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Bug in scipy.sparse.csgraph.min_weight_full_bipartite_matching

See original GitHub issue

min_weight_full_bipartite_matching gets stuck when running, python is not responding to SIGINT, needed to use cltr+\ to send SIGTERM.

To reproduce:

import pickle
from scipy.sparse.csgraph import min_weight_full_bipartite_matching
t = ... # see comment bellow
min_weight_full_bipartite_matching(t)

The matrix is a coo matrix, which is representing the dense matrix below, all 0s are implicit (no 0 values in coo matrix):

[[0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.001      0.         0.         0.         0.         0.         0.         0.         0.        ]
 [0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.001      0.         0.         0.         0.         0.         0.         0.        ]
 [0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.001      0.         0.         0.         0.         0.         0.        ]
 [0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.001      0.         0.         0.         0.         0.        ]
 [0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.001      0.         0.         0.         0.        ]
 [0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.001      0.         0.         0.        ]
 [0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.001      0.         0.        ]
 [0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.001      0.        ]
 [0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.001     ]
 [0.         0.11687445 0.         0.         0.01319788 0.07509257 0.         0.         0.         0.74228317 0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.        ]
 [0.         0.         0.         0.81087935 0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.        ]
 [0.         0.         0.         0.         0.8408466  0.         0.         0.         0.         0.01194389 0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.        ]
 [0.         0.82994211 0.         0.         0.         0.11468516 0.         0.         0.         0.11173505 0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.        ]
 [0.18796507 0.         0.04002318 0.         0.         0.         0.         0.         0.75883335 0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.        ]
 [0.         0.         0.71545464 0.         0.         0.         0.         0.         0.02748488 0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.        ]
 [0.78470564 0.         0.         0.         0.         0.         0.         0.         0.14829198 0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.        ]
 [0.         0.10870609 0.         0.         0.         0.8918677  0.         0.         0.         0.06306644 0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.        ]
 [0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.63844085 0.         0.         0.         0.         0.         0.         0.         0.         0.        ]
 [0.         0.         0.         0.         0.         0.         0.7442354  0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.        ]
 [0.         0.         0.         0.         0.         0.         0.         0.09850549 0.         0.         0.18638258 0.2769244  0.         0.         0.         0.         0.         0.         0.         0.         0.         0.        ]
 [0.         0.         0.         0.         0.         0.         0.         0.73182464 0.         0.         0.46443561 0.38589284 0.         0.         0.         0.         0.         0.         0.         0.         0.         0.        ]
 [0.29510278 0.         0.         0.         0.         0.         0.         0.         0.09666032 0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.         0.        ]]

Issue Analytics

State:
Created a year ago
Comments:12 (8 by maintainers)

Top GitHub Comments

1reaction

rossbarcommented, Nov 7, 2022

From the documentation of scipy.sparse.csgraph, it expects a biadjacency_matrix

Thanks @Code-Gratefully , you are right: since the matrix was square I misinterpreted it as an adjacency matrix rather than a biadjacency matrix (which, as you point out, the csgraph.min_weight_full_bipartite_matching docs explicitly warn against) - my mistake!

If we instead interpret the input matrix correctly as a biadjacency matrix, then we hit a different exception in NetworkX:

>>> import networkx as nx
>>> import scipy as sp
>>> a = <copied from above>
>>> m = sp.sparse.csr_matrix(a)  # nx.bipartite.from_biadjacency_matrix expects a scipy.sparse array
>>> G = nx.bipartite.from_biadjacency_matrix(m)
>>> G.number_of_nodes()  # Expect 44 (sum(a.shape))
44
>>> top_nodes = list(range(a.shape[0]))  # Be explicit about node sets
>>> nx.bipartite.minimum_weight_full_matching(G, top_nodes=top_nodes)
Traceback (most recent call last)
   ...
ValueError: cost matrix is infeasible

Note that the NetworkX version just calls scipy.optimize.linear_sum_assignment on the dense biadjacency_matrix (with inf representing non-edges rather than 0), which is where the exception originates. Full traceback included below

Traceback

nx.bipartite.minimum_weight_full_matching(G, top_nodes=list(range(a.shape[0])))
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In [104], line 1
----> 1 nx.bipartite.minimum_weight_full_matching(G, top_nodes=list(range(a.shape[0])))
File ~/repos/networkx/networkx/algorithms/bipartite/matching.py:574, in minimum_weight_full_matching(G, top_nodes, weight)
572 weights = np.full(weights_sparse.shape, np.inf)
573 weights[weights_sparse.row, weights_sparse.col] = weights_sparse.data
–> 574 left_matches = sp.optimize.linear_sum_assignment(weights)
575 d = {U[u]: V[v] for u, v in zip(*left_matches)}
576 # d will contain the matching from edges in left to right; we need to
577 # add the ones from right to left as well.
ValueError: cost matrix is infeasible

The next step would be to chase down why specifically the input is infeasible, then see if that’s something that csgraph.min_weight_full_bipartite_matching can check for to raise an exception rather than hang.

1reaction

Code-Gratefullycommented, Nov 2, 2022

Sure, how about this plain code:

import numpy as np

a = np.array([[0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.001     , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        ],
        [0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.001     ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        ],
        [0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.001     , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        ],
        [0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.001     , 0.        , 0.        , 0.        ,
         0.        , 0.        ],
        [0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.001     , 0.        , 0.        ,
         0.        , 0.        ],
        [0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.001     , 0.        ,
         0.        , 0.        ],
        [0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.001     ,
         0.        , 0.        ],
        [0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.001     , 0.        ],
        [0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.001     ],
        [0.        , 0.11687445, 0.        , 0.        , 0.01319788,
         0.07509257, 0.        , 0.        , 0.        , 0.74228317,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        ],
        [0.        , 0.        , 0.        , 0.81087935, 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        ],
        [0.        , 0.        , 0.        , 0.        , 0.8408466 ,
         0.        , 0.        , 0.        , 0.        , 0.01194389,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        ],
        [0.        , 0.82994211, 0.        , 0.        , 0.        ,
         0.11468516, 0.        , 0.        , 0.        , 0.11173505,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        ],
        [0.18796507, 0.        , 0.04002318, 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.75883335, 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        ],
        [0.        , 0.        , 0.71545464, 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.02748488, 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        ],
        [0.78470564, 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.14829198, 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        ],
        [0.        , 0.10870609, 0.        , 0.        , 0.        ,
         0.8918677 , 0.        , 0.        , 0.        , 0.06306644,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        ],
        [0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.63844085, 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        ],
        [0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.7442354 , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        ],
        [0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.09850549, 0.        , 0.        ,
         0.18638258, 0.2769244 , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        ],
        [0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.73182464, 0.        , 0.        ,
         0.46443561, 0.38589284, 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        ],
        [0.29510278, 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.09666032, 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        , 0.        , 0.        , 0.        ,
         0.        , 0.        ]])

from scipy.sparse.csgraph import min_weight_full_bipartite_matching
from scipy.sparse.coo import coo_matrix
min_weight_full_bipartite_matching(coo_matrix(a))

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