p)
193
194#if MIN_VERSION_QuickCheck(2,0,0)
195#else
196 coarbitrary = undefined
197#endif
198 135
199 136
200-- a pair of matrices that can be multiplied 137-- a pair of matrices that can be multiplied
@@ -208,11 +145,7 @@ instance (Field a, Arbitrary a) => Arbitrary (Consistent a) where
208 lb <- vector (k*m) 145 lb <- vector (k*m)
209 return $ Consistent ((n><k) la, (k><m) lb) 146 return $ Consistent ((n><k) la, (k><m) lb)
210 147
211#if MIN_VERSION_QuickCheck(2,0,0)
212 shrink (Consistent (x,y)) = [ Consistent (u,v) | (u,v) <- shrinkPair (x,y) ] 148 shrink (Consistent (x,y)) = [ Consistent (u,v) | (u,v) <- shrinkPair (x,y) ]
213#else
214 coarbitrary = undefined
215#endif
216 149
217 150
218 151
diff --git a/packages/tests/src/Numeric/LinearAlgebra/Tests/Properties.hs b/packages/tests/src/Numeric/LinearAlgebra/Tests/Properties.hs
index a5c37f4..207a303 100644
--- a/packages/tests/src/Numeric/LinearAlgebra/Tests/Properties.hs
+++ b/packages/tests/src/Numeric/LinearAlgebra/Tests/Properties.hs
@@ -1,5 +1,4 @@
1{-# LANGUAGE CPP, FlexibleContexts #-} 1{-# LANGUAGE FlexibleContexts #-}
2{-# OPTIONS_GHC -fno-warn-unused-imports #-}
3{-# LANGUAGE TypeFamilies #-} 2{-# LANGUAGE TypeFamilies #-}
4 3
5----------------------------------------------------------------------------- 4-----------------------------------------------------------------------------
@@ -29,7 +28,7 @@ module Numeric.LinearAlgebra.Tests.Properties (
29 pinvProp, 28 pinvProp,
30 detProp, 29 detProp,
31 nullspaceProp, 30 nullspaceProp,
32 bugProp, 31-- bugProp,
33 svdProp1, svdProp1a, svdProp1b, svdProp2, svdProp3, svdProp4, 32 svdProp1, svdProp1a, svdProp1b, svdProp2, svdProp3, svdProp4,
34 svdProp5a, svdProp5b, svdProp6a, svdProp6b, svdProp7, 33 svdProp5a, svdProp5b, svdProp6a, svdProp6b, svdProp7,
35 eigProp, eigSHProp, eigProp2, eigSHProp2, 34 eigProp, eigSHProp, eigProp2, eigSHProp2,
@@ -43,20 +42,15 @@ module Numeric.LinearAlgebra.Tests.Properties (
43 linearSolveProp, linearSolveProp2 42 linearSolveProp, linearSolveProp2
44) where 43) where
45 44
46import Numeric.Container 45import Numeric.LinearAlgebra.HMatrix hiding (Testable,unitary)
47import Numeric.LinearAlgebra --hiding (real,complex) 46import Test.QuickCheck
48import Numeric.LinearAlgebra.LAPACK
49import Debug.Trace
50import Test.QuickCheck(Arbitrary,arbitrary,coarbitrary,choose,vector
51 ,sized,classify,Testable,Property
52 ,quickCheckWith,maxSize,stdArgs,shrink)
53 47
54trivial :: Testable a => Bool -> a -> Property 48trivial :: Testable a => Bool -> a -> Property
55trivial = (`classify` "trivial") 49trivial = (`classify` "trivial")
56 50
57-- relative error 51-- relative error
58dist :: (Normed c t, Num (c t)) => c t -> c t -> Double 52dist :: (Num a, Normed a) => a -> a -> Double
59dist = relativeError Infinity 53dist = relativeError norm_Inf
60 54
61infixl 4 |~| 55infixl 4 |~|
62a |~| b = a :~10~: b 56a |~| b = a :~10~: b
@@ -73,11 +67,11 @@ a :~n~: b = dist a b < 10^^(-n)
