apply bsxfun or arrayfun to every row of a matrix

Question

There are two matrices, A and B with size m-by-4 and n-by-4 respectively. My question is how to apply a function f, which takes two 1x4 vectors as input, on every row of A and B. The result will be a matrix with size mxn. The element [i, j] in result is f(A(i, :), B(j, :)).

For example:

A = rand(3, 4);
B = rand(5, 4);
for i = 1 : 3
    for j = 1 : 5
        result(i, j) = rectint(A(i, :), B(j, :));
    end
end

Can I use bsxfun or arrayfun to do this job?

Answer 1

You can use arrayfun, if you first use meshgrid to generate all combinations of rows:

[ii jj] = meshgrid(1:size(A,1),1:size(B,1));
result = arrayfun(@(n) rectint( A(ii(n),:), B(jj(n),:) ), 1:numel(ii) );
result = reshape(result, size(B,1), size(A,1)).';

You could of course substitute rectint by any other function that accepts two vector inputs and returns a number.

Answer 2

This functionality is built into rectint. For the syntax rectint(A,B):

A and B can also be matrices, where each row is a position vector. AREA is then a matrix giving the intersection of all rectangles specified by A with all the rectangles specified by B. That is, if A is M-by-4 and B is N-by-4, then AREA is an M-by-N matrix...

So, you can just do result = rectint(A,B); to get the matrix you are after.