mirror of
https://github.com/pfloos/quack
synced 2024-09-01 09:03:44 +02:00
added non-sym diag with biorthog condition
This commit is contained in:
parent
08bf6632df
commit
eb6e0bcc02
134
src/LR/ppLR.f90
134
src/LR/ppLR.f90
@ -1,93 +1,123 @@
|
|||||||
subroutine ppLR(TDA,nOO,nVV,Bpp,Cpp,Dpp,Om1,X1,Y1,Om2,X2,Y2,EcRPA)
|
|
||||||
|
|
||||||
! Solve the pp-RPA linear eigenvalue problem
|
! ---
|
||||||
|
|
||||||
|
subroutine ppLR(TDA, nOO, nVV, Bpp, Cpp, Dpp, Om1, X1, Y1, Om2, X2, Y2, EcRPA)
|
||||||
|
|
||||||
|
!
|
||||||
|
! Solve the pp-RPA linear eigenvalue problem
|
||||||
|
!
|
||||||
|
! right eigen-problem: H R = R w
|
||||||
|
! left eigen-problem: H.T L = L w
|
||||||
|
!
|
||||||
|
! where L.T R = 1
|
||||||
|
!
|
||||||
|
!
|
||||||
|
! (+C +B)
|
||||||
|
! H = ( ) where C = C.T and D = D.T
|
||||||
|
! (-B.T -D)
|
||||||
|
!
|
||||||
|
! (w1 0) (X1 X2) (+X1 +X2)
|
||||||
|
! w = ( ), R = ( ) and L = ( )
|
||||||
|
! (0 w2) (Y1 Y2) (-Y1 -Y2)
|
||||||
|
!
|
||||||
|
!
|
||||||
|
! the normalisation condition reduces to
|
||||||
|
!
|
||||||
|
! X1.T X2 - Y1.T Y2 = 0
|
||||||
|
! X1.T X1 - Y1.T Y1 = 1
|
||||||
|
! X2.T X2 - Y2.T Y2 = 1
|
||||||
|
!
|
||||||
|
|
||||||
implicit none
|
implicit none
|
||||||
include 'parameters.h'
|
include 'parameters.h'
|
||||||
|
|
||||||
! Input variables
|
logical, intent(in) :: TDA
|
||||||
|
integer, intent(in) :: nOO, nVV
|
||||||
|
double precision, intent(in) :: Bpp(nVV,nOO), Cpp(nVV,nVV), Dpp(nOO,nOO)
|
||||||
|
double precision, intent(out) :: Om1(nVV), X1(nVV,nVV), Y1(nOO,nVV)
|
||||||
|
double precision, intent(out) :: Om2(nOO), X2(nVV,nOO), Y2(nOO,nOO)
|
||||||
|
double precision, intent(out) :: EcRPA
|
||||||
|
|
||||||
logical,intent(in) :: TDA
|
logical :: imp_bio, verbose
|
||||||
integer,intent(in) :: nOO
|
integer :: i, j, N
|
||||||
integer,intent(in) :: nVV
|
double precision :: EcRPA1, EcRPA2
|
||||||
double precision,intent(in) :: Bpp(nVV,nOO)
|
double precision :: thr_d, thr_nd, thr_deg
|
||||||
double precision,intent(in) :: Cpp(nVV,nVV)
|
double precision,allocatable :: M(:,:), Z(:,:), Om(:)
|
||||||
double precision,intent(in) :: Dpp(nOO,nOO)
|
|
||||||
|
|
||||||
! Local variables
|
double precision, external :: trace_matrix
|
||||||
|
|
||||||
double precision :: trace_matrix
|
|
||||||
double precision :: EcRPA1
|
|
||||||
double precision :: EcRPA2
|
|
||||||
double precision,allocatable :: M(:,:)
|
|
||||||
double precision,allocatable :: Z(:,:)
|
|
||||||
double precision,allocatable :: Om(:)
|
|
||||||
|
|
||||||
! Output variables
|
|
||||||
|
|
||||||
double precision,intent(out) :: Om1(nVV)
|
N = nOO + nVV
|
||||||
double precision,intent(out) :: X1(nVV,nVV)
|
|
||||||
double precision,intent(out) :: Y1(nOO,nVV)
|
|
||||||
double precision,intent(out) :: Om2(nOO)
|
|
||||||
double precision,intent(out) :: X2(nVV,nOO)
|
|
||||||
double precision,intent(out) :: Y2(nOO,nOO)
|
|
||||||
double precision,intent(out) :: EcRPA
|
|
||||||
|
|
||||||
! Memory allocation
|
allocate(M(N,N), Z(N,N), Om(N))
|
||||||
|
|
||||||
allocate(M(nOO+nVV,nOO+nVV),Z(nOO+nVV,nOO+nVV),Om(nOO+nVV))
|
|
||||||
|
|
||||||
!-------------------------------------------------!
|
|
||||||
! Solve the p-p eigenproblem !
|
|
||||||
!-------------------------------------------------!
|
|
||||||
! !
