Re: [Numpy-discussion] Getting non-normalized eigenvectors from generalized eigenvalue solution?
Dear Fahreddın, I think, the norm of the eigenvectors corresponds to some generic amplitude. But that is something you cannot extract from the solution of the eigenvalue problem but it depends on the initial deflection or velocities. So I think you should be able to use the normalized values just as well as the non-, un- or not normalized ones. Octave seems to normalize that way that, transpose(Z).B.Z=I, where Z is the matrix of eigenvectors, B is matrix B of the generalized eigenvalue problem and I is the identity. It uses lapack functions. But that's only true if A,B are symmetric. If not it normalizes the magnitude of largest element of each eigenvector to 1. I believe you can get it like that. If U is a Matrix with normalization factors it is diagonal and Z.A contains the normalized column vectors. then it is: transpose(Z.A).B.Z.A =transpose(A).transpose(Z).B.Z.A =A.transpose(Z).B.Z.A=I and thus invert(A).invert(A)=transpose(Z).B.Z As A is diagonal invert(A) has the reciprocal elements on the diagonal. So you can easily extract them A=diag(1/sqrt(diag(transpose(Z).B.Z))) I hope that's correct. Best Regards Lennart ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Getting non-normalized eigenvectors from generalized eigenvalue solution?
Aaah, thanks a lot Lennart, I knew there had to be some logic to Octave's output, but I couldn't see it... -=- Olivier 2011/12/21 Lennart Fricke pge08...@studserv.uni-leipzig.de Dear Fahreddın, I think, the norm of the eigenvectors corresponds to some generic amplitude. But that is something you cannot extract from the solution of the eigenvalue problem but it depends on the initial deflection or velocities. So I think you should be able to use the normalized values just as well as the non-, un- or not normalized ones. Octave seems to normalize that way that, transpose(Z).B.Z=I, where Z is the matrix of eigenvectors, B is matrix B of the generalized eigenvalue problem and I is the identity. It uses lapack functions. But that's only true if A,B are symmetric. If not it normalizes the magnitude of largest element of each eigenvector to 1. I believe you can get it like that. If U is a Matrix with normalization factors it is diagonal and Z.A contains the normalized column vectors. then it is: transpose(Z.A).B.Z.A =transpose(A).transpose(Z).B.Z.A =A.transpose(Z).B.Z.A=I and thus invert(A).invert(A)=transpose(Z).B.Z As A is diagonal invert(A) has the reciprocal elements on the diagonal. So you can easily extract them A=diag(1/sqrt(diag(transpose(Z).B.Z))) I hope that's correct. Best Regards Lennart ___ 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
Re: [Numpy-discussion] Getting non-normalized eigenvectors from generalized eigenvalue solution?
Just to be completely clear, there is no such thing as a non-normalized eigenvector. An eigenvector is only determined *up to a scalar normalization*, which is obvious from the eigenvalue equation: A v = l v where A is the matrix, l is the eigenvalue, and v is the eigenvector. Obviously v is only determined up to a constant factor. A given eigen routine can return anything at all, but there is no native non-normalized version. Traditionally, you can decide to return normalized eigenvectors with the scalar factor determined by norm(v)=1 for some suitable norm. (I could imagine that an algorithm could depend on that.) Andrew On 21/12/2011 07:01, Olivier Delalleau wrote: Aaah, thanks a lot Lennart, I knew there had to be some logic to Octave's output, but I couldn't see it... -=- Olivier 2011/12/21 Lennart Fricke pge08...@studserv.uni-leipzig.de mailto:pge08...@studserv.uni-leipzig.de Dear Fahreddın, I think, the norm of the eigenvectors corresponds to some generic amplitude. But that is something you cannot extract from the solution of the eigenvalue problem but it depends on the initial deflection or velocities. So I think you should be able to use the normalized values just as well as the non-, un- or not normalized ones. Octave seems to normalize that way that, transpose(Z).B.Z=I, where Z is the matrix of eigenvectors, B is matrix B of the generalized eigenvalue problem and I is the identity. It uses lapack functions. But that's only true if A,B are symmetric. If not it normalizes the magnitude of largest element of each eigenvector to 1. I believe you can get it like that. If U is a Matrix with normalization factors it is diagonal and Z.A contains the normalized column vectors. then it is: transpose(Z.A).B.Z.A =transpose(A).transpose(Z).B.Z.A =A.transpose(Z).B.Z.A=I and thus invert(A).invert(A)=transpose(Z).B.Z As A is diagonal invert(A) has the reciprocal elements on the diagonal. So you can easily extract them A=diag(1/sqrt(diag(transpose(Z).B.Z))) I hope that's correct. Best Regards Lennart ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org mailto: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
Re: [Numpy-discussion] Getting non-normalized eigenvectors from generalized eigenvalue solution?
