sudo apt-get install libboost-graph-dev libeigen3-dev

make example

Before: mat = 
0 3 2 0 3 1 1 0
3 2 3 3 0 4 1 4
3 2 1 2 4 3 3 3
0 4 0 0 1 3 1 1
3 0 4 0 1 0 2 3
1 4 4 3 1 3 3 2
0 2 1 4 2 0 1 0
4 2 3 4 4 1 3 0

w = 21

After: mat = 
3 3 2 0 3 1 1 8
3 3 3 3 0 4 1 4
3 2 1 2 4 3 3 3
4 4 0 0 1 9 2 1
3 1 7 0 5 0 2 3
1 4 4 3 1 3 3 2
0 2 1 9 3 0 6 0
4 2 3 4 4 1 3 0
Is it a doubly stochastic matrix 1

make demo

Generating random matches ...
        (0, 5) (1, 7) (2, 3) (3, 1) (4, 4) (5, 0) (6, 6) (7, 2) 
        (0, 0) (1, 7) (2, 3) (3, 2) (4, 5) (5, 6) (6, 4) (7, 1) 
        (0, 4) (1, 7) (2, 5) (3, 1) (4, 2) (5, 3) (6, 0) (7, 6) 
Done

Got 3 matchings:
        (0, 4) (1, 7) (2, 3) (3, 1) (4, 5) (5, 0) (6, 6) (7, 2) 
        (0, 5) (1, 7) (2, 3) (3, 2) (4, 4) (5, 6) (6, 0) (7, 1) 
        (0, 0) (1, 7) (2, 5) (3, 1) (4, 2) (5, 3) (6, 4) (7, 6)