73square m = rows m == cols m 67square m = rows m == cols m
74 68
75-- orthonormal columns 69-- orthonormal columns
76orthonormal m = ctrans m <> m |~| ident (cols m) 70orthonormal m = tr m <> m |~| ident (cols m)
77 71
78unitary m = square m && orthonormal m 72unitary m = square m && orthonormal m
79 73
80hermitian m = square m && m |~| ctrans m 74hermitian m = square m && m |~| tr m
81 75
82wellCond m = rcond m > 1/100 76wellCond m = rcond m > 1/100
83 77
@@ -85,12 +79,12 @@ positiveDefinite m = minimum (toList e) > 0
85 where (e,_v) = eigSH m 79 where (e,_v) = eigSH m
86 80
87upperTriang m = rows m == 1 || down == z 81upperTriang m = rows m == 1 || down == z
88 where down = fromList $ concat $ zipWith drop [1..] (toLists (ctrans m)) 82 where down = fromList $ concat $ zipWith drop [1..] (toLists (tr m))
89 z = konst 0 (dim down) 83 z = konst 0 (size down)
90 84
91upperHessenberg m = rows m < 3 || down == z 85upperHessenberg m = rows m < 3 || down == z
92 where down = fromList $ concat $ zipWith drop [2..] (toLists (ctrans m)) 86 where down = fromList $ concat $ zipWith drop [2..] (toLists (tr m))
93 z = konst 0 (dim down) 87 z = konst 0 (size down)
94 88
95zeros (r,c) = reshape c (konst 0 (r*c)) 89zeros (r,c) = reshape c (konst 0 (r*c))
96 90
@@ -118,81 +112,94 @@ detProp m = s d1 |~| s d2
118 s x = fromList [x] 112 s x = fromList [x]
119 113
120nullspaceProp m = null nl `trivial` (null nl || m <> n |~| zeros (r,c) 114nullspaceProp m = null nl `trivial` (null nl || m <> n |~| zeros (r,c)
121 && orthonormal (fromColumns nl)) 115 && orthonormal n)
122 where nl = nullspacePrec 1 m 116 where n = nullspaceSVD (Left (1*peps)) m (rightSV m)
123 n = fromColumns nl 117 nl = toColumns n
124 r = rows m 118 r = rows m
125 c = cols m - rank m 119 c = cols m - rank m
126 120
127------------------------------------------------------------------ 121------------------------------------------------------------------
128 122{-
129-- testcase for nonempty fpu stack 123-- testcase for nonempty fpu stack
130-- uncommenting unitary' signature eliminates the problem 124-- uncommenting unitary' signature eliminates the problem
131bugProp m = m |~| u <> real d <> trans v && unitary' u && unitary' v 125bugProp m = m |~| u <> real d <> tr v && unitary' u && unitary' v
132 where (u,d,v) = fullSVD m 126 where (u,d,v) = svd m
133 -- unitary' :: (Num (Vector t), Field t) => Matrix t -> Bool 127 -- unitary' :: (Num (Vector t), Field t) => Matrix t -> Bool
134 unitary' a = unitary a 128 unitary' a = unitary a
135 129-}
136------------------------------------------------------------------ 130------------------------------------------------------------------
137 131
138-- fullSVD 132-- fullSVD
139svdProp1 m = m |~| u <> real d <> trans v && unitary u && unitary v 133svdProp1 m = m |~| u <> real d <> tr v && unitary u && unitary v
140 where (u,d,v) = fullSVD m 134 where
135 (u,s,v) = svd m
136 d = diagRect 0 s (rows m) (cols m)
141 137
