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https://github.com/LCPQ/quantum_package
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414
src/MRCC/davidson.irp.f
Normal file
414
src/MRCC/davidson.irp.f
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subroutine davidson_diag_mrcc(dets_in,u_in,energies,dim_in,sze,N_st,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
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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)
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double precision, intent(out) :: energies(N_st)
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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 (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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!$OMP PARALLEL DEFAULT(NONE) &
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!$OMP SHARED(sze,H_jj,dets_in,Nint,istate,delta_ij) &
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!$OMP PRIVATE(i)
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!$OMP DO SCHEDULE(guided)
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do i=1,sze
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H_jj(i) = diag_h_mat_elem(dets_in(1,1,i),Nint) + delta_ij(i,i,istate)
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enddo
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!$OMP END DO
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!$OMP END PARALLEL
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call davidson_diag_hjj_mrcc(dets_in,u_in,H_jj,energies,dim_in,sze,N_st,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,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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! 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, 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)
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double precision, intent(out) :: energies(N_st)
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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 :: overlap(N_st,N_st)
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double precision :: u_dot_v, u_dot_u
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integer, allocatable :: kl_pairs(:,:)
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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 :: diag_h_mat_elem
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double precision :: residual_norm(N_st)
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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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PROVIDE det_connections
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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,sze,'Number of determinants')
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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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allocate( &
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kl_pairs(2,N_st*(N_st+1)/2), &
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W(sze,N_st,davidson_sze_max), &
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U(sze,N_st,davidson_sze_max), &
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R(sze,N_st), &
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h(N_st,davidson_sze_max,N_st,davidson_sze_max), &
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y(N_st,davidson_sze_max,N_st,davidson_sze_max), &
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lambda(N_st*davidson_sze_max))
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ASSERT (N_st > 0)
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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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k_pairs=0
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do l=1,N_st
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do k=1,l
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k_pairs+=1
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kl_pairs(1,k_pairs) = k
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kl_pairs(2,k_pairs) = l
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enddo
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enddo
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!$OMP PARALLEL DEFAULT(NONE) &
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!$OMP SHARED(U,sze,N_st,overlap,kl_pairs,k_pairs, &
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!$OMP Nint,dets_in,u_in) &
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!$OMP PRIVATE(k,l,kl,i)
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! Orthonormalize initial guess
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! ============================
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!$OMP DO
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do kl=1,k_pairs
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k = kl_pairs(1,kl)
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l = kl_pairs(2,kl)
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if (k/=l) then
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overlap(k,l) = u_dot_v(U_in(1,k),U_in(1,l),sze)
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overlap(l,k) = overlap(k,l)
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else
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overlap(k,k) = u_dot_u(U_in(1,k),sze)
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endif
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enddo
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!$OMP END DO
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!$OMP END PARALLEL
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call ortho_lowdin(overlap,size(overlap,1),N_st,U_in,size(U_in,1),sze)
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! Davidson iterations
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! ===================
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converged = .False.
