BEGIN_PROVIDER [ character*(64), diag_algorithm ] implicit none BEGIN_DOC ! Diagonalization algorithm (Davidson or Lapack) END_DOC if (N_det > N_det_max_full) then diag_algorithm = "Davidson" else diag_algorithm = "Lapack" endif if (N_det < N_states) then diag_algorithm = "Lapack" endif END_PROVIDER BEGIN_PROVIDER [ double precision, threshold_davidson_pt2 ] implicit none BEGIN_DOC ! Threshold of Davidson's algorithm, using PT2 as a guide END_DOC threshold_davidson_pt2 = threshold_davidson END_PROVIDER BEGIN_PROVIDER [ integer, dressed_column_idx, (N_states) ] implicit none BEGIN_DOC ! Index of the dressed columns END_DOC integer :: i double precision :: tmp integer, external :: idamax do i=1,N_states dressed_column_idx(i) = idamax(N_det, psi_coef(1,i), 1) enddo END_PROVIDER subroutine davidson_diag_hs2(dets_in,u_in,s2_out,dim_in,energies,sze,N_st,N_st_diag,Nint,dressing_state,converged) 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 ! ! Initial guess vectors are not necessarily orthonormal END_DOC integer, intent(in) :: dim_in, sze, N_st, N_st_diag, Nint 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), s2_out(N_st_diag) integer, intent(in) :: dressing_state logical, intent(out) :: converged double precision, allocatable :: H_jj(:) double precision, external :: diag_H_mat_elem, diag_S_mat_elem integer :: i,k ASSERT (N_st > 0) ASSERT (sze > 0) ASSERT (Nint > 0) ASSERT (Nint == N_int) PROVIDE mo_two_e_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, dets_in,Nint) & !$OMP PRIVATE(i) !$OMP DO SCHEDULE(static) do i=2,sze H_jj(i) = diag_H_mat_elem(dets_in(1,1,i),Nint) enddo !$OMP END DO !$OMP END PARALLEL if (dressing_state > 0) then do k=1,N_st do i=1,sze H_jj(i) += u_in(i,k) * dressing_column_h(i,k) enddo enddo endif call davidson_diag_hjj_sjj(dets_in,u_in,H_jj,S2_out,energies,dim_in,sze,N_st,N_st_diag,Nint,dressing_state,converged) deallocate (H_jj) end subroutine davidson_diag_hjj_sjj(dets_in,u_in,H_jj,s2_out,energies,dim_in,sze,N_st,N_st_diag_in,Nint,dressing_state,converged) use bitmasks use mmap_module 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_out : Output : s^2 ! ! 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_in : Number of states in which H is diagonalized. Assumed > sze ! ! Initial guess vectors are not necessarily orthonormal END_DOC integer, intent(in) :: dim_in, sze, N_st, N_st_diag_in, Nint integer(bit_kind), intent(in) :: dets_in(Nint,2,sze) double precision, intent(in) :: H_jj(sze) integer, intent(in) :: dressing_state double precision, intent(inout) :: s2_out(N_st_diag_in) double precision, intent(inout) :: u_in(dim_in,N_st_diag_in) double precision, intent(out) :: energies(N_st_diag_in) integer :: iter, N_st_diag integer :: i,j,k,l,m logical, intent(inout) :: converged double precision, external :: u_dot_v, u_dot_u integer :: k_pairs, kl integer :: iter2, itertot double precision, allocatable :: y(:,:), h(:,:), h_p(:,:), lambda(:), s2(:) real, allocatable :: y_s(:,:) double precision, allocatable :: 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, istate double precision :: r1, r2, alpha logical :: state_ok(N_st_diag_in*davidson_sze_max) integer :: nproc_target integer :: order(N_st_diag_in) double precision :: cmax double precision, allocatable :: U(:,:), overlap(:,:), S_d(:,:) double precision, pointer :: W(:,:) real, pointer :: S(:,:) logical :: disk_based double