diagonal & permutation matrices

[David Bateman]

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.
> 
> 2. If D is a diagonal matrix, the even D(i,i) = x with scalar i will
> promote D to a full matrix. There does not seem to be an easy solution
> avoiding this. (Just like even emtpy assignment to a range promotes it
> to a matrix)
> 
> comments?
> 


Isn't this why Matlab added the 'vector' option to functions like QR? 
Then you replace the matrix multiplication with a matrix index 
operation. If you prefer to keep the matrix multiply syntax, then why 
not just make P a sparse matrix, whose matrix multiplication should be 
relatively fast.

D.


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David Bateman                                dbateman at dbateman.org
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