Question

I am trying to understand numpy’s nonzero function. The following is an example application:

import numpy
arr = numpy.array([[1,0],[1,1]])
arr.nonzero()
--> (array([0, 1, 1]), array([0, 0, 1]))

I can see that because arr is 2-D, the output of nonzero() is a 2-tuple. However, I do not understand why the number of indices in each element of the tuple exceeds the number of rows/columns of the array. I can see that

arr[arr.nonzero()]
--> array([1, 1, 1])

But how…?

Answer 1

Each element of the tuple contains one of the indices for each nonzero value. Therefore, the length of each tuple element is the number of nonzeros in the array.

From your example, the indices of the nonzeros are [0, 0], [1, 0], and [1, 1]. The first element of the tuple is the first index for each of the nonzero values: ([0, 1, 1]), and the second element of the tuple is the second index for each of the nonzero values: ([0, 0, 1]).

Your second code block just returns the nonzero values of the array (I am not clear from the question if the return value is part of the confusion).

>>> arr[arr.nonzero()]
array([1, 1, 1])

This is more clear if we use an example array with other values.

>>> arr = numpy.array([[1,0],[2,3]])
>>> arr[arr.nonzero()]
array([1, 2, 3])