numpy.triu_indices

numpy.triu_indices(n, k=0, m=None)[source]

Return the indices for the upper-triangle of an (n, m) array.

Parameters:

nint

The size of the arrays for which the returned indices will be valid.

kint, optional

Diagonal offset (see triu for details).

mint, optional

The column dimension of the arrays for which the returned arrays will be valid. By default m is taken equal to n.

Returns:

indstuple, shape(2) of ndarrays, shape(n)

The row and column indices, respectively. The row indices are sorted in non-decreasing order, and the corresponding column indices are strictly increasing for each row.

See also

tril_indices

similar function, for lower-triangular.

mask_indices

generic function accepting an arbitrary mask function.

triu, tril

Examples

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>>> import numpy as np

Compute two different sets of indices to access 4x4 arrays, one for the upper triangular part starting at the main diagonal, and one starting two diagonals further right:

>>> iu1 = np.triu_indices(4)
>>> iu1
(array([0, 0, 0, 0, 1, 1, 1, 2, 2, 3]), array([0, 1, 2, 3, 1, 2, 3, 2, 3, 3]))

Note that row indices (first array) are non-decreasing, and the corresponding column indices (second array) are strictly increasing for each row.

Here is how they can be used with a sample array:

>>> a = np.arange(16).reshape(4, 4)
>>> a
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11],
       [12, 13, 14, 15]])

Both for indexing:

>>> a[iu1]
array([ 0,  1,  2, ..., 10, 11, 15])

And for assigning values:

>>> a[iu1] = -1
>>> a
array([[-1, -1, -1, -1],
       [ 4, -1, -1, -1],
       [ 8,  9, -1, -1],
       [12, 13, 14, -1]])

These cover only a small part of the whole array (two diagonals right of the main one):

>>> iu2 = np.triu_indices(4, 2)
>>> a[iu2] = -10
>>> a
array([[ -1,  -1, -10, -10],
       [  4,  -1,  -1, -10],
       [  8,   9,  -1,  -1],
       [ 12,  13,  14,  -1]])

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