Re: [eigen] Optimization advice for a specific expression |

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*To*: eigen@xxxxxxxxxxxxxxxxxxx*Subject*: Re: [eigen] Optimization advice for a specific expression*From*: Christoph Hertzberg <chtz@xxxxxxxxxxxxxxxxxxxxxxxx>*Date*: Thu, 4 Feb 2016 17:46:24 +0100

On 2016-02-04 17:02, Alberto Luaces wrote:

Other than that: * What exactly do you mean by homogeneous?G = [ v3x3 | 0] [ 0ᵀ | 1] where "v3x3" is a 3x3 matrix, and "0" a vector of 3 zero-valued elements.Can you make any assumptions on the determinant of G? (Calculating the det didn't not seem to be the bottleneck, though)No, I cannot, but as you point, removing the determinant computation for testing purposes does not yield any improvement.

Given the above, you have: G.determinant() == v3x3.determinant(), which should be significantly faster than the full determinant. If v3x3 happens to be a rotation matrix, G.determinant()==1;

Does it have any special form (e.g. low rank, or Identity+lowRank)It is just symmetric: Eplus << 2 , 1 , 1 , 5, 1 , 2 , 1 , 5, 1 , 1 , 2 , 5, 5 , 5 , 5 , 20;

The upper left is Identity + [1,1,1]^T*[1,1,1]. I'll abbreviate V=v3x3.

[ V*V^T + w*w^T, 5*w ] [ 5*w^T , 20 ] Again, if V happens to be a rotation, then V*V^T=Identity

Cheers, Christoph -- Dipl. Inf., Dipl. Math. Christoph Hertzberg Universität Bremen FB 3 - Mathematik und Informatik AG Robotik Robert-Hooke-Straße 1 28359 Bremen, Germany Zentrale: +49 421 178 45-6611 Besuchsadresse der Nebengeschäftsstelle: Robert-Hooke-Straße 5 28359 Bremen, Germany Tel.: +49 421 178 45-4021 Empfang: +49 421 178 45-6600 Fax: +49 421 178 45-4150 E-Mail: chtz@xxxxxxxxxxxxxxxxxxxxxxxx Weitere Informationen: http://www.informatik.uni-bremen.de/robotik

**Follow-Ups**:**Re: [eigen] Optimization advice for a specific expression***From:*Alberto Luaces

**References**:**[eigen] Optimization advice for a specific expression***From:*Alberto Luaces

**Re: [eigen] Optimization advice for a specific expression***From:*Gael Guennebaud

**Re: [eigen] Optimization advice for a specific expression***From:*Alberto Luaces

**Re: [eigen] Optimization advice for a specific expression***From:*Christoph Hertzberg

**Re: [eigen] Optimization advice for a specific expression***From:*Alberto Luaces

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