Indexing 3d numpy array with 2d array

Question

I would like to create a numpy 2d-array based on values in a numpy 3d-array, using another numpy 2d-array to determine which element to use in axis 3.

import numpy as np
#--------------------------------------------------------------------
arr_3d = np.arange(2*3*4).reshape(2,3,4)
print('arr_3d shape=', arr_3d.shape, '\n', arr_3d)
arr_2d = np.array(([3,2,0], [2,3,2]))
print('\n', 'arr_2d shape=', arr_2d.shape, '\n', arr_2d)
res_2d = arr_3d[:, :, 2]
print('\n','res_2d example using element 2 of each 3rd axis...\n', res_2d)
res_2d = arr_3d[:, :, 3]
print('\n','res_2d example using element 3 of each 3rd axis...\n', res_2d)

Results...

arr_3d shape= (2, 3, 4) 
 [[[ 0  1  2  3]
  [ 4  5  6  7]
  [ 8  9 10 11]]

 [[12 13 14 15]
  [16 17 18 19]
  [20 21 22 23]]]

 arr_2d shape= (2, 3) 
 [[3 2 0]
 [2 3 2]]

 res_2d example using element 2 of each 3rd axis...
 [[ 2  6 10]
 [14 18 22]]

 res_2d example using element 3 of each 3rd axis...
 [[ 3  7 11]
 [15 19 23]]

The 2 example results show what I get if I use the 2nd and then the 3rd element of axis 3. But I would like to get the element from arr_3d, specified by arr_2d. So...

- res_2d[0,0] would use the element 3 of arr_3d axis 3
- res_2d[0,1] would use the element 2 of arr_3d axis 3
- res_2d[0,2] would use the element 0 of arr_3d axis 3
etc

So res_2d should look like this...

[[3 6 8]
[14 19 22]]

I tried using this line to get the arr_2d entries, but it results in a 4-dim array and I want a 2-dim array.

res_2d = arr_3d[:, :, arr_2d[:,:]]

Answer 1

While functionally the same as the other answers, I prefer to use numpy.ogrid to generate the (sparse) index arrays that index the remaining dimensions:

import numpy as np

# example data
arr_3d = np.arange(2*3*4).reshape(2, 3, 4)
arr_2d = np.array(([3, 2, 0], [2, 3, 2]))

m, n, _ = arr_3d.shape
ind0, ind1 = np.ogrid[:m, :n]
res_2d = arr_3d[ind0, ind1, arr_2d]
print(res_2d)
# [[ 3  6  8]
#  [14 19 22]]

One could also use np.meshgrid with sparse=True, but that would force us to create 1d index ranges which we can avoid with the np.ogrid helper.

Answer 2

The shape of the result from fancy index and broadcasting is the shape of the indexing array. You need passing 2d array for each axis of arr_3d

ax_0 = np.arange(arr_3d.shape[0])[:,None]
ax_1 = np.arange(arr_3d.shape[1])[None,:]

arr_3d[ax_0, ax_1, arr_2d]

Out[1127]:
array([[ 3,  6,  8],
       [14, 19, 22]])

Answer 3

In [107]: arr_3d = np.arange(2*3*4).reshape(2,3,4)                                                           
In [108]: arr_2d = np.array(([3,2,0], [2,3,2]))                                                              
In [109]: arr_2d.shape                                                                                       
Out[109]: (2, 3)
In [110]: arr_3d[[[0],[1]],[0,1,2],arr_2d]                                                                   
Out[110]: 
array([[ 3,  6,  8],
       [14, 19, 22]])

[[0],[1]],[0,1,2] broadcast with each other to index a (2,3) block, the same size as `arr_2d.

ix_ can be used to construct those 2 indices:

In [114]: I,J = np.ix_(range(2), range(3))                                                                   
In [115]: I,J                                                                                                
Out[115]: 
(array([[0],
        [1]]), array([[0, 1, 2]]))
In [116]: arr_3d[I, J, arr_2d]                                                                               
Out[116]: 
array([[ 3,  6,  8],
       [14, 19, 22]])