diff options
Diffstat (limited to 'packages/base')
-rw-r--r-- | packages/base/CHANGELOG | 7 | ||||
-rw-r--r-- | packages/base/hmatrix.cabal | 49 | ||||
-rw-r--r-- | packages/base/src/Data/Packed/IO.hs | 1 | ||||
-rw-r--r-- | packages/base/src/Data/Packed/Internal/Numeric.hs | 1 | ||||
-rw-r--r-- | packages/base/src/Data/Packed/Internal/Vector.hs | 1 | ||||
-rw-r--r-- | packages/base/src/Data/Packed/Numeric.hs | 8 | ||||
-rw-r--r-- | packages/base/src/Numeric/Chain.hs | 2 | ||||
-rw-r--r-- | packages/base/src/Numeric/LinearAlgebra.hs | 231 | ||||
-rw-r--r-- | packages/base/src/Numeric/LinearAlgebra/Algorithms.hs | 18 | ||||
-rw-r--r-- | packages/base/src/Numeric/LinearAlgebra/HMatrix.hs | 228 | ||||
-rw-r--r-- | packages/base/src/Numeric/LinearAlgebra/LAPACK.hs | 6 | ||||
-rw-r--r-- | packages/base/src/Numeric/LinearAlgebra/Static.hs | 32 | ||||
-rw-r--r-- | packages/base/src/Numeric/LinearAlgebra/Static/Internal.hs | 4 | ||||
-rw-r--r-- | packages/base/src/Numeric/LinearAlgebra/Util.hs | 58 | ||||
-rw-r--r-- | packages/base/src/Numeric/LinearAlgebra/Util/CG.hs | 6 | ||||
-rw-r--r-- | packages/base/src/Numeric/Vectorized.hs | 1 |
16 files changed, 294 insertions, 359 deletions
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 @@ | |||
1 | 0.17.0.0 | ||
2 | -------- | ||
3 | |||
4 | * old compatibility modules removed | ||
5 | |||
6 | * added "unitary" and "pairwiseD2" | ||
7 | |||
1 | 0.16.1.0 | 8 | 0.16.1.0 |
2 | -------- | 9 | -------- |
3 | 10 | ||
diff --git a/packages/base/hmatrix.cabal b/packages/base/hmatrix.cabal index 3895dc1..69ec8fa 100644 --- a/packages/base/hmatrix.cabal +++ b/packages/base/hmatrix.cabal | |||
@@ -1,5 +1,5 @@ | |||
1 | Name: hmatrix | 1 | Name: hmatrix |
2 | Version: 0.16.1.5 | 2 | Version: 0.17.0.0 |
3 | License: BSD3 | 3 | License: BSD3 |
4 | License-file: LICENSE | 4 | License-file: LICENSE |
5 | Author: Alberto Ruiz | 5 | Author: Alberto Ruiz |
@@ -9,16 +9,6 @@ Homepage: https://github.com/albertoruiz/hmatrix | |||
9 | Synopsis: Numeric Linear Algebra | 9 | Synopsis: Numeric Linear Algebra |
10 | Description: Linear algebra based on BLAS and LAPACK. | 10 | Description: 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 | ||
24 | Category: Math | 14 | Category: Math |
@@ -39,7 +29,7 @@ flag openblas | |||
39 | 29 | ||
40 | library | 30 | library |
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 | 49 | ||
73 | 50 | other-modules: Data.Packed, | |
74 | other-modules: Data.Packed.Internal, | 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 |
@@ -101,7 +87,12 @@ library | |||
101 | -fno-warn-missing-signatures | 87 | -fno-warn-missing-signatures |
102 | -fno-warn-orphans | 88 | -fno-warn-orphans |
103 | 89 | ||
104 | cc-options: -O4 -msse2 -Wall | 90 | cc-options: -O4 -Wall |
91 | |||
92 | if arch(x86_64) | ||
93 | cc-options: -msse2 | ||
94 | if arch(i386) | ||
95 | cc-options: -msse2 | ||
105 | 96 | ||
106 | cpp-options: -DBINARY | 97 | cpp-options: -DBINARY |
107 | 98 | ||
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) | |||
22 | import Data.List(intersperse) | 22 | import Data.List(intersperse) |
23 | import Data.Complex | 23 | import Data.Complex |
24 | import Numeric.Vectorized(vectorScan,saveMatrix) | 24 | import Numeric.Vectorized(vectorScan,saveMatrix) |
25 | import Control.Applicative((<$>)) | ||
