mirror of
https://github.com/LCPQ/quantum_package
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282 lines
7.8 KiB
Fortran
282 lines
7.8 KiB
Fortran
BEGIN_PROVIDER [ integer, davidson_iter_max]
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implicit none
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BEGIN_DOC
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! Max number of Davidson iterations
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END_DOC
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davidson_iter_max = 100
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END_PROVIDER
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BEGIN_PROVIDER [ integer, davidson_sze_max]
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implicit none
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BEGIN_DOC
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! Max number of Davidson sizes
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END_DOC
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ASSERT (davidson_sze_max <= davidson_iter_max)
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davidson_sze_max = 8
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END_PROVIDER
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subroutine davidson_diag(dets_in,u_in,energies,dim_in,sze,N_st,Nint)
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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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! 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
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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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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(:,:,:), H_jj(:), 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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PROVIDE ref_bitmask_energy
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allocate( &
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kl_pairs(2,N_st*(N_st+1)/2), &
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H_jj(sze), &
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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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!$OMP H_jj,Nint,dets_in,u_in) &
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!$OMP PRIVATE(k,l,kl,i)
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!$OMP DO
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do i=1,sze
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H_jj(i) = diag_h_mat_elem(dets_in(1,1,i),Nint)
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enddo
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!$OMP END DO NOWAIT
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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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print *, 'iter = ',iter
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! print *, '***************'
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! do i=1,iter
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! do k=1,N_st
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! do j=1,iter
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! do l=1,N_st
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! print '(4(I4,X),F16.8)', i,j,k,l, u_dot_v(U(1,k,i),U(1,l,j),sze)
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! enddo
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! enddo
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! enddo
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! enddo
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! print *, '***************'
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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(W(1,k,iter),U(1,k,iter),H_jj,sze,dets_in,Nint)
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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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! 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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print *, lambda(1:4)
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! Express eigenvectors of h in the determinant basis
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! --------------------------------------------------
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! call dgemm ( 'N','N', sze, N_st*iter, N_st, &
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! 1.d0, U(1,1,1), size(U,1), y(1,1,1,1), size(y,1)*size(y,2), &
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! 0.d0, U(1,1,iter+1), size(U,1) )
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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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enddo
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print *, 'Lambda'
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print *, lambda(1:N_st) + nuclear_repulsion
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print *, 'Residual_norm'
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print *, residual_norm(1:N_st)
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print *, ''
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converged = maxval(residual_norm) < 1.d-5
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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/(lambda(k) - H_jj(i)) * 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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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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deallocate ( &
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kl_pairs, &
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H_jj, &
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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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end
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