diagonal & permutation matrices

[Ben Abbott]

On Nov 16, 2008, at 6:42 AM, Jaroslav Hajek wrote:

> hi all,
>
> I'm working on patches allowing special treatment of diagonal and
> permutation matrices in the Octave interpreter.
>
> The motivation is that the natural syntax using diagonal & permutation
> matrices, e.g.
> D = norm (A, 'cols');
> A /= D;
> [Q,R,P] = qr (A); X = P' * R \ (Q' * B);
> is currently formidable if performance is of any concern.
> Multiplication & division by a permutation or diagonal matrix
> is orders of magnitude slower that the "direct" counterpart
> (subscripting by the permutation vector or using dmult).
> And even though Matlab does the same, I think it's a bit shameful.
>
> So my aim is to supply five octave_base_value subclasses:
> octave_diag_matrix, octave_float_diag_matrix,
> octave_complex_diag_matrix, octave_float_complex_diag_matrix,
> octave_permutation_matrix
> (it seems that a single permutation matrix subclass will be enough,
> provided it will remember its numeric class)
> and implement the necessary operations. Diagonal matrix support is
> already present in liboctave, permutation matrix support needs to be
> implemented (but I think it's no big deal, really).
>
> I've run into two issues:
>
> 1. What to do when printing/saving? To honor Matlab compatibility, we
> should display & save them as full matrices. However, it is certainly
> much more informational to print them specially, and seems a little
> bit weird for Octave to cripple its own data when saving variables.

If saving the mat-files then they will need to be converted to full,  
but for octave's format(s) there is no need for compatibility. As this  
is quite obvious, perhaps I am missing some point?

Regarding displaying the matrices, there are already differences.

For example, from Matlab

 >> {'a','b','c',1,2,3}
ans =
     'a'    'b'    'c'    [1]    [2]    [3]

Now from Octave

octave:24> {'a','b','c',1,2,3}
ans =
{
   [1,1] = a
   [1,2] = b
   [1,3] = c
   [1,4] =  1
   [1,5] =  2
   [1,6] =  3
}

Notice the display doesn't even indicate whether 1,2,3 are numeric or  
character.

So, I wouldn't worry about how things are displayed ... but, as  
Thorsten has already asked, perhaps you can give us an example to  
demonstrate what would be expected?

Ben