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quantum_package/plugins/MRCC_Utils/davidson.irp.f

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subroutine davidson_diag_mrcc(dets_in,u_in,energies,dim_in,sze,N_st,N_st_diag,Nint,iunit,istate)
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, istate, N_st_diag
integer(bit_kind), intent(in) :: dets_in(Nint,2,sze)
double precision, intent(inout) :: u_in(dim_in,N_st_diag)
double precision, intent(out) :: energies(N_st_diag)
double precision, allocatable :: H_jj(:)
double precision :: diag_h_mat_elem
integer :: i
ASSERT (N_st > 0)
ASSERT (N_st_diag >= N_st)
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,N_det_ref,dets_in,Nint,istate,delta_ii,idx_ref) &
!$OMP PRIVATE(i)
!$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 DO SCHEDULE(guided)
do i=1,N_det_ref
H_jj(idx_ref(i)) += delta_ii(istate,i)
enddo
!$OMP END DO
!$OMP END PARALLEL
call davidson_diag_hjj_mrcc(dets_in,u_in,H_jj,energies,dim_in,sze,N_st,N_st_diag,Nint,iunit,istate)
deallocate (H_jj)
end
subroutine davidson_diag_hjj_mrcc(dets_in,u_in,H_jj,energies,dim_in,sze,N_st,N_st_diag,Nint,iunit,istate)
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
!
! N_st_diag : Number of states in which H is diagonalized
!
! iunit : Unit for the I/O
!
! Initial guess vectors are not necessarily orthonormal
END_DOC
integer, intent(in) :: dim_in, sze, N_st, N_st_diag, Nint, istate
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_diag)
double precision, intent(out) :: energies(N_st_diag)
integer :: sze_8
integer :: iter
integer :: i,j,k,l,m
logical :: converged
double precision, allocatable :: overlap(:,:)
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, allocatable :: c(:), H_small(:,:)
double precision :: diag_h_mat_elem
double precision, allocatable :: residual_norm(:)
character*(16384) :: write_buffer
double precision :: to_print(2,N_st)
double precision :: cpu, wall
include 'constants.include.F'
!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: U, W, R, y, h, lambda
PROVIDE nuclear_repulsion
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,N_st_diag,'Number of states in diagonalization')
call write_int(iunit,sze,'Number of determinants')
call write_int(iunit,istate,'Using dressing for state ')
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)
integer, external :: align_double
sze_8 = align_double(sze)
allocate( &
kl_pairs(2,N_st_diag*(N_st_diag+1)/2), &
W(sze_8,N_st_diag,davidson_sze_max), &
U(sze_8,N_st_diag,davidson_sze_max), &
R(sze_8,N_st_diag), &
h(N_st_diag,davidson_sze_max,N_st_diag,davidson_sze_max), &
y(N_st_diag,davidson_sze_max,N_st_diag,davidson_sze_max), &
residual_norm(N_st_diag), &
overlap(N_st_diag,N_st_diag), &
c(N_st_diag*davidson_sze_max), &
H_small(N_st_diag,N_st_diag), &
lambda(N_st_diag*davidson_sze_max))
ASSERT (N_st > 0)
ASSERT (N_st_diag >= N_st)
ASSERT (sze > 0)
ASSERT (Nint > 0)
ASSERT (Nint == N_int)
! Initialization
! ==============
do k=1,N_st_diag
if (k > N_st) then
do i=1,sze
double precision :: r1, r2
call random_number(r1)
call random_number(r2)
u_in(i,k) = dsqrt(-2.d0*dlog(r1))*dcos(dtwo_pi*r2)
enddo
endif
! Gram-Schmidt
! ------------
call dgemv('T',sze,k-1,1.d0,u_in,size(u_in,1), &
u_in(1,k),1,0.d0,c,1)
call dgemv('N',sze,k-1,-1.d0,u_in,size(u_in,1), &
c,1,1.d0,u_in(1,k),1)
call normalize(u_in(1,k),sze)
enddo
converged = .False.