26 | import Data.Packed.Internal | 25 | import 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 | |||
48 | import Data.Packed.Development | 48 | import Data.Packed.Development |
49 | import Numeric.Vectorized | 49 | import Numeric.Vectorized |
50 | import Data.Complex | 50 | import Data.Complex |
51 | import Control.Applicative((<*>)) | ||
52 | 51 | ||
53 | import Numeric.LinearAlgebra.LAPACK(multiplyR,multiplyC,multiplyF,multiplyQ) | 52 | import Numeric.LinearAlgebra.LAPACK(multiplyR,multiplyC,multiplyF,multiplyQ) |
54 | import Data.Packed.Internal | 53 | import 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) | |||
35 | import Foreign.Storable(Storable, peekElemOff, pokeElemOff, sizeOf) | 35 | import Foreign.Storable(Storable, peekElemOff, pokeElemOff, sizeOf) |
36 | import Foreign.C.Types | 36 | import Foreign.C.Types |
37 | import Data.Complex | 37 | import Data.Complex |
38 | import Control.Monad(when) | ||
39 | import System.IO.Unsafe(unsafePerformIO) | 38 | import 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 | |||
71 | import Data.Packed.Internal.Numeric | 71 | import Data.Packed.Internal.Numeric |
72 | import Data.Complex | 72 | import Data.Complex |
73 | import Numeric.LinearAlgebra.Algorithms(Field,linearSolveSVD) | 73 | import Numeric.LinearAlgebra.Algorithms(Field,linearSolveSVD) |
74 | import Data.Monoid(Monoid(mconcat)) | ||
75 | import Data.Packed.IO | 74 | import Data.Packed.IO |
76 | import Numeric.LinearAlgebra.Random | 75 | import Numeric.LinearAlgebra.Random |
77 | 76 | ||
@@ -142,6 +141,11 @@ fromList [140.0,320.0] | |||
142 | app :: Numeric t => Matrix t -> Vector t -> Vector t | 141 | app :: Numeric t => Matrix t -> Vector t -> Vector t |
143 | app = (#>) | 142 | app = (#>) |
144 | 143 | ||
144 | infixl 8 <# | ||
145 | -- | dense vector-matrix product | ||
146 | (<#) :: Numeric t => Vector t -> Matrix t -> Vector t | ||
147 | (<#) = vXm | ||
148 | |||
145 | -------------------------------------------------------------------------------- | 149 | -------------------------------------------------------------------------------- |
146 | 150 | ||
147 | class Mul a b c | a b -> c where | 151 | class 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 | {- | |
3 | Module : Numeric.LinearAlgebra | 3 | Module : Numeric.LinearAlgebra |
4 | Copyright : (c) Alberto Ruiz 2006-14 | 4 | Copyright : (c) Alberto Ruiz 2006-15 |
5 | License : BSD3 | 5 | License : BSD3 |
6 | Maintainer : Alberto Ruiz | 6 | Maintainer : Alberto Ruiz |
7 | Stability : provisional | 7 | Stability : provisional |
8 | 8 | ||
9 | -} | 9 | -} |
10 | -------------------------------------------------------------------------------- | 10 | ----------------------------------------------------------------------------- |
11 | {-# OPTIONS_HADDOCK hide #-} | ||
12 | |||
13 | module Numeric.LinearAlgebra ( | 11 | module 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 | ||
18 | import Numeric.Container | 151 | import Numeric.LinearAlgebra.Data |
19 | import Numeric.LinearAlgebra.Algorithms | 152 | |
20 | import Numeric.Matrix() | 153 | import Numeric.Matrix() |
21 | import Numeric.Vector() | 154 | import Numeric.Vector() |
155 | import Data.Packed.Numeric hiding ((<>), mul) | ||
156 | import Numeric.LinearAlgebra.Algorithms hiding (linearSolve,Normed,orth) | ||
