|RE: [eigen] part<SelfAdjoint> in Eigen3|
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- To: <eigen@xxxxxxxxxxxxxxxxxxx>
- Subject: RE: [eigen] part<SelfAdjoint> in Eigen3
- From: "ESCANDE Adrien 222264" <adrien.escande@xxxxxx>
- Date: Thu, 29 Jul 2010 17:14:08 +0200
- Thread-index: AcsvHxib6WrRC3CxR72mbTSPawvw0AADTsDg
- Thread-topic: [eigen] part<SelfAdjoint> in Eigen3
The problem is that there doesn't seems to be an Eigen3 way to indicate that the result of an operation is a selfadjoint matrix and thus that the computation can be optimized (i.e. only about half of the coefficients need to be really evaluated).
n.selfadjointView<UpLo>() does not have an operator= (or so my compiler tells me when I try to write Eq (1)).
No way thus to optimize (1) or something like n = m.transpose()*weight.asDiagonal()*m, with weight a vector. (No direct way at least, I could explicitly compute a triangular part of n then copy it into the other).
Template parameter UpLo tells to consider only the coefficients in the upper/lower part of the matrix and deduce the other coefficients from them as can be seen in this example.
MatrixXd M = MatrixXd::Random(8,8);
std::cout << M << std::endl << std::endl;
//std::cout << M.selfadjointView<Upper>() << std::endl; //FAILS
//MatrixXd M2 = M.selfadjointView<Upper>(); //FAILS
MatrixXd M2 = M.selfadjointView<Lower>()*MatrixXd::Identity(8,8);
std::cout << M2 << std::endl << std::endl;
The example underlines two problems: you can print out a View (triangular or selfadjoint), and while you can assign a TriangularView to a Matrix, you can't assign a SelfAdjointView.
De : Listengine [mailto:listengine@xxxxxxxxxxxxxxxxx] De la part de Benoit Jacob
Envoyé : jeudi 29 juillet 2010 15:08
À : eigen@xxxxxxxxxxxxxxxxxxx
Objet : Re: [eigen] part<SelfAdjoint> in Eigen3
2010/7/29 ESCANDE Adrien 222264 <adrien.escande@xxxxxx>:
> Eigen2 documentation mentions the way to obtain an optimized computation for
> an expression evaluating to a selfadjoint matrix:
> n.part<SelfAdjoint>() = m+m.adjoint ; (1)
> n.part<SelfAdjoint>() = (m*m.adjoint()).lazy(); (2)
> I didn't find the way to have that in Eigen3 (MatrixBase>Derived>::part is
> still there but flagged as deprecated). The Porting from Eigen2 to Eigen3
> page does not mention this case (it gives only the translation for
> part<SelfAdjoint|Upper> and part<SelfAdjoint|Lower>). Is there a new direct
> way to perform such computations?
The new method is selfadjointView().
> And what would be the best way to write (2) when m itself is selfadjoint?
Gael would know better, but I think that your best bet is rankUpdate() here.
I can't see any way to do that using arithmetic operators, but that
seems OK as indeed the API for doing that should only take one operand
What I am a bit more puzzled about is that this API forces the user to
pass Upper... I need an explanation as to why this is useful ?
Maybe it would be useful to add a productByAdjoint(), perhaps
abbreviated as .xxt(), method in MatrixBase so the user could do:
n = m.productByAdjoint();