1139 lines
34 KiB
Fortran
1139 lines
34 KiB
Fortran
subroutine davidson_diag_mrcc(dets_in,u_in,energies,dim_in,sze,N_st,N_st_diag,Nint,iunit,istate)
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use bitmasks
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implicit none
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BEGIN_DOC
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! Davidson diagonalization.
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!
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! dets_in : bitmasks corresponding to determinants
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!
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! u_in : guess coefficients on the various states. Overwritten
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! on exit
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!
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! dim_in : leftmost dimension of u_in
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!
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! sze : Number of determinants
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!
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! N_st : Number of eigenstates
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!
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! iunit : Unit number for the I/O
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!
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! Initial guess vectors are not necessarily orthonormal
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END_DOC
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integer, intent(in) :: dim_in, sze, N_st, Nint, iunit, istate, N_st_diag
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integer(bit_kind), intent(in) :: dets_in(Nint,2,sze)
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double precision, intent(inout) :: u_in(dim_in,N_st_diag)
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double precision, intent(out) :: energies(N_st_diag)
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double precision, allocatable :: H_jj(:)
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double precision :: diag_h_mat_elem
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integer :: i
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ASSERT (N_st > 0)
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ASSERT (N_st_diag >= N_st)
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ASSERT (sze > 0)
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ASSERT (Nint > 0)
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ASSERT (Nint == N_int)
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PROVIDE mo_bielec_integrals_in_map
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allocate(H_jj(sze))
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H_jj(1) = diag_h_mat_elem(dets_in(1,1,1),Nint)
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!$OMP PARALLEL DEFAULT(NONE) &
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!$OMP SHARED(sze,H_jj,N_det_ref,dets_in,Nint,istate,delta_ii,idx_ref) &
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!$OMP PRIVATE(i)
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!$OMP DO
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do i=2,sze
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H_jj(i) = diag_h_mat_elem(dets_in(1,1,i),Nint)
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enddo
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!$OMP END DO
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!$OMP END PARALLEL
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do i=1,N_det_ref
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H_jj(idx_ref(i)) += delta_ii(istate,i)
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enddo
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call davidson_diag_hjj_mrcc(dets_in,u_in,H_jj,energies,dim_in,sze,N_st,N_st_diag,Nint,iunit,istate)
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deallocate (H_jj)
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end
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subroutine davidson_diag_hjj_mrcc(dets_in,u_in,H_jj,energies,dim_in,sze,N_st,N_st_diag,Nint,iunit,istate)
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use bitmasks
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implicit none
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BEGIN_DOC
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! Davidson diagonalization with specific diagonal elements of the H matrix
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!
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! H_jj : specific diagonal H matrix elements to diagonalize de Davidson
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!
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! dets_in : bitmasks corresponding to determinants
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!
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! u_in : guess coefficients on the various states. Overwritten
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! on exit
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!
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! dim_in : leftmost dimension of u_in
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!
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! sze : Number of determinants
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!
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! N_st : Number of eigenstates
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!
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! N_st_diag : Number of states in which H is diagonalized
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!
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! iunit : Unit for the I/O
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!