|
|
||||||
! | C B | | X1 X2 | | w1 0 | | X1 X2 | !
|
|
||||||
! | | | | = | | | | !
|
|
||||||
! | -Bt -D | | Y1 Y2 | | 0 w2 | | Y1 Y2 | !
|
|
||||||
! !
|
|
||||||
!-------------------------------------------------!
|
|
||||||
|
|
||||||
if(TDA) then
|
if(TDA) then
|
||||||
|
|
||||||
X1(:,:) = +Cpp(:,:)
|
X1(:,:) = +Cpp(:,:)
|
||||||
Y1(:,:) = 0d0
|
Y1(:,:) = 0d0
|
||||||
if(nVV > 0) call diagonalize_matrix(nVV,X1,Om1)
|
if(nVV > 0) call diagonalize_matrix(nVV, X1, Om1)
|
||||||
|
|
||||||
X2(:,:) = 0d0
|
X2(:,:) = 0d0
|
||||||
Y2(:,:) = -Dpp(:,:)
|
Y2(:,:) = -Dpp(:,:)
|
||||||
if(nOO > 0) call diagonalize_matrix(nOO,Y2,Om2)
|
if(nOO > 0) call diagonalize_matrix(nOO, Y2, Om2)
|
||||||
|
|
||||||
else
|
else
|
||||||
|
|
||||||
! Diagonal blocks
|
! Diagonal blocks
|
||||||
|
|
||||||
M( 1:nVV , 1:nVV) = + Cpp(1:nVV,1:nVV)
|
M( 1:nVV , 1:nVV) = + Cpp(1:nVV,1:nVV)
|
||||||
M(nVV+1:nVV+nOO,nVV+1:nVV+nOO) = - Dpp(1:nOO,1:nOO)
|
M(nVV+1:nVV+nOO,nVV+1:nVV+nOO) = - Dpp(1:nOO,1:nOO)
|
||||||
|
|
||||||
! Off-diagonal blocks
|
! Off-diagonal blocks
|
||||||
|
|
||||||
M( 1:nVV ,nVV+1:nOO+nVV) = - Bpp(1:nVV,1:nOO)
|
M( 1:nVV ,nVV+1:nOO+nVV) = - Bpp(1:nVV,1:nOO)
|
||||||
M(nVV+1:nOO+nVV, 1:nVV) = + transpose(Bpp(1:nVV,1:nOO))
|
M(nVV+1:nOO+nVV, 1:nVV) = + transpose(Bpp(1:nVV,1:nOO))
|
||||||
|
|
||||||
! call matout(nOO,nOO,Dpp)
|
!! Diagonalize the p-p matrix
|
||||||
|
!if(nOO+nVV > 0) call diagonalize_general_matrix(nOO+nVV, M, Om, Z)
|
||||||
|
!! Split the various quantities in p-p and h-h parts
|
||||||
|
!call sort_ppRPA(nOO, nVV, Om, Z, Om1, X1, Y1, Om2, X2, Y2)
|
||||||
|
|
||||||
! Diagonalize the p-p matrix
|
|
||||||
|
|
||||||
if(nOO+nVV > 0) call diagonalize_general_matrix(nOO+nVV,M,Om,Z)
|
thr_d = 1d-6 ! to determine if diagonal elements of L.T x R are close enouph to 1
|
||||||
|
thr_nd = 1d-6 ! to determine if non-diagonal elements of L.T x R are close enouph to 1
|
||||||
|
thr_deg = 1d-8 ! to determine if two eigenvectors are degenerate or not
|
||||||
|
imp_bio = .True. ! impose bi-orthogonality
|
||||||
|
verbose = .False.
|
||||||
|
call diagonalize_nonsym_matrix(N, M, Z, Om, thr_d, thr_nd, thr_deg, imp_bio, verbose)
|
||||||
|
|
||||||
! Split the various quantities in p-p and h-h parts
|
do i = 1, nOO
|
||||||
|
Om2(i) = Om(i)
|
||||||
|
do j = 1, nVV
|
||||||
|
X2(j,i) = Z(j,i)
|
||||||
|
enddo
|
||||||
|
do j = 1, nOO
|
||||||
|
Y2(j,i) = Z(nVV+j,i)
|
||||||
|
enddo
|
||||||
|
enddo
|
||||||
|
|
||||||
call sort_ppRPA(nOO,nVV,Om,Z,Om1,X1,Y1,Om2,X2,Y2)
|
do i = 1, nVV
|
||||||
|
Om1(i) = Om(nOO+i)
|
||||||
|
do j = 1, nVV
|
||||||
|
X1(j,i) = M(j,nOO+i)
|
||||||
|
enddo
|
||||||
|
do j = 1, nOO
|
||||||
|
Y1(j,i) = M(nVV+j,nOO+i)
|
||||||
|
enddo
|
||||||
|
enddo
|
||||||
|
|
||||||
end if
|
end if
|
||||||
|
|
||||||
! Compute the RPA correlation energy
|
! Compute the RPA correlation energy
|
||||||
|
EcRPA = 0.5d0 * (sum(Om1) - sum(Om2) - trace_matrix(nVV, Cpp) - trace_matrix(nOO, Dpp))
|
||||||
|
EcRPA1 = +sum(Om1) - trace_matrix(nVV, Cpp)
|
||||||
|
EcRPA2 = -sum(Om2) - trace_matrix(nOO, Dpp)
|
||||||
|
|
||||||
EcRPA = 0.5d0*( sum(Om1) - sum(Om2) - trace_matrix(nVV,Cpp) - trace_matrix(nOO,Dpp) )
|
if(abs(EcRPA - EcRPA1) > 1d-6 .or. abs(EcRPA - EcRPA2) > 1d-6) then
|
||||||
EcRPA1 = +sum(Om1) - trace_matrix(nVV,Cpp)
|
|
||||||
EcRPA2 = -sum(Om2) - trace_matrix(nOO,Dpp)
|
|
||||||
|
|
||||||
if(abs(EcRPA - EcRPA1) > 1d-6 .or. abs(EcRPA - EcRPA2) > 1d-6) &
|
|
||||||
print*,'!!! Issue in pp-RPA linear reponse calculation RPA1 != RPA2 !!!'
