2016-10-11 23:42:05 +02:00
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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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2016-09-27 16:28:27 +02:00
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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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2016-11-11 23:07:58 +01:00
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double precision, intent(out) :: energies(N_st_diag), s2_out(N_st_diag)
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2016-09-27 16:28:27 +02:00
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double precision, allocatable :: H_jj(:), S2_jj(:)
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2017-04-14 15:04:29 +02:00
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double precision :: diag_H_mat_elem, diag_S_mat_elem
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2016-09-27 16:28:27 +02:00
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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), S2_jj(sze))
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!$OMP PARALLEL DEFAULT(NONE) &
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!$OMP SHARED(sze,H_jj,S2_jj, dets_in,Nint) &
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!$OMP PRIVATE(i)
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2017-04-14 15:04:29 +02:00
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!$OMP DO SCHEDULE(static)
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2016-09-27 16:28:27 +02:00
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do i=1,sze
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2017-04-14 15:04:29 +02:00
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H_jj(i) = diag_H_mat_elem(dets_in(1,1,i),Nint)
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S2_jj(i) = diag_S_mat_elem(dets_in(1,1,i),Nint)
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2016-09-27 16:28:27 +02:00
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enddo
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!$OMP END DO
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!$OMP END PARALLEL
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2016-11-18 22:08:08 +01:00
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if (disk_based_davidson) then
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call davidson_diag_hjj_sjj_mmap(dets_in,u_in,H_jj,S2_jj,energies,dim_in,sze,N_st,N_st_diag,Nint,iunit)
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else
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call davidson_diag_hjj_sjj(dets_in,u_in,H_jj,S2_jj,energies,dim_in,sze,N_st,N_st_diag,Nint,iunit)
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endif
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2016-10-11 23:42:05 +02:00
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do i=1,N_st_diag
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s2_out(i) = S2_jj(i)
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enddo
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2016-09-27 16:28:27 +02:00
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deallocate (H_jj,S2_jj)
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end
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subroutine davidson_diag_hjj_sjj(dets_in,u_in,H_jj,S2_jj,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_jj : specific diagonal S^2 matrix elements
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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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2016-09-30 15:12:17 +02:00
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! N_st_diag : Number of states in which H is diagonalized. Assumed > sze
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2016-09-27 16:28:27 +02:00
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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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2016-10-11 23:42:05 +02:00
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double precision, intent(in) :: H_jj(sze)
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2016-11-18 22:08:08 +01:00
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double precision, intent(inout) :: S2_jj(sze)
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integer, intent(in) :: iunit
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2016-09-27 16:28:27 +02:00
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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 :: sze_8
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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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2016-11-18 22:08:08 +01:00
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double precision, allocatable :: W(:,:), U(:,:), S(:,:), overlap(:,:)
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2016-09-30 21:38:01 +02:00
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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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2016-09-27 16:28:27 +02:00
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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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2017-04-17 01:36:16 +02:00
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integer :: shift, shift2, itermax
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2016-11-18 22:08:08 +01:00
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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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2016-09-27 16:28:27 +02:00
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include 'constants.include.F'
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2016-10-18 21:36:45 +02:00
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!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: U, W, S, y, h, lambda
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2016-10-18 19:29:50 +02:00
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if (N_st_diag*3 > sze) then
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2016-11-18 22:08:08 +01:00
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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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2016-09-30 15:12:17 +02:00
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endif
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2016-11-18 22:08:08 +01:00
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2017-02-27 10:43:57 +01:00
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integer, external :: align_double
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sze_8 = align_double(sze)
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itermax = max(3,min(davidson_sze_max, sze/N_st_diag))
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2017-04-18 14:52:23 +02:00
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PROVIDE nuclear_repulsion expected_s2
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2016-11-18 22:08:08 +01:00
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2016-09-27 16:28:27 +02:00
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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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2017-04-18 14:52:23 +02:00
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r1 = 8.d0*(3.d0*dble(sze_8*N_st_diag*itermax+5.d0*(N_st_diag*itermax)**2 &
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2017-04-18 00:32:22 +02:00
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+ 4.d0*(N_st_diag*itermax)+nproc*(4.d0*N_det_alpha_unique+2.d0*N_st_diag*sze_8)))/(1024.d0**3)
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2017-02-27 10:43:57 +01:00
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call write_double(iunit, r1, 'Memory(Gb)')
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2016-09-27 16:28:27 +02:00
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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)') trim(write_buffer)
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write_buffer = ' Iter'
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do i=1,N_st
