How to compare each element of two arrays fullfilling a set condition more efficiently / quickly?

I need to compare to each element of an array to each element within another array under the conidition that the elements are only allowed to differ within a specific tolerance range. Afterwards I want to extract the values from each array fullfilling the set condition. I have already figured it out for arrays with a small number of elements (see the code below). However, it appears to be way to slow for the comparison of large arrays, e.g. A and B being [>20000 x 1] since the iteration of the for loops explodes due to iteration count is equal to the array size to the power of two. Is there a more effiecent/ faster way to conduct the comparison and value extraction?

A = randi([0,5],10,1);
B = randi([0,5],10,1);

i=0;
err = 0.5; % error range for if statement
for k = 1:10 
    for m = 1:10
        i=i+1;
        if A(k)<(1+err)*B(m) && A(k)>(1-err)*B(m) % basically, B-value*0.5 < A < B-value*1.5
            row(i,1)= k; % noting the row of A which fullfills the if condition
            row(i,2)= m; % noting the row of B which fullfills the if condition
        end
    end
end
search_row = find(row(:,1)>1); % finding the non-zero rows
nnz_row = row(search_row,:); % extracting the non-zero rows
res(:,1) = A(nnz_row(:,1)); % extratcting the values from array A which fullfill the if condition
res(:,2) = B(nnz_row(:,2)); % extratcting the values from array B which fullfill the if condition

[KSSV]

You need to initialize the variable row inside the for loop for impoving speed.

row = zeros([],2) ; 

Include the above line before the for loop.

[Eugen]

Thanks for the hint! I did so and it works already faster. However, the code you posted below is faster by a lot so I guess I will the answer below! Thanks again!

Answer 1

[KSSV]

A = randi([0,5],10,1);
B = randi([0,5],10,1);

err = 0.5;

[a,b] = meshgrid(A,B) ; 
idx = a<(1+err)*b & a>(1-err)*b ;  
res =  [a(idx) b(idx)] ; 

[Eugen]

Works perfectly. The meshgrid is a real game changer. Thanks!