program buildpsi_diagSVDit_v0 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, nn, na, nb double precision :: norm_psi, inv_sqrt_norm_psi double precision, allocatable :: Uref(:,:), Dref(:), Vtref(:,:), Aref(:,:), Vref(:,:) double precision :: E0_av, E0_ap, E0pt2 double precision :: err0, err_tmp, e_tmp, E0, overlop, E0_old, tol_energy double precision :: ctmp, htmp, Ept2 double precision :: E0_postsvd, overlop_postsvd double precision :: norm_coeff_psi, inv_sqrt_norm_coeff_psi double precision :: overlopU, overlopU_mat, overlopV, overlopV_mat, overlop_psi double precision, allocatable :: Hdiag(:), Hkl(:,:), H0(:,:) double precision, allocatable :: psi_postsvd(:), coeff_psi(:), coeff_psi_perturb(:) integer :: n_FSVD, n_selected, n_toselect, n_tmp, it_svd, it_svd_max integer :: n_selected2 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 ) ! --------------------------------------------------------------------------------------- nn = n_det_beta_unique ! --------------------------------------------------------------------------------------- ! numerote vectors ! Full rank n_FSVD = nn * nn print*, ' Full psi space rank = ', n_FSVD ! Truncated rank n_selected = 20 n_selected2 = n_selected * n_selected 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, nn do i = 1, n_det_alpha_unique err_tmp = 0.d0 do l = 1, n_selected err_tmp = err_tmp + Dref(l) * Uref(i,l) * Vref(j,l) 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 k = 0 n_toselect = nn*nn - 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, nn k = k + 1 numalpha_toselect(k) = j numbeta_toselect (k) = i enddo enddo do j = 1, n_selected do i = n_selected+1, nn k = k + 1 numalpha_toselect(k) = j numbeta_toselect (k) = i enddo enddo ! diagonal bloc do i = n_selected+1, nn do j = n_selected+1, nn k = k + 1 numalpha_toselect(k) = j numbeta_toselect (k) = i enddo enddo 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 norm_coeff_psi = 0.d0 do j = 1, n_selected norm_coeff_psi += Dref(j) * Dref(j) enddo inv_sqrt_norm_coeff_psi = 1.d0 / dsqrt(norm_coeff_psi) do j = 1, n_selected Dref(j) = Dref(j) * inv_sqrt_norm_coeff_psi enddo allocate( H0(n_selected2,n_selected2) ) print *, '' print *, '' print *, '' print *, '-- Compute H --' call const_psihpsi_postsvd_H0(n_selected, n_selected2, Uref, Vref, H0) ! avant SVD E0 = 0.d0 do i = 1, n_selected ii = (i-1)*n_selected + i do j = 1, n_selected jj = (j-1)*n_selected + j E0 += Dref(j) * H0(jj,ii) * Dref(i) enddo enddo E0_av = E0 + nuclear_repulsion print *,' E0 (avant SVD) =', E0_av allocate( psi_postsvd(n_selected2) ) print *, ' --- Diag post-SVD --- ' call diag_postsvd(n_selected, n_selected2, Dref, H0, E0_postsvd, overlop_postsvd, psi_postsvd) print*, ' postsvd energy = ', E0_postsvd deallocate( H0 ) ! post-SVD print *, ' --- SVD --- ' !Dref(:) = 0.d0 call perform_newpostSVD(n_selected, n_selected2, psi_postsvd, Uref, Vref, Dref) deallocate( psi_postsvd ) allocate( H0(n_selected2,n_selected2) ) print *, ' --- Compute H --- ' call const_psihpsi_postsvd_H0(n_selected, n_selected2, Uref, Vref, H0) E0 = 0.d0 norm_coeff_psi = 0.d0 do i = 1, n_selected ii = (i-1)*n_selected + i do j = 1, n_selected jj = (j-1)*n_selected + j E0 += Dref(j) * H0(jj,ii) * Dref(i) enddo norm_coeff_psi += Dref(i) * Dref(i) enddo E0_ap = E0 + nuclear_repulsion print *,' E0 (apres SVD) =', E0_ap !print *,' norm =', norm_coeff_psi deallocate(H0) print *, ' --- Perturbation --- ' allocate( Hdiag(n_toselect), Hkl(n_selected2,n_toselect) ) call const_Hdiag_Hkl(n_selected, n_selected2, n_toselect, Uref, Vref, numalpha_toselect, numbeta_toselect, Hdiag, Hkl) !do l = 1, n_toselect ! na = numalpha_toselect(l) ! nb = numbeta_toselect (l) ! print *, na, nb, Hdiag(l) !enddo ! evaluate the coefficients for all the vectors allocate( coeff_psi_perturb(n_toselect) ) ept2 = 0.d0 do ii = 1, n_toselect !na = numalpha_toselect(ii) !nb = numbeta_toselect (ii) ctmp = 0.d0 do i = 1, n_selected l = (i-1)*n_selected + i ctmp += Dref(i) * Hkl(l,ii) enddo coeff_psi_perturb(ii) = ctmp / ( E0_ap - (Hdiag(ii)+nuclear_repulsion) ) ept2 += ctmp*ctmp / ( E0_ap - (Hdiag(ii)+nuclear_repulsion) ) enddo E0pt2 = E0_ap + ept2 print *, ' perturb energy = ', E0pt2, ept2 tol_energy = 100.d0 * dabs(E0pt2-E0_old) / dabs(E0pt2) E0_old = E0pt2 deallocate( Hdiag, Hkl) print *, ' --- SVD --- ' call perform_newSVD(n_selected, n_selected2, n_toselect, numalpha_toselect, numbeta_toselect, coeff_psi_perturb, Uref, Vref, Dref) deallocate( coeff_psi_perturb ) write(11,'(i5,4x,4(f22.15,2x))') it_svd, E0_av, E0_postsvd, E0_ap, 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 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 '(//, 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 print *,' ___________________________________________________________________' end subroutine const_psihpsi_postsvd_H0(n_selected, n_selected2, Uref, Vref, H0) USE OMP_LIB implicit none integer, intent(in) :: n_selected, n_selected2 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_selected2,n_selected2) integer(bit_kind) :: det1(N_int,2), det2(N_int,2) integer :: i, j, k, l, degree integer :: ii0, jj0, ii, jj, n, m, np, mp integer :: nn0, mm0, nn, mm, ind_gs double precision :: h12, x double precision, allocatable :: H0_tmp(:,:) H0(:,:) = 0.d0 !$OMP PARALLEL DEFAULT(NONE) & !$OMP PRIVATE(n,np,nn0,nn,ii0,jj0,x,m,mp,mm0,mm,ii,jj,i,j,k,l,h12,det1,det2,H0_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_selected2,Uref,Vref,H0 ) allocate( H0_tmp(n_selected2,n_selected2) ) H0_tmp(:,:) = 0.d0 !$OMP DO COLLAPSE(2) SCHEDULE(DYNAMIC,8) do i = 1, n_det_alpha_unique do k = 1, n_det_alpha_unique det1(:,1) = psi_det_alpha_unique(:,i) det2(:,1) = psi_det_alpha_unique(:,k) call get_excitation_degree_spin(det1(1,1),det2(1,1),degree,N_int) if (degree .gt. 2) then cycle endif do j = 1, n_det_beta_unique det1(:,2) = psi_det_beta_unique(:,j) do l = 1, n_det_beta_unique det2(:,2) = psi_det_beta_unique(:,l) call get_excitation_degree(det1,det2,degree,N_int) if (degree .gt. 2) then cycle endif ! !!! call i_H_j(det1, det2, N_int, h12) ! !!! ! ~~~ H0 ~~~ do n = 1, n_selected nn0 = (n-1)*n_selected do np = 1, n_selected nn = nn0 + np x = Uref(k,n) * Vref(l,np) * h12 do m = 1, n_selected mm0 = (m-1)*n_selected do mp = 1, n_selected mm = mm0 + mp H0_tmp(mm,nn) += Uref(i,m) * Vref(j,mp) * x enddo enddo enddo enddo ! ~~~ ~~~~~~ ~~~ enddo enddo enddo enddo !$OMP END DO !$OMP CRITICAL do n = 1, n_selected2 do m = 1, n_selected2 H0(m,n) += H0_tmp(m,n) enddo enddo !$OMP END CRITICAL deallocate( H0_tmp ) !$OMP END PARALLEL return end subroutine const_psihpsi_postsvd_H0 subroutine diag_postsvd(n_selected, n_selected2, Dref, H0, E0, overlop, psi_postsvd ) USE OMP_LIB implicit none integer, intent(in) :: n_selected, n_selected2 double precision, intent(in) :: H0(n_selected2,n_selected2) double precision, intent(in) :: Dref(n_det_beta_unique) double precision, intent(out) :: E0, overlop, psi_postsvd(n_selected2) integer(bit_kind) :: det1(N_int,2), det2(N_int,2) integer :: i, j, k, l, degree integer :: ii0, jj0, ii, jj, n, m, np, mp integer :: nn0, mm0, nn, mm, ind_gs double precision :: h12, x double precision, allocatable :: eigvec0(:,:), eigval0(:), check_ov(:) ! diagonalize H0 allocate( eigvec0(n_selected2,n_selected2), eigval0(n_selected2) ) call lapack_diag(eigval0, eigvec0, H0, n_selected2, n_selected2) ! get the postsvd ground state allocate( check_ov(n_selected2) ) do