Re: [eigen] [PATCH] Toeplitz matrix specialization

[Ricard Marxer Piñón <email@xxxxxxxxxxxxxxxx>]

Ok, that's cool.

Just for the record the next special matrix I was thinking of would be the Toeplitz symmetric.  This means that we only need storage for the first row (or first col) and that also allows more optimization on the Levinson-Durbin recursion for solving.

Finally another interesting special matrix is the Circulant, same as for the Toeplitz symmetric, but the first col is the reversed of the first row.

Here are the wikipedia references:
http://en.wikipedia.org/wiki/Toeplitz_matrix
http://en.wikipedia.org/wiki/Levinson_recursion
http://en.wikipedia.org/wiki/Circulant_matrix

I just post this in case it can be helpful for the rethinking process.

On Wed, Jan 28, 2009 at 9:00 PM, Benoit Jacob <jacob.benoit.1@xxxxxxxxx> wrote:

Hi,

Thanks for your patch.
We are in the process of rethinking completely how we deal with
special matrices.
The first kind of such matrices in Eigen was diagonal matrices.
Then, Mauro came by with a patch for tridiagonal matrices, showing
that we need to rethink that completely.
We're going to decide for a general approach to this subject very
soon, and then it'll be a perfect time to add Toeplitz matrices.
But it's very good that you sent this now as it gives us one more
example to keep in mind when deciding for an approach for special
matrices.

Cheers,
Benoit

2009/1/27 Ricard Marxer Piñón <email@xxxxxxxxxxxxxxxx>:

> Here is a first draft of a Toeplitz Matrix specialization.
> ( http://en.wikipedia.org/wiki/Toeplitz_matrix )
>
> A couple of things:
>   - I added a few methods to MatrixBase to easily construct Toeplitz
> matrices the same way as Diagonal matrices (asToeplitz(), isToeplitz())
>   - I added a flag ConstantDiagsBit (maybe it would be better to call it
> ToeplitzBit, I don't know)
>
> Let me know if I'm going on the right direction and what I did wrong.
>
> Toeplitz matrices allow for specialized solver Levinson-Durbin recursion
> which exploits its structure.
>
> --
> ricard
> http://www.ricardmarxer.com
> http://www.caligraft.com
>

-- 
ricard
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