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! Initial guess vectors are not necessarily orthonormal
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END_DOC
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integer, intent(in) :: dim_in, sze, N_st, N_st_diag, Nint, istate
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integer(bit_kind), intent(in) :: dets_in(Nint,2,sze)
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double precision, intent(in) :: H_jj(sze)
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integer, intent(in) :: iunit
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double precision, intent(inout) :: u_in(dim_in,N_st_diag)
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double precision, intent(out) :: energies(N_st_diag)
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integer :: sze_8
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integer :: iter
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integer :: i,j,k,l,m
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logical :: converged
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double precision, allocatable :: overlap(:,:)
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double precision :: u_dot_v, u_dot_u
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integer :: k_pairs, kl
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integer :: iter2
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double precision, allocatable :: W(:,:,:), U(:,:,:), R(:,:)
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double precision, allocatable :: y(:,:,:,:), h(:,:,:,:), lambda(:)
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double precision, allocatable :: c(:), H_small(:,:)
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double precision :: diag_h_mat_elem
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double precision, allocatable :: residual_norm(:)
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character*(16384) :: write_buffer
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double precision :: to_print(2,N_st)
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double precision :: cpu, wall
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include 'constants.include.F'
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!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: U, W, R, y, h, lambda
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PROVIDE nuclear_repulsion
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call write_time(iunit)
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call wall_time(wall)
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call cpu_time(cpu)
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write(iunit,'(A)') ''
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write(iunit,'(A)') 'Davidson Diagonalization'
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write(iunit,'(A)') '------------------------'
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write(iunit,'(A)') ''
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call write_int(iunit,N_st,'Number of states')
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call write_int(iunit,N_st_diag,'Number of states in diagonalization')
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call write_int(iunit,sze,'Number of determinants')
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call write_int(iunit,istate,'Using dressing for state ')
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write(iunit,'(A)') ''
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write_buffer = '===== '
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do i=1,N_st
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write_buffer = trim(write_buffer)//' ================ ================'
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enddo
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write(iunit,'(A)') trim(write_buffer)
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write_buffer = ' Iter'
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do i=1,N_st
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write_buffer = trim(write_buffer)//' Energy Residual'
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enddo
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write(iunit,'(A)') trim(write_buffer)
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write_buffer = '===== '
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do i=1,N_st
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write_buffer = trim(write_buffer)//' ================ ================'
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enddo
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write(iunit,'(A)') trim(write_buffer)
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integer, external :: align_double
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sze_8 = align_double(sze)
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allocate( &
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W(sze_8,N_st_diag,davidson_sze_max), &
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U(sze_8,N_st_diag,davidson_sze_max), &
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R(sze_8,N_st_diag), &
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h(N_st_diag,davidson_sze_max,N_st_diag,davidson_sze_max), &
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y(N_st_diag,davidson_sze_max,N_st_diag,davidson_sze_max), &
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residual_norm(N_st_diag), &
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overlap(N_st_diag,N_st_diag), &
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c(N_st_diag*davidson_sze_max), &
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H_small(N_st_diag,N_st_diag), &
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lambda(N_st_diag*davidson_sze_max))
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ASSERT (N_st > 0)
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ASSERT (N_st_diag >= N_st)
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ASSERT (sze > 0)
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ASSERT (Nint > 0)
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ASSERT (Nint == N_int)
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! Initialization
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! ==============
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do k=1,N_st_diag
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if (k > N_st) then
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do i=1,sze
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double precision :: r1, r2
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call random_number(r1)
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call random_number(r2)
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u_in(i,k) = dsqrt(-2.d0*dlog(r1))*dcos(dtwo_pi*r2)
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enddo
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endif
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! Gram-Schmidt
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! ------------
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call dgemv('T',sze,k-1,1.d0,u_in,size(u_in,1), &
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u_in(1,k),1,0.d0,c,1)
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call dgemv('N',sze,k-1,-1.d0,u_in,size(u_in,1), &
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c,1,1.d0,u_in(1,k),1)
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call normalize(u_in(1,k),sze)
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enddo
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converged = .False.
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do while (.not.converged)
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do k=1,N_st_diag
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do i=1,sze
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U(i,k,1) = u_in(i,k)
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enddo
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enddo
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do iter=1,davidson_sze_max-1
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! Compute |W_k> = \sum_i |i><i|H|u_k>
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! -----------------------------------------
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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)
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! Compute h_kl = <u_k | W_l> = <u_k| H |u_l>
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! -------------------------------------------
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call dgemm('T','N', N_st_diag*iter, N_st_diag, sze, &
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1.d0, U, size(U,1), W(1,1,iter), size(W,1), &
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0.d0, h(1,1,1,iter), size(h,1)*size(h,2))
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! Diagonalize h
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! -------------
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call lapack_diag(lambda,y,h,N_st_diag*davidson_sze_max,N_st_diag*iter)
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! Express eigenvectors of h in the determinant basis
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! --------------------------------------------------
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do k=1,N_st_diag
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do i=1,sze
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U(i,k,iter+1) = 0.d0
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W(i,k,iter+1) = 0.d0
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enddo
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enddo
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!
