summaryrefslogtreecommitdiff
path: root/packages/tests/src/Numeric/LinearAlgebra/Tests/Properties.hs
blob: 0de9f3764dd72cea1713ad84763358798eb102ca (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE DataKinds #-}

-----------------------------------------------------------------------------
{- |
Module      :  Numeric.LinearAlgebra.Tests.Properties
Copyright   :  (c) Alberto Ruiz 2008
License     :  BSD3
Maintainer  :  Alberto Ruiz
Stability   :  provisional

Testing properties.

-}

module Numeric.LinearAlgebra.Tests.Properties (
    dist, (|~|), (~~), (~:), Aprox((:~)), (~=),
    zeros, ones,
    square,
    unitary,
    hermitian,
    wellCond,
    positiveDefinite,
    upperTriang,
    upperHessenberg,
    luProp,
    invProp,
    pinvProp,
    detProp,
    nullspaceProp,
--    bugProp,
    svdProp1, svdProp1a, svdProp1b, svdProp2, svdProp3, svdProp4,
    svdProp5a, svdProp5b, svdProp6a, svdProp6b, svdProp7,
    eigProp, eigSHProp, eigProp2, eigSHProp2,
    qrProp, rqProp, rqProp1, rqProp2, rqProp3,
    hessProp,
    schurProp1, schurProp2,
    cholProp, exactProp,
    expmDiagProp,
    multProp1, multProp2,
    subProp,
    linearSolveProp, linearSolvePropH, linearSolveProp2,

    -- Binary properties
    vectorBinaryRoundtripProp
  , staticVectorBinaryRoundtripProp
  , matrixBinaryRoundtripProp
  , staticMatrixBinaryRoundtripProp
  , staticVectorBinaryFailProp
) where

import Numeric.LinearAlgebra.HMatrix hiding (Testable,unitary)
import qualified Numeric.LinearAlgebra.Static as Static
import Test.QuickCheck

import Data.Binary
import Data.Binary.Get (runGet)
import Data.Either (isLeft)
import Debug.Trace (traceShowId)

(~=) :: Double -> Double -> Bool
a ~= b = abs (a - b) < 1e-10

trivial :: Testable a => Bool -> a -> Property
trivial = (`classify` "trivial")

-- relative error
dist :: (Num a, Normed a) => a -> a -> Double
dist = relativeError norm_Inf

infixl 4 |~|
a |~| b = a :~10~: b
--a |~| b = dist a b < 10^^(-10)

a ~~ b = fromList a |~| fromList b

data Aprox a = (:~) a Int
-- (~:) :: (Normed a, Num a) => Aprox a -> a -> Bool
a :~n~: b = dist a b < 10^^(-n)

------------------------------------------------------

square m = rows m == cols m

-- orthonormal columns
orthonormal m = tr m <> m |~| ident (cols m)

unitary m = square m && orthonormal m

hermitian m = square m && m |~| tr m

wellCond m = rcond m > 1/100

positiveDefinite m = minimum (toList e) > 0
    where (e,_v) = eigSH m

upperTriang m = rows m == 1 || down == z
    where down = fromList $ concat $ zipWith drop [1..] (toLists (tr m))
          z = konst 0 (size down)

upperHessenberg m = rows m < 3 || down == z
    where down = fromList $ concat $ zipWith drop [2..] (toLists (tr m))
          z = konst 0 (size down)

zeros (r,c) = reshape c (konst 0 (r*c))

ones (r,c) = zeros (r,c) + 1

-----------------------------------------------------

luProp m = m |~| p <> l <> u && f (det p) |~| f s
    where (l,u,p,s) = lu m
          f x = fromList [x]

invProp m = m <> inv m |~| ident (rows m)

pinvProp m =  m <> p <> m |~| m
           && p <> m <> p |~| p
           && hermitian (m<>p)
           && hermitian (p<>m)
    where p = pinv m

detProp m = s d1 |~| s d2
    where d1 = det m
          d2 = det' * det q
          det' = product $ toList $ takeDiag r
          (q,r) = qr m
          s x = fromList [x]

nullspaceProp m = null nl `trivial` (null nl || m <> n |~| zeros (r,c)
                                     && orthonormal n)
    where n = nullspaceSVD (Left (1*peps)) m (rightSV m)
          nl = toColumns n
          r = rows m
          c = cols m - rank m

------------------------------------------------------------------
{-
-- testcase for nonempty fpu stack
-- uncommenting unitary' signature eliminates the problem
bugProp m = m |~| u <> real d <> tr v && unitary' u && unitary' v
    where (u,d,v) = svd m
          -- unitary' :: (Num (Vector t), Field t) => Matrix t -> Bool
          unitary' a = unitary a
-}
------------------------------------------------------------------

-- fullSVD
svdProp1 m = m |~| u <> real d <> tr v && unitary u && unitary v
  where
    (u,s,v) = svd m
    d = diagRect 0 s (rows m) (cols m)

svdProp1a svdfun m = m |~| u <> real d <> tr v && unitary u && unitary v
  where
    (u,s,v) = svdfun m
    d = diagRect 0 s (rows m) (cols m)

svdProp1b svdfun m = unitary u && unitary v
  where
    (u,_,v) = svdfun m

-- thinSVD
svdProp2 thinSVDfun m
    =  m |~| u <> diag (real s) <> tr v
    && orthonormal u && orthonormal v
    && size s == min (rows m) (cols m)
  where
    (u,s,v) = thinSVDfun m

