Fortran90: Subroutine DSYEV and associating eigenvalues and eigenvectors.

[Animastryfe]

Greetings. I am using the LAPACK (Linear Algebra Package) software package to find the eigenvalues and eigenvectors of a large symmetrical real matrix. Specifically, I calculate a scalar from each eigenvector, and I want to graph it against its associated eigenvalue.

I am using the subroutine DSYEV of LAPACK to do this. However, DSYEV outputs the eigenvalues in ascending order, and I'm not sure how it orders the eigenvectors. Is there a way to associate each eigenvector with its eigenvalue?

Edit: The official page for DSYEV is here: http://www.netlib.org/lapack/double/dsyev.f
Here is another page about it: http://www.nag.co.uk/numeric/fl/nagdoc_fl22/xhtml/F08/f08faf.xml

 

[AlephZero]

The eigenvectors are returned in the A matrix in the same order as the eigenvalues.

A(1:N, 1) is the vector for W(1), A(1:N, 2) is the vector for W(2), etc.

 

[Animastryfe]

Thank you very much for the reply.

Just to be completely clear: the columns of the matrix A are the eigenvectors?

 

[AlephZero]

If you set JOBV = "V", then yes. Otherwise, no!

 

[LudusRex]

Hello, thank you for reaching out. I understand your concern about associating eigenvalues and eigenvectors using the DSYEV subroutine in Fortran90. After reviewing the documentation for DSYEV, it seems that the subroutine does not explicitly associate the eigenvalues and eigenvectors in its output. However, there are a few ways you can approach this problem.

One option is to use the output eigenvalues in ascending order as a reference for the eigenvectors. Since the eigenvectors are returned in the same order as the eigenvalues, you can use the index of each eigenvalue to associate it with its corresponding eigenvector.

Another option is to use the LAPACK subroutine DSYEVR, which allows you to specify the range of eigenvalues you are interested in. This subroutine also returns the eigenvalues and eigenvectors in the same order, making it easier to associate them.

Additionally, you can use the LAPACK subroutine DSYEVX, which allows you to specify the desired eigenvalues or a range of eigenvalues and returns the associated eigenvectors.

I hope this helps. As always, I recommend consulting the official documentation and possibly reaching out to the developers of LAPACK for further clarification or assistance. Best of luck with your research.