486 lines
15 KiB
Fortran
486 lines
15 KiB
Fortran
subroutine davidson_diag_hs2(dets_in,u_in,s2_out,dim_in,energies,sze,N_st,N_st_diag,Nint,iunit)
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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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! iunit : Unit number for the I/O
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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, N_st_diag, Nint, iunit
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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_diag)
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double precision, intent(out) :: energies(N_st_diag), s2_out(N_st_diag)
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double precision, allocatable :: H_jj(:)
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double precision :: diag_H_mat_elem, diag_S_mat_elem
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integer :: i
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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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PROVIDE mo_bielec_integrals_in_map
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allocate(H_jj(sze) )
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!$OMP PARALLEL DEFAULT(NONE) &
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!$OMP SHARED(sze,H_jj, dets_in,Nint) &
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!$OMP PRIVATE(i)
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!$OMP DO SCHEDULE(static)
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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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!$OMP END DO
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!$OMP END PARALLEL
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call davidson_diag_hjj_sjj(dets_in,u_in,H_jj,S2_out,energies,dim_in,sze,N_st,N_st_diag,Nint,iunit)
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deallocate (H_jj)
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end
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subroutine davidson_diag_hjj_sjj(dets_in,u_in,H_jj,s2_out,energies,dim_in,sze,N_st,N_st_diag,Nint,iunit)
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use bitmasks
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implicit none
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BEGIN_DOC
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! Davidson diagonalization with specific diagonal elements of the H matrix
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!
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! H_jj : specific diagonal H matrix elements to diagonalize de Davidson
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!
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! S2_out : Output : s^2
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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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! N_st_diag : Number of states in which H is diagonalized. Assumed > sze
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!
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! iunit : Unit for the I/O
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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, N_st_diag, Nint
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integer(bit_kind), intent(in) :: dets_in(Nint,2,sze)
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double precision, intent(in) :: H_jj(sze)
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double precision, intent(inout) :: s2_out(N_st_diag)
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integer, intent(in) :: iunit
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double precision, intent(inout) :: u_in(dim_in,N_st_diag)
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double precision, intent(out) :: energies(N_st_diag)
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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 :: u_dot_v, u_dot_u
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integer :: k_pairs, kl
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integer :: iter2
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double precision, allocatable :: W(:,:), U(:,:), S(:,:), overlap(:,:)
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double precision, allocatable :: y(:,:), h(:,:), lambda(:), s2(:)
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double precision, allocatable :: c(:), s_(:,:), s_tmp(:,:)
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double precision :: diag_h_mat_elem
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double precision, allocatable :: residual_norm(:)
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character*(16384) :: write_buffer
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double precision :: to_print(3,N_st)
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double precision :: cpu, wall
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integer :: shift, shift2, itermax
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double precision :: r1, r2
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logical :: state_ok(N_st_diag*davidson_sze_max)
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include 'constants.include.F'
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!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: U, W, S, y, h, lambda
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if (N_st_diag*3 > sze) then
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print *, 'error in Davidson :'
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print *, 'Increase n_det_max_jacobi to ', N_st_diag*3
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stop -1
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endif
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itermax = max(3,min(davidson_sze_max, sze/N_st_diag))
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PROVIDE nuclear_repulsion expected_s2 psi_bilinear_matrix_order psi_bilinear_matrix_order_reverse
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call write_time(iunit)
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call wall_time(wall)
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call cpu_time(cpu)
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write(iunit,'(A)') ''
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write(iunit,'(A)') 'Davidson Diagonalization'
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write(iunit,'(A)') '------------------------'
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write(iunit,'(A)') ''
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call write_int(iunit,N_st,'Number of states')
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call write_int(iunit,N_st_diag,'Number of states in diagonalization')
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call write_int(iunit,sze,'Number of determinants')
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r1 = 8.d0*(3.d0*dble(sze*N_st_diag*itermax+5.d0*(N_st_diag*itermax)**2 &
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+ 4.d0*(N_st_diag*itermax)+nproc*(4.d0*N_det_alpha_unique+2.d0*N_st_diag*sze)))/(1024.d0**3)
