numpy.nonzero()

Return the indices of the elements that are non-zero.

Returns a tuple of arrays, one for each dimension of a, containing the indices of the non-zero elements in that dimension. The values in a are always tested and returned in row-major, C-style order. The corresponding non-zero values can be obtained with:

a[nonzero(a)]

To group the indices by element, rather than dimension, use:

transpose(nonzero(a))

The result of this is always a 2-D array, with a row for each non-zero element.

Examples

>>> x = np.eye(3)
>>> x
array([[ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  1.]])
>>> np.nonzero(x)
(array([0, 1, 2]), array([0, 1, 2]))

>>> x[np.nonzero(x)]
array([ 1.,  1.,  1.])
>>> np.transpose(np.nonzero(x))
array([[0, 0],
       [1, 1],
       [2, 2]])

A common use for nonzero is to find the indices of an array, where a condition is True. Given an array a, the condition a > 3 is a boolean array and since False is interpreted as 0, np.nonzero(a > 3) yields the indices of the a where the condition is true.

>>> a = np.array([[1,2,3],[4,5,6],[7,8,9]])
>>> a > 3
array([[False, False, False],
       [ True,  True,  True],
       [ True,  True,  True]], dtype=bool)
>>> np.nonzero(a > 3)
(array([1, 1, 1, 2, 2, 2]), array([0, 1, 2, 0, 1, 2]))

The nonzero method of the boolean array can also be called.

>>> (a > 3).nonzero()
(array([1, 1, 1, 2, 2, 2]), array([0, 1, 2, 0, 1, 2]))