module Tests.Chebyshev ( tests ) where import Data.Vector.Unboxed (fromList) import Test.Framework import Test.Framework.Providers.QuickCheck2 import Test.QuickCheck (Arbitrary(..)) import Tests.Helpers import Numeric.Polynomial.Chebyshev tests :: Test tests = testGroup "Chebyshev polynomials" [ testProperty "Chebyshev 0" \$ \a0 (Ch x) -> (ch0 x * a0) ≈ (chebyshev x \$ fromList [a0]) , testProperty "Chebyshev 1" \$ \a0 a1 (Ch x) -> (a0*ch0 x + a1*ch1 x) ≈ (chebyshev x \$ fromList [a0,a1]) , testProperty "Chebyshev 2" \$ \a0 a1 a2 (Ch x) -> (a0*ch0 x + a1*ch1 x + a2*ch2 x) ≈ (chebyshev x \$ fromList [a0,a1,a2]) , testProperty "Chebyshev 3" \$ \a0 a1 a2 a3 (Ch x) -> (a0*ch0 x + a1*ch1 x + a2*ch2 x + a3*ch3 x) ≈ (chebyshev x \$ fromList [a0,a1,a2,a3]) , testProperty "Chebyshev 4" \$ \a0 a1 a2 a3 a4 (Ch x) -> (a0*ch0 x + a1*ch1 x + a2*ch2 x + a3*ch3 x + a4*ch4 x) ≈ (chebyshev x \$ fromList [a0,a1,a2,a3,a4]) ] where (≈) = eq 1e-12 -- Chebyshev polynomials of low order ch0,ch1,ch2,ch3,ch4 :: Double -> Double ch0 _ = 1 ch1 x = x ch2 x = 2*x^2 - 1 ch3 x = 4*x^3 - 3*x ch4 x = 8*x^4 - 8*x^2 + 1 -- Double in the [-1 .. 1] range newtype Ch = Ch Double deriving Show instance Arbitrary Ch where arbitrary = do x <- arbitrary return \$ Ch \$ 2 * (snd . properFraction) x - 1