precision :: energy_shift(N_st_diag_in*davidson_sze_max) include 'constants.include.F' N_st_diag = N_st_diag_in !DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: U, W, S, y, y_s, S_d, h, lambda if (N_st_diag*3 > sze) then print *, 'error in Davidson :' print *, 'Increase n_det_max_full to ', N_st_diag*3 stop -1 endif itermax = max(2,min(davidson_sze_max, sze/N_st_diag))+1 itertot = 0 if (state_following) then allocate(overlap(N_st_diag*itermax, N_st_diag*itermax)) else allocate(overlap(1,1)) ! avoid 'if' for deallocate endif overlap = 0.d0 PROVIDE nuclear_repulsion expected_s2 psi_bilinear_matrix_order psi_bilinear_matrix_order_reverse threshold_davidson_pt2 threshold_davidson_from_pt2 call write_time(6) write(6,'(A)') '' write(6,'(A)') 'Davidson Diagonalization' write(6,'(A)') '------------------------' write(6,'(A)') '' ! Find max number of cores to fit in memory ! ----------------------------------------- nproc_target = nproc double precision :: rss integer :: maxab maxab = max(N_det_alpha_unique, N_det_beta_unique)+1 m=1 disk_based = .False. call resident_memory(rss) do r1 = 8.d0 * &! bytes ( dble(sze)*(N_st_diag*itermax) &! U + 1.5d0*dble(sze*m)*(N_st_diag*itermax) &! W,S + 1.d0*dble(sze)*(N_st_diag) &! S_d + 4.5d0*(N_st_diag*itermax)**2 &! h,y,y_s,s_,s_tmp + 2.d0*(N_st_diag*itermax) &! s2,lambda + 1.d0*(N_st_diag) &! residual_norm ! In H_S2_u_0_nstates_zmq + 3.d0*(N_st_diag*N_det) &! u_t, v_t, s_t on collector + 3.d0*(N_st_diag*N_det) &! u_t, v_t, s_t on slave + 0.5d0*maxab &! idx0 in H_S2_u_0_nstates_openmp_work_* + nproc_target * &! In OMP section ( 1.d0*(N_int*maxab) &! buffer + 3.5d0*(maxab) ) &! singles_a, singles_b, doubles, idx ) / 1024.d0**3 if (nproc_target == 0) then call check_mem(r1,irp_here) nproc_target = 1 exit endif if (r1+rss < qp_max_mem) then exit endif if (itermax > 4) then itermax = itermax - 1 else if (m==1.and.disk_based_davidson) then m=0 disk_based = .True. itermax = 6 else nproc_target = nproc_target - 1 endif enddo nthreads_davidson = nproc_target TOUCH nthreads_davidson call write_int(6,N_st,'Number of states') call write_int(6,N_st_diag,'Number of states in diagonalization') call write_int(6,sze,'Number of determinants') call write_int(6,nproc_target,'Number of threads for diagonalization') call write_double(6, r1, 'Memory(Gb)') if (disk_based) then print *, 'Using swap space to reduce RAM' endif !--------------- write(6,'(A)') '' write_buffer = '=====' do i=1,N_st write_buffer = trim(write_buffer)//' ================ =========== ===========' enddo write(6,'(A)') write_buffer(1:6+41*N_st) write_buffer = 'Iter' do i=1,N_st write_buffer = trim(write_buffer)//' Energy S^2 Residual ' enddo write(6,'(A)') write_buffer(1:6+41*N_st) write_buffer = '=====' do i=1,N_st write_buffer = trim(write_buffer)//' ================ =========== ===========' enddo write(6,'(A)') write_buffer(1:6+41*N_st) if (disk_based) then ! Create memory-mapped files for W and S type(c_ptr) :: ptr_w, ptr_s integer :: fd_s, fd_w call mmap(trim(ezfio_work_dir)//'davidson_w', (/int(sze,8),int(N_st_diag*itermax,8)/),& 8, fd_w, .False., ptr_w) call mmap(trim(ezfio_work_dir)//'davidson_s', (/int(sze,8),int(N_st_diag*itermax,8)/),& 4, fd_s, .False., ptr_s) call c_f_pointer(ptr_w, w, (/sze,N_st_diag*itermax/)) call c_f_pointer(ptr_s, s, (/sze,N_st_diag*itermax/)) else allocate(W(sze,N_st_diag*itermax), S(sze,N_st_diag*itermax)) endif