Re: ublas: hermitean matrices

From: walter_at_[hidden]
Date: 2001-11-29 16:48:32

--- In boost_at_y..., Peter Schmitteckert (boost) <boost_at_s...> wrote:
> Dear all,
> 
> I've started to take a closer look at the ublas library.
> First of all, I'm quite impressed by sources, which are
> very readable. 
 
Thanks.
 
> However, I'm currently only at the lowest
> level of understanding ublas.
> 
> I have the the following questions / comments concerning
> the hermitean matrices:
> 
> -> Is it correct, that the diagonal elements are of the
>   same type as the off-diagonal elements, or have I missed
>   missed something?

Yes, all elements are complex (if value_type is complex<> ;-).
 
>   I'd prefer the diagonal elements of a complex hermitean
>   matrix to be real. Or at least to have a function
>   returning the diagonal elements as real values.

How would you design the corresponding iterator interface using real 
diagonal elements? Shouldn't we better assert, that imag (m [i] [i]) 
== 0? I'll think about an special accessor for diagonal elements.
 
> -> In the same spirit one should not be allowed to
>   multiply a complex hermitean matrix with a non-real
>   scalar, or at least this shouldn't return a hermitean matrix.

The most critical part here is hermitean_matrix *= scalar. Again I'd 
prefer to assert that imag (scalar) == 0.
 
> -> Shouldn't hermitean matrices be square matrices ?

Yuk. I'll change that accordingly (for symmetric matrices likewise).
 
> -> Suppose I want to implement a banded hermitean matrix.
>    What do I need besides  corresponding functors ?

I think, you'll need to modify or extend the storage layout functors 
only, if you intend to support banded hermitean matrices with column 
and row major storage for example.
 
I imagine, that deriving banded_hermitean_matrix (or 
hermitean_banded_matrix :-) statically from matrix_expression should 
give you the neccessary ET support.
 
A hint: may be you better try to implement a somewhat simpler form 
like skew_hermitean_matrix ;-) first.
 
Thanks for your feedback. 
 
Regards
 
Joerg