yade-dev team mailing list archive

[Anton Gladky <gladky.anton@xxxxxxxxx>]

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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