Re: [eigen] Fast QR for 2x2, 3x3 |

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*To*: eigen@xxxxxxxxxxxxxxxxxxx*Subject*: Re: [eigen] Fast QR for 2x2, 3x3*From*: Andrea Arteaga <yo.eres@xxxxxxxxx>*Date*: Wed, 25 Feb 2009 11:30:42 +0100*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; bh=eRIqcpMQDRb3A8pLoW7r+uQdvghvG6EWwHiUd4Cp1DI=; b=ZZPX+YoQ0U8R9VeYO8ToaJs7DL12hHQWc20D362YpX2S5lJ5H4TN14lu2Ty3vr29JO OVbWm2hDsH8TcJx55eAzU5i9hgnKhANkbnLa3Ply9A8CM22eQ377PbKo6Ct+u2LfgIj9 JkLr71v95pGd/m7nMeah+ycKnKhvmQI6hNwGA=*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; b=oclQ8NG8pV5oxeaK8ObT9j5cEtgEY8OiUBZwaN7P92XxT78KPJlKyipSlySbn5R2AS jWuUrvKGqgac4gAJOZey3SqWZPyUWQINltBVekbcNyIj54CcahxSqU836gWyl+dAvNyn XPDcO0YneB8Sl7OJgvP6xolcLDJkTik366MhY=

2009/2/25 Gael Guennebaud <gael.guennebaud@xxxxxxxxx>

I don't think we want to provide multiple algorithms for the

same matrix sizes.

That were useful to provide a performance comparation between Givens and Gram-Schmidt in simply way, but for all other 'normal' jobs that is actually useless. In this case we can simply write specialized QR class, such as

template<typename _Scalar>

class QR<Matrix<_Scalar, 2, 2>;

I didn't completely understand what matrix m_qr and Vector m_hCoeffs are and how does QR compute the Q and the R from m_qr. But if m_qr is a matrix with Householder vectors, she's not compatible with a specialized QR for others algorithms, isn't it?

So if we want to specialize some QR class, we must to reimplement _compute(), matrixQ() and matrixR(). Perhaps for small matrices, it makes sense to compute and store directly Q and R at construction-time, with _compute(), without m_q and m_hCoeffs. Or, if we find some method to directly say at construction-time which matrices must be computed, we no longer need m_qr, like gael said.

Before code something, I want to actualy understand all aspects of this QR class.

Last note: don't forget the 2x3 and 3x2 matrices. QR is very useful for non-quadratic matrices.

I'll be offline until saturday.

Andrea

**Follow-Ups**:**Re: [eigen] Fast QR for 2x2, 3x3***From:*Gael Guennebaud

**References**:**[eigen] Fast QR for 2x2, 3x3***From:*Andrea Arteaga

**Re: [eigen] Fast QR for 2x2, 3x3***From:*Benoit Jacob

**Re: [eigen] Fast QR for 2x2, 3x3***From:*Andrea Arteaga

**Re: [eigen] Fast QR for 2x2, 3x3***From:*grey_earl

**Re: [eigen] Fast QR for 2x2, 3x3***From:*Andrea Arteaga

**Re: [eigen] Fast QR for 2x2, 3x3***From:*Gael Guennebaud

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