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call write_double(iunit, r1, 'Memory(Gb)')
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write(iunit,'(A)') ''
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write_buffer = '====='
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do i=1,N_st
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write_buffer = trim(write_buffer)//' ================ =========== ==========='
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enddo
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write(iunit,'(A)') write_buffer(1:6+41*N_states)
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write_buffer = 'Iter'
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do i=1,N_st
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write_buffer = trim(write_buffer)//' Energy S^2 Residual '
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enddo
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write(iunit,'(A)') write_buffer(1:6+41*N_states)
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write_buffer = '====='
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do i=1,N_st
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write_buffer = trim(write_buffer)//' ================ =========== ==========='
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enddo
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write(iunit,'(A)') write_buffer(1:6+41*N_states)
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allocate( &
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! Large
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W(sze,N_st_diag*itermax), &
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U(sze,N_st_diag*itermax), &
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S(sze,N_st_diag*itermax), &
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! Small
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h(N_st_diag*itermax,N_st_diag*itermax), &
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y(N_st_diag*itermax,N_st_diag*itermax), &
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s_(N_st_diag*itermax,N_st_diag*itermax), &
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s_tmp(N_st_diag*itermax,N_st_diag*itermax), &
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residual_norm(N_st_diag), &
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c(N_st_diag*itermax), &
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s2(N_st_diag*itermax), &
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overlap(N_st_diag*itermax, N_st_diag*itermax), &
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lambda(N_st_diag*itermax))
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h = 0.d0
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U = 0.d0
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W = 0.d0
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S = 0.d0
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y = 0.d0
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s_ = 0.d0
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s_tmp = 0.d0
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ASSERT (N_st > 0)
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ASSERT (N_st_diag >= N_st)
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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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! Davidson iterations
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! ===================
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converged = .False.
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do k=N_st+1,N_st_diag
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u_in(k,k) = 10.d0
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do i=1,sze
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call random_number(r1)
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call random_number(r2)
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r1 = dsqrt(-2.d0*dlog(r1))
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r2 = dtwo_pi*r2
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u_in(i,k) = r1*dcos(r2)
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enddo
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enddo
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do k=1,N_st_diag
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call normalize(u_in(1,k),sze)
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enddo
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do while (.not.converged)
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do k=1,N_st_diag
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do i=1,sze
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U(i,k) = u_in(i,k)
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enddo
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enddo
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do iter=1,itermax-1
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shift = N_st_diag*(iter-1)
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shift2 = N_st_diag*iter
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call ortho_qr(U,size(U,1),sze,shift2)
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! Compute |W_k> = \sum_i |i><i|H|u_k>
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! -----------------------------------------
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if ((sze > 100000).and.distributed_davidson) then
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call H_S2_u_0_nstates_zmq (W(1,shift+1),S(1,shift+1),U(1,shift+1),N_st_diag,sze)
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else
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call H_S2_u_0_nstates_openmp(W(1,shift+1),S(1,shift+1),U(1,shift+1),N_st_diag,sze)
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endif
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! Compute h_kl = <u_k | W_l> = <u_k| H |u_l>
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! -------------------------------------------
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call dgemm('T','N', shift2, shift2, sze, &
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1.d0, U, size(U,1), W, size(W,1), &
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0.d0, h, size(h,1))
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call dgemm('T','N', shift2, shift2, sze, &
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1.d0, U, size(U,1), S, size(S,1), &
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0.d0, s_, size(s_,1))
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! ! Diagonalize S^2
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! ! ---------------
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!
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! call lapack_diag(s2,y,s_,size(s_,1),shift2)
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!
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!
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! ! Rotate H in the basis of eigenfunctions of s2
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! ! ---------------------------------------------
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!
