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

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*To*: eigen@xxxxxxxxxxxxxxxxxxx*Subject*: [eigen] request for help: 4x4 matrix inverse*From*: Benoît Jacob <jacob@xxxxxxxxxxxxxxx>*Date*: Mon, 14 Apr 2008 19:25:30 +0200

Hi List, I have started coding the LU module and committed already this: - optimized determinants for sizes <=4 (Thanks to Geoff for pointing me to the 30-mul technique for size 4). - general matrix inversion (good for sizes >= 5) - bruteforce matrix inversion using cofactors for sizes <=3 - unrolled version of the general method for size 4 Since the latter unrolled version is clumsy and is only used for size 4, since after all it seems that a bruteforce (cofactor) technique would be faster, and since size 4 is a common case that we want to optimize, I am asking: do you have good 4x4 matrix inversion code that you could contribute? Or can you point me to a good "algorithm" ? I put quotation marks because we know the algorithm is just brutefore, the question is how to implement it to minimize the number of ops and perhaps to take advantage of vectorization... Markos: if I remember correctly, you mentioned you had AltiVec code for that. When you mentioned it I was still hoping that the unrolled gaussian elimination would be good but now I realize that it's not, so I'm very much interested in your code if you want to contribute it :) Extra points if it also works with SSE. I am also -- and most importantly -- looking for an optimized non-vectorized path! As you'll see in src/LU/Inverse.h, we have a template parameter bool CheckExistence. If true, we must carefully check that the inverse exists. Ideally, your implementation would do that in an optimized way when CheckExistence==true, and we would not pay any cost when CheckExistence==false. The API is: Matrix4d m; m.inverse(); // CheckExistence==true m.quickInverse(); // CheckExistence==false Inverse<Matrix4d> inverse_of_m(m); // or, if you prefer, Inverse<Matrix4d> inverse_of_m = m.inverse(); if(inverse_of_m.exists()) { cout << inverse_of_m << endl; } Cheers, Benoit

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