|
print*,'!!! Issue in pp-RPA linear reponse calculation RPA1 != RPA2 !!!'
|
||||||
|
endif
|
||||||
|
|
||||||
|
deallocate(M, Z, Om)
|
||||||
|
|
||||||
end subroutine
|
end subroutine
|
||||||
|
|
||||||
|
|
||||||
|
@ -89,8 +89,8 @@ FIX_ORDER_OF_LIBS=-Wl,--start-group
|
|||||||
|
|
||||||
if sys.platform in ["linux", "linux2"]:
|
if sys.platform in ["linux", "linux2"]:
|
||||||
# compiler = compile_gfortran_linux
|
# compiler = compile_gfortran_linux
|
||||||
# compiler = compile_ifort_linux
|
compiler = compile_ifort_linux
|
||||||
compiler = compile_olympe
|
# compiler = compile_olympe
|
||||||
elif sys.platform == "darwin":
|
elif sys.platform == "darwin":
|
||||||
compiler = compile_gfortran_mac
|
compiler = compile_gfortran_mac
|
||||||
else:
|
else:
|
||||||
|
571
src/utils/non_sym_diag.f90
Normal file
571
src/utils/non_sym_diag.f90
Normal file
@ -0,0 +1,571 @@
|
|||||||
|
|
||||||
|
! ---
|
||||||
|
|
||||||
|
subroutine diagonalize_nonsym_matrix(N, A, L, e_re, thr_d, thr_nd, thr_deg, imp_bio, verbose)
|
||||||
|
|
||||||
|
! Diagonalize a non-symmetric matrix
|
||||||
|
!
|
||||||
|
! Output
|
||||||
|
! right-eigenvectors are saved in A
|
||||||
|
! left-eigenvectors are saved in L
|
||||||
|
! eigenvalues are saved in e = e_re + i e_im
|
||||||
|
|
||||||
|
implicit none
|
||||||
|
|
||||||
|
integer, intent(in) :: N
|
||||||
|
logical, intent(in) :: imp_bio, verbose
|
||||||
|
double precision, intent(in) :: thr_d, thr_nd, thr_deg
|
||||||
|
double precision, intent(inout) :: A(N,N)
|
||||||
|
double precision, intent(out) :: e_re(N), L(N,N)
|
||||||
|
|
||||||
|
integer :: i, j, ii
|
||||||
|
integer :: lwork, info
|
||||||
|
double precision :: accu_d, accu_nd
|
||||||
|
integer, allocatable :: iorder(:), deg_num(:)
|
||||||
|
double precision, allocatable :: Atmp(:,:), Ltmp(:,:), work(:), e_im(:)
|
||||||
|
double precision, allocatable :: S(:,:)
|
||||||
|
|
||||||
|
if(verbose) then
|
||||||
|
print*, ' Starting a non-Hermitian diagonalization ...'
