mirror of
https://github.com/QuantumPackage/qp2.git
synced 2024-11-19 04:22:32 +01:00
671 lines
21 KiB
Fortran
671 lines
21 KiB
Fortran
subroutine non_hrmt_diag_split_degen_bi_orthog(n, A, 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)
|
|
integer, intent(out) :: n_real_eigv
|
|
double precision, intent(out) :: reigvec(n,n), leigvec(n,n), eigval(n)
|
|
double precision, allocatable :: reigvec_tmp(:,:), leigvec_tmp(:,:)
|
|
|
|
integer :: i, j, n_degen,k , iteration
|
|
double precision :: shift_current
|
|
double precision :: r,thr,accu_d, accu_nd
|
|
integer, allocatable :: iorder_origin(:),iorder(:)
|
|
double precision, allocatable :: WR(:), WI(:), Vl(:,:), VR(:,:),S(:,:)
|
|
double precision, allocatable :: Aw(:,:),diag_elem(:),A_save(:,:)
|
|
double precision, allocatable :: im_part(:),re_part(:)
|
|
double precision :: accu,thr_cut, thr_norm=1d0
|
|
|
|
|
|
thr_cut = 1.d-15
|
|
print*,'Computing the left/right eigenvectors ...'
|
|
print*,'Using the degeneracy splitting algorithm'
|
|
! initialization
|
|
shift_current = 1.d-15
|
|
iteration = 0
|
|
print*,'***** iteration = ',iteration
|
|
|
|
|
|
! pre-processing the matrix :: sorting by diagonal elements
|
|
allocate(reigvec_tmp(n,n), leigvec_tmp(n,n))
|
|
allocate(diag_elem(n),iorder_origin(n),A_save(n,n))
|
|
! print*,'Aw'
|
|
do i = 1, n
|
|
iorder_origin(i) = i
|
|
diag_elem(i) = A(i,i)
|
|
! write(*,'(100(F16.10,X))')A(:,i)
|
|
enddo
|
|
call dsort(diag_elem, iorder_origin, n)
|
|
do i = 1, n
|
|
do j = 1, n
|
|
A_save(j,i) = A(iorder_origin(j),iorder_origin(i))
|
|
enddo
|
|
enddo
|
|
|
|
allocate(WR(n), WI(n), VL(n,n), VR(n,n), Aw(n,n))
|
|
allocate(im_part(n),iorder(n))
|
|
allocate( S(n,n) )
|
|
|
|
|
|
Aw = A_save
|
|
call cancel_small_elmts(aw,n,thr_cut)
|
|
call lapack_diag_non_sym(n,Aw,WR,WI,VL,VR)
|
|
do i = 1, n
|
|
im_part(i) = -dabs(WI(i))
|
|
iorder(i) = i
|
|
enddo
|
|
call dsort(im_part, iorder, n)
|
|
n_real_eigv = 0
|
|
do i = 1, n
|
|
if(dabs(WI(i)).lt.1.d-20)then
|
|
n_real_eigv += 1
|
|
else
|
|
! print*,'Found an imaginary component to eigenvalue'
|
|
! print*,'Re(i) + Im(i)',WR(i),WI(i)
|
|
endif
|
|
enddo
|
|
if(n_real_eigv.ne.n)then
|
|
shift_current = max(10.d0 * dabs(im_part(1)),shift_current*10.d0)
|
|
print*,'Largest imaginary part found in eigenvalues = ',im_part(1)
|
|
print*,'Splitting the degeneracies by ',shift_current
|
|
else
|
|
print*,'All eigenvalues are real !'
|
|
endif
|
|
|
|
|
|
do while(n_real_eigv.ne.n)
|
|
iteration += 1
|
|
print*,'***** iteration = ',iteration
|
|
if(shift_current.gt.1.d-3)then
|
|
print*,'shift_current > 1.d-3 !!'