157 | import qualified Numeric.LinearAlgebra.Algorithms as A | ||
158 | import Numeric.LinearAlgebra.Util | ||
159 | import Numeric.LinearAlgebra.Random | ||
160 | import Numeric.Sparse((!#>)) | ||
161 | import 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 | ||
190 | infixr 8 <> | ||
191 | |||
192 | -- | dense matrix product | ||
193 | mul :: Numeric t => Matrix t -> Matrix t -> Matrix t | ||
194 | mul = 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 | @ | ||
200 | a = (2><2) | ||
201 | [ 1.0, 2.0 | ||
202 | , 3.0, 5.0 ] | ||
203 | @ | ||
204 | |||
205 | @ | ||
206 | b = (2><3) | ||
207 | [ 6.0, 1.0, 10.0 | ||
208 | , 15.0, 3.0, 26.0 ] | ||
209 | @ | ||
210 | |||
211 | >>> linearSolve a b | ||
212 | Just (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 | ||
218 | 2x3 | ||
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 | -} | ||
228 | linearSolve m b = A.mbLinearSolve m b | ||
229 | |||
230 | -- | return an orthonormal basis of the null space of a matrix. See also 'nullspaceSVD'. | ||
231 | nullspace m = nullspaceSVD (Left (1*eps)) m (rightSV m) | ||
232 | |||
233 | -- | return an orthonormal basis of the range space of a matrix. See also 'orthSVD'. | ||
234 | orth 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 | -} |
230 | svd :: Field t => Matrix t -> (Matrix t, Vector Double, Matrix t) | 230 | svd :: Field t => Matrix t -> (Matrix t, Vector Double, Matrix t) |
231 | svd = {-# SCC "svd" #-} svd' | 231 | svd = {-# 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 | -} |
274 | thinSVD :: Field t => Matrix t -> (Matrix t, Vector Double, Matrix t) | 276 | thinSVD :: Field t => Matrix t -> (Matrix t, Vector Double, Matrix t) |
275 | thinSVD = {-# SCC "thinSVD" #-} thinSVD' | 277 | thinSVD = {-# 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. |
278 | singularValues :: Field t => Matrix t -> Vector Double | 283 | singularValues :: Field t => Matrix t -> Vector Double |
@@ -587,7 +592,7 @@ m = (3><3) [ 1, 0, 0 | |||
587 | -} | 592 | -} |
588 | 593 | ||
589 | pinvTol :: Field t => Double -> Matrix t -> Matrix t | 594 | pinvTol :: Field t => Double -> Matrix t -> Matrix t |
590 | pinvTol t m = conj v' `mXm` diag s' `mXm` ctrans u' where | 595 | pinvTol 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 | ||
938 | relativeError :: (Normed c t, Num (c t)) => NormType -> c t -> c t -> Double | 943 | relativeError :: Num a => (a -> Double) -> a -> a -> Double |
939 | relativeError t a b = realToFrac r | 944 | relativeError 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 | {- | |
3 | Module : Numeric.LinearAlgebra.HMatrix | 3 | Module : Numeric.LinearAlgebra.HMatrix |
4 | Copyright : (c) Alberto Ruiz 2006-14 | 4 | Copyright : (c) Alberto Ruiz 2006-14 |
@@ -7,229 +7,11 @@ Maintainer : Alberto Ruiz | |||
7 | Stability : provisional | 7 | Stability : provisional |
8 | 8 | ||
9 | -} | 9 | -} |
10 | ----------------------------------------------------------------------------- | 10 | -------------------------------------------------------------------------------- |
11 | module 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, | 12 | module 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 | ||
151 | import Numeric.LinearAlgebra.Data | 16 | import Numeric.LinearAlgebra |
152 | |||
