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

Warning

tril is switching to the sparse array interface.

For the case where no input arrays are sparse, this function is switching to returning a sparse array instead of sparse matrix. Control the sparse return class by making at least one input sparse, e.g., tril(coo_matrix(A)), or tril(coo_array(A)). That removes any deprecation warnings as well. For more general information about sparrays, see Migration from spmatrix to sparray. Handling of this no sparse input case will change no earlier than v1.20.

Parameters:
Adense or sparse array or matrix

Matrix whose lower trianglar portion is desired.

kintoptional

The top-most diagonal of the lower triangle.

formatstr

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]], dtype=int32)
>>> tril(A).toarray()
array([[1, 0, 0, 0, 0],
       [4, 5, 0, 0, 0],
       [0, 0, 8, 0, 0]], dtype=int32)
>>> 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]], dtype=int32)
>>> tril(A, k=-1).toarray()
array([[0, 0, 0, 0, 0],
       [4, 0, 0, 0, 0],
       [0, 0, 0, 0, 0]], dtype=int32)
>>> tril(A, format='csc')
<Compressed Sparse Column sparse array of dtype 'int32'
    with 4 stored elements and shape (3, 5)>
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