Pearson Correlation between two Matrices

Question

So I want to compute the correlation between every row of one matrix and every column of the other matrix. This is with what I have come up, it works, but I think its pretty slow (takes about 60 seconds for two matrices of shape 500x30000 and 500x16).

def matrix_corr(array1,array2):

array1= array1.T #transposed in order to have same dimension in the middle of both matrices


corr_pear = np.empty((array1.shape[0],array2.shape[1]))


for n in range(array1.shape[0]): #30000 rowvectors
    array1_mean = np.mean(array1[n,:]) #n-th rowvector 
    array1_squared = np.sum(np.square(array1[n,:]-array1_mean))
    for m in range(array2.shape[1]): #256 columnvectors of hypothesis
        array2_mean = np.mean(array1[:,m])
        array2_squared = np.sum(np.square(array1[:,m]-array2_mean))
        corr_pear[n,m] = (np.inner((array1[n,:]-array1_mean),(array2[:,m]-array2_mean))/
        float(math.sqrt(array1_squared*array2_squared)))

return corr_pear

I guss there is a more pythonic way to solve this.

I hope someone of you could tell me how to tweak it.

Thanks!