create matrix of integers with specified sum in column and row

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Zaid Ali Basharat 2021-2-23

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编辑： Matt J 2021-2-24

I want to create a 4x4 matrix of integers such that:-

Say, M=[ A B C D ; E F G H ; I J K L ; M N O P ]

A+B+C+D>=value from user

A+B+C+D<=value from user

A+E+I+M>=value from user

A+E+I+M<=value from user

and likewise for all columns and rows.

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Rik 2021-2-23

What have you tried?

Also, don't forget that this might not be possible for some values provided by the user.

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Matt J 2021-2-23

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You can try to formulate it as an integer program.

M=optimvar('M',[4,4],'type','integer');
Constraints.columns=sum(M,1)<=colvalues;
Constraints.rows=sum(M,2)<=rowvalues;
prob=optimproblem('Objective', 0,'Constraints',Constraints );
sol=solve(prob)

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Matt J 2021-2-24

编辑：Matt J 2021-2-24

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Your example doesn't clarify what you see as wrong with the solution given by solve(). Are you saying you don't believe the input ranges were satisfied. That is fairly easy to test.

M=optimvar('M',[4,4]);
upper_colvalues=[12 12 12 12]*4;
lower_colvalues=[6 6 6 6];
upper_rowvalues=[40 40 40 40]';
lower_rowvalues=[20 20 20 20]';
Constraints.columnsUB= sum(M,1)<=upper_colvalues;
Constraints.columnsLB= sum(M,1)>=lower_colvalues;
Constraints.rowsUB = sum(M,2)<=upper_rowvalues;
Constraints.rowsLB = sum(M,2)>=lower_rowvalues;
prob=optimproblem('Objective', 0,'Constraints',Constraints );
sol=solve(prob); sol.M,
Solving problem using linprog.

Optimal solution found.
ans = 4×4
    20     0     0     0
     0     0     0    20
     0     0     0    20
     0     6     6     8

The bounds look well-satisfied to me:

column_check =[lower_colvalues;sum(sol.M,1); upper_colvalues],
column_check = 3×4
     6     6     6     6
    20     6     6    48
    48    48    48    48
row_check =[lower_rowvalues,sum(sol.M,2), upper_rowvalues].'
row_check = 3×4
    20    20    20    20
    20    20    20    20
    40    40    40    40