Matrix.hs

module Matrix where

type Matrix = [[Double]]

isMatrixValid :: Matrix -> Bool
isMatrixValid matrix =
 if length lenghts == 0 then
  False
 else
  (all (== head lenghts) lenghts)
 where
  lenghts = map length matrix

newMatrix :: Matrix -> Maybe Matrix
newMatrix matrix =
 if isMatrixValid matrix then Just matrix else Nothing

transpose ([]:_) = []
transpose x = (map head x) : transpose (map tail x)

getMatrixSize :: Matrix -> (Int,Int)
getMatrixSize matrix =
 let
  rows = length matrix
 in
  if rows == 0 then
   (0, 0)
  else
   (rows, length $ head matrix)

sumMatrixes :: Matrix -> Matrix -> Maybe Matrix
sumMatrixes matrix0 matrix1 =
 if getMatrixSize matrix0 /= getMatrixSize matrix1 then
  Nothing
 else
  Just $ zipWith (zipWith (+)) matrix0 matrix1

scaleMatrix :: Double -> Matrix -> Matrix
scaleMatrix value matrix =
 map (map (* value)) matrix

subtractMatrixes :: Matrix -> Matrix -> Maybe Matrix
subtractMatrixes matrix0 matrix1 =
 sumMatrixes matrix0 (scaleMatrix (-1) matrix1)

multiplyMatrixes :: Matrix -> Matrix -> Maybe Matrix
multiplyMatrixes matrix0 matrix1 =
 let
  size0 = getMatrixSize matrix0
  size1 = getMatrixSize matrix1
  rows = fst size0
  columns = snd size1
 in
  if snd size0 /= fst size1 then
   Nothing
  else
   Just [[ term i j | j <- [0..(columns-1)] ] | i <- [0..(rows-1)] ]
 where
  transpose1 = transpose matrix1
  term i j = sum $ zipWith (*) (matrix0 !! i) (transpose1 !! j)

newMatrixWithValue rows columns value =
 [[ value | j <- [1..columns] ] | i <- [1..rows] ]

pivot matrix i j =
 let
  size = getMatrixSize matrix
  filteredRows = filter (/=i) [0..(fst size - 1)]
  filteredColumns = filter (/=j) [0..(snd size - 1)]
 in
  [ let row = matrix !! i in [row !! j | j <- filteredColumns ] | i <- filteredRows ]

cofactorSign i j =
 if (mod (i + j) 2) == 0 then 1.0 else -1.0

determinant matrix =
 if fst size /= snd size then
  Nothing
 else
  if n == 1 then
   Just $ matrix !! 0 !! 0
  else
   if n == 2 then
    Just $ determinant2x2 matrix
   else
    Just $ determinantNxN matrix
 where
  size = getMatrixSize matrix
  n = fst size
  sign j = if (mod j 2) == 0 then 1.0 else -1.0
  determinant2x2 matrix =
   (matrix !! 0 !! 0) * (matrix !! 1 !! 1) - (matrix !! 0 !! 1) * (matrix !! 1 !! 0)
  determinantNxN matrix =
   sum [ let Just det = (determinant $ pivot matrix 0 j) in (cofactorSign 0 j) * (matrix !! 0 !! j) * det | j <- [0..n-1] ]

cofactorsMatrix matrix =
 if fst size /= snd size then
  Nothing
 else
  Just [ [ let Just det = (determinant $ pivot matrix i j) in (cofactorSign i j) * det | j <- [0..n-1] ] | i <- [0..n-1]]
 where
  size = getMatrixSize matrix
  n = fst size

inverse matrix =
 cofactorsMatrix matrix >>= \cofactors ->
 determinant matrix >>= \det ->
 if det == 0.0 then
  Nothing
 else
  Just $ scaleMatrix (1.0/det) (transpose cofactors)

identity n =
 [[if i == j then 1.0 else 0.0 | j <- [0..n-1]] | i <- [0..n-1]]