# Holt-Winters algorithms to forecasting
# Coded in Python 2 by: Andre Queiroz
# Reference: Brockwell, P. J.; Davis, R. A. Introduction to Time Series and Forecasting. New York: Springer-Verlang, 2002. 434 p.

from sys import maxint
from math import sqrt

def non_seasonal(x, fc):

  alpha_opt = 0
	beta_opt = 0
	erro = maxint

	for alpha in range(101):

		for beta in range(101):

			a = [x[1]]
			b = [x[1] - x[0]]
			y = [a[0] + b[0]]
			e = []

			for i in range(2, len(x)):

				a.append(alpha / float(100) * x[i] + (1 - alpha / float(100)) * (a[i - 2] + b[i - 2]))
				b.append(beta / float(100) * (a[i - 1] - a[i - 2]) + (1 - beta / float(100)) * b[i - 2])
				y.append(a[i - 1] + b[i - 1])
				e.append((x[i] - y[i - 2]) ** 2)

			if sum(e) < erro:
				erro = sum(e)
				alpha_opt = alpha / float(100)
				beta_opt = beta / float(100)

	a = [x[1]]
	b = [x[1] - x[0]]
	y = [a[0] + b[0]]
	e = []
	mse = 0

	for i in range(2, len(x) + fc):

		if i == len(x):
			x.append(a[-1] + b[-1])

		a.append(alpha_opt * x[i] + (1 - alpha_opt) * (a[i - 2] + b[i - 2]))
		b.append(beta_opt * (a[i - 1] - a[i - 2]) + (1 - beta_opt) * b[i - 2])
		y.append(a[i - 1] + b[i - 1])
		e.append((x[i] - y[i - 2]) ** 2)
		
	mse = sqrt(sum([(m - n) ** 2 for m, n in zip(x[2:-fc], y[:-fc - 1])]) / len(x[2:-fc]))

	return x[-fc:], alpha_opt, beta_opt, mse