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2016-11-18 22:08:08 +01:00
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write_buffer = trim(write_buffer)//' Energy S^2 Residual '
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2016-09-27 16:28:27 +02:00
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enddo
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write(iunit,'(A)') trim(write_buffer)
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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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2016-11-18 22:08:08 +01:00
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2017-02-27 10:43:57 +01:00
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2016-09-27 16:28:27 +02:00
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allocate( &
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2017-02-27 10:43:57 +01:00
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! Large
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2016-11-18 22:08:08 +01:00
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W(sze_8,N_st_diag*itermax), &
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U(sze_8,N_st_diag*itermax), &
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S(sze_8,N_st_diag*itermax), &
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2017-02-27 10:43:57 +01:00
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! Small
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2016-11-18 22:08:08 +01:00
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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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2016-09-27 16:28:27 +02:00
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residual_norm(N_st_diag), &
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2016-11-18 22:08:08 +01:00
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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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2016-10-18 19:29:50 +02:00
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lambda(N_st_diag*itermax))
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2016-09-27 16:28:27 +02:00
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2016-11-18 22:08:08 +01:00
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h = 0.d0
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2016-10-06 16:39:34 +02:00
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U = 0.d0
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2016-10-18 19:29:50 +02:00
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W = 0.d0
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2016-10-06 16:39:34 +02:00
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S = 0.d0
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y = 0.d0
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2016-11-18 22:08:08 +01:00
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s_ = 0.d0
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s_tmp = 0.d0
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2016-10-06 16:39:34 +02:00
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2016-09-27 16:28:27 +02:00
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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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2016-11-15 18:39:44 +01:00
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do k=N_st+1,N_st_diag
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2016-11-18 22:08:08 +01:00
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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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2016-10-18 21:36:45 +02:00
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enddo
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2016-11-15 18:39:44 +01:00
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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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2016-09-27 16:28:27 +02:00
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enddo
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2017-04-14 15:04:29 +02:00
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2016-11-18 22:08:08 +01:00
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2016-09-27 16:28:27 +02:00
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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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2016-09-30 21:38:01 +02:00
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U(i,k) = u_in(i,k)
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2016-09-27 16:28:27 +02:00
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enddo
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enddo
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2016-11-18 22:08:08 +01:00
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2016-10-18 19:29:50 +02:00
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do iter=1,itermax-1
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2016-09-27 16:28:27 +02:00
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2016-09-30 21:38:01 +02:00
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shift = N_st_diag*(iter-1)
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shift2 = N_st_diag*iter
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2016-11-18 22:08:08 +01:00
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2016-10-18 19:29:50 +02:00
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call ortho_qr(U,size(U,1),sze,shift2)
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2016-09-30 21:38:01 +02:00
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2016-09-27 16:28:27 +02:00
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! Compute |W_k> = \sum_i |i><i|H|u_k>
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! -----------------------------------------
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2016-09-30 21:38:01 +02:00
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2017-01-18 16:06:23 +01:00
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if (distributed_davidson) then
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2017-04-17 01:36:16 +02:00
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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_8)
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2017-01-18 16:06:23 +01:00
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else
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2017-04-14 15:04:29 +02:00
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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_8)
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2017-01-18 16:06:23 +01:00
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endif
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2016-09-27 16:28:27 +02:00
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! Compute h_kl = <u_k | W_l> = <u_k| H |u_l>
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! -------------------------------------------
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2016-11-04 17:31:39 +01:00
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call dgemm('T','N', shift2, shift2, sze, &
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2016-11-04 18:03:32 +01:00
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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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2016-11-04 17:31:39 +01:00
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call dgemm('T','N', shift2, shift2, sze, &
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2016-11-04 18:03:32 +01:00
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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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2016-09-30 21:38:01 +02:00
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2016-09-27 16:28:27 +02:00
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2016-11-18 22:08:08 +01:00
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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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|
! ! -------------
|
|
|
|
!