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call dgemm('N','N', sze, N_st_diag, N_st_diag*iter, &
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1.d0, U, size(U,1), y, size(y,1)*size(y,2), 0.d0, U(1,1,iter+1), size(U,1))
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call dgemm('N','N',sze,N_st_diag,N_st_diag*iter, &
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1.d0, W, size(W,1), y, size(y,1)*size(y,2), 0.d0, W(1,1,iter+1), size(W,1))
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! Compute residual vector
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! -----------------------
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do k=1,N_st_diag
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do i=1,sze
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R(i,k) = lambda(k) * U(i,k,iter+1) - W(i,k,iter+1)
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enddo
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if (k <= N_st) then
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residual_norm(k) = u_dot_u(R(1,k),sze)
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to_print(1,k) = lambda(k) + nuclear_repulsion
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to_print(2,k) = residual_norm(k)
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endif
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enddo
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write(iunit,'(X,I3,X,100(X,F16.10,X,E16.6))') iter, to_print(:,1:N_st)
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call davidson_converged(lambda,residual_norm,wall,iter,cpu,N_st,converged)
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if (converged) then
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exit
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endif
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! Davidson step
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! -------------
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do k=1,N_st_diag
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do i=1,sze
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U(i,k,iter+1) = -1.d0/max(H_jj(i) - lambda(k),1.d-2) * R(i,k)
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enddo
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enddo
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! Gram-Schmidt
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! ------------
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do k=1,N_st_diag
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call dgemv('T',sze,N_st_diag*iter,1.d0,U,size(U,1), &
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U(1,k,iter+1),1,0.d0,c,1)
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call dgemv('N',sze,N_st_diag*iter,-1.d0,U,size(U,1), &
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c,1,1.d0,U(1,k,iter+1),1)
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call dgemv('T',sze,k-1,1.d0,U(1,1,iter+1),size(U,1), &
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U(1,k,iter+1),1,0.d0,c,1)
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call dgemv('N',sze,k-1,-1.d0,U(1,1,iter+1),size(U,1), &
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c,1,1.d0,U(1,k,iter+1),1)
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call normalize( U(1,k,iter+1), sze )
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enddo
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enddo
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if (.not.converged) then
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iter = davidson_sze_max-1
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endif
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! Re-contract to u_in
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! -----------
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do k=1,N_st_diag
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do i=1,sze
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u_in(i,k) = 0.d0
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enddo
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enddo
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call dgemm('N','N', sze, N_st_diag, N_st_diag*iter, 1.d0, &
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U, size(U,1), y, N_st_diag*davidson_sze_max, &
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0.d0, u_in, size(u_in,1))
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enddo
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do k=1,N_st_diag
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energies(k) = lambda(k)
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enddo
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write_buffer = '===== '
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do i=1,N_st
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write_buffer = trim(write_buffer)//' ================ ================'
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enddo
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write(iunit,'(A)') trim(write_buffer)
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write(iunit,'(A)') ''
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call write_time(iunit)
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deallocate ( &
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W, residual_norm, &
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U, overlap, &
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R, c, &
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h, &
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y, &
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lambda &
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)
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end
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subroutine u_0_H_u_0_mrcc_nstates(e_0,u_0,n,keys_tmp,Nint,istate,N_st,sze_8)
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use bitmasks
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implicit none
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BEGIN_DOC
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! Computes e_0 = <u_0|H|u_0>/<u_0|u_0>
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!