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do while (.not.converged)
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!$OMP PARALLEL DEFAULT(NONE) &
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!$OMP PRIVATE(k,i) SHARED(U,u_in,sze,N_st)
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do k=1,N_st
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!$OMP DO
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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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!$OMP END DO
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enddo
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!$OMP END PARALLEL
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do iter=1,davidson_sze_max-1
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! Compute W_k = H |u_k>
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! ----------------------
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do k=1,N_st
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call H_u_0_mrcc(W(1,k,iter),U(1,k,iter),H_jj,sze,dets_in,Nint,istate)
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enddo
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! Compute h_kl = <u_k | W_l> = <u_k| H |u_l>
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! -------------------------------------------
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do l=1,N_st
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do k=1,N_st
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do iter2=1,iter-1
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h(k,iter2,l,iter) = u_dot_v(U(1,k,iter2),W(1,l,iter),sze)
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h(k,iter,l,iter2) = h(k,iter2,l,iter)
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enddo
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enddo
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do k=1,l
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h(k,iter,l,iter) = u_dot_v(U(1,k,iter),W(1,l,iter),sze)
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h(l,iter,k,iter) = h(k,iter,l,iter)
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enddo
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enddo
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!DEBUG H MATRIX
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!do i=1,iter
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! print '(10(x,F16.10))', h(1,i,1,1:i)
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!enddo
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!print *, ''
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!END
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! Diagonalize h
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! -------------
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call lapack_diag(lambda,y,h,N_st*davidson_sze_max,N_st*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
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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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do l=1,N_st
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do iter2=1,iter
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U(i,k,iter+1) = U(i,k,iter+1) + U(i,l,iter2)*y(l,iter2,k,1)
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W(i,k,iter+1) = W(i,k,iter+1) + W(i,l,iter2)*y(l,iter2,k,1)
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enddo
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enddo
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enddo
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enddo
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! Compute residual vector
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! -----------------------
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do k=1,N_st
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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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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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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
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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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double precision :: c
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do k=1,N_st
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do iter2=1,iter
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do l=1,N_st
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c = u_dot_v(U(1,k,iter+1),U(1,l,iter2),sze)
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do i=1,sze
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U(i,k,iter+1) -= c * U(i,l,iter2)
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enddo
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enddo
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enddo
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do l=1,k-1
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c = u_dot_v(U(1,k,iter+1),U(1,l,iter+1),sze)
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do i=1,sze
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U(i,k,iter+1) -= c * U(i,l,iter+1)
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enddo
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enddo
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call normalize( U(1,k,iter+1), sze )
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enddo
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!DEBUG : CHECK OVERLAP
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!print *, '==='
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!do k=1,iter+1
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! do l=1,k
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! c = u_dot_v(U(1,1,k),U(1,1,l),sze)
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! print *, k,l, c
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! enddo
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!enddo
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!print *, '==='
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!pause
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!END DEBUG
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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
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energies(k) = lambda(k)
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do i=1,sze
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u_in(i,k) = 0.d0
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do iter2=1,iter
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do l=1,N_st
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u_in(i,k) += U(i,l,iter2)*y(l,iter2,k,1)
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enddo
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enddo
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enddo
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enddo
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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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kl_pairs, &
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W, &
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U, &
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R, &
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h, &
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y, &
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lambda &
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)
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abort_here = abort_all
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end
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subroutine H_u_0_mrcc(v_0,u_0,H_jj,n,keys_tmp,Nint,istate)
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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
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double precision, intent(out) :: v_0(n)
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double precision, intent(in) :: u_0(n)
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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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integer, allocatable :: idx(:)
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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
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integer :: i0, j0
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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 delta_ij
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integer, parameter :: block_size = 157
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!$OMP PARALLEL DEFAULT(NONE) &
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!$OMP PRIVATE(i,hij,j,k,idx,jj,vt) &
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!$OMP SHARED(n,H_jj,u_0,keys_tmp,Nint,v_0,istate,delta_ij)
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!$OMP DO SCHEDULE(static)
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do i=1,n
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v_0(i) = H_jj(i) * u_0(i)
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enddo
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!$OMP END DO
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allocate(idx(0:n), vt(n))
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Vt = 0.d0
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!$OMP DO SCHEDULE(guided)
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do i=1,n
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idx(0) = i
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call filter_connected_davidson(keys_tmp,keys_tmp(1,1,i),Nint,i-1,idx)
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do jj=1,idx(0)
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j = idx(jj)
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if ( (dabs(u_0(j)) > 1.d-7).or.((dabs(u_0(i)) > 1.d-7)) ) then
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call i_H_j(keys_tmp(1,1,j),keys_tmp(1,1,i),Nint,hij)
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hij = hij + delta_ij(j,i,istate)
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vt (i) = vt (i) + hij*u_0(j)
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vt (j) = vt (j) + hij*u_0(i)
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endif
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enddo
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enddo
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!$OMP END DO
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!$OMP CRITICAL
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do i=1,n
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v_0(i) = v_0(i) + vt(i)
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enddo
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!$OMP END CRITICAL
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deallocate(idx,vt)
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!$OMP END PARALLEL
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end
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