Generalized diagonalization with Lapack

Question

I am having some problems using the subroutine DSYGV of Lapack:

DSYGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,LWORK, INFO )

This is the diagonalization I want to carry out:

v_mat*x = eig*t_mat*x

This is the crucial piece of my code:

program pruebadiago

real, dimension(:,:), allocatable :: v_mat, t_mat

real, dimension(:), allocatable   :: eig,WORK

real , parameter                  :: k=3.0,m=4.0

integer, parameter                :: n=2

integer                           :: i

! EXPECTED EIGENVALUES AND EIGENVECTORS

!eig = 0.286475  ------>  u = (0.262866 , 0.425325)

!eig = 1.96353   ------>  u = (0.425325, -0.262866)

allocate(v_mat(n,n),t_mat(n,n),eig(n))

!--------------------------

v_mat(1,1:2) = (/2.0*k,-k/)

v_mat(2,1:2) = (/-k,k/)

!--------------------------

!--------------------------

t_mat(1,1:2) = (/m,0.0/)

t_mat(2,1:2) = (/0.0,m/)

!---------------------------

!diagonalizacion

call DSYGV( 1, 'v', 'u', n , v_mat, 2 , t_mat, 2, eig, WORK,-1, INF )

LWORK=WORK(1)

allocate(WORK(LWORK))

call  DSYGV( 1, 'v', 'u', n , v_mat, 2 , t_mat, 2, eig, WORK,LWORK, INF )

open(unit=100,file="pruebadiago.dat",status="replace",action="write")

do i = 1,n

write(unit=100,fmt=*) "E",i,"=",eig(i),(v_mat(i,j),j=1,n)

!autofuntzioak zutabeka doaz"(100f12.6)"

enddo

close(unit=100)

deallocate(v_mat,t_mat,eig,WORK)

end program pruebadiago

I think I understood everything given in this document:

http://www.netlib.org/lapack/lapack-3.1.1/html/dsygv.f.html

But the argument LWORK which I did not understand so I just try different values.

I know something is wrong because I know what are the eigenvalues and eigenvectors of this matrix and I get wrong eigenvalues and eigenvectors, and I am doing such a simple calculation in order to understand the way it works and then compute huge diagonalizations.

Does anybody see what is the problem?

Thank you

Answer 1

There are missing some elements from the code you posted. Basically the array declarations of WORK,eig,v_mat and t_mat.

Anyway, LWORK argument actually is the size of WORK vector. i.e

DOUBLE PRECISION WORK(100)
LWORK=100

Lapack specifies as minimum value of LWORK=3*N-1. In your case N=2.

For this example case I would suggested to use a big WORK vector (i.e. 100) so that you will not encounter any problems from that.

For large matrices you should use double call of DSYGV.

• First call with LWORK=-1 and get suggested size from WORK(1)
• Allocate a NEW WORK vector with suggested size.
• Finally solve eigenproblem with DSYGV.

Sample code is:

CALL DSYGV( 1, 'V', 'U', 2 , v_mat, 2 , t_mat, 2, eig, W, -1, INF )
LWORK=W(1)
ALLOCATE ( WORK(LWORK) )
CALL DSYGV( 1, 'V', 'U', 2 , v_mat, 2 , t_mat, 2, eig, WORK, LWORK, INF ) 

Additionally, you need to check INF value after DSYGV call. If it is not zero then an error occurred.

EDIT: Fixed source code

program pruebadiago

double precision, dimension(:,:), allocatable :: v_mat, t_mat
double precision, dimension(:), allocatable :: eig,WORK
double precision :: W
double precision , parameter :: k=3.0,m=4.0
integer, parameter :: n=2
integer :: i

! EXPECTED EIGENVALUES AND EIGENVECTORS
!eig = 0.286475 ------> u = (0.262866 , 0.425325)
!eig = 1.96353 ------> u = (0.425325, -0.262866)

allocate(v_mat(n,n),t_mat(n,n),eig(n))

!--------------------------
v_mat(1,1:2) = (/2.0*k,-k/)
v_mat(2,1:2) = (/-k,k/)
!--------------------------
t_mat(1,1:2) = (/m,0.0d0/)
t_mat(2,1:2) = (/0.0d0,m/)
!---------------------------

call DSYGV( 1, 'v', 'u', n , v_mat, 2 , t_mat, 2, eig, W,-1, INF )

LWORK=W
allocate(WORK(LWORK))

call DSYGV( 1, 'v', 'u', n , v_mat, 2 , t_mat, 2, eig, WORK,LWORK, INF )
open(unit=100,file="pruebadiago.dat",status="replace",action="write")
do i = 1,n
  write(unit=100,fmt=*) "E",i,"=",eig(i),(v_mat(i,j),j=1,n)
enddo

close(unit=100)
deallocate(v_mat,t_mat,eig,WORK)

end program pruebadiago