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Function matchpairs does not work in MATLAB R2023a when I use a sparse cost matrix. Please help me out ASAP!

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You can run this simple code and see my problem. Am I doing something wrong?
% testing matchpairs ----------------------------------------------------------------
clear;clc
% --- using matrix in usual form (not sparse) --- WORKS
M = 99*ones(16,16);
M(1,1) = 2;
M(2,1) = 1;
M(1,2) = 1;
M(3,2) = 2;
M(2,3) = 2;
M(4,3) = 1;
M(6,3) = 4;
M(3,4) = 1;
M(4,4) = 2;
M(7,4) = 4;
M(6,5) = 2;
M(8,5) = 1;
M(3,6) = 4;
M(5,6) = 2;
M(7,6) = 1;
M(4,7) = 4;
M(6,7) = 1;
M(10,7) = 2;
M(5,8) = 1;
M(9,8) = 2;
M(8,9) = 2;
M(12,9) = 1;
M(7,10) = 2;
M(11,10) = 1;
M(13,10) = 4;
M(10,11) = 1;
M(12,11) = 2;
M(14,11) = 4;
M(9,12) = 1;
M(11,12) = 2;
M(10,13) = 4;
M(13,13) = 2;
M(14,13) = 1;
M(11,14) = 4;
M(13,14) = 1;
M(15,14) = 2;
M(14,15) = 2;
M(16,15) = 1;
M(15,16) = 1;
M(16,16) = 2;
[matchings, unassignedRows, unassignedCols] = matchpairs(M,12345)
matchings = 16x2
2 1 1 2 4 3 3 4 8 5 7 6 6 7 5 8 12 9 11 10
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
unassignedRows = 0x1 empty double column vector unassignedCols = 0x1 empty double column vector
OUTPUT IS CORRECT:
% --- using sparse matrix --- DOES NOT WORK
Ms = sparse(16,16);
Ms(1,1) = 2;
Ms(2,1) = 1;
Ms(1,2) = 1;
Ms(3,2) = 2;
Ms(2,3) = 2;
Ms(4,3) = 1;
Ms(6,3) = 4;
Ms(3,4) = 1;
Ms(4,4) = 2;
Ms(7,4) = 4;
Ms(6,5) = 2;
Ms(8,5) = 1;
Ms(3,6) = 4;
Ms(5,6) = 2;
Ms(7,6) = 1;
Ms(4,7) = 4;
Ms(6,7) = 1;
Ms(10,7) = 2;
Ms(5,8) = 1;
Ms(9,8) = 2;
Ms(8,9) = 2;
Ms(12,9) = 1;
Ms(7,10) = 2;
Ms(11,10) = 1;
Ms(13,10) = 4;
Ms(10,11) = 1;
Ms(12,11) = 2;
Ms(14,11) = 4;
Ms(9,12) = 1;
Ms(11,12) = 2;
Ms(10,13) = 4;
Ms(13,13) = 2;
Ms(14,13) = 1;
Ms(11,14) = 4;
Ms(13,14) = 1;
Ms(15,14) = 2;
Ms(14,15) = 2;
Ms(16,15) = 1;
Ms(15,16) = 1;
Ms(16,16) = 2;
[matchings, unassignedRows, unassignedCols] = matchpairs(Ms,-1)
matchings = 0x2 empty double matrix
unassignedRows = 16x1
1 2 3 4 5 6 7 8 9 10
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
unassignedCols = 16x1
1 2 3 4 5 6 7 8 9 10
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>

