|Re: [eigen] cache-friendly matrix inverse|
[ Thread Index |
| More lists.tuxfamily.org/eigen Archives
- To: eigen@xxxxxxxxxxxxxxxxxxx
- Subject: Re: [eigen] cache-friendly matrix inverse
- From: Benoit Jacob <jacob.benoit.1@xxxxxxxxx>
- Date: Wed, 13 May 2009 22:10:40 +0200
- Dkim-signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:mime-version:received:in-reply-to:references :date:message-id:subject:from:to:content-type :content-transfer-encoding; bh=qllIodeJGp5Z8EVJw3VNf0sydkjTmWyC0TGc0PyHA+U=; b=GcU9kEWpqPX09cj/6ToXFnrCodNxoCcdxeMO4obFHW/Y701SPbJOy3MffxR3iF6joU Xw3/bA3hC+wP+zUnSCb46dNmNkw3nKm9nZvXhLuZD10jGnk/y1gm5nzXZUkMguVROJyd P058YU5tItHQ6kDwpO9V9i6DWwf8v8XGDABwo=
- Domainkey-signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=mime-version:in-reply-to:references:date:message-id:subject:from:to :content-type:content-transfer-encoding; b=AFett4K0tDGIzXi1YIFNx/2rWASt3mmflGcq9ebSycJnn6gQw/qU6LBiSJeyE6f83O zPmcQ2bY01skT45vNCP2y/AVAeDaxZCtD1BKsCNG2DO5NAPL0yTd4O3+eCDK95uQxC7N 9N8W1aaV+E41xEMRyl7yMudQx4tdyn9fbd1tY=
It's actually something I never considered before: for me, as a
mathematician, matrix inversion is a basic operation that "of course"
i consider important, without even asking myself why; if you ask about
practical uses for it, well I'm pretty sure that there must be
situations where you want to solve Ax=b for a single given matrix A,
but for a lot of vectors b and you don't know in advance what these
vectors b will be, you just want to be able to solve very fast
whenever they show up; then the best thing you can do is to precompute
A^-1 so you only have a matrix-vector product to compute whenever a
"b" vector shows up.
2009/5/13, Christian Mayer <mail@xxxxxxxxxxxxxxxxx>:
> -----BEGIN PGP SIGNED MESSAGE-----
> Hash: SHA256
> Robert Lupton the Good schrieb:
>> I'm not sure that this is still on-topic, but if you have a model
>> [...] least-squares estimate [...]
>> So you really need to invert a matrix. You can invert it any
>> way you like (e.g. eigen-value decomposition; Gaussian elimination; ...)
>> but invert it you must.
> Well, I knew that you don't need to calculate an explicit inverse there
> (it would have surprised me that such a standard task would invalidate
> the no-inversion-in-numerics rule).
> You need a SVD in this case. Anyway, as soon as you've got a numerical
> task to solve, it's allways a good idea to have a look at the numerical
> recepies book, in this case Chapter 15.4:
> This leaves the question unanswered if these few posts are off-topic?
> I guess: no. It's just a discussion about a usecase of Eigen ;)
> -----BEGIN PGP SIGNATURE-----
> Version: GnuPG v1.4.9 (GNU/Linux)
> -----END PGP SIGNATURE-----