-- compactSVD
svdProp3 m = (m |~| u <> real (diag s) <> tr v
             && orthonormal u && orthonormal v)
  where
    (u,s,v) = compactSVD m

svdProp4 m' = m |~| u <> real (diag s) <> tr v
           && orthonormal u && orthonormal v
           && (size s == r || r == 0 && size s == 1)
  where
    (u,s,v) = compactSVD m
    m = fromBlocks [[m'],[m']]
    r = rank m'

svdProp5a m = all (s1|~|) [s3,s5] where
    s1       = singularValues (m :: Matrix Double)
--  s2       = svRd m
    (_,s3,_) = svd m
--  (_,s4,_) = svdRd m
    (_,s5,_) = thinSVD m
--  (_,s6,_) = thinSVDRd m

svdProp5b m = all (s1|~|) [s3,s5] where
    s1       = singularValues (m :: Matrix (Complex Double))
--  s2       = svCd m
    (_,s3,_) = svd m
--  (_,s4,_) = svdCd m
    (_,s5,_) = thinSVD m
--  (_,s6,_) = thinSVDCd m

svdProp6a m = s |~| s' && v |~| v' && s |~| s'' && u |~| u'
  where
    (u,s,v) = svd (m :: Matrix Double)
    (s',v') = rightSV m
    (u',s'') = leftSV m

svdProp6b m = s |~| s' && v |~| v' && s |~| s'' && u |~| u'
  where
    (u,s,v) = svd (m :: Matrix (Complex Double))
    (s',v') = rightSV m
    (u',s'') = leftSV m

svdProp7 m = s |~| s' && u |~| u' && v |~| v' && s |~| s'''
  where
    (u,s,v) = svd m
    (s',v') = rightSV m
    (u',_s'') = leftSV m
    s''' = singularValues m

------------------------------------------------------------------

eigProp m = complex m <> v |~| v <> diag s
    where (s, v) = eig m

eigSHProp m = m <> v |~| v <> real (diag s)
              && unitary v
              && m |~| v <> real (diag s) <> tr v
    where (s, v) = eigSH' m

eigProp2 m = fst (eig m) |~| eigenvalues m

eigSHProp2 m = fst (eigSH' m) |~| eigenvaluesSH' m

------------------------------------------------------------------

qrProp m = q <> r |~| m && unitary q && upperTriang r
    where (q,r) = qr m

rqProp m = r <> q |~| m && unitary q && upperTriang' r
    where (r,q) = rq m

rqProp1 m = r <> q |~| m
    where (r,q) = rq m

rqProp2 m = unitary q
    where (_r,q) = rq m

rqProp3 m = upperTriang' r
    where (r,_q) = rq m

upperTriang' r = upptr (rows r) (cols r) * r |~| r
    where upptr f c = build (f,c) $ \r' c' -> if r'-t > c' then 0 else 1
              where t = fromIntegral (f-c)

hessProp m = m |~| p <> h <> tr p && unitary p && upperHessenberg h
    where (p,h) = hess m

schurProp1 m = m |~| u <> s <> tr u && unitary u && upperTriang s
    where (u,s) = schur m

schurProp2 m = m |~| u <> s <> tr u && unitary u && upperHessenberg s -- fixme
    where (u,s) = schur m

cholProp m = m |~| tr c <> c && upperTriang c
    where c = chol (trustSym m)

exactProp m = chol (trustSym m) == chol (trustSym (m+0))

expmDiagProp m = expm (logm m) :~ 7 ~: complex m
    where logm = matFunc log

-- reference multiply
mulH a b = fromLists [[ doth ai bj | bj <- toColumns b] | ai <- toRows a ]
    where doth u v = sum $ zipWith (*) (toList u) (toList v)

multProp1 p (a,b) = (a <> b) :~p~: (mulH a b)

multProp2 p (a,b) = (tr (a <> b)) :~p~: (tr b <> tr a)

linearSolveProp f m = f m m |~| ident (rows m)

linearSolvePropH f m = f m (unSym m) |~| ident (rows (unSym m))

linearSolveProp2 f (a,x) = not wc `trivial` (not wc || a <> f a b |~| b)
    where q = min (rows a) (cols a)
          b = a <> x
          wc = rank a == q

subProp m = m == (conj . tr . fromColumns . toRows) m

------------------------------------------------------------------

vectorBinaryRoundtripProp :: Vector Double -> Bool
vectorBinaryRoundtripProp vec = decode (encode vec) == vec

staticVectorBinaryRoundtripProp :: Static.R 5 -> Bool
staticVectorBinaryRoundtripProp vec =
  let
    decoded = decode (encode vec) :: Static.R 500
  in
    Static.extract decoded == Static.extract vec

matrixBinaryRoundtripProp :: Matrix Double -> Bool
matrixBinaryRoundtripProp mat = decode (encode mat) == mat

staticMatrixBinaryRoundtripProp :: Static.L 100 200 -> Bool
staticMatrixBinaryRoundtripProp mat =
  let
    decoded = decode (encode mat) :: Static.L 100 200
  in
    (Static.extract decoded) == (Static.extract mat)

staticVectorBinaryFailProp :: Static.R 20 -> Bool
staticVectorBinaryFailProp vec =
  let
    decoded = runGet get (encode vec) :: Either String (Static.R 50)
  in
    isLeft decoded