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)) H_jj(1) = diag_h_mat_elem(dets_in(1,1,1),Nint) !$OMP PARALLEL DEFAULT(NONE) & !$OMP SHARED(sze,H_jj,N_det_ref,dets_in,Nint,istate,delta_ii,idx_ref) & !$OMP PRIVATE(i) !$OMP DO do i=2,sze H_jj(i) = diag_h_mat_elem(dets_in(1,1,i),Nint) 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_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 :: 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( & 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> ! ----------------------------------------- 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 = = ! ------------------------------------------- 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 ! 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 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) 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 do i=1,sze u_in(i,k) = 0.d0 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 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, & 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 = / ! ! 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 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(static,1) 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 !$OMP END DO !$OMP DO SCHEDULE(static,1) 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> ! ----------------------------------------- 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 = = ! ------------------------------------------- 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 ! 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 ! ! S2_jj : array of 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