403 lines
13 KiB
Fortran
403 lines
13 KiB
Fortran
subroutine get_s2(key_i,key_j,s2,Nint)
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implicit none
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use bitmasks
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BEGIN_DOC
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! Returns <S^2>
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END_DOC
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integer, intent(in) :: Nint
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integer(bit_kind), intent(in) :: key_i(Nint,2)
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integer(bit_kind), intent(in) :: key_j(Nint,2)
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double precision, intent(out) :: s2
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integer :: exc(0:2,2,2)
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integer :: degree
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double precision :: phase_spsm
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integer :: nup, i
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s2 = 0.d0
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!$FORCEINLINE
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call get_excitation_degree(key_i,key_j,degree,Nint)
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select case (degree)
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case(2)
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call get_double_excitation(key_j,key_i,exc,phase_spsm,Nint)
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if (exc(0,1,1) == 1) then ! Mono alpha + mono-beta
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if ( (exc(1,1,1) == exc(1,2,2)).and.(exc(1,1,2) == exc(1,2,1)) ) then
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s2 = -phase_spsm
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endif
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endif
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case(0)
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nup = 0
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do i=1,Nint
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nup += popcnt(iand(xor(key_i(i,1),key_i(i,2)),key_i(i,1)))
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enddo
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s2 = dble(nup)
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end select
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end
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BEGIN_PROVIDER [ double precision, S_z ]
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&BEGIN_PROVIDER [ double precision, S_z2_Sz ]
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implicit none
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BEGIN_DOC
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! z component of the Spin
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END_DOC
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S_z = 0.5d0*dble(elec_alpha_num-elec_beta_num)
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S_z2_Sz = S_z*(S_z-1.d0)
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END_PROVIDER
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BEGIN_PROVIDER [ double precision, expected_s2]
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implicit none
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BEGIN_DOC
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! Expected value of S2 : S*(S+1)
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END_DOC
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logical :: has_expected_s2
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call ezfio_has_determinants_expected_s2(has_expected_s2)
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if (has_expected_s2) then
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call ezfio_get_determinants_expected_s2(expected_s2)
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else
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double precision :: S
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S = (elec_alpha_num-elec_beta_num)*0.5d0
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expected_s2 = S * (S+1.d0)
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! expected_s2 = elec_alpha_num - elec_beta_num + 0.5d0 * ((elec_alpha_num - elec_beta_num)**2*0.5d0 - (elec_alpha_num-elec_beta_num))
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endif
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END_PROVIDER
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BEGIN_PROVIDER [ double precision, s2_values, (N_states) ]
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implicit none
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BEGIN_DOC
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! array of the averaged values of the S^2 operator on the various states
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END_DOC
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integer :: i
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double precision :: s2
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do i = 1, N_states
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call get_s2_u0(psi_det,psi_coef(1,i),n_det,size(psi_coef,1),s2)
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s2_values(i) = s2
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enddo
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END_PROVIDER
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subroutine get_s2_u0_old(psi_keys_tmp,psi_coefs_tmp,n,nmax,s2)
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implicit none
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use bitmasks
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integer, intent(in) :: n,nmax
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integer(bit_kind), intent(in) :: psi_keys_tmp(N_int,2,nmax)
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double precision, intent(in) :: psi_coefs_tmp(nmax)
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double precision, intent(out) :: s2
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integer :: i,j,l
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double precision :: s2_tmp
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s2 = 0.d0
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!$OMP PARALLEL DO DEFAULT(NONE) &
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!$OMP PRIVATE(i,j,s2_tmp) SHARED(n,psi_coefs_tmp,psi_keys_tmp,N_int) REDUCTION(+:s2) SCHEDULE(dynamic)
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do i=1,n
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do j=i+1,n
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call get_s2(psi_keys_tmp(1,1,i),psi_keys_tmp(1,1,j),s2_tmp,N_int)
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s2 += psi_coefs_tmp(i)*psi_coefs_tmp(j)*s2_tmp
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enddo
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enddo
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!$OMP END PARALLEL DO
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s2 = s2+s2
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do i=1,n
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call get_s2(psi_keys_tmp(1,1,i),psi_keys_tmp(1,1,i),s2_tmp,N_int)
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s2 += psi_coefs_tmp(i)*psi_coefs_tmp(i)*s2_tmp
