open Impact

let a = [| [| 4.; 8.; 4.|]; 
           [| -3.; -1.; 7.|] |]

let b = [| [| 2.; 1.; -1.; 8.|];
           [| -3.; -1.; 2.; -11.|]; 
           [| -2.; 1.; 2.; -3.|] |] 

let printMatrix(matrix : float[][]) =
    for rowNum in 0 .. matrix.Length-1 do
        let row = matrix.[rowNum]
        for colNum in 0 .. row.Length-1 do
            printf "  %10f" row.[colNum]
        printfn ""
    printfn ""
 
let scalarMult (vector : float [], multiplier : float) =
    [| for i in 0 .. vector.Length-1 -> vector.[i] * multiplier |]
 
let vectorAdd(v1 : float [], v2 : float []) =
    [| for i in 0 .. v1.Length-1 -> v1.[i] + v2.[i]|]

let scaleRow(matrix: float [][], r: int) =
   matrix.[r] <- scalarMult(matrix.[r], 1.0/matrix.[r].[r])
   
let eliminateColInRow(matrix: float [][], c: int, r: int) =
   matrix.[r] <- vectorAdd(matrix.[r], scalarMult(matrix.[c], -matrix.[r].[c]))
   
let clearCol(matrix: float [][], c: int) =
   scaleRow(matrix, c)
   for r in 0 .. matrix.Length-1 do
      if not (r = c) then
         eliminateColInRow(matrix, c, r)

let solve(matrix: float [][]) =
   for r in 0 .. matrix.Length-1 do
      clearCol(matrix, r)