module Feldspar.Matrix where
import qualified Prelude as P
import Data.List (genericLength)
import qualified Data.TypeLevel as TL
import Feldspar.Prelude
import Feldspar.Core
import Feldspar.Vector
type Matrix a = Vector (Vector (Data a))
freezeMatrix :: Type a => Matrix a -> Data [[a]]
freezeMatrix = freezeVector . map freezeVector
unfreezeMatrix :: Type a => Data [[a]] -> Matrix a
unfreezeMatrix = map unfreezeVector . unfreezeVector
unfreezeMatrix' :: Type a => Length -> Length -> Data [[a]] -> Matrix a
unfreezeMatrix' y x = map (unfreezeVector' x) . (unfreezeVector' y)
matrix :: Type a => [[a]] -> Matrix a
matrix = unfreezeMatrix . value
indexedMat
:: Data Length
-> Data Length
-> (Data Index -> Data Index -> Data a)
-> Matrix a
indexedMat m n idx = indexed m $ \k -> indexed n $ \l -> idx k l
transpose :: Type a => Matrix a -> Matrix a
transpose a = indexedMat (length $ head a) (length a) $ \y x -> a ! x ! y
flatten :: Type a => Matrix a -> Vector (Data a)
flatten matr = Indexed (m*n) ixf Empty
where
m = length matr
n = (m==0) ? (0, length (head matr))
ixf i = matr ! y ! x
where
y = i `div` n
x = i `mod` n
diagonal :: Type a => Matrix a -> Vector (Data a)
diagonal m = zipWith (!) m (0 ... (length m 1))
distributeL :: (a -> b -> c) -> a -> Vector b -> Vector c
distributeL f = map . f
distributeR :: (a -> b -> c) -> Vector a -> b -> Vector c
distributeR = flip . distributeL . flip
class Mul a b
where
type Prod a b
(***) :: a -> b -> Prod a b
instance Numeric a => Mul (Data a) (Data a)
where
type Prod (Data a) (Data a) = Data a
(***) = (*)
instance Numeric a => Mul (Data a) (DVector a)
where
type Prod (Data a) (DVector a) = DVector a
(***) = distributeL (***)
instance Numeric a => Mul (DVector a) (Data a)
where
type Prod (DVector a) (Data a) = DVector a
(***) = distributeR (***)
instance Numeric a => Mul (Data a) (Matrix a)
where
type Prod (Data a) (Matrix a) = Matrix a
(***) = distributeL (***)
instance Numeric a => Mul (Matrix a) (Data a)
where
type Prod (Matrix a) (Data a) = Matrix a
(***) = distributeR (***)
instance Numeric a => Mul (DVector a) (DVector a)
where
type Prod (DVector a) (DVector a) = Data a
(***) = scalarProd
instance Numeric a => Mul (DVector a) (Matrix a)
where
type Prod (DVector a) (Matrix a) = (DVector a)
vec *** mat = distributeL (***) vec (transpose mat)
instance Numeric a => Mul (Matrix a) (DVector a)
where
type Prod (Matrix a) (DVector a) = (DVector a)
(***) = distributeR (***)
instance Numeric a => Mul (Matrix a) (Matrix a)
where
type Prod (Matrix a) (Matrix a) = (Matrix a)
(***) = distributeR (***)
mulMat :: Numeric a => Matrix a -> Matrix a -> Matrix a
mulMat = (***)
class Syntactic a => ElemWise a
where
type Elem a
elemWise :: (Elem a -> Elem a -> Elem a) -> a -> a -> a
instance Type a => ElemWise (Data a)
where
type Elem (Data a) = Data a
elemWise = id
instance (ElemWise a, Syntactic (Vector a)) => ElemWise (Vector a)
where
type Elem (Vector a) = Elem a
elemWise = zipWith . elemWise
(.+) :: (ElemWise a, Num (Elem a)) => a -> a -> a
(.+) = elemWise (+)
(.-) :: (ElemWise a, Num (Elem a)) => a -> a -> a
(.-) = elemWise ()
(.*) :: (ElemWise a, Num (Elem a)) => a -> a -> a
(.*) = elemWise (*)
instance (Type a) => Wrap (Matrix a) (Data [[a]]) where
wrap = freezeMatrix
instance (Wrap t u, Type a, TL.Nat row, TL.Nat col) => Wrap (Matrix a -> t) (Data' (row,col) [[a]] -> u) where
wrap f = \(Data' d) -> wrap $ f $ unfreezeMatrix' row' col' d where
row' = fromInteger $ toInteger $ TL.toInt (undefined :: row)
col' = fromInteger $ toInteger $ TL.toInt (undefined :: col)