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enddo
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s2 += S_z2_Sz
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end
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subroutine get_s2_u0(psi_keys_tmp,psi_coefs_tmp,n,nmax,s2)
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implicit none
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use bitmasks
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integer, intent(in) :: n,nmax
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integer(bit_kind), intent(in) :: psi_keys_tmp(N_int,2,nmax)
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double precision, intent(in) :: psi_coefs_tmp(nmax)
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double precision, intent(out) :: s2
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double precision :: s2_tmp
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integer :: i,j,l,jj,ii
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integer, allocatable :: idx(:)
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integer, allocatable :: shortcut(:), sort_idx(:)
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integer(bit_kind), allocatable :: sorted(:,:), version(:,:)
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integer :: sh, sh2, ni, exa, ext, org_i, org_j, endi, pass
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double precision :: davidson_threshold_bis
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allocate (shortcut(0:n+1), sort_idx(n), sorted(N_int,n), version(N_int,n))
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s2 = 0.d0
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davidson_threshold_bis = threshold_davidson
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call sort_dets_ab_v(psi_keys_tmp, sorted, sort_idx, shortcut, version, n, N_int)
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!$OMP PARALLEL DEFAULT(NONE) &
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!$OMP PRIVATE(i,j,s2_tmp,sh, sh2, ni, exa, ext, org_i, org_j, endi, pass)&
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!$OMP SHARED(n,psi_coefs_tmp,psi_keys_tmp,N_int,threshold_davidson,shortcut,sorted,sort_idx,version)&
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!$OMP REDUCTION(+:s2)
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!$OMP DO SCHEDULE(dynamic)
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do sh=1,shortcut(0)
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do sh2=1,sh
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exa = 0
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do ni=1,N_int
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exa += popcnt(xor(version(ni,sh), version(ni,sh2)))
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end do
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if(exa > 2) then
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cycle
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end if
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do i=shortcut(sh),shortcut(sh+1)-1
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if(sh==sh2) then
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endi = i-1
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else
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endi = shortcut(sh2+1)-1
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end if
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do j=shortcut(sh2),endi
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ext = exa
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do ni=1,N_int
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ext += popcnt(xor(sorted(ni,i), sorted(ni,j)))
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end do
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if(ext <= 4) then
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org_i = sort_idx(i)
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org_j = sort_idx(j)
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if ( dabs(psi_coefs_tmp(org_j)) + dabs(psi_coefs_tmp(org_i))&
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> threshold_davidson ) then
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call get_s2(psi_keys_tmp(1,1,org_i),psi_keys_tmp(1,1,org_j),s2_tmp,N_int)
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s2 = s2 + psi_coefs_tmp(org_i)*psi_coefs_tmp(org_j)*s2_tmp
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endif
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end if
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end do
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end do
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end do
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enddo
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!$OMP END DO
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!$OMP END PARALLEL
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call sort_dets_ba_v(psi_keys_tmp, sorted, sort_idx, shortcut, version, n, N_int)
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!$OMP PARALLEL DEFAULT(NONE) &
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!$OMP PRIVATE(i,j,s2_tmp,sh, sh2, ni, exa, ext, org_i, org_j, endi, pass)&
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!$OMP SHARED(n,psi_coefs_tmp,psi_keys_tmp,N_int,threshold_davidson,shortcut,sorted,sort_idx,version)&
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!$OMP REDUCTION(+:s2)
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!$OMP DO SCHEDULE(dynamic)
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do sh=1,shortcut(0)
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do i=shortcut(sh),shortcut(sh+1)-1
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do j=shortcut(sh),i-1
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ext = 0
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do ni=1,N_int
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ext += popcnt(xor(sorted(ni,i), sorted(ni,j)))
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end do
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if(ext == 4) then
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org_i = sort_idx(i)
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org_j = sort_idx(j)
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if ( dabs(psi_coefs_tmp(org_j)) + dabs(psi_coefs_tmp(org_i))&
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> threshold_davidson ) then
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call get_s2(psi_keys_tmp(1,1,org_i),psi_keys_tmp(1,1,org_j),s2_tmp,N_int)
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s2 = s2 + psi_coefs_tmp(org_i)*psi_coefs_tmp(org_j)*s2_tmp
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endif
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end if
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end do
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end do
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enddo
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!$OMP END DO
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!$OMP END PARALLEL
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s2 = s2+s2
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do i=1,n
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call get_s2(psi_keys_tmp(1,1,i),psi_keys_tmp(1,1,i),s2_tmp,N_int)