|
|
|
|
! call dgemm('N','T',shift2,shift2,shift2, &
|
|
|
|
! 1.d0, h, size(h,1), y, size(y,1), &
|
|
|
|
! 0.d0, s_tmp, size(s_tmp,1))
|
|
|
|
!
|
|
|
|
! call dgemm('N','N',shift2,shift2,shift2, &
|
|
|
|
! 1.d0, y, size(y,1), s_tmp, size(s_tmp,1), &
|
|
|
|
! 0.d0, h, size(h,1))
|
|
|
|
|
|
|
|
|
2016-09-27 16:28:27 +02:00
|
|
|
! Diagonalize h
|
|
|
|
! -------------
|
2016-11-18 22:08:08 +01:00
|
|
|
|
2016-09-30 21:38:01 +02:00
|
|
|
call lapack_diag(lambda,y,h,size(h,1),shift2)
|
2016-09-27 16:28:27 +02:00
|
|
|
|
2016-09-30 21:38:01 +02:00
|
|
|
! Compute S2 for each eigenvector
|
|
|
|
! -------------------------------
|
|
|
|
|
2016-10-11 23:42:05 +02:00
|
|
|
call dgemm('N','N',shift2,shift2,shift2, &
|
|
|
|
1.d0, s_, size(s_,1), y, size(y,1), &
|
2016-09-30 21:38:01 +02:00
|
|
|
0.d0, s_tmp, size(s_tmp,1))
|
2016-10-11 23:42:05 +02:00
|
|
|
|
|
|
|
call dgemm('T','N',shift2,shift2,shift2, &
|
|
|
|
1.d0, y, size(y,1), s_tmp, size(s_tmp,1), &
|
2016-09-30 21:38:01 +02:00
|
|
|
0.d0, s_, size(s_,1))
|
2016-11-11 23:07:58 +01:00
|
|
|
|
|
|
|
|
2016-10-11 23:42:05 +02:00
|
|
|
|
2016-09-30 21:38:01 +02:00
|
|
|
do k=1,shift2
|
|
|
|
s2(k) = s_(k,k) + S_z2_Sz
|
|
|
|
enddo
|
|
|
|
|
|
|
|
if (s2_eig) then
|
2016-11-18 22:08:08 +01:00
|
|
|
do k=1,shift2
|
|
|
|
state_ok(k) = (dabs(s2(k)-expected_s2) < 0.6d0)
|
|
|
|
enddo
|
|
|
|
else
|
2016-11-30 20:09:50 +01:00
|
|
|
do k=1,size(state_ok)
|
|
|
|
state_ok(k) = .True.
|
|
|
|
enddo
|
2016-11-18 22:08:08 +01:00
|
|
|
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
|
|
|
|
|
2016-11-21 21:25:38 +01:00
|
|
|
integer :: order(N_st_diag)
|
|
|
|
double precision :: cmax
|
|
|
|
|
2016-11-18 22:08:08 +01:00
|
|
|
overlap = -1.d0
|
2016-11-21 21:25:38 +01:00
|
|
|
do k=1,shift2
|
|
|
|
do i=1,shift2
|
2016-11-18 22:08:08 +01:00
|
|
|
overlap(k,i) = dabs(y(k,i))
|
|
|
|
enddo
|
2016-09-30 21:38:01 +02:00
|
|
|
enddo
|
2016-11-18 22:08:08 +01:00
|
|
|
do k=1,N_st
|
2016-11-21 21:25:38 +01:00
|
|
|
cmax = -1.d0
|
2016-11-21 21:42:28 +01:00
|
|
|
do i=1,N_st
|
2016-11-21 21:25:38 +01:00
|
|
|
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
|
2016-11-18 22:22:46 +01:00
|
|
|
enddo
|
|
|
|
enddo
|
2016-11-21 21:25:38 +01:00
|
|
|
overlap = y
|
2016-11-18 22:08:08 +01:00
|
|
|
do k=1,N_st
|
|
|
|
l = order(k)
|
|
|
|
if (k /= l) then
|
2016-11-21 21:25:38 +01:00
|
|
|
y(1:shift2,k) = overlap(1:shift2,l)
|
2016-09-30 21:38:01 +02:00
|
|
|
endif
|
|
|
|
enddo
|
2016-11-18 22:08:08 +01:00
|
|
|
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
|
|
|
|
|
2016-09-30 21:38:01 +02:00
|
|
|
