3D versus 2D Indexing and the Speed Thereof

[John W. Eaton]

On 20-Nov-2006, Luis Ortiz wrote:

| 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.

The two functions to start with are Array<T>::index2 and
Array<T>::indexN in the file liboctave/Array.h.  The 2-d function is
the original, from the olden times when Octave only had 2-d arrays.
The N-d version should be able to handle 2-d arrays too, but as you
noticed it is much slower so we kept the strictly 2-d version around.
It would be better to have just one function that handles all arrays,
but clearly I don't know how to make it as efficient as the
specialized 2-d case.

This reminds me that I have an idea about a new logo for Octave.  It
should be a dancing bear because the amazing thing about a dancing
bear is not how well it dances.  The amazing thing is that it dances
at all.

jwe