{-# LANGUAGE DeriveDataTypeable #-} {-# LANGUAGE FlexibleContexts #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE MultiParamTypeClasses #-} {-# LANGUAGE NoMonomorphismRestriction #-} {-# LANGUAGE OverlappingInstances #-} {-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE TypeFamilies #-} {-# LANGUAGE UndecidableInstances #-} module Math.Coordinate.Parabolic where import Data.Typeable (Typeable) import Control.Applicative import Data.Array.Accelerate import Data.Array.Accelerate.Smart import Data.Array.Accelerate.Tuple import Data.Array.Accelerate.Array.Sugar import Data.Complex import qualified Data.Foldable as F import qualified Math.Coordinate.Cartesian as Cartesian import Math.Coordinate.Cartesian (Cartesian) import Math.Coordinate.Coordinate (CoordConversion(..), ManualConversion(..), convertCoord) import Math.Space.Space (Space2) data Parabolic = Parabolic deriving (Show) data Point a = Point { rho :: !a , tau :: !a } deriving (Eq, Ord, Show, Read, Typeable) toParabolic = convertCoord Parabolic -------------------------------------------------------------------------------- -- Instances -------------------------------------------------------------------------------- instance Floating a => CoordConversion ManualConversion Cartesian space (Point a) (Cartesian.Point2 a) where convertCoordBase _ _ _ (Point rho tau) = Cartesian.Point2 x y where x = rho * tau y = (rho**2 - tau**2)/2 instance Floating a => CoordConversion ManualConversion Parabolic space (Cartesian.Point2 a) (Point a) where convertCoordBase _ _ _ (Cartesian.Point2 x y) = Point rho tau where rho = sqrt \$ y + (sqrt \$ x**2 + y**2) tau = x/rho -------------------------------------------------------------------------------- -- Point -------------------------------------------------------------------------------- instance Functor Point where fmap f (Point a b) = Point (f a) (f b) instance Applicative Point where pure a = Point a a {-# INLINE pure #-} Point a b <*> Point d e = Point (a d) (b e) {-# INLINE (<*>) #-} instance Num a => Num (Point a) where (+) = liftA2 (+) {-# INLINE (+) #-} (-) = liftA2 (-) {-# INLINE (-) #-} (*) = liftA2 (*) {-# INLINE (*) #-} negate = fmap negate {-# INLINE negate #-} abs = fmap abs {-# INLINE abs #-} signum = fmap signum {-# INLINE signum #-} fromInteger = pure . fromInteger {-# INLINE fromInteger #-} instance Fractional a => Fractional (Point a) where recip = fmap recip {-# INLINE recip #-} (/) = liftA2 (/) {-# INLINE (/) #-} fromRational = pure . fromRational {-# INLINE fromRational #-} type instance EltRepr (Point a) = EltRepr (a, a) type instance EltRepr' (Point a) = EltRepr' (a, a) instance Elt a => Elt (Point a) where eltType _ = eltType (undefined :: (a,a)) toElt p = case toElt p of (x, y) -> Point x y fromElt (Point x y) = fromElt (x, y) eltType' _ = eltType' (undefined :: (a,a)) toElt' p = case toElt' p of (x, y) -> Point x y fromElt' (Point x y) = fromElt' (x, y) instance IsTuple (Point a) where type TupleRepr (Point a) = TupleRepr (a,a) fromTuple (Point x y) = fromTuple (x,y) toTuple t = case toTuple t of (x, y) -> Point x y instance (Lift Exp a, Elt (Plain a)) => Lift Exp (Point a) where type Plain (Point a) = Point (Plain a) --lift = Exp . Tuple . F.foldl SnocTup NilTup lift (Point x y) = Exp \$ Tuple \$ NilTup `SnocTup` lift x `SnocTup` lift y instance (Elt a, e ~ Exp a) => Unlift Exp (Point e) where unlift t = Point (Exp \$ SuccTupIdx ZeroTupIdx `Prj` t) (Exp \$ ZeroTupIdx `Prj` t)