endif
|
|
|
|
|
|
|
|
|
2016-09-27 16:28:27 +02:00
|
|
|
! Express eigenvectors of h in the determinant basis
|
|
|
|
! --------------------------------------------------
|
|
|
|
|
2016-09-30 21:38:01 +02:00
|
|
|
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))
|
2016-09-27 16:28:27 +02:00
|
|
|
|
2016-10-18 21:36:45 +02:00
|
|
|
! Compute residual vector and davidson step
|
|
|
|
! -----------------------------------------
|
2016-09-27 16:28:27 +02:00
|
|
|
|
|
|
|
do k=1,N_st_diag
|
2016-12-03 18:58:07 +01:00
|
|
|
do i=1,sze
|
|
|
|
U(i,shift2+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 &
|
|
|
|
)/max(H_jj(i) - lambda (k),1.d-2)
|
|
|
|
enddo
|
2016-11-18 22:08:08 +01:00
|
|
|
|
2016-09-27 16:28:27 +02:00
|
|
|
if (k <= N_st) then
|
2016-10-18 21:36:45 +02:00
|
|
|
residual_norm(k) = u_dot_u(U(1,shift2+k),sze)
|
2016-09-27 16:28:27 +02:00
|
|
|
to_print(1,k) = lambda(k) + nuclear_repulsion
|
|
|
|
to_print(2,k) = s2(k)
|
|
|
|
to_print(3,k) = residual_norm(k)
|
|
|
|
endif
|
|
|
|
enddo
|
|
|
|
|
2017-04-12 19:29:21 +02:00
|
|
|
write(iunit,'(1X,I3,1X,100(1X,F16.10,1X,F11.6,1X,E11.3))') iter, to_print(1:3,1:N_st)
|
2016-09-27 16:28:27 +02:00
|
|
|
call davidson_converged(lambda,residual_norm,wall,iter,cpu,N_st,converged)
|
2016-10-18 19:29:50 +02:00
|
|
|
do k=1,N_st
|
2016-11-04 17:34:05 +01:00
|
|
|
if (residual_norm(k) > 1.e8) then
|
2016-10-18 19:29:50 +02:00
|
|
|
print *, ''
|
|
|
|
stop 'Davidson failed'
|
|
|
|
endif
|
|
|
|
enddo
|
2016-09-27 16:28:27 +02:00
|
|
|
if (converged) then
|
|
|
|
exit
|
|
|
|
endif
|
|
|
|
|
|
|
|
enddo
|
|
|
|
|
|
|
|
! Re-contract to u_in
|
|
|
|
! -----------
|
|
|
|
|
2016-11-04 23:17:38 +01:00
|
|
|
call dgemm('N','N', sze, N_st_diag, shift2, 1.d0, &
|
2016-09-30 21:38:01 +02:00
|
|
|
U, size(U,1), y, size(y,1), 0.d0, u_in, size(u_in,1))
|
2016-09-27 16:28:27 +02:00
|
|
|
|
|
|
|
enddo
|
|
|
|
|
2016-10-18 19:29:50 +02:00
|
|
|
do k=1,N_st_diag
|
2016-11-11 23:07:58 +01:00
|
|
|
energies(k) = lambda(k)
|
2016-10-18 19:29:50 +02:00
|
|
|
S2_jj(k) = s2(k)
|
|
|
|
enddo
|
2016-09-27 16:28:27 +02:00
|
|
|
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 ( &
|
|
|
|
W, residual_norm, &
|
2016-11-18 22:08:08 +01:00
|
|
|
U, overlap, &
|
2016-10-18 21:36:45 +02:00
|
|
|
c, S, &
|
2016-09-27 16:28:27 +02:00
|
|
|
h, &
|
2016-09-30 21:38:01 +02:00
|
|
|
y, s_, s_tmp, &
|
2016-09-27 16:28:27 +02:00
|
|
|
lambda &
|
|
|
|
)
|
|
|
|
end
|
|
|
|
|
2016-11-16 10:17:37 +01:00
|
|
|
subroutine davidson_diag_hjj_sjj_mmap(dets_in,u_in,H_jj,S2_jj,energies,dim_in,sze,N_st,N_st_diag,Nint,iunit)
|
|
