Hi John, Thanks for the bug fix. Just a small comment on the test program posted below: comparing the entries of U and V directly doesn't make much sense to me since the order of the singular vectors can differ for multiple singular values of the same size. Still, your test result from Eigen is weird.
Jonas On 11/30/2015 11:39 PM, John Peterson wrote: > > > On Mon, Nov 23, 2015 at 9:37 AM, Jonas Ballani <jonas.ball...@epfl.ch > <mailto:jonas.ball...@epfl.ch>> wrote: > > Dear all, > > I am relatively new to libmesh and would like to report a problem > using the SVD routine of the DenseMatrix class for rectangular > matrices. My example program looks as follows: > > > Hi Jonas, > > #734 fixes the bug and is almost ready to be merged, but I had just one > more comment on this issue. While testing, I noticed a difference in > the Eigen::JacobiSVD results compared to Lapack, even for what I assumed > was a trivial problem. This is probably because an iterative algorithm > is used by Eigen, compared to some direct method in Lapack, but there > does not seem to be a way to control the tolerance in Eigen... To test > this, I computed the SVD of the 3x2 matrix: > > A = > 1 2 > 3 4 > 5 6 > > then multiplied the factors together to get > > A_computed = U * S * V^T, > > and then computed ||A - A_computed||_{\infty}. The results were: > > Lapack: ||A - A_computed||=1.33226762955019e-15 > Eigen: ||A - A_computed||=0.700409889221191 > > Note that this was the case even though the entries of U, S, and V^T > didn't differ by much between Lapack and Eigen: > > Norm of difference in U entries: 1.09504813838868e-06 > Norm of difference in V^T entries: 1.82409692905949e-07 > Norm of difference in Sigma entries: 2.94426321312269e-06 > > > > This may be an expected result for JacobiSVD, and I don't know what it > implies about the accuracy of computing least-squares solutions with the > SVD decomposition (we don't yet have a method for that in libmesh) but I > thought I would mention it in any case... > > An expanded version of your test code is here if you are interested: > https://gist.github.com/jwpeterson/5872e267e6d5011f84d0 > > -- > John ------------------------------------------------------------------------------ Go from Idea to Many App Stores Faster with Intel(R) XDK Give your users amazing mobile app experiences with Intel(R) XDK. Use one codebase in this all-in-one HTML5 development environment. Design, debug & build mobile apps & 2D/3D high-impact games for multiple OSs. http://pubads.g.doubleclick.net/gampad/clk?id=254741911&iu=/4140 _______________________________________________ Libmesh-users mailing list Libmesh-users@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/libmesh-users
