Access numpy elements from an array of indexes

Question

I have an array a of dimension n, and an array b of dimension n-1. The values of the last axis of b correspond to the indexes of the values I want to extract from the array a, in an array res of dimension n-1.

For exemple with n=2 :

a = np.array([[1,  2,  3,  4],
              [5,  6,  7,  8],
              [9, 10, 11, 12])
b = np.array([1,3,0])

I would like

res = [a[1], a[3], a[0]]

# i.e. res = [2, 8, 9]

Is there a function that does it in an efficient way, with a higher number of dimensions ? I know I could use for loops, but I hope there is something more efficient.

EDIT:

With n=3, let a have a shape of (2,2,3).

Then b and res have shapes of (2,2):

a = np.array([[[ 1, 2, 3],
               [ 4, 5, 6]],
              [[ 7, 8, 9],
               [10,11,12]]])

b = np.array([[0,2],
              [1,2]]

# res = np.array([[1,6],
#                 [8,12]])

Related: The 2d case is answered here.

jpp
– jpp

2018-10-05 11:27:27 +00:00
Commented Oct 5, 2018 at 11:27 — jpp
– jpp, Commented Oct 5, 2018 at 11:27
Would the new np.take_along_axis apply?

hpaulj
– hpaulj

2018-10-05 11:32:52 +00:00
Commented Oct 5, 2018 at 11:32 — hpaulj
– hpaulj, Commented Oct 5, 2018 at 11:32
Tkanks it works perfectly ! I need it at the right time ;)

Axel Puig
– Axel Puig

2018-10-05 13:14:59 +00:00
Commented Oct 5, 2018 at 13:14 — Axel Puig
– Axel Puig, Commented Oct 5, 2018 at 13:14

hpaulj · Accepted Answer · 2018-10-05 19:55:11Z

The latest numpy (1.15) has added a take_along_axis function:

In [36]: np.take_along_axis(a, b[:,None], 1)
Out[36]: 
array([[2],
       [8],
       [9]])

It uses a helper function to construct an indexing tuple:

In [37]: np.lib.shape_base._make_along_axis_idx((3,4), b[:,None], 1)
Out[37]: 
(array([[0],
        [1],
        [2]]), 
 array([[1],
        [3],
        [0]]))

Prior to this, I (and others) would have recommended:

In [38]: a[np.arange(3), b]
Out[38]: array([2, 8, 9])

which is essentially the same thing (except for an added dimension). As take_along_axis docs show this was designed to take things like the results of argsort along an axis.

for the higher dimension case:

In [39]: a1 = np.array([[[ 1, 2, 3],
    ...:                [ 4, 5, 6]],
    ...:               [[ 7, 8, 9],
    ...:                [10,11,12]]])
    ...: b1 = np.array([[0,2],
    ...:               [1,2]])               
In [40]: a1.shape
Out[40]: (2, 2, 3)
In [41]: b1.shape
Out[41]: (2, 2)

In [42]: np.take_along_axis(a1, b1[...,None], -1)
Out[42]: 
array([[[ 1],
        [ 6]],

       [[ 8],
        [12]]])

In [45]: np.lib.shape_base._make_along_axis_idx(a1.shape, b1[...,None], 2)
Out[45]: 
(array([[[0]],

        [[1]]]), 
 array([[[0],
         [1]]]), 
 array([[[0],
         [2]],

        [[1],
         [2]]]))
In [46]: [i.shape for i in _]
Out[46]: [(2, 1, 1), (1, 2, 1), (2, 2, 1)]

Again, the equivalent do-it-yourself indexing:

In [48]: a1[np.arange(2)[:,None], np.arange(2)[None,:], b1]
Out[48]: 
array([[ 1,  6],
       [ 8, 12]])

Once you understand array broadcasting and how it applies to indexing, the concepts here are not difficult. But the take_along_axis may make applying them easier. It is in a sense an extension of np.ix_.

In [50]: np.ix_(np.arange(2), np.arange(2), np.arange(3))
Out[50]: 
(array([[[0]],

        [[1]]]), array([[[0],
         [1]]]), array([[[0, 1, 2]]]))
In [51]: [i.shape for i in _]
Out[51]: [(2, 1, 1), (1, 2, 1), (1, 1, 3)]
In [55]: a1[(*np.ix_(np.arange(2), np.arange(2)),b1)]
Out[55]: 
array([[ 1,  6],
       [ 8, 12]])

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