Accepted Answer

Bruno Luong
Bruno Luong on 9 Apr 2024
Edited: Bruno Luong on 9 Apr 2024
Your sparse matrix filled default cost wit 0 not 99. Then your expectation on that the result is identocal for different cost matrices (regardless data structure using) is simply plain wrong.
If you fill sparse or dense matrix with the same values it give identical outputs:
% testing matchpairs ----------------------------------------------------------------
clear;clc
% --- using matrix in usual form (not sparse) --- WORKS
M = 99*ones(16,16);
M(1,1) = 2;
M(2,1) = 1;
M(1,2) = 1;
M(3,2) = 2;
M(2,3) = 2;
M(4,3) = 1;
M(6,3) = 4;
M(3,4) = 1;
M(4,4) = 2;
M(7,4) = 4;
M(6,5) = 2;
M(8,5) = 1;
M(3,6) = 4;
M(5,6) = 2;
M(7,6) = 1;
M(4,7) = 4;
M(6,7) = 1;
M(10,7) = 2;
M(5,8) = 1;
M(9,8) = 2;
M(8,9) = 2;
M(12,9) = 1;
M(7,10) = 2;
M(11,10) = 1;
M(13,10) = 4;
M(10,11) = 1;
M(12,11) = 2;
M(14,11) = 4;
M(9,12) = 1;
M(11,12) = 2;
M(10,13) = 4;
M(13,13) = 2;
M(14,13) = 1;
M(11,14) = 4;
M(13,14) = 1;
M(15,14) = 2;
M(14,15) = 2;
M(16,15) = 1;
M(15,16) = 1;
M(16,16) = 2;
[matchings, unassignedRows, unassignedCols] = matchpairs(M,12345)
matchings = 16x2
2 1 1 2 4 3 3 4 8 5 7 6 6 7 5 8 12 9 11 10
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
unassignedRows = 0x1 empty double column vector unassignedCols = 0x1 empty double column vector
matchings
matchings = 16x2
2 1 1 2 4 3 3 4 8 5 7 6 6 7 5 8 12 9 11 10
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
Ms = sparse(M);
[matchings, unassignedRows, unassignedCols] = matchpairs(M,12345);
matchings
matchings = 16x2
2 1 1 2 4 3 3 4 8 5 7 6 6 7 5 8 12 9 11 10
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
Cross check, now both filled with 0s
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% --- using sparse matrix --- DOES NOT WORK
Ms = sparse(16,16);
Ms(1,1) = 2;
Ms(2,1) = 1;
Ms(1,2) = 1;
Ms(3,2) = 2;
Ms(2,3) = 2;
Ms(4,3) = 1;
Ms(6,3) = 4;
Ms(3,4) = 1;
Ms(4,4) = 2;
Ms(7,4) = 4;
Ms(6,5) = 2;
Ms(8,5) = 1;
Ms(3,6) = 4;
Ms(5,6) = 2;
Ms(7,6) = 1;
Ms(4,7) = 4;
Ms(6,7) = 1;
Ms(10,7) = 2;
Ms(5,8) = 1;
Ms(9,8) = 2;
Ms(8,9) = 2;
Ms(12,9) = 1;
Ms(7,10) = 2;
Ms(11,10) = 1;
Ms(13,10) = 4;
Ms(10,11) = 1;
Ms(12,11) = 2;
Ms(14,11) = 4;
Ms(9,12) = 1;
Ms(11,12) = 2;
Ms(10,13) = 4;
Ms(13,13) = 2;
Ms(14,13) = 1;
Ms(11,14) = 4;
Ms(13,14) = 1;
Ms(15,14) = 2;
Ms(14,15) = 2;
Ms(16,15) = 1;
Ms(15,16) = 1;
Ms(16,16) = 2;
[matchings, unassignedRows, unassignedCols] = matchpairs(Ms,-1);
matchings
matchings = 0x2 empty double matrix
Mf = full(Ms);
[matchings, unassignedRows, unassignedCols] = matchpairs(Mf,-1);
matchings
matchings = 0x2 empty double matrix
  2 Comments
Bruno Luong
Bruno Luong on 9 Apr 2024
One way to use sparse and keep filling 0 is to shift the value of the cost matrix
% testing matchpairs ----------------------------------------------------------------
Ms = sparse(16,16);
Ms(1,1) = 2;
Ms(2,1) = 1;
Ms(1,2) = 1;
Ms(3,2) = 2;
Ms(2,3) = 2;
Ms(4,3) = 1;
Ms(6,3) = 4;
Ms(3,4) = 1;
Ms(4,4) = 2;
Ms(7,4) = 4;
Ms(6,5) = 2;
Ms(8,5) = 1;
Ms(3,6) = 4;
Ms(5,6) = 2;
Ms(7,6) = 1;
Ms(4,7) = 4;
Ms(6,7) = 1;
Ms(10,7) = 2;
Ms(5,8) = 1;
Ms(9,8) = 2;
Ms(8,9) = 2;
Ms(12,9) = 1;
Ms(7,10) = 2;
Ms(11,10) = 1;
Ms(13,10) = 4;
Ms(10,11) = 1;
Ms(12,11) = 2;
Ms(14,11) = 4;
Ms(9,12) = 1;
Ms(11,12) = 2;
Ms(10,13) = 4;
Ms(13,13) = 2;
Ms(14,13) = 1;
Ms(11,14) = 4;
Ms(13,14) = 1;
Ms(15,14) = 2;
Ms(14,15) = 2;
Ms(16,15) = 1;
Ms(15,16) = 1;
Ms(16,16) = 2;
% Shift matrix
[I,J,K] = find(Ms);
fillvalue = 99;
Msshift = sparse(I,J,K-fillvalue,16,16);
[matchings, unassignedRows, unassignedCols] = matchpairs(Msshift,12345);
matchings
matchings = 16x2
2 1 1 2 4 3 3 4 8 5 7 6 6 7 5 8 12 9 11 10
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>

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