用GM(1.1)-S预测空气质量季节性python代码

以下是用Python实现GM(1,1)-S模型进行季节性空气质量预测的代码：

import numpy as np

def gm11(x0):
    # 累加生成序列
    x1 = np.cumsum(x0)
    n = len(x0)
    # 生成矩阵B和Y
    B = np.zeros((n-1, 2))
    Y = np.zeros((n-1, 1))
    for i in range(n-1):
        B[i][0] = -(x1[i] + x1[i+1]) / 2.0
        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.linalg.inv(B.T.dot(B)).dot(B.T).dot(Y)
    a = A[0][0]
    u = A[1][0]
    # 计算原序列的预测值
    x_pred = np.zeros((n,))
    x_pred[0] = x0[0]
    for i in range(1, n):
        x_pred[i] = (x0[0] - u/a) * (1 - np.exp(a)) * np.exp(-a*(i))
    return x_pred

def seasonal_gm11(x0, m):
    # 将原序列分解为m个子序列
    groups = []
    for i in range(m):
        group = []
        j = i
        while j < len(x0):
            group.append(x0[j])
            j += m
        groups.append(group)
    # 对每个子序列分别进行GM(1,1)-S模型预测
    x_pred = []
    for group in groups:
        x_pred.extend(gm11(group))
    return x_pred

# 示例
x0 = np.array([101, 102, 100, 103, 105, 107, 110, 109, 106, 105, 103, 101])
x_pred = seasonal_gm11(x0, 4)
print(x_pred)

上述代码中，`gm11`函数是GM(1,1)模型的实现，`seasonal_gm11`函数则是针对季节性序列的GM(1,1)-S模型的实现，其中`x0`为原始序列，`m`为子序列的个数。在上述示例中，原始序列为12个月的空气质量指数，`m`取4，即将其分解为4个子序列，然后对每个子序列进行GM(1,1)模型拟合，最终得到整个季节性序列的预测结果。