|
||||||
|
print*, ' Good Luck ;)'
|
||||||
|
print*, ' imp_bio = ', imp_bio
|
||||||
|
endif
|
||||||
|
|
||||||
|
! ---
|
||||||
|
! diagonalize
|
||||||
|
|
||||||
|
allocate(Atmp(N,N), e_im(N))
|
||||||
|
Atmp(1:N,1:N) = A(1:N,1:N)
|
||||||
|
|
||||||
|
allocate(work(1))
|
||||||
|
lwork = -1
|
||||||
|
call dgeev('V', 'V', N, Atmp, N, e_re, e_im, L, N, A, N, work, lwork, info)
|
||||||
|
if(info .gt. 0) then
|
||||||
|
print*,'dgeev failed !!', info
|
||||||
|
stop
|
||||||
|
endif
|
||||||
|
|
||||||
|
lwork = max(int(work(1)), 1)
|
||||||
|
deallocate(work)
|
||||||
|
allocate(work(lwork))
|
||||||
|
|
||||||
|
call dgeev('V', 'V', N, Atmp, N, e_re, e_im, L, N, A, N, work, lwork, info)
|
||||||
|
if(info .ne. 0) then
|
||||||
|
print*,'dgeev failed !!', info
|
||||||
|
stop
|
||||||
|
endif
|
||||||
|
|
||||||
|
deallocate(Atmp, WORK)
|
||||||
|
|
||||||
|
|
||||||
|
! ---
|
||||||
|
! check if eigenvalues are real
|
||||||
|
|
||||||
|
i = 1
|
||||||
|
ii = 0
|
||||||
|
do while(i .le. N)
|
||||||
|
if(dabs(e_im(i)) .gt. 1.d-12) then
|
||||||
|
ii = ii + 1
|
||||||
|
if(verbose) then
|
||||||
|
print*, ' Warning: complex eigenvalue !'
|
||||||
|
print*, i, e_re(i), e_im(i)
|
||||||
|
if(dabs(e_im(i)/e_re(i)) .lt. 1.d-6) then
|
||||||
|
print*, ' small enouph to be igored'
|
||||||
|
else
|
||||||
|
print*, ' IMAGINARY PART IS SIGNIFANT !!!'
|
||||||
|
endif
|
||||||
|
endif
|
||||||
|
endif
|
||||||
|
i = i + 1
|
||||||
|
enddo
|
||||||
|
|
||||||
|
if(verbose) then
|
||||||
|
if(ii .eq. 0) print*, ' congratulations :) eigenvalues are real-valued !!'
|
||||||
|
endif
|
||||||
|
|
||||||
|
|
||||||
|
! ---
|
||||||
|
! track & sort the real eigenvalues
|
||||||
|
|
||||||
|
allocate(Atmp(N,N), Ltmp(N,N), iorder(N))
|
||||||
|
|
||||||
|
do i = 1, N
|
||||||
|
iorder(i) = i
|
||||||
|
enddo
|
||||||
|
call quick_sort(e_re, iorder, N)
|
||||||
|
|
||||||
|
Atmp(:,:) = A(:,:)
|
||||||
|
Ltmp(:,:) = L(:,:)
|
||||||
|
do i = 1, N
|
||||||
|
do j = 1, N
|
||||||
|
A(j,i) = Atmp(j,iorder(i))
|
||||||
|
L(j,i) = Ltmp(j,iorder(i))
|
||||||
|
enddo
|
||||||
|
enddo
|
||||||
|
|
||||||
|
deallocate(Atmp, Ltmp, iorder)
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
! ---
|
||||||
|
! check bi-orthog
|
||||||
|
|
||||||
|
allocate(S(N,N))
|
||||||
|
call check_biorthog(N, N, L, A, accu_d, accu_nd, S, thr_d, thr_nd, .false., verbose)
|
||||||
|
|
||||||
|
if((accu_nd .lt. thr_nd) .and. (dabs(accu_d-dble(N))/dble(N) .lt. thr_d)) then
|
||||||
|
|
||||||
|
if(verbose) then
|
||||||
|
print *, ' lapack vectors are normalized and bi-orthogonalized'
|
||||||
|
endif
|
||||||
|
|
||||||
|
elseif((accu_nd .lt. thr_nd) .and. (dabs(accu_d - dble(N)) .gt. thr_d)) then
|
||||||
|
|
||||||
|
if(verbose) then
|
||||||
|
print *, ' lapack vectors are not normalized but bi-orthogonalized'
|
||||||
|
endif
|
||||||
|
|
||||||
|
call check_biorthog_binormalize(N, N, L, A, thr_d, thr_nd, .true.)
|
||||||
|
call check_biorthog(N, N, L, A, accu_d, accu_nd, S, thr_d, thr_nd, .true., verbose)
|
||||||
|
|
||||||
|
else
|
||||||
|
|
||||||
|
if(verbose) then
|
||||||
|
print *, ' lapack vectors are not normalized neither bi-orthogonalized'
|
||||||
|
endif
|
||||||
|
|
||||||
|
allocate(deg_num(N))
|
||||||
|
call reorder_degen_eigvec(N, thr_deg, deg_num, e_re, L, A)
|
||||||
|
call impose_biorthog_degen_eigvec(N, deg_num, e_re, L, A)
|
||||||
|
deallocate(deg_num)
|
||||||
|
|
||||||
|
call check_biorthog(N, N, L, A, accu_d, accu_nd, S, thr_d, thr_nd, .false., verbose)
|
||||||
|
if((accu_nd .lt. thr_nd) .and. (dabs(accu_d-dble(N))/dble(N) .lt. thr_d)) then
|
||||||
|
if(verbose) then
|
||||||
|
print *, ' lapack vectors are now normalized and bi-orthogonalized'
|
||||||
|
endif
|
||||||
|
elseif((accu_nd .lt. thr_nd) .and. (dabs(accu_d - dble(N)) .gt. thr_d)) then
|
||||||
|
if(verbose) then
|
||||||
|
print *, ' lapack vectors are now not normalized but bi-orthogonalized'
|
||||||
|
endif
|
||||||
|
call check_biorthog_binormalize(N, N, L, A, thr_d, thr_nd, .true.)
