{-# LANGUAGE DataKinds #-}
{-# LANGUAGE ExistentialQuantification #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE MagicHash #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE PatternSynonyms #-}
{-# LANGUAGE PolyKinds #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE UnboxedTuples #-}
{-# LANGUAGE UndecidableInstances #-}
{-# LANGUAGE ViewPatterns #-}
module Numeric.Vector.Internal
(
Vector
, Vec2f, Vec3f, Vec4f, Vec2d, Vec3d, Vec4d
, Vec2i, Vec3i, Vec4i, Vec2w, Vec3w, Vec4w
, Vector2 (..), Vector3 (..), Vector4 (..)
, DataFrame(Vec2, Vec3, Vec4)
, (.*.), dot, (·)
, normL1, normL2, normLPInf, normLNInf, normLP
, normalized
, det2, cross, (×)
) where
import Numeric.DataFrame.SubSpace
import Numeric.DataFrame.Type
import Numeric.Scalar.Internal
type Vector (t :: l) (n :: k) = DataFrame t '[n]
type Vec2f = Vector Float 2
type Vec3f = Vector Float 3
type Vec4f = Vector Float 4
type Vec2d = Vector Double 2
type Vec3d = Vector Double 3
type Vec4d = Vector Double 4
type Vec2i = Vector Int 2
type Vec3i = Vector Int 3
type Vec4i = Vector Int 4
type Vec2w = Vector Word 2
type Vec3w = Vector Word 3
type Vec4w = Vector Word 4
pattern Vec4 :: Vector4 t => t -> t -> t -> t -> Vector t 4
pattern Vec4 a b c d <- (unpackV4# -> (# a, b, c, d #))
where
Vec4 = vec4
{-# COMPLETE Vec4 #-}
pattern Vec3 :: Vector3 t => t -> t -> t -> Vector t 3
pattern Vec3 a b c <- (unpackV3# -> (# a, b, c #))
where
Vec3 = vec3
{-# COMPLETE Vec3 #-}
pattern Vec2 :: Vector2 t => t -> t -> Vector t 2
pattern Vec2 a b <- (unpackV2# -> (# a, b #))
where
Vec2 = vec2
{-# COMPLETE Vec2 #-}
class Vector2 t where
vec2 :: t -> t -> Vector t 2
unpackV2# :: Vector t 2 -> (# t, t #)
class Vector3 t where
vec3 :: t -> t -> t -> Vector t 3
unpackV3# :: Vector t 3 -> (# t, t, t #)
class Vector4 t where
vec4 :: t -> t -> t -> t -> Vector t 4
unpackV4# :: Vector t 4 -> (# t, t, t, t #)
instance {-# OVERLAPPABLE #-} SubSpace t '[2] '[] '[2] => Vector2 t where
vec2 a b = iwgen f
where
f (0 :* U) = scalar a
f _ = scalar b
{-# INLINE vec2 #-}
unpackV2# v =
(# unScalar (indexOffset# 0# v)
, unScalar (indexOffset# 1# v) #)
{-# INLINE unpackV2# #-}
instance {-# OVERLAPPABLE #-} SubSpace t '[3] '[] '[3] => Vector3 t where
vec3 a b c = iwgen f
where
f (0 :* U) = scalar a
f (1 :* U) = scalar b
f _ = scalar c
{-# INLINE vec3 #-}
unpackV3# v =
(# unScalar (indexOffset# 0# v)
, unScalar (indexOffset# 1# v)
, unScalar (indexOffset# 2# v) #)
{-# INLINE unpackV3# #-}
instance {-# OVERLAPPABLE #-} SubSpace t '[4] '[] '[4] => Vector4 t where
vec4 a b c d = iwgen f
where
f (0 :* U) = scalar a
f (1 :* U) = scalar b
f (2 :* U) = scalar c
f _ = scalar d
{-# INLINE vec4 #-}
unpackV4# v =
(# unScalar (indexOffset# 0# v)
, unScalar (indexOffset# 1# v)
, unScalar (indexOffset# 2# v)
, unScalar (indexOffset# 3# v) #)
{-# INLINE unpackV4# #-}
(.*.) :: ( Num t
, Num (Vector t n)
, SubSpace t '[n] '[] '[n]
)
=> Vector t n -> Vector t n -> Vector t n
(.*.) a b = fromScalar . ewfoldl (+) 0 $ a * b
infixl 7 .*.
dot :: ( Num t
, Num (Vector t n)
, SubSpace t '[n] '[] '[n]
)
=> Vector t n -> Vector t n -> Scalar t
dot a b = ewfoldl (+) 0 $ a * b
infixl 7 ·
(·) :: ( Num t
, Num (Vector t n)
, SubSpace t '[n] '[] '[n]
)
=> Vector t n -> Vector t n -> Scalar t
(·) = dot
{-# INLINE (·) #-}
normL1 :: ( Num t, SubSpace t '[n] '[] '[n] )
=> Vector t n -> Scalar t
normL1 = ewfoldr (\a -> (abs a +)) 0
normL2 :: ( Floating t , SubSpace t '[n] '[] '[n] )
=> Vector t n -> Scalar t
normL2 = sqrt . ewfoldr (\a -> (a*a +)) 0
normalized :: ( Floating t , Fractional (Vector t n), SubSpace t '[n] '[] '[n] )
=> Vector t n -> Vector t n
normalized v = v / n
where
n = fromScalar . sqrt $ ewfoldr (\a -> (a*a +)) 0 v
normLPInf :: ( Ord t, Num t , SubSpace t '[n] '[] '[n] )
=> Vector t n -> Scalar t
normLPInf = ewfoldr (max . abs) 0
normLNInf :: ( Ord t, Num t , SubSpace t '[n] '[] '[n] )
=> Vector t n -> Scalar t
normLNInf x = ewfoldr (min . abs) (scalar . abs $ ixOff 0 x) x
normLP :: ( Floating t , SubSpace t '[n] '[] '[n] )
=> Int -> Vector t n -> Scalar t
normLP i' = (**ri) . ewfoldr (\a -> (a**i +)) 0
where
i = fromIntegral i'
ri = recip i
{-# INLINE [2] normLP #-}
{-# RULES
"normLP/L1" normLP 1 = normL1
"normLP/L2" normLP 2 = normL2
#-}
det2 :: ( Num t, SubSpace t '[2] '[] '[2] )
=> Vector t 2 -> Vector t 2 -> Scalar t
det2 a b = (a ! 0 :* U) * (b ! 1 :* U)
- (a ! 1 :* U) * (b ! 0 :* U)
cross :: ( Num t, SubSpace t '[3] '[] '[3] )
=> Vector t 3 -> Vector t 3 -> Vector t 3
cross a b = vec3 ( unScalar
$ (a ! 1 :* U) * (b ! 2 :* U)
- (a ! 2 :* U) * (b ! 1 :* U) )
( unScalar
$ (a ! 2 :* U) * (b ! 0 :* U)
- (a ! 0 :* U) * (b ! 2 :* U) )
( unScalar
$ (a ! 0 :* U) * (b ! 1 :* U)
- (a ! 1 :* U) * (b ! 0 :* U) )
infixl 7 ×
(×) :: ( Num t, SubSpace t '[3] '[] '[3] )
=> Vector t 3 -> Vector t 3 -> Vector t 3
(×) = cross
{-# INLINE (×) #-}