NumPy

numpy.tril_indices

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

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

Parameters
nint

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

kint, optional

Diagonal offset (see tril for details).

mint, optional

New in version 1.9.0.

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

Returns
indstuple of arrays

The indices for the triangle. The returned tuple contains two arrays, each with the indices along one dimension of the array.

See also

triu_indices

similar function, for upper-triangular.

mask_indices

generic function accepting an arbitrary mask function.

tril, triu

Notes

New in version 1.4.0.

Examples

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)
>>> il2 = np.tril_indices(4, 2)

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, ..., 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):

>>> a[il2] = -10
>>> a
array([[-10, -10, -10,   3],
       [-10, -10, -10, -10],
       [-10, -10, -10, -10],
       [-10, -10, -10, -10]])

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