If 'eigen' is used instead of Wm3 to find principal axes of inertia,
eigenvalues must NOT be ordered (as Wm3 do).
So don't forgot to disable "ordering" in 'eigen' (if possible)
Le 8 févr. 2010 à 17:05, Anton Gladky a écrit :
> Thanks for comments.
> You are right, eigendecomposition in yade uses in:
> - Tetra.cpp { * The inertia tensor is in global coordinates; by
> eigendecomposition, we find principal axes}
> - Clump.cpp
>
> We have a next comment there:
> http://bazaar.launchpad.net/%7Eyade-dev/yade/trunk/annotate/head%3A/pkg/dem/DataClass/Clump.cpp#L240
>
> /*! @bug eigendecomposition might be wrong. see
> http://article.gmane.org/gmane.science.physics.yade.devel/99 for message. It
> is worked around below, however.
> */
> Vaclav, it seems, it is your comment.
>
> So, we just let it be?
> ______________________________
>
> Anton Gladkyy
>
>
> 2010/2/8 Vincent Richefeu <[email protected]>
> 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 <[email protected]>
>> 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 <[email protected]>
>>>
>>> > 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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