NumPy: Unsort/undo a reverse/descending sort

Question

I can do an in-place reverse sort (descending sort) of a numpy array, but I also need to be able to unsort (undo) it later.

Given an unsorted example:

a = np.array([-1, -2,  1, -3,  2,  0])

I tried:

i = a[::-1].argsort().argsort()  # BAD attempt to store original index
# i = array([3, 5, 0, 4, 1, 2])

a[::-1].sort()  # in-place reverse sort (works correctly)
# a= array([ 2,  1,  0, -1, -2, -3])

a = a[i]  # FAILS to restore original a
# a = array([-1, -3,  2, -2,  1,  0])

The above doesn't work. What would be the correct i that would work? Assume the array is very large, and so we don't want to make any unnecessary copies.

Answer 1

The following idiom is cheaper (O(n)) than the second argsort (O(n log n)).

Example array x with sort order y

>>> x = np.random.random(10)
>>> y = x.argsort()[::-1]

Build inverse i

>>> i = np.empty_like(y)
>>> i[y] = np.arange(y.size)

Check:

>>> x
array([0.44257134, 0.573158  , 0.07762422, 0.31507426, 0.43414726,
       0.34923861, 0.22161337, 0.14090133, 0.66903264, 0.38888105])
>>> x[y]
array([0.66903264, 0.573158  , 0.44257134, 0.43414726, 0.38888105,
       0.34923861, 0.31507426, 0.22161337, 0.14090133, 0.07762422])
>>> x[y][i]
array([0.44257134, 0.573158  , 0.07762422, 0.31507426, 0.43414726,
       0.34923861, 0.22161337, 0.14090133, 0.66903264, 0.38888105])

Answer 2

Given the unsorted example:

a = np.array([-1, -2,  1, -3,  2,  0])

To unsort/undo its reverse/descending sort:

i = a.argsort()[::-1]
# i = array([4, 2, 5, 0, 1, 3])

a = a[i]  # descending sort using i
# a = array([ 2,  1,  0, -1, -2, -3])

a = a[i.argsort()]  # unsort using i
# a = array([-1, -2,  1, -3,  2,  0])

Credit: This answer is motivated by one on how to unsort a sort which doesn't concern with reverse sort.