142svdProp1a svdfun m = m |~| u <> real d <> trans v && unitary u && unitary v where 138svdProp1a svdfun m = m |~| u <> real d <> tr v && unitary u && unitary v
139 where
143 (u,s,v) = svdfun m 140 (u,s,v) = svdfun m
144 d = diagRect 0 s (rows m) (cols m) 141 d = diagRect 0 s (rows m) (cols m)
145 142
146svdProp1b svdfun m = unitary u && unitary v where 143svdProp1b svdfun m = unitary u && unitary v
144 where
147 (u,_,v) = svdfun m 145 (u,_,v) = svdfun m
148 146
149-- thinSVD 147-- thinSVD
150svdProp2 thinSVDfun m = m |~| u <> diag (real s) <> trans v && orthonormal u && orthonormal v && dim s == min (rows m) (cols m) 148svdProp2 thinSVDfun m
151 where (u,s,v) = thinSVDfun m 149 = m |~| u <> diag (real s) <> tr v
150 && orthonormal u && orthonormal v
151 && size s == min (rows m) (cols m)
152 where
153 (u,s,v) = thinSVDfun m
152 154
153-- compactSVD 155-- compactSVD
154svdProp3 m = (m |~| u <> real (diag s) <> trans v 156svdProp3 m = (m |~| u <> real (diag s) <> tr v
155 && orthonormal u && orthonormal v) 157 && orthonormal u && orthonormal v)
156 where (u,s,v) = compactSVD m 158 where
159 (u,s,v) = compactSVD m
157 160
158svdProp4 m' = m |~| u <> real (diag s) <> trans v 161svdProp4 m' = m |~| u <> real (diag s) <> tr v
159 && orthonormal u && orthonormal v 162 && orthonormal u && orthonormal v
160 && (dim s == r || r == 0 && dim s == 1) 163 && (size s == r || r == 0 && size s == 1)
161 where (u,s,v) = compactSVD m 164 where
162 m = fromBlocks [[m'],[m']] 165 (u,s,v) = compactSVD m
163 r = rank m' 166 m = fromBlocks [[m'],[m']]
164 167 r = rank m'
165svdProp5a m = all (s1|~|) [s2,s3,s4,s5,s6] where 168
166 s1 = svR m 169svdProp5a m = all (s1|~|) [s3,s5] where
167 s2 = svRd m 170 s1 = singularValues (m :: Matrix Double)
168 (_,s3,_) = svdR m 171-- s2 = svRd m
169 (_,s4,_) = svdRd m 172 (_,s3,_) = svd m
170 (_,s5,_) = thinSVDR m 173-- (_,s4,_) = svdRd m
171 (_,s6,_) = thinSVDRd m 174 (_,s5,_) = thinSVD m
172 175-- (_,s6,_) = thinSVDRd m
173svdProp5b m = all (s1|~|) [s2,s3,s4,s5,s6] where 176
174 s1 = svC m 177svdProp5b m = all (s1|~|) [s3,s5] where
175 s2 = svCd m 178 s1 = singularValues (m :: Matrix (Complex Double))
176 (_,s3,_) = svdC m 179-- s2 = svCd m
177 (_,s4,_) = svdCd m 180 (_,s3,_) = svd m
178 (_,s5,_) = thinSVDC m 181-- (_,s4,_) = svdCd m
179 (_,s6,_) = thinSVDCd m 182 (_,s5,_) = thinSVD m
183-- (_,s6,_) = thinSVDCd m
180 184
181svdProp6a m = s |~| s' && v |~| v' && s |~| s'' && u |~| u' 185svdProp6a m = s |~| s' && v |~| v' && s |~| s'' && u |~| u'
182 where (u,s,v) = svdR m 186 where
183 (s',v') = rightSVR m 187 (u,s,v) = svd (m :: Matrix Double)
184 (u',s'') = leftSVR m 188 (s',v') = rightSV m
189 (u',s'') = leftSV m
185 190
186svdProp6b m = s |~| s' && v |~| v' && s |~| s'' && u |~| u' 191svdProp6b m = s |~| s' && v |~| v' && s |~| s'' && u |~| u'
187 where (u,s,v) = svdC m 192 where
188 (s',v') = rightSVC m 193 (u,s,v) = svd (m :: Matrix (Complex Double))
189 (u',s'') = leftSVC m 194 (s',v') = rightSV m
195 (u',s'') = leftSV m
