mirror of
https://github.com/QuantumPackage/qp2.git
synced 2024-11-19 20:42:36 +01:00
179 lines
4.6 KiB
Fortran
179 lines
4.6 KiB
Fortran
|
|
! ---
|
|
|
|
subroutine non_hrmt_bieig(n, A, thr_d, thr_nd, leigvec, reigvec, n_real_eigv, eigval)
|
|
|
|
BEGIN_DOC
|
|
!
|
|
! routine which returns the sorted REAL EIGENVALUES ONLY and corresponding LEFT/RIGHT eigenvetors
|
|
! of a non hermitian matrix A(n,n)
|
|
!
|
|
! n_real_eigv is the number of real eigenvalues, which might be smaller than the dimension "n"
|
|
!
|
|
END_DOC
|
|
|
|
implicit none
|
|
integer, intent(in) :: n
|
|
double precision, intent(in) :: A(n,n)
|
|
double precision, intent(in) :: thr_d, thr_nd
|
|
integer, intent(out) :: n_real_eigv
|
|
double precision, intent(out) :: reigvec(n,n), leigvec(n,n), eigval(n)
|
|
|
|
integer :: i, j,k
|
|
integer :: n_good
|
|
double precision :: thr, thr_cut, thr_diag, thr_norm
|
|
double precision :: accu_d, accu_nd
|
|
|
|
integer, allocatable :: list_good(:), iorder(:), deg_num(:)
|
|
double precision, allocatable :: WR(:), WI(:), VL(:,:), VR(:,:)
|
|
double precision, allocatable :: S(:,:)
|
|
double precision, allocatable :: phi_1_tilde(:),phi_2_tilde(:),chi_1_tilde(:),chi_2_tilde(:)
|
|
|
|
allocate(phi_1_tilde(n),phi_2_tilde(n),chi_1_tilde(n),chi_2_tilde(n))
|
|
|
|
allocate(WR(n), WI(n), VL(n,n), VR(n,n))
|
|
|
|
call lapack_diag_non_sym(n, A, WR, WI, VL, VR)
|
|
|
|
thr_diag = 1d-06
|
|
thr_norm = 1d+10
|
|
|
|
! ---
|
|
|
|
! track & sort the real eigenvalues
|
|
|
|
n_good = 0
|
|
thr = Im_thresh_tc
|
|
do i = 1, n
|
|
if(dabs(WI(i)) .lt. thr) then
|
|
n_good += 1
|
|
else
|
|
print*, 'Found an imaginary component to eigenvalue on i = ', i
|
|
print*, 'Re(i) + Im(i)', WR(i), WI(i)
|
|
endif
|
|
enddo
|
|
|
|
if(n_good.ne.n) then
|
|
print*,'there are some imaginary eigenvalues '
|
|
thr_diag = 1d-03
|
|
n_good = n
|
|
endif
|
|
|
|
allocate(list_good(n_good), iorder(n_good))
|
|
|
|
n_good = 0
|
|
do i = 1, n
|
|
n_good += 1
|
|
list_good(n_good) = i
|
|
eigval(n_good) = WR(i)
|
|
enddo
|
|
|
|
deallocate( WR, WI )
|
|
|
|
n_real_eigv = n_good
|
|
do i = 1, n_good
|
|
iorder(i) = i
|
|
enddo
|
|
call dsort(eigval, iorder, n_good)
|
|
|
|
reigvec(:,:) = 0.d0
|
|
leigvec(:,:) = 0.d0
|
|
do i = 1, n_real_eigv
|
|
do j = 1, n
|
|
reigvec(j,i) = VR(j,list_good(iorder(i)))
|
|
leigvec(j,i) = VL(j,list_good(iorder(i)))
|
|
enddo
|
|
enddo
|
|
|
|
deallocate( list_good, iorder )
|
|
deallocate( VL, VR )
|
|
|
|
ASSERT(n==n_real_eigv)
|
|
|
|
! ---
|
|
|
|
! check bi-orthogonality
|
|
|
|
thr_diag = 10.d0
|
|
thr_norm = 1d+10
|
|
|
|
allocate( S(n_real_eigv,n_real_eigv) )
|
|
call check_biorthog(n, n_real_eigv, leigvec, reigvec, accu_d, accu_nd, S, thr_d, thr_nd, .false.)
