SML Vectors

vector.sml

type vector = real list;

fun map2 (f1 : 'a * 'b -> 'c) (f2 : 'a -> 'c) (f3 : 'b -> 'c) (xs : 'a list) (ys : 'b list) = 
    let
        fun m2 [] [] = []
          | m2 xs [] = f2 (hd xs)        :: m2 (tl xs) []
          | m2 [] ys = f3 (hd ys)        :: m2 []      (tl ys)
          | m2 xs ys = f1 (hd xs, hd ys) :: m2 (tl xs) (tl ys)
    in
        m2 xs ys
    end;

    
fun scale (x:real) (v:vector) :vector = map (fn n => x * n) v;

fun dot (v:vector) (w:vector) = foldr (op +) 0.0 ((map2 (op * ) (fn x => 0.0) (fn y => 0.0) v w));

fun magn (v:vector) = Math.sqrt (dot v v);

fun add (v:vector) (w:vector) : vector = map2 (op +) (fn x => x) (fn y => y) v w

fun project w v = scale ((dot v w) / (dot w w)) w;

fun projectAll(S:vector list,v:vector):vector = 
    foldr (fn (a,b) => add a b) [0.0] (map (fn w => project w v) S);

fun residue [] v = v
  | residue (S:(vector list)) (v:vector) = 
    let 
        val w1 = residue (tl S) (hd S)
    in
         residue (tl S) (add v (scale ~1.0 (project w1 v)))
    end;

fun inSpan (S:vector list) (v:vector) = 
    let
        val FUDGE = 0.000001
    in
        magn (residue S v) < FUDGE
    end;