According to this page eigenvectors are normalized with respect to the second matrix. Do you guys have any idea how that's done? http://www.kxcad.net/Altair/HyperWorks/oshelp/frequency_response_analysis.htm If the eigenvectors are normalized with respect to the mass matrix, the modal mass matrix is the unity matrix and the modal stiffness matrix is a diagonal matrix holding the eigenvalues of the system. This way, the system equation is reduced to a set of uncoupled equations for the components of d that can be solved easily. On Wed, Dec 21, 2011 at 7:31 AM, Andrew Jaffe a.h.ja...@gmail.com wrote: Just to be completely clear, there is no such thing as a non-normalized eigenvector. An eigenvector is only determined *up to a scalar normalization*, which is obvious from the eigenvalue equation: A v = l v where A is the matrix, l is the eigenvalue, and v is the eigenvector. Obviously v is only determined up to a constant factor. A given eigen routine can return anything at all, but there is no native non-normalized version. Traditionally, you can decide to return normalized eigenvectors with the scalar factor determined by norm(v)=1 for some suitable norm. (I could imagine that an algorithm could depend on that.) Andrew On 21/12/2011 07:01, Olivier Delalleau wrote: Aaah, thanks a lot Lennart, I knew there had to be some logic to Octave's output, but I couldn't see it... -=- Olivier 2011/12/21 Lennart Fricke pge08...@studserv.uni-leipzig.de mailto:pge08...@studserv.uni-leipzig.de Dear Fahreddın, I think, the norm of the eigenvectors corresponds to some generic amplitude. But that is something you cannot extract from the solution of the eigenvalue problem but it depends on the initial deflection or velocities. So I think you should be able to use the normalized values just as well as the non-, un- or not normalized ones. Octave seems to normalize that way that, transpose(Z).B.Z=I, where Z is the matrix of eigenvectors, B is matrix B of the generalized eigenvalue problem and I is the identity. It uses lapack functions. But that's only true if A,B are symmetric. If not it normalizes the magnitude of largest element of each eigenvector to 1. I believe you can get it like that. If U is a Matrix with normalization factors it is diagonal and Z.A contains the normalized column vectors. then it is: transpose(Z.A).B.Z.A =transpose(A).transpose(Z).B.Z.A =A.transpose(Z).B.Z.A=I and thus invert(A).invert(A)=transpose(Z).B.Z As A is diagonal invert(A) has the reciprocal elements on the diagonal. So you can easily extract them A=diag(1/sqrt(diag(transpose(Z).B.Z))) I hope that's correct. Best Regards Lennart ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org mailto: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
Re: [Numpy-discussion] Getting non-normalized eigenvectors from generalized eigenvalue solution?
