Question

I tried to solve this problem, but I could not implement.
Could you help me anything for this?

Problem

Mat1 | Mat2 | Mat3

 1 2 | 1 3  | 2 6

 1 3 | 2 6  | 2 5

 2 4 | 3 1  | 3 1

 3 1 | 3 5  | 5 2

 4 5 |

When there are 3 matrices(for example above), I want to get this result for the intersection rows in [column1 column2 matrixnumber] form.

The result for above example would be

1 3 1

1 3 2

2 6 2

2 6 3

3 1 1

3 1 2

3 1 3

It would be OK if the result is in the form [column1 column2 firstmatrix secondmatrix, ...]

1 3 1 2

2 6 2 3

3 1 1 2 3

For this problem, I want to use at most one for-loop.

Do you have any idea for this?

Answer 1

Here an alternative solution (which seems to run faster than Gunther’s) using MATLAB’s intersect:

Mat = {[1 2; 1 3; 2 4; 3 1; 4 5],
       [1 3; 2 6; 3 1; 3 5],
       [2 6; 2 5; 3 1; 5 2]};

result = zeros(sum(cellfun(@(x)size(x, 1), Mat)), 3); % # Preallocate memory
k = 1;
for cc = transpose(nchoosek(1:numel(Mat), 2))
    x = intersect(Mat{cc}, 'rows');                   % # Find intersection
    y = ones(size(x, 1), 2) * diag(cc);               % # Generate matrix indices
    result(k:k + numel(y) - 1, :) = [[x; x], y(:)];
    k = k + numel(y);
end

result(all(~result, 2), :) = [];                      % # Discard zero rows
result = unique(result, 'rows');                      % # Discard repeated rows

The matrix result should now contain the unique intersection rows and their corresponding matrix indices, just like you want:

result =   
     1     3     1
     1     3     2
     2     6     2
     2     6     3
     3     1     1
     3     1     2
     3     1     3