Re: Help-gsl Digest, Vol 229, Issue 1

[Brorson, Stuart]

Without seeing the actual eigenvectors you receive,  my first reaction is to 
suggest that your eigenvectors differ by a sign.

The definition of an eigenvector doesn't specify the sign of the elements (i.e. 
the handedness of the space).  Therefore, different programs (different 
algorithms) might emit eigenvectors which differ only by a sign.  For example, 
the following vectors are all valid eigenvectors spanning a 2D space:

v1, v2 = [1 1]', [1 -1]'
v1, v2 = [1 1]', [-1 1]'
v1, v2 = [-1 -1]', [1 -1]'
v1, v2 = [-1 -1]', [-1 1]'

Since the definition is ambiguous, different programs may emit one or another 
of these eigenvector pairs.

Best regards,
Stuart Brorson
Northeastern University
Boston, Mass.





________________________________
From: help-gsl-bounces+s.brorson=northeastern.edu@gnu.org 
<help-gsl-bounces+s.brorson=northeastern.edu@gnu.org> on behalf of 
help-gsl-request@gnu.org <help-gsl-request@gnu.org>
Sent: Thursday, January 4, 2024 12:00 PM
To: help-gsl@gnu.org <help-gsl@gnu.org>
Subject: Help-gsl Digest, Vol 229, Issue 1

Send Help-gsl mailing list submissions to
        help-gsl@gnu.org

To subscribe or unsubscribe via the World Wide Web, visit
        
https://nam12.safelinks.protection.outlook.com/?url=https%3A%2F%2Flists.gnu.org%2Fmailman%2Flistinfo%2Fhelp-gsl&data=05%7C02%7Cs.brorson%40northeastern.edu%7C2d3f98b335804a9eb43e08dc0d46ca9c%7Ca8eec281aaa34daeac9b9a398b9215e7%7C0%7C0%7C638399844927330730%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=z1OO4VU282tn5LiGXrYJUfx%2F7AcLaLFVDWW3YPYR6DI%3D&reserved=0<https://lists.gnu.org/mailman/listinfo/help-gsl>
or, via email, send a message with subject or body 'help' to
        help-gsl-request@gnu.org

You can reach the person managing the list at
        help-gsl-owner@gnu.org

When replying, please edit your Subject line so it is more specific
than "Re: Contents of Help-gsl digest..."


Today's Topics:

   1. Different eigenvectors obtained from gsl_eigen_hermv compared
      with scipy.linalg.eigh (Jiasen Guo)


----------------------------------------------------------------------

Message: 1
Date: Wed, 3 Jan 2024 23:39:34 -0500
From: Jiasen Guo <jiasenguo1993@gmail.com>
To: help-gsl@gnu.org
Subject: Different eigenvectors obtained from gsl_eigen_hermv compared
        with scipy.linalg.eigh
Message-ID:
        <CAL+Ws-BSKOMZNh=m92U-Twj_TntWaajbvM13ovT8AX5tf0uvVw@mail.gmail.com>
Content-Type: text/plain; charset="utf-8"

Dear all,
I am having an issue using gsl_eigen_hermv to reproduce a complex hermitian
eigenvalue problem previously solved with scipy.linalg.eigh. I have
included the cpp and python code in the attached zip file. Basically, the
matrix is created in cpp and solved using gsl. the same matrix (*real.csv*
for the real part and *imag.csv* for the imaginary part) is dumped out and
solved in Python again. While I get the same eigenvalues from the two
approaches, the eigenvalues are, however, different. And if I calculated
the module of the complex numbers in the eigenvector, then they are
identical from both methods.

I use g++ --std=c++11 test.cpp -o test.o -lgsl -lgslcblas for compilation.
Please help me understand what is the problem here. Thanks for your kind
help.

Best,
Jiasen
-------------- next part --------------
A non-text attachment was scrubbed...
Name: test.zip
Type: application/x-zip-compressed
Size: 2376 bytes
Desc: not available
URL: 
<https://nam12.safelinks.protection.outlook.com/?url=https%3A%2F%2Flists.gnu.org%2Farchive%2Fhtml%2Fhelp-gsl%2Fattachments%2F20240103%2F7dafe09b%2Fattachment.bin&data=05%7C02%7Cs.brorson%40northeastern.edu%7C2d3f98b335804a9eb43e08dc0d46ca9c%7Ca8eec281aaa34daeac9b9a398b9215e7%7C0%7C0%7C638399844927330730%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=GWsPeV4c6qlerT2BJH5VfD2AuSQxQCStnkf4GZY2cyA%3D&reserved=0<https://lists.gnu.org/archive/html/help-gsl/attachments/20240103/7dafe09b/attachment.bin>>

------------------------------

Subject: Digest Footer

_______________________________________________
Help-gsl mailing list
Help-gsl@gnu.org
https://nam12.safelinks.protection.outlook.com/?url=https%3A%2F%2Flists.gnu.org%2Fmailman%2Flistinfo%2Fhelp-gsl&data=05%7C02%7Cs.brorson%40northeastern.edu%7C2d3f98b335804a9eb43e08dc0d46ca9c%7Ca8eec281aaa34daeac9b9a398b9215e7%7C0%7C0%7C638399844927330730%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=z1OO4VU282tn5LiGXrYJUfx%2F7AcLaLFVDWW3YPYR6DI%3D&reserved=0<https://lists.gnu.org/mailman/listinfo/help-gsl>


------------------------------

End of Help-gsl Digest, Vol 229, Issue 1
****************************************
Without