MATLAB: Help to make a code faster/memory efficient

arrayfuncpuefficientfasterforgpuloopmemorypagefunsingle

Dear all, I am trying to improve the computation speed/memory usage of a code I've done for a electromagnetism problem. I have converted the arrays to single values which has helped a bit and also tried converting to gpuArrays but this seems slower. I've copied the most time consuming part of my code, other parts are coded similarly so any suggestion in this piece of code would be helpful. It seems the cross product calculation consumes a lot of time, I think maybe using something like pagefun, arrayfun? but I have no idea how to convert this to that. Any ideas would be deeply appreciated.
 magnetic=zeros(19128960,3,'single');
 for u = 1:2592 
    for n = 1:7380 
    q =1+(n-1)+(7380*(u-1));
    magne1=cross((PosS(n,:)-PosSeg1(u,:)),(ExtPosSeg1(u,:)-PosSeg1(u,:)));
    magnetic(q,1)=magne1(:,1);
    magnetic(q,2)=magne1(:,2);
    magnetic(q,3)=magne1(:,3);
    end
 end

Best Answer

Check this out:
 n1         = 7380 ;
 n2         = 2592 ;
 PosS       = rand( n1, 3 ) ;
 PosSeg1    = rand( n2, 3 ) ;
 ExtPosSeg1 = rand( n2, 3 ) ;
Loop-based:
 tic ;
 magnetic=zeros(n1*n2, 3,'single');
 for u = 1:n2 
    for n = 1:n1
        q =1+(n-1)+(n1*(u-1));
        magne1=cross((PosS(n,:)-PosSeg1(u,:)),(ExtPosSeg1(u,:)-PosSeg1(u,:)));
        magnetic(q,1)=magne1(:,1);
        magnetic(q,2)=magne1(:,2);
        magnetic(q,3)=magne1(:,3);
    end
 end
 toc
outputs
 Elapsed time is 86.585071 seconds.
and here is a vector version
 tic ; 
 magnetic_CW = reshape( permute( cross( ...
    bsxfun( @minus, permute( PosS, [3,2,1] ), PosSeg1 ), ...
    repmat( ExtPosSeg1 - PosSeg1, 1, 1, n1 )), [2,3,1] ), 3, [] ).' ;
 toc
outputs
 Elapsed time is 2.267693 seconds.
Both outputs are equal:
 isequal( magnetic, single( magnetic_CW ))
 ans =
  logical
   1
No need to convert to single, however, I did it for the comparison.
Cheers,
Cedric
NOTES
  1. It looks awfully complicated because I wanted to avoid creating intermediary variables, but what we do is just a cross product on two 3D arrays, one containing PosS-PosSeg1 for all columns of both (hence the call to BSXFUN), and the second being the corresponding 3D array of ExtPosSeg1-PosSeg1. All the rest is about permuting/reshaping/repeating so dimensions are appropriate.
  2. You may not need to work with 2D arrays actually, and you can probably eliminate the external RESHAPE and PERMUTE operations.
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