Ok well I'm sorry, I have no idea what would be the difference between "non-normalized" and "un-normalized".
In PCA you may decide to scale your eigenvectors by the inverse of the square root of their corresponding eigenvalue so that your projected data has unit variance, but it doesn't seem to be what you're after. Can you point to a link that explains what are the "non-normalized eigenvectors" in your application? -=- Olivier 2011/12/20 Fahreddın Basegmez <mangab...@gmail.com> > I think I am interested in the non-normalized eigenvectors not the > un-normalized ones. Once the eig function computes the generalized > eigenvectors I would like to use them as they are. > I would think this would be a common request since the normal-mode > frequency response is used in many different fields like chemical and > biomolecular sciences as well as engineering and physics. Mathematically > there may be no difference between the normalized and non-normalized > eigenvectors but physically there is. In my case those values represent > deflections. Advantage of the normal-modes is you can apply damping in > each direction independent of each other. Amount of damping we apply may > be dependent on those deflections so I would need to use the non-normalized > results. > > > On Tue, Dec 20, 2011 at 10:15 PM, Olivier Delalleau <sh...@keba.be> wrote: > >> What I don't get is that "un-normalized" eigenvectors can be pretty much >> anything. If you care about the specific output of Matlab / Octave, it >> means you understand the particular "un-normalization" that these programs >> use. In that case you should be able to recover it from the normalized >> output from numpy. >> >> >> -=- Olivier >> >> 2011/12/20 Fahreddın Basegmez <mangab...@gmail.com> >> >>> I don't think I can do that. I can go to the normalized results but not >>> the other way. >>> >>> >>> On Tue, Dec 20, 2011 at 9:45 PM, Olivier Delalleau <sh...@keba.be>wrote: >>> >>>> Hmm, sorry, I don't see any obvious logic that would explain how Octave >>>> obtains this result, although of course there is probably some logic... >>>> >>>> Anyway, since you seem to know what you want, can't you obtain the same >>>> result by doing whatever un-normalizing operation you are after? >>>> >>>> >>>> -=- Olivier >>>> >>>> 2011/12/20 Fahreddın Basegmez <mangab...@gmail.com> >>>> >>>>> I should include the scipy response too I guess. >>>>> >>>>> >>>>> scipy.linalg.eig(STIFM, MASSM) >>>>> (array([ 3937.15984097+0.j, 3937.15984097+0.j, 3937.15984097+0.j, >>>>> 3923.07692308+0.j, 3923.07692308+0.j, 7846.15384615+0.j]), >>>>> array([[ 1., 0., 0., 0., 0., 0.], >>>>> [ 0., 1., 0., 0., 0., 0.], >>>>> [ 0., 0., 1., 0., 0., 0.], >>>>> [ 0., 0., 0., 1., 0., 0.], >>>>> [ 0., 0., 0., 0., 1., 0.], >>>>> [ 0., 0., 0., 0., 0., 1.]])) >>>>> >>>>> On Tue, Dec 20, 2011 at 9:14 PM, Fahreddın Basegmez < >>>>> mangab...@gmail.com> wrote: >>>>> >>>>>> If I can get the same response as Matlab I would be all set. >>>>>> >>>>>> >>>>>> Octave results >>>>>> >>>>>> >> STIFM >>>>>> STIFM = >>>>>> >>>>>> Diagonal Matrix >>>>>> >>>>>> 1020 0 0 0 0 0 >>>>>> 0 1020 0 0 0 0 >>>>>> 0 0 1020 0 0 0 >>>>>> 0 0 0 102000 0 0 >>>>>> 0 0 0 0 102000 0 >>>>>> 0 0 0 0 0 204000 >>>>>> >>>>>> >> MASSM >>>>>> MASSM = >>>>>> >>>>>> Diagonal Matrix >>>>>> >>>>>> 0.25907 0 0 0 0 0 >>>>>> 0 0.25907 0 0 0 0 >>>>>> 0 0 0.25907 0 0 0 >>>>>> 0 0 0 26.00000 0 0 >>>>>> 0 0 0 0 26.00000 0 >>>>>> 0 0 0 0 0 26.00000 >>>>>> >>>>>> >> [a, b] = eig(STIFM, MASSM) >>>>>> a = >>>>>> >>>>>> 0.00000 0.00000 0.00000 1.96468 0.00000 0.00000 >>>>>> 0.00000 0.00000 0.00000 0.00000 1.96468 0.00000 >>>>>> 0.00000 0.00000 1.96468 0.00000 0.00000 0.00000 >>>>>> 0.19612 0.00000 0.00000 0.00000 0.00000 0.00000 >>>>>> 0.00000 0.19612 0.00000 0.00000 0.00000 0.00000 >>>>>> 0.00000 0.00000 0.00000 0.00000 0.00000 0.19612 >>>>>> >>>>>> b = >>>>>> >>>>>> Diagonal Matrix >>>>>> >>>>>> 3923.1 0 0 0 0 0 >>>>>> 0 3923.1 0 0 0 0 >>>>>> 0 0 3937.2 0 0 0 >>>>>> 0 0 0 3937.2 0 0 >>>>>> 0 0 0 0 3937.2 0 >>>>>> 0 0 0 0 0 7846.2 >>>>>> >>>>>> >>>>>> Numpy Results >>>>>> >>>>>> >>> STIFM >>>>>> array([[ 1020., 0., 0., 0., 0., 0.], >>>>>> [ 0., 1020., 0., 0., 0., 0.], >>>>>> [ 0., 0., 1020., 0., 0., 0.], >>>>>> [ 0., 0., 0., 102000., 0., 0.], >>>>>> [ 0., 0., 0., 0., 102000., 0.], >>>>>> [ 0., 0., 0., 0., 0., 204000.]]) >>>>>> >>>>>> >>> MASSM >>>>>> >>>>>> array([[ 0.25907, 0. , 0. , 0. , 0. , 0. >>>>>> ], >>>>>> [ 0. , 0.25907, 0. , 0. , 0. , 0. >>>>>> ], >>>>>> [ 0. , 0. , 0.25907, 0. , 0. , 0. >>>>>> ], >>>>>> [ 0. , 0. , 0. , 26. , 0. , 0. >>>>>> ], >>>>>> [ 0. , 0. , 0. , 0. , 26. , 0. >>>>>> ], >>>>>> [ 0. , 0. , 0. , 0. , 0. , 26. >>>>>> ]]) >>>>>> >>>>>> >>> a, b = linalg.eig(dot( linalg.pinv(MASSM), STIFM)) >>>>>> >>>>>> >>> a >>>>>> >>>>>> array([ 3937.15984097, 3937.15984097, 3937.15984097, 3923.07692308, >>>>>> 3923.07692308, 7846.15384615]) >>>>>> >>>>>> >>> b >>>>>> >>>>>> array([[ 1., 0., 0., 0., 0., 0.], >>>>>> [ 0., 1., 0., 0., 0., 0.], >>>>>> [ 0., 0., 1., 0., 0., 0.], >>>>>> [ 0., 0., 0., 1., 0., 0.], >>>>>> [ 0., 0., 0., 0., 1., 0.], >>>>>> [ 0., 0., 0., 0., 0., 1.]]) >>>>>> >>>>>> On Tue, Dec 20, 2011 at 8:40 PM, Olivier Delalleau <sh...@keba.be>wrote: >>>>>> >>>>>>> Hmm... ok ;) (sorry, I can't follow you there) >>>>>>> >>>>>>> Anyway, what kind of non-normalization are you after? I looked at >>>>>>> the doc for Matlab and it just says eigenvectors are not normalized, >>>>>>> without additional details... so it looks like it could be anything. >>>>>>> >>>>>>> >>>>>>> -=- Olivier >>>>>>> >>>>>>> 2011/12/20 Fahreddın Basegmez <mangab...@gmail.com> >>>>>>> >>>>>>>> I am computing normal-mode frequency response of a mass-spring >>>>>>>> system. The algorithm I am using requires it. >>>>>>>> >>>>>>>> On Tue, Dec 20, 2011 at 8:10 PM, Olivier Delalleau >>>>>>>> <sh...@keba.be>wrote: >>>>>>>> >>>>>>>>> I'm probably missing something, but... Why would you want >>>>>>>>> non-normalized eigenvectors? >>>>>>>>> >>>>>>>>> -=- Olivier >>>>>>>>> >>>>>>>>> >>>>>>>>> 2011/12/20 Fahreddın Basegmez <mangab...@gmail.com> >>>>>>>>> >>>>>>>>>> Howdy, >>>>>>>>>> >>>>>>>>>> Is it possible to get non-normalized eigenvectors from >>>>>>>>>> scipy.linalg.eig(a, b)? Preferably just by using numpy. >>>>>>>>>> >>>>>>>>>> BTW, Matlab/Octave provides this with its eig(a, b) function but >>>>>>>>>> I would like to use numpy for obvious reasons. >>>>>>>>>> >>>>>>>>>> Regards, >>>>>>>>>> >>>>>>>>>> Fahri >>>>>>>>>> >>>>>>>>> >>>>>>> _______________________________________________ >>>>>>> NumPy-Discussion mailing list >>>>>>> NumPy-Discussion@scipy.org >>>>>>> http://mail.scipy.org/mailman/listinfo/numpy-discussion >>>>>>> >>>>>>> >>>>>> >>>>> >>>>> _______________________________________________ >>>>> NumPy-Discussion mailing list >>>>> NumPy-Discussion@scipy.org >>>>> http://mail.scipy.org/mailman/listinfo/numpy-discussion >>>>> >>>>> >>>> >>>> _______________________________________________ >>>> NumPy-Discussion mailing list >>>> NumPy-Discussion@scipy.org >>>> http://mail.scipy.org/mailman/listinfo/numpy-discussion >>>> >>>> >>> >>> _______________________________________________ >>> NumPy-Discussion mailing list >>> NumPy-Discussion@scipy.org >>> http://mail.scipy.org/mailman/listinfo/numpy-discussion >>> >>> >> >> _______________________________________________ >> NumPy-Discussion mailing list >> NumPy-Discussion@scipy.org >> http://mail.scipy.org/mailman/listinfo/numpy-discussion >> >> > > _______________________________________________ > NumPy-Discussion mailing list > NumPy-Discussion@scipy.org > http://mail.scipy.org/mailman/listinfo/numpy-discussion > >
_______________________________________________ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
