poly-0.3.0.0: test/Sparse.hs

{-# LANGUAGE FlexibleContexts           #-}
{-# LANGUAGE FlexibleInstances          #-}
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
{-# LANGUAGE ScopedTypeVariables        #-}
{-# LANGUAGE UndecidableInstances       #-}

{-# OPTIONS_GHC -fno-warn-orphans #-}

module Sparse
  ( testSuite
  ) where

import Prelude hiding (quotRem)
import Data.Euclidean
import Data.Function
import Data.Int
import Data.List
import Data.Poly.Sparse
import qualified Data.Poly.Sparse.Semiring as S
import Data.Proxy
import Data.Semiring (Semiring)
import qualified Data.Vector as V
import qualified Data.Vector.Generic as G
import qualified Data.Vector.Unboxed as U
import Test.Tasty
import Test.Tasty.QuickCheck hiding (scale)
import Test.QuickCheck.Classes

instance (Eq a, Semiring a, Arbitrary a, G.Vector v (Word, a)) => Arbitrary (Poly v a) where
  arbitrary = S.toPoly . G.fromList <$> arbitrary
  shrink = fmap (S.toPoly . G.fromList) . shrink . G.toList . unPoly

newtype ShortPoly a = ShortPoly { unShortPoly :: a }
  deriving (Eq, Show, Semiring, GcdDomain, Euclidean)

instance (Eq a, Semiring a, Arbitrary a, G.Vector v (Word, a)) => Arbitrary (ShortPoly (Poly v a)) where
  arbitrary = ShortPoly . S.toPoly . G.fromList . (\xs -> take (length xs `mod` 5) xs) <$> arbitrary
  shrink = fmap (ShortPoly . S.toPoly . G.fromList) . shrink . G.toList . unPoly . unShortPoly

testSuite :: TestTree
testSuite = testGroup "Sparse"
    [ arithmeticTests
    , otherTests
    , semiringTests
    , evalTests
    , derivTests
    ]

semiringTests :: TestTree
semiringTests
  = testGroup "Semiring"
  $ map (uncurry testProperty)
  $ concatMap lawsProperties
  [ semiringLaws (Proxy :: Proxy (Poly U.Vector ()))
  ,     ringLaws (Proxy :: Proxy (Poly U.Vector ()))
  , semiringLaws (Proxy :: Proxy (Poly U.Vector Int8))
  ,     ringLaws (Proxy :: Proxy (Poly U.Vector Int8))
  , semiringLaws (Proxy :: Proxy (Poly V.Vector Integer))
  ,     ringLaws (Proxy :: Proxy (Poly V.Vector Integer))
  ]

arithmeticTests :: TestTree
arithmeticTests = testGroup "Arithmetic"
  [ testProperty "addition matches reference" $
    \(xs :: [(Word, Int)]) ys -> toPoly (V.fromList (addRef xs ys)) ===
      toPoly (V.fromList xs) + toPoly (V.fromList ys)
  , testProperty "subtraction matches reference" $
    \(xs :: [(Word, Int)]) ys -> toPoly (V.fromList (subRef xs ys)) ===
      toPoly (V.fromList xs) - toPoly (V.fromList ys)
  , testProperty "multiplication matches reference" $
    \(xs :: [(Word, Int)]) ys -> toPoly (V.fromList (mulRef xs ys)) ===
      toPoly (V.fromList xs) * toPoly (V.fromList ys)
  ]

addRef :: Num a => [(Word, a)] -> [(Word, a)] -> [(Word, a)]
addRef [] ys = ys
addRef xs [] = xs
addRef xs@((xp, xc) : xs') ys@((yp, yc) : ys') =
  case xp `compare` yp of
    LT -> (xp, xc) : addRef xs' ys
    EQ -> (xp, xc + yc) : addRef xs' ys'
    GT -> (yp, yc) : addRef xs ys'

subRef :: Num a => [(Word, a)] -> [(Word, a)] -> [(Word, a)]
subRef [] ys = map (fmap negate) ys
subRef xs [] = xs
subRef xs@((xp, xc) : xs') ys@((yp, yc) : ys') =
  case xp `compare` yp of
    LT -> (xp, xc) : subRef xs' ys
    EQ -> (xp, xc - yc) : subRef xs' ys'
    GT -> (yp, negate yc) : subRef xs ys'

