`numpy:tril_indices`

source: /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

✓

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

✓

(array([0, 1, 1, 2, 2, 2, 3, 3, 3, 3]), array([0, 0, 1, 0, 1, 2, 0, 1, 2, 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[il1]

✓

array([ 0,  4,  5,  8,  9, 10, 12, 13, 14, 15])

And for assigning values:

a[il1] = -1
a

✓

array([[-1,  1,  2,  3],
       [-1, -1,  6,  7],
       [-1, -1, -1, 11],
       [-1, -1, -1, -1]])

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

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

✓

array([[-10, -10, -10,   3],
       [-10, -10, -10, -10],
       [-10, -10, -10, -10],
       [-10, -10, -10, -10]])

`numpy:tril_indices`

Signature

Summary

Parameters

Returns

Examples

See also

Aliases

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