{-# LANGUAGE DataKinds #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE MagicHash #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE PolyKinds #-}
{-# LANGUAGE RecordWildCards #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE StandaloneDeriving #-}
{-# LANGUAGE TypeApplications #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE UnboxedTuples #-}
{-# LANGUAGE UndecidableInstances #-}
module Numeric.Matrix.Internal
( MatrixTranspose (..)
, SquareMatrix (..)
, MatrixDeterminant (..)
, MatrixInverse (..)
, Matrix
, HomTransform4 (..)
, Mat22f, Mat23f, Mat24f
, Mat32f, Mat33f, Mat34f
, Mat42f, Mat43f, Mat44f
, Mat22d, Mat23d, Mat24d
, Mat32d, Mat33d, Mat34d
, Mat42d, Mat43d, Mat44d
, mat22, mat33, mat44
, (%*)
) where
import GHC.Base
import Numeric.DataFrame.Contraction ((%*))
import Numeric.DataFrame.Internal.PrimArray
import Numeric.DataFrame.Type
import Numeric.Dimensions
import Numeric.Scalar.Internal
import Numeric.Vector.Internal
type Matrix (t :: l) (n :: k) (m :: k) = DataFrame t '[n,m]
class MatrixTranspose t (n :: k) (m :: k) where
transpose :: Matrix t n m -> Matrix t m n
class SquareMatrix t (n :: Nat) where
eye :: Matrix t n n
diag :: Scalar t -> Matrix t n n
trace :: Matrix t n n -> Scalar t
class MatrixDeterminant t (n :: Nat) where
det :: Matrix t n n -> Scalar t
class MatrixInverse t (n :: Nat) where
inverse :: Matrix t n n -> Matrix t n n
class HomTransform4 t where
translate4 :: Vector t 4 -> Matrix t 4 4
translate3 :: Vector t 3 -> Matrix t 4 4
rotateX :: t -> Matrix t 4 4
rotateY :: t -> Matrix t 4 4
rotateZ :: t -> Matrix t 4 4
rotate :: Vector t 3 -> t -> Matrix t 4 4
rotateEuler :: t
-> t
-> t
-> Matrix t 4 4
lookAt :: Vector t 3
-> Vector t 3
-> Vector t 3
-> Matrix t 4 4
perspective :: t
-> t
-> t
-> t
-> Matrix t 4 4
orthogonal :: t
-> t
-> t
-> t
-> Matrix t 4 4
toHomPoint :: Vector t 3 -> Vector t 4
toHomVector :: Vector t 3 -> Vector t 4
fromHom :: Vector t 4 -> Vector t 3
type Mat22f = Matrix Float 2 2
type Mat32f = Matrix Float 3 2
type Mat42f = Matrix Float 4 2
type Mat23f = Matrix Float 2 3
type Mat33f = Matrix Float 3 3
type Mat43f = Matrix Float 4 3
type Mat24f = Matrix Float 2 4
type Mat34f = Matrix Float 3 4
type Mat44f = Matrix Float 4 4
type Mat22d = Matrix Double 2 2
type Mat32d = Matrix Double 3 2
type Mat42d = Matrix Double 4 2
type Mat23d = Matrix Double 2 3
type Mat33d = Matrix Double 3 3
type Mat43d = Matrix Double 4 3
type Mat24d = Matrix Double 2 4
type Mat34d = Matrix Double 3 4
type Mat44d = Matrix Double 4 4
mat22 :: PrimBytes (t :: Type)
=> Vector t 2 -> Vector t 2 -> Matrix t 2 2
mat22 = packDF @_ @2 @'[2]
{-# INLINE mat22 #-}
mat33 :: PrimBytes (t :: Type)
=> Vector t 3 -> Vector t 3 -> Vector t 3 -> Matrix t 3 3
mat33 = packDF @_ @3 @'[3]
{-# INLINE mat33 #-}
mat44 :: PrimBytes (t :: Type)
=> Vector t 4
-> Vector t 4
-> Vector t 4
-> Vector t 4
-> Matrix t 4 4
mat44 = packDF @_ @4 @'[4]
{-# INLINE mat44 #-}
instance ( KnownDim n, KnownDim m
, PrimArray t (Matrix t n m)
, PrimArray t (Matrix t m n)
) => MatrixTranspose t (n :: Nat) (m :: Nat) where
transpose df = case uniqueOrCumulDims df of
Left a -> broadcast a
Right _
| wm <- dimVal' @m
, wn <- dimVal' @n
, m <- case wm of W# w -> word2Int# w
, n <- case wn of W# w -> word2Int# w
-> let f ( I# i, I# j )
| isTrue# (i ==# n) = f ( 0, I# (j +# 1#) )
| otherwise = (# ( I# (i +# 1#), I# j )
, ix# (i *# m +# j) df
#)
in case gen# (CumulDims [wm*wn, wn, 1]) f (0,0) of (# _, r #) -> r
instance MatrixTranspose (t :: Type) (xn :: XNat) (xm :: XNat) where
transpose (XFrame (df :: DataFrame t ns))
| ((D :: Dim n) :* (D :: Dim m) :* U) <- dims @ns
, Dict <- inferPrimElem df
= XFrame (transpose df :: Matrix t m n)
transpose _ = error "MatrixTranspose/transpose: impossible argument"
instance (KnownDim n, PrimArray t (Matrix t n n), Num t)
=> SquareMatrix t n where
eye
| n <- dimVal' @n
= let f 0 = (# n , 1 #)
f k = (# k - 1, 0 #)
in case gen# (CumulDims [n*n, n, 1]) f 0 of
(# _, r #) -> r
diag se
| n <- dimVal' @n
, e <- unScalar se
= let f 0 = (# n , e #)
f k = (# k - 1, 0 #)
in case gen# (CumulDims [n*n, n, 1]) f 0 of
(# _, r #) -> r
trace df
| I# n <- fromIntegral $ dimVal' @n
, n1 <- n +# 1#
= let f 0# = ix# 0# df
f k = ix# k df + f (k -# n1)
in scalar $ f (n *# n -# 1#)