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! n : number of determinants
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!
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END_DOC
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integer, intent(in) :: n,Nint,N_st,sze_8
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double precision, intent(out) :: e_0(N_st)
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double precision, intent(in) :: u_0(sze_8,N_st)
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integer(bit_kind),intent(in) :: keys_tmp(Nint,2,n)
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integer,intent(in) :: istate
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double precision, allocatable :: v_0(:,:), H_jj(:)
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double precision :: u_dot_u,u_dot_v,diag_H_mat_elem
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integer :: i,j
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allocate(H_jj(n), v_0(sze_8,N_st))
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do i = 1, n
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H_jj(i) = diag_H_mat_elem(keys_tmp(1,1,i),Nint)
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enddo
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do i=1,N_det_ref
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H_jj(idx_ref(i)) += delta_ii(istate,i)
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enddo
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call H_u_0_mrcc_nstates(v_0,u_0,H_jj,n,keys_tmp,Nint,istate,N_st,sze_8)
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do i=1,N_st
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e_0(i) = u_dot_v(v_0(1,i),u_0(1,i),n)/u_dot_u(u_0(1,i),n)
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enddo
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deallocate(H_jj, v_0)
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end
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subroutine H_u_0_mrcc_nstates(v_0,u_0,H_jj,n,keys_tmp,Nint,istate_in,N_st,sze_8)
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use bitmasks
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implicit none
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BEGIN_DOC
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! Computes v_0 = H|u_0>
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!
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! n : number of determinants
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!
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! H_jj : array of <j|H|j>
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END_DOC
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integer, intent(in) :: n,Nint,istate_in,N_st,sze_8
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double precision, intent(out) :: v_0(sze_8,N_st)
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double precision, intent(in) :: u_0(sze_8,N_st)
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double precision, intent(in) :: H_jj(n)
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integer(bit_kind),intent(in) :: keys_tmp(Nint,2,n)
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double precision :: hij
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double precision, allocatable :: vt(:,:)
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integer :: i,j,k,l, jj,ii
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integer :: i0, j0
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integer(bit_kind) :: sorted_i(Nint)
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integer,allocatable :: shortcut(:,:), sort_idx(:,:)
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integer(bit_kind), allocatable :: sorted(:,:,:), version(:,:,:)
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integer :: sh, sh2, ni, exa, ext, org_i, org_j, endi, pass, istate
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ASSERT (Nint > 0)
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ASSERT (Nint == N_int)
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ASSERT (n>0)
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PROVIDE ref_bitmask_energy