do while (.not.converged)
do k=1,N_st_diag
do i=1,sze
U(i,k,1) = u_in(i,k)
enddo
enddo
do iter=1,davidson_sze_max-1
! Compute |W_k> = \sum_i |i><i|H|u_k>
! -----------------------------------------
call H_u_0_mrcc_nstates(W(1,1,iter),U(1,1,iter),H_jj,sze,dets_in,Nint,istate,N_st_diag,sze_8)
! Compute h_kl = <u_k | W_l> = <u_k| H |u_l>
! -------------------------------------------
! do l=1,N_st_diag
! do k=1,N_st_diag
! 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
call dgemm('T','N', N_st_diag*iter, N_st_diag, sze, &
1.d0, U, size(U,1), W(1,1,iter), size(W,1), &
0.d0, h(1,1,1,iter), size(h,1)*size(h,2))
! Diagonalize h
! -------------
call lapack_diag(lambda,y,h,N_st_diag*davidson_sze_max,N_st_diag*iter)
! Express eigenvectors of h in the determinant basis
! --------------------------------------------------
do k=1,N_st_diag
do i=1,sze
U(i,k,iter+1) = 0.d0
W(i,k,iter+1) = 0.d0
enddo
enddo
! do k=1,N_st_diag
! do iter2=1,iter
! do l=1,N_st_diag
! do i=1,sze
! 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
!
!
call dgemm('N','N', sze, N_st_diag, N_st_diag*iter, &
1.d0, U, size(U,1), y, size(y,1)*size(y,2), 0.d0, U(1,1,iter+1), size(U,1))
call dgemm('N','N',sze,N_st_diag,N_st_diag*iter, &
1.d0, W, size(W,1), y, size(y,1)*size(y,2), 0.d0, W(1,1,iter+1), size(W,1))
! Compute residual vector
! -----------------------
do k=1,N_st_diag
do i=1,sze
R(i,k) = lambda(k) * U(i,k,iter+1) - W(i,k,iter+1)
enddo
if (k <= N_st) then
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)
endif
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_diag
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
! ------------
do k=1,N_st_diag
! do iter2=1,iter
! do l=1,N_st_diag
! c(1) = u_dot_v(U(1,k,iter+1),U(1,l,iter2),sze)
! do i=1,sze
! U(i,k,iter+1) = U(i,k,iter+1) - c(1) * U(i,l,iter2)
! enddo
! enddo
! enddo
!
call dgemv('T',sze,N_st_diag*iter,1.d0,U,size(U,1), &
U(1,k,iter+1),1,0.d0,c,1)
call dgemv('N',sze,N_st_diag*iter,-1.d0,U,size(U,1), &
c,1,1.d0,U(1,k,iter+1),1)
!
! do l=1,k-1
! c(1) = u_dot_v(U(1,k,iter+1),U(1,l,iter+1),sze)
! do i=1,sze
! U(i,k,iter+1) = U(i,k,iter+1) - c(1) * U(i,l,iter+1)
! enddo
! enddo
!
call dgemv('T',sze,k-1,1.d0,U(1,1,iter+1),size(U,1), &
U(1,k,iter+1),1,0.d0,c,1)
call dgemv('N',sze,k-1,-1.d0,U(1,1,iter+1),size(U,1), &
c,1,1.d0,U(1,k,iter+1),1)
call normalize( U(1,k,iter+1), sze )
enddo
enddo
if (.not.converged) then
iter = davidson_sze_max-1
endif
! Re-contract to u_in
! -----------
do k=1,N_st_diag
energies(k) = lambda(k)
do i=1,sze
u_in(i,k) = 0.d0
enddo
enddo
! do k=1,N_st_diag
! do i=1,sze
! do iter2=1,iter
! do l=1,N_st_diag
! u_in(i,k) += U(i,l,iter2)*y(l,iter2,k,1)
! enddo
! enddo
! enddo
! enddo
call dgemm('N','N', sze, N_st_diag, N_st_diag*iter, 1.d0, &
U, size(U,1), y, N_st_diag*davidson_sze_max, &
0.d0, u_in, size(u_in,1))
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, residual_norm, &
U, overlap, &
R, c, &
h, &
y, &
lambda &
)
end
subroutine u_0_H_u_0_mrcc_nstates(e_0,u_0,n,keys_tmp,Nint,istate,N_st,sze_8)
use bitmasks
implicit none
BEGIN_DOC
! Computes e_0 = <u_0|H|u_0>/<u_0|u_0>
!
! n : number of determinants
!