|
|
print*,'Your matrix intrinsically contains complex eigenvalues'
|
|
stop
|
|
endif
|
|
Aw = A_save
|
|
call cancel_small_elmts(Aw,n,thr_cut)
|
|
call split_matrix_degen(Aw,n,shift_current)
|
|
call lapack_diag_non_sym(n,Aw,WR,WI,VL,VR)
|
|
n_real_eigv = 0
|
|
do i = 1, n
|
|
if(dabs(WI(i)).lt.1.d-20)then
|
|
n_real_eigv+= 1
|
|
else
|
|
! print*,'Found an imaginary component to eigenvalue'
|
|
! print*,'Re(i) + Im(i)',WR(i),WI(i)
|
|
endif
|
|
enddo
|
|
if(n_real_eigv.ne.n)then
|
|
do i = 1, n
|
|
im_part(i) = -dabs(WI(i))
|
|
iorder(i) = i
|
|
enddo
|
|
call dsort(im_part, iorder, n)
|
|
shift_current = max(10.d0 * dabs(im_part(1)),shift_current*10.d0)
|
|
print*,'Largest imaginary part found in eigenvalues = ',im_part(1)
|
|
print*,'Splitting the degeneracies by ',shift_current
|
|
else
|
|
print*,'All eigenvalues are real !'
|
|
endif
|
|
enddo
|
|
!!!!!!!!!!!!!!!! SORTING THE EIGENVALUES
|
|
do i = 1, n
|
|
eigval(i) = WR(i)
|
|
iorder(i) = i
|
|
enddo
|
|
call dsort(eigval,iorder,n)
|
|
do i = 1, n
|
|
! print*,'eigval(i) = ',eigval(i)
|
|
reigvec_tmp(:,i) = VR(:,iorder(i))
|
|
leigvec_tmp(:,i) = Vl(:,iorder(i))
|
|
enddo
|
|
|
|
!!! ONCE ALL EIGENVALUES ARE REAL ::: CHECK BI-ORTHONORMALITY
|
|
! check bi-orthogonality
|
|
call check_biorthog(n, n, leigvec_tmp, reigvec_tmp, accu_d, accu_nd, S, thresh_biorthog_diag, thresh_biorthog_nondiag, .false.)
|
|
print *, ' accu_nd bi-orthog = ', accu_nd
|
|
if(accu_nd .lt. thresh_biorthog_nondiag) then
|
|
print *, ' bi-orthogonality: ok'
|
|
else
|
|
print *, ' '
|
|
print *, ' bi-orthogonality: not imposed yet'
|
|
print *, ' '
|
|
print *, ' '
|
|
print *, ' orthog between degen eigenvect'
|
|
print *, ' '
|
|
double precision, allocatable :: S_nh_inv_half(:,:)
|
|
allocate(S_nh_inv_half(n,n))
|
|
logical :: complex_root
|
|
deallocate(S_nh_inv_half)
|
|
call impose_orthog_degen_eigvec(n, eigval, reigvec_tmp)
|
|
call impose_orthog_degen_eigvec(n, eigval, leigvec_tmp)
|
|
call check_biorthog(n, n, leigvec_tmp, reigvec_tmp, accu_d, accu_nd, S, thresh_biorthog_diag, thresh_biorthog_nondiag, .false.)
|
|
if(accu_nd .lt. thresh_biorthog_nondiag) then
|
|
print *, ' bi-orthogonality: ok'
|
|
else
|
|
print*,'New vectors not bi-orthonormals at ',accu_nd
|
|
call impose_biorthog_qr(n, n, leigvec_tmp, reigvec_tmp, S)
|
|
call check_biorthog(n, n, leigvec_tmp, reigvec_tmp, accu_d, accu_nd, S, thresh_biorthog_diag, thresh_biorthog_nondiag, .false.)
|
|
if(accu_nd .lt. thresh_biorthog_nondiag) then
|
|
print *, ' bi-orthogonality: ok'
|
|
else
|
|
print*,'New vectors not bi-orthonormals at ',accu_nd
|
|
print*,'Must be a deep problem ...'
