jdh30

type rec Tree = Tree((Number, Number), Stack Tree)

let mkFree n =
  for 0 1 (n-1) (Set.empty()) [ps, x ->
    for 0 1 (n-1) ps [ps, y ->
      Set.add (x, y) ps]]

let rec search free (i, j as ij) =
  let moves =
    Random.next 4

jdh30

let trajectory p dt n =
  let s, t, u = 10, 8/3, 28 in
  Array.unfold [(x, y, z), i ->
    if i=n then None else
    let p = x+s*(y-x)*dt, y+(x*(u-z)-y)*dt, z+(x*y-t*z)*dt in
    Some(p, (p, i+1))] (p, 0)

let () =
  trajectory (10, 0, 20) (1/200) 2000
  @ Array.map [x, y, z -> x, y]

jdh30

let qr mA =
  let m, n = Matrix.dimensions mA in
  let mI = Matrix.identity m in
  for 0 1 (n-1) (mI, mI, mA) [(mQ, mR, mQA), k ->
    let x = Matrix.column 0 mQA in
    let xb = Vector.norm x in
    let u = Array.mapi [i, xi -> if i=0 then xi - xb else xi] x in
    let v = Vector.scale (1 / Vector.norm u) u in
    let q k (i, j) =
      let x = if i=j then 1 else 0 in

jdh30

let s = Array.Unsafe.set
let g = Array.get
let g2 = Matrix.get
let s2 = Matrix.Unsafe.set

let swap a (i0, j0) (i1, j1) =
  let t = g2 a (i0, j0) in
  let () = g2 a (i1, j1) @ s2 a (i0, j0) in
  s2 a (i1, j1) t

jdh30

let cholesky zero √ conj a =
  let get = Matrix.get in
  let set = Matrix.set in
  let n = Matrix.checkSquare a in
  let l = Matrix.zero n n in
  let () =
    for 0 1 (n-1) () [(), j ->
      for j 1 (n-1) () [(), i ->
        let psum =
          for 0 1 (j-1) 0 [psum, k ->

jdh30

let ff ((rx, ry), i) =
  if i=3000 then None else
  let ((a,b),(c,d)), (vx,vy) =
    let r = Random.next 100 in
    if r < 75 then ((85, 4), (-4, 85)), (0, 160)
    else if r < 88 then ((-15, 28), (-26, 24)), (0, 44)
    else if r < 98 then ((20, -26), (23, 22)), (0, 160)
    else ((0, 0), (0, 16)), (0, 0) in
  Some((rx, ry), (((a*rx+b*ry+vx)/100, (c*rx+d*ry+vy)/100), i+1))

jdh30

type Nation = British | Swedish | Danish | Norwegian | German
type House = Red | Green | Blue | White | Yellow
type Drink = Milk | Coffee | Water | Beer | Tea
type Smoke = PallMall | Dunhill | Marlboro | Rothmans | Winfield
type Pet = Dog | Cat | Fish | Horse | Bird

let nations = {British; Swedish; Danish; Norwegian; German}
let houses = {Red; Green; Blue; White; Yellow}
let drinks = {Milk; Coffee; Water; Beer; Tea}
let smokes = {PallMall; Dunhill; Marlboro; Rothmans; Winfield}

jdh30

let distance s1 s2 =
  let indexable s =
    let a = Array.ofString s in
    Array.length a, Array.get a in
  let (m, u), (n, v) = indexable s1, indexable s2 in
  let d1 = Array.init n id in
  let d0 = Array.init n [_ → 0] in
  let () = for 1 1 (m-1) () [(), i →
    let () = Array.Unsafe.set d0 0 i in
    let ui = u i in

jdh30

let ! = Array.get

let x (x, _) = x
let y (_, y) = y
let add (x1,y1) (x2,y2) = x2+x1, y2+y1
let sub (x1,y1) (x2,y2) = x2-x1, y2-y1
let scale s (x,y) = s*x, s*y
let dot (x1,y1) (x2,y2) = x1*x2 + y1*y2
let length u = √(dot u u)
let cross (x1,y1) (x2,y2) = x1*y2 - x2*y1

jdh30

let det₃((a₁₁,a₁₂,a₁₃),(a₂₁,a₂₂,a₂₃),(a₃₁,a₃₂,a₃₃)) =
  -a₁₃*a₂₂*a₃₁ + a₁₂*a₂₃*a₃₁ + a₁₃*a₂₁*a₃₂ -
   a₁₁*a₂₃*a₃₂ - a₁₂*a₂₁*a₃₃ + a₁₁*a₂₂*a₃₃

let createCircle ((x₁, y₁), (x₂, y₂), (x₃, y₃)) =
  let a = det₃((x₁, y₁, 1), (x₂, y₂, 1), (x₃, y₃, 1)) in
  let d = -det₃((sqr x₁ + sqr y₁, y₁, 1), (sqr x₂ + sqr y₂, y₂, 1), (sqr x₃ + sqr y₃, y₃, 1)) in
  let e = det₃((sqr x₁ + sqr y₁, x₁, 1), (sqr x₂ + sqr y₂, x₂, 1), (sqr x₃ + sqr y₃, x₃, 1)) in
  let f = -det₃((sqr x₁ + sqr y₁, x₁, y₁), (sqr x₂ + sqr y₂, x₂, y₂), (sqr x₃ + sqr y₃, x₃, y₃)) in
  let r = (sqr d + sqr e)/(4 * sqr a) - f/a @ sqrt in