scipy.linalg.tri

scipy.linalg.tri(N, M=None, k=0, dtype=None)

Construct (N, M) matrix filled with ones at and below the k-th diagonal.

The matrix has A[i,j] == 1 for i <= j + k

Parameters :

N : integer

The size of the first dimension of the matrix.

M : integer or None

The size of the second dimension of the matrix. If M is None, M = N is assumed.

k : integer

Number of subdiagonal below which matrix is filled with ones. k = 0 is the main diagonal, k < 0 subdiagonal and k > 0 superdiagonal.

dtype : dtype

Data type of the matrix.

Returns :

A : array, shape (N, M)

Examples

>>> from scipy.linalg import tri
>>> tri(3, 5, 2, dtype=int)
array([[1, 1, 1, 0, 0],
       [1, 1, 1, 1, 0],
       [1, 1, 1, 1, 1]])
>>> tri(3, 5, -1, dtype=int)
array([[0, 0, 0, 0, 0],
       [1, 0, 0, 0, 0],
       [1, 1, 0, 0, 0]])