yade-dev team mailing list archive

[Vincent Richefeu <richefeu@xxxxxxxxxxxxxxx>]

Hi,

At first glance, it seems the eigenvalues (and thus the eigenvectors) are not ordered with Wm3.
The difference can also be due to the fact that the solution is not converged.

If needed, I can send a peace of code (based on "jacobi" in numerical recipes) for doing that task

VR 


Le 8 févr. 2010 à 13:46, Anton Gladky a écrit :

> Thanks, Vaclav!
> So, it seems Wm3 is broken for that function?
> 
> I have taken another matrix, which is positive definite:
> 1 7 3
> 6 2 4
> 2 5 3
> ========================
> Eigen gives:
> 
> Rot:
> -0.584754 -0.665682 -0.466054
> -0.617452 0.703421 -0.301128
> -0.526133 -0.266722 0.841805
> Diag:
> 11.0907 0 0
> 0 -5.19482 0
> 0 0 0.104141
> 
> ========================
> Numpy gives (see checkEigen.py):
> Rot:
> array([[-0.58475406, -0.66268234, -0.46225138],
>        [-0.61745205,  0.70025076, -0.29867115],
>        [-0.52613273, -0.26552022,  0.83493665]])
> Diag:
> array([ 11.09067395,  -5.1948153 ,   0.10414135])
> 
> So, it was similar to Eigen results.
> ========================
> But Wm3:
> Rot:
> 0.710682 0.404879 0.57533
> -0.699213 0.316215 0.641178
> 0.0776719 -0.857952 0.507825
> Diag:
> -5.55916 0 0
> 0 0.10998 0
> 0 0 11.4492
> ========================
> 
> Is it the Wm3 library problem?
> 
> ______________________________
> 
> Anton Gladkyy
> 
> 
> 2010/2/8 Václav Šmilauer <eudoxos@xxxxxxxx>
> 
> > I'm trying to create a wrapper for Eigen library. Almost all functions
> > are already done, but I have a problem with EigenDecomposition.
> > Unfortunately, I never used this functions and do not clearly
> > understand what it implements.
> >
> > Eigen library has an EigenSolver for those tasks
> > http://eigen.tuxfamily.org/dox/classEigen_1_1EigenSolver.html
> >
> > I tried to get all values from that solver and compare with results,
> > what Wm3 gives. It is completely different.
> 
> Using numpy to check:
> 
> >>> from numpy import array
> >>> fron numpy.linalg import eig
> >>> a=array([[-26.8141,20.0536,-37.6382],[-17.0536,-4.37217,13.4546],[39.0891,8.34892,-21.6416]])
> >>> eig(a)                                 ## http://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.eig.html
> 
> (array([-26.91393664+42.69101435j, -26.91393664-42.69101435j, 1.00000328 +0.j        ]),
>  array([[ 0.70584131+0.j       ,  0.70584131+0.j        ,  0.05979811+0.j        ],
>       [-0.03806586+0.30786093j, -0.03806586-0.30786093j,  0.89863520+0.j        ],
>       [-0.01840919-0.63657033j, -0.01840919+0.63657033j,  0.43460208+0.j        ]]))
> 
> You've picked matrix that has complex eigenvalues, that explains the
> difference; eigen handles it just fine ("(real,imag)" notation), wm3
> obviously doesn't. (the matrix should be positive definite for real
> eigenvalues, iirc).
> 
> Cheers, Vaclav
> 
> > Here is the source matrix:
> >
> > -26.8141 20.0536 -37.6382
> > -17.0536 -4.37217 13.4546
> > 39.0891 8.34892 -21.6416
> >
> >
> > =======================
> > wm3:
> >
> > tRot:
> > -0.698021 -0.0166317 -0.715884
> > 0.339616 -0.887829 -0.310515
> > -0.630419 -0.459872 0.625372
> >
> > tDiag:
> > -70.5641 0 0
> > 0 2.97262 0
> > 0 0 14.7635
> >
> > =======================
> > Eigen:
> > eigenvalues:
> > (-26.91,42.69)
> > (-26.91,-42.69)
> > (1,0)
> >
> > eigenvectors:
> > (-0.117,0.6961) (-0.117,-0.6961) (0.0598,0)
> > (-0.2973,-0.08855) (-0.2973,0.08855) (0.8986,0)
> > (0.6308,0.08732) (0.6308,-0.08732) (0.4346,0)
> >
> > pseudoEigenvalueMatrix:
> > -26.91 42.69 0
> > -42.69 -26.91 0
> > 0 0 1
> >
> > pseudoEigenvectors:
> > -0.1654 0.9844 0.0598
> > -0.4204 -0.1252 0.8986
> > 0.8921 0.1235 0.4346
> > =======================
> 
> 
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