how to make argsort result to be random between equal values?

Question

Say you have a numpy vector [0,3,1,1,1] and you run argsort you will get [0,2,3,4,1] but all the ones are the same! What I want is an efficient way to shuffle indices of identical values. Any idea how to do that without a while loop with two indices on the sorted vector?

numpy.array([0,3,1,1,1]).argsort()

Answer 1

Use lexsort: np.lexsort((b,a)) means Sort by a, then by b

>>> a
array([0, 3, 1, 1, 1])
>>> b=np.random.random(a.size)
>>> b
array([ 0.00673736,  0.90089115,  0.31407214,  0.24299867,  0.7223546 ])
>>> np.lexsort((b,a))
array([0, 3, 2, 4, 1])
>>> a.argsort()
array([0, 2, 3, 4, 1])
>>> a[[0, 3, 2, 4, 1]]
array([0, 1, 1, 1, 3])
>>> a[[0, 2, 3, 4, 1]]
array([0, 1, 1, 1, 3])

Answer 2

This is a bit of a hack, but if your array contains integers only you could add random values and argsort the result. np.random.rand gives you results in [0, 1) so in this case you're guaranteed to maintain the order for non-identical elements.

>>> import numpy as np
>>> arr = np.array([0,3,1,1,1])
>>> np.argsort(arr + np.random.rand(*arr.shape))
array([0, 4, 3, 2, 1])
>>> np.argsort(arr + np.random.rand(*arr.shape))
array([0, 3, 4, 2, 1])
>>> np.argsort(arr + np.random.rand(*arr.shape))
array([0, 3, 4, 2, 1])
>>> np.argsort(arr + np.random.rand(*arr.shape))
array([0, 2, 3, 4, 1])
>>> np.argsort(arr + np.random.rand(*arr.shape))
array([0, 2, 3, 4, 1])
>>> np.argsort(arr + np.random.rand(*arr.shape))
array([0, 4, 2, 3, 1])

Here we see index 0 is always first in the argsort result and index 1 is last, but the rest of the results are in a random order.

In general you could generate random values bounded by np.diff(np.sort(arr)).max(), but you might run into precision issues at some point.