END_DOC
integer, intent(in) :: n,Nint,N_st,sze_8
double precision, intent(out) :: e_0(N_st)
double precision, intent(in) :: u_0(sze_8,N_st)
integer(bit_kind),intent(in) :: keys_tmp(Nint,2,n)
integer,intent(in) :: istate
double precision, allocatable :: v_0(:,:), H_jj(:)
double precision :: u_dot_u,u_dot_v,diag_H_mat_elem
integer :: i,j
allocate(H_jj(n), v_0(sze_8,N_st))
do i = 1, n
H_jj(i) = diag_H_mat_elem(keys_tmp(1,1,i),Nint)
enddo
do i=1,N_det_ref
H_jj(idx_ref(i)) += delta_ii(istate,i)
enddo
call H_u_0_mrcc_nstates(v_0,u_0,H_jj,n,keys_tmp,Nint,istate,N_st,sze_8)
do i=1,N_st
e_0(i) = u_dot_v(v_0(1,i),u_0(1,i),n)/u_dot_u(u_0(1,i),n)
enddo
deallocate(H_jj, v_0)
end
subroutine H_u_0_mrcc_nstates(v_0,u_0,H_jj,n,keys_tmp,Nint,istate_in,N_st,sze_8)
use bitmasks
implicit none
BEGIN_DOC
! Computes v_0 = H|u_0>
!
! n : number of determinants
!
! H_jj : array of <j|H|j>
END_DOC
integer, intent(in) :: n,Nint,istate_in,N_st,sze_8
double precision, intent(out) :: v_0(sze_8,N_st)
double precision, intent(in) :: u_0(sze_8,N_st)
double precision, intent(in) :: H_jj(n)
integer(bit_kind),intent(in) :: keys_tmp(Nint,2,n)
double precision :: hij
double precision, allocatable :: vt(:,:)
integer :: i,j,k,l, jj,ii
integer :: i0, j0
integer(bit_kind) :: sorted_i(Nint)
integer,allocatable :: shortcut(:,:), sort_idx(:,:)
integer(bit_kind), allocatable :: sorted(:,:,:), version(:,:,:)
integer :: sh, sh2, ni, exa, ext, org_i, org_j, endi, pass, istate
ASSERT (Nint > 0)
ASSERT (Nint == N_int)
ASSERT (n>0)
PROVIDE ref_bitmask_energy
allocate (shortcut(0:n+1,2), sort_idx(n,2), sorted(Nint,n,2), version(Nint,n,2))
v_0 = 0.d0
call sort_dets_ab_v(keys_tmp, sorted(1,1,1), sort_idx(1,1), shortcut(0,1), version(1,1,1), n, Nint)
call sort_dets_ba_v(keys_tmp, sorted(1,1,2), sort_idx(1,2), shortcut(0,2), version(1,1,2), n, Nint)
!$OMP PARALLEL DEFAULT(NONE) &
!$OMP PRIVATE(i,hij,j,k,jj,vt,ii,sh,sh2,ni,exa,ext,org_i,org_j,endi,sorted_i,istate)&
!$OMP SHARED(n,H_jj,u_0,keys_tmp,Nint,v_0,sorted,shortcut,sort_idx,version,N_st,sze_8,&
!$OMP istate_in,delta_ij,N_det_ref,N_det_non_ref,idx_ref,idx_non_ref)
allocate(vt(sze_8,N_st))
Vt = 0.d0
!$OMP DO SCHEDULE(dynamic)
do sh=1,shortcut(0,1)
do sh2=sh,shortcut(0,1)
exa = 0
do ni=1,Nint
exa = exa + popcnt(xor(version(ni,sh,1), version(ni,sh2,1)))
end do
if(exa > 2) then
cycle
end if
do i=shortcut(sh,1),shortcut(sh+1,1)-1
org_i = sort_idx(i,1)
if(sh==sh2) then
endi = i-1
else
endi = shortcut(sh2+1,1)-1
end if
do ni=1,Nint
sorted_i(ni) = sorted(ni,i,1)
enddo
do j=shortcut(sh2,1),endi
org_j = sort_idx(j,1)
ext = exa
do ni=1,Nint
ext = ext + popcnt(xor(sorted_i(ni), sorted(ni,j,1)))
end do
if(ext <= 4) then
call i_H_j(keys_tmp(1,1,org_j),keys_tmp(1,1,org_i),Nint,hij)
do istate=1,N_st
vt (org_i,istate) = vt (org_i,istate) + hij*u_0(org_j,istate)
vt (org_j,istate) = vt (org_j,istate) + hij*u_0(org_i,istate)
