gram-schmidt修改的python 3

Question

我刚开始使用python 3语言进行编码，我正在尝试为gram-schmidt修改的QR分解编写代码。我已经成功地使用numpy编写了代码，但是现在我尝试不使用numpy编写新的代码。任何帮助将非常感谢。我的numpy代码如下。

import numpy as np
def gram_schmidt(A):
""" Representation of Gram-Schmidt Process or QR Diagonalization 
    for an mxn system of linear equations. """

m = np.shape(A)[0]
n = np.shape(A)[1]

Q =  np.zeros((m, m))
R =  np.zeros((n, n)) 

for j in xrange(n):

    v = A[:,j]

    for i in xrange(j):

        R[i,j] = Q[:,i].T * A[:,j]

        v = v.squeeze() - (R[i,j] * Q[:,i])

    R[j,j] =  np.linalg.norm(v)
    Q[:,j] = (v / R[j,j]).squeeze()

return Q, R