module Numeric.LinearAlgebra.Tests(
qCheck, runTests
) 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
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*rx*xy*y))
0 r (const 0) (\x->sqrt (r*rx*x))
besselTest = utest "bessel_J0_e" ( abs (rexpected) < 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)
runTests :: Int
-> 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 "------ 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*i51).*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 ()