|
|
stop
|
|
endif
|
|
endif
|
|
endif
|
|
|
|
!! EIGENVECTORS SORTED AND BI-ORTHONORMAL
|
|
do i = 1, n
|
|
do j = 1, n
|
|
VR(iorder_origin(j),i) = reigvec_tmp(j,i)
|
|
VL(iorder_origin(j),i) = leigvec_tmp(j,i)
|
|
enddo
|
|
enddo
|
|
|
|
!! RECOMPUTING THE EIGENVALUES
|
|
eigval = 0.d0
|
|
do i = 1, n
|
|
iorder(i) = i
|
|
accu = 0.d0
|
|
do j = 1, n
|
|
accu += VL(j,i) * VR(j,i)
|
|
do k = 1, n
|
|
eigval(i) += VL(j,i) * A(j,k) * VR(k,i)
|
|
enddo
|
|
enddo
|
|
eigval(i) *= 1.d0/accu
|
|
! print*,'eigval(i) = ',eigval(i)
|
|
enddo
|
|
!! RESORT JUST TO BE SURE
|
|
call dsort(eigval, iorder, n)
|
|
do i = 1, n
|
|
do j = 1, n
|
|
reigvec(j,i) = VR(j,iorder(i))
|
|
leigvec(j,i) = VL(j,iorder(i))
|
|
enddo
|
|
enddo
|
|
print*,'Checking for final reigvec/leigvec'
|
|
shift_current = max(1.d-10,shift_current)
|
|
print*,'Thr for eigenvectors = ',shift_current
|
|
call check_EIGVEC(n, n, A, eigval, leigvec, reigvec, shift_current, thr_norm, .false.)
|
|
call check_biorthog(n, n, leigvec, reigvec, accu_d, accu_nd, S, thresh_biorthog_diag, thresh_biorthog_nondiag, .false.)
|
|
print *, ' accu_nd bi-orthog = ', accu_nd
|
|
|
|
if(accu_nd .lt. thresh_biorthog_nondiag) then
|
|
print *, ' bi-orthogonality: ok'
|
|
else
|
|
print*,'Something went wrong in non_hrmt_diag_split_degen_bi_orthog'
|
|
print*,'Eigenvectors are not bi orthonormal ..'
|
|
print*,'accu_nd = ',accu_nd
|
|
stop
|
|
endif
|
|
|
|
end
|
|
|
|
|
|
|
|
subroutine non_hrmt_diag_split_degen_s_inv_half(n, A, 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)
|
|
integer, intent(out) :: n_real_eigv
|
|
double precision, intent(out) :: reigvec(n,n), leigvec(n,n), eigval(n)
|
|
double precision, allocatable :: reigvec_tmp(:,:), leigvec_tmp(:,:)
|
|
|
|
integer :: i, j, n_degen,k , iteration
|
|
double precision :: shift_current
|
|
double precision :: r,thr,accu_d, accu_nd
|
|
integer, allocatable :: iorder_origin(:),iorder(:)
|
|
double precision, allocatable :: WR(:), WI(:), Vl(:,:), VR(:,:),S(:,:)
|
|
double precision, allocatable :: Aw(:,:),diag_elem(:),A_save(:,:)
|
|
double precision, allocatable :: im_part(:),re_part(:)
|
|
double precision :: accu,thr_cut, thr_norm=1.d0
|
|
double precision, allocatable :: S_nh_inv_half(:,:)
|
|
logical :: complex_root
|
|
|
|
|
|
thr_cut = 1.d-15
|
|
print*,'Computing the left/right eigenvectors ...'
