#year time_id number
1994 1 10
1995 2 3
1996 3 27
1997 4 13
1998 5 12
1999 6 13
2000 7 14
2001 8 23
2002 9 32
2003 10 30
2004 11 36
2005 12 40
2006 13 58
2007 14 51
2008 15 73
2009 16 80
2010 17 106
2011 18 127
2012 19 135
2013 20 161
2014 21 149
2015 22 142

# -*- coding: utf-8 -*-
# @Date  : 2017-04-11 21:27:00
# @Author : Alan Lau (rlalan@outlook.com)
# @Language : Python3.5

import numpy as np
from matplotlib import pyplot as plt

#指數平滑公式
def exponential_smoothing(alpha, s):
 s2 = np.zeros(s.shape)
 s2[0] = s[0]
 for i in range(1, len(s2)):
  s2[i] = alpha*s[i]+(1-alpha)*s2[i-1]
 return s2

#繪制預測曲線
def show_data(new_year, pre_year, data, s_pre_double, s_pre_triple):
 year, time_id, number = data.T

 plt.figure(figsize=(14, 6), dpi=80)#設置繪圖區域的大小和像素
 plt.plot(year, number, color='blue', label="actual value")#將實際值的折線設置為藍色
 plt.plot(new_year[1:], s_pre_double[2:],color='red', label="double predicted value")#將二次指數平滑法計算的預測值的折線設置為紅色
 plt.plot(new_year[1:], s_pre_triple[2:],color='green', label="triple predicted value")#將三次指數平滑法計算的預測值的折線設置為綠色
 plt.legend(loc='lower right')#顯示圖例的位置，這里為右下方
 plt.title('Projects')
 plt.xlabel('year')#x軸標簽
 plt.ylabel('number')#y軸標簽
 plt.xticks(new_year)#設置x軸的刻度線為new_year
 plt.show()


def main():
 alpha = .70#設置alphe，即平滑系數
 pre_year = np.array([2016, 2017])#將需要預測的兩年存入numpy的array對象里
 data_path = r'data1.txt'#設置數據路徑
 data = np.loadtxt(data_path)#用numpy讀取數據
 year, time_id, number = data.T#將數據分別賦值給year, time_id, number
 initial_line = np.array([0, 0, number[0]])#初始化，由于平滑指數是根據上一期的數值進行預測的，原始數據中的最早數據為1995，沒有1994年的數據，這里定義1994年的數據和1995年數據相同
 initial_data = np.insert(data, 0, values=initial_line, axis=0)#插入初始化數據
 initial_year, initial_time_id, initial_number = initial_data.T#插入初始化年

 s_single = exponential_smoothing(alpha, initial_number)#計算一次指數平滑
 s_double = exponential_smoothing(alpha, s_single)#計算二次平滑字數，二次平滑指數是在一次指數平滑的基礎上進行的，三次指數平滑以此類推

 a_double = 2*s_single-s_double#計算二次指數平滑的a
 b_double = (alpha/(1-alpha))*(s_single-s_double)#計算二次指數平滑的b
 s_pre_double = np.zeros(s_double.shape)#建立預測軸
 for i in range(1, len(initial_time_id)):
  s_pre_double[i] = a_double[i-1]+b_double[i-1]#循環計算每一年的二次指數平滑法的預測值，下面三次指數平滑法原理相同
 pre_next_year = a_double[-1]+b_double[-1]*1#預測下一年
 pre_next_two_year = a_double[-1]+b_double[-1]*2#預測下兩年
 insert_year = np.array([pre_next_year, pre_next_two_year])
 s_pre_double = np.insert(s_pre_double, len(s_pre_double), values=np.array([pre_next_year, pre_next_two_year]), axis=0)#組合預測值

 s_triple = exponential_smoothing(alpha, s_double)

 a_triple = 3*s_single-3*s_double+s_triple
 b_triple = (alpha/(2*((1-alpha)**2)))*((6-5*alpha)*s_single -2*((5-4*alpha)*s_double)+(4-3*alpha)*s_triple)
 c_triple = ((alpha**2)/(2*((1-alpha)**2)))*(s_single-2*s_double+s_triple)

 s_pre_triple = np.zeros(s_triple.shape)

 for i in range(1, len(initial_time_id)):
  s_pre_triple[i] = a_triple[i-1]+b_triple[i-1]*1 + c_triple[i-1]*(1**2)

 pre_next_year = a_triple[-1]+b_triple[-1]*1 + c_triple[-1]*(1**2)
 pre_next_two_year = a_triple[-1]+b_triple[-1]*2 + c_triple[-1]*(2**2)
 insert_year = np.array([pre_next_year, pre_next_two_year])
 s_pre_triple = np.insert(s_pre_triple, len(s_pre_triple), values=np.array([pre_next_year, pre_next_two_year]), axis=0)

 new_year = np.insert(year, len(year), values=pre_year, axis=0)
 output = np.array([new_year, s_pre_double, s_pre_triple])
 print(output)
 show_data(new_year, pre_year, data, s_pre_double, s_pre_triple)#傳入預測值和數據


if __name__ == '__main__':
 main()