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quantum_package/src/Dets/davidson.irp.f

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BEGIN_PROVIDER [ integer, davidson_iter_max ]
implicit none
BEGIN_DOC
! Max number of Davidson iterations
END_DOC
davidson_iter_max = 100
END_PROVIDER
BEGIN_PROVIDER [ integer, davidson_sze_max ]
implicit none
BEGIN_DOC
! Max number of Davidson sizes
END_DOC
ASSERT (davidson_sze_max <= davidson_iter_max)
davidson_sze_max = 8*N_states_diag
END_PROVIDER
subroutine davidson_diag(dets_in,u_in,energies,dim_in,sze,N_st,Nint,iunit)
use bitmasks
implicit none
BEGIN_DOC
! Davidson diagonalization.
!
! dets_in : bitmasks corresponding to determinants
!
! u_in : guess coefficients on the various states. Overwritten
! on exit
!
! dim_in : leftmost dimension of u_in
!
! sze : Number of determinants
!
! N_st : Number of eigenstates
!
! iunit : Unit number for the I/O
!
! Initial guess vectors are not necessarily orthonormal
END_DOC
integer, intent(in) :: dim_in, sze, N_st, Nint, iunit
integer(bit_kind), intent(in) :: dets_in(Nint,2,sze)
double precision, intent(inout) :: u_in(dim_in,N_st)
double precision, intent(out) :: energies(N_st)
double precision, allocatable :: H_jj(:)
double precision :: diag_h_mat_elem
integer :: i
ASSERT (N_st > 0)
ASSERT (sze > 0)
ASSERT (Nint > 0)
ASSERT (Nint == N_int)
PROVIDE mo_bielec_integrals_in_map
allocate(H_jj(sze))
!$OMP PARALLEL DEFAULT(NONE) &
!$OMP SHARED(sze,H_jj,dets_in,Nint) &
!$OMP PRIVATE(i)
!$OMP DO SCHEDULE(guided)
do i=1,sze
H_jj(i) = diag_h_mat_elem(dets_in(1,1,i),Nint)
enddo
!$OMP END DO
!$OMP END PARALLEL
call davidson_diag_hjj(dets_in,u_in,H_jj,energies,dim_in,sze,N_st,Nint,iunit)
deallocate (H_jj)
end
subroutine davidson_diag_hjj(dets_in,u_in,H_jj,energies,dim_in,sze,N_st,Nint,iunit)
use bitmasks
implicit none
BEGIN_DOC
! Davidson diagonalization with specific diagonal elements of the H matrix
!
! H_jj : specific diagonal H matrix elements to diagonalize de Davidson
!
! dets_in : bitmasks corresponding to determinants
!
! u_in : guess coefficients on the various states. Overwritten
! on exit
!
! dim_in : leftmost dimension of u_in
!
! sze : Number of determinants
!
! N_st : Number of eigenstates
!
! iunit : Unit for the I/O
!
! Initial guess vectors are not necessarily orthonormal
END_DOC
integer, intent(in) :: dim_in, sze, N_st, Nint
integer(bit_kind), intent(in) :: dets_in(Nint,2,sze)
double precision, intent(in) :: H_jj(sze)
integer, intent(in) :: iunit
double precision, intent(inout) :: u_in(dim_in,N_st)
double precision, intent(out) :: energies(N_st)
integer :: iter
integer :: i,j,k,l,m
logical :: converged
double precision :: overlap(N_st,N_st)
double precision :: u_dot_v, u_dot_u
integer, allocatable :: kl_pairs(:,:)
integer :: k_pairs, kl
integer :: iter2
double precision, allocatable :: W(:,:,:), U(:,:,:), R(:,:)
double precision, allocatable :: y(:,:,:,:), h(:,:,:,:), lambda(:)
double precision :: diag_h_mat_elem
double precision :: residual_norm(N_st)
character*(16384) :: write_buffer
double precision :: to_print(2,N_st)
double precision :: cpu, wall
PROVIDE det_connections
