slow access to consecutive matrix elements

[Francesco Potorti`]

This is a real life example that demonstrates how access to matrix
elements is not optimised for the case of complete ranges in the first
dimensions.  I am sending it here and not to the bug list because this
example may be useful to others, at least until this cases is optimised
in the sources.

# This is a big 5-dim matrix, about 100MB size
octave> kk=rand(156,222,1,44,8);

# I access a slice of it, which is sequential in memory
octave> t=cputime; for ii=1:44, for jj=1:8
  mm=kk(:,:,:,ii,jj); endfor, endfor, cputime-t
ans =  5.9124

# Using a linear index is much faster
octave> span=(1:156*222);
        t=cputime; for ii=1:44, for jj=1:8
  mm=kk(sub2ind(size(kk),1,1,1,ii,jj)+span-1); endfor, endfor, cputime-t
ans =  2.6642

# Removing the call to sub2ind reaches top speed
octave> cp=[1,cumprod(size(kk)(1:end-1))]; span=(1:156*222);
        t=cputime; for ii=1:44, for jj=1:8
  mm=kk(sum(([1,1,1,ii,jj]-1).*cp)+span); endfor, endfor, cputime-t
ans =  1.4001

Still, I wish access were faster yet.  Is there a reason why copying
consecutive memory is so slow?  I wish I could help with optimising
this, even if I am certainly not the most qualified person to do it.

-- 
Francesco Potortì (ricercatore)        Voice: +39 050 315 3058 (op.2111)
ISTI - Area della ricerca CNR          Fax:   +39 050 315 2040
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