Bin interaction frequencies - matlab

Question

I have 10 bins, and each bin contains a specific number of observations, e.g.:
a = [0,0,1,0,0,2,0,0,0,2]
I'd like to subsequently tally how many times any given pair of (non-zero) bins co-occur - based on the number of observations.
Given the above example, bin#3 = 1, bin#6 = 2 and bin#10 = 2.
This means that bin 3 and 6 co-occurred once, bin 3 and 10 co-occurred once, and bin 6 and 10 co-occurred twice (the minimum value of the pair is taken).
My desired output is a full matrix, listing every possible bin combination (columns 1-2) and the tally of what was observed (column 3):
1 2 0
1 3 0
1 4 0
1 5 0
1 6 0
1 7 0
1 8 0
1 9 0
1 10 0
2 3 0
2 4 0
2 5 0
2 6 0
2 7 0
2 8 0
2 9 0
2 10 0
3 4 0
3 5 0
3 6 1
3 7 0
3 8 0
3 9 0
3 10 1
4 5 0
4 6 0
4 7 0
4 8 0
4 9 0
4 10 0
5 6 0
5 7 0
5 8 0
5 9 0
5 10 0
6 7 0
6 8 0
6 9 0
6 10 2
7 8 0
7 9 0
7 10 0
8 9 0
8 10 0
9 10 0
Is there a short and/or fast way of doing this?

Answer 1

You can get all combinations of the bin numbers in many ways. I'll use combvec for ease.
Then it's relatively simple to vectorise this using min...
a = [0,0,1,0,0,2,0,0,0,2];
n = 1:numel(a);
% Use unique and sort to get rid of duplicate pairs when order doesn't matter
M = unique( sort( combvec( n, n ).', 2 ), 'rows' );
% Get rid of rows where columns 1 and 2 are equal
M( M(:,1) == M(:,2), : ) = [];
% Get the overlap count for bins
M( :, 3 ) = min( a(M), [], 2 );

Answer 2

Try this.
bin_output = [....];
bin_matrix = [0,0,1,0,0,2,0,0,0,2];
bin_nonzero = find(bin_matrix);
for j = 1:length(bin_nonzero);
if isequal(j,length(bin_nonzero))
break;
end
for k = (j+1):(length(bin_nonzero))
for m = 1:length(bin_output)
if isequal(bin_output(m,1),j) && isequal(bin_output(m,2),k)
bin_output(m,3) = bin_output(m,3) + min([bin_matrix(1,bin_nonzero(1,j)),bin_matrix(1,bin_nonzero(1,k))]);
end
end
end
end