enddo
endif
enddo
enddo
enddo
enddo
!$OMP END DO NOWAIT
!$OMP DO SCHEDULE(dynamic)
do sh=1,shortcut(0,2)
do i=shortcut(sh,2),shortcut(sh+1,2)-1
org_i = sort_idx(i,2)
do j=shortcut(sh,2),i-1
org_j = sort_idx(j,2)
ext = 0
do ni=1,Nint
ext = ext + popcnt(xor(sorted(ni,i,2), sorted(ni,j,2)))
end do
if(ext == 4) then
call i_H_j(keys_tmp(1,1,org_j),keys_tmp(1,1,org_i),Nint,hij)
do istate=1,N_st
vt (org_i,istate) = vt (org_i,istate) + hij*u_0(org_j,istate)
vt (org_j,istate) = vt (org_j,istate) + hij*u_0(org_i,istate)
enddo
end if
end do
end do
enddo
!$OMP END DO NOWAIT
!$OMP DO
do ii=1,n_det_ref
i = idx_ref(ii)
do jj = 1, n_det_non_ref
j = idx_non_ref(jj)
do istate=1,N_st
vt (i,istate) = vt (i,istate) + delta_ij(istate_in,jj,ii)*u_0(j,istate)
vt (j,istate) = vt (j,istate) + delta_ij(istate_in,jj,ii)*u_0(i,istate)
enddo
enddo
enddo
!$OMP END DO
!$OMP CRITICAL
do istate=1,N_st
do i=n,1,-1
v_0(i,istate) = v_0(i,istate) + vt(i,istate)
enddo
enddo
!$OMP END CRITICAL
deallocate(vt)
!$OMP END PARALLEL
do istate=1,N_st
do i=1,n
v_0(i,istate) += H_jj(i) * u_0(i,istate)
enddo
enddo
deallocate (shortcut, sort_idx, sorted, version)
end
subroutine davidson_diag_mrcc_hs2(dets_in,u_in,dim_in,energies,sze,N_st,N_st_diag,Nint,iunit,istate)
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, N_st_diag, Nint, iunit, istate
integer(bit_kind), intent(in) :: dets_in(Nint,2,sze)
double precision, intent(inout) :: u_in(dim_in,N_st_diag)
double precision, intent(out) :: energies(N_st)
double precision, allocatable :: H_jj(:), S2_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), S2_jj(sze))
!$OMP PARALLEL DEFAULT(NONE) &
!$OMP SHARED(sze,H_jj,S2_jj, dets_in,Nint,N_det_ref,delta_ii, &
!$OMP idx_ref, istate) &
!$OMP PRIVATE(i)
!$OMP DO SCHEDULE(guided)
do i=1,sze
H_jj(i) = diag_h_mat_elem(dets_in(1,1,i),Nint)
call get_s2(dets_in(1,1,i),dets_in(1,1,i),Nint,S2_jj(i))
enddo
!$OMP END DO
!$OMP DO SCHEDULE(guided)
do i=1,N_det_ref
H_jj(idx_ref(i)) += delta_ii(istate,i)
enddo
!$OMP END DO
!$OMP END PARALLEL
call davidson_diag_hjj_sjj_mrcc(dets_in,u_in,H_jj,S2_jj,energies,dim_in,sze,N_st,N_st_diag,Nint,iunit,istate)
deallocate (H_jj,S2_jj)
end
subroutine davidson_diag_hjj_sjj_mrcc(dets_in,u_in,H_jj,S2_jj,energies,dim_in,sze,N_st,N_st_diag,Nint,iunit,istate )
use bitmasks
implicit none
BEGIN_DOC
! Davidson diagonalization with specific diagonal elements of the H matrix
!
! H_jj : specific diagonal H matrix elements to diagonalize de Davidson
!
! S2_jj : specific diagonal S^2 matrix elements
!
! dets_in : bitmasks corresponding to determinants
!
! u_in : guess coefficients on the various states. Overwritten
! on exit
!
! dim_in : leftmost dimension of u_in
!
! sze : Number of determinants
!
! N_st : Number of eigenstates
!
! N_st_diag : Number of states in which H is diagonalized. Assumed > sze
!
