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ChebyshevSpec.hs
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ChebyshevSpec.hs
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module ChebyshevSpec where
import Test.QuickCheck
import Test.QuickCheck.Instances()
import Chebyshev
-- | Approximate floating-point equality
approx :: (RealFrac a, Show a) => a -> a -> a -> Property
approx eps x y = counterexample (show x ++ " /= " ++ show y) (abs (x - y) < eps)
-- | n-th Chebyshev polynomial
cheb :: Num a => Int -> a -> a
cheb n = chebyshev (replicate n 0 ++ [1])
-- | Recurrence relation for Chebyshev polynomials
recur :: Num a => Int -> a -> a
recur n x = if | n == 0 -> 1
| n == 1 -> x
| otherwise -> 2 * x * cheb (n - 1) x - cheb (n - 2) x
prop_Chebyshev_recurrence ::
NonNegative (Small Int) -> Integer -> Property
prop_Chebyshev_recurrence (NonNegative (Small n)) x =
cheb n x === recur n x
-- prop_Chebyshev_approx :: NonNegative (Small Int) -> Property
-- prop_Chebyshev_approx (NonNegative (Small n)) =
-- conjoin (zipWith (approx 1.0e-13) coeffs' coeffs)
-- where phi :: Double -> Double
-- phi = cheb n
-- coeffs = replicate n 0 ++ [1] ++ replicate n 0
-- coeffs' = chebyshevApprox (2 * n + 1) phi
newtype Small1 a = Small1 a
deriving (Eq, Ord, Read, Show, Prelude.Functor)
instance Arbitrary a => Arbitrary (Small1 a) where
arbitrary = Small1 Prelude.<$> scale (`div` 10) arbitrary
shrink (Small1 x) = Small1 Prelude.<$> shrink x
prop_Chebyshev_approx :: Small1 [Double] -> Property
prop_Chebyshev_approx (Small1 cs') =
conjoin (zipWith (approx (1.0e-13 * maxc)) cs fcs)
where cs = cs' ++ [1]
maxc = maximum (fmap abs cs)
n = length cs
f = chebyshev cs
fcs = chebyshevApprox n f