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 >> > ======================= >> >> >> _______________________________________________ >> Mailing list: https://launchpad.net/~yade-dev >> Post to : [email protected] >> Unsubscribe : https://launchpad.net/~yade-dev >> More help : https://help.launchpad.net/ListHelp >> >> _______________________________________________ >> Mailing list: https://launchpad.net/~yade-dev >> Post to : [email protected] >> Unsubscribe : https://launchpad.net/~yade-dev >> More help : https://help.launchpad.net/ListHelp > > > _______________________________________________ > Mailing list: https://launchpad.net/~yade-dev > Post to : [email protected] > Unsubscribe : https://launchpad.net/~yade-dev > More help : https://help.launchpad.net/ListHelp > > > _______________________________________________ > Mailing list: https://launchpad.net/~yade-dev > Post to : [email protected] > Unsubscribe : https://launchpad.net/~yade-dev > More help : https://help.launchpad.net/ListHelp
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