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# Holt-Winters algorithms to forecasting
# Coded in Python 2 by: Andre Queiroz
# Description: This module contains three exponential smoothing algorithms. They are Holt's linear trend method and Holt-Winters seasonal methods (additive and multiplicative).
# References:
# Hyndman, R. J.; Athanasopoulos, G. (2013) Forecasting: principles and practice. http://otexts.com/fpp/. Accessed on 07/03/2013.
# Byrd, R. H.; Lu, P.; Nocedal, J. A Limited Memory Algorithm for Bound Constrained Optimization, (1995), SIAM Journal on Scientific and Statistical Computing, 16, 5, pp. 1190-1208.
from sys import exit
from math import sqrt
from numpy import array