【Python数学建模常用算法代码（六）之灰色预测模型】

Python数学建模常用算法代码（六）
注意！
注意！
注意：Python数学建模常用算法代码就更新到这里！！！
后面会看心情不定时更新数学建模知识
废话不多说，灰色预测来一波！！

灰色预测模型代码

import numpy as np
import math

history_data = [724.57,746.62,778.27,800.8,827.75,871.1,912.37,954.28,995.01,1037.2]
n = len(history_data)
X0 = np.array(history_data)

#累加生成
history_data_agg = [sum(history_data[0:i+1]) for i in range(n)]
X1 = np.array(history_data_agg)

#计算数据矩阵B和数据向量Y
B = np.zeros([n-1,2])
Y = np.zeros([n-1,1])
for i in range(0,n-1):
    B[i][0] = -0.5*(X1[i] + X1[i+1])
    B[i][1] = 1
    Y[i][0] = X0[i+1]

#计算GM(1,1)微分方程的参数a和u
#A = np.zeros([2,1])
A = np.linalg.inv(B.T.dot(B)).dot(B.T).dot(Y)
a = A[0][0]
u = A[1][0]

#建立灰色预测模型
XX0 = np.zeros(n)
XX0[0] = X0[0]
for i in range(1,n):
    XX0[i] = (X0[0] - u/a)*(1-math.exp(a))*math.exp(-a*(i));


#模型精度的后验差检验
e = 0      #求残差平均值
for i in range(0,n):
    e += (X0[i] - XX0[i])
e /= n

#求历史数据平均值
aver = 0;     
for i in range(0,n):
    aver += X0[i]
aver /= n

#求历史数据方差
s12 = 0;     
for i in range(0,n):
    s12 += (X0[i]-aver)**2;
s12 /= n

#求残差方差
s22 = 0;       
for i in range(0,n):
    s22 += ((X0[i] - XX0[i]) - e)**2;
s22 /= n

#求后验差比值
C = s22 / s12   

#求小误差概率
cout = 0
for i in range(0,n):
    if abs((X0[i] - XX0[i]) - e) < 0.6754*math.sqrt(s12):
        cout = cout+1
    else:
        cout = cout
P = cout / n

if (C < 0.35 and P > 0.95):
    #预测精度为一级
    m = 10   #请输入需要预测的年数
    #print('往后m各年负荷为：')
    f = np.zeros(m)
    for i in range(0,m):
        f[i] = (X0[0] - u/a)*(1-math.exp(a))*math.exp(-a*(i+n))    
else:
    print('灰色预测法不适用')