How to speed up calculation taking inputs from 2 separate and very large matrices (working code below)

Hi. The code below works. updated portion the REAL is 'a' is at 10600X5 and and 'b' at 60X5 and takes forever to run. How can I massively speed up the calculation?

 *updated*
 tic
 a = randi([0,100],10600,5)   % example only to run the code
 b = randi([0,20],60,5)
 new = zeros(size(a,1)*size(b,1),size(a,2));
 w = 0;
 for s= 1:size(a,1)
    for t= 1:size(b,1)
        new(w+t,:)= [(3*a(s,1)+b(t,1)), (5*a(s,2)+b(t,2)), (1*a(s,3)+b(t,3)),   (5*a(s,4)+b(t,4)) , (2*a(s,5)+b(t,5))];
    end
    w=w+size(b,1);
 end
 toc

[Jan]

The code does not run for the inputs with 5 columns, because the definition inside the loops have 4 elements only. So please post the real running code with some rand calls as input.

[klb]

Hi Jan. Updated code as you indicated and of course ran it- and it took just 2.005 seconds for the entire iteration(!!). In my 'real' code, which I cant share for privacy reason, it goes on forever. Matlab does not see any error, executes the code and runs forever. I Stopped the code after 40mins, and about 300,000 iterations had been competed but cant see why it was taking so long. And here the code is running lightning fast. But thank you! - simulating a large matrix totally helped get another view on the problem. Will look into my code and its formula.

[Jan]

@klb: Do I understand correctly: The posted code works with the needed speed, but some other code, which you do not show, is much slower? We cannot know the reason of this difference without seeing the other code. So all I can do is to suggest letting the profile find out, where the time is spent.

[per isakson]

"massively speed up" How much is that?

Answer 1

[per isakson]

Try

>> cssm()
Elapsed time is 0.073258 seconds.
Elapsed time is 0.073459 seconds.
Elapsed time is 0.042250 seconds.
Elapsed time is 0.019368 seconds.
ans =
  1×3 logical array
   1   1   1

where

function  cssm()

      a = randi([0,100],10800,5);   % example only to run the code
      b = randi([0,20],60,5);

      tic, new1 = cssm_1( a, b ); toc
      tic, new2 = cssm_2( a, b ); toc
      tic, new3 = cssm_3( a, b ); toc
      tic, new4 = cssm_4( a, b ); toc
      [ all(new1(:)==new2(:)), all(new1(:)==new3(:)), ll(new1(:)==new4(:)) ]
  end
  function    new = cssm_1( a, b )
      %%*updated*
      new = zeros(size(a,1)*size(b,1),size(a,2));
      w = 0;
      for s = 1:size(a,1)
          for t = 1:size(b,1)
              new(w+t,:)= [(3*a(s,1)+b(t,1))  ...
                          ,(5*a(s,2)+b(t,2))  ...
                          ,(1*a(s,3)+b(t,3))  ...
                          ,(5*a(s,4)+b(t,4))  ...
                          ,(2*a(s,5)+b(t,5))  ];
          end
          w=w+size(b,1);
      end
  end
  function    new = cssm_2( a, b )

      new = zeros(size(a,1)*size(b,1),size(a,2));
      w = 0;
      a = [3,5,1,5,2].*a;
      for s = 1:size(a,1)
          for t = 1:size(b,1)
              new(w+t,:)= [(a(s,1)+b(t,1))  ...
                          ,(a(s,2)+b(t,2))  ...
                          ,(a(s,3)+b(t,3))  ...
                          ,(a(s,4)+b(t,4))  ...
                          ,(a(s,5)+b(t,5))  ];
          end
          w=w+size(b,1);
      end
  end
  function    new = cssm_3( a, b )

      new = zeros(size(a,1)*size(b,1),size(a,2));
      w = 0;
      a = [3,5,1,5,2].*a;
      for s = 1:size(a,1)
          for t = 1:size(b,1)
              new(w+t,:)= a(s,:)+b(t,:);
          end
          w=w+size(b,1);
      end
  end
  function    new = cssm_4( a, b )

      new = zeros(size(a,1)*size(b,1),size(a,2));
      w = size(b,1);
      a = [3,5,1,5,2].*a;
      for s = 1:size(a,1)
          new( ( 1+(s-1)*w : s*w ), : ) = a(s,:)+b;
      end
  end

Caveat: I increased 10600 to 10800 to make it a multiple of 60.