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s2 = s2 + psi_coefs_tmp(i)*psi_coefs_tmp(i)*s2_tmp
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enddo
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s2 = s2 + S_z2_Sz
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deallocate (shortcut, sort_idx, sorted, version)
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end
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subroutine get_uJ_s2_uI(psi_keys_tmp,psi_coefs_tmp,n,nmax_coefs,nmax_keys,s2,nstates)
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implicit none
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use bitmasks
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integer(bit_kind), intent(in) :: psi_keys_tmp(N_int,2,nmax_keys)
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integer, intent(in) :: n,nmax_coefs,nmax_keys,nstates
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double precision, intent(in) :: psi_coefs_tmp(nmax_coefs,nstates)
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double precision, intent(out) :: s2(nstates,nstates)
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double precision :: s2_tmp,accu
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integer :: i,j,l,jj,ll,kk
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integer, allocatable :: idx(:)
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BEGIN_DOC
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! returns the matrix elements of S^2 "s2(i,j)" between the "nstates" states
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! psi_coefs_tmp(:,i) and psi_coefs_tmp(:,j)
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END_DOC
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s2 = 0.d0
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do ll = 1, nstates
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do jj = 1, nstates
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accu = 0.d0
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!$OMP PARALLEL DEFAULT(NONE) &
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!$OMP PRIVATE (i,j,kk,idx,s2_tmp) &
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!$OMP SHARED (ll,jj,psi_keys_tmp,psi_coefs_tmp,N_int,n,nstates)&
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!$OMP REDUCTION(+:accu)
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allocate(idx(0:n))
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!$OMP DO SCHEDULE(dynamic)
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do i = n,1,-1 ! Better OMP scheduling
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call get_s2(psi_keys_tmp(1,1,i),psi_keys_tmp(1,1,i),s2_tmp,N_int)
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accu += psi_coefs_tmp(i,ll) * s2_tmp * psi_coefs_tmp(i,jj)
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call filter_connected(psi_keys_tmp,psi_keys_tmp(1,1,i),N_int,i-1,idx)
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do kk=1,idx(0)
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j = idx(kk)
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call get_s2(psi_keys_tmp(1,1,i),psi_keys_tmp(1,1,j),s2_tmp,N_int)
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accu += psi_coefs_tmp(i,ll) * s2_tmp * psi_coefs_tmp(j,jj) + psi_coefs_tmp(i,jj) * s2_tmp * psi_coefs_tmp(j,ll)
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enddo
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enddo
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!$OMP END DO
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deallocate(idx)
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!$OMP END PARALLEL
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s2(ll,jj) += accu
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enddo
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enddo
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do i = 1, nstates
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do j =i+1,nstates
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accu = 0.5d0 * (s2(i,j) + s2(j,i))
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s2(i,j) = accu
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s2(j,i) = accu
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enddo
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enddo
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end
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subroutine diagonalize_s2_betweenstates(keys_tmp,psi_coefs_inout,n,nmax_keys,nmax_coefs,nstates,s2_eigvalues)
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BEGIN_DOC
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! You enter with nstates vectors in psi_coefs_inout that may be coupled by S^2
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! The subroutine diagonalize the S^2 operator in the basis of these states.
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! The vectors that you obtain in output are no more coupled by S^2,
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! which does not necessary mean that they are eigenfunction of S^2.
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! n,nmax,nstates = number of determinants, physical dimension of the arrays and number of states
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! keys_tmp = array of integer(bit_kind) that represents the determinants
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! psi_coefs(i,j) = coeff of the ith determinant in the jth state
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! VECTORS ARE SUPPOSED TO BE ORTHONORMAL IN INPUT
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END_DOC
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implicit none
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use bitmasks
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integer, intent(in) :: n,nmax_keys,nmax_coefs,nstates
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integer(bit_kind), intent(in) :: keys_tmp(N_int,2,nmax_keys)
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double precision, intent(inout) :: psi_coefs_inout(nmax_coefs,nstates)
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!integer, intent(in) :: ndets_real,ndets_keys,ndets_coefs,nstates
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!integer(bit_kind), intent(in) :: keys_tmp(N_int,2,ndets_keys)
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!double precision, intent(inout) :: psi_coefs_inout(ndets_coefs,nstates)
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double precision, intent(out) :: s2_eigvalues(nstates)
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double precision,allocatable :: s2(:,:),overlap(:,:)
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double precision, allocatable :: eigvalues(:),eigvectors(:,:)
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integer :: i,j,k
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double precision, allocatable :: psi_coefs_tmp(:,:)
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double precision :: accu,coef_contract
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double precision :: u_dot_u,u_dot_v
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print*,''
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print*,'*********************************************************************'
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print*,'Cleaning the various vectors by diagonalization of the S^2 matrix ...'
