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Module « numpy.matlib »

Fonction tril_indices - module numpy.matlib

Signature de la fonction tril_indices

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

Description

help(numpy.matlib.tril_indices)

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 correspdonding column indices are
    strictly increasing for each row.

See also
--------
triu_indices : similar function, for upper-triangular.
mask_indices : generic function accepting an arbitrary mask function.
tril, triu

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, ..., 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]])

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