|
|
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_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)
|
2016-11-18 22:08:08 +01:00
|
|
|
double precision, intent(inout) :: S2_jj(sze)
|
|
|
|
integer, intent(in) :: iunit
|
2016-11-16 10:17:37 +01:00
|
|
|
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 :: u_dot_v, u_dot_u
|
|
|
|
|
|
|
|
integer :: k_pairs, kl
|
|
|
|
|
|
|
|
integer :: iter2
|
2016-11-18 22:08:08 +01:00
|
|
|
double precision, pointer :: W(:,:), U(:,:), S(:,:), overlap(:,:)
|
2016-11-16 10:17:37 +01:00
|
|
|
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
|
2016-11-18 22:08:08 +01:00
|
|
|
logical :: state_ok(N_st_diag*davidson_sze_max)
|
2016-11-16 10:17:37 +01:00
|
|
|
integer :: shift, shift2, itermax
|
|
|
|
include 'constants.include.F'
|
|
|
|
|
|
|
|
!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: U, W, S, y, h, lambda
|
|
|
|
if (N_st_diag*3 > sze) then
|
2016-11-18 22:08:08 +01:00
|
|
|
print *, 'error in Davidson :'
|
|
|
|
print *, 'Increase n_det_max_jacobi to ', N_st_diag*3
|
|
|
|
stop -1
|
2016-11-16 10:17:37 +01:00
|
|
|
endif
|
2016-11-18 22:08:08 +01:00
|
|
|
|
2017-04-18 14:52:23 +02:00
|
|
|
PROVIDE nuclear_repulsion expected_s2
|
2016-11-18 22:08:08 +01:00
|
|
|
|
2016-11-16 10:17:37 +01:00
|
|
|
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
|
2016-11-18 22:08:08 +01:00
|
|
|
write_buffer = trim(write_buffer)//' Energy S^2 Residual '
|
2016-11-16 10:17:37 +01:00
|
|
|
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)
|
2016-11-18 22:08:08 +01:00
|
|
|
|
|
|
|
integer, external :: align_double
|
|
|
|
integer :: fd(3)
|
|
|
|
type(c_ptr) :: c_pointer(3)
|
2016-11-16 10:17:37 +01:00
|
|
|
sze_8 = align_double(sze)
|
2016-11-18 22:08:08 +01:00
|
|
|
|
2016-11-16 10:17:37 +01:00
|
|
|
itermax = min(davidson_sze_max, sze/N_st_diag)
|
|
|
|
|
2016-11-18 22:08:08 +01:00
|
|
|
call mmap( &
|
|
|
|
trim(ezfio_work_dir)//'U', &
|
|
|
|
(/ int(sze_8,8),int(N_st_diag*itermax,8) /), &
|
2016-11-16 10:17:37 +01:00
|
|
|
8, fd(1), .False., c_pointer(1))
|
|
|
|
call c_f_pointer(c_pointer(1), W, (/ sze_8,N_st_diag*itermax /) )
|
|
|
|
|
2016-11-18 22:08:08 +01:00
|
|
|
call mmap( &
|
|
|
|
trim(ezfio_work_dir)//'W', &
|
|
|
|
(/ int(sze_8,8),int(N_st_diag*itermax,8) /), &
|
2016-11-16 10:17:37 +01:00
|
|
|
8, fd(2), .False., c_pointer(2))
|
|
|
|
call c_f_pointer(c_pointer(2), U, (/ sze_8,N_st_diag*itermax /) )
|
|
|
|
|
2016-11-18 22:08:08 +01:00
|
|
|
call mmap( &
|
|
|
|
trim(ezfio_work_dir)//'S', &
|
|
|
|
(/ int(sze_8,8),int(N_st_diag*itermax,8) /), &
|
2016-11-16 10:17:37 +01:00
