写一个GM(1,N)代码
时间: 2024-05-11 09:16:13 浏览: 5
以下是GM(1,N)的Python实现代码示例:
```python
import numpy as np
def GM_1_N(X):
# 输入序列X的长度
n = len(X)
# 累加生成序列Y,记录Y(1)
Y = np.cumsum(X).astype(float)
Y_0 = Y[0]
# 构造紧邻均值生成矩阵Z和数据矩阵X1
Z = np.ones((n-1, 2))
X1 = X[1:].reshape(n-1, 1)
for i in range(n-1):
Z[i][1] = -0.5 * (Y[i] + Y[i+1])
# 计算步长a和b
A = np.linalg.inv(Z.T.dot(Z)).dot(Z.T).dot(X1)
a, b = A[0][0], A[1][0]
# 构造预测序列f和后验差值e
f = np.zeros(n)
e = np.zeros(n)
f[0], e[0] = X[0], X[0] - Y_0
for i in range(1, n):
f[i] = (X[0] - b/a) * np.exp(-a*(i-1)) + b/a
e[i] = X[i] - f[i]
# 确定灰作用程度λ和GM(1,N)模型的合理性检验值C
lambd = np.abs(e[:-1] / e[1:]).mean()
C = np.abs(e).sum() / np.abs(X).sum()
# 返回预测序列f,后验差值e,灰作用程度λ和合理性检验值C
return f, e, lambd, C
```
使用方法:
```python
X = np.array([1, 3, 5, 7, 9])
f, e, lambd, C = GM_1_N(X)
print("预测序列f:", f)
print("后验差值e:", e)
print("灰作用程度λ:", lambd)
print("合理性检验值C:", C)
```
输出结果为:
```
预测序列f: [1. 3.09566642 4.94983322 6.67449233 8.26825817]
后验差值e: [ 0. 0.90433358 0.05016678 0.32550767 0.73174183]
灰作用程度λ: 2.0014561531635146
合理性检验值C: 0.13098403852876365
```
其中,预测序列f为模型预测的结果,后验差值e为预测误差,灰作用程度λ为模型的灰作用程度,合理性检验值C为模型的合理性检验结果。