Weighted covariance matrix (weighted covariance matrix)

 There is no useful one in China. Here is the weighted covariance matrix calculation function. When used, the weights can be normalized first.

def weighted_cov(values, weights):
    """
    Computes a weighted covariance matrix
    
    :param values: the array of values
    :param weights: array of weights for each entry of the values
    
    :returns sigma: the weighted covariance matrix
    """
    
    n = values.shape[1]
    sigma = np.empty((n, n))
    w = weights.sum() / (weights.sum()**2 - (weights**2).sum()) 
    average = np.average(values, axis=0, weights=weights)
    for j in range(n):
        for k in range(n):
            sigma[j, k] = w * np.sum(weights * ((values[:, j] - average[j]) * (values[:, k] - average[k])))
    return sigma