Re: [eigen] eigen3 SelfAdjointEigenSolver<Matrix3f> still "buggy" |

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*To*: eigen@xxxxxxxxxxxxxxxxxxx*Subject*: Re: [eigen] eigen3 SelfAdjointEigenSolver<Matrix3f> still "buggy"*From*: Radu Bogdan Rusu <rusu@xxxxxxxxxxxxxxxx>*Date*: Tue, 31 Aug 2010 09:17:20 -0700*Cc*: Gael Guennebaud <gael.guennebaud@xxxxxxxxx>*Organization*: Willow Garage

Gael,

[3double] 0.21281 seconds. 0.168841 -0.161623 -0.972302 0.451632 0.889498 -0.0694329 0.876083 -0.4274 0.223178 [3float] 0.123755 seconds. -0.168841 0.161623 0.972302 -0.451632 -0.889498 0.0694328 -0.876083 0.4274 -0.223178 For matrices:

I also had to apply the following patch to get rid of some compilation warnings about "n defined but not used": 1 --- Eigen/src/Eigenvalues/Tridiagonalization.h 2010-08-31 09:02:15.000000000 -0700 2 +++ Eigen/src/Eigenvalues/Tridiagonalization.h 2010-08-31 09:02:30.000000000 -0700 3 @@ -433,8 +433,8 @@ 4 void ei_tridiagonalization_inplace(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag, bool extractQ) 5 { 6 typedef typename MatrixType::Index Index; 7 - Index n = mat.rows(); 8 - ei_assert(mat.cols()==n && diag.size()==n && subdiag.size()==n-1); 9 + //Index n = mat.rows(); 10 + ei_assert(mat.cols()==mat.rows() && diag.size()==mat.rows() && subdiag.size()==mat.rows()-1); 11 ei_tridiagonalization_inplace_selector<MatrixType>::run(mat, diag, subdiag, extractQ); 12 } Thanks, Radu. On 08/31/2010 01:14 AM, Gael Guennebaud wrote:

Hi, I'm glad to see you already made the switch :) Regarding your issue, it has been fixed after beta1, but you can apply the following two changesets: a332a2b37265 1f979f8b9d99 or directly use the attached patch which simply contains these two changesets. I hope they apply well to beta1 (I did not check). If you want an even faster 3x3 eigen decomposition, you can have a look at the file bench/eig33.cpp (in the hg repo), which compares current Eigen's 3x3 eigensolver against a direct method solving the underlying degree 3 polynomial. To test it: g++ -I .. -O2 -lrt eig33.cpp -DNDEBUG&& ./a.out Here it is about 4 times faster though the speed of the default method is not constant since this is an iterative method. I'm still unsure about how to integrate it into Eigen because I don't want to make it the default. Indeed, it might suffers from some numerical issues if the matrix is not well conditioned. It also involves some trigonometric functions that is not very nice. So I guess we could add a template option to SelfAdjointEigenSolver or add a special class... well there are many possibilities! gael On Tue, Aug 31, 2010 at 5:10 AM, Radu Bogdan Rusu<rusu@xxxxxxxxxxxxxxxx> wrote:We've started adopting Eigen3 in ROS (http://www.ros.org/wiki/eigen3), and so far a thumbs up to the developers for doing a great job keeping most of the API intact! We documented some of the minor changes that we had to do to our code at the URL mentioned above, but all in all it was a walk in the park to switch one of our larger code libraries (PCL - http://www.ros.org/wiki/pcl) to Eigen3 today. One of the Eigen2 problems however still remains: the usage of SelfAdjointEigenSolver for Matrix3f matrices still gives a different ("incorrect") solution than for Matrix3d. This was already discussed on this mailing list, and the patch that we adopted in ROS for Eigen2 was: (http://bitbucket.org/eigen/eigen/issue/149/selfadjointeigensolver-matrix3f-vs) 1 --- Eigen/src/QR/Tridiagonalization.h 2010-07-22 14:45:32.000000000 -0700 2 +++ Eigen/src/QR/Tridiagonalization.h 2010-07-22 14:46:26.000000000 -0700 3 @@ -391,7 +391,7 @@ 4 { 5 diag[0] = ei_real(mat(0,0)); 6 RealScalar v1norm2 = ei_abs2(mat(0,2)); 7 - if (ei_isMuchSmallerThan(v1norm2, RealScalar(1))) 8 + if (v1norm2==RealScalar(0)) 9 { 10 diag[1] = ei_real(mat(1,1)); 11 diag[2] = ei_real(mat(2,2)); (https://code.ros.org/svn/ros-pkg/stacks/geometry/trunk/eigen/matrix.patch) This allowed us to perform the eigen decomposition and get the same values without much precision loss, while keeping everything else as floats. In Eigen3 however, the structure of QR changed dramatically, and the 3.0-beta1.tar.bz2 snapshot has not fixed this issue, meaning that: Eigen::SelfAdjointEigenSolver<Eigen::Matrix3d> ei_symm_d; and Eigen::SelfAdjointEigenSolver<Eigen::Matrix3f> ei_symm_f; would give different values on compute (matrix_{f,d}), where matrix_f = matrix_d (minus the type). Is there a patch that we can apply against Eigen3 beta1 that would solve this issue? Thank you in advance. PS. One of the reasons why we'd like to stick to SelfAdjointEigenSolver<Matrix3f> is the speed. We wrote a few tests in ROS (under http://www.ros.org/wiki/eigen_tests) for testing the performance of different eigenvector estimation methods in Eigen. Here are some results on an i7 laptop: [3double] 0.212725 seconds. [3float] 0.104199 seconds. [4double] 0.3162 seconds. [4float] 0.21743 seconds. [svd_3double] 0.451361 seconds. [svd_3float] 0.339349 seconds. [svd_4double] 0.534939 seconds. [svd_4float] 0.43122 seconds. where 3double = Matrix3d, 3float = Matrix3f, 4{double,float} = 4x4 matrix with added 0s for padding (we thought that keeping the matrix SSE aligned would result in some speedups, but it didn't), and svd_XX = Eigen::SVD<XX>. Overall, the good old Matrix3f seems to be the fastest. Cheers, Radu. -- | Radu Bogdan Rusu | http://rbrusu.com/

-- | Radu Bogdan Rusu | http://rbrusu.com/

**References**:**[eigen] eigen3 SelfAdjointEigenSolver<Matrix3f> still "buggy"***From:*Radu Bogdan Rusu

**Re: [eigen] eigen3 SelfAdjointEigenSolver<Matrix3f> still "buggy"***From:*Gael Guennebaud

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