allocate( & ! Large U(sze,N_st_diag*itermax), & S_d(sze,N_st_diag), & ! Small h(N_st_diag*itermax,N_st_diag*itermax), & h_p(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), & s2(N_st_diag*itermax), & y_s(N_st_diag*itermax,N_st_diag*itermax), & lambda(N_st_diag*itermax)) h = 0.d0 U = 0.d0 y = 0.d0 s_ = 0.d0 s_tmp = 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. do k=N_st+1,N_st_diag 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) * u_in(i,k-N_st) enddo u_in(k,k) = u_in(k,k) + 10.d0 enddo do k=1,N_st_diag call normalize(u_in(1,k),sze) enddo do k=1,N_st_diag do i=1,sze U(i,k) = u_in(i,k) enddo enddo do while (.not.converged) itertot = itertot+1 if (itertot == 8) then exit endif do iter=1,itermax-1 shift = N_st_diag*(iter-1) shift2 = N_st_diag*iter if ((iter > 1).or.(itertot == 1)) then ! Compute |W_k> = \sum_i |i> ! ----------------------------------- if ((sze > 100000).and.distributed_davidson) then call H_S2_u_0_nstates_zmq (W(1,shift+1),S_d,U(1,shift+1),N_st_diag,sze) else call H_S2_u_0_nstates_openmp(W(1,shift+1),S_d,U(1,shift+1),N_st_diag,sze) endif S(1:sze,shift+1:shift+N_st_diag) = real(S_d(1:sze,1:N_st_diag)) else ! Already computed in update below continue endif if (dressing_state > 0) then if (N_st == 1) then l = dressed_column_idx(1) double precision :: f f = 1.0d0/psi_coef(l,1) do istate=1,N_st_diag do i=1,sze W(i,shift+istate) += dressing_column_h(i,1) *f * U(l,shift+istate) W(l,shift+istate) += dressing_column_h(i,1) *f * U(i,shift+istate) S(i,shift+istate) += real(dressing_column_s(i,1) *f * U(l,shift+istate)) S(l,shift+istate) += real(dressing_column_s(i,1) *f * U(i,shift+istate)) enddo enddo else call dgemm('T','N', N_st, N_st_diag, sze, 1.d0, & psi_coef, size(psi_coef,1), & U(1,shift+1), size(U,1), 0.d0, s_tmp, size(s_tmp,1)) call dgemm('N','N', sze, N_st_diag, N_st, 1.0d0, & dressing_column_h, size(dressing_column_h,1), s_tmp, size(s_tmp,1), & 1.d0, W(1,shift+1), size(W,1)) call dgemm('N','N', sze, N_st_diag, N_st, 1.0d0, & dressing_column_s, size(dressing_column_s,1), s_tmp, size(s_tmp,1), & 1.d0, S_d, size(S_d,1)) call dgemm('T','N', N_st, N_st_diag, sze, 1.d0, & dressing_column_h, size(dressing_column_h,1), & U(1,shift+1), size(U,1), 0.d0, s_tmp, size(s_tmp,1)) call dgemm('N','N', sze, N_st_diag, N_st, 1.0d0, & psi_coef, size(psi_coef,1), s_tmp, size(s_tmp,1), & 1.d0, W(1,shift+1), size(W,1)) call dgemm('T','N', N_st, N_st_diag, sze, 1.d0, & dressing_column_s, size(dressing_column_s,1), & U(1,shift+1), size(U,1), 0.d0, s_tmp, size(s_tmp,1)) call dgemm('N','N', sze, N_st_diag, N_st, 1.0d0, & psi_coef, size(psi_coef,1), s_tmp, size(s_tmp,1), & 1.d0, S_d, size(S_d,1)) endif endif ! Compute s_kl = = ! ------------------------------------------- !$OMP PARALLEL DO DEFAULT(SHARED) PRIVATE(i,j,k) COLLAPSE(2) do j=1,shift2 do i=1,shift2 s_(i,j) = 0.d0 do k=1,sze s_(i,j) = s_(i,j) + U(k,i) * dble(S(k,j)) enddo enddo enddo !$OMP END PARALLEL DO ! 