|
|
|
|
if( (accu_nd .lt. thr_nd) .and. (dabs(accu_d-dble(n_real_eigv))/dble(n_real_eigv) .lt. thr_d) ) then
|
|
|
|
print *, ' lapack vectors are normalized and bi-orthogonalized'
|
|
deallocate(S)
|
|
return
|
|
|
|
! accu_nd is modified after adding the normalization
|
|
elseif( (accu_nd .lt. thr_nd) .and. (dabs(accu_d-dble(n_real_eigv))/dble(n_real_eigv) .gt. thr_d) ) then
|
|
|
|
print *, ' lapack vectors are not normalized but bi-orthogonalized'
|
|
call check_biorthog_binormalize(n, n_real_eigv, leigvec, reigvec, thr_d, thr_nd, .true.)
|
|
|
|
call check_biorthog(n, n_real_eigv, leigvec, reigvec, accu_d, accu_nd, S, thr_d, thr_nd, .true.)
|
|
call check_EIGVEC(n, n, A, eigval, leigvec, reigvec, thr_diag, thr_norm, .true.)
|
|
|
|
deallocate(S)
|
|
return
|
|
|
|
else
|
|
|
|
print *, ' lapack vectors are not normalized neither bi-orthogonalized'
|
|
|
|
allocate(deg_num(n))
|
|
call reorder_degen_eigvec(n, deg_num, eigval, leigvec, reigvec)
|
|
call impose_biorthog_degen_eigvec(n, deg_num, eigval, leigvec, reigvec)
|
|
deallocate(deg_num)
|
|
|
|
call check_biorthog(n, n_real_eigv, leigvec, reigvec, accu_d, accu_nd, S, thr_d, thr_nd, .false.)
|
|
if( (accu_nd .lt. thr_nd) .and. (dabs(accu_d-dble(n_real_eigv)) .gt. thr_d) ) then
|
|
call check_biorthog_binormalize(n, n_real_eigv, leigvec, reigvec, thr_d, thr_nd, .true.)
|
|
endif
|
|
call check_biorthog(n, n_real_eigv, leigvec, reigvec, accu_d, accu_nd, S, thr_d, thr_nd, .true.)
|
|
|
|
deallocate(S)
|
|
|
|
endif
|
|
|
|
return
|
|
|
|
end
|
|
|
|
! ---
|
|
|
|
subroutine check_bi_ortho(reigvec, leigvec, n, S, accu_nd)
|
|
|
|
BEGIN_DOC
|
|
! retunrs the overlap matrix S = Leigvec^T Reigvec
|
|
!
|
|
! and the square root of the sum of the squared off-diagonal elements of S
|
|
END_DOC
|
|
|
|
implicit none
|
|
integer, intent(in) :: n
|
|
double precision, intent(in) :: reigvec(n,n), leigvec(n,n)
|
|
double precision, intent(out) :: S(n,n), accu_nd
|
|
|
|
integer :: i,j
|
|
|
|
! S = VL x VR
|
|
call dgemm( 'T', 'N', n, n, n, 1.d0 &
|
|
, leigvec, size(leigvec, 1), reigvec, size(reigvec, 1) &
|
|
, 0.d0, S, size(S, 1) )
|
|
|
|
accu_nd = 0.d0
|
|
do i = 1, n
|
|
do j = 1, n
|
|
if(i.ne.j) then
|
|
accu_nd = accu_nd + S(j,i) * S(j,i)
|
|
endif
|
|
enddo
|
|
enddo
|
|
accu_nd = dsqrt(accu_nd)
|
|
|
|
end
|
|
|
|
|