|
|
print*,'Using the degeneracy splitting algorithm'
|
|
! initialization
|
|
shift_current = 1.d-15
|
|
iteration = 0
|
|
print*,'***** iteration = ',iteration
|
|
|
|
|
|
! pre-processing the matrix :: sorting by diagonal elements
|
|
allocate(reigvec_tmp(n,n), leigvec_tmp(n,n))
|
|
allocate(diag_elem(n),iorder_origin(n),A_save(n,n))
|
|
! print*,'Aw'
|
|
do i = 1, n
|
|
iorder_origin(i) = i
|
|
diag_elem(i) = A(i,i)
|
|
! write(*,'(100(F16.10,X))')A(:,i)
|
|
enddo
|
|
call dsort(diag_elem, iorder_origin, n)
|
|
do i = 1, n
|
|
do j = 1, n
|
|
A_save(j,i) = A(iorder_origin(j),iorder_origin(i))
|
|
enddo
|
|
enddo
|
|
|
|
allocate(WR(n), WI(n), VL(n,n), VR(n,n), Aw(n,n))
|
|
allocate(im_part(n),iorder(n))
|
|
allocate( S(n,n) )
|
|
allocate(S_nh_inv_half(n,n))
|
|
|
|
|
|
Aw = A_save
|
|
call cancel_small_elmts(aw,n,thr_cut)
|
|
call lapack_diag_non_sym(n,Aw,WR,WI,VL,VR)
|
|
do i = 1, n
|
|
im_part(i) = -dabs(WI(i))
|
|
iorder(i) = i
|
|
enddo
|
|
call dsort(im_part, iorder, n)
|
|
n_real_eigv = 0
|
|
do i = 1, n
|
|
if(dabs(WI(i)).lt.1.d-20)then
|
|
n_real_eigv += 1
|
|
else
|
|
! print*,'Found an imaginary component to eigenvalue'
|
|
! print*,'Re(i) + Im(i)',WR(i),WI(i)
|
|
endif
|
|
enddo
|
|
if(n_real_eigv.ne.n)then
|
|
shift_current = max(10.d0 * dabs(im_part(1)),shift_current*10.d0)
|
|
print*,'Largest imaginary part found in eigenvalues = ',im_part(1)
|
|
print*,'Splitting the degeneracies by ',shift_current
|
|
else
|
|
print*,'All eigenvalues are real !'
|
|
endif
|
|
|
|
|
|
do while(n_real_eigv.ne.n)
|
|
iteration += 1
|
|
print*,'***** iteration = ',iteration
|
|
if(shift_current.gt.1.d-3)then
|
|
print*,'shift_current > 1.d-3 !!'
|
|
print*,'Your matrix intrinsically contains complex eigenvalues'
|
|
stop
|
|
endif
|
|
Aw = A_save
|
|
! thr_cut = shift_current
|
|
call cancel_small_elmts(Aw,n,thr_cut)
|
|
call split_matrix_degen(Aw,n,shift_current)
|
|
call lapack_diag_non_sym(n,Aw,WR,WI,VL,VR)
|
|
n_real_eigv = 0
|
|
do i = 1, n
|
|
if(dabs(WI(i)).lt.1.d-20)then
|
|
n_real_eigv+= 1
|
|
else
|
|
! print*,'Found an imaginary component to eigenvalue'
|
|
! print*,'Re(i) + Im(i)',WR(i),WI(i)
|
|
endif
|
|
enddo
|
|
if(n_real_eigv.ne.n)then
|
|
do i = 1, n
|
|
im_part(i) = -dabs(WI(i))
|
|
iorder(i) = i
|
|
enddo
|
|
call dsort(im_part, iorder, n)
|
|
shift_current = max(10.d0 * dabs(im_part(1)),shift_current*10.d0)
|
|
print*,'Largest imaginary part found in eigenvalues = ',im_part(1)
|
|
print*,'Splitting the degeneracies by ',shift_current
|
|
else
|
|
print*,'All eigenvalues are real !'
|
|
endif
|
|
enddo
|
|
!!!!!!!!!!!!!!!! SORTING THE EIGENVALUES
|
|
do i = 1, n
|
|
eigval(i) = WR(i)
|
|
iorder(i) = i
|
|
enddo
|
|
call dsort(eigval,iorder,n)
|
|
do i = 1, n
|
|
! print*,'eigval(i) = ',eigval(i)
|
|
reigvec_tmp(:,i) = VR(:,iorder(i))
|
|
leigvec_tmp(:,i) = Vl(:,iorder(i))
|
|
enddo
|
|
|
|
!!! ONCE ALL EIGENVALUES ARE REAL ::: CHECK BI-ORTHONORMALITY
|
|
! check bi-orthogonality
|
|
call check_biorthog(n, n, leigvec_tmp, reigvec_tmp, accu_d, accu_nd, S, thresh_biorthog_diag, thresh_biorthog_nondiag, .false.)
