How to save multiple output in recursive function - matlab

Question

Given a matrix A, I have to make all possible combinations of entries of A such that only one number is selected for each row. I have made a recursive program which is running successfully. But I am not able to save the output vector. So, for example in the following matrix A, there will be 27 such combinations, I want to save them in matrix of order 3x27.
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

Answer 1

Here's one of the possible approaches:
To make your variable visible in all contexts, you need to declare a global variable:
global OUT;
%rest of the code
Then, you just define OUT in you main file as empty variable:
OUT = [];
And in function script, you instruct to append X to OUT whenever the if-statement is satisfied:
if (n > 3)
OUT = [OUT,X];
return
end
The resulting code is as follows:
global OUT;
OUT = [];
A = [3 4 0; 2 3 7; 45 7 0];
n = 1;
X = zeros(3,1);
comb_SO(n, X, A);
OUT
function X = comb_SO(n, X, A)
global OUT;
if (n > 3)
OUT = [OUT,X];
return
end
for i = 1:3
X(n) = A(n, i);
comb_SO(n + 1, X, A);
end
end
The sought result is in OUT variable:
3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 0 0 0 0 0 0 0 0 0
2 2 2 3 3 3 7 7 7 2 2 2 3 3 3 7 7 7 2 2 2 3 3 3 7 7 7
45 7 0 45 7 0 45 7 0 45 7 0 45 7 0 45 7 0 45 7 0 45 7 0 45 7 0
But, MATLAB functionality allows your goal to be achieved without any recursion:
A = [3 4 0; 2 3 7; 45 7 0];
OUT = combvec(A(1,:),A(2,:),A(3,:))
Or, even without combvec, for arbitrary size of A:
A = reshape(1:20,4,5);
[n,m] = size(A);
Q = repmat({1:m},n,1);
B = cell(n,1);
[B{:}] = ndgrid(Q{:})
tmp = [];
OUT = [];
for k = 1:n
tmp = [tmp,B{k}(:)];
OUT = [OUT;A(k,tmp(:,k))];
end
Hope, that helps