对于矩阵A、B,矩阵A和B的行表示时间序列,如若干个年份,矩阵A和B列表示若干个指标。首先将矩阵A、B中的各指标元素标准化,然后识别主因子并给各指标赋予相应的权重;然后将将矩阵A、B转化为相同维度的矩阵;最后计算矩阵A和矩阵B相互作用协同发展所带来的协同效应指数并避免分母为零的情况。请给出pytho具体完整代码
时间: 2024-03-22 11:39:19 浏览: 34
以下是Python完整代码:
```python
import numpy as np
from sklearn.decomposition import PCA
# 定义标准化函数
def standardize(matrix):
"""
matrix: 待标准化矩阵
"""
mean = np.mean(matrix, axis=0)
std = np.std(matrix, axis=0)
standardized_matrix = (matrix - mean) / std
return standardized_matrix
# 定义计算主成分函数
def get_principal_component(matrix):
"""
matrix: 标准化后的矩阵
"""
pca = PCA(n_components=1)
principal_component = pca.fit_transform(matrix)
return principal_component
# 定义计算权重函数
def get_weight(matrix):
"""
matrix: 标准化后的矩阵
"""
num_of_factors = matrix.shape[1]
weight = np.zeros(num_of_factors)
for i in range(num_of_factors):
principal_component = get_principal_component(matrix[:, i].reshape(-1, 1))
weight[i] = np.abs(principal_component)
weight /= np.sum(weight)
return weight
# 定义计算协同效应指数函数
def get_collaboration_effect(matrix_a, matrix_b):
"""
matrix_a: 矩阵A
matrix_b: 矩阵B
"""
standardized_matrix_a = standardize(matrix_a)
standardized_matrix_b = standardize(matrix_b)
weight_a = get_weight(standardized_matrix_a)
weight_b = get_weight(standardized_matrix_b)
weighted_matrix_a = standardized_matrix_a * weight_a
weighted_matrix_b = standardized_matrix_b * weight_b
# 转换为相同维度矩阵
if standardized_matrix_a.shape[0] > standardized_matrix_b.shape[0]:
weighted_matrix_a = weighted_matrix_a[:standardized_matrix_b.shape[0], :]
elif standardized_matrix_a.shape[0] < standardized_matrix_b.shape[0]:
weighted_matrix_b = weighted_matrix_b[:standardized_matrix_a.shape[0], :]
# 计算协同效应指数
numerator = np.sum(weighted_matrix_a * weighted_matrix_b)
denominator = np.sqrt(np.sum(np.square(weighted_matrix_a))) * np.sqrt(np.sum(np.square(weighted_matrix_b)))
if denominator == 0:
collaboration_effect = 0
else:
collaboration_effect = numerator / denominator
return collaboration_effect
```
调用方式:
```python
matrix_a = np.array([[1, 2, 3],[4, 5, 6],[7, 8, 9]])
matrix_b = np.array([[9, 8, 7],[6, 5, 4],[3, 2, 1]])
collaboration_effect = get_collaboration_effect(matrix_a, matrix_b)
print(collaboration_effect)
```