MATLAB: How to save output of a recursive function

recursionsave

Given a matrix A, I have to make all possible combinations of entries of A such that only one number is selected from each row. I have made the following recursive program which is running successfully. But I am not able to save the output vector X. So, for example in the following matrix A, there will be 27 such combinations, I want to save them in matrix of order 3×27.
A=[3 4 0;2 3 7;45 7 0]
n=1;
X=zeros(3,1);
comb(n, X, A); %function to calculate all combinations.
function X =comb(n,X, A)
if (n>3)
   X  
  return 
end
for i=1:3
    X(n)= A(n,i); 
    comb(n+1,X,A);
end
end

Best Answer

In the line comb(n+1,X,A); the function comb is called, but this does not change the value of X, because the output of this function is not assigned. Do you mean x = comb(n+1,X,A)?
A recursive function might not be the best choice. Either use a method from the FEX, e.g. FEX: Combinator or FEX: VChooseKRO.
Or create a loop:
A       = [3 4 0;2 3 7;45 7 0];
[nRow, nCol] = size(A);
nResult = nCol ^ nRow;
index   = ones(1, nRow);
Result  = zeros(nRow, nResult);
for k = 1:nResult
  Result(:, k) = A(sub2ind(size(A), 1:nRow, index));
    % Update the index vector:
    for k = nRow:-1:1
      index(k) = index(k) + 1;
      if index(k) <= nCol
        break;       % index(k) increased successfully, leave "for k" loop
      end
      index(k) = 1;  % index(k) reached the limit, reset it and iterate index(k-1)
    end
  end
This is equivalent to nRow nested for loops, which count from 1 to nCol and insert the corresponding element into the output. Hard coding this does not work, because the number of loops is flexible. There instead of a bunch of for loops, this has one loop and the list of for loop indices is store in the vector indices. Each index value is incremented and if it exceeds nCol, it is reset to 1 and the next index element is processed.
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