lapack zheevd gives wrong results - fortran

Question

I am trying to use lapack's zheevd in order to diagonalize a complex Hermitian matrix. I' ve written a small example which doesn't produce any compile or run time error but gives wrong results for the eigenvalues... Here's the code:
program test
implicit none
INTEGER, PARAMETER :: N=4
INTEGER, PARAMETER :: LDA = N
INTEGER, PARAMETER :: LWMAX = 1000
INTEGER :: INFO, LWORK, LIWORK, LRWORK,i,j
INTEGER :: IWORK( LWMAX )
REAL(8) :: W(N), RWORK( LWMAX )
COMPLEX(16) :: A(LDA, N), WORK(LWMAX), zero
character(len=1) :: job,uplo
! the matrix I want to diagonalize is:
! ( 3.40, 0.00) ( -2.36, -1.93) ( -4.68, 9.55) ( 5.37, -1.23)
! A= ( -2.36, 1.93) ( 6.94, 0.00) ( 8.13, -1.47) ( 2.07, -5.78)
! ( -4.68, -9.55) ( 8.13, 1.47) ( -2.14, 0.00) ( 4.68, 7.44)
! ( 5.37, 1.23) ( 2.07, 5.78) ( 4.68, -7.44) ( -7.42, 0.00)
zero=dcmplx(0.0d0,0.0d0)
A=zero
A(1,1)= dcmplx( 3.40d0, 0.0d0); A(1,2)=dcmplx(-2.36d0, -1.93d0); A(1,3)= dcmplx(-4.68d0,9.55d0)
A(1,4)= dcmplx( 5.37d0, -1.23d0)
A(2,2)= dcmplx( 6.94d0, 0.0d0); A(2,3)=dcmplx( 8.13d0, -1.47d0); A(2,4)= dcmplx( 2.07d0, -5.78d0)
A(3,3)= dcmplx(-2.14d0, 0.0d0); A(3,4)=dcmplx( 4.68d0, 7.44d0); A(4,4)= dcmplx(-7.42d0, 0.0d0)
job='V'; uplo='U'
LWORK= N**2 + 2*N; LRWORK= 2*N**2 + 5*N + 1; LIWORK= 5*N+3
CALL ZHEEVD( job, uplo, N, A, LDA, W, WORK, LWORK, RWORK,LRWORK,IWORK,LIWORK, INFO )
IF( INFO > 0 ) THEN
WRITE(*,*)'The algorithm failed to compute eigenvalues.'
STOP
END IF
print*, 'eigenvalues found'
do i=1,N
print*, W(i)
end do
open(1, file='eigenvectors.dat')
write(1,10) ((A(i,j),j=1,N),i=1,N)
10 format(4(F10.5,2X,F10.5))
end program test
when I run the code the results I get for the eigenvalues are:
-2.8413, 0, 0, 2.8413
while the actual eigenvalues are: -21.968, 16.3387, 6.45946, -0.0501069
I keep seeing the routine's reference guide and it seems I have everything correct so it should work properly expect it doesn't... Has anyone an idea about what is wrong with my code?
Thanks

Answer 1

There are three main problems here that I can see:
The most serious issue is that you have translated the COMPLEX*16 types in the MKL example you have based your code on as COMPLEX(16). That is incorrect. You should use COMPLEX(8). I don't know whether your toolchain actually has an extended precision complex type, but there could be a size mismatch between your code and the LAPACK call
There is a typo in the code that means that the values of the matrix you pass to LAPACK are not the same as in your comments (and presumably also not the same as the matrix you computed the eigenvalues for)
Lastly, and just as importantly, you have not defined an interface for ZHEEVD (or declared it as external). This will lead to an implicit interface being guessed by the compiler, and it is quite probable that there are inconsistencies between the argument passing within your code and what LAPACK expects. Especially given the type mismatch in the complex arguments.
I would expect that some combination of all three should fix the results.