Sort an array and trace back the indices to their sorted order

Question

I am trying to sort this array,

[[15 12 10 8 7]
[7 8 4 3 1]
[8 5 9 12 4]
[6 10 14 7 5]]

to

[[5 4 3 2 1]
[4 5 3 2 1]
[3 2 4 5 1]
[2 4 5 3 1]]

I have tried using nm.argsort(a, axis=1) but this doesn't give desired output, may be I am using it incorrectly. The same operation would apply to second array but at column level. Any help would be appreciated. Thanks.

Why are the first two elements of the first row `5 4`? – user2357112 Sep 13 '17 at 16:37 — user2357112, Sep 13 '17 at 16:37

Divakar · Accepted Answer · 2017-09-13T16:50:17.707

It seems you are trying to trace back the elements positions in the sorted order.

Approach #1 : One way to do so would be to use argsort twice, like so -

a.argsort(1).argsort(1)+1

Approach #2 : Efficient method inspired by this post -

def argsort_unique2D(idx):
    m,n = idx.shape
    sidx = np.empty((m,n),dtype=int)
    sidx[np.arange(m)[:,None], idx] = np.arange(n)
    return sidx

out = argsort_unique2D(a.argsort(1))+1

Sample run -

In [42]: a
Out[42]: 
array([[15, 12, 10,  8,  7],
       [ 7,  8,  4,  3,  1],
       [ 8,  5,  9, 12,  4],
       [ 6, 10, 14,  7,  5]])

In [43]: a.argsort(1).argsort(1)+1
Out[43]: 
array([[5, 4, 3, 2, 1],
       [4, 5, 3, 2, 1],
       [3, 2, 4, 5, 1],
       [2, 4, 5, 3, 1]])

In [71]: argsort_unique2D(a.argsort(1))+1
Out[71]: 
array([[5, 4, 3, 2, 1],
       [4, 5, 3, 2, 1],
       [3, 2, 4, 5, 1],
       [2, 4, 5, 3, 1]])

Runtime test -

In [76]: a = np.random.rand(100,10000)

In [77]: %timeit a.argsort(1).argsort(1)+1
10 loops, best of 3: 115 ms per loop

In [78]: %timeit argsort_unique2D(a.argsort(1))+1
10 loops, best of 3: 67.8 ms per loop

Thanks for answer. It worked. How to do same but with column — Apu Dar, Sep 13 '17 at 16:55
@ApuDar Use `a.argsort(0).argsort(0)+1` to replace approach#1. — Divakar, Sep 13 '17 at 16:56

Sort an array and trace back the indices to their sorted order

1 Answers1