Creating two random matrices
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loukil sana
le 8 Nov 2016
Modifié(e) : James Tursa
le 8 Nov 2016
Hi. I have 2 matrices. M1(4,6) and M2(4,2). The generation of the two matrices is random. Attached you can find an explanation of the constraints. How can I formulate that with an ILP? Thanks
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/157805/image.png)
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James Tursa
le 8 Nov 2016
Modifié(e) : James Tursa
le 8 Nov 2016
E.g.,
% random matrix
M = rand(4,8);
% normalize per the 4-element sums
M(:,1:4) = bsxfun(@rdivide,M(:,1:4),sum(M(:,1:4),2));
M(:,5:8) = bsxfun(@rdivide,M(:,5:8),sum(M(:,5:8),2));
% scale per the desired sum
M(1:2,1:4) = M(1:2,1:4) * 0.50 * 2000;
M(1:2,5:8) = M(1:2,5:8) * 0.50 * 2000;
M(3:4,1:4) = M(3:4,1:4) * 0.70 * 2000;
M(3:4,5:8) = M(3:4,5:8) * 0.30 * 2000;
% divy up the results
M1 = M(:,[1:3 5:7]);
M2 = M(:,[4 8]);
EDIT: For required integer entries, you can use this ad-hoc modification (not quite exactly uniform since the fractional parts always go into M2, but maybe close enough for your purposes)
% random matrix
M = rand(4,8);
% normalize per the 4-element sums
M(:,1:4) = bsxfun(@rdivide,M(:,1:4),sum(M(:,1:4),2));
M(:,5:8) = bsxfun(@rdivide,M(:,5:8),sum(M(:,5:8),2));
% scale per the desired sum
M(1:2,1:4) = M(1:2,1:4) * 0.50 * 2000;
M(1:2,5:8) = M(1:2,5:8) * 0.50 * 2000;
M(3:4,1:4) = M(3:4,1:4) * 0.70 * 2000;
M(3:4,5:8) = M(3:4,5:8) * 0.30 * 2000;
% Adjust values to integers
F = floor(M);
D = M - F;
F(:,4) = F(:,4) + round(sum(D(:,1:4),2));
F(:,8) = F(:,8) + round(sum(D(:,5:8),2));
% divy up the results
M1 = F(:,[1:3 5:7]);
M2 = F(:,[4 8]);
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Image Analyst
le 8 Nov 2016
Try Roger Stafford's utility: http://www.mathworks.com/matlabcentral/fileexchange/9700-random-vectors-with-fixed-sum
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