|
||||||
|
call check_biorthog(N, N, L, A, accu_d, accu_nd, S, thr_d, thr_nd, .true., verbose)
|
||||||
|
else
|
||||||
|
if(verbose) then
|
||||||
|
print*, ' bi-orthogonalization failed !'
|
||||||
|
endif
|
||||||
|
if(imp_bio) then
|
||||||
|
print*, ' bi-orthogonalization failed !'
|
||||||
|
deallocate(S)
|
||||||
|
stop
|
||||||
|
endif
|
||||||
|
endif
|
||||||
|
|
||||||
|
endif
|
||||||
|
|
||||||
|
deallocate(S)
|
||||||
|
return
|
||||||
|
|
||||||
|
end
|
||||||
|
|
||||||
|
! ---
|
||||||
|
|
||||||
|
subroutine check_biorthog(n, m, Vl, Vr, accu_d, accu_nd, S, thr_d, thr_nd, stop_ifnot, verbose)
|
||||||
|
|
||||||
|
implicit none
|
||||||
|
|
||||||
|
integer, intent(in) :: n, m
|
||||||
|
logical, intent(in) :: stop_ifnot, verbose
|
||||||
|
double precision, intent(in) :: Vl(n,m), Vr(n,m)
|
||||||
|
double precision, intent(in) :: thr_d, thr_nd
|
||||||
|
double precision, intent(out) :: accu_d, accu_nd, S(m,m)
|
||||||
|
|
||||||
|
integer :: i, j
|
||||||
|
double precision, allocatable :: SS(:,:)
|
||||||
|
|
||||||
|
if(verbose) then
|
||||||
|
print *, ' check bi-orthogonality'
|
||||||
|
endif
|
||||||
|
|
||||||
|
! ---
|
||||||
|
|
||||||
|
call dgemm( 'T', 'N', m, m, n, 1.d0 &
|
||||||
|
, Vl, size(Vl, 1), Vr, size(Vr, 1) &
|
||||||
|
, 0.d0, S, size(S, 1) )
|
||||||
|
|
||||||
|
accu_d = 0.d0
|
||||||
|
accu_nd = 0.d0
|
||||||
|
do i = 1, m
|
||||||
|
do j = 1, m
|
||||||
|
if(i==j) then
|
||||||
|
accu_d = accu_d + dabs(S(i,i))
|
||||||
|
else
|
||||||
|
accu_nd = accu_nd + S(j,i) * S(j,i)
|
||||||
|
endif
|
||||||
|
enddo
|
||||||
|
enddo
|
||||||
|
accu_nd = dsqrt(accu_nd) / dble(m)
|
||||||
|
|
||||||
|
if(verbose) then
|
||||||
|
if((accu_nd .gt. thr_nd) .or. dabs(accu_d-dble(m))/dble(m) .gt. thr_d) then
|
||||||
|
print *, ' non bi-orthogonal vectors !'
|
||||||
|
print *, ' accu_nd = ', accu_nd
|
||||||
|
print *, ' accu_d = ', dabs(accu_d-dble(m))/dble(m)
|
||||||
|
else
|
||||||
|
print *, ' vectors are bi-orthogonals'
|
||||||
|
endif
|
||||||
|
endif
|
||||||
|
|
||||||
|
! ---
|
||||||
|
|
||||||
|
if(stop_ifnot .and. ((accu_nd .gt. thr_nd) .or. dabs(accu_d-dble(m))/dble(m) .gt. thr_d)) then
|
||||||
|
print *, ' non bi-orthogonal vectors !'