! iunit : Unit for the I/O
!
! Initial guess vectors are not necessarily orthonormal
END_DOC
integer, intent(in) :: dim_in, sze, N_st, N_st_diag, Nint, istate
integer(bit_kind), intent(in) :: dets_in(Nint,2,sze)
double precision, intent(in) :: H_jj(sze), S2_jj(sze)
integer, intent(in) :: iunit
double precision, intent(inout) :: u_in(dim_in,N_st_diag)
double precision, intent(out) :: energies(N_st_diag)
integer :: sze_8
integer :: iter
integer :: i,j,k,l,m
logical :: converged
double precision, allocatable :: overlap(:,:)
double precision :: u_dot_v, u_dot_u
integer, allocatable :: kl_pairs(:,:)
integer :: k_pairs, kl
integer :: iter2
double precision, allocatable :: W(:,:), U(:,:), R(:,:), S(:,:)
double precision, allocatable :: y(:,:), h(:,:), lambda(:), s2(:)
double precision, allocatable :: c(:), s_(:,:), s_tmp(:,:)
double precision :: diag_h_mat_elem
double precision, allocatable :: residual_norm(:)
character*(16384) :: write_buffer
double precision :: to_print(3,N_st)
double precision :: cpu, wall
integer :: shift, shift2
include 'constants.include.F'
!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: U, W, R, S, y, h, lambda
if (N_st_diag > sze) then
stop 'error in Davidson : N_st_diag > sze'
endif
PROVIDE nuclear_repulsion
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,N_st_diag,'Number of states in diagonalization')
call write_int(iunit,sze,'Number of determinants')
call write_int(iunit,istate,'Using dressing for state ')
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 S^2 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)
integer, external :: align_double
sze_8 = align_double(sze)
double precision :: delta
if (s2_eig) then
delta = 1.d0
else
delta = 0.d0
endif
allocate( &
kl_pairs(2,N_st_diag*(N_st_diag+1)/2), &
W(sze_8,N_st_diag*davidson_sze_max), &
U(sze_8,N_st_diag*davidson_sze_max), &
R(sze_8,N_st_diag), &
S(sze_8,N_st_diag*davidson_sze_max), &
h(N_st_diag*davidson_sze_max,N_st_diag*davidson_sze_max), &
y(N_st_diag*davidson_sze_max,N_st_diag*davidson_sze_max), &
s_(N_st_diag*davidson_sze_max,N_st_diag*davidson_sze_max), &
s_tmp(N_st_diag*davidson_sze_max,N_st_diag*davidson_sze_max), &
residual_norm(N_st_diag), &
overlap(N_st_diag,N_st_diag), &
c(N_st_diag*davidson_sze_max), &
s2(N_st_diag*davidson_sze_max), &
lambda(N_st_diag*davidson_sze_max))
ASSERT (N_st > 0)
ASSERT (N_st_diag >= N_st)
ASSERT (sze > 0)
ASSERT (Nint > 0)
ASSERT (Nint == N_int)
! Davidson iterations
! ===================
converged = .False.
