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- To: eigen@xxxxxxxxxxxxxxxxxxx
- Subject: Re: [eigen] Positive Definitenes?
- From: Benoit Jacob <jacob.benoit.1@xxxxxxxxx>
- Date: Tue, 2 Mar 2010 12:12:54 -0500
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Hi,
If you don't have big performance requirements, the safe way is
definitely to use the self-adjoint eigensolver to check the
eigenvalues (assuming that you already know that your matrix is
self-adjoint). If you already know that your matrix is positive
semidefinite and just want to check for invertibility, then of course
any rank-revealing decomposition will do (in the devel branch,
ColPivHouseholderQR is quite fast).
Then it might be possible to do something more efficient with LDLt but
i don't know how numerically stable that would be: this is not, in
principle, a rank-revealing decomposition, and while it allows to get
the determinant, the determinant is not always the right invertibility
check for all situations.
Benoit
2010/3/2 Gabriel <gabrielvc@xxxxxxxxx>:
> Hi list,
>
> I have not found a way to determine if a matrix is positive definite or not,
> in eigen. Is there a way? Which is it?
> Thanks, I am new to eigen,
>
> --
> ==============
> = Gabriel Villalobos,
> = Candidato a Doctor en Ciencias - Física, UN
> = M.Sc. Physics, Georgia Institute of Technology
> = Físico, Universidad Nacional de Colombia
> = Tel. Oficina. (571) 3165000 - 13031
> = gvillalobosc@xxxxxxxxxxxxxx
> = Enamoradamente Casado
> ===============
> = Acuerdos Toltecas:
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> = esfuerzo,
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> ==============
>
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>