How do I get indices of N maximum values in a NumPy array?

NumPy proposes a way to get the index of the maximum value of an array via np.argmax.

I would like a similar thing, but returning the indexes of the N maximum values.

For instance, if I have an array, [1, 3, 2, 4, 5], function(array, n=3) would return the indices [4, 3, 1] which correspond to the elements [5, 4, 3].

Solution 1:

Newer NumPy versions (1.8 and up) have a function called argpartition for this. To get the indices of the four largest elements, do

>>> a = np.array([9, 4, 4, 3, 3, 9, 0, 4, 6, 0])
>>> a
array([9, 4, 4, 3, 3, 9, 0, 4, 6, 0])
>>> ind = np.argpartition(a, -4)[-4:]
>>> ind
array([1, 5, 8, 0])
>>> a[ind]
array([4, 9, 6, 9])

Unlike argsort, this function runs in linear time in the worst case, but the returned indices are not sorted, as can be seen from the result of evaluating a[ind]. If you need that too, sort them afterwards:

>>> ind[np.argsort(a[ind])]
array([1, 8, 5, 0])

To get the top-k elements in sorted order in this way takes O(n + k log k) time.

Solution 2:

The simplest I've been able to come up with is:

In [1]: import numpy as np

In [2]: arr = np.array([1, 3, 2, 4, 5])

In [3]: arr.argsort()[-3:][::-1]
Out[3]: array([4, 3, 1])

This involves a complete sort of the array. I wonder if numpy provides a built-in way to do a partial sort; so far I haven't been able to find one.

If this solution turns out to be too slow (especially for small n), it may be worth looking at coding something up in Cython.