what is the fastest way to search a huge matrix

I have 2 huge matrices, A and B, with the same size (9000 by 9000). I need to search two numbers x and y from A and B, respectively, and return the indices where x and y appears in A and B. I have 10,000+ pairs of x and y saved in a table of C, therefore need to do 10,000+ such searches.

I am currently using the following code, but it took me 4+ hours to finish the searching.

linearIdx=rowfun(@(x, y)find(A==x & B == y),C ) ;
[I,J]=ind2sub(size(A), linearIdx.Var1);

Is there faster way to do it? Maybe I should save A and B into hashtable? Thanks.

Answer 1

[Guillaume]

I'm assuming that the (x, y) pair is always present and only present once in (A, B). Otherwise the code you've posted would fail at the rowfun point.

The best way to find the locations of all the elements of an array within another array is to use ismember. In your case, the best thing to do would be to reshape A and B into columns, concatenate them into a 2 column array, and perform the search with ismember plus the 'rows' option:

[isrowfound, linearidx] = ismember(C, table(A(:), B(:)), 'rows'); 
%note: I wouldn't bother with tables and instead just have C as a matrix, in which case:
%[isrowfound, linearidx] = ismember(C, [A(:), B(:)], 'rows'); 
assert(all(isrowfound), 'Some rows in C were not present in (A, B)')
[I, J] = ind2sub(size(A), linearidx);

If a pair (x, y) is not found then the call to sub2ind will fail (due to linearidx containing 0).

If a pair (x, y) is found several time, you'll only get the location of the first one. Unlike your code, it won't cause an error.

[Li Xue]

Many thanks. The code is now only taking seconds to run! Thanks a lot! Yes, (x, y) pair is always present and only present once in (A, B). By the way, you had a typo in your code: sub2ind should be ind2sub.

[Guillaume]

Do'h. For some reason I always swap these two. I've corrected my original post.