How make this code execute faster?

Hi, I'm just trying to figure out how to make this code faster:

    N = size(X);
    temp = 1:N;
    S1 = temp(~ismember(temp,S));%this runs slow
    M = X(S,S1); %this runs slos
    m = min(M);
    cost = sum(m);
    

X is a square matrix.

Given array of indexes S, I want to extract the submatrix M of S rows, and S1 columns, where S1 are the indexes which are not in S.

Hope I explained it well.

There is a way to achieve the same results faster ?

[madhan ravi]

What is size of X?

[Andrea Abbate]

X is a square matrix, NxN, it is variable. What does you mean with size? I don't know which exact size will it be

Answer 1

[Adam Danz]

Sidx = ismember(1:size(X,1),S); 
M = X(Sidx,~Sidx); 
cost = sum(min(M,[],1)); 

This versions is slightly faster. I ran your and my versions 100,000 times with X set as a 32x32 matrix and compared the median speeds. This version is 1.11 times faster (p<0.001, Wilcoxon Signed Rank test).

[Andrea Abbate]

Thank you for your answer!

I tried using your suggestion and I came up to this:

S1 = ~ismember(1:size(X,1),S); 
M = X(S,S1);
cost = sum(min(M,[],1)); 

Which seems to run even faster, but I'm not sure it is the same. The results seems to be good

[Adam Danz]

" but I'm not sure it is the same"

That's easy to check. Run both versions on the same inputs and compare the results. Spoiler alert: they are the same ;)

I ran you're new version vs my version 100,000 times and their difference in run time has a factor of 1.0 (meaning no difference).

Answer 2

[dpb]

Try

S1 = setdiff(1:N;S));

What is the precise definition of "runs slow(ly)"? In what context and how have you deduced/concluded this is so?

[Andrea Abbate]

I used the profiler and that is the part of code that runs slower than the others.

However, I tried setdiff before, but it runs slower