|
|
print *, ' accu_nd bi-orthog = ', accu_nd
|
|
if(accu_nd .lt. thresh_biorthog_nondiag) then
|
|
print *, ' bi-orthogonality: ok'
|
|
else
|
|
print *, ' '
|
|
print *, ' bi-orthogonality: not imposed yet'
|
|
if(complex_root) then
|
|
print *, ' '
|
|
print *, ' '
|
|
print *, ' orthog between degen eigenvect'
|
|
print *, ' '
|
|
! bi-orthonormalization using orthogonalization of left, right and then QR between left and right
|
|
call impose_orthog_degen_eigvec(n, eigval, reigvec_tmp) ! orthogonalization of reigvec
|
|
call impose_orthog_degen_eigvec(n, eigval, leigvec_tmp) ! orthogonalization of leigvec
|
|
call check_biorthog(n, n, leigvec_tmp, reigvec_tmp, accu_d, accu_nd, S, thresh_biorthog_diag, thresh_biorthog_nondiag, .false.)
|
|
|
|
if(accu_nd .lt. thresh_biorthog_nondiag) then
|
|
print *, ' bi-orthogonality: ok'
|
|
else
|
|
print*,'New vectors not bi-orthonormals at ', accu_nd
|
|
call get_inv_half_nonsymmat_diago(S, n, S_nh_inv_half, complex_root)
|
|
if(complex_root)then
|
|
call impose_biorthog_qr(n, n, leigvec_tmp, reigvec_tmp, S) ! bi-orthonormalization using QR
|
|
else
|
|
print*,'S^{-1/2} exists !!'
|
|
call bi_ortho_s_inv_half(n,leigvec_tmp,reigvec_tmp,S_nh_inv_half) ! use of S^{-1/2} bi-orthonormalization
|
|
endif
|
|
endif
|
|
else ! the matrix S^{-1/2} exists
|
|
print*,'S^{-1/2} exists !!'
|
|
call bi_ortho_s_inv_half(n,leigvec_tmp,reigvec_tmp,S_nh_inv_half) ! use of S^{-1/2} bi-orthonormalization
|
|
endif
|
|
call check_biorthog(n, n, leigvec_tmp, reigvec_tmp, accu_d, accu_nd, S, thresh_biorthog_diag, thresh_biorthog_nondiag, .false.)
|
|
if(accu_nd .lt. thresh_biorthog_nondiag) then
|
|
print *, ' bi-orthogonality: ok'
|
|
else
|
|
print*,'New vectors not bi-orthonormals at ',accu_nd
|
|
print*,'Must be a deep problem ...'
|
|
stop
|
|
endif
|
|
endif
|
|
|
|
!! EIGENVECTORS SORTED AND BI-ORTHONORMAL
|
|
do i = 1, n
|
|
do j = 1, n
|
|
VR(iorder_origin(j),i) = reigvec_tmp(j,i)
|
|
VL(iorder_origin(j),i) = leigvec_tmp(j,i)
|
|
enddo
|
|
enddo
|
|
|
|
!! RECOMPUTING THE EIGENVALUES
|
|
eigval = 0.d0
|
|
do i = 1, n
|
|
iorder(i) = i
|
|
accu = 0.d0
|
|
do j = 1, n
|
|
accu += VL(j,i) * VR(j,i)
|
|
do k = 1, n
|
|
eigval(i) += VL(j,i) * A(j,k) * VR(k,i)
|
|
enddo
|
|
enddo
|
|
eigval(i) *= 1.d0/accu
|
|
! print*,'eigval(i) = ',eigval(i)
|
|
enddo
|
|
!! RESORT JUST TO BE SURE
|
|
call dsort(eigval, iorder, n)
|
|
do i = 1, n
|
|
do j = 1, n
|
|
reigvec(j,i) = VR(j,iorder(i))
|
|
leigvec(j,i) = VL(j,iorder(i))
|
|
enddo
|
|
enddo
|
|
print*,'Checking for final reigvec/leigvec'
|
|
shift_current = max(1.d-10,shift_current)
|
|
print*,'Thr for eigenvectors = ',shift_current
|
|
call check_EIGVEC(n, n, A, eigval, leigvec, reigvec, shift_current, thr_norm, .false.)
