NumPy array permute columns 3D matrix with argsort

Question

I need to permute elements of columns in the matrix A ( 3D matrix by axis 0) by 2D permutation matrix pi obtained from argsort , that contains new indices for all columns.

By application permutation matrix pi on the matrix A ( A[pi] ) I will get a 4D matrix with new shape. For example, the shape of A is (2,3,4) and the shape of A[pi] is (2,3,3,4).

I am able to extract the required sorted matrix from A[pi] using the command:

swapaxes (diagonal(A[pi], axis1=2, axis2=1),1,2)

But it seems to be too complicated and slow.

Is there another elegant solution?

Example:

print(A)
[[[   73   701  2411  2414]
  [ 5515  8292  8414 16135]
  [  100  1241  2146  2931]]

 [[ 1335  1747  3418  6312]
  [ 3788  5449  5753  9738]
  [  565  3038  3800  5430]]]

pi=argsort(Norm_order(A),0)

print(pi)
[[1, 0, 1],
 [0, 1, 0]]

print(swapaxes(diagonal(A[pi],axis1=2,axis2=1),1,2))
[[[ 1335  1747  3418  6312]
  [ 5515  8292  8414 16135]
  [  565  3038  3800  5430]]

 [[   73   701  2411  2414]
  [ 3788  5449  5753  9738]
  [  100  1241  2146  2931]]]

Answer 1

Maybe a matter of taste, but I find the following a bit more readable:

i, j = np.ogrid[:3, :4]
A[pi[..., None], i, j]

Output:

array([[[ 1335,  1747,  3418,  6312],
        [ 5515,  8292,  8414, 16135],
        [  565,  3038,  3800,  5430]],

       [[   73,   701,  2411,  2414],
        [ 3788,  5449,  5753,  9738],
        [  100,  1241,  2146,  2931]]])