numpy-整个矩阵的运算

Question

Say I have a numpy array

a = np.array([[a11 a12 a13],
          [a21 a22 a23],
          [a31 a32 a33]])

I want to return the following result:

np.array([[a11/a1 a12/a1 a13/a1],
          [a21/a2 a22/a2 a23/a2],
          [a31/a3 a32/a3 a33/a3]])

where:

  a1 = np.sqrt(a11**2 + a12**2 + a13**2)
  a2 = np.sqrt(a21**2 + a22**2 + a23**2)
  a3 = np.sqrt(a31**2 + a32**2 + a33**2)

In other words, I want to divide each element of the array by the norm of the row it belongs to.

I have written some code which does this, but it is frankly horrible - I am looping through rows of the array, which I know is not what numpy as designed for. I have a feeling the same could be achieved by using two numpy library calls which I just don't know.

Another thing I thought of is:

a/np.reshape(np.linalg.norm(a,axis=1),(a.shape[0],1))

but I'm not sure if this is a particularly efficient way. Any advice?

Answer 1

import numpy as np

a = np.array([[11, 12, 13],
          [21, 22, 23],
          [31, 32, 33]], float)

a / np.sum(a**2, 1, keepdims=True)**0.5