subroutine davidson_diag_hs2(dets_in,u_in,dim_in,energies,sze,N_st,N_st_diag,Nint,iunit) 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 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) 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)) !$OMP PARALLEL DEFAULT(NONE) & !$OMP SHARED(sze,H_jj,S2_jj, dets_in,Nint) & !$OMP PRIVATE(i) !$OMP DO SCHEDULE(guided) do i=1,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 call davidson_diag_hjj_sjj(dets_in,u_in,H_jj,S2_jj,energies,dim_in,sze,N_st,N_st_diag,Nint,iunit) deallocate (H_jj,S2_jj) end subroutine davidson_diag_hjj_sjj(dets_in,u_in,H_jj,S2_jj,energies,dim_in,sze,N_st,N_st_diag,Nint,iunit) 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 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, allocatable :: overlap(:,:) double precision :: u_dot_v, u_dot_u integer, allocatable :: kl_pairs(:,:) integer :: k_pairs, kl integer :: iter2 double precision, allocatable :: W(:,:), U(:,:), R(:,:), S(:,:) 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 include 'constants.include.F' !DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: U, W, R, S, y, h, lambda if (N_st_diag > sze) then stop 'error in Davidson : N_st_diag > sze' 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') 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) double precision :: delta if (s2_eig) then delta = 1.d0 else delta = 0.d0 endif allocate( & kl_pairs(2,N_st_diag*(N_st_diag+1)/2), & W(sze_8,N_st_diag*davidson_sze_max), & U(sze_8,N_st_diag*davidson_sze_max), & R(sze_8,N_st_diag), & S(sze_8,N_st_diag*davidson_sze_max), & 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), & s_(N_st_diag*davidson_sze_max,N_st_diag*davidson_sze_max), & s_tmp(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), & s2(N_st_diag*davidson_sze_max), & 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) ! Davidson iterations ! =================== converged = .False. do k=1,N_st call normalize(u_in(1,k),sze) enddo do k=N_st+1,N_st_diag 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 ! 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 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 ! Compute |W_k> = \sum_i |i> ! ----------------------------------------- call H_S2_u_0_nstates(W(1,shift+1),S(1,shift+1),U(1,shift+1),H_jj,S2_jj,sze,dets_in,Nint,N_st_diag,sze_8) ! Compute h_kl = = ! ------------------------------------------- ! do l=1,N_st_diag ! do k=1,N_st_diag ! do iter2=1,iter-1 ! h(k,iter2,l,iter) = u_dot_v(U(1,k,iter2),W(1,l,iter),sze) ! h(k,iter,l,iter2) = h(k,iter2,l,iter) ! enddo ! enddo ! do k=1,l ! h(k,iter,l,iter) = u_dot_v(U(1,k,iter),W(1,l,iter),sze) ! h(l,iter,k,iter) = h(k,iter,l,iter) ! enddo ! enddo call dgemm('T','N', shift2, N_st_diag, sze, & 1.d0, U, size(U,1), W(1,shift+1), size(W,1), & 0.d0, h(1,shift+1), size(h,1)) call dgemm('T','N', shift2, N_st_diag, sze, & 1.d0, U, size(U,1), S(1,shift+1), size(S,1), & 0.d0, s_(1,shift+1), size(s_,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) < 0.3d0) enddo 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 endif ! Express eigenvectors of h in the determinant basis ! -------------------------------------------------- ! do k=1,N_st_diag ! do i=1,sze ! U(i,shift2+k) = 0.d0 ! W(i,shift2+k) = 0.d0 ! S(i,shift2+k) = 0.d0 ! enddo ! do l=1,N_st_diag*iter ! do i=1,sze ! U(i,shift2+k) = U(i,shift2+k) + U(i,l)*y(l,k) ! W(i,shift2+k) = W(i,shift2+k) + W(i,l)*y(l,k) ! S(i,shift2+k) = S(i,shift2+k) + S(i,l)*y(l,k) ! enddo ! enddo ! enddo ! ! 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 ! print *, s2(k) ! s2(k) = u_dot_v(U(1,shift2+k), S(1,shift2+k), sze) + S_z2_Sz ! print *, s2(k) ! print *, '' ! pause ! enddo do k=1,N_st_diag do i=1,sze R(i,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) 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) = s2(k) to_print(3,k) = residual_norm(k) if (residual_norm(k) > 1.e9) then stop 'Davidson failed' endif endif enddo write(iunit,'(X,I3,X,100(X,F16.10,X,F11.6,X,E11.3))') 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,shift2+k) = - R(i,k)/max(H_jj(i) - lambda(k),1.d-2) enddo enddo ! Gram-Schmidt ! ------------ do k=1,N_st_diag ! do l=1,N_st_diag*iter ! c(1) = u_dot_v(U(1,shift2+k),U(1,l),sze) ! do i=1,sze ! U(i,k,iter+1) = U(i,shift2+k) - c(1) * U(i,l) ! enddo ! enddo ! call dgemv('T',sze,N_st_diag*iter,1.d0,U,size(U,1), & U(1,shift2+k),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,shift2+k),1) ! ! do l=1,k-1 ! c(1) = u_dot_v(U(1,shift2+k),U(1,shift2+l),sze) ! do i=1,sze ! U(i,k,iter+1) = U(i,shift2+k) - c(1) * U(i,shift2+l) ! enddo ! enddo ! call dgemv('T',sze,k-1,1.d0,U(1,shift2+1),size(U,1), & U(1,shift2+k),1,0.d0,c,1) call dgemv('N',sze,k-1,-1.d0,U(1,shift2+1),size(U,1), & c,1,1.d0,U(1,shift2+k),1) call normalize( U(1,shift2+k), sze ) enddo enddo if (.not.converged) then iter = davidson_sze_max-1 endif ! Re-contract to u_in ! ----------- do k=1,N_st_diag energies(k) = lambda(k) enddo ! do k=1,N_st_diag ! do i=1,sze ! do l=1,iter*N_st_diag ! u_in(i,k) += U(i,l)*y(l,k) ! enddo ! enddo ! enddo ! enddo call dgemm('N','N', sze, N_st_diag, N_st_diag*iter, 1.d0, & U, size(U,1), y, size(y,1), 0.d0, u_in, size(u_in,1)) 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 ( & kl_pairs, & W, residual_norm, & U, overlap, & R, c, S, & h, & y, s_, s_tmp, & lambda & ) end