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allocate (shortcut(0:n+1,2), sort_idx(n,2), sorted(Nint,n,2), version(Nint,n,2))
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v_0 = 0.d0
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call sort_dets_ab_v(keys_tmp, sorted(1,1,1), sort_idx(1,1), shortcut(0,1), version(1,1,1), n, Nint)
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call sort_dets_ba_v(keys_tmp, sorted(1,1,2), sort_idx(1,2), shortcut(0,2), version(1,1,2), n, Nint)
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!$OMP PARALLEL DEFAULT(NONE) &
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!$OMP PRIVATE(i,hij,j,k,jj,vt,ii,sh,sh2,ni,exa,ext,org_i,org_j,endi,sorted_i,istate)&
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!$OMP SHARED(n,H_jj,u_0,keys_tmp,Nint,v_0,sorted,shortcut,sort_idx,version,N_st,sze_8,&
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!$OMP istate_in,delta_ij,N_det_ref,N_det_non_ref,idx_ref,idx_non_ref)
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allocate(vt(sze_8,N_st))
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Vt = 0.d0
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!$OMP DO SCHEDULE(static,1)
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do sh=1,shortcut(0,1)
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do sh2=sh,shortcut(0,1)
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exa = 0
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do ni=1,Nint
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exa = exa + popcnt(xor(version(ni,sh,1), version(ni,sh2,1)))
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end do
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if(exa > 2) then
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cycle
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end if
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do i=shortcut(sh,1),shortcut(sh+1,1)-1
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org_i = sort_idx(i,1)
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if(sh==sh2) then
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endi = i-1
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else
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endi = shortcut(sh2+1,1)-1
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end if
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do ni=1,Nint
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sorted_i(ni) = sorted(ni,i,1)
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enddo
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do j=shortcut(sh2,1),endi
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org_j = sort_idx(j,1)
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ext = exa
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do ni=1,Nint
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ext = ext + popcnt(xor(sorted_i(ni), sorted(ni,j,1)))
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end do
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if(ext <= 4) then
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call i_H_j(keys_tmp(1,1,org_j),keys_tmp(1,1,org_i),Nint,hij)
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do istate=1,N_st
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vt (org_i,istate) = vt (org_i,istate) + hij*u_0(org_j,istate)
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vt (org_j,istate) = vt (org_j,istate) + hij*u_0(org_i,istate)
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enddo
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endif
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enddo
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enddo
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enddo
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enddo
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!$OMP END DO
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!$OMP DO SCHEDULE(static,1)
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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
|
|
!$OMP END DO
|
|
|
|
!$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
|
|
!$OMP END DO
|
|
|
|
do istate=1,N_st
|
|
do i=n,1,-1
|
|
!$OMP ATOMIC
|
|
v_0(i,istate) = v_0(i,istate) + vt(i,istate)
|
|
enddo
|
|
enddo
|
|
|
|
deallocate(vt)
|
|