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print*,''
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print*,'nstates = ',nstates
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allocate(s2(nstates,nstates),overlap(nstates,nstates))
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!$OMP PARALLEL DO COLLAPSE(2) DEFAULT(NONE) SCHEDULE(dynamic) &
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!$OMP PRIVATE(i,j) SHARED(overlap,psi_coefs_inout,nstates,n)
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do i = 1, nstates
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do j = 1, nstates
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if (i < j) then
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cycle
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else if (i == j) then
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overlap(i,i) = u_dot_u(psi_coefs_inout(1,i),n)
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else
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overlap(i,j) = u_dot_v(psi_coefs_inout(1,j),psi_coefs_inout(1,i),n)
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overlap(j,i) = overlap(i,j)
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endif
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enddo
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enddo
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!$OMP END PARALLEL DO
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print*,'Overlap matrix in the basis of the states considered'
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do i = 1, nstates
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write(*,'(10(F16.10,X))')overlap(i,:)
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enddo
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call ortho_lowdin(overlap,size(overlap,1),nstates,psi_coefs_inout,size(psi_coefs_inout,1),n)
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print*,'passed ortho'
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!$OMP PARALLEL DO COLLAPSE(2) DEFAULT(NONE) SCHEDULE(dynamic) &
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!$OMP PRIVATE(i,j) SHARED(overlap,psi_coefs_inout,nstates,n)
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do i = 1, nstates
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do j = 1, nstates
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if (i < j) then
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cycle
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else if (i == j) then
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overlap(i,i) = u_dot_u(psi_coefs_inout(1,i),n)
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else
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overlap(i,j) = u_dot_v(psi_coefs_inout(1,j),psi_coefs_inout(1,i),n)
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overlap(j,i) = overlap(i,j)
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endif
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enddo
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enddo
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!$OMP END PARALLEL DO
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print*,'Overlap matrix in the basis of the Lowdin orthonormalized states '
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do i = 1, nstates
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write(*,'(10(F16.10,X))')overlap(i,:)
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enddo
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call get_uJ_s2_uI(keys_tmp,psi_coefs_inout,n_det,size(psi_coefs_inout,1),size(keys_tmp,3),s2,nstates)
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print*,'S^2 matrix in the basis of the states considered'
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double precision :: accu_precision_diag,accu_precision_of_diag
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accu_precision_diag = 0.d0
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accu_precision_of_diag = 0.d0
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do i = 1, nstates
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do j = i+1, nstates
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if( ( dabs(s2(i,i) - s2(j,j)) .le.1.d-10 ) .and. (dabs(s2(i,j) + dabs(s2(i,j)))) .le.1.d-10) then
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s2(i,j) = 0.d0
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s2(j,i) = 0.d0
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endif
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enddo
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enddo
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do i = 1, nstates
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write(*,'(10(F10.6,X))')s2(i,:)
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enddo
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print*,'Diagonalizing the S^2 matrix'
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allocate(eigvalues(nstates),eigvectors(nstates,nstates))
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call lapack_diagd(eigvalues,eigvectors,s2,nstates,nstates)
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print*,'Eigenvalues of s^2'
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do i = 1, nstates
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print*,'s2 = ',eigvalues(i)
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s2_eigvalues(i) = eigvalues(i)
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enddo
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print*,'Building the eigenvectors of the S^2 matrix'
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allocate(psi_coefs_tmp(nmax_coefs,nstates))
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psi_coefs_tmp = 0.d0
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do j = 1, nstates
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do k = 1, nstates
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coef_contract = eigvectors(k,j) ! <phi_k|Psi_j>
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do i = 1, n_det
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psi_coefs_tmp(i,j) += psi_coefs_inout(i,k) * coef_contract
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enddo
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enddo
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enddo
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do j = 1, nstates
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accu = 0.d0
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do i = 1, n_det
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accu += psi_coefs_tmp(i,j) * psi_coefs_tmp(i,j)
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enddo
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print*,'Norm of vector = ',accu
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accu = 1.d0/dsqrt(accu)
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do i = 1, n_det
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psi_coefs_inout(i,j) = psi_coefs_tmp(i,j) * accu
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enddo
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enddo
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!call get_uJ_s2_uI(keys_tmp,psi_coefs_inout,n_det,size(psi_coefs_inout,1),size(keys_tmp,3),s2,nstates)
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!print*,'S^2 matrix in the basis of the NEW states considered'
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!do i = 1, nstates
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! write(*,'(10(F16.10,X))')s2(i,:)
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!enddo
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deallocate(s2,eigvalues,eigvectors,psi_coefs_tmp,overlap)
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end
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