153 | import Numeric.Matrix() | ||
154 | import Numeric.Vector() | ||
155 | import Data.Packed.Numeric hiding ((<>), mul) | ||
156 | import Numeric.LinearAlgebra.Algorithms hiding (linearSolve,Normed,orth) | ||
157 | import qualified Numeric.LinearAlgebra.Algorithms as A | ||
158 | import Numeric.LinearAlgebra.Util | ||
159 | import Numeric.LinearAlgebra.Random | ||
160 | import Numeric.Sparse((!#>)) | ||
161 | import 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 | ||
190 | infixr 8 <> | ||
191 | |||
192 | -- | dense matrix product | ||
193 | mul :: Numeric t => Matrix t -> Matrix t -> Matrix t | ||
194 | mul = 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 | @ | ||
200 | a = (2><2) | ||
201 | [ 1.0, 2.0 | ||
202 | , 3.0, 5.0 ] | ||
203 | @ | ||
204 | |||
205 | @ | ||
206 | b = (2><3) | ||
207 | [ 6.0, 1.0, 10.0 | ||
208 | , 15.0, 3.0, 26.0 ] | ||
209 | @ | ||
210 | |||
211 | >>> linearSolve a b | ||
212 | Just (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 | ||
218 | 2x3 | ||
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 | -} | ||
228 | linearSolve m b = A.mbLinearSolve m b | ||
229 | |||
230 | -- | return an orthonormal basis of the null space of a matrix. See also 'nullspaceSVD'. | ||
231 | nullspace m = nullspaceSVD (Left (1*eps)) m (rightSV m) | ||
232 | |||
233 | -- | return an orthonormal basis of the range space of a matrix. See also 'orthSVD'. | ||
234 | orth 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 | ||
65 | import GHC.TypeLits | 62 | import GHC.TypeLits |
66 | import Numeric.LinearAlgebra.HMatrix hiding ( | 63 | import 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) |
72 | import qualified Numeric.LinearAlgebra.HMatrix as LA | 69 | import qualified Numeric.LinearAlgebra as LA |
73 | import Data.Proxy(Proxy) | 70 | import Data.Proxy(Proxy) |
74 | import Numeric.LinearAlgebra.Static.Internal | 71 | import Numeric.LinearAlgebra.Static.Internal |
75 | import Control.Arrow((***)) | 72 | import Control.Arrow((***)) |
@@ -184,8 +181,9 @@ a ¦ b = tr (tr a —— tr b) | |||
184 | type Sq n = L n n | 181 | type Sq n = L n n |
185 | --type CSq n = CL n n | 182 | --type CSq n = CL n n |
186 | 183 | ||
187 | type GL = forall n m. (KnownNat n, KnownNat m) => L m n | 184 | |
188 | type GSq = forall n. KnownNat n => Sq n | 185 | type GL = forall n m . (KnownNat n, KnownNat m) => L m n |
186 | type GSq = forall n . KnownNat n => Sq n | ||
189 | 187 | ||
190 | isKonst :: forall m n . (KnownNat m, KnownNat n) => L m n -> Maybe (ℝ,(Int,Int)) | 188 | isKonst :: forall m n . (KnownNat m, KnownNat n) => L m n -> Maybe (ℝ,(Int,Int)) |
191 | isKonst s@(unwrap -> x) | 189 | isKonst 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 | {- | | ||
624 | Module : Numeric.LinearAlgebra.Static | ||
625 | Copyright : (c) Alberto Ruiz 2014 | ||
626 | License : BSD3 | ||
627 | Stability : experimental | ||
628 | |||
629 | Experimental interface with statically checked dimensions. | ||
630 | |||
631 | This module requires GHC >= 7.8 | ||
632 | |||
633 | -} | ||
634 | |||
635 | module Numeric.LinearAlgebra.Static | ||
636 | {-# WARNING "This module requires GHC >= 7.8" #-} | ||
637 | where | ||
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 | ||
26 | import GHC.TypeLits | 26 | import GHC.TypeLits |