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! call dgemm('N','N',shift2,shift2,shift2, &
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! 1.d0, h, size(h,1), y, size(y,1), &
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! 0.d0, s_tmp, size(s_tmp,1))
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!
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! call dgemm('T','N',shift2,shift2,shift2, &
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! 1.d0, y, size(y,1), s_tmp, size(s_tmp,1), &
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! 0.d0, h, size(h,1))
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!
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! ! Damp interaction between different spin states
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! ! ------------------------------------------------
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!
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! do k=1,shift2
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! do l=1,shift2
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! if (dabs(s2(k) - s2(l)) > 1.d0) then
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! h(k,l) = h(k,l)*(max(0.d0,1.d0 - dabs(s2(k) - s2(l))))
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! endif
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! enddo
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! enddo
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!
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! ! Rotate back H
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! ! -------------
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!
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! call dgemm('N','T',shift2,shift2,shift2, &
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! 1.d0, h, size(h,1), y, size(y,1), &
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! 0.d0, s_tmp, size(s_tmp,1))
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!
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! call dgemm('N','N',shift2,shift2,shift2, &
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! 1.d0, y, size(y,1), s_tmp, size(s_tmp,1), &
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! 0.d0, h, size(h,1))
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! Diagonalize h
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! -------------
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call lapack_diag(lambda,y,h,size(h,1),shift2)
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! Compute S2 for each eigenvector
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! -------------------------------
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call dgemm('N','N',shift2,shift2,shift2, &
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1.d0, s_, size(s_,1), y, size(y,1), &
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0.d0, s_tmp, size(s_tmp,1))
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call dgemm('T','N',shift2,shift2,shift2, &
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1.d0, y, size(y,1), s_tmp, size(s_tmp,1), &
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0.d0, s_, size(s_,1))
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do k=1,shift2
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s2(k) = s_(k,k) + S_z2_Sz
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enddo
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if (s2_eig) then
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do k=1,shift2
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state_ok(k) = (dabs(s2(k)-expected_s2) < 0.6d0)
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enddo
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else
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do k=1,size(state_ok)
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state_ok(k) = .True.
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enddo
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endif
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do k=1,shift2
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if (.not. state_ok(k)) then
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do l=k+1,shift2
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if (state_ok(l)) then
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call dswap(shift2, y(1,k), 1, y(1,l), 1)
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call dswap(1, s2(k), 1, s2(l), 1)
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call dswap(1, lambda(k), 1, lambda(l), 1)
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state_ok(k) = .True.
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state_ok(l) = .False.
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exit
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endif
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enddo
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endif
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enddo
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if (state_following) then
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integer :: order(N_st_diag)
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double precision :: cmax
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overlap = -1.d0
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do k=1,shift2
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do i=1,shift2
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overlap(k,i) = dabs(y(k,i))
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enddo
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enddo
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do k=1,N_st
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cmax = -1.d0
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do i=1,N_st
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if (overlap(i,k) > cmax) then
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cmax = overlap(i,k)
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order(k) = i
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endif
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enddo
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do i=1,N_st_diag
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overlap(order(k),i) = -1.d0
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enddo
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enddo
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overlap = y
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do k=1,N_st
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l = order(k)
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if (k /= l) then
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y(1:shift2,k) = overlap(1:shift2,l)
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endif
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enddo
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do k=1,N_st
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overlap(k,1) = lambda(k)
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overlap(k,2) = s2(k)
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enddo
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do k=1,N_st
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l = order(k)
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if (k /= l) then
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lambda(k) = overlap(l,1)
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s2(k) = overlap(l,2)
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endif
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enddo
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endif
