summaryrefslogtreecommitdiff
path: root/lib/Numeric/LinearAlgebra/Tests.hs
blob: 7b280750fa05ed3a65ec217b0815c4b823f21a03 (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
-----------------------------------------------------------------------------
{- |
Module      :  Numeric.LinearAlgebra.Tests
Copyright   :  (c) Alberto Ruiz 2007
License     :  GPL-style

Maintainer  :  Alberto Ruiz (aruiz at um dot es)
Stability   :  provisional
Portability :  portable

Some tests.

-}

module Numeric.LinearAlgebra.Tests(
--  module Numeric.LinearAlgebra.Tests.Instances,
--  module Numeric.LinearAlgebra.Tests.Properties,
  qCheck, runTests
--, runBigTests
) where

import Numeric.LinearAlgebra
import Numeric.LinearAlgebra.Tests.Instances
import Numeric.LinearAlgebra.Tests.Properties
import Test.QuickCheck
import Test.HUnit hiding ((~:),test)
import System.Info
import Data.List(foldl1')
import Numeric.GSL hiding (sin,cos,exp,choose)

qCheck n = check defaultConfig {configSize = const n}

utest str b = TestCase $ assertBool str b

feye n = flipud (ident n) :: Matrix Double

detTest1 = det m == 26
        && det mc == 38 :+ (-3)
        && det (feye 2) == -1
    where
        m = (3><3) 
            [ 1, 2, 3
            , 4, 5, 7
            , 2, 8, 4 :: Double
            ]
        mc = (3><3)
            [ 1, 2, 3
            , 4, 5, 7
            , 2, 8, i
            ]

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

polyEval cs x = foldr (\c ac->ac*x+c) 0 cs

polySolveProp p = length p <2 || last p == 0|| 1E-8 > maximum (map magnitude $ map (polyEval (map (:+0) p)) (polySolve p))

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

quad f a b = fst $ integrateQAGS 1E-9 100 f a b

-- A multiple integral can be easily defined using partial application
quad2 f a b g1 g2 = quad h a b
    where h x = quad (f x) (g1 x) (g2 x)

volSphere r = 8 * quad2 (\x y -> sqrt (r*r-x*x-y*y)) 
                        0 r (const 0) (\x->sqrt (r*r-x*x))

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

besselTest = utest "bessel_J0_e" ( abs (r-expected) < e )
    where (r,e) = bessel_J0_e 5.0
          expected = -0.17759677131433830434739701

exponentialTest = utest "exp_e10_e" ( abs (v*10^e - expected) < 4E-2 )
    where (v,e,err) = exp_e10_e 30.0
          expected = exp 30.0

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

nd1 = (3><3) [ 1/2, 1/4, 1/4
             , 0/1, 1/2, 1/4
             , 1/2, 1/4, 1/2 :: Double]

nd2 = (2><2) [1, 0, 1, 1:: Complex Double]

expmTest1 = expm nd1 :~14~: (3><3)
 [ 1.762110887278176
 , 0.478085470590435
 , 0.478085470590435
 , 0.104719410945666
 , 1.709751181805343
 , 0.425725765117601
 , 0.851451530235203
 , 0.530445176063267
 , 1.814470592751009 ]

expmTest2 = expm nd2 :~15~: (2><2)
 [ 2.718281828459045
 , 0.000000000000000
 , 2.718281828459045
 , 2.718281828459045 ]


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

rot :: Double -> Matrix Double
rot a = (3><3) [ c,0,s
               , 0,1,0
               ,-s,0,c ]
    where c = cos a
          s = sin a

rotTest = fun (10^5) :~12~: rot 5E4
    where fun n = foldl1' (<>) (map rot angles)
              where angles = toList $ linspace n (0,1)


-- | All tests must pass with a maximum dimension of about 20
--  (some tests may fail with bigger sizes due to precision loss).
runTests :: Int  -- ^ maximum dimension
         -> IO ()
runTests n = do
    setErrorHandlerOff
    let test p = qCheck n p
    putStrLn "------ lu"
    test (luProp    . rM)
    test (luProp    . cM)
    putStrLn "------ inv"
    test (invProp   . rSqWC)
    test (invProp   . cSqWC)
    putStrLn "------ pinv"
    test (pinvProp  . rM)
    if os == "mingw32"
        then putStrLn "complex pinvTest skipped in this OS"
        else test (pinvProp  . cM)
    putStrLn "------ det"
    test (detProp   . rSqWC)
    test (detProp   . cSqWC)
    putStrLn "------ svd"
    test (svdProp1  . rM)
    test (svdProp1  . cM)
    test (svdProp2  . rM)
    test (svdProp2  . cM)
    putStrLn "------ eig"
    test (eigSHProp . rHer)
    test (eigSHProp . cHer)
    test (eigProp   . rSq)
    test (eigProp   . cSq)
    putStrLn "------ nullSpace"
    test (nullspaceProp . rM)
    test (nullspaceProp . cM)
    putStrLn "------ qr"
    test (qrProp     . rM)
    test (qrProp     . cM)
    putStrLn "------ hess"
    test (hessProp   . rSq)
    test (hessProp   . cSq)
    putStrLn "------ schur"
    test (schurProp2 . rSq)
    if os == "mingw32"
        then putStrLn "complex schur skipped in this OS"
        else test (schurProp1 . cSq)
    putStrLn "------ chol"
    test (cholProp   . rPosDef)
    test (cholProp   . cPosDef)
    putStrLn "------ expm"
    test (expmDiagProp . rSqWC)
    test (expmDiagProp . cSqWC)
    putStrLn "------ fft"
    test (\v -> ifft (fft v) |~| v)
    putStrLn "------ vector operations"
    test (\u -> sin u ^ 2 + cos u ^ 2 |~| (1::RM))
    test (\u -> sin u ** 2 + cos u ** 2 |~| (1::RM))
    test (\u -> cos u * tan u |~| sin (u::RM))
    test (\u -> (cos u * tan u) |~| sin (u::CM))
    putStrLn "------ read . show"
    test (\m -> (m::RM) == read (show m))
    test (\m -> (m::CM) == read (show m))
    test (\m -> toRows (m::RM) == read (show (toRows m)))
    test (\m -> toRows (m::CM) == read (show (toRows m)))
    putStrLn "------ some unit tests"
    runTestTT $ TestList
        [ utest "1E5 rots" rotTest
        , utest "det1" detTest1
        , utest "expm1" (expmTest1)
        , utest "expm2" (expmTest2)
        , utest "arith1" $ ((ones (100,100) * 5 + 2)/0.5 - 7)**2 |~| (49 :: RM)
        , utest "arith2" $ (((1+i) .* ones (100,100) * 5 + 2)/0.5 - 7)**2 |~| ( (140*i-51).*1 :: CM)
        , utest "arith3" $ exp (i.*ones(10,10)*pi) + 1 |~| 0
        , utest "<\\>"   $ (3><2) [2,0,0,3,1,1::Double] <\> 3|>[4,9,5] |~| 2|>[2,3]
        , utest "gamma" (gamma 5 == 24.0)
        , besselTest
        , exponentialTest
        , utest "integrate" (abs (volSphere 2.5 - 4/3*pi*2.5^3) < 1E-8)
        , utest "polySolve" (polySolveProp [1,2,3,4])
        ]
    return ()

-- -- | Some additional tests on big matrices. They take a few minutes.
-- runBigTests :: IO ()
-- runBigTests = undefined