3D versus 2D Indexing and the Speed Thereof

[John W. Eaton]

On 20-Nov-2006, Luis Ortiz wrote:

| Folks:
| 
| One of my engineers reported an odd performance problem in Octave, 
| which I am afraid to tackle without a little bit of guidance.
| The first snippet of code he gave me to consider was:
|          x=zeros(100,50,100);
|          tic;
|          for i = 1:100
|              z = x(:,:,i);
|          end
|          toc
| 
| The second snippet of code he gave me to consider was:
|          x=zeros(5000,100);
|          tic;
|          for i = 1:100
|              z = x(:,i);
|          end
|          toc
| 
| Now the 2D form is about 22 times faster than the 3D form, even though
| the amount of data being slung about is the same.

BTW, on my system, I see the following results.  Not great, but not a
factor of 22 either.

  octave:4> for i = 1:3
  >   x = zeros (n, 50, 100);
  >   t = cputime ();
  >   for i = 1:100
  >     z = x(:,:,i);
  >   end
  >   t1 = cputime () - t;
  >   x = zeros (50*n, 100);
  >   t = cputime ();
  >   for i = 1:100
  >     z = x(:,i);
  >   end
  >   t2 = cputime () - t;
  >   fprintf ("%6d %f %f %f\n", n, t1, t2, t1/t2);
  >   n = n * 10;
  > end
      10 0.068005 0.012000 5.667083
     100 0.604037 0.100006 6.040008
    1000 5.996376 1.036065 5.787645

OTOH, if Octave's Array class knew how to do slices and if we
recognized these operations as slices, then the time should be
constant here, not proportional to the number of elements copied.

jwe