def maximum_bipartite_matching(A, perm_type='row'):
"""
Returns an array of row or column permutations that removes nonzero
elements from the diagonal of a nonsingular square CSC sparse matrix. Such
a permutation is always possible provided that the matrix is nonsingular.
This function looks at the structure of the matrix only.
The input matrix will be converted to CSC matrix format if
necessary.
Parameters
----------
A : sparse matrix
Input matrix
perm_type : str {'row', 'column'}
Type of permutation to generate.
Returns
-------
perm : array
Array of row or column permutations.
Notes
-----
This function relies on a maximum cardinality bipartite matching algorithm
based on a breadth-first search (BFS) of the underlying graph[1]_.
References
----------
.. [1] I. S. Duff, K. Kaya, and B. Ucar, "Design, Implementation, and
Analysis of Maximum Transversal Algorithms", ACM Trans. Math. Softw.
38, no. 2, (2011).
"""
nrows = A.shape[0]
if A.shape[0] != A.shape[1]:
raise ValueError(
'Maximum bipartite matching requires a square matrix.')
if sp.isspmatrix_csr(A) or sp.isspmatrix_coo(A):
A = A.tocsc()
elif not sp.isspmatrix_csc(A):
raise TypeError("matrix must be in CSC, CSR, or COO format.")
if perm_type == 'column':
A = A.transpose().tocsc()
perm = _maximum_bipartite_matching(A.indices, A.indptr, nrows)
if np.any(perm == -1):
raise Exception('Possibly singular input matrix.')
return perm
def maximum_bipartite_matching(A, perm_type='row'):
"""
Returns an array of row or column permutations that removes nonzero
elements from the diagonal of a nonsingular square CSC sparse matrix. Such
a permutation is always possible provided that the matrix is nonsingular.
This function looks at the structure of the matrix only.
The input matrix will be converted to CSC matrix format if
necessary.
Parameters
----------
A : sparse matrix
Input matrix
perm_type : str {'row', 'column'}
Type of permutation to generate.
Returns
-------
perm : array
Array of row or column permutations.
Notes
-----
This function relies on a maximum cardinality bipartite matching algorithm
based on a breadth-first search (BFS) of the underlying graph[1]_.
References
----------
I. S. Duff, K. Kaya, and B. Ucar, "Design, Implementation, and
Analysis of Maximum Transversal Algorithms", ACM Trans. Math. Softw.
38, no. 2, (2011).
"""
nrows = A.shape[0]
if A.shape[0] != A.shape[1]:
raise ValueError(
'Maximum bipartite matching requires a square matrix.')
if sp.isspmatrix_csr(A) or sp.isspmatrix_coo(A):
A = A.tocsc()
elif not sp.isspmatrix_csc(A):
raise TypeError("matrix must be in CSC, CSR, or COO format.")
if perm_type == 'column':
A = A.transpose().tocsc()
perm = _maximum_bipartite_matching(A.indices, A.indptr, nrows)
if np.any(perm == -1):
raise Exception('Possibly singular input matrix.')
return perm