灰色预测模型

https://blog.csdn.net/qq_39798423/article/details/89283000
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

dir = ‘C:/Users/Administrator/Desktop/‘

data = pd.read_excel(dir+‘test.xls‘, sheetname=‘Sheet1‘)
data = np.array(data[‘db‘])
lens = len(data)  # 数据量

# 数据检验
## 计算级比
lambds = []
for i in range(1, lens):
    lambds.append(data[i-1]/data[i])
## 计算区间
X_min = np.e**(-2/(lens+1))
X_max = np.e**(2/(lens+1))
## 检验
is_ok = True
for lambd in lambds:
    if (lambd < X_min or lambd > X_max):
        is_ok = False
if (is_ok == False):
    print(‘该数据未通过检验‘)
else:
    print(‘该数据通过检验‘)

# 构建灰色模型GM(1,1)
## 累加数列
data_1 = []
data_1.append(data[0])
for i in range(1, lens):
    data_1.append(data_1[i-1]+data[i])
## 灰导数及临值生成数列
ds = []
zs = []
for i in range(1, lens):
    ds.append(data[i])
    zs.append(-1/2*(data_1[i-1]+data_1[i]))
## 求a、b
B = np.array(zs).reshape(lens-1,1)
one = np.ones(lens-1)
B = np.c_[B, one]  # 加上一列1
Y = np.array(ds).reshape(lens-1,1)
a, b = np.dot(np.dot(np.linalg.inv(np.dot(B.T, B)), B.T), Y)
print(‘a=‘+str(a))
print(‘b=‘+str(b))

# 预测
def func(k):
    c = b/a
    return (data[0]-c)*(np.e**(-a*k))+c
data_1_hat = []  # 累加预测值
data_0_hat = []  # 原始预测值
data_1_hat.append(func(0))
data_0_hat.append(data_1_hat[0])
for i in range(1, lens+5):  # 多预测5次
    data_1_hat.append(func(i))
    data_0_hat.append(data_1_hat[i]-data_1_hat[i-1])
print(‘预测值为：‘)
for i in data_0_hat:
    print(i)

# 模型检验
## 预测结果方差
data_h = np.array(data_0_hat[0:7]).T
sum_h = data_h.sum()
mean_h = sum_h/lens
S1 = np.sum((data_h-mean_h)**2)/lens
## 残差方差
e = data - data_h
sum_e = e.sum()
mean_e = sum_e/lens
S2 = np.sum((e-mean_e)**2)/lens
## 后验差比
C = S2/S1
## 结果
if (C <= 0.35):
    print(‘1级，效果好‘)
elif (C <= 0.5 and C >= 0.35):
    print(‘2级，效果合格‘)
elif (C <= 0.65 and C >= 0.5):
    print(‘3级，效果勉强‘)
else:
    print(‘4级，效果不合格‘)

# 画图
plt.figure(figsize=(9, 4), dpi=100)
x1 = np.linspace(1, 7, 7)
x2 = np.linspace(1, 12, 12)
plt.subplot(121)
plt.title(‘x^0‘)
plt.plot(x2, data_0_hat, ‘r--‘, marker=‘*‘)
plt.scatter(x1, data, marker=‘^‘)
plt.subplot(122)
plt.title(‘x^1‘)
plt.plot(x2, data_1_hat, ‘r--‘, marker=‘*‘)
plt.scatter(x1, data_1, marker=‘^‘)
plt.show()