Question

I am trying to optimize my code and am not sure how and if I would be able to vectorize this particular section??

for base_num = 1:base_length
    for sub_num = 1:base_length
    dist{base_num}(sub_num) = sqrt((x(base_num) - x(sub_num))^2 + (y(base_num) - y(sub_num))^2);
    end
end

Answer 1

The following example provides one method of vectorization:

%# Set example parameters
N = 10;
X = randn(N, 1);
Y = randn(N, 1);

%# Your loop based solution
Dist1 = cell(N, 1);    
for n = 1:N
    for m = 1:N
        Dist1{n}(m) = sqrt((X(n) - X(m))^2 + (Y(n) - Y(m))^2);
    end
end

%# My vectorized solution
Dist2 = sqrt(bsxfun(@minus, X, X').^2 + bsxfun(@minus, Y, Y').^2);
Dist2Cell = num2cell(Dist2, 2);

A quick speed test at N = 1000 has the vectorized solution running two orders of magnitude faster than the loop solution.

Note: I’ve used a second line in my vectorized solution to mimic your cell array output structure. Up to you whether you want to include it or two combine it into one line etc.

By the way, +1 for posting code in the question. However, two small suggestions for the future: 1) When posting to SO, use simple variable names – especially for loop subscripts – such as I have in my answer. 2) It is nice when we can copy and paste example code straight into a script and run it without having to do any changes or additions (again such as in my answer). This allows us to converge on a solution more rapidly.