tril(A, k=0, format=None)

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

A : dense or sparse matrix

Matrix whose lower trianglar portion is desired.

k : integer : optional

The top-most diagonal of the lower triangle.

format : string

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

Returns

L : sparse matrix

Lower triangular portion of A in sparse format.

Return the lower triangular portion of a matrix in sparse format

See Also

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>

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.sparse._extract.tril scipy.sparse._extract.triu

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