Re: A Simple Matrix Construction Question

[John W. Eaton]

On 23-Jan-2003, Carlo de Falco <address@hidden> wrote:

| 
| Giovedì, 23 Gen 2003, alle 20:34 Europe/Rome, David Pruitt ha scritto:
| 
| > This is known as "Tony's trick" from the Matlab support website.  My
| > question is: why does this work?
| >
| 
| M = Y(ones(5,1),:)
| 
| means:
| 
| M = [ Y(1,1:5)
|       Y(1,1:5)
|       Y(1,1:5)
|       Y(1,1:5)
|       Y(1,1:5)
| ];
| 
| in other words, replicate Y five times with first index always 1 and  
| second index spanning 1:5
| neat!

You might be surprised to find that the multiplication solution can be
faster than either this trick or kron, particularly if your copy of
Octave is linked with ATLAS.  The reason is that indexing is not all
that fast in Octave, and kron is not optimized in the same way that
the matrix multiply routine from the BLAS is.  For example, on my
system:

  octave:1> y = rand (1, 1000);
  octave:2> x = ones (1000, 1);
  octave:3> t = cputime (); y(x,:); cputime () - t
  ans = 0.11000
  octave:4> t = cputime (); kron (x, y); cputime () - t
  ans = 0.070000
  octave:5> t = cputime (); x*y; cputime () - t
  ans = 0.030000

jwe



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