|
|
call check_biorthog(n, n, leigvec, reigvec, accu_d, accu_nd, S, thresh_biorthog_diag, thresh_biorthog_nondiag, .false.)
|
|
print *, ' accu_nd bi-orthog = ', accu_nd
|
|
|
|
if(accu_nd .lt. thresh_biorthog_nondiag) then
|
|
print *, ' bi-orthogonality: ok'
|
|
else
|
|
print*,'Something went wrong in non_hrmt_diag_split_degen_bi_orthog'
|
|
print*,'Eigenvectors are not bi orthonormal ..'
|
|
print*,'accu_nd = ',accu_nd
|
|
stop
|
|
endif
|
|
|
|
end
|
|
|
|
|
|
subroutine non_hrmt_fock_mat(n, A, leigvec, reigvec, n_real_eigv, eigval)
|
|
|
|
BEGIN_DOC
|
|
!
|
|
! routine returning the eigenvalues and left/right eigenvectors of the TC fock matrix
|
|
!
|
|
END_DOC
|
|
|
|
implicit none
|
|
|
|
integer, intent(in) :: n
|
|
double precision, intent(in) :: A(n,n)
|
|
integer, intent(out) :: n_real_eigv
|
|
double precision, intent(out) :: reigvec(n,n), leigvec(n,n), eigval(n)
|
|
double precision, allocatable :: reigvec_tmp(:,:), leigvec_tmp(:,:)
|
|
|
|
integer :: i, j, n_degen,k , iteration
|
|
double precision :: shift_current
|
|
double precision :: r,thr,accu_d, accu_nd
|
|
integer, allocatable :: iorder_origin(:),iorder(:)
|
|
double precision, allocatable :: WR(:), WI(:), Vl(:,:), VR(:,:),S(:,:)
|
|
double precision, allocatable :: Aw(:,:),diag_elem(:),A_save(:,:)
|
|
double precision, allocatable :: im_part(:),re_part(:)
|
|
double precision :: accu,thr_cut
|
|
double precision, allocatable :: S_nh_inv_half(:,:)
|
|
logical :: complex_root
|
|
double precision :: thr_norm=1d0
|
|
|
|
|
|
thr_cut = 1.d-15
|
|
print*,'Computing the left/right eigenvectors ...'
|
|
print*,'Using the degeneracy splitting algorithm'
|
|
! initialization
|
|
shift_current = 1.d-15
|
|
iteration = 0
|
|
print*,'***** iteration = ',iteration
|
|
|
|
|
|
! pre-processing the matrix :: sorting by diagonal elements
|
|
allocate(reigvec_tmp(n,n), leigvec_tmp(n,n))
|
|
allocate(diag_elem(n),iorder_origin(n),A_save(n,n))
|
|
! print*,'Aw'
|
|
do i = 1, n
|
|
iorder_origin(i) = i
|
|
diag_elem(i) = A(i,i)
|
|
! write(*,'(100(F16.10,X))')A(:,i)
|
|
enddo
|
|
call dsort(diag_elem, iorder_origin, n)
|
|
do i = 1, n
|
|
do j = 1, n
|
|
A_save(j,i) = A(iorder_origin(j),iorder_origin(i))
|
|
enddo
|
|
enddo
|
|
|
|
allocate(WR(n), WI(n), VL(n,n), VR(n,n), Aw(n,n))
|
|
allocate(im_part(n),iorder(n))
|
|
allocate( S(n,n) )
|
|
allocate(S_nh_inv_half(n,n))
|
|
|
|
|
|
Aw = A_save
|
|
call cancel_small_elmts(aw,n,thr_cut)
|
|
call lapack_diag_non_sym(n,Aw,WR,WI,VL,VR)
|
|
do i = 1, n
|
|
im_part(i) = -dabs(WI(i))
|
|
iorder(i) = i
|
|
enddo
|
|
call dsort(im_part, iorder, n)
|
|
n_real_eigv = 0
|
|
do i = 1, n
|
|
if(dabs(WI(i)).lt.1.d-20)then
|
|
n_real_eigv += 1
|
|
else
|
|
! print*,'Found an imaginary component to eigenvalue'
|
|
! print*,'Re(i) + Im(i)',WR(i),WI(i)
|
|
endif
|
|
enddo
|
|
if(n_real_eigv.ne.n)then
|
|
shift_current = max(10.d0 * dabs(im_part(1)),shift_current*10.d0)
|
|
print*,'Largest imaginary part found in eigenvalues = ',im_part(1)
|
|
print*,'Splitting the degeneracies by ',shift_current
|
|
else
|
|
print*,'All eigenvalues are real !'