!$OMP END PARALLEL
|
|
|
|
do istate=1,N_st
|
|
do i=1,n
|
|
v_0(i,istate) += H_jj(i) * u_0(i,istate)
|
|
enddo
|
|
enddo
|
|
deallocate (shortcut, sort_idx, sorted, version)
|
|
|
|
end
|
|
|
|
|
|
subroutine davidson_diag_mrcc_hs2(dets_in,u_in,dim_in,energies,sze,N_st,N_st_diag,Nint,iunit,istate)
|
|
use bitmasks
|
|
implicit none
|
|
BEGIN_DOC
|
|
! Davidson diagonalization.
|
|
!
|
|
! dets_in : bitmasks corresponding to determinants
|
|
!
|
|
! u_in : guess coefficients on the various states. Overwritten
|
|
! on exit
|
|
!
|
|
! dim_in : leftmost dimension of u_in
|
|
!
|
|
! sze : Number of determinants
|
|
!
|
|
! N_st : Number of eigenstates
|
|
!
|
|
! iunit : Unit number for the I/O
|
|
!
|
|
! Initial guess vectors are not necessarily orthonormal
|
|
END_DOC
|
|
integer, intent(in) :: dim_in, sze, N_st, N_st_diag, Nint, iunit, istate
|
|
integer(bit_kind), intent(in) :: dets_in(Nint,2,sze)
|
|
double precision, intent(inout) :: u_in(dim_in,N_st_diag)
|
|
double precision, intent(out) :: energies(N_st_diag)
|
|
double precision, allocatable :: H_jj(:), S2_jj(:)
|
|
|
|
double precision :: diag_h_mat_elem
|
|
integer :: i
|
|
ASSERT (N_st > 0)
|
|
ASSERT (sze > 0)
|
|
ASSERT (Nint > 0)
|
|
ASSERT (Nint == N_int)
|
|
PROVIDE mo_bielec_integrals_in_map
|
|
allocate(H_jj(sze), S2_jj(sze))
|
|
|
|
H_jj(1) = diag_h_mat_elem(dets_in(1,1,1),Nint)
|
|
call get_s2(dets_in(1,1,1),dets_in(1,1,1),Nint,S2_jj(1))
|
|
!$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
|
|
do i=2,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 END PARALLEL
|
|
|
|
do i=1,N_det_ref
|
|
H_jj(idx_ref(i)) += delta_ii(istate,i)
|
|
enddo
|
|
|
|
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 :: u_dot_v, u_dot_u
|
|
|
|
integer :: k_pairs, kl
|
|
|
|
integer :: iter2
|
|
double precision, allocatable :: W(:,:), U(:,:), S(:,:), overlap(:,:)
|
|
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, itermax
|
|
include 'constants.include.F'
|
|
|
|
!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: U, W, S, y, h, lambda
|
|
if (N_st_diag*3 > sze) then
|
|
print *, 'error in Davidson :'
|
|
print *, 'Increase n_det_max_jacobi to ', N_st_diag*3
|
|
stop -1
|
|
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)
|
|
|
|
itermax = min(davidson_sze_max, sze/N_st_diag)
|
|
allocate( &
|
|
W(sze_8,N_st_diag*itermax), &
|
|
U(sze_8,N_st_diag*itermax), &
|
|
S(sze_8,N_st_diag*itermax), &
|
|
h(N_st_diag*itermax,N_st_diag*itermax), &
|
|
y(N_st_diag*itermax,N_st_diag*itermax), &
|
|
s_(N_st_diag*itermax,N_st_diag*itermax), &
|
|
s_tmp(N_st_diag*itermax,N_st_diag*itermax), &
|
|
residual_norm(N_st_diag), &
|
|
c(N_st_diag*itermax), &
|
|
s2(N_st_diag*itermax), &
|
|
overlap(N_st_diag*itermax,N_st_diag*itermax), &
|
|
lambda(N_st_diag*itermax))
|
|
|
|
h = 0.d0
|
|
s_ = 0.d0
|
|
s_tmp = 0.d0
|
|
U = 0.d0
|
|
W = 0.d0
|
|
S = 0.d0
|
|
y = 0.d0
|
|
|
|
|
|
ASSERT (N_st > 0)
|
|
ASSERT (N_st_diag >= N_st)
|
|
ASSERT (sze > 0)
|
|
ASSERT (Nint > 0)
|
|
ASSERT (Nint == N_int)
|
|
|
|
! Davidson iterations
|
|
! ===================
|
|
|
|
converged = .False.
|
|
|
|
double precision :: r1, r2
|
|
do k=N_st+1,N_st_diag
|
|
u_in(k,k) = 10.d0
|
|
do i=1,sze
|
|
call random_number(r1)
|
|
call random_number(r2)
|
|
r1 = dsqrt(-2.d0*dlog(r1))
|
|
r2 = dtwo_pi*r2
|
|
u_in(i,k) = r1*dcos(r2)
|
|
enddo
|
|
enddo
|
|
do k=1,N_st_diag
|
|
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
|
|
|
|
call ortho_qr(U,size(U,1),sze,shift2)
|
|
|
|
! 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>
|
|
! -------------------------------------------
|
|
|
|
|
|
call dgemm('T','N', shift2, shift2, sze, &
|
|
1.d0, U, size(U,1), W, size(W,1), &
|
|
0.d0, h, size(h,1))
|
|
|
|
call dgemm('T','N', shift2, shift2, sze, &
|
|
1.d0, U, size(U,1), S, size(S,1), &
|
|
0.d0, s_, size(s_,1))
|
|
|
|
! ! Diagonalize S^2
|
|
! ! ---------------
|
|
!
|
|
! call lapack_diag(s2,y,s_,size(s_,1),shift2)
|
|
!
|
|
! ! Rotate H in the basis of eigenfunctions of s2
|
|
! ! ---------------------------------------------
|
|
!
|
|
! call dgemm('N','N',shift2,shift2,shift2, &
|
|
! 1.d0, h, size(h,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, h, size(h,1))
|
|
!
|
|
! ! Damp interaction between different spin states
|
|
! ! ------------------------------------------------
|
|
!
