如何摆脱循环并使我的相关矩阵函数更有效

Question

I have this function that computes the correlation matrix and works as expect however I am trying to make it more efficient and get rid of the loops but I'm having trouble doing so. My function below:

def correlation(X):
    N = X.shape[0]  # num of rows
    D = X.shape[1]  # num of cols

    covarianceMatrix = np.cov(X)  # start with covariance matrix

    # use covarianceMatrix to create size of M
    M = np.zeros([covarianceMatrix.shape[0], covarianceMatrix.shape[1]])

    for i in range(covarianceMatrix.shape[0]):
        for j in range(covarianceMatrix.shape[1]):

           corr = covarianceMatrix[i, j] / np.sqrt(np.dot(covarianceMatrix[i, i], covarianceMatrix[j, j]))
           M[i,j]  = corr

    return M

What would be a more efficient way to perform this computation using numpy and not using its built it functions such as corrcoef().

Answer 1

Once you have the covariance matrix you simply need to multiply by the product of the diagonal inverse square root. Using bits of your code as a starting point:

covarianceMatrix = np.cov(X)
tmp = 1.0 / np.sqrt(np.diag(covarianceMatrix))

corr = covarianceMatrix.copy()
corr *= tmp[:, None]
corr *= tmp[None, :]

A bit more difficult if you have complex values, and you should probably clip between -1 and 1 via:

np.clip(corr, -1, 1, out=corr)