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_p,1)) call dgemm('T','N', shift2, shift2, sze, & 1.d0, U, size(U,1), U, size(U,1), & 0.d0, s_tmp, size(s_tmp,1)) ! Penalty method ! -------------- if (s2_eig) then h_p = s_ do k=1,shift2 h_p(k,k) = h_p(k,k) - expected_s2 enddo if (only_expected_s2) then alpha = 0.1d0 h_p = h + alpha*h_p else alpha = 0.0001d0 h_p = h + alpha*h_p endif else h_p = h alpha = 0.d0 endif ! Diagonalize h_p ! --------------- integer :: lwork, info double precision, allocatable :: work(:) y = h lwork = -1 allocate(work(1)) call dsygv(1,'V','U',shift2,y,size(y,1), & s_tmp,size(s_tmp,1), lambda, work,lwork,info) lwork = int(work(1)) deallocate(work) allocate(work(lwork)) call dsygv(1,'V','U',shift2,y,size(y,1), & s_tmp,size(s_tmp,1), lambda, work,lwork,info) deallocate(work) if (info /= 0) then stop 'DSYGV Diagonalization failed' endif ! Compute Energy for each eigenvector ! ----------------------------------- 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)) do k=1,shift2 lambda(k) = h(k,k) enddo ! 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) enddo if (only_expected_s2) then 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 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,N_st_diag 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)) y_s(:,:) = real(y(:,:)) call sgemm('N','N', sze, N_st_diag, shift2, & 1., S, size(S,1), y_s, size(y_s,1), 0., S(1,shift2+1), size(S,1)) ! Compute residual vector and davidson step ! ----------------------------------------- !$OMP PARALLEL DO DEFAULT(SHARED) PRIVATE(i,k) do k=1,N_st_diag do i=1,sze U(i,shift2+k) = & (lambda(k) * U(i,shift2+k) - W(i,shift2+k) ) & /max(H_jj(i) - lambda (k),1.d-2) enddo 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 !$OMP END PARALLEL DO if ((itertot>1).and.(iter == 1)) then !don't print continue else write(*,'(1X,I3,1X,100(1X,F16.10,1X,F11.6,1X,E11.3))') iter-1, to_print(1:3,1:N_st) endif ! Check convergence if (iter > 1) then if (threshold_davidson_from_pt2) then converged = dabs(maxval(residual_norm(1:N_st))) < threshold_davidson_pt2 else converged = dabs(maxval(residual_norm(1:N_st))) < threshold_davidson endif endif do k=1,N_st if (residual_norm(k) > 1.d8) then print *, 'Davidson failed' stop -1 endif enddo if (converged) then exit endif logical, external :: qp_stop if (qp_stop()) then converged = .True. exit endif enddo ! Re-contract U and update S and W ! -------------------------------- call sgemm('N','N', sze, N_st_diag, shift2, 1., & S, size(S,1), y_s, size(y_s,1), 0., S(1,shift2+1), size(S,1)) do k=1,N_st_diag do i=1,sze S(i,k) = S(i,shift2+k) enddo enddo call dgemm('N','N', sze, N_st_diag, shift2, 1.d0, & W, size(W,1), y, size(y,1), 0.d0, u_in, size(u_in,1)) do k=1,N_st_diag do i=1,sze W(i,k) = u_in(i,k) enddo enddo 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)) do k=1,N_st_diag do i=1,sze U(i,k) = u_in(i,k) enddo enddo enddo call nullify_small_elements(sze,N_st_diag,U,size(U,1),threshold_davidson_pt2) do k=1,N_st_diag do i=1,sze u_in(i,k) = U(i,k) enddo enddo do k=1,N_st_diag energies(k) = lambda(k) s2_out(k) = s2(k) enddo write_buffer = '======' do i=1,N_st write_buffer = trim(write_buffer)//' ================ =========== ===========' enddo write(6,'(A)') trim(write_buffer) write(6,'(A)') '' call write_time(6) if (disk_based)then ! Remove temp files integer, external :: getUnitAndOpen call munmap( (/int(sze,8),int(N_st_diag*itermax,8)/), 8, fd_w, ptr_w ) fd_w = getUnitAndOpen(trim(ezfio_work_dir)//'davidson_w','r') close(fd_w,status='delete') call munmap( (/int(sze,8),int(N_st_diag*itermax,8)/), 4, fd_s, ptr_s ) fd_s = getUnitAndOpen(trim(ezfio_work_dir)//'davidson_s','r') close(fd_s,status='delete') else deallocate(W,S) endif deallocate ( & residual_norm, & U, overlap, & h, y_s, S_d, & y, s_, s_tmp, & lambda & ) FREE nthreads_davidson end