190 196
191svdProp7 m = s |~| s' && u |~| u' && v |~| v' && s |~| s''' 197svdProp7 m = s |~| s' && u |~| u' && v |~| v' && s |~| s'''
192 where (u,s,v) = svd m 198 where
193 (s',v') = rightSV m 199 (u,s,v) = svd m
194 (u',_s'') = leftSV m 200 (s',v') = rightSV m
195 s''' = singularValues m 201 (u',_s'') = leftSV m
202 s''' = singularValues m
196 203
197------------------------------------------------------------------ 204------------------------------------------------------------------
198 205
@@ -201,7 +208,7 @@ eigProp m = complex m <> v |~| v <> diag s
201 208
202eigSHProp m = m <> v |~| v <> real (diag s) 209eigSHProp m = m <> v |~| v <> real (diag s)
203 && unitary v 210 && unitary v
204 && m |~| v <> real (diag s) <> ctrans v 211 && m |~| v <> real (diag s) <> tr v
205 where (s, v) = eigSH m 212 where (s, v) = eigSH m
206 213
207eigProp2 m = fst (eig m) |~| eigenvalues m 214eigProp2 m = fst (eig m) |~| eigenvalues m
@@ -226,19 +233,19 @@ rqProp3 m = upperTriang' r
226 where (r,_q) = rq m 233 where (r,_q) = rq m
227 234
228upperTriang' r = upptr (rows r) (cols r) * r |~| r 235upperTriang' r = upptr (rows r) (cols r) * r |~| r
229 where upptr f c = buildMatrix f c $ \(r',c') -> if r'-t > c' then 0 else 1 236 where upptr f c = build (f,c) $ \r' c' -> if r'-t > c' then 0 else 1
230 where t = f-c 237 where t = fromIntegral (f-c)
231 238
232hessProp m = m |~| p <> h <> ctrans p && unitary p && upperHessenberg h 239hessProp m = m |~| p <> h <> tr p && unitary p && upperHessenberg h
233 where (p,h) = hess m 240 where (p,h) = hess m
234 241
235schurProp1 m = m |~| u <> s <> ctrans u && unitary u && upperTriang s 242schurProp1 m = m |~| u <> s <> tr u && unitary u && upperTriang s
236 where (u,s) = schur m 243 where (u,s) = schur m
237 244
238schurProp2 m = m |~| u <> s <> ctrans u && unitary u && upperHessenberg s -- fixme 245schurProp2 m = m |~| u <> s <> tr u && unitary u && upperHessenberg s -- fixme
239 where (u,s) = schur m 246 where (u,s) = schur m
240 247
241cholProp m = m |~| ctrans c <> c && upperTriang c 248cholProp m = m |~| tr c <> c && upperTriang c
242 where c = chol m 249 where c = chol m
243 250
244exactProp m = chol m == chol (m+0) 251exactProp m = chol m == chol (m+0)
@@ -252,7 +259,7 @@ mulH a b = fromLists [[ doth ai bj | bj <- toColumns b] | ai <- toRows a ]
252 259
253multProp1 p (a,b) = (a <> b) :~p~: (mulH a b) 260multProp1 p (a,b) = (a <> b) :~p~: (mulH a b)
254 261
255multProp2 p (a,b) = (ctrans (a <> b)) :~p~: (ctrans b <> ctrans a) 262multProp2 p (a,b) = (tr (a <> b)) :~p~: (tr b <> tr a)
256 263
257linearSolveProp f m = f m m |~| ident (rows m) 264linearSolveProp f m = f m m |~| ident (rows m)
258 265
@@ -261,5 +268,5 @@ linearSolveProp2 f (a,x) = not wc `trivial` (not wc || a <> f a b |~| b)
261 b = a <> x 268 b = a <> x
262 wc = rank a == q 269 wc = rank a == q
263 270
264subProp m = m == (trans . fromColumns . toRows) m 271subProp m = m == (conj . tr . fromColumns . toRows) m
265 272