call write_time(iunit)
call wall_time(wall)
call cpu_time(cpu)
write(iunit,'(A)') ''
write(iunit,'(A)') 'Davidson Diagonalization'
write(iunit,'(A)') '------------------------'
write(iunit,'(A)') ''
call write_int(iunit,N_st,'Number of states')
call write_int(iunit,sze,'Number of determinants')
write(iunit,'(A)') ''
write_buffer = '===== '
do i=1,N_st
write_buffer = trim(write_buffer)//' ================ ================'
enddo
write(iunit,'(A)') trim(write_buffer)
write_buffer = ' Iter'
do i=1,N_st
write_buffer = trim(write_buffer)//' Energy Residual'
enddo
write(iunit,'(A)') trim(write_buffer)
write_buffer = '===== '
do i=1,N_st
write_buffer = trim(write_buffer)//' ================ ================'
enddo
write(iunit,'(A)') trim(write_buffer)
allocate( &
kl_pairs(2,N_st*(N_st+1)/2), &
W(sze,N_st,davidson_sze_max), &
U(sze,N_st,davidson_sze_max), &
R(sze,N_st), &
h(N_st,davidson_sze_max,N_st,davidson_sze_max), &
y(N_st,davidson_sze_max,N_st,davidson_sze_max), &
lambda(N_st*davidson_sze_max))
ASSERT (N_st > 0)
ASSERT (sze > 0)
ASSERT (Nint > 0)
ASSERT (Nint == N_int)
! Initialization
! ==============
k_pairs=0
do l=1,N_st
do k=1,l
k_pairs+=1
kl_pairs(1,k_pairs) = k
kl_pairs(2,k_pairs) = l
enddo
enddo
!$OMP PARALLEL DEFAULT(NONE) &
!$OMP SHARED(U,sze,N_st,overlap,kl_pairs,k_pairs, &
!$OMP Nint,dets_in,u_in) &
!$OMP PRIVATE(k,l,kl,i)
! Orthonormalize initial guess
! ============================
!$OMP DO
do kl=1,k_pairs
k = kl_pairs(1,kl)
l = kl_pairs(2,kl)
if (k/=l) then
overlap(k,l) = u_dot_v(U_in(1,k),U_in(1,l),sze)
overlap(l,k) = overlap(k,l)
else
overlap(k,k) = u_dot_u(U_in(1,k),sze)
endif
enddo
!$OMP END DO
!$OMP END PARALLEL
call ortho_lowdin(overlap,size(overlap,1),N_st,U_in,size(U_in,1),sze)
! Davidson iterations
! ===================
converged = .False.
do while (.not.converged)
!$OMP PARALLEL DEFAULT(NONE) &
!$OMP PRIVATE(k,i) SHARED(U,u_in,sze,N_st)
do k=1,N_st
!$OMP DO
do i=1,sze
U(i,k,1) = u_in(i,k)
enddo
!$OMP END DO
enddo
!$OMP END PARALLEL
do iter=1,davidson_sze_max-1
! Compute W_k = H |u_k>
! ----------------------
do k=1,N_st
call H_u_0(W(1,k,iter),U(1,k,iter),H_jj,sze,dets_in,Nint)
enddo
! Compute h_kl = <u_k | W_l> = <u_k| H |u_l>
! -------------------------------------------
do l=1,N_st
do k=1,N_st
do iter2=1,iter-1
h(k,iter2,l,iter) = u_dot_v(U(1,k,iter2),W(1,l,iter),sze)
h(k,iter,l,iter2) = h(k,iter2,l,iter)
enddo
enddo
do k=1,l
h(k,iter,l,iter) = u_dot_v(U(1,k,iter),W(1,l,iter),sze)
h(l,iter,k,iter) = h(k,iter,l,iter)
enddo
enddo
!DEBUG H MATRIX
!do i=1,iter
! print '(10(x,F16.10))', h(1,i,1,1:i)
!enddo
!print *, ''
!END
! Diagonalize h
! -------------
call lapack_diag(lambda,y,h,N_st*davidson_sze_max,N_st*iter)
! Express eigenvectors of h in the determinant basis
! --------------------------------------------------
do k=1,N_st
do i=1,sze
U(i,k,iter+1) = 0.d0
W(i,k,iter+1) = 0.d0
do l=1,N_st
do iter2=1,iter
U(i,k,iter+1) = U(i,k,iter+1) + U(i,l,iter2)*y(l,iter2,k,1)
W(i,k,iter+1) = W(i,k,iter+1) + W(i,l,iter2)*y(l,iter2,k,1)
enddo
enddo
enddo
enddo
! Compute residual vector
! -----------------------
do k=1,N_st
do i=1,sze
R(i,k) = lambda(k) * U(i,k,iter+1) - W(i,k,iter+1)
