On Mon, Nov 23, 2015 at 9:37 AM, Jonas Ballani <[email protected]>
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
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