|
|
endif
|
|
|
|
|
|
do while(n_real_eigv.ne.n)
|
|
iteration += 1
|
|
print*,'***** iteration = ',iteration
|
|
if(shift_current.gt.1.d-3)then
|
|
print*,'shift_current > 1.d-3 !!'
|
|
print*,'Your matrix intrinsically contains complex eigenvalues'
|
|
stop
|
|
endif
|
|
Aw = A_save
|
|
! thr_cut = shift_current
|
|
call cancel_small_elmts(Aw,n,thr_cut)
|
|
call split_matrix_degen(Aw,n,shift_current)
|
|
call lapack_diag_non_sym(n,Aw,WR,WI,VL,VR)
|
|
n_real_eigv = 0
|
|
do i = 1, n
|
|
if(dabs(WI(i)).lt.1.d-20)then
|
|
n_real_eigv+= 1
|
|
else
|
|
! print*,'Found an imaginary component to eigenvalue'
|
|
! print*,'Re(i) + Im(i)',WR(i),WI(i)
|
|
endif
|
|
enddo
|
|
if(n_real_eigv.ne.n)then
|
|
do i = 1, n
|
|
im_part(i) = -dabs(WI(i))
|
|
iorder(i) = i
|
|
enddo
|
|
call dsort(im_part, iorder, n)
|
|
shift_current = max(10.d0 * dabs(im_part(1)),shift_current*10.d0)
|
|
print*,'Largest imaginary part found in eigenvalues = ',im_part(1)
|
|
print*,'Splitting the degeneracies by ',shift_current
|
|
else
|
|
print*,'All eigenvalues are real !'
|
|
endif
|
|
enddo
|
|
!!!!!!!!!!!!!!!! SORTING THE EIGENVALUES
|
|
do i = 1, n
|
|
eigval(i) = WR(i)
|
|
iorder(i) = i
|
|
enddo
|
|
call dsort(eigval,iorder,n)
|
|
do i = 1, n
|
|
! print*,'eigval(i) = ',eigval(i)
|
|
reigvec_tmp(:,i) = VR(:,iorder(i))
|
|
leigvec_tmp(:,i) = Vl(:,iorder(i))
|
|
enddo
|
|
|
|
!!! ONCE ALL EIGENVALUES ARE REAL ::: CHECK BI-ORTHONORMALITY
|
|
! check bi-orthogonality
|
|
call check_biorthog(n, n, leigvec_tmp, reigvec_tmp, accu_d, accu_nd, S, thresh_biorthog_diag, thresh_biorthog_nondiag, .false.)
|
|
print *, ' accu_nd bi-orthog = ', accu_nd
|
|
if(accu_nd .lt. thresh_biorthog_nondiag) then
|
|
print *, ' bi-orthogonality: ok'
|
|
else
|
|
print *, ' '
|
|
print *, ' bi-orthogonality: not imposed yet'
|
|
print *, ' '
|
|
print *, ' '
|
|
print *, ' Using impose_unique_biorthog_degen_eigvec'
|
|
print *, ' '
|
|
! bi-orthonormalization using orthogonalization of left, right and then QR between left and right
|
|
call impose_unique_biorthog_degen_eigvec(n, eigval, mo_coef, leigvec_tmp, reigvec_tmp)
|
|
call check_biorthog(n, n, leigvec_tmp, reigvec_tmp, accu_d, accu_nd, S, thresh_biorthog_diag, thresh_biorthog_nondiag, .false.)
