Re: [eigen] [PATCH] Toeplitz matrix specialization |

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*To*: eigen@xxxxxxxxxxxxxxxxxxx*Subject*: Re: [eigen] [PATCH] Toeplitz matrix specialization*From*: Ricard Marxer Piñón <email@xxxxxxxxxxxxxxxx>*Date*: Wed, 28 Jan 2009 21:20:01 +0100*Dkim-signature*: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:mime-version:sender:received:in-reply-to :references:date:x-google-sender-auth:message-id:subject:from:to :content-type; bh=68y8WvkI0NAhJpDVUFnq5yDwr0nK1JVpuuGyN5xYNj8=; b=MRXCYE/PsjgJ2zsPVSga1vSh3ioICtjpnV5G0kRUBcr02Axx7JA54hBCqNJaAuyDEf jjhFsQdMzT16QcJZTsdMfOW0FNuWwlNZ3ffT+sae2GJCQuF+8DocRs4t9lABzorOGhJS esiYc6EJR5/bM2vuv7D/dtn9IxPM0CvD3ntfc=*Domainkey-signature*: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=mime-version:sender:in-reply-to:references:date :x-google-sender-auth:message-id:subject:from:to:content-type; b=wQ53Qgi75a9vGgJ7QQeiuSsjr2zbHpQjZf3Of8W/oLT5HG4tkpdqwhXIJuhA+ewrmf v93beY/kD0umrQBEVKSnfirDze7uV12A+A8XGXepjQ3n4HNbmBk0tooMiOYwsjxPeZ4i SH4yiWy/f90r177+z+MzG+DjDdIBl1gcDm6M8=

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

http://www.ricardmarxer.com

http://www.caligraft.com

**References**:**[eigen] [PATCH] Toeplitz matrix specialization***From:*Ricard Marxer Piñón

**Re: [eigen] [PATCH] Toeplitz matrix specialization***From:*Benoit Jacob

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