do k=1,N_st
call normalize(u_in(1,k),sze)
enddo
do k=N_st+1,N_st_diag
do i=1,sze
double precision :: r1, r2
call random_number(r1)
call random_number(r2)
u_in(i,k) = dsqrt(-2.d0*dlog(r1))*dcos(dtwo_pi*r2)
enddo
! Gram-Schmidt
! ------------
call dgemv('T',sze,k-1,1.d0,u_in,size(u_in,1), &
u_in(1,k),1,0.d0,c,1)
call dgemv('N',sze,k-1,-1.d0,u_in,size(u_in,1), &
c,1,1.d0,u_in(1,k),1)
call normalize(u_in(1,k),sze)
enddo
do while (.not.converged)
do k=1,N_st_diag
do i=1,sze
U(i,k) = u_in(i,k)
enddo
enddo
do iter=1,davidson_sze_max-1
shift = N_st_diag*(iter-1)
shift2 = N_st_diag*iter
! Compute |W_k> = \sum_i |i><i|H|u_k>
! -----------------------------------------
call H_S2_u_0_mrcc_nstates(W(1,shift+1),S(1,shift+1),U(1,shift+1),H_jj,S2_jj,sze,dets_in,Nint,&
istate,N_st_diag,sze_8)
! Compute h_kl = <u_k | W_l> = <u_k| H |u_l>
! -------------------------------------------
! do l=1,N_st_diag
! do k=1,N_st_diag
! 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
call dgemm('T','N', shift2, N_st_diag, sze, &
1.d0, U, size(U,1), W(1,shift+1), size(W,1), &
0.d0, h(1,shift+1), size(h,1))
call dgemm('T','N', shift2, N_st_diag, sze, &
1.d0, U, size(U,1), S(1,shift+1), size(S,1), &
0.d0, s_(1,shift+1), size(s_,1))
! Diagonalize h
! -------------
call lapack_diag(lambda,y,h,size(h,1),shift2)
! Compute S2 for each eigenvector
! -------------------------------
call dgemm('N','N',shift2,shift2,shift2, &
1.d0, s_, size(s_,1), y, size(y,1), &
0.d0, s_tmp, size(s_tmp,1))
call dgemm('T','N',shift2,shift2,shift2, &
1.d0, y, size(y,1), s_tmp, size(s_tmp,1), &
0.d0, s_, size(s_,1))
do k=1,shift2
s2(k) = s_(k,k) + S_z2_Sz
enddo
if (s2_eig) then
logical :: state_ok(N_st_diag*davidson_sze_max)
do k=1,shift2
state_ok(k) = (dabs(s2(k)-expected_s2) < 0.3d0)
enddo
do k=1,shift2
if (.not. state_ok(k)) then
do l=k+1,shift2
if (state_ok(l)) then
call dswap(shift2, y(1,k), 1, y(1,l), 1)
call dswap(1, s2(k), 1, s2(l), 1)
call dswap(1, lambda(k), 1, lambda(l), 1)
state_ok(k) = .True.
state_ok(l) = .False.
exit
endif
enddo
endif
enddo
endif
! Express eigenvectors of h in the determinant basis
! --------------------------------------------------
! do k=1,N_st_diag
! do i=1,sze
! U(i,shift2+k) = 0.d0
! W(i,shift2+k) = 0.d0
! S(i,shift2+k) = 0.d0
! enddo
! do l=1,N_st_diag*iter
! do i=1,sze
! U(i,shift2+k) = U(i,shift2+k) + U(i,l)*y(l,k)
! W(i,shift2+k) = W(i,shift2+k) + W(i,l)*y(l,k)
! S(i,shift2+k) = S(i,shift2+k) + S(i,l)*y(l,k)
! enddo
! enddo
! enddo
!
!
call dgemm('N','N', sze, N_st_diag, shift2, &
1.d0, U, size(U,1), y, size(y,1), 0.d0, U(1,shift2+1), size(U,1))
call dgemm('N','N', sze, N_st_diag, shift2, &
1.d0, W, size(W,1), y, size(y,1), 0.d0, W(1,shift2+1), size(W,1))
call dgemm('N','N', sze, N_st_diag, shift2, &
1.d0, S, size(S,1), y, size(y,1), 0.d0, S(1,shift2+1), size(S,1))
! Compute residual vector
! -----------------------
! do k=1,N_st_diag
! print *, s2(k)
! s2(k) = u_dot_v(U(1,shift2+k), S(1,shift2+k), sze) + S_z2_Sz
! print *, s2(k)
! print *, ''
! pause
! enddo
do k=1,N_st_diag
do i=1,sze
R(i,k) = (lambda(k) * U(i,shift2+k) - W(i,shift2+k) ) &
* (1.d0 + s2(k) * U(i,shift2+k) - S(i,shift2+k) - S_z2_Sz)
enddo
if (k <= N_st) then
residual_norm(k) = u_dot_u(R(1,k),sze)
to_print(1,k) = lambda(k) + nuclear_repulsion
to_print(2,k) = s2(k)
to_print(3,k) = residual_norm(k)
if (residual_norm(k) > 1.e9) then
stop 'Davidson failed'
endif
endif
enddo
write(iunit,'(X,I3,X,100(X,F16.10,X,F11.6,X,E11.3))') 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_diag
do i=1,sze
U(i,shift2+k) = - R(i,k)/max(H_jj(i) - lambda(k),1.d-2)
enddo
enddo
! Gram-Schmidt
! ------------
do k=1,N_st_diag
! do l=1,N_st_diag*iter
! c(1) = u_dot_v(U(1,shift2+k),U(1,l),sze)
! do i=1,sze
! U(i,k,iter+1) = U(i,shift2+k) - c(1) * U(i,l)
! enddo
! enddo
!
call dgemv('T',sze,N_st_diag*iter,1.d0,U,size(U,1), &
U(1,shift2+k),1,0.d0,c,1)
call dgemv('N',sze,N_st_diag*iter,-1.d0,U,size(U,1), &
c,1,1.d0,U(1,shift2+k),1)
!
