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Message #03338
Re: EigenDecomposition wrapper problem
Ok, thanks all for comments and opinions!
______________________________
Anton Gladkyy
2010/2/9 Bruno Chareyre <bruno.chareyre@xxxxxxxxxxx>
> The ordering of values will be reflected in the rotation matrix, and the
> code always uses both simultaneously.
> So, it should not be a problem to get different ordering. It is just a
> matter of convention, with no effect on the result.
>
> Bruno
>
> Vincent Richefeu a écrit :
>
>> 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 <richefeu@xxxxxxxxxxxxxxx <mailto:
>>> 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
>>>> <mailto: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
>>>>> <mailto: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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>>>>
>>>>
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>>>
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>>
>> ------------------------------------------------------------------------
>>
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>
>
> --
> _______________
> Bruno Chareyre
> Associate Professor
> Grenoble INP
> Lab. 3SR
> BP 53 - 38041, Grenoble cedex 9 - France
> Tél : 33 4 56 52 86 21
> Fax : 33 4 76 82 70 43
> ________________
>
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