> 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