! do l=1,k-1
! c(1) = u_dot_v(U(1,shift2+k),U(1,shift2+l),sze)
! do i=1,sze
! U(i,k,iter+1) = U(i,shift2+k) - c(1) * U(i,shift2+l)
! enddo
! enddo
!
call dgemv('T',sze,k-1,1.d0,U(1,shift2+1),size(U,1), &
U(1,shift2+k),1,0.d0,c,1)
call dgemv('N',sze,k-1,-1.d0,U(1,shift2+1),size(U,1), &
c,1,1.d0,U(1,shift2+k),1)
call normalize( U(1,shift2+k), sze )
enddo
enddo
if (.not.converged) then
iter = davidson_sze_max-1
endif
! Re-contract to u_in
! -----------
do k=1,N_st_diag
energies(k) = lambda(k)
enddo
! do k=1,N_st_diag
! do i=1,sze
! do l=1,iter*N_st_diag
! u_in(i,k) += U(i,l)*y(l,k)
! enddo
! enddo
! enddo
! enddo
call dgemm('N','N', sze, N_st_diag, N_st_diag*iter, 1.d0, &
U, size(U,1), y, size(y,1), 0.d0, u_in, size(u_in,1))
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, residual_norm, &
U, overlap, &
R, c, S, &
h, &
y, s_, s_tmp, &
lambda &
)
end
subroutine H_S2_u_0_mrcc_nstates(v_0,s_0,u_0,H_jj,S2_jj,n,keys_tmp,Nint,istate_in,N_st,sze_8)
use bitmasks
implicit none
BEGIN_DOC
! Computes v_0 = H|u_0> and s_0 = S^2 |u_0>
!
! n : number of determinants
!
! H_jj : array of <j|H|j>
!
! S2_jj : array of <j|S^2|j>
END_DOC
integer, intent(in) :: N_st,n,Nint, sze_8, istate_in
double precision, intent(out) :: v_0(sze_8,N_st), s_0(sze_8,N_st)
double precision, intent(in) :: u_0(sze_8,N_st)
double precision, intent(in) :: H_jj(n), S2_jj(n)
integer(bit_kind),intent(in) :: keys_tmp(Nint,2,n)
double precision :: hij,s2
double precision, allocatable :: vt(:,:), ut(:,:), st(:,:)
integer :: i,j,k,l, jj,ii
integer :: i0, j0
integer, allocatable :: shortcut(:,:), sort_idx(:,:)
integer(bit_kind), allocatable :: sorted(:,:,:), version(:,:,:)
integer(bit_kind) :: sorted_i(Nint)
integer :: sh, sh2, ni, exa, ext, org_i, org_j, endi, istate
integer :: N_st_8
integer, external :: align_double
!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: vt, ut
N_st_8 = align_double(N_st)
ASSERT (Nint > 0)
ASSERT (Nint == N_int)
ASSERT (n>0)
PROVIDE ref_bitmask_energy
allocate (shortcut(0:n+1,2), sort_idx(n,2), sorted(Nint,n,2), version(Nint,n,2))
allocate(ut(N_st_8,n))
v_0 = 0.d0
s_0 = 0.d0
do i=1,n
do istate=1,N_st
ut(istate,i) = u_0(i,istate)
enddo
enddo
call sort_dets_ab_v(keys_tmp, sorted(1,1,1), sort_idx(1,1), shortcut(0,1), version(1,1,1), n, Nint)
call sort_dets_ba_v(keys_tmp, sorted(1,1,2), sort_idx(1,2), shortcut(0,2), version(1,1,2), n, Nint)
!$OMP PARALLEL DEFAULT(NONE) &
!$OMP PRIVATE(i,hij,s2,j,k,jj,vt,st,ii,sh,sh2,ni,exa,ext,org_i,org_j,endi,sorted_i,istate)&
!$OMP SHARED(n,keys_tmp,ut,Nint,v_0,s_0,sorted,shortcut,sort_idx,version,N_st,N_st_8, &
!$OMP N_det_ref, idx_ref, N_det_non_ref, idx_non_ref, delta_ij,istate_in)