|
|
|
8, fd(3), .False., c_pointer(3))
|
|
|
|
call c_f_pointer(c_pointer(3), S, (/ sze_8,N_st_diag*itermax /) )
|
|
|
|
|
|
|
|
allocate( &
|
2016-11-18 22:08:08 +01:00
|
|
|
h(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), &
|
|
|
|
overlap(N_st_diag*itermax, N_st_diag*itermax), &
|
2016-11-16 10:17:37 +01:00
|
|
|
residual_norm(N_st_diag), &
|
2016-11-18 22:08:08 +01:00
|
|
|
c(N_st_diag*itermax), &
|
|
|
|
s2(N_st_diag*itermax), &
|
2016-11-16 10:17:37 +01:00
|
|
|
lambda(N_st_diag*itermax))
|
|
|
|
|
2016-11-18 22:08:08 +01:00
|
|
|
h = 0.d0
|
2016-11-16 10:17:37 +01:00
|
|
|
U = 0.d0
|
|
|
|
W = 0.d0
|
|
|
|
S = 0.d0
|
|
|
|
y = 0.d0
|
2016-11-18 22:08:08 +01:00
|
|
|
s_ = 0.d0
|
|
|
|
s_tmp = 0.d0
|
|
|
|
|
|
|
|
|
2016-11-16 10:17:37 +01:00
|
|
|
ASSERT (N_st > 0)
|
|
|
|
ASSERT (N_st_diag >= N_st)
|
|
|
|
ASSERT (sze > 0)
|
|
|
|
ASSERT (Nint > 0)
|
|
|
|
ASSERT (Nint == N_int)
|
|
|
|
|
|
|
|
! Davidson iterations
|
|
|
|
! ===================
|
|
|
|
|
|
|
|
converged = .False.
|
|
|
|
|
|
|
|
double precision :: r1, r2
|
|
|
|
do k=N_st+1,N_st_diag
|
2016-11-18 22:08:08 +01:00
|
|
|
u_in(k,k) = 10.d0
|
2016-11-16 10:17:37 +01:00
|
|
|
do i=1,sze
|
|
|
|
call random_number(r1)
|
|
|
|
r1 = dsqrt(-2.d0*dlog(r1))
|
|
|
|
r2 = dtwo_pi*r2
|
|
|
|
u_in(i,k) = r1*dcos(r2)
|
|
|
|
enddo
|
|
|
|
enddo
|
|
|
|
do k=1,N_st_diag
|
|
|
|
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,itermax-1
|
|
|
|
|
|
|
|
shift = N_st_diag*(iter-1)
|
|
|
|
shift2 = N_st_diag*iter
|
|
|
|
|
|
|
|
call ortho_qr(U,size(U,1),sze,shift2)
|
|
|
|
|
|
|
|
! Compute |W_k> = \sum_i |i><i|H|u_k>
|
|
|
|
! -----------------------------------------
|
|
|
|
|
|
|
|
|
2017-04-17 01:36:16 +02:00
|
|
|
if (distributed_davidson) then
|
|
|
|
call H_S2_u_0_nstates_zmq(W(1,shift+1),S(1,shift+1),U(1,shift+1),N_st_diag,sze_8)
|
|
|
|
else
|
|
|
|
call H_S2_u_0_nstates_openmp(W(1,shift+1),S(1,shift+1),U(1,shift+1),N_st_diag,sze_8)
|
|
|
|
endif
|
2016-11-16 10:17:37 +01:00
|
|
|
|
|
|
|
|
|
|
|
! Compute h_kl = <u_k | W_l> = <u_k| H |u_l>
|
|
|
|
! -------------------------------------------
|
|
|
|
|
|
|
|
do k=1,iter
|
|
|
|
shift = N_st_diag*(k-1)
|
|
|
|
call dgemm('T','N', N_st_diag, shift2, sze, &
|
|
|
|
1.d0, U(1,shift+1), size(U,1), W, size(W,1), &
|
|
|
|
0.d0, h(shift+1,1), size(h,1))
|
|
|
|
|
|
|
|
call dgemm('T','N', N_st_diag, shift2, sze, &
|
|
|
|
1.d0, U(1,shift+1), size(U,1), S, size(S,1), &
|
|
|
|
0.d0, s_(shift+1,1), size(s_,1))
|
|
|
|
enddo
|
|
|
|
|
2016-11-18 22:08:08 +01:00
|
|
|
! ! Diagonalize S^2
|
|
|
|
! ! ---------------
|
|
|
|
!