|
|
print*,'accu_nd = ',accu_nd
|
|
if(accu_nd .lt. thresh_biorthog_nondiag) then
|
|
print *, ' bi-orthogonality: ok'
|
|
else
|
|
print*,'New vectors not bi-orthonormals at ',accu_nd
|
|
call get_inv_half_nonsymmat_diago(S, n, S_nh_inv_half,complex_root)
|
|
if(complex_root)then
|
|
print*,'S^{-1/2} does not exits, using QR bi-orthogonalization'
|
|
call impose_biorthog_qr(n, n, leigvec_tmp, reigvec_tmp, S) ! bi-orthonormalization using QR
|
|
else
|
|
print*,'S^{-1/2} exists !!'
|
|
call bi_ortho_s_inv_half(n,leigvec_tmp,reigvec_tmp,S_nh_inv_half) ! use of S^{-1/2} bi-orthonormalization
|
|
endif
|
|
endif
|
|
call check_biorthog(n, n, leigvec_tmp, reigvec_tmp, accu_d, accu_nd, S, thresh_biorthog_diag, thresh_biorthog_nondiag, .false.)
|
|
if(accu_nd .lt. thresh_biorthog_nondiag) then
|
|
print *, ' bi-orthogonality: ok'
|
|
else
|
|
print*,'New vectors not bi-orthonormals at ',accu_nd
|
|
print*,'Must be a deep problem ...'
|
|
stop
|
|
endif
|
|
endif
|
|
|
|
!! EIGENVECTORS SORTED AND BI-ORTHONORMAL
|
|
do i = 1, n
|
|
do j = 1, n
|
|
VR(iorder_origin(j),i) = reigvec_tmp(j,i)
|
|
VL(iorder_origin(j),i) = leigvec_tmp(j,i)
|
|
enddo
|
|
enddo
|
|
|
|
!! RECOMPUTING THE EIGENVALUES
|
|
eigval = 0.d0
|
|
do i = 1, n
|
|
iorder(i) = i
|
|
accu = 0.d0
|
|
do j = 1, n
|
|
accu += VL(j,i) * VR(j,i)
|
|
do k = 1, n
|
|
eigval(i) += VL(j,i) * A(j,k) * VR(k,i)
|
|
enddo
|
|
enddo
|
|
eigval(i) *= 1.d0/accu
|
|
! print*,'eigval(i) = ',eigval(i)
|
|
enddo
|
|
!! RESORT JUST TO BE SURE
|
|
call dsort(eigval, iorder, n)
|
|
do i = 1, n
|
|
do j = 1, n
|
|
reigvec(j,i) = VR(j,iorder(i))
|
|
leigvec(j,i) = VL(j,iorder(i))
|
|
enddo
|
|
enddo
|
|
print*,'Checking for final reigvec/leigvec'
|
|
shift_current = max(1.d-10,shift_current)
|
|
print*,'Thr for eigenvectors = ',shift_current
|
|
call check_EIGVEC(n, n, A, eigval, leigvec, reigvec, shift_current, thr_norm, .false.)
|
|
call check_biorthog(n, n, leigvec, reigvec, accu_d, accu_nd, S, thresh_biorthog_diag, thresh_biorthog_nondiag, .false.)
|
|
print *, ' accu_nd bi-orthog = ', accu_nd
|
|
|
|
if(accu_nd .lt. thresh_biorthog_nondiag) then
|
|
print *, ' bi-orthogonality: ok'
|
|
else
|
|
print*,'Something went wrong in non_hrmt_diag_split_degen_bi_orthog'
|
|
print*,'Eigenvectors are not bi orthonormal ..'
|
|
print*,'accu_nd = ',accu_nd
|
|
stop
|
|
endif
|
|
|
|
end
|
|
|
|
|