implementation module Data.Matrix

import StdEnv

instance * (Matrix a) | *, +, zero a where
  (*) m1 m2 = {let m1row = row i m1
               in  {let m2col = col j m2
                    in  dotVec m1row m2col \\ j <- [0..cols m2 - 1]} \\ i <- [0..rows m1 - 1]}

dotVec :: (Vector a) (Vector a) -> a | *, +, zero a
dotVec vl vr
  = sum [vl.[i] * vr.[i] \\ i <- [0..size vl - 1]]

mulVecMatrix :: (Vector a) (Matrix a) -> Matrix a | *, +, zero a
mulVecMatrix vec m = {{v} \\ v <-: vec} * m

mulMatrixVec :: (Matrix a) (Vector a) -> Matrix a | *, +, zero a
mulMatrixVec m vec = m * {{v} \\ v <-: vec}

row :: Int (Matrix a) -> Vector a
row n matrix = matrix.[n]

col :: Int (Matrix a) -> Vector a
col n matrix = {row.[n] \\ row <-: matrix}

cols :: (Matrix a) -> Int
cols matrix
  | size matrix > 0 = size matrix.[0]
  | otherwise       = 0

rows :: (Matrix a) -> Int
rows matrix = size matrix