How do I find rows that match a list of vectors without using a loop?

Let's say I have a list of length 2 vectors that can occur, which I put in a matrix as rows:

possible = [1 2; 1 3; 1 4; 1 5;
            2 1; 2 3; 2 4; 2 5;
            3 1; 3 2; 3 4; 3 5;
            4 1; 4 2; 4 3; 4 5;
            5 1; 5 2; 5 3; 5 4];

and I have a set of observed vectors of length 2 that did occur:

observed = [1 3;
            1 5;
            4 2;
            4 3;
            3 2;
            4 2]; % ... and so on 

I need to go through the rows in the list of possible length 2 vectors, and get the index of where each row occurs in observed, like this:

for c = 1:size(possible, 1)
    [~, index{c}] = ismember(observed, possible(c,:),'rows');        
end

Whilst this approach does work, it proves to be very slow for my approach, as I have many observed matrices to run through, and many possible matrices to run through as well.

Is there a way of making this more efficient? Perhaps by using something other than a for loop?

Answer 1

[Matt J]

It would be advisable to obtain the indices as a logical matrix rather than as subscripts. This can be done looplessly with pdist2 as below.

observed = [1 3;
            1 5;
            4 2;
            4 3;
            3 2;
            4 2]; % ... and so on 

possible = [1 2; 1 3; 1 4; 1 5;
            2 1; 2 3; 2 4; 2 5;
            3 1; 3 2; 3 4; 3 5;
            4 1; 4 2; 4 3; 4 5;
            5 1; 5 2; 5 3; 5 4];

index=pdist2(observed,possible)==0

index = 6×20 logical array
   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
   0   0   0   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0
   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0
   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   0
   0   0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   0   0

[David Haydock]

Hi Matt,

Thanks very much for the response. I assume that the 1 at position [1,2] indicates that the second row of possible occurred at the first row of observed?

[Matt J]

Yes.

[David Haydock]

Thank you so much. I just implemented it into my code and I am not joking when I say it will have saved me a day of processing time. Thank you so much.