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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_diag, shift2, &
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1.d0, U, size(U,1), y, size(y,1), 0.d0, U(1,shift2+1), size(U,1))
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call dgemm('N','N', sze, N_st_diag, shift2, &
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1.d0, W, size(W,1), y, size(y,1), 0.d0, W(1,shift2+1), size(W,1))
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call dgemm('N','N', sze, N_st_diag, shift2, &
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1.d0, S, size(S,1), y, size(y,1), 0.d0, S(1,shift2+1), size(S,1))
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! Compute residual vector and davidson step
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! -----------------------------------------
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do k=1,N_st_diag
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do i=1,sze
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U(i,shift2+k) = &
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(lambda(k) * U(i,shift2+k) - W(i,shift2+k) ) &
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* (1.d0 + s2(k) * U(i,shift2+k) - S(i,shift2+k) - S_z2_Sz &
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)/max(H_jj(i) - lambda (k),1.d-2)
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enddo
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if (k <= N_st) then
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residual_norm(k) = u_dot_u(U(1,shift2+k),sze)
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to_print(1,k) = lambda(k) + nuclear_repulsion
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to_print(2,k) = s2(k)
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to_print(3,k) = residual_norm(k)
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endif
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enddo
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write(iunit,'(1X,I3,1X,100(1X,F16.10,1X,F11.6,1X,E11.3))') iter, to_print(1:3,1:N_st)
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call davidson_converged(lambda,residual_norm,wall,iter,cpu,N_st,converged)
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do k=1,N_st
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if (residual_norm(k) > 1.e8) then
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print *, ''
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stop 'Davidson failed'
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endif
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enddo
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if (converged) then
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exit
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endif
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enddo
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! Re-contract to u_in
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! -----------
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call dgemm('N','N', sze, N_st_diag, shift2, 1.d0, &
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U, size(U,1), y, size(y,1), 0.d0, u_in, size(u_in,1))
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enddo
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do k=1,N_st_diag
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energies(k) = lambda(k)
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s2_out(k) = s2(k)
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enddo
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write_buffer = '======'
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do i=1,N_st
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write_buffer = trim(write_buffer)//' ================ =========== ==========='
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enddo
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write(iunit,'(A)') trim(write_buffer)
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write(iunit,'(A)') ''
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call write_time(iunit)
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deallocate ( &
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W, residual_norm, &
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U, overlap, &
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c, S, &
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h, &
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y, s_, s_tmp, &
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lambda &
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)
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end
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subroutine u_0_H_u_0(e_0,u_0,n,keys_tmp,Nint,N_st,sze)
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use bitmasks
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implicit none
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BEGIN_DOC
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! Computes e_0 = <u_0|H|u_0>/<u_0|u_0>
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!
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! n : number of determinants
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!
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END_DOC
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integer, intent(in) :: n,Nint, N_st, sze
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double precision, intent(out) :: e_0(N_st)
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double precision, intent(inout) :: u_0(sze,N_st)
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integer(bit_kind),intent(in) :: keys_tmp(Nint,2,n)
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double precision, allocatable :: v_0(:,:), s_0(:,:), u_1(:,:)
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double precision :: u_dot_u,u_dot_v,diag_H_mat_elem
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integer :: i,j
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if ((sze > 100000).and.distributed_davidson) then
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allocate (v_0(sze,N_states_diag),s_0(sze,N_states_diag), u_1(sze,N_states_diag))
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u_1(1:sze,1:N_states) = u_0(1:sze,1:N_states)
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u_1(1:sze,N_states+1:N_states_diag) = 0.d0
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call H_S2_u_0_nstates_zmq(v_0,s_0,u_1,N_states_diag,sze)
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deallocate(u_1)
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else
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allocate (v_0(sze,N_st),s_0(sze,N_st))
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call H_S2_u_0_nstates_openmp(v_0,s_0,u_0,N_st,sze)
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endif
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double precision :: norm
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do i=1,N_st
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norm = u_dot_u(u_0(1,i),n)
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if (norm /= 0.d0) then
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e_0(i) = u_dot_v(v_0(1,i),u_0(1,i),n)
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else
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e_0(i) = 0.d0
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endif
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enddo
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deallocate (s_0, v_0)
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end
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