|
|
! do k=1,shift2
|
|
! do l=1,shift2
|
|
! if (dabs(s2(k) - s2(l)) > 1.d0) then
|
|
! h(k,l) = h(k,l)*(max(0.d0,1.d0 - dabs(s2(k) - s2(l))))
|
|
! endif
|
|
! enddo
|
|
! enddo
|
|
!
|
|
! ! Rotate back H
|
|
! ! -------------
|
|
!
|
|
! call dgemm('N','T',shift2,shift2,shift2, &
|
|
! 1.d0, h, size(h,1), y, size(y,1), &
|
|
! 0.d0, s_tmp, size(s_tmp,1))
|
|
!
|
|
! call dgemm('N','N',shift2,shift2,shift2, &
|
|
! 1.d0, y, size(y,1), s_tmp, size(s_tmp,1), &
|
|
! 0.d0, h, size(h,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) < 0.6d0)
|
|
enddo
|
|
else
|
|
do k=1,size(state_ok)
|
|
state_ok(k) = .True.
|
|
enddo
|
|
endif
|
|
|
|
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
|
|
|
|
if (state_following) then
|
|
|
|
! Compute overlap with U_in
|
|
! -------------------------
|
|
|
|
integer :: order(N_st_diag)
|
|
double precision :: cmax
|
|
overlap = -1.d0
|
|
do k=1,shift2
|
|
do i=1,shift2
|
|
overlap(k,i) = dabs(y(k,i))
|
|
enddo
|
|
enddo
|
|
do k=1,N_st
|
|
cmax = -1.d0
|
|
do i=1,N_st
|
|
if (overlap(i,k) > cmax) then
|
|
cmax = overlap(i,k)
|
|
order(k) = i
|
|
endif
|
|
enddo
|
|
do i=1,shift2
|
|
overlap(order(k),i) = -1.d0
|
|
enddo
|
|
enddo
|
|
overlap = y
|
|
do k=1,N_st
|
|
l = order(k)
|
|
if (k /= l) then
|
|
y(1:shift2,k) = overlap(1:shift2,l)
|
|
endif
|
|
enddo
|
|
do k=1,N_st
|
|
overlap(k,1) = lambda(k)
|
|
overlap(k,2) = s2(k)
|
|
enddo
|
|
do k=1,N_st
|
|
l = order(k)
|
|
if (k /= l) then
|
|
lambda(k) = overlap(l,1)
|
|
s2(k) = overlap(l,2)
|
|
endif
|
|
enddo
|
|
|
|
endif
|
|
|
|
|
|
! Express eigenvectors of h in the determinant basis
|
|
! --------------------------------------------------
|
|
|
|
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
|
|
! if (state_ok(k)) then
|
|
do i=1,sze
|
|
U(i,shift2+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 &
|
|
)/max(H_jj(i) - lambda (k),1.d-2)
|
|
enddo
|
|
! else
|
|
! ! Randomize components with bad <S2>
|
|
! do i=1,sze-2,2
|
|
! call random_number(r1)
|
|
! call random_number(r2)
|
|
! r1 = dsqrt(-2.d0*dlog(r1))
|
|
! r2 = dtwo_pi*r2
|
|
! U(i,shift2+k) = r1*dcos(r2)
|
|
! U(i+1,shift2+k) = r1*dsin(r2)
|
|
! enddo
|
|
! do i=sze-2+1,sze
|
|
! call random_number(r1)
|
|
! call random_number(r2)
|
|
! r1 = dsqrt(-2.d0*dlog(r1))
|
|
! r2 = dtwo_pi*r2
|
|
! U(i,shift2+k) = r1*dcos(r2)
|
|
! enddo
|
|
! endif
|
|
|
|
if (k <= N_st) then
|
|
residual_norm(k) = u_dot_u(U(1,shift2+k),sze)
|
|
to_print(1,k) = lambda(k) + nuclear_repulsion
|
|
to_print(2,k) = s2(k)
|
|
to_print(3,k) = residual_norm(k)
|
|
endif
|
|
enddo
|