|
||||||
|
print *, ' accu_nd = ', accu_nd
|
||||||
|
print *, ' accu_d = ', dabs(accu_d-dble(m))/dble(m)
|
||||||
|
stop
|
||||||
|
endif
|
||||||
|
|
||||||
|
end
|
||||||
|
|
||||||
|
! ---
|
||||||
|
|
||||||
|
subroutine check_biorthog_binormalize(n, m, Vl, Vr, thr_d, thr_nd, stop_ifnot)
|
||||||
|
|
||||||
|
implicit none
|
||||||
|
|
||||||
|
integer, intent(in) :: n, m
|
||||||
|
logical, intent(in) :: stop_ifnot
|
||||||
|
double precision, intent(in) :: thr_d, thr_nd
|
||||||
|
double precision, intent(inout) :: Vl(n,m), Vr(n,m)
|
||||||
|
|
||||||
|
integer :: i, j
|
||||||
|
double precision :: accu_d, accu_nd, s_tmp
|
||||||
|
double precision, allocatable :: S(:,:)
|
||||||
|
|
||||||
|
! ---
|
||||||
|
|
||||||
|
allocate(S(m,m))
|
||||||
|
call dgemm( 'T', 'N', m, m, n, 1.d0 &
|
||||||
|
, Vl, size(Vl, 1), Vr, size(Vr, 1) &
|
||||||
|
, 0.d0, S, size(S, 1) )
|
||||||
|
|
||||||
|
do i = 1, m
|
||||||
|
if(S(i,i) .lt. 0.d0) then
|
||||||
|
do j = 1, n
|
||||||
|
Vl(j,i) = -1.d0 * Vl(j,i)
|
||||||
|
enddo
|
||||||
|
S(i,i) = -S(i,i)
|
||||||
|
endif
|
||||||
|
enddo
|
||||||
|
|
||||||
|
accu_d = 0.d0
|
||||||
|
accu_nd = 0.d0
|
||||||
|
do i = 1, m
|
||||||
|
do j = 1, m
|
||||||
|
if(i==j) then
|
||||||
|
accu_d = accu_d + S(i,i)
|
||||||
|
else
|
||||||
|
accu_nd = accu_nd + S(j,i) * S(j,i)
|
||||||
|
endif
|
||||||
|
enddo
|
||||||
|
enddo
|
||||||
|
accu_nd = dsqrt(accu_nd) / dble(m)
|
||||||
|
|
||||||
|
! ---
|
||||||
|
|
||||||
|
if( (accu_nd .lt. thr_nd) .and. (dabs(accu_d-dble(m))/dble(m) .gt. thr_d) ) then
|
||||||
|
|
||||||
|
do i = 1, m
|
||||||
|
if(S(i,i) <= 0.d0) then
|
||||||
|
print *, ' overap negative'
|
||||||
|
print *, i, S(i,i)
|
||||||
|
exit
|
||||||
|
endif
|
||||||
|
if(dabs(S(i,i) - 1.d0) .gt. thr_d) then
|
||||||
|
s_tmp = 1.d0 / dsqrt(S(i,i))
|
||||||
|
do j = 1, n
|
||||||
|
Vl(j,i) = Vl(j,i) * s_tmp
|
||||||
|
Vr(j,i) = Vr(j,i) * s_tmp
|
||||||
|
enddo
|
||||||
|
endif
|
||||||
|
|
||||||
|
enddo
|
||||||
|
|
||||||
|
endif
|
||||||
|
|
||||||
|
! ---
|
||||||
|
|
||||||
|
call dgemm( 'T', 'N', m, m, n, 1.d0 &
|
||||||
|
, Vl, size(Vl, 1), Vr, size(Vr, 1) &
|
||||||
|
, 0.d0, S, size(S, 1) )
|
||||||
|
|
||||||
|
accu_d = 0.d0
|
||||||
|
accu_nd = 0.d0
|
||||||
|
do i = 1, m
|
||||||
|
do j = 1, m
|
||||||
|
if(i==j) then
|
||||||
|
accu_d = accu_d + S(i,i)
|
||||||
|
else
|
||||||
|
accu_nd = accu_nd + S(j,i) * S(j,i)
|
||||||
|
endif
|
||||||
|
enddo
|
||||||
|
enddo
|
||||||
|
accu_nd = dsqrt(accu_nd) / dble(m)
|
||||||
|
|
||||||
|
deallocate(S)
|
||||||
|
|
||||||
|
! ---
|
||||||
|
|
||||||
|
if( stop_ifnot .and. ((accu_nd .gt. thr_nd) .or. (dabs(accu_d-dble(m))/dble(m) .gt. thr_d)) ) then
|
||||||
|
print *, accu_nd, thr_nd
|
||||||
|
print *, dabs(accu_d-dble(m))/dble(m), thr_d
|
||||||
|
print *, ' biorthog_binormalize failed !'
