program buildpsi_SVDit implicit none BEGIN_DOC ! perturbative approach to build psi_postsvd END_DOC read_wf = .True. TOUCH read_wf PROVIDE N_int call run() end subroutine run USE OMP_LIB implicit none integer(bit_kind) :: det1(N_int,2), det2(N_int,2) integer :: degree, i_state double precision :: h12 integer :: i, j, k, l, ii, jj double precision :: norm_psi double precision, allocatable :: Uref(:,:), Dref(:), Vtref(:,:), Aref(:,:), Vref(:,:) double precision :: err0, err_tmp, e_tmp double precision :: E0, E0pt2, ept2, E0_old, tol_energy double precision :: ctmp, htmp double precision, allocatable :: H0(:,:), Hdiag(:), Hkl(:,:) double precision, allocatable :: coeff_psi_selected(:), coeff_psi_toselect(:) integer :: n_FSVD, n_selected, n_toselect, it_svd, it_svd_max integer, allocatable :: numalpha_selected(:), numbeta_selected(:) integer, allocatable :: numalpha_toselect(:), numbeta_toselect(:) integer, allocatable :: numalpha_tmp(:), numbeta_tmp(:) integer(kind=8) :: W_tbeg, W_tend, W_tbeg_it, W_tend_it, W_ir real(kind=8) :: W_tot_time, W_tot_time_it real(kind=8) :: CPU_tbeg, CPU_tend, CPU_tbeg_it, CPU_tend_it real(kind=8) :: CPU_tot_time, CPU_tot_time_it real(kind=8) :: speedup, speedup_it integer :: nb_taches !$OMP PARALLEL nb_taches = OMP_GET_NUM_THREADS() !$OMP END PARALLEL call CPU_TIME(CPU_tbeg) call SYSTEM_CLOCK(COUNT=W_tbeg, COUNT_RATE=W_ir) i_state = 1 det1(:,1) = psi_det_alpha_unique(:,1) det2(:,1) = psi_det_alpha_unique(:,1) call get_excitation_degree_spin(det1(1,1),det2(1,1),degree,N_int) det1(:,2) = psi_det_beta_unique(:,1) det2(:,2) = psi_det_beta_unique(:,1) call get_excitation_degree(det1,det2,degree,N_int) call i_H_j(det1, det2, N_int, h12) ! --------------------------------------------------------------------------------------- ! construct the initial CISD matrix print *, ' ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~' print *, ' CISD matrix:', n_det_alpha_unique,'x',n_det_beta_unique print *, ' N det :', N_det print *, ' ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~' norm_psi = 0.d0 do k = 1, N_det norm_psi = norm_psi + psi_bilinear_matrix_values(k,i_state) & * psi_bilinear_matrix_values(k,i_state) enddo print *, ' initial norm = ', norm_psi allocate( Aref(n_det_alpha_unique,n_det_beta_unique) ) Aref(:,:) = 0.d0 do k = 1, N_det i = psi_bilinear_matrix_rows(k) j = psi_bilinear_matrix_columns(k) Aref(i,j) = psi_bilinear_matrix_values(k,i_state) enddo ! --------------------------------------------------------------------------------------- ! --------------------------------------------------------------------------------------- ! perform a Full SVD allocate( Uref(n_det_alpha_unique,n_det_beta_unique) ) allocate( Dref(n_det_beta_unique) ) allocate( Vref(n_det_beta_unique,n_det_beta_unique) ) allocate( Vtref(n_det_beta_unique,n_det_beta_unique) ) call svd_s(Aref, size(Aref,1), Uref, size(Uref,1), Dref, Vtref, size(Vtref,1) & , n_det_alpha_unique, n_det_beta_unique) print *, ' ~~~~~~~~~~~~~~~~~~~~~~~~~~~ ' print *, ' --- First SVD: ok --- ' print *, ' ~~~~~~~~~~~~~~~~~~~~~~~~~~~ ' do l = 1, n_det_beta_unique do i = 1, n_det_beta_unique Vref(i,l) = Vtref(l,i) enddo enddo deallocate( Vtref ) ! --------------------------------------------------------------------------------------- ! --------------------------------------------------------------------------------------- ! numerote vectors ! Full rank n_FSVD = n_det_beta_unique*n_det_beta_unique print*, ' Full psi space rank = ', n_FSVD ! Truncated rank n_selected = 20 print*, ' initial psi space rank = ', n_selected allocate( numalpha_selected(n_selected) , numbeta_selected(n_selected) ) do i = 1, n_selected numalpha_selected(i) = i numbeta_selected (i) = i enddo ! check SVD error err0 = 0.d0 do j = 1, n_det_beta_unique do i = 1, n_det_alpha_unique err_tmp = 0.d0 do l = 1, n_selected ii = numalpha_selected(l) jj = numbeta_selected (l) err_tmp = err_tmp + Dref(l) * Uref(i,ii) * Vref(j,jj) enddo err_tmp = Aref(i,j) - err_tmp err0 += err_tmp * err_tmp enddo enddo print *, ' SVD err (%) = ', 100.d0 * dsqrt(err0/norm_psi) deallocate( Aref ) ! perturbative space rank l = 3 k = 0 if( l.eq.1 ) then n_toselect = 2*n_selected * ( n_det_beta_unique - n_selected ) allocate( numalpha_toselect(n_toselect) , numbeta_toselect(n_toselect) ) ! nondiagonal blocs do i = 1, n_selected do j = n_selected+1, n_det_beta_unique k = k + 1 numalpha_toselect(k) = i numbeta_toselect (k) = j enddo enddo do j = 1, n_selected do i = n_selected+1, n_det_beta_unique k = k + 1 numalpha_toselect(k) = i numbeta_toselect (k) = j enddo enddo elseif( l.eq.2 ) then n_toselect = n_FSVD - n_selected*n_selected allocate( numalpha_toselect(n_toselect) , numbeta_toselect(n_toselect) ) ! nondiagonal blocs do i = 1, n_selected do j = n_selected+1, n_det_beta_unique k = k + 1 numalpha_toselect(k) = i numbeta_toselect (k) = j enddo enddo do j = 1, n_selected do i = n_selected+1, n_det_beta_unique k = k + 1 numalpha_toselect(k) = i numbeta_toselect (k) = j enddo enddo ! diagonal bloc do i = n_selected+1, n_det_beta_unique do j = n_selected+1, n_det_beta_unique k = k + 1 numalpha_toselect(k) = i numbeta_toselect (k) = j enddo enddo elseif( l.eq.3 ) then n_toselect = n_FSVD - n_selected allocate( numalpha_toselect(n_toselect) , numbeta_toselect(n_toselect) ) do i = 1, n_det_beta_unique do j = 1, n_det_beta_unique if( (i.eq.j).and.(i.le.n_selected)) then cycle else k = k + 1 numalpha_toselect(k) = i numbeta_toselect (k) = j endif enddo enddo elseif( l.eq.4 ) then n_toselect = n_FSVD - n_selected - (n_det_beta_unique-n_selected)**2 allocate( numalpha_toselect(n_toselect) , numbeta_toselect(n_toselect) ) ! nondiagonal blocs do i = 1, n_selected do j = i+1, n_det_beta_unique k = k + 1 numalpha_toselect(k) = i numbeta_toselect (k) = j enddo enddo do j = 1, n_selected do i = j+1, n_det_beta_unique k = k + 1 numalpha_toselect(k) = i numbeta_toselect (k) = j enddo enddo endif if( k.ne.n_toselect ) then print*, ' error in numeroting ' stop endif print*, ' perturbative psi space rank = ', n_toselect ! --------------------------------------------------------------------------------------- !