| Re: [eigen] Fast QR for 2x2, 3x3 |
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- To: eigen@xxxxxxxxxxxxxxxxxxx
- Subject: Re: [eigen] Fast QR for 2x2, 3x3
- From: Benoit Jacob <jacob.benoit.1@xxxxxxxxx>
- Date: Mon, 23 Feb 2009 00:08:01 +0100
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But indeed i was thinking (I could be wrong...) that for such small
sizes, nothing could beat just the plain direct Gram-Schmidt approach.
I'd be a little surprised if Givens rotations were faster.
Cheers,
Benoit
2009/2/23 Benoit Jacob <jacob.benoit.1@xxxxxxxxx>:
> Hi,
>
> It would be very useful to have fixed-size specializations of QR for
> 2x2 and 3x3. You're very welcome to help us with that, and for that
> matter you can submit us the code in any format, it'll be easy to
> integrate in Eigen.
>
> I can't tell what's going to be faster, Givens or Householder or
> something else. All I can say for sure is that Givens rotations don't
> require computing cosines and sines!
>
> Here you can find a copy of Golub & van Loan: download.tuxfamily.org/eigen
>
> Cheers,
> Benoit
>
>
> 2009/2/22 Andrea Arteaga <yo.eres@xxxxxxxxx>:
>> Hi.
>> I'm Andrea Arteaga and I'm student of Computing Science and Engeneering at
>> ETH
>> Zurich.
>> I read this in the todo-page
>> (http://eigen.tuxfamily.org/index.php?title=Todo#QR_module):
>>
>> implement efficient QR decomposition for 2x2 and 3x3 matrix with optional
>> computation of R (maybe using Gram-Schmitd instead of Householder
>> transformations ?)
>>
>> I thought that Givens Rotations
>> (http://en.wikipedia.org/wiki/Givens_rotation) are perfect for that: the
>> computation of a givens-matrix requires only (execution of sin()) +
>> (execution of cos()) operations; the product between two 2x2 matrices
>> requires only 8 operations and maybe less than that.
>> If you need it, I can help a little bit, QR is one of my preferred topics!
>>
>> [I'm sorry for my bad english, I live in Switzerland and I never studied
>> well english...]
>>
>>
>