Gradient descent function minimization

GradientDescent.tq

let rec fixedPoint f x =
  let fx = f x in
  if fx = x then x else fixedPoint f fx

let ∂ fxs f xs (i, xi) =
  let () = xi + δ @ Array.Unsafe.set xs i in
  let f2 = (f xs - fxs) / δ in
  let () = xi @ Array.Unsafe.set xs i in
  f2

let ∇ f xs = Array.mapi (∂ (f xs) f xs) xs

let descend α β f df (λ, xs, fxs) =
  let xs2 = Array.map2 [a, b → a-b] xs (Array.map [x → λ*x] (df xs)) in
  let fxs2 = f xs2 in
  if fxs2 ≥ fxs then α*λ, xs, fxs else β*λ, xs2, fxs2

let minimize f df xs =
  let _, xs, _ = fixedPoint (descend 0.5 1.1 f df) (1, xs, f xs) in
  xs