|
|
|
|
! call lapack_diag(s2,y,s_,size(s_,1),shift2)
|
|
|
|
!
|
|
|
|
!
|
|
|
|
! ! Rotate H in the basis of eigenfunctions of s2
|
|
|
|
! ! ---------------------------------------------
|
|
|
|
!
|
|
|
|
! 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))
|
|
|
|
!
|
|
|
|
! ! Damp interaction between different spin states
|
|
|
|
! ! ------------------------------------------------
|
|
|
|
!
|
|
|
|
! do k=1,shift2
|
|
|
|
! do l=1,shift2
|
|
|
|
! if (dabs(s2(k) - s2(l)) > 1.d0) then
|
|
|
|
! h(k,l) = h(k,l)*(max(0.d0,1.d0 - dabs(s2(k) - s2(l))))
|
|
|
|
! endif
|
|
|
|
! enddo
|
|
|
|
! enddo
|
|
|
|
!
|
|
|
|
! ! Rotate back H
|
|
|
|
! ! -------------
|
|
|
|
!
|
|
|
|
! call dgemm('N','T',shift2,shift2,shift2, &
|
|
|
|
! 1.d0, h, size(h,1), y, size(y,1), &
|
|
|
|
! 0.d0, s_tmp, size(s_tmp,1))
|
|
|
|
!
|
|
|
|
! call dgemm('N','N',shift2,shift2,shift2, &
|
|
|
|
! 1.d0, y, size(y,1), s_tmp, size(s_tmp,1), &
|
|
|
|
! 0.d0, h, size(h,1))
|
|
|
|
|
2016-11-16 10:17:37 +01:00
|
|
|
|
|
|
|
! 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
|
|
|
|
|
2016-11-18 22:08:08 +01:00
|
|
|
|
2016-11-16 10:17:37 +01:00
|
|
|
if (s2_eig) then
|
2016-11-18 22:08:08 +01:00
|
|
|
do k=1,shift2
|
|
|
|
state_ok(k) = (dabs(s2(k)-expected_s2) < 0.6d0)
|
|
|
|
enddo
|
|
|
|
else
|
|
|
|
state_ok(k) = .True.
|
|
|
|
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
|
|
|
|
|
2016-11-19 00:39:02 +01:00
|
|
|
! Compute overlap with U_in
|
|
|
|
! -------------------------
|
|
|
|
|
|
|
|
integer :: order(N_st_diag)
|
|
|
|
double precision :: cmax
|
2016-11-18 22:08:08 +01:00
|
|
|
overlap = -1.d0
|
2016-11-16 10:17:37 +01:00
|
|
|
do k=1,shift2
|
2016-11-18 22:08:08 +01:00
|
|
|
do i=1,shift2
|
|
|
|
overlap(k,i) = dabs(y(k,i))
|
|
|
|
enddo
|
2016-11-16 10:17:37 +01:00
|
|
|
enddo
|
2016-11-18 22:08:08 +01:00
|
|
|
do k=1,N_st
|
2016-11-19 00:39:02 +01:00
|
|
|
cmax = -1.d0
|
2016-11-18 22:22:46 +01:00
|
|
|
do i=1,shift2
|
2016-11-19 00:39:02 +01:00
|
|
|
if (overlap(i,k) > cmax) then
|
|
|
|
cmax = overlap(i,k)
|
|
|
|
order(k) = i
|
|
|
|
endif
|
|
|
|
enddo
|
|
|
|
do i=1,shift2
|
|
|
|
overlap(order(k),i) = -1.d0
|
2016-11-18 22:22:46 +01:00
|
|
|
enddo
|
2016-11-18 22:08:08 +01:00
|
|
|
enddo
|
|
|
|
overlap = y
|
|
|
|
do k=1,N_st
|
|
|
|
l = order(k)
|
|
|
|
if (k /= l) then
|
|
|
|
y(1:shift2,k) = overlap(1:shift2,l)
|
2016-11-16 10:17:37 +01:00
|
|
|
endif
|
|
|
|
enddo
|
2016-11-18 22:08:08 +01:00
|
