This is documentation for an old release of NumPy (version 1.13). Read this page Search for this page in the documentation of the latest stable release (version 2.2).

numpy.nonzero

numpy.nonzero(a)

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.

Parameters:

a : array_like

Input array.

Returns:

tuple_of_arrays : tuple

Indices of elements that are non-zero.

See also

flatnonzero

Return indices that are non-zero in the flattened version of the input array.

ndarray.nonzero

Equivalent ndarray method.

count_nonzero

Counts the number of non-zero elements in the input array.

Examples

>>> x = np.array([[1,0,0], [0,2,0], [1,1,0]])
>>> x
array([[1, 0, 0],
       [0, 2, 0],
       [1, 1, 0]])
>>> np.nonzero(x)
(array([0, 1, 2, 2], dtype=int64), array([0, 1, 0, 1], dtype=int64))

>>> 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]))