Re: [eigen] SVD with singular matrices

[Benoit Jacob <jacob.benoit.1@xxxxxxxxx>]

Everybody--- how about letting SVD wrap around JacobiSVD for now
(possibly for 3.0) and make it faster in 3.1 (new SVD) ?

I think the current SVD is too high-maintenance.

Benoit

2010/9/29  <hamelin.philippe@xxxxxxx>:
> Thank you for the follow up. I will use JacobiSVD until then.
>
> -----Message d'origine-----
> De : Listengine [mailto:listengine@xxxxxxxxxxxxxxxxx] De la part de Benoit Jacob
> Envoyé : 29 septembre 2010 11:10
> À : eigen@xxxxxxxxxxxxxxxxxxx
> Objet : Re: [eigen] SVD with singular matrices
>
> Here's a diff for the SVD unit test, exposing the problem.
>
> The sorting of eigenvalues isn't the problem, the bidiagonalization is.
>
> The most productive thing I can say is: let's declare SVD not-for-exactly-singular-matrices for now, and ... yeah , yeah, make the new SVD happen :-P .. in the meanwhile you have JacobiSVD.
>
> Benoit
>
> 2010/9/29 Benoit Jacob <jacob.benoit.1@xxxxxxxxx>:
>> OK, i've attached a compilable variant that also prints the
>> reconstructed matrix.
>>
>> It turns out that the reconstructed matrix is
>>  1 0
>>  1 0
>>
>> I.e. we seem to have a problem with row/column permutations. Which
>> could be related to the sorting of singvals.
>>
>> I'm trying to understand why our unit test is not catching this. It's
>> true that we're not testing matrices with exactly 0 singvals.
>>
>> Benoit
>>
>> 2010/9/29  <hamelin.philippe@xxxxxxx>:
>>> This simple test fails:
>>>
>>> bool testSingularMatrixSVD()
>>> {
>>>    MatrixXd a(2,2), avalidation(2,2);
>>>    unsigned int rows = 2;
>>>    unsigned int cols = 2;
>>>
>>>    a <<    1,     1,
>>>            0,     0;
>>>
>>>    Eigen::SVD<MatrixXd> svd(a);
>>>    MatrixXd sigma = MatrixXd::Zero(rows,cols);
>>>    MatrixXd matU  = MatrixXd::Zero(rows,rows);
>>>    sigma.diagonal() = svd.singularValues();
>>>    matU = svd.matrixU();
>>>    avalidation = matU * sigma * svd.matrixV().transpose();
>>>
>>>    cout << "testSingularMatrixSVD() : ";
>>>    if((a).isApprox(avalidation, 1e-12))
>>>    {
>>>        cout << "Success." << endl;
>>>        return true;
>>>    }
>>>    else
>>>    {
>>>        cout << "Fail." << endl;
>>>        return false;
>>>    }
>>>
>>> }
>>>
>>>
>>> -----Message d'origine-----
>>> De : Listengine [mailto:listengine@xxxxxxxxxxxxxxxxx] De la part de
>>> Benoit Jacob Envoyé : 29 septembre 2010 10:32 À :
>>> eigen@xxxxxxxxxxxxxxxxxxx Objet : Re: [eigen] SVD with singular
>>> matrices
>>>
>>> 2010/9/29  <hamelin.philippe@xxxxxxx>:
>>>> Hello,
>>>>
>>>> when updating from eigen2 to eigen3, I found that my pseudo-inverse
>>>> was not working correctly for singular matrices. However, just
>>>> replacing SVD with JacobiSVD makes it work. Before looking further,
>>>> is there any limitation with SVD with singular matrices such as:
>>>>
>>>> [1 1;0 0]
>>>
>>> JacobiSVD always works, and is always precise. But it's slow for large matrices.
>>>
>>> SVD uses the Golub-Kahan bidiagonalization approach. So it's faster,
>>> but potentially inaccurate for certain singular matrices.
>>>
>>> I would be surprised though if the above 2x2 matrix was enough to
>>> expose problems in it. That would be a bug. Can you make a compilable
>>> test case?
>>>
>>> Thanks,
>>> Benoit
>>>
>>>>
>>>> Thank you,
>>>>
>>>> ------------------------------------
>>>> Philippe Hamelin, ing. jr, M. Ing
>>>> Chercheur / Researcher
>>>>
>>>> T: 450-652-8499 x2198
>>>> F: 450-652-1316
>>>>
>>>> Expertise robotique et civil
>>>> Institut de recherche d'Hydro-Québec (IREQ) 1740, boul.
>>>> Lionel-Boulet Varennes (QC) J3X 1S1, Canada
>>>>
>>>
>>>
>>>
>>>
>>>
>>
>
>
>