# scipy.sparse.tril#

scipy.sparse.tril(A, k=0, format=None)[source]#

Return the lower triangular portion of a matrix in sparse format

Returns the elements on or below the k-th diagonal of the matrix A.
• k = 0 corresponds to the main diagonal

• k > 0 is above the main diagonal

• k < 0 is below the main diagonal

Parameters:

Matrix whose lower trianglar portion is desired.

kintegeroptional

The top-most diagonal of the lower triangle.

formatstring

Sparse format of the result, e.g. format=”csr”, etc.

Returns:
Lsparse matrix

Lower triangular portion of A in sparse format.

`triu`

upper triangle in sparse format

Examples

```>>> from scipy.sparse import csr_matrix, tril
>>> A = csr_matrix([[1, 2, 0, 0, 3], [4, 5, 0, 6, 7], [0, 0, 8, 9, 0]],
...                dtype='int32')
>>> A.toarray()
array([[1, 2, 0, 0, 3],
[4, 5, 0, 6, 7],
[0, 0, 8, 9, 0]])
>>> tril(A).toarray()
array([[1, 0, 0, 0, 0],
[4, 5, 0, 0, 0],
[0, 0, 8, 0, 0]])
>>> tril(A).nnz
4
>>> tril(A, k=1).toarray()
array([[1, 2, 0, 0, 0],
[4, 5, 0, 0, 0],
[0, 0, 8, 9, 0]])
>>> tril(A, k=-1).toarray()
array([[0, 0, 0, 0, 0],
[4, 0, 0, 0, 0],
[0, 0, 0, 0, 0]])
>>> tril(A, format='csc')
<3x5 sparse matrix of type '<class 'numpy.int32'>'
with 4 stored elements in Compressed Sparse Column format>
```