27 | import qualified Numeric.LinearAlgebra.HMatrix as LA | 27 | import qualified Numeric.LinearAlgebra as LA |
28 | import Numeric.LinearAlgebra.HMatrix hiding (konst,size) | 28 | import Numeric.LinearAlgebra hiding (konst,size) |
29 | import Data.Packed as D | 29 | import Data.Packed as D |
30 | import Data.Packed.ST | 30 | import Data.Packed.ST |
31 | import Data.Proxy(Proxy) | 31 | import 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 | ||
21 | module Numeric.LinearAlgebra.Util( | 20 | module 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 | ||
70 | import Data.Packed.Numeric | 58 | import Data.Packed.Numeric |
@@ -227,10 +215,11 @@ infixl 9 ¿ | |||
227 | (¿)= flip extractColumns | 215 | (¿)= flip extractColumns |
228 | 216 | ||
229 | 217 | ||
230 | cross :: Vector Double -> Vector Double -> Vector Double | 218 | cross :: Product t => Vector t -> Vector t -> Vector t |
231 | -- ^ cross product (for three-element real vectors) | 219 | -- ^ cross product (for three-element vectors) |
232 | cross x y | dim x == 3 && dim y == 3 = fromList [z1,z2,z3] | 220 | cross 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 | |||
241 | norm :: Vector Double -> Double | 233 | norm :: Vector Double -> Double |
242 | -- ^ 2-norm of real vector | 234 | -- ^ 2-norm of real vector |
243 | norm = pnorm PNorm2 | 235 | norm = pnorm PNorm2 |
@@ -403,40 +395,6 @@ null1sym = last . toColumns . snd . eigSH' | |||
403 | 395 | ||
404 | -------------------------------------------------------------------------------- | 396 | -------------------------------------------------------------------------------- |
405 | 397 | ||
406 | vec :: Element t => Matrix t -> Vector t | ||
407 | -- ^ stacking of columns | ||
408 | vec = flatten . trans | ||
409 | |||
410 | |||
411 | vech :: Element t => Matrix t -> Vector t | ||
412 | -- ^ half-vectorization (of the lower triangular part) | ||
413 | vech m = vjoin . zipWith f [0..] . toColumns $ m | ||
414 | where | ||
415 | f k v = subVector k (dim v - k) v | ||
416 | |||
417 | |||
418 | dup :: (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) | ||
420 | dup 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 | |||
431 | vtrans :: Element t => Int -> Matrix t -> Matrix t | ||
432 | -- ^ generalized \"vector\" transposition: @'vtrans' 1 == 'trans'@, and @'vtrans' ('rows' m) m == 'asColumn' ('vec' m)@ | ||
433 | vtrans 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 | |||
440 | infixl 0 ~!~ | 398 | infixl 0 ~!~ |
441 | c ~!~ msg = when c (error msg) | 399 | c ~!~ 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( | |||
9 | import Data.Packed.Numeric | 9 | import Data.Packed.Numeric |
10 | import Numeric.Sparse | 10 | import Numeric.Sparse |
11 | import Numeric.Vector() | 11 | import Numeric.Vector() |
12 | import Numeric.LinearAlgebra.Algorithms(linearSolveLS, relativeError, NormType(..)) | 12 | import Numeric.LinearAlgebra.Algorithms(linearSolveLS, relativeError, pnorm, NormType(..)) |
13 | import Control.Arrow((***)) | 13 | import 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 | |||
37 | import System.IO.Unsafe(unsafePerformIO) | 37 | import System.IO.Unsafe(unsafePerformIO) |
38 | 38 | ||
39 | import Control.Monad(when) | 39 | import Control.Monad(when) |
40 | import Control.Applicative((<$>)) | ||
41 | 40 | ||
42 | 41 | ||
43 | 42 | ||