# numpy.tril_indices_from

numpy.tril_indices_from(arr, k=0)

  Return the indices for the lower-triangle of arr.

  See `tril_indices` for full details.

  Parameters:
    arr array_like

      The indices will be valid for square arrays whose dimensions are the same as arr.

    k int, optional

      Diagonal offset (see `tril` for details).

  See also

  `tril_indices`, `tril`, `triu_indices_from`

  Notes

  New in version 1.4.0.

  Examples

  Create a 4 by 4 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]])

  Pass the array to get the indices of the lower triangular elements.

      >>> trili = np.tril_indices_from(a)
      >>> trili
      (array([0, 1, 1, 2, 2, 2, 3, 3, 3, 3]), array([0, 0, 1, 0, 1, 2, 0, 1, 2, 3]))

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

  This is syntactic sugar for tril_indices().

      >>> np.tril_indices(a.shape[0])
      (array([0, 1, 1, 2, 2, 2, 3, 3, 3, 3]), array([0, 0, 1, 0, 1, 2, 0, 1, 2, 3]))

  Use the k parameter to return the indices for the lower triangular array up to the k-th diagonal.

      >>> trili1 = np.tril_indices_from(a, k=1)
      >>> a[trili1]
      array([ 0,  1,  4,  5,  6,  8,  9, 10, 11, 12, 13, 14, 15])