Sorry about that. I don't think that terminology is commonly used. This is what I mean. Let's say I solve the equations and compute the eigenvalues and eigenvectors for the given two matrices. I call these results "non-normalized". Then they can be normalized. Once they are normalized if I multiply them by any scalar they would become "un-normalized". They would still be eigenvectors but not necessarily the "non-normalized" ones. I think there is a specific algorithm that Matlab uses to solve them but I do not know what that algorithm is.
On Tue, Dec 20, 2011 at 11:01 PM, Olivier Delalleau <sh...@keba.be> wrote: > 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 > >
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