`numpy:tril_indices`

source: /dev/numpy/build-install/usr/lib/python3.14/site-packages/numpy/lib/_twodim_base_impl.py :907

Signature

def tril_indices ( n , k = 0 , m = None )

Summary

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

Parameters

n : int: The row dimension of the arrays for which the returned indices will be valid.
k : int, optional: Diagonal offset (see tril for details).
m : int, optional: The column dimension of the arrays for which the returned arrays will be valid. By default m is taken equal to n.

Returns

inds : tuple of arrays: 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.

Examples

import numpy as np

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

il1 = np.tril_indices(4)
il1

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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

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Both for indexing:

a[il1]

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And for assigning values:

a[il1] = -1
a

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These cover almost the whole array (two diagonals right of the main one):

il2 = np.tril_indices(4, 2)
a[il2] = -10
a

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Aliases