! --- subroutine davidson_hs2_nonsym_b1space(u_in, H_jj, s2_out,energies, sze, N_st, N_st_diag_in, n_it_max_dav, converged, hcalc) use mmap_module BEGIN_DOC ! Generic modified-Davidson diagonalization ! ! H_jj : specific diagonal H matrix elements to diagonalize de Davidson ! ! u_in : guess coefficients on the various states. Overwritten on exit by right eigenvectors ! ! sze : Number of determinants ! ! N_st : Number of eigenstates ! ! N_st_diag_in : Number of states in which H is diagonalized. Assumed > N_st ! ! Initial guess vectors are not necessarily orthonormal ! ! hcalc subroutine to compute W = H U (see routine hcalc_template for template of input/output) ! ! !!! WARNING !!! IT SEEMS THAT IF THE NUMBER OF MACRO ITERATIONS EXCEEDS n_it_max_dav, ! ! THE RECONTRACTION IS WRONG. YOU SHOULD CONSIDER CALLING MULTIPLE TIME THE ROUTINE ! ! SEE FOR INSTANCE IN tc_bi_ortho/tc_h_eigvectors.irp.f END_DOC implicit none integer, intent(in) :: sze, N_st, N_st_diag_in, n_it_max_dav double precision, intent(in) :: H_jj(sze) logical, intent(inout) :: converged double precision, intent(inout) :: u_in(sze,N_st_diag_in) double precision, intent(out) :: energies(N_st) double precision, intent(inout) :: s2_out(N_st) external hcalc character*(16384) :: write_buffer integer :: iter, N_st_diag integer :: i, j, k, l, m integer :: iter2, itertot logical :: disk_based integer :: shift, shift2, itermax integer :: nproc_target integer :: order(N_st_diag_in) double precision :: to_print(3,N_st) double precision :: r1, r2, alpha double precision :: cpu, wall double precision :: cmax double precision :: energy_shift(N_st_diag_in*davidson_sze_max) double precision, allocatable :: U(:,:) double precision, allocatable :: y(:,:), h(:,:), lambda(:), h_p(:,:), s2(:) real, allocatable :: y_s(:,:) double precision, allocatable :: s_(:,:), s_tmp(:,:) double precision, allocatable :: residual_norm(:) double precision :: lambda_tmp integer, allocatable :: i_omax(:) double precision, allocatable :: U_tmp(:), overlap(:), S_d(:,:) double precision, allocatable :: W(:,:) real, pointer :: S(:,:) !double precision, pointer :: W(:,:) double precision, external :: u_dot_v, u_dot_u include 'constants.include.F' N_st_diag = N_st_diag_in ! print*,'trial vector' do i = 1, sze if(isnan(u_in(i,1)))then print*,'pb in input vector of davidson_general_ext_rout_nonsym_b1space' print*,i,u_in(i,1) stop else if (dabs(u_in(i,1)).lt.1.d-16)then u_in(i,1) = 0.d0 endif enddo !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 provide threshold_nonsym_davidson 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 = sze 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 + 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 basis functions') 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) ! --- allocate( W(sze,N_st_diag*itermax), S(sze,N_st_diag*itermax) ) 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), & lambda(N_st_diag*itermax), & residual_norm(N_st_diag), & i_omax(N_st), & s2(N_st_diag*itermax), & y_s(N_st_diag*itermax,N_st_diag*itermax) & ) U = 0.d0 h = 0.d0 y = 0.d0 s_ = 0.d0 s_tmp = 0.d0 lambda = 0.d0 residual_norm = 0.d0 ASSERT (N_st > 0) ASSERT (N_st_diag >= N_st) ASSERT (sze > 0) ! Davidson iterations ! =================== converged = .False. ! Initialize from N_st to N_st_diag with gaussian random numbers ! to be sure to have overlap with any eigenvectors 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 ! Normalize all states do k = 1, N_st_diag call normalize(u_in(1,k), sze) enddo ! Copy from the guess input "u_in" to the working vectors "U" do k = 1, N_st_diag do i = 1, sze U(i,k) = u_in(i,k) enddo enddo ! --- itertot = 0 ! do while (.not.converged.or.itertot.le.n_it_max_dav) integer :: iiii do iiii = 1, n_it_max_dav 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 ! Gram-Schmidt to orthogonalize all new guess with the previous vectors call ortho_qr(U, size(U, 1), sze, shift2) call ortho_qr(U, size(U, 1), sze, shift2) ! W = H U ! call hcalc(W(1,shift+1), U(1,shift+1), N_st_diag, sze) call hcalc(W(1,shift+1),S_d,U(1,shift+1),N_st_diag,sze) 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 ! 