mulRef :: Num a => [(Word, a)] -> [(Word, a)] -> [(Word, a)]
mulRef xs ys
  = map (\ws -> (fst (head ws), sum (map snd ws)))
  $ groupBy ((==) `on` fst)
  $ sortOn fst
  $ [ (xp + yp, xc * yc) | (xp, xc) <- xs, (yp, yc) <- ys ]

otherTests :: TestTree
otherTests = testGroup "Other"
  [ testProperty "leading p 0 == Nothing" $
    \p -> leading (monomial p 0 :: UPoly Int) === Nothing
  , testProperty "leading . monomial = id" $
    \p c -> c /= 0 ==> leading (monomial p c :: UPoly Int) === Just (p, c)
  , testProperty "monomial matches reference" $
    \p (c :: Int) -> monomial p c === toPoly (V.fromList (monomialRef p c))
  , testProperty "scale matches multiplication by monomial" $
    \p c (xs :: UPoly Int) -> scale p c xs === monomial p c * xs
  ]

monomialRef :: Num a => Word -> a -> [(Word, a)]
monomialRef p c = [(p, c)]

evalTests :: TestTree
evalTests = testGroup "eval" $ concat
  [ evalTestGroup (Proxy :: Proxy (Poly U.Vector Int8))
  , evalTestGroup (Proxy :: Proxy (Poly V.Vector Integer))
  ]

evalTestGroup
  :: forall v a.
     (Eq a, Num a, Semiring a, Arbitrary a, Show a, Eq (v (Word, a)), Show (v (Word, a)), G.Vector v (Word, a))
  => Proxy (Poly v a)
  -> [TestTree]
evalTestGroup _ =
  [ testProperty "eval (p + q) r = eval p r + eval q r" $
    \p q r -> e (p + q) r === e p r + e q r
  , testProperty "eval (p * q) r = eval p r * eval q r" $
    \p q r -> e (p * q) r === e p r * e q r
  , testProperty "eval x p = p" $
    \p -> e X p === p
  , testProperty "eval (monomial 0 c) p = c" $
    \c p -> e (monomial 0 c) p === c

  , testProperty "eval' (p + q) r = eval' p r + eval' q r" $
    \p q r -> e' (p + q) r === e' p r + e' q r
  , testProperty "eval' (p * q) r = eval' p r * eval' q r" $
    \p q r -> e' (p * q) r === e' p r * e' q r
  , testProperty "eval' x p = p" $
    \p -> e' S.X p === p
  , testProperty "eval' (S.monomial 0 c) p = c" $
    \c p -> e' (S.monomial 0 c) p === c
  ]

  where
    e :: Poly v a -> a -> a
    e = eval
    e' :: Poly v a -> a -> a
    e' = S.eval

derivTests :: TestTree
derivTests = testGroup "deriv"
  [ testProperty "deriv = S.deriv" $
    \(p :: Poly V.Vector Integer) -> deriv p === S.deriv p
  , testProperty "deriv . integral = id" $
    \(p :: Poly V.Vector Rational) -> deriv (integral p) === p
  , testProperty "deriv c = 0" $
    \c -> deriv (monomial 0 c :: Poly V.Vector Int) === 0
  , testProperty "deriv cX = c" $
    \c -> deriv (monomial 0 c * X :: Poly V.Vector Int) === monomial 0 c
  , testProperty "deriv (p + q) = deriv p + deriv q" $
    \p q -> deriv (p + q) === (deriv p + deriv q :: Poly V.Vector Int)
  , testProperty "deriv (p * q) = p * deriv q + q * deriv p" $
    \p q -> deriv (p * q) === (p * deriv q + q * deriv p :: Poly V.Vector Int)
  -- The following property takes too long for a regular test-suite
  -- , testProperty "deriv (eval p q) = deriv q * eval (deriv p) q" $
  --   \(p :: Poly V.Vector Int) (q :: Poly U.Vector Int) ->
  --     deriv (eval (toPoly $ fmap (fmap $ monomial 0) $ unPoly p) q) ===
  --       deriv q * eval (toPoly $ fmap (fmap $ monomial 0) $ unPoly $ deriv p) q
  ]