CODEWITHSUNDEEP
matlabmatrixcombinations
Jack
Jack

Reputation: 209

Cycling Through Possible Matrixes MatLab

I'm trying to write a program to check the results of all possible combinations of 5 separate 5x5 matrices, where each element in all the matrices are booleans. However, my problem is I can't figure out a way to cause the matrices to check through every combination.

Illustrating what I would like to happen for a 2x2 matrix. I want my program to produce the matrix as follow: 

(1) [0 0;0 0] 
(2) [1 0;0 0] 
(3) [1 1;0 0]
(4) [1 1;1 0]
(5) [1 1;1 1]
(6) [1 0;0 1]
(7) [1 1;0 1]
…

and so on until every possible matrix has been done. How I may achieve this, so that I do some operation with every one of these matrix combinations?

(I realise this will probably take an impossibly long time to completely cycle through 5 5x5 matrices, however I also wish to do it for smaller matrices (3 3x3's) and I would also like to just leave it running as long as possible to check through as many possible 5 5x5's and seeing, out of the ones I've checked, which is the best result.)

Upvotes: 0

Views: 204

Answers (1)

Werner
Werner

Reputation: 2557

So, as you can see, you have several combinations of a zero matrix you want to add a one, right?

We could say that you have the following possible combinations you want to add a one. For the 2 dimensional case:

addOnes =

   Empty matrix: 1-by-0


onePossibleCombination =

     0     0
     0     0


addOnes =

     1


onePossibleCombination =

     1     0
     0     0


addOnes =

     2


onePossibleCombination =

     0     0
     1     0


addOnes =

     3


onePossibleCombination =

     0     1
     0     0


addOnes =

     4


onePossibleCombination =

     0     0
     0     1


addOnes =

     1     2


onePossibleCombination =

     1     0
     1     0


addOnes =

     1     3


onePossibleCombination =

     1     1
     0     0


addOnes =

     1     4


onePossibleCombination =

     1     0
     0     1


addOnes =

     2     3


onePossibleCombination =

     0     1
     1     0


addOnes =

     2     4


onePossibleCombination =

     0     0
     1     1


addOnes =

     3     4


onePossibleCombination =

     0     1
     0     1


addOnes =

     1     2     3


onePossibleCombination =

     1     1
     1     0


addOnes =

     1     2     4


onePossibleCombination =

     1     0
     1     1


addOnes =

     1     3     4


onePossibleCombination =

     1     1
     0     1


addOnes =

     2     3     4


onePossibleCombination =

     0     1
     1     1


addOnes =

     1     2     3     4


onePossibleCombination =

     1     1
     1     1

How can we achieve that? All we need is to take all combinations taken by 0, 1, 2, 3 and 4. For that we use the nchoosek method as follows:

matrixSize = 2;
for k=0:matrixSize^2
  combinations=nchoosek(1:matrixSize^2,k);
  for m = 1:size(combinations,1)
    addOnes = combinations(m,:);
    onePossibleCombination = zeros(matrixSize,matrixSize);
    onePossibleCombination(addOnes) = 1;
    % Do your operation here with the matrix onePossibleCombination
  end
end

Upvotes: 2

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