I read it like that: (**T is the transpose) Let's call M the mass matrix and N the modal mass matrix. Then X**T*M*X=N. If X (matrix of eigenvectors) is normalized with respect to M, N is I (unity) so it just mean that X**T*M*X=I. That is what octave and matlab give you. For this to be true. x**T*M*x=1 must be true for each column x of X. Thus if y is the not normalized eigenvector. a*y**T*M*a*y=1 a**2 * y**T*M*y=1 a**2 = 1/(y**T*M*y) For me the question, why X diagonalizes M and K at the same time, remains. Another hint. If the matrizes are hermitian (symmetric if real) you can use scipy.linalg.eigh, which gives you result with correct normalization. Best regards Lennart ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
[Numpy-discussion] Getting non-normalized eigenvectors from generalized eigenvalue solution?
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
Re: [Numpy-discussion] Getting non-normalized eigenvectors from generalized eigenvalue solution?
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
Re: [Numpy-discussion] Getting non-normalized eigenvectors from generalized eigenvalue solution?
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
Re: [Numpy-discussion] Getting non-normalized eigenvectors from generalized eigenvalue solution?
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
Re: [Numpy-discussion] Getting non-normalized eigenvectors from generalized eigenvalue solution?
If I can get the same response as Matlab I would be all set. Octave results STIFM STIFM = Diagonal Matrix 102000000 0 10200000 00 1020000 000 10200000 0000 1020000 00000 204000 MASSM MASSM = Diagonal Matrix 0.25907 0 0 0 0 0 00.25907 0 0 0 0 0 00.25907 0 0 0 0 0 0 26.0 0 0 0 0 0 0 26.0 0 0 0 0 0 0 26.0 [a, b] = eig(STIFM, MASSM) a = 0.0 0.0 0.0 1.96468 0.0 0.0 0.0 0.0 0.0 0.0 1.96468 0.0 0.0 0.0 1.96468 0.0 0.0 0.0 0.19612 0.0 0.0 0.0 0.0 0.0 0.0 0.19612 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.19612 b = Diagonal Matrix 3923.100000 0 3923.10000 00 3937.2000 000 3937.200 0000 3937.20 00000 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
Re: [Numpy-discussion] Getting non-normalized eigenvectors from generalized eigenvalue solution?
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.comwrote: If I can get the same response as Matlab I would be all set. Octave results STIFM STIFM = Diagonal Matrix 102000000 0 10200000 00 1020000 000 10200000 0000 1020000 00000 204000 MASSM MASSM = Diagonal Matrix 0.25907 0 0 0 0 0 00.25907 0 0 0 0 0 00.25907 0 0 0 0 0 0 26.0 0 0 0 0 0 0 26.0 0 0 0 0 0 0 26.0 [a, b] = eig(STIFM, MASSM) a = 0.0 0.0 0.0 1.96468 0.0 0.0 0.0 0.0 0.0 0.0 1.96468 0.0 0.0 0.0 1.96468 0.0 0.0 0.0 0.19612 0.0 0.0 0.0 0.0 0.0 0.0 0.19612 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.19612 b = Diagonal Matrix 3923.100000 0 3923.10000 00 3937.2000 000 3937.200 0000 3937.20 00000 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.bewrote: 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
Re: [Numpy-discussion] Getting non-normalized eigenvectors from generalized eigenvalue solution?
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.comwrote: If I can get the same response as Matlab I would be all set. Octave results STIFM STIFM = Diagonal Matrix 102000000 0 10200000 00 1020000 000 10200000 0000 1020000 00000 204000 MASSM MASSM = Diagonal Matrix 0.25907 0 0 0 0 0 00.25907 0 0 0 0 0 00.25907 0 0 0 0 0 0 26.0 0 0 0 0 0 0 26.0 0 0 0 0 0 0 26.0 [a, b] = eig(STIFM, MASSM) a = 0.0 0.0 0.0 1.96468 0.0 0.0 0.0 0.0 0.0 0.0 1.96468 0.0 0.0 0.0 1.96468 0.0 0.0 0.0 0.19612 0.0 0.0 0.0 0.0 0.0 0.0 0.19612 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.19612 b = Diagonal Matrix 3923.100000 0 3923.10000 00 3937.2000 000 3937.200 0000 3937.20 00000 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.bewrote: 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
Re: [Numpy-discussion] Getting non-normalized eigenvectors from generalized eigenvalue solution?