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, 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 y = lambda y ! --------------------------- call diag_nonsym_right(shift2, h_p(1,1), size(h_p, 1), y(1,1), size(y, 1), lambda(1), size(lambda, 1)) do k = 1, N_st_diag ! print*,'lambda(k) before = ',lambda(k) lambda(k) = 0.d0 do l = 1, shift2 do m = 1, shift2 lambda(k) += y(m,k) * h(m,l) * y(l,k) enddo enddo ! print*,'lambda(k) new = ',lambda(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 ! Express eigenvectors of h in the determinant basis: ! --------------------------------------------------- ! y(:,k) = rk ! U(:,k) = Bk ! U(:,shift2+k) = Rk = Bk x rk 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) ) do k = 1, N_st_diag call normalize(U(1,shift2+k), sze) enddo ! --- ! select the max overlap ! ! start test ------------------------------------------------------------------------ ! !double precision, allocatable :: Utest(:,:), Otest(:) !allocate( Utest(sze,shift2), Otest(shift2) ) !call dgemm( 'N', 'N', sze, shift2, shift2, 1.d0 & ! , U, size(U, 1), y, size(y, 1), 0.d0, Utest(1,1), size(Utest, 1) ) !do k = 1, shift2 ! call normalize(Utest(1,k), sze) !enddo !do j = 1, sze ! write(455, '(100(1X, F16.10))') (Utest(j,k), k=1,shift2) !enddo !do k = 1, shift2 ! Otest(k) = 0.d0 ! do i = 1, sze ! Otest(k) += Utest(i,k) * u_in(i,1) ! enddo ! Otest(k) = dabs(Otest(k)) ! print *, ' Otest =', k, Otest(k), lambda(k) !enddo !deallocate(Utest, Otest) ! ! end test ------------------------------------------------------------------------ ! ! TODO ! state_following is more efficient do l = 1, N_st allocate( overlap(N_st_diag) ) do k = 1, N_st_diag overlap(k) = 0.d0 do i = 1, sze overlap(k) = overlap(k) + U(i,shift2+k) * u_in(i,l) enddo overlap(k) = dabs(overlap(k)) !print *, ' overlap =', k, overlap(k) enddo lambda_tmp = 0.d0 do k = 1, N_st_diag if(overlap(k) .gt. lambda_tmp) then i_omax(l) = k lambda_tmp = overlap(k) endif enddo deallocate(overlap) if(lambda_tmp .lt. 0.7d0) then print *, ' very small overlap ...', l, i_omax(l) print *, ' max overlap = ', lambda_tmp !stop endif if(i_omax(l) .ne. l) then print *, ' !!! WARNONG !!!' print *, ' index of state', l, i_omax(l) endif enddo ! y(:,k) = rk ! W(:,k) = H x Bk ! W(:,shift2+k) = H x Bk x rk ! = Wk 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) ) ! --- ! 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 l = k residual_norm(k) = u_dot_u(U(1,shift2+l), sze) to_print(1,k) = lambda(l) to_print(2,k) = s2(l) to_print(3,k) = residual_norm(l) endif enddo !$OMP END PARALLEL DO !residual_norm(1) = u_dot_u(U(1,shift2+1), sze) !to_print(1,1) = lambda(1) !to_print(2,1) = residual_norm(1) if( (itertot > 1) .and. (iter == 1) ) then !don't print continue else write(*, '(1X, I3, 1X, 100(1X, F16.10, 1X, F16.10, 1X, F16.10))') iter-1, to_print(1:3,1:N_st) endif ! Check convergence if(iter > 1) then converged = dabs(maxval(residual_norm(1:N_st))) < threshold_nonsym_davidson endif do k = 1, N_st if(residual_norm(k) > 1.e8) 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 ! loop over iter ! Re-contract U and update W ! -------------------------------- 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 call ortho_qr(U, size(U, 1), sze, N_st_diag) call ortho_qr(U, size(U, 1), sze, N_st_diag) do j = 1, N_st_diag k = 1 do while( (k < sze) .and. (U(k,j) == 0.d0) ) k = k+1 enddo if(U(k,j) * u_in(k,j) < 0.d0) then do i = 1, sze W(i,j) = -W(i,j) enddo endif enddo if(converged)exit enddo ! loop over while ! --- do k = 1, N_st 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) deallocate(W) deallocate(U, h, y, lambda, residual_norm, i_omax) FREE nthreads_davidson end subroutine davidson_general_ext_rout_nonsym_b1space ! ---