How to effectively run loops and save time in computation? I have a matrix of size 'm' and run five loops from 1 to m.. How to optimize the code and save time of calculation for the code below

Can you help in optimizing the code below so that the execution time can be reduced? For a very large matrix of size 500x500, the computation time is huge. How to reduce it?

Since floor function is used here, is there any way to effectively compute the below code with both Time and Space efficiency..

function [PS] = PS_sparse(H)
[m,n]=size(H);
Ohmega=H*H';
for k=1:m
  for i=1:m
    for j=1:m
      if j~=i
        x(j)=abs(Ohmega(i,k)+Ohmega(j,k));
      end
    end
    mask=x~=0; % mark the non-zero elements
    x=x(mask); % keep the non-zero elements
    x0=sort(x,'ascend');  % order the x so that lomed can be calculated
    y(i)=x0(floor((length(x0)+1)/2)); % calculate the low median 
  end
  y0=sort(y,'ascend'); % order the x so that lomed can be calculated
  sm(k)=1.1926*y0(floor((length(y0)+1)/2));% calculate the low median
end
for k=1:m
  for i=1:m
    aux(i)=abs(Ohmega(k,i))/sm(i);
  end
  PS(k,1)=max(aux);
end

The above code was taken from https://in.mathworks.com/matlabcentral/fileexchange/60838-matlab-code-of-robust-gm-estimator-for-power-system-state-estimation-using-projection-statistics?focused=7509217&tab=function

[Stephen23]

"Can you help in optimizing the code below so that the execution time can be reduced? ... How to reduce it?"

Follow the guidelines in the MATLAB documentation:

https://www.mathworks.com/help/matlab/matlab_prog/techniques-for-improving-performance.html

Answer 1

[dpb]

Innermost loop

    for j=1:m
      if j~=i
        x(j)=abs(Ohmega(i,k)+Ohmega(j,k));
      end

has "issues" -- first off, x isn't preallocated nor reinitialized so after the first loop there will be remnants of the previous left over.

In the loop on j, i, k are invariant so there's really no need for the loop at all...it can be replaced with

x=abs(Ohmega(i,k)+Ohmega(:,k));  % build the vector
x(i)=0;                          % fixup the diagonal location

There's superfluous code following...

 ...
  mask=x~=0; % mark the non-zero elements
  x=x(mask); % keep the non-zero elements
  ...

can be just

x=x(~=0);     % don't need the temporary mask array for anything

Then

...
x0=sort(x,'ascend');  % order the x so that lomed can be calculated
y(i)=x0(floor((length(x0)+1)/2)); % calculate the low median 
...

can use builtin median that should be faster. It returns MEAN(two center elements) if m is even; if algorithm must use the actual data point within the vector then augment the x vector with an artificial zero; possibly just eliminating the previous step would suffice in that case.

y(i)=median(x);

Similarly for y0 on the way to sm

None of the LHS variables are preallocated; similar logic can also be applied to the last loop as well.

That's a fast-brush look-see...