|
|
|
write(iunit,'(X,I3,X,100(X,F16.10,X,F11.6,X,E11.3))') iter, to_print(1:3,1:N_st)
|
|
call davidson_converged(lambda,residual_norm,wall,iter,cpu,N_st,converged)
|
|
do k=1,N_st
|
|
if (residual_norm(k) > 1.e8) then
|
|
print *, ''
|
|
stop 'Davidson failed'
|
|
endif
|
|
enddo
|
|
if (converged) then
|
|
exit
|
|
endif
|
|
|
|
enddo
|
|
|
|
! Re-contract to u_in
|
|
! -----------
|
|
|
|
call dgemm('N','N', sze, N_st_diag, shift2, &
|
|
1.d0, U, size(U,1), y, size(y,1), 0.d0, u_in, size(u_in,1))
|
|
|
|
enddo
|
|
|
|
do k=1,N_st_diag
|
|
energies(k) = lambda(k)
|
|
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 ( &
|
|
W, residual_norm, &
|
|
U, overlap, &
|
|
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 : $IRP_ALIGN :: vt, ut
|
|
|
|
N_st_8 = align_double(N_st)
|
|
|
|
ASSERT (Nint > 0)
|
|
ASSERT (Nint == N_int)
|
|
ASSERT (n>0)
|
|
PROVIDE ref_bitmask_energy
|
|
|
|
allocate (shortcut(0:n+1,2), sort_idx(n,2), sorted(Nint,n,2), version(Nint,n,2))
|
|
allocate(ut(N_st_8,n))
|
|
|
|
v_0 = 0.d0
|
|
s_0 = 0.d0
|
|
|
|
do i=1,n
|
|
do istate=1,N_st
|
|
ut(istate,i) = u_0(i,istate)
|
|
enddo
|
|
enddo
|
|
|
|
call sort_dets_ab_v(keys_tmp, sorted(1,1,1), sort_idx(1,1), shortcut(0,1), version(1,1,1), n, Nint)
|
|
call sort_dets_ba_v(keys_tmp, sorted(1,1,2), sort_idx(1,2), shortcut(0,2), version(1,1,2), n, Nint)
|
|
|
|
PROVIDE delta_ij_s2
|
|
!$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, &
|
|
!$OMP N_det_ref, idx_ref, N_det_non_ref, idx_non_ref, delta_ij, delta_ij_s2,istate_in)
|
|
allocate(vt(N_st_8,n),st(N_st_8,n))
|
|
Vt = 0.d0
|
|
St = 0.d0
|
|
|
|
!$OMP DO SCHEDULE(guided)
|
|
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
|
|
!$OMP END DO
|
|
|
|
!$OMP DO SCHEDULE(guided)
|
|
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
|
|
!$OMP END DO
|
|
|
|
! --------------------------
|
|
! Begin Specific to dressing
|
|
! --------------------------
|
|
|
|
!$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)
|
|
st (istate,i) = st (istate,i) + delta_ij_s2(istate_in,jj,ii)*ut(istate,j)
|
|
st (istate,j) = st (istate,j) + delta_ij_s2(istate_in,jj,ii)*ut(istate,i)
|
|
enddo
|
|
enddo
|
|
enddo
|
|
!$OMP END DO
|
|
|
|
! ------------------------
|
|
! End Specific to dressing
|
|
! ------------------------
|
|
|
|
do istate=1,N_st
|
|
do i=n,1,-1
|
|
!$OMP ATOMIC
|
|
v_0(i,istate) = v_0(i,istate) + vt(istate,i)
|
|
!$OMP ATOMIC
|
|
s_0(i,istate) = s_0(i,istate) + st(istate,i)
|
|
enddo
|
|
enddo
|
|
|
|
deallocate(vt,st)
|
|
!$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
|
|
|