Re: [eigen] Re: Eigenvalues and eigenvectors of 2x2 self-adjoint matrix

[Alexey Korepanov <khumarahn@xxxxxxxxx>]

I see. Looks like this is a new feature. It gives much better results 
for 2x2.

Thank you much!

On 06/30/2012 03:51 PM, Gael Guennebaud wrote:
> sorry, its coputeDirect():
> http://eigen.tuxfamily.org/dox/classEigen_1_1SelfAdjointEigenSolver.html#a85cda7e77edf4923f3fc0512c83f6323
>
> in short:
>
> SeflAdjointEigenSolver<Matrix2f> eig;
> eig.computeDirect(A);
>
> eig.eigenvalues();
> eig.eigenvectors();
>
> gael
>
> On Sat, Jun 30, 2012 at 10:41 PM, Alexey Korepanov <khumarahn@xxxxxxxxx> wrote:
> > I couldn't find a trace of directCompute() in documentation and source code.
> > How does it work?
> >
> >
> > On 06/30/2012 03:03 PM, Gael Guennebaud wrote:
> > > Hi,
> > >
> > > there is a directCompute() method that does perform the decomposition
> > > using closed form formulas for 2x2 and 3x3 real matrices.
> > >
> > > Maybe the 2x2 algorithm could be used by default if it appears to be
> > > 100% reliable, that is clearly not the case for the 3x3 case.
> > >
> > >
> > > gael
> > >
> > > On Sat, Jun 30, 2012 at 8:49 PM, Alexey Korepanov <khumarahn@xxxxxxxxx>
> > > wrote:
> > > > Hello.
> > > >
> > > > I am comparing precision of computation of eigenvectors and eigenvalues
> > > > of
> > > > eigen and matlab. I started with a simple 2x2 self-adjoint case, working
> > > > with long double datatype.  The best method seems to be.. "by hand":
> > > > solving
> > > > the quadratic equation for eigenvalues, and then computing eigenvectors.
> > > > Both matlab and eigen are slower and give less precise results. As a
> > > > measure
> > > > of precision I take Frobenius norm of AV-VD, where A is original matrix,
> > > > V
> > > > is matrix of eigenvectors, D is diagonal matrix of eigenvalues.
> > > >
> > > > Difference in precision is probably not a very big deal (like 4 last bits
> > > > in
> > > > long double), but it would be interesting to understand what eigen does
> > > > to
> > > > compute the decomposition for self-adjoint 2x2 matrix. It looks like
> > > > eigen
> > > > gives least precise results when discriminant of equation for eigenvalues
> > > > is
> > > > large. Can somebody comment on this?
> > > >
> > > > Best