[Trilinos-Users] trillinos diagonalization

Wed Jul 8 08:30:53 EDT 2015

I don't have experience with LOBPCG specifically but I'm guessing it behaves similar to other Anasazi solvers.  Typically, a solver needs to start with a number of vectors equal to the block size of the algorithm.  A common default value for the block size is the number of requested eigenvalues (NEV), so in this case it is likely that the block size is k.  These initial vectors must be linearly independent (they will be used to form a basis for a subspace), and if the vectors provided by the user are not linearly independent then they will be augmented with random vectors until the necessary number of linearly independent vectors is produced.  Because all of the vectors provided by the user are the same in this case, I suspect LOBPCG is using a single copy of that vector in addition to (k-1) random vectors as the initial guess.  It is not necessary to provide an initial guess for all k eigenvectors, only provide vectors where an actual meaningful initial guess is available.  You can simply provide a single vector as an initial guess and LOBPCG will generate a suitable (random) initial guess for the remaining vectors.

I hope this gives some insight into the behavior that you are seeing.

- Steven

--
Steven Hamilton
Radiation Transport Group
Reactor and Nuclear Systems Division
Oak Ridge National Laboratory
Phone: (865) 574-3646

From: Alicia Klinvex <aklinvex at purdue.edu<mailto:aklinvex at purdue.edu>>
Date: Tuesday, July 7, 2015 10:50 PM
To: 임재창 <ljchang94 at kaist.ac.kr<mailto:ljchang94 at kaist.ac.kr>>, "trilinos-users at trilinos.org<mailto:trilinos-users at trilinos.org>" <trilinos-users at trilinos.org<mailto:trilinos-users at trilinos.org>>
Subject: Re: [Trilinos-Users] trillinos diagonalization

Hello,

I'm copying your message to the trilinos-users list, which includes the other Trilinos developers.  Some of their backgrounds align more closely with yours, so I wanted to make sure they can read what you're trying to do (in case they have something to contribute to the discussion).

It looks to me like you're trying to solve the time-independent Schroedinger equation, which I have limited experience with.  My understanding is that you want the eigenvectors corresponding to the smallest magnitude eigenvalues.  Just out of curiosity, is your Hamiltonian matrix symmetric positive definite?

I don't quite understand your orthogonal condition, or the single vector you mentioned.  Do you mean that you want the eigenvectors returned by LOBPCG to be orthogonal to that single vector?  If that's what you're trying to do, I can point you to an example on the Anasazi website.

Best wishes,
Alicia

On Tue, Jul 7, 2015 at 7:38 PM, 임재창 <ljchang94 at kaist.ac.kr<mailto:ljchang94 at kaist.ac.kr>> wrote:

Thank you for your response.

As you say, it is true that i provides initial nxk MultiVector of rank 1 as the initial subspace.(because each vectors are same)

I am using LOBPCG solver to diagonalize hamiltonian matrix of DFT.

and i know the initial information of density but don't have initial information of orbitals which is eigenvector of hamiltonian matrix

and sum of square of orbitals should be density.

But it is not easy to find these orbitals with orthogonal condition, so i just used same orbitals as an initial guess.

-----------------------원본메일-----------------------
보낸사람 : Alicia Klinvex <aklinvex at purdue.edu<mailto:aklinvex at purdue.edu>>
받는사람: 임재창<ljchang94 at kaist.ac.kr<mailto:ljchang94 at kaist.ac.kr>>
참 조: "Hoemmen,Mark" <mhoemme at sandia.gov<mailto:mhoemme at sandia.gov>>,"trilinos-users at trilinos.org<mailto:trilinos-users at trilinos.org>" <trilinos-users at trilinos.org<mailto:trilinos-users at trilinos.org>>
보낸날짜: 2015-07-08 02:36:47 GMT +0900 (ROK)

제목: Re: [Trilinos-Users] trillinos diagonalization

Hello,

I can think of a couple of reasons you might be seeing that behavior, but I have a question first.  Each of the Anasazi eigensolvers needs an initial n x k MultiVector of rank k, which is used as the initial subspace.  (I think each eigensolver deals with rank deficiency differently; I'm not sure how the LOBPCG solver handles it.)  From your email, it sounds like your subspace is of rank 1.  Is that true, and if so, why are you providing a subspace of rank 1?

Best wishes,
Alicia Klinvex

On Mon, Jul 6, 2015 at 7:48 PM, 임재창 <ljchang94 at kaist.ac.kr<mailto:ljchang94 at kaist.ac.kr>> wrote:

i used LOBPCG solver and i didn't set any parameters.

-----------------------원본메일-----------------------
보낸사람 : "Hoemmen, Mark" <mhoemme at sandia.gov<mailto:mhoemme at sandia.gov>>
받는사람: "trilinos-users at trilinos.org<mailto:trilinos-users at trilinos.org>" <trilinos-users at trilinos.org<mailto:trilinos-users at trilinos.org>>
보낸날짜: 2015-06-30 08:33:52 GMT +0900 (ROK)
제목: Re: [Trilinos-Users] trillinos diagonalization

On 6/29/15, 5:12 PM, "trilinos-users-request at trilinos.org<mailto:trilinos-users-request at trilinos.org>"
<trilinos-users-request at trilinos.org<mailto:trilinos-users-request at trilinos.org>> wrote:
>Message: 1
>Date: Mon, 29 Jun 2015 20:34:23 +0900 (KST)
>From: =?UTF-8?B?7J6E7J6s7LC9?=<ljchang94 at kaist.ac.kr<mailto:ljchang94 at kaist.ac.kr>>
>To: trilinos-users at trilinos.org<mailto:trilinos-users at trilinos.org>
>Subject: [Trilinos-Users] trillinos diagonalization
>Message-ID: <55912e883fb6_ at _imoxion.com<http://imoxion.com>>
>Content-Type: text/plain; charset="utf-8"
>
>?Dear Trilinos developers and users,
>
>
>I'm using Anasazi package to diagonalize sparse matrices with
>Epetra_CrsMatrix.
>i gave same vectors as an initial eigenvectorw(so it is not orthogonal)
>and the time and iteration number of first step of diagnoalization were
>different between each trial with same input.
>however eigenvalues were almost same in tolerance value.
>
>and other steps didn't show this phenomena
>
>i guess that the program randomized the initial eigenvectors even i set
>some initial eigenvectors.
>
>is there any reason of this phenomena?

Greetings!

Which eigensolver did you use, and did you set any parameters?

mfh

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