speed up for loops

how can I speed up these for loops? it seems to run forever! shrtPth is an array which contains shortest path of two nodes. i.e. this code is a kind of Floyd algorithm for nodes with two indices, such as: E(:,ii,i) & E(:,jj,j).

for m=1:N
        for n=1:blk
            for i=1:N
                for ii=1:blk
                    for j=1:N
                        for jj=1:blk
                           shrtPth(i,ii,j,jj)=min(shrtPth(i,ii,j,jj),shrtPth(i,ii,m,n)+shrtPth(m,n,j,jj));
                        end
                    end
                end
            end
        end
end

thanks by advance...

Answer 1

[Matt J]

There doesn't seem to be a good reason to have two indices per node. You can equally well index them with one index and then you will have fewer for-loops, which should be faster.

However, before you reinvent the wheel, you should know that there are many shortest path routines on the File Exchange,

http://www.mathworks.com/matlabcentral/fileexchange/index?utf8=%25E2%259C%2593&term=shortest+path

[parmida nabi]

I want to make a geodesic distance. I'm working on a manifold learning algorithm for face recognition, but I don't know how to use 1 index instead of 4 !

[Matt J]

Using SUB2IND, you can convert multi-dimensional indices to one-dimensional linear indices.

[parmida nabi]

do you mean I should use: shrtPth([sub2ind(size(shrtPth),i,ii,j,jj)]) ? and now what about for loops? don't we need them any more?!

Answer 2

[Image Analyst]

Reverse the order of the indexes. You're doing it the exact opposite way you should be doing it. You're doing it the slowest way possible. MATLAB goes down the rows (left most index) before it does the others. Look, try this code:

n=300;
m = rand(n,n,n);
tic;
for i1 = 1 : n
  for i2 = 1 : n
    for i3 = 1 : n
      m(i1,i2,i3) = m(i1,i2,i3)+1;
    end
  end
end
toc;

tic;
for i3 = 1 : n
  for i2 = 1 : n
    for i1 = 1 : n
      m(i1,i2,i3) = m(i1,i2,i3)+1;
    end
  end
end
toc;

In the command window, notice almost a 4x speedup:

Elapsed time is 0.911281 seconds.
Elapsed time is 0.246471 seconds.

[parmida nabi]

your example is about for loops with same size, but mine have different sizes: N & blk. changing the order may be helpful, but not enough in my code. however, I have checked your example and now I know a key point, thanks...

[Image Analyst]

The sizes don't matter. I could have made different sizes and the results would be the same. It was faster to create the code with the same size so that's why I did it. I hope it didn't confuse you. If the total number of iterations on the inner most loop is not more than a million or so, then you might not notice any difference in time.