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.comwrote: If I can get the same response as Matlab I would be all set. Octave results STIFM STIFM = Diagonal Matrix 102000000 0 10200000 00 1020000 000 10200000 0000 1020000 00000 204000 MASSM MASSM = Diagonal Matrix 0.25907 0 0 0 0 0 00.25907 0 0 0 0 0 00.25907 0 0 0 0 0 0 26.0 0 0 0 0 0 0 26.0 0 0 0 0 0 0 26.0 [a, b] = eig(STIFM, MASSM) a = 0.0 0.0 0.0 1.96468 0.0 0.0 0.0 0.0 0.0 0.0 1.96468 0.0 0.0 0.0 1.96468 0.0 0.0 0.0 0.19612 0.0 0.0 0.0 0.0 0.0 0.0 0.19612 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.19612 b = Diagonal Matrix 3923.100000 0 3923.10000 00 3937.2000 000 3937.200 0000 3937.20 00000 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.bewrote: 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.bewrote: 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
Re: [Numpy-discussion] Getting non-normalized eigenvectors from generalized eigenvalue solution?
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 102000000 0 10200000 00 1020000 000 10200000 0000 1020000 00000 204000 MASSM MASSM = Diagonal Matrix 0.25907 0 0 0 0 0 00.25907 0 0 0 0 0 00.25907 0 0 0 0 0 0 26.0 0 0 0 0 0 0 26.0 0 0 0 0 0 0 26.0 [a, b] = eig(STIFM, MASSM) a = 0.0 0.0 0.0 1.96468 0.0 0.0 0.0 0.0 0.0 0.0 1.96468 0.0 0.0 0.0 1.96468 0.0 0.0 0.0 0.19612 0.0 0.0 0.0 0.0 0.0 0.0 0.19612 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.19612 b = Diagonal Matrix 3923.100000 0 3923.10000 00 3937.2000 000 3937.200 0000 3937.20 00000 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.bewrote: 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
Re: [Numpy-discussion] Getting non-normalized eigenvectors from generalized eigenvalue solution?
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 102000000 0 10200000 00 1020000 000 10200000 0000 1020000 00000 204000 MASSM MASSM = Diagonal Matrix 0.25907 0 0 0 0 0 00.25907 0 0 0 0 0 00.25907 0 0 0 0 0 0 26.0 0 0 0 0 0 0 26.0 0 0 0 0 0 0 26.0 [a, b] = eig(STIFM, MASSM) a = 0.0 0.0 0.0 1.96468 0.0 0.0 0.0 0.0 0.0 0.0 1.96468 0.0 0.0 0.0 1.96468 0.0 0.0 0.0 0.19612 0.0 0.0 0.0 0.0 0.0 0.0 0.19612 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.19612 b = Diagonal Matrix 3923.100000 0 3923.10000 00 3937.2000 000 3937.200 0000 3937.20 00000 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,
Re: [Numpy-discussion] Getting non-normalized eigenvectors from generalized eigenvalue solution?
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.bewrote: 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.bewrote: 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 102000000 0 10200000 00 1020000 000 10200000 0000 1020000 00000 204000 MASSM MASSM = Diagonal Matrix 0.25907 0 0 0 0 0 00.25907 0 0 0 0 0 00.25907 0 0 0 0 0 0 26.0 0 0 0 0 0 0 26.0 0 0 0 0 0 0 26.0 [a, b] = eig(STIFM, MASSM) a = 0.0 0.0 0.0 1.96468 0.0 0.0 0.0 0.0 0.0 0.0 1.96468 0.0 0.0 0.0 1.96468 0.0 0.0 0.0 0.19612 0.0 0.0 0.0 0.0 0.0 0.0 0.19612 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.19612 b = Diagonal Matrix 3923.100000 0 3923.10000 00 3937.2000 000 3937.200 00
