yade-dev team mailing list archive

[Vincent Richefeu <richefeu@xxxxxxxxxxxxxxx>]

if numerical recipes, numpy and eigen give the same result, we can have some confidence with this result.
It means that Wm3 result is "less good".
However, I don't know where eigen values and vectors are needed in yade (maybe for the computation of inertia?).

I don't know if my comments help (sorry), but all I can say is that eigenvalues from Wm3 seems correct but unordered, and eigenvectors seems not well converged (maybe it is not a problem)


Le 8 févr. 2010 à 16:21, Anton Gladky a écrit :

> Vincent, what do you think, if we use these "new values" it will not work?
> ______________________________
> 
> Anton Gladkyy
> 
> 
> 2010/2/8 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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