RE: [eigen] SVD with singular matrices
• To: <eigen@xxxxxxxxxxxxxxxxxxx>
• Subject: RE: [eigen] SVD with singular matrices
• From: <hamelin.philippe@xxxxxxx>
• Date: Wed, 29 Sep 2010 11:14:06 -0400
• Thread-topic: [eigen] SVD with singular matrices

```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
>>>
>>
>>
>>
>>
>>
>

```

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