________________________________________________________________________________________________________ ! ! loop over SVD iterations !________________________________________________________________________________________________________ E0_old = 0.d0 tol_energy = 1.d0 it_svd = 0 it_svd_max = 100 do while( ( it_svd .lt. it_svd_max) .and. ( tol_energy .gt. 1d-8 ) ) call CPU_TIME(CPU_tbeg_it) call SYSTEM_CLOCK(COUNT=W_tbeg_it, COUNT_RATE=W_ir) it_svd = it_svd + 1 print*, '+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +' print*, ' ' print*, ' iteration', it_svd ! --------------------------------------------------------------------------------------- ! calculate the energy allocate( coeff_psi_selected(n_selected) ) ! normalise | psi0 > norm_psi = 0.d0 do i = 1, n_selected norm_psi += Dref(i) * Dref(i) enddo norm_psi = 1.d0 / dsqrt(norm_psi) do i = 1, n_selected coeff_psi_selected(i) = Dref(i) * norm_psi enddo ! H0(i,j) = < u_i v_j | H | u_i v_j > print *, '' print *, '' print *, '' print *, '-- Compute H --' allocate( H0(n_selected,n_selected) ) call const_psiHpsi(n_selected, Uref, Vref, numalpha_selected, numbeta_selected, H0) ! avant SVD ! E0 = < psi_0 | H | psi_0 > / < psi_0 | psi_0 > E0 = 0.d0 do i = 1, n_selected ii = numalpha_selected(i) htmp = 0.d0 do j = 1, n_selected jj = numalpha_selected(j) htmp = htmp + coeff_psi_selected(j) * H0(jj,ii) enddo E0 = E0 + htmp * coeff_psi_selected(i) enddo E0 = E0 + nuclear_repulsion print *,' E0 (avant SVD) =', E0 deallocate( H0 ) ! --------------------------------------------------------------------------------------- ! --------------------------------------------------------------------------------------- ! nondiagonal elements print *, ' --- Perturbation --- ' allocate( Hdiag(n_toselect), Hkl(n_selected,n_toselect) ) call const_Hdiag_Hkl(n_selected, n_toselect, Uref, Vref & , numalpha_selected, numbeta_selected, numalpha_toselect, numbeta_toselect, Hdiag, Hkl) ! evaluate the coefficients for all the vectors allocate( coeff_psi_toselect(n_toselect) ) ept2 = 0.d0 do ii = 1, n_toselect ctmp = 0.d0 do l = 1, n_selected ctmp += coeff_psi_selected(l) * Hkl(l,ii) enddo coeff_psi_toselect(ii) = ctmp / ( E0 - (Hdiag(ii)+nuclear_repulsion) ) ept2 += ctmp * ctmp / ( E0 - (Hdiag(ii)+nuclear_repulsion) ) enddo E0pt2 = E0 + ept2 deallocate( Hdiag, Hkl) print *, ' perturb energy = ', E0pt2, ept2 print*, ' delta E0 = ', E0pt2 - E0_old tol_energy = 100.d0 * dabs(E0pt2-E0_old)/dabs(E0pt2) E0_old = E0pt2 ! normalize the new psi and perform a new SVD norm_psi = 0.d0 do l = 1, n_toselect norm_psi = norm_psi + coeff_psi_toselect(l)*coeff_psi_toselect(l) enddo norm_psi = norm_psi + 1.d0 norm_psi = 1.d0 / dsqrt(norm_psi) do i = 1, n_toselect coeff_psi_toselect(i) = coeff_psi_toselect(i) * norm_psi enddo do i = 1, n_selected coeff_psi_selected(i) = coeff_psi_selected(i) * norm_psi enddo print *, ' --- SVD --- ' call perform_newSVD(n_selected, n_toselect, numalpha_selected, numbeta_selected & , numalpha_toselect, numbeta_toselect, coeff_psi_selected, coeff_psi_toselect & , Uref, Vref, Dref ) ! --------------------------------------------------------------------------------------- deallocate( coeff_psi_toselect ) deallocate( coeff_psi_selected ) write(55,'(i5,4x,4(f22.15,2x))') it_svd, E0, E0pt2 call CPU_TIME(CPU_tend_it) call SYSTEM_CLOCK(COUNT=W_tend_it, COUNT_RATE=W_ir) CPU_tot_time_it = CPU_tend_it - CPU_tbeg_it W_tot_time_it = real(W_tend_it-W_tbeg_it, kind=8) / real(W_ir, kind=8) speedup_it = CPU_tot_time_it / W_tot_time_it print '(//, 3X, "elapsed time = ", 1PE10.3, " min.", /, & & 3X, "CPU time = ", 1PE10.3, " min.", /, & & 3X, "speed up = ", 1PE10.3,//)', W_tot_time_it/60.d0, CPU_tot_time_it/60.d0, speedup_it !print*, '+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +' !print*, ' ' end do !________________________________________________________________________________________________________ !________________________________________________________________________________________________________ deallocate( Uref, Vref, Dref ) call CPU_TIME(CPU_tend) call SYSTEM_CLOCK(COUNT=W_tend, COUNT_RATE=W_ir) CPU_tot_time = CPU_tend - CPU_tbeg W_tot_time = real(W_tend - W_tbeg, kind=8) / real(W_ir, kind=8) speedup = CPU_tot_time / W_tot_time print *,' ___________________________________________________________________' print '(//,3X,"Execution avec ",i2," threads")',nb_taches print *,' ___________________________________________________________________' print '(//, 3X, "elapsed time = ", 1PE10.3, " min.", /, & & 3X, "CPU time = ", 1PE10.3, " min.", /, & & 3X, "speed up = ", 1PE10.3 ,//)', W_tot_time/60.d0, CPU_tot_time/60.d0, speedup end subroutine const_psiHpsi(n_selected, Uref, Vref, numalpha_selected, numbeta_selected, H0) USE OMP_LIB implicit none integer, intent(in) :: n_selected integer, intent(in) :: numalpha_selected(n_selected), numbeta_selected(n_selected) double precision, intent(in) :: Uref(n_det_alpha_unique,n_det_beta_unique) double precision, intent(in) :: Vref(n_det_beta_unique ,n_det_beta_unique) double precision, intent(out) :: H0(n_selected,n_selected) integer(bit_kind) :: det1(N_int,2) integer(bit_kind) :: det2(N_int,2) integer :: degree integer :: i, j, k, l integer :: ii0, jj0, ii, jj, n, m, np, mp double precision :: h12, x H0(:,:) = 0.d0 do i = 1, n_det_alpha_unique det1(:,1) = psi_det_alpha_unique(:,i) do k = 1, n_det_alpha_unique det2(:,1) = psi_det_alpha_unique(:,k) call get_excitation_degree_spin(det1(1,1),det2(1,1),degree,N_int) if (degree .gt. 2) then cycle endif do j = 1, n_det_beta_unique det1(:,2) = psi_det_beta_unique(:,j) do l = 1, n_det_beta_unique det2(:,2) = psi_det_beta_unique(:,l) call get_excitation_degree(det1,det2,degree,N_int) if (degree .gt. 2) then cycle endif ! !!! call i_H_j(det1, det2, N_int, h12) ! !!! ! ~~~ H0 ~~~ do n = 1, n_selected ii0 = numalpha_selected(n) jj0 = numbeta_selected (n) x = Uref(k,ii0) * Vref(l,jj0) * h12 do m = 1, n_selected ii = numalpha_selected(m) jj = numbeta_selected (m) H0(m,n) += Uref(i,ii) * Vref(j,jj) * x enddo enddo ! ~~~ ~~~~~~ ~~~ enddo enddo enddo enddo end subroutine const_psiHpsi subroutine const_Hdiag_Hkl(n_selected, n_toselect, Uref, Vref & , numalpha_selected, numbeta_selected, numalpha_toselect, numbeta_toselect, Hdiag, Hkl) USE OMP_LIB implicit none integer, intent(in) :: n_selected,n_toselect integer, intent(in) :: numalpha_selected(n_selected), numbeta_selected(n_selected) integer, intent(in) :: numalpha_toselect(n_toselect), numbeta_toselect(n_toselect) double precision, intent(in) :: Uref(n_det_alpha_unique,n_det_beta_unique) double precision, intent(in) :: Vref(n_det_beta_unique ,n_det_beta_unique) double precision, intent(out) :: Hdiag(n_toselect), Hkl(n_selected,n_toselect) integer(bit_kind) :: det1(N_int,2) integer(bit_kind) :: det2(N_int,2) integer :: degree integer :: i, j, k, l integer :: ii0, jj0, ii, jj, n, m, np, mp double precision :: h12, y double precision, allocatable :: Hdiag_tmp(:), Hkl_tmp(:,:) Hdiag(:) = 0.d0 Hkl(:,:) = 0.d0 !$OMP PARALLEL DEFAULT(NONE) & !$OMP PRIVATE(n,ii0,jj0,y,m,ii,jj,i,j,k,l,h12,det1,det2,Hdiag_tmp,Hkl_tmp,degree) & !$OMP SHARED(n_det_alpha_unique,n_det_beta_unique,psi_det_alpha_unique,psi_det_beta_unique, & !$OMP N_int,n_selected,n_toselect,Uref,Vref,numalpha_toselect,numbeta_toselect, & !$OMP numalpha_selected, numbeta_selected,Hkl,Hdiag ) allocate( Hdiag_tmp(n_toselect), Hkl_tmp(n_selected,n_toselect) ) Hdiag_tmp(:) = 0.d0 Hkl_tmp(:,:) = 0.d0 !$OMP DO COLLAPSE(2) SCHEDULE(DYNAMIC,8) do i = 1, n_det_alpha_unique do k = 1, n_det_alpha_unique det1(:,1) = psi_det_alpha_unique(:,i) det2(:,1) = psi_det_alpha_unique(:,k) ! !!! ! ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ call get_excitation_degree_spin(det1(1,1),det2(1,1),degree,N_int) if (degree .gt. 2) then cycle endif ! ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ! !!! do j = 1, n_det_beta_unique det1(:,2) = psi_det_beta_unique(:,j) do l = 1, n_det_beta_unique det2(:,2) = psi_det_beta_unique(:,l) ! !!! ! ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ call get_excitation_degree(det1,det2,degree,N_int) if (degree .gt. 2) then cycle endif ! ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ! !!! call i_H_j(det1, det2, N_int, h12) ! ~ ~ ~ H ~ ~ ~ do n = 1, n_toselect ii0 = numalpha_toselect(n) jj0 = numbeta_toselect (n) y = Uref(k,ii0) * Vref(l,jj0) * h12 ! Hdiag Hdiag_tmp(n) += Uref(i,ii0) * Vref(j,jj0) * y do m = 1, n_selected ii = numalpha_selected(m) jj = numbeta_selected (m) ! Hkl Hkl_tmp(m,n) += Uref(i,ii) * Vref(j,jj) * y enddo enddo ! ~ ~ ~ ! ! ! ~ ~ ~ enddo enddo ! !!! enddo enddo !$OMP END DO !$OMP CRITICAL do n = 1, n_toselect Hdiag(n) += Hdiag_tmp(n) do m = 1, n_selected Hkl(m,n) += Hkl_tmp(m,n) enddo enddo !$OMP END CRITICAL deallocate( Hdiag_tmp,Hkl_tmp ) !