Re: [eigen] request for help: 4x4 matrix inverse |

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*To*: eigen@xxxxxxxxxxxxxxxxxxx*Subject*: Re: [eigen] request for help: 4x4 matrix inverse*From*: Benoît Jacob <jacob@xxxxxxxxxxxxxxx>*Date*: Tue, 15 Apr 2008 15:28:16 +0200

> I don't do divs as well (reciprocal approximation and Newton-Raphson > instead, much faster than div), I confess I didn't know about these concepts! > no branching, but i haven't > benchmarked it yet. The nice thing about this method is that > calculating the determinant is more than half-way to getting the > inverse, as most quantities are already calculated. Indeed, it looks optimal for a determinant+inverse computation. Well, both are always closely related, but in your approach one gets both faster than with brute-force. We just need to figure out what to do when detP=0... I have a rough idea: since we may permute rows and cols, it is enough that there exist integers i,j,k,l between 0 and 3 such that the following 2x2 submatrix of M, ( M_{ik} M_{il} ) ( K_{jk} M_{jl} ) is invertible. Such i,j,k,l sure exist whenever M is invertible, so we just need to find them. Speed is not even important here since in 98% of cases we'll have detP!=0 anyway, so this doesn't impact the "mean complexity" very much. Cheers, Benoit

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**Re: [eigen] request for help: 4x4 matrix inverse***From:*Konstantinos Margaritis

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