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|
{-# OPTIONS_GHC -fno-warn-unused-imports -fno-warn-incomplete-patterns #-}
{- |
Module : Numeric.GLS.Tests
Copyright : (c) Alberto Ruiz 2014
License : BSD3
Maintainer : Alberto Ruiz
Stability : provisional
Tests for GSL bindings.
-}
module Numeric.GSL.Tests(
runTests
) where
import Control.Monad(when)
import System.Exit (exitFailure)
import Test.HUnit (runTestTT, failures, Test(..), errors)
import Numeric.LinearAlgebra.HMatrix
import Numeric.GSL
import Numeric.GSL.SimulatedAnnealing
import Numeric.LinearAlgebra.Tests (qCheck, utest)
import Numeric.LinearAlgebra.Tests.Properties ((|~|), (~~), (~=))
---------------------------------------------------------------------
fittingTest = utest "levmar" (ok1 && ok2)
where
xs = map return [0 .. 39]
sigma = 0.1
ys = map return $ toList $ fromList (map (head . expModel [5,0.1,1]) xs)
+ scalar sigma * (randomVector 0 Gaussian 40)
dats = zip xs (zip ys (repeat sigma))
dat = zip xs ys
expModel [a,lambda,b] [t] = [a * exp (-lambda * t) + b]
expModelDer [a,lambda,_b] [t] = [[exp (-lambda * t), -t * a * exp(-lambda*t) , 1]]
sols = fst $ fitModelScaled 1E-4 1E-4 20 (expModel, expModelDer) dats [1,0,0]
sol = fst $ fitModel 1E-4 1E-4 20 (expModel, expModelDer) dat [1,0,0]
ok1 = and (zipWith f sols [5,0.1,1]) where f (x,d) r = abs (x-r)<2*d
ok2 = norm_2 (fromList (map fst sols) - fromList sol) < 1E-5
---------------------------------------------------------------------
odeTest = utest "ode" (last (toLists sol) ~~ newsol)
where
sol = odeSolveV RK8pd 1E-6 1E-6 0 (l2v $ vanderpol 10) (fromList [1,0]) ts
ts = linspace 101 (0,100)
l2v f = \t -> fromList . f t . toList
vanderpol mu _t [x,y] = [y, -x + mu * y * (1-x**2) ]
newsol = [-1.758888036617841, 8.364349410519058e-2]
-- oldsol = [-1.7588880332411019, 8.364348908711941e-2]
---------------------------------------------------------------------
rootFindingTest = TestList [ utest "root Hybrids" (fst sol1 ~~ [1,1])
, utest "root Newton" (rows (snd sol2) == 2)
]
where sol1 = root Hybrids 1E-7 30 (rosenbrock 1 10) [-10,-5]
sol2 = rootJ Newton 1E-7 30 (rosenbrock 1 10) (jacobian 1 10) [-10,-5]
rosenbrock a b [x,y] = [ a*(1-x), b*(y-x**2) ]
jacobian a b [x,_y] = [ [-a , 0]
, [-2*b*x, b] ]
--------------------------------------------------------------------
interpolationTest = TestList [
utest "interpolation evaluateV" (esol ~= ev)
, utest "interpolation evaluate" (esol ~= eval)
, utest "interpolation evaluateDerivativeV" (desol ~= dev)
, utest "interpolation evaluateDerivative" (desol ~= de)
, utest "interpolation evaluateDerivative2V" (d2esol ~= d2ev)
, utest "interpolation evaluateDerivative2" (d2esol ~= d2e)
, utest "interpolation evaluateIntegralV" (intesol ~= intev)
, utest "interpolation evaluateIntegral" (intesol ~= inte)
]
where
xtest = 2.2
applyVec f = f Akima xs ys xtest
applyList f = f Akima (zip xs' ys') xtest
esol = xtest**2
ev = applyVec evaluateV
eval = applyList evaluate
desol = 2*xtest
dev = applyVec evaluateDerivativeV
de = applyList evaluateDerivative
d2esol = 2
d2ev = applyVec evaluateDerivative2V
d2e = applyList evaluateDerivative2
intesol = 1/3 * xtest**3
intev = evaluateIntegralV Akima xs ys 0 xtest
inte = evaluateIntegral Akima (zip xs' ys') (0, xtest)
xs' = [-1..10]
ys' = map (**2) xs'
xs = vector xs'
ys = vector ys'
---------------------------------------------------------------------
simanTest = TestList [
-- We use a slightly more relaxed tolerance here because the
-- simulated annealer is randomized
utest "simulated annealing manual example" $ abs (result - 1.3631300) < 1e-6
]
where
-- This is the example from the GSL manual.
result = simanSolve 0 1 exampleParams 15.5 exampleE exampleM exampleS Nothing
exampleParams = SimulatedAnnealingParams 200 10000 1.0 1.0 0.008 1.003 2.0e-6
exampleE x = exp (-(x - 1)**2) * sin (8 * x)
exampleM x y = abs $ x - y
exampleS rands stepSize current = (rands ! 0) * 2 * stepSize - stepSize + current
---------------------------------------------------------------------
minimizationTest = TestList
[ utest "minimization conjugatefr" (minim1 f df [5,7] ~~ [1,2])
, utest "minimization nmsimplex2" (minim2 f [5,7] `elem` [24,25])
]
where f [x,y] = 10*(x-1)**2 + 20*(y-2)**2 + 30
df [x,y] = [20*(x-1), 40*(y-2)]
minim1 g dg ini = fst $ minimizeD ConjugateFR 1E-3 30 1E-2 1E-4 g dg ini
minim2 g ini = rows $ snd $ minimize NMSimplex2 1E-2 30 [1,1] g ini
---------------------------------------------------------------------
derivTest = abs (d (\x-> x * d (\y-> x+y) 1) 1 - 1) < 1E-10
where d f x = fst $ derivCentral 0.01 f x
---------------------------------------------------------------------
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
--------------------------------------------------------------------
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))
-- | 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
let test p = qCheck n p
putStrLn "------ fft"
test (\v -> ifft (fft v) |~| v)
c <- runTestTT $ TestList
[ fittingTest
, odeTest
, rootFindingTest
, minimizationTest
, interpolationTest
, simanTest
, utest "deriv" derivTest
, utest "integrate" (abs (volSphere 2.5 - 4/3*pi*2.5**3) < 1E-8)
, utest "polySolve" (polySolveProp [1,2,3,4])
]
when (errors c + failures c > 0) exitFailure
return ()
|
