scipy.sparse.tril#

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

Return the lower triangular portion of a sparse array or matrix

Returns the elements on or below the k-th diagonal of A.

k = 0 corresponds to the main diagonal
k > 0 is above the main diagonal
k < 0 is below the main diagonal

Parameters:

Adense or sparse array or matrix: 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.

See also

triu: upper triangle in sparse format

Examples

>>> from scipy.sparse import csr_array, tril
>>> A = csr_array([[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 array of type '<class 'numpy.int32'>'
        with 4 stored elements in Compressed Sparse Column format>