steepest descent method

steepest_descent.coffee

# 最急降下法
steepest = (f, alpha, x0)->
  alpha = 1/2 * (Math.abs Math.random()) + 0.1 if typeof alpha isnt "number"
  alpha = Math.abs alpha
  x0 = Math.random() if typeof x0 isnt "number"

  fx0 = f(x0)
  x = x0 + 0.01 # for approximating gradient

  loop
    fx = f(x)
    gradient = (fx - fx0) / (x - x0)
    delta = gradient * (-alpha)
    break if Math.abs(delta) < 1e-10
    x0 = x
    fx0 = fx
    x = x + delta

  return x

console.log steepest (x)->
  return Math.pow(x,2) - 4*x + 3