program to create matrix obeying constraints

Question

reshdev 2014-9-20

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https://ww2.mathworks.cn/matlabcentral/answers/155516-program-to-create-matrix-obeying-constraints

评论： Matt J 2014-9-20

Hello all,

i have following code to create n*n matrix(say n=5 this time) which is following certain constraints.

 function selectingset
 % n = input ('Enter Num_Nodes  :');
 % inputData=input ('Enter inputdata  :');
n=5;
inputData=[5 1 2];
 for z = 1:n
    f   = inputData(1,1); % f= Demand
    S   = inputData(1,2); % S= Source node
    T   = inputData(1,3); % T= Termination node
 [idx,p] = sort(rand(n-1,f));
 M = accumarray([reshape(p+(p>=T),[],1),repmat([1:S-1,S+1:n]',f,1)],1,[n,n]);
 M(1:n+1:n^2) = 0;
 end
 disp(M);
end

So, my o/p from following code is---

   0     2     3     0
   0     0     0     0
   0     0     0     3
   4     1     0     0
   1     0     2     0

Note that as in given code

input S=1, so column 1 is zero and

As T=2, so row 2 is zero.

As f= 5, so sum of row S(i.e. S=1)=Sum of column T(i.e. T=2)= 5

and i am making diagonal elements zero.

all the remaining rows and columns, sum of row(i)=sum of column(i)

Now, How can i modify code such that row(1,3) will always come zero in output but output still follows previous mentioned constraints.

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Matt J 2014-9-20

Do all the matrix entries have to be integers?

reshdev 2014-9-20

Hello,

S will never be equal to T.

row(1,3) means third element in first row.

all the matrix elements should be integers between 0 to f.

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Answer 1

Matt J 2014-9-20

0
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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/155516-program-to-create-matrix-obeying-constraints#answer_152345

编辑：Matt J 2014-9-20

If you have the latext version of the Optimization Toolbox, you can use intlinprog to solve for the unknown elements of the matrix. You can choose any objective function that you want. See this recent thread for a very similar problem related to constraining rows and columns of matrices:

http://www.mathworks.com/matlabcentral/answers/154934-how-to-choose-one-value-for-each-row-and-column-in-a-matrix-so-that-the-sum-of-values-in-the-matrix

This assumes that you require the entries to be integer-valued and that a solution exists, see also My Comments. If they don't have to be integer-valued, you could just use linprog .