python - Indexing one array by another in numpy

Question

Suppose I have a matrix A with some arbitrary values:

array([[ 2, 4, 5, 3],
       [ 1, 6, 8, 9],
       [ 8, 7, 0, 2]])

And a matrix B which contains indices of elements in A:

array([[0, 0, 1, 2],
       [0, 3, 2, 1],
       [3, 2, 1, 0]])

How do I select values from A pointed by B, i.e.:

A[B] = [[2, 2, 4, 5],
        [1, 9, 8, 6],
        [2, 0, 7, 8]]

Answer 1

EDIT: np.take_along_axis is a builtin function for this use case implemented since numpy 1.15. See @hpaulj 's answer below for how to use it.

---

You can use NumPy's advanced indexing -

A[np.arange(A.shape[0])[:,None],B]

One can also use linear indexing -

m,n = A.shape
out = np.take(A,B + n*np.arange(m)[:,None])

Sample run -

In [40]: A
Out[40]: 
array([[2, 4, 5, 3],
       [1, 6, 8, 9],
       [8, 7, 0, 2]])

In [41]: B
Out[41]: 
array([[0, 0, 1, 2],
       [0, 3, 2, 1],
       [3, 2, 1, 0]])

In [42]: A[np.arange(A.shape[0])[:,None],B]
Out[42]: 
array([[2, 2, 4, 5],
       [1, 9, 8, 6],
       [2, 0, 7, 8]])

In [43]: m,n = A.shape

In [44]: np.take(A,B + n*np.arange(m)[:,None])
Out[44]: 
array([[2, 2, 4, 5],
       [1, 9, 8, 6],
       [2, 0, 7, 8]])

Answer 2

More recent versions have added a take_along_axis function that does the job:

A = np.array([[ 2, 4, 5, 3], 
              [ 1, 6, 8, 9], 
              [ 8, 7, 0, 2]])  
                                          
B = np.array([[0, 0, 1, 2], 
              [0, 3, 2, 1], 
              [3, 2, 1, 0]])     
                                        
np.take_along_axis(A, B, 1)  
                                       
Out[]: 
array([[2, 2, 4, 5],
       [1, 9, 8, 6],
       [2, 0, 7, 8]])

There's also a put_along_axis.

Answer 3

I know this is an old question, but another way of doing it using indices is:

A[np.indices(B.shape)[0], B]

output:

[[2 2 4 5]
 [1 9 8 6]
 [2 0 7 8]]

Answer 4

Following is the solution using for loop:

outlist = []
for i in range(len(B)):
    lst = []    
    for j in range(len(B[i])):
        lst.append(A[i][B[i][j]])
    outlist.append(lst)
outarray = np.asarray(outlist)
print(outarray)

Above can also be written in more succinct list comprehension form:

outlist = [ [A[i][B[i][j]] for j in range(len(B[i]))]
                for i in range(len(B))  ]
outarray = np.asarray(outlist)
print(outarray)

Output:

[[2 2 4 5]
 [1 9 8 6]
 [2 0 7 8]]