题解|计算相关矩阵

相关矩阵（Correlation Matrix）是一种常用的矩阵，其计算公式为：

其中，和是两个向量。

标准代码如下

def calculate_correlation_matrix(X, Y=None):
    # Helper function to calculate standard deviation
    def calculate_std_dev(A):
        return np.sqrt(np.mean((A - A.mean(0))**2, axis=0))
    
    if Y is None:
        Y = X
    n_samples = np.shape(X)[0]
    # Calculate the covariance matrix
    covariance = (1 / n_samples) * (X - X.mean(0)).T.dot(Y - Y.mean(0))
    # Calculate the standard deviations
    std_dev_X = np.expand_dims(calculate_std_dev(X), 1)
    std_dev_y = np.expand_dims(calculate_std_dev(Y), 1)
    # Calculate the correlation matrix
    correlation_matrix = np.divide(covariance, std_dev_X.dot(std_dev_y.T))

    return np.array(correlation_matrix, dtype=float)

也可以使用sklearn库的corrcoef函数或numpy库的一些函数实现。