allocate(vt(N_st_8,n),st(N_st_8,n))
Vt = 0.d0
St = 0.d0
!$OMP DO SCHEDULE(dynamic)
do sh=1,shortcut(0,1)
do sh2=sh,shortcut(0,1)
exa = 0
do ni=1,Nint
exa = exa + popcnt(xor(version(ni,sh,1), version(ni,sh2,1)))
end do
if(exa > 2) then
cycle
end if
do i=shortcut(sh,1),shortcut(sh+1,1)-1
org_i = sort_idx(i,1)
if(sh==sh2) then
endi = i-1
else
endi = shortcut(sh2+1,1)-1
end if
do ni=1,Nint
sorted_i(ni) = sorted(ni,i,1)
enddo
do j=shortcut(sh2,1),endi
org_j = sort_idx(j,1)
ext = exa
do ni=1,Nint
ext = ext + popcnt(xor(sorted_i(ni), sorted(ni,j,1)))
end do
if(ext <= 4) then
call i_h_j (keys_tmp(1,1,org_j),keys_tmp(1,1,org_i),nint,hij)
call get_s2(keys_tmp(1,1,org_j),keys_tmp(1,1,org_i),nint,s2)
do istate=1,n_st
vt (istate,org_i) = vt (istate,org_i) + hij*ut(istate,org_j)
vt (istate,org_j) = vt (istate,org_j) + hij*ut(istate,org_i)
st (istate,org_i) = st (istate,org_i) + s2*ut(istate,org_j)
st (istate,org_j) = st (istate,org_j) + s2*ut(istate,org_i)
enddo
endif
enddo
enddo
enddo
enddo
!$OMP END DO NOWAIT
!$OMP DO SCHEDULE(dynamic)
do sh=1,shortcut(0,2)
do i=shortcut(sh,2),shortcut(sh+1,2)-1
org_i = sort_idx(i,2)
do j=shortcut(sh,2),i-1
org_j = sort_idx(j,2)
ext = 0
do ni=1,Nint
ext = ext + popcnt(xor(sorted(ni,i,2), sorted(ni,j,2)))
end do
if(ext == 4) then
call i_h_j (keys_tmp(1,1,org_j),keys_tmp(1,1,org_i),nint,hij)
call get_s2(keys_tmp(1,1,org_j),keys_tmp(1,1,org_i),nint,s2)
do istate=1,n_st
vt (istate,org_i) = vt (istate,org_i) + hij*ut(istate,org_j)
vt (istate,org_j) = vt (istate,org_j) + hij*ut(istate,org_i)
st (istate,org_i) = st (istate,org_i) + s2*ut(istate,org_j)
st (istate,org_j) = st (istate,org_j) + s2*ut(istate,org_i)
enddo
end if
end do
end do
enddo
!$OMP END DO NOWAIT
! --------------------------
! Begin Specific to dressing
! --------------------------
!$OMP DO
do ii=1,n_det_ref
i = idx_ref(ii)
do jj = 1, n_det_non_ref
j = idx_non_ref(jj)
do istate=1,N_st
vt (istate,i) = vt (istate,i) + delta_ij(istate_in,jj,ii)*ut(istate,j)
vt (istate,j) = vt (istate,j) + delta_ij(istate_in,jj,ii)*ut(istate,i)
enddo
enddo
enddo
!$OMP END DO
! ------------------------
! End Specific to dressing
! ------------------------
!$OMP CRITICAL
do istate=1,N_st
do i=n,1,-1
v_0(i,istate) = v_0(i,istate) + vt(istate,i)
s_0(i,istate) = s_0(i,istate) + st(istate,i)
enddo
enddo
!$OMP END CRITICAL
deallocate(vt,st)
!$OMP END PARALLEL
do istate=1,N_st
do i=1,n
v_0(i,istate) = v_0(i,istate) + H_jj(i) * u_0(i,istate)
s_0(i,istate) = s_0(i,istate) + s2_jj(i)* u_0(i,istate)
enddo
enddo
deallocate (shortcut, sort_idx, sorted, version, ut)
end
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