$OMP END PARALLEL end subroutine const_Hdiag_Hkl subroutine perform_newSVD(n_selected, n_toselect, numalpha_selected, numbeta_selected & , numalpha_toselect, numbeta_toselect, coeff_psi_selected, coeff_psi_toselect & , Uref, Vref, Dref ) USE OMP_LIB implicit none integer, intent(in) :: n_selected, n_toselect integer, intent(in) :: numalpha_selected(n_selected), numbeta_selected(n_selected) integer, intent(in) :: numalpha_toselect(n_toselect), numbeta_toselect(n_toselect) double precision, intent(in) :: coeff_psi_selected(n_selected), coeff_psi_toselect(n_toselect) double precision, intent(inout) :: Uref(n_det_alpha_unique,n_det_beta_unique) double precision, intent(inout) :: Vref(n_det_beta_unique ,n_det_beta_unique) double precision, intent(inout) :: Dref(n_det_beta_unique) integer :: mm, nn, i, j, ii0, ii, l, jj double precision :: err0, err_norm, err_tmp double precision, allocatable :: S_mat(:,:), SxVt(:,:) double precision, allocatable :: U_svd(:,:), V_svd(:,:) double precision, allocatable :: U_newsvd(:,:), V_newsvd(:,:), Vt_newsvd(:,:), D_newsvd(:), A_newsvd(:,:) mm = n_det_alpha_unique nn = n_det_beta_unique allocate( U_svd(n_det_alpha_unique,n_det_beta_unique) ) allocate( V_svd(n_det_beta_unique ,n_det_beta_unique) ) allocate( S_mat(n_det_beta_unique ,n_det_beta_unique) ) U_svd(:,:) = Uref(:,:) V_svd(:,:) = Vref(:,:) S_mat(:,:) = 0.d0 do l = 1, n_selected ii = numalpha_selected(l) jj = numbeta_selected (l) S_mat(ii,jj) = coeff_psi_selected(l) enddo do l = 1, n_toselect ii = numalpha_toselect(l) jj = numbeta_toselect (l) S_mat(ii,jj) = coeff_psi_toselect(l) enddo ! construct the new matrix: U_svd x S_mat x transpose(V_svd) ! (NaxNb) (NbxNb) transpose(NbxNb) ! first compute S_mat x transpose(V_svd) allocate( SxVt(nn,nn) ) call dgemm( 'N', 'T', nn, nn, nn, 1.d0 & , S_mat , size(S_mat,1) & , V_svd , size(V_svd,1) & , 0.d0, SxVt, size(SxVt ,1) ) ! then compute U_svd x SxVt allocate( A_newsvd(mm,nn) ) call dgemm( 'N', 'N', mm, nn, nn, 1.d0 & , U_svd , size(U_svd ,1) & , SxVt , size(SxVt ,1) & , 0.d0, A_newsvd, size(A_newsvd,1) ) deallocate( SxVt ) ! perform new SVD allocate( U_newsvd(mm,nn), Vt_newsvd(nn,nn), D_newsvd(nn) ) call svd_s( A_newsvd, size(A_newsvd,1), U_newsvd, size(U_newsvd,1), D_newsvd & , Vt_newsvd, size(Vt_newsvd,1), mm, nn) print *, ' ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ' print *, ' +++ new SVD is performed +++ ' allocate( V_newsvd(nn,nn) ) do l = 1, nn do j = 1, nn V_newsvd(j,l) = Vt_newsvd(l,j) enddo enddo ! check SVD error err0 = 0.d0 err_norm = 0.d0 do j = 1, nn do i = 1, mm err_tmp = 0.d0 do l = 1, mm err_tmp = err_tmp + D_newsvd(l) * U_newsvd(i,l) * V_newsvd(j,l) enddo err_tmp = A_newsvd(i,j) - err_tmp err0 += err_tmp * err_tmp err_norm += A_newsvd(i,j) * A_newsvd(i,j) enddo enddo print *, ' SVD err (%) = ', 100.d0 * dsqrt(err0/err_norm) print *, ' ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ' do l = 1, nn Dref(l) = D_newsvd(l) Uref(:,l) = U_newsvd(:,l) Vref(:,l) = V_newsvd(:,l) enddo deallocate( U_newsvd, V_newsvd, Vt_newsvd, D_newsvd, A_newsvd ) return end subroutine perform_newSVD