In the example you provided you aren't actually storing any of the indices. It is also important to consider that you will get results where more than one neighbour matches a square, or none match a square at all - you're going to need to store the indices in a cell array. To go through some different approaches, lets first generate some similar data:
neighbour = randi(1000,65000,2);
squares = randi(1000,35000,4);
B = cell(height(squares),1);
I've done three approaches to the problem the first one being based on the example you provided.
Approach 1 based on the example you provided:
tic
for i = 1:length(neighbour)
B{i} = find( ...
any(squares == (neighbour(i,1)),2) &...
any(squares == (neighbour(i,2)),2)...
);
end
toc
% Elapsed time is 33.780513 seconds. (Mathworks Server)
% Elapsed time is 21.165682 seconds. (My PC)
It's taking about 21 seconds on my computer, we can get some improvent with approach 2.
Approach 2 Instead of using &, it's faster to index into squares with the first logical expression. In this way, you're only scanning a portion of squares for neighbour(i,2) instead of the whole array, that is a significant improvement. In a sense, this is the vector equivalent of logical short-circuiting.
B = cell(height(squares),1);
tic
for i = 1:length(neighbour)
idx = find(any(squares == (neighbour(i,1)),2));
B{i} = idx(any(squares(idx,:) == (neighbour(i,2)),2));
end
toc
% Elapsed time is 21.825993 seconds. (Mathworks Server)
% Elapsed time is 12.312727 seconds. (My PC)
Approach 3 It turns out that any(someArray,1), is faster than any(someArray,2), which isn't surpising as MATLAB is column major-order. With some modification we can get another improvement.
B = cell(height(squares),1);
tic
squares = squares.';
for i = 1:length(neighbour)
idx = find(any(squares == neighbour(i,1),1));
B{i} = idx(any(squares(:, idx) == (neighbour(i,2)),1)).';
end
toc
%Elapsed time is 11.630071 seconds. (Mathworks Server)
%Elapsed time is 6.896441 seconds. (My PC)
So for me that was about a 3x improvement, and it does about a 3x improvement on MathWorks servers as well.
Edit: find needed to be used on the first logical expression in approaches 2 and 3.