|
||||||
|
stop
|
||||||
|
endif
|
||||||
|
|
||||||
|
end
|
||||||
|
|
||||||
|
! ---
|
||||||
|
|
||||||
|
subroutine reorder_degen_eigvec(n, thr_deg, deg_num, e0, L0, R0)
|
||||||
|
|
||||||
|
implicit none
|
||||||
|
|
||||||
|
integer, intent(in) :: n
|
||||||
|
double precision, intent(in) :: thr_deg
|
||||||
|
double precision, intent(inout) :: e0(n), L0(n,n), R0(n,n)
|
||||||
|
integer, intent(out) :: deg_num(n)
|
||||||
|
|
||||||
|
logical :: complex_root
|
||||||
|
integer :: i, j, k, m, ii, j_tmp
|
||||||
|
double precision :: ei, ej, de
|
||||||
|
double precision :: accu_d, accu_nd
|
||||||
|
double precision :: e0_tmp, L0_tmp(n), R0_tmp(n)
|
||||||
|
double precision, allocatable :: L(:,:), R(:,:), S(:,:), S_inv_half(:,:)
|
||||||
|
|
||||||
|
do i = 1, n
|
||||||
|
deg_num(i) = 1
|
||||||
|
enddo
|
||||||
|
|
||||||
|
do i = 1, n-1
|
||||||
|
ei = e0(i)
|
||||||
|
|
||||||
|
! already considered in degen vectors
|
||||||
|
if(deg_num(i) .eq. 0) cycle
|
||||||
|
|
||||||
|
ii = 0
|
||||||
|
do j = i+1, n
|
||||||
|
ej = e0(j)
|
||||||
|
de = dabs(ei - ej)
|
||||||
|
|
||||||
|
if(de .lt. thr_deg) then
|
||||||
|
ii = ii + 1
|
||||||
|
|
||||||
|
j_tmp = i + ii
|
||||||
|
|
||||||
|
deg_num(j_tmp) = 0
|
||||||
|
|
||||||
|
e0_tmp = e0(j_tmp)
|
||||||
|
e0(j_tmp) = e0(j)
|
||||||
|
e0(j) = e0_tmp
|
||||||
|
|
||||||
|
L0_tmp(1:n) = L0(1:n,j_tmp)
|
||||||
|
L0(1:n,j_tmp) = L0(1:n,j)
|
||||||
|
L0(1:n,j) = L0_tmp(1:n)
|
||||||
|
|
||||||
|
R0_tmp(1:n) = R0(1:n,j_tmp)
|
||||||
|
R0(1:n,j_tmp) = R0(1:n,j)
|
||||||
|
R0(1:n,j) = R0_tmp(1:n)
|
||||||
|
endif
|
||||||
|
enddo
|
||||||
|
|
||||||
|
deg_num(i) = ii + 1
|
||||||
|
enddo
|
||||||
|
|
||||||
|
ii = 0
|
||||||
|
do i = 1, n
|
||||||
|
if(deg_num(i) .gt. 1) then
|
||||||
|
ii = ii + 1
|
||||||
|
endif
|
||||||
|
enddo
|
||||||
|
|
||||||
|
if(ii .eq. 0) then
|
||||||
|
print*, ' WARNING: bi-orthogonality is lost but there is no degeneracies'
|
||||||
|
print*, ' rotations may change energy'
|
||||||
|
stop
|
||||||
|
endif
|
||||||
|
|
||||||
|
end
|
||||||
|
|
||||||
|
! ---
|
||||||
|
|
||||||
|
subroutine impose_biorthog_degen_eigvec(n, deg_num, e0, L0, R0)
|
||||||
|
|
||||||
|
implicit none
|
||||||
|
|
||||||
|
integer, intent(in) :: n, deg_num(n)
|
||||||
|
double precision, intent(in) :: e0(n)
|
||||||
|
double precision, intent(inout) :: L0(n,n), R0(n,n)
|
||||||
|
|
||||||
|
logical :: complex_root
|
||||||
|
integer :: i, j, k, m
|
||||||
|
double precision :: ei, ej, de
|
||||||
|
double precision :: accu_d, accu_nd
|
||||||
|
double precision, allocatable :: L(:,:), R(:,:), S(:,:), S_inv_half(:,:)
|
||||||
|
|
||||||
|
!do i = 1, n
|
||||||
|
! if(deg_num(i) .gt. 1) then
|
||||||
|
! print *, ' degen on', i, deg_num(i), e0(i)
|
||||||
|
! endif
|
||||||
|
!enddo
|
||||||
|
|
||||||
|
! ---
|
||||||
|
|
||||||
|
do i = 1, n
|
||||||
|
m = deg_num(i)
|
||||||
|
|
||||||
|
if(m .gt. 1) then
|
||||||
|
|
||||||
|
allocate(L(n,m), R(n,m), S(m,m))
|
||||||
|
|
||||||
|
do j = 1, m
|
||||||
|
L(1:n,j) = L0(1:n,i+j-1)
|
||||||
|
R(1:n,j) = R0(1:n,i+j-1)
|
||||||
|
enddo
|
||||||
|
|
||||||
|
! ---
|
||||||
|
|
||||||
|
call dgemm( 'T', 'N', m, m, n, 1.d0 &
|
||||||
|
, L, size(L, 1), R, size(R, 1) &
|
||||||
|
, 0.d0, S, size(S, 1) )
|
||||||
|
|
||||||
|
accu_nd = 0.d0
|
||||||
|
do j = 1, m
|
||||||
|
do k = 1, m
|
||||||
|
if(j==k) cycle
|
||||||
|
accu_nd = accu_nd + dabs(S(j,k))
|
||||||
|
enddo
|
||||||
|
enddo
|
||||||
|
|
||||||
|
if(accu_nd .lt. 1d-12) then
|
||||||
|
deallocate(S, L, R)
|
||||||
|
cycle
|
||||||
|
endif
|
||||||
|
|
||||||
|
call impose_biorthog_svd(n, m, L, R)
|
||||||
|
|
||||||
|
call dgemm( 'T', 'N', m, m, n, 1.d0 &
|
||||||
|
, L, size(L, 1), R, size(R, 1) &
|
||||||
|
, 0.d0, S, size(S, 1) )
|
||||||
|
accu_nd = 0.d0
|
||||||
|
do j = 1, m
|
||||||
|
do k = 1, m
|
||||||
|
if(j==k) cycle
|
||||||
|
accu_nd = accu_nd + dabs(S(j,k))
|
||||||
|
enddo
|
||||||
|
enddo
|
||||||
|
if(accu_nd .gt. 1d-12) then
|
||||||
|
print*, ' accu_nd =', accu_nd
|
||||||
|
print*, ' your strategy for degenerates orbitals failed !'