enddo
residual_norm(k) = u_dot_u(R(1,k),sze)
to_print(1,k) = lambda(k) + nuclear_repulsion
to_print(2,k) = residual_norm(k)
enddo
write(iunit,'(X,I3,X,100(X,F16.10,X,E16.6))'), iter, to_print(:,1:N_st)
call davidson_converged(lambda,residual_norm,wall,iter,cpu,N_st,converged)
if (converged) then
exit
endif
! Davidson step
! -------------
do k=1,N_st
do i=1,sze
U(i,k,iter+1) = -1.d0/max(H_jj(i) - lambda(k),1.d-2) * R(i,k)
enddo
enddo
! Gram-Schmidt
! ------------
double precision :: c
do k=1,N_st
do iter2=1,iter
do l=1,N_st
c = u_dot_v(U(1,k,iter+1),U(1,l,iter2),sze)
do i=1,sze
U(i,k,iter+1) -= c * U(i,l,iter2)
enddo
enddo
enddo
do l=1,k-1
c = u_dot_v(U(1,k,iter+1),U(1,l,iter+1),sze)
do i=1,sze
U(i,k,iter+1) -= c * U(i,l,iter+1)
enddo
enddo
call normalize( U(1,k,iter+1), sze )
enddo
!DEBUG : CHECK OVERLAP
!print *, '==='
!do k=1,iter+1
! do l=1,k
! c = u_dot_v(U(1,1,k),U(1,1,l),sze)
! print *, k,l, c
! enddo
!enddo
!print *, '==='
!pause
!END DEBUG
enddo
if (.not.converged) then
iter = davidson_sze_max-1
endif
! Re-contract to u_in
! -----------
do k=1,N_st
energies(k) = lambda(k)
do i=1,sze
u_in(i,k) = 0.d0
do iter2=1,iter
do l=1,N_st
u_in(i,k) += U(i,l,iter2)*y(l,iter2,k,1)
enddo
enddo
enddo
enddo
enddo
write_buffer = '===== '
do i=1,N_st
write_buffer = trim(write_buffer)//' ================ ================'
enddo
write(iunit,'(A)') trim(write_buffer)
write(iunit,'(A)') ''
call write_time(iunit)
deallocate ( &
kl_pairs, &
W, &
U, &
R, &
h, &
y, &
lambda &
)
abort_here = abort_all
end
BEGIN_PROVIDER [ character(64), davidson_criterion ]
&BEGIN_PROVIDER [ double precision, davidson_threshold ]
implicit none
BEGIN_DOC
! Can be : [ energy | residual | both | wall_time | cpu_time | iterations ]
END_DOC
davidson_criterion = 'residual'
davidson_threshold = 1.d-6
END_PROVIDER
subroutine davidson_converged(energy,residual,wall,iterations,cpu,N_st,converged)
implicit none
BEGIN_DOC
! True if the Davidson algorithm is converged
END_DOC
integer, intent(in) :: N_st, iterations
logical, intent(out) :: converged
double precision, intent(in) :: energy(N_st), residual(N_st)
double precision, intent(in) :: wall, cpu
double precision :: E(N_st), time
double precision, allocatable, save :: energy_old(:)
if (.not.allocated(energy_old)) then
allocate(energy_old(N_st))
energy_old = 0.d0
endif
E = energy - energy_old
energy_old = energy
if (davidson_criterion == 'energy') then
converged = dabs(maxval(E(1:N_st))) < davidson_threshold
else if (davidson_criterion == 'residual') then
converged = dabs(maxval(residual(1:N_st))) < davidson_threshold
else if (davidson_criterion == 'both') then
converged = dabs(maxval(residual(1:N_st))) + dabs(maxval(E(1:N_st)) ) &
< davidson_threshold
else if (davidson_criterion == 'wall_time') then
call wall_time(time)
converged = time - wall > davidson_threshold
else if (davidson_criterion == 'cpu_time') then
call cpu_time(time)
converged = time - cpu > davidson_threshold
else if (davidson_criterion == 'iterations') then
converged = iterations >= int(davidson_threshold)
endif
converged = converged.or.abort_here
end
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