|
|
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
|
|
|
|
|
2016-11-16 10:17:37 +01:00
|
|
|
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))
|
|
|
|
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 and davidson step
|
|
|
|
! -----------------------------------------
|
|
|
|
|
|
|
|
do k=1,N_st_diag
|
2016-11-18 22:08:08 +01:00
|
|
|
if (state_ok(k)) then
|
|
|
|
do i=1,sze
|
|
|
|
U(i,shift2+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 &
|
|
|
|
)/max(H_jj(i) - lambda (k),1.d-2)
|
|
|
|
enddo
|
|
|
|
else
|
|
|
|
! Randomize components with bad <S2>
|
|
|
|
do i=1,sze-2,2
|
|
|
|
call random_number(r1)
|
|
|
|
call random_number(r2)
|
|
|
|
r1 = dsqrt(-2.d0*dlog(r1))
|
|
|
|
r2 = dtwo_pi*r2
|
|
|
|
U(i,shift2+k) = r1*dcos(r2)
|
|
|
|
U(i+1,shift2+k) = r1*dsin(r2)
|
|
|
|
enddo
|
|
|
|
do i=sze-2+1,sze
|
|
|
|
call random_number(r1)
|
|
|
|
call random_number(r2)
|
|
|
|
r1 = dsqrt(-2.d0*dlog(r1))
|
|
|
|
r2 = dtwo_pi*r2
|
|
|
|
U(i,shift2+k) = r1*dcos(r2)
|
|
|
|
enddo
|
|
|
|
endif
|
|
|
|
|
2016-11-16 10:17:37 +01:00
|
|
|
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
|
|
|
|
|
2017-04-12 19:29:21 +02:00
|
|
|
write(iunit,'(1X,I3,1X,100(1X,F16.10,1X,F11.6,1X,E11.3))') iter, to_print(1:3,1:N_st)
|
2016-11-16 10:17:37 +01:00
|
|
|
call davidson_converged(lambda,residual_norm,wall,iter,cpu,N_st,converged)
|
|
|
|
do k=1,N_st
|
|
|
|
if (residual_norm(k) > 1.e8) then
|
|
|
|
print *, ''
|
|
|
|
stop 'Davidson failed'
|
|
|
|
endif
|
|
|
|
enddo
|
|
|
|
if (converged) then
|
|
|
|
exit
|
|
|
|
endif
|
|
|
|
|
|
|
|
enddo
|
|
|
|
|
|
|
|
! Re-contract to u_in
|
|
|
|
! -----------
|
|
|
|
|
|
|
|
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))
|
|
|
|
|
|
|
|
enddo
|
|
|
|
|
|
|
|
do k=1,N_st_diag
|
|
|
|
energies(k) = lambda(k)
|
|
|
|
S2_jj(k) = s2(k)
|
|
|
|
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)
|
|
|
|
|
|
|
|
call munmap( &
|
|
|
|
(/ int(sze_8,8),int(N_st_diag*itermax,8) /), &
|
|
|
|
8, fd(1), c_pointer(1))
|
|
|
|
|
|
|
|
call munmap( &
|
|
|
|
(/ int(sze_8,8),int(N_st_diag*itermax,8) /), &
|
|
|
|
8, fd(2), c_pointer(2))
|
|
|
|
|
|
|
|
call munmap( &
|
|
|
|
(/ int(sze_8,8),int(N_st_diag*itermax,8) /), &
|
|
|
|
8, fd(3), c_pointer(3))
|
|
|
|
|
|
|
|
deallocate ( &
|
|
|
|
residual_norm, &
|
2016-11-18 22:08:08 +01:00
|
|
|
c, overlap, &
|
2016-11-16 10:17:37 +01:00
|
|
|
h, &
|
|
|
|
y, s_, s_tmp, &
|
|
|
|
lambda &
|
|
|
|
)
|
|
|
|
end
|
|
|
|
|