|
||||||
|
print*, m, 'deg on', i
|
||||||
|
stop
|
||||||
|
endif
|
||||||
|
|
||||||
|
deallocate(S)
|
||||||
|
|
||||||
|
! ---
|
||||||
|
|
||||||
|
do j = 1, m
|
||||||
|
L0(1:n,i+j-1) = L(1:n,j)
|
||||||
|
R0(1:n,i+j-1) = R(1:n,j)
|
||||||
|
enddo
|
||||||
|
|
||||||
|
deallocate(L, R)
|
||||||
|
|
||||||
|
endif
|
||||||
|
enddo
|
||||||
|
|
||||||
|
end
|
||||||
|
|
||||||
|
! ---
|
||||||
|
|
||||||
|
subroutine impose_biorthog_svd(n, m, L, R)
|
||||||
|
|
||||||
|
implicit none
|
||||||
|
|
||||||
|
integer, intent(in) :: n, m
|
||||||
|
double precision, intent(inout) :: L(n,m), R(n,m)
|
||||||
|
|
||||||
|
integer :: i, j, num_linear_dependencies
|
||||||
|
double precision :: threshold
|
||||||
|
double precision, allocatable :: S(:,:), tmp(:,:)
|
||||||
|
double precision, allocatable :: U(:,:), V(:,:), Vt(:,:), D(:)
|
||||||
|
|
||||||
|
allocate(S(m,m))
|
||||||
|
|
||||||
|
call dgemm( 'T', 'N', m, m, n, 1.d0 &
|
||||||
|
, L, size(L, 1), R, size(R, 1) &
|
||||||
|
, 0.d0, S, size(S, 1) )
|
||||||
|
|
||||||
|
! ---
|
||||||
|
|
||||||
|
allocate(U(m,m), Vt(m,m), D(m))
|
||||||
|
|
||||||
|
call svd(S, m, U, m, D, Vt, m, m, m)
|
||||||
|
|
||||||
|
deallocate(S)
|
||||||
|
|
||||||
|
threshold = 1.d-6
|
||||||
|
num_linear_dependencies = 0
|
||||||
|
do i = 1, m
|
||||||
|
if(abs(D(i)) <= threshold) then
|
||||||
|
D(i) = 0.d0
|
||||||
|
num_linear_dependencies = num_linear_dependencies + 1
|
||||||
|
else
|
||||||
|
D(i) = 1.d0 / dsqrt(D(i))
|
||||||
|
endif
|
||||||
|
enddo
|
||||||
|
if(num_linear_dependencies > 0) then
|
||||||
|
write(*,*) ' linear dependencies = ', num_linear_dependencies
|
||||||
|
write(*,*) ' m = ', m
|
||||||
|
stop
|
||||||
|
endif
|
||||||
|
|
||||||
|
allocate(V(m,m))
|
||||||
|
do i = 1, m
|
||||||
|
do j = 1, m
|
||||||
|
V(j,i) = Vt(i,j)
|
||||||
|
enddo
|
||||||
|
enddo
|
||||||
|
deallocate(Vt)
|
||||||
|
|
||||||
|
! ---
|
||||||
|
|
||||||
|
! R <-- R x V x D^{-0.5}
|
||||||
|
! L <-- L x U x D^{-0.5}
|
||||||
|
|
||||||
|
do i = 1, m
|
||||||
|
do j = 1, m
|
||||||
|
V(j,i) = V(j,i) * D(i)
|
||||||
|
U(j,i) = U(j,i) * D(i)
|
||||||
|
enddo
|
||||||
|
enddo
|
||||||
|
|
||||||
|
allocate(tmp(n,m))
|
||||||
|
tmp(:,:) = R(:,:)
|
||||||
|
call dgemm( 'N', 'N', n, m, m, 1.d0 &
|
||||||
|
, tmp, size(tmp, 1), V, size(V, 1) &
|
||||||
|
, 0.d0, R, size(R, 1))
|
||||||
|
|
||||||
|
tmp(:,:) = L(:,:)
|
||||||
|
call dgemm( 'N', 'N', n, m, m, 1.d0 &
|
||||||
|
, tmp, size(tmp, 1), U, size(U, 1) &
|
||||||
|
, 0.d0, L, size(L, 1))
|
||||||
|
|
||||||
|
deallocate(tmp, U, V, D)
|
||||||
|
|
||||||
|
end
|
||||||
|
|
||||||
|
! ---
|
||||||
|
|
Loading…
Reference in New Issue
Block a user