l = 1, n_selected2 overlop = 0.d0 do i = 1, n_selected ii = n_selected*(i-1) + i overlop = overlop + eigvec0(ii,l) * Dref(i) enddo check_ov(l) = dabs(overlop) enddo ind_gs = MAXLOC( check_ov, DIM=1 ) !ind_gs = 1 overlop = check_ov(ind_gs) E0 = eigval0(ind_gs)+nuclear_repulsion psi_postsvd = eigvec0(:,ind_gs) deallocate( check_ov, eigvec0, eigval0 ) return end subroutine diag_postsvd subroutine const_Hdiag_Hkl(n_selected, n_selected2, n_toselect, Uref, Vref, numalpha_toselect, numbeta_toselect, Hdiag, Hkl) implicit none integer, intent(in) :: n_selected, n_selected2, n_toselect 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_selected2,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) & !$OMP PRIVATE(n,ii0,jj0,y,m,mp,ii,jj,i,j,k,l,h12,det1,det2,Hdiag_tmp,Hkl_tmp,degree) & !$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 Hkl,Hdiag,n_selected2 ) allocate( Hdiag_tmp(n_toselect), Hkl_tmp(n_selected2,n_toselect) ) Hdiag_tmp(:) = 0.d0 Hkl_tmp(:,:) = 0.d0 !$OMP DO COLLAPSE(2) SCHEDULE(DYNAMIC,8) do i = 1, n_det_alpha_unique do k = 1, n_det_alpha_unique det1(:,1) = psi_det_alpha_unique(:,i) det2(:,1) = psi_det_alpha_unique(:,k) ! !!! ! ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ call get_excitation_degree_spin(det1(1,1),det2(1,1),degree,N_int) if (degree .gt. 2) then cycle endif ! ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ! !!! do j = 1, n_det_beta_unique det1(:,2) = psi_det_beta_unique(:,j) do l = 1, n_det_beta_unique det2(:,2) = psi_det_beta_unique(:,l) ! !!! ! ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ call get_excitation_degree(det1,det2,degree,N_int) if (degree .gt. 2) then cycle endif ! ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ! !!! call i_H_j(det1, det2, N_int, h12) ! ~ ~ ~ H ~ ~ ~ do n = 1, n_toselect ii0 = numalpha_toselect(n) jj0 = numbeta_toselect (n) y = Uref(k,ii0) * Vref(l,jj0) * h12 ! Hdiag Hdiag_tmp(n) += y * Uref(i,ii0) * Vref(j,jj0) do m = 1, n_selected ii = (m-1)*n_selected do mp = 1, n_selected jj = ii + mp ! Hkl Hkl_tmp(jj,n) += Uref(i,m) * Vref(j,mp) * y enddo enddo enddo ! ~ ~ ~ ! ! ! ~ ~ ~ enddo enddo ! !!! enddo enddo !$OMP END DO !$OMP CRITICAL do n = 1, n_toselect Hdiag(n) += Hdiag_tmp(n) do m = 1, n_selected2 Hkl(m,n) += Hkl_tmp(m,n) enddo enddo !$OMP END CRITICAL deallocate( Hdiag_tmp,Hkl_tmp ) !$OMP END PARALLEL end subroutine const_Hdiag_Hkl subroutine perform_newSVD(n_selected, n_selected2, n_toselect, numalpha_toselect, numbeta_toselect, coeff_psi_perturb, Uref, Vref, Dref) USE OMP_LIB integer, intent(in) :: n_selected, n_toselect, n_selected2 integer, intent(in) :: numalpha_toselect(n_toselect), numbeta_toselect(n_toselect) double precision, intent(in) :: coeff_psi_perturb(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, na, nb double precision :: err0, err_norm, err_tmp, norm_tmp double precision :: overlopU_mat, overlopV_mat, overlopU, overlopV 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(mm,nn) , V_svd(nn,nn) , S_mat(nn,nn) ) U_svd(:,:) = Uref(:,:) V_svd(:,:) = Vref(:,:) S_mat(:,:) = 0.d0 norm_tmp = 0.d0 do j = 1, n_det_beta_unique S_mat(j,j) = Dref(j) norm_tmp += S_mat(j,j)*S_mat(j,j) enddo do l = 1, n_toselect na = numalpha_toselect(l) nb = numbeta_toselect (l) S_mat(na,nb) = coeff_psi_perturb(l) norm_tmp += S_mat(na,nb)*S_mat(na,nb) enddo print*, ' norm de S_mat =', norm_tmp !norm_tmp = 1.d0/dsqrt(norm_tmp) !do i = 1, nn ! do j = 1, nn ! S_mat(j,i) = S_mat(j,i) * norm_tmp ! enddo !enddo ! 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 *, ' +++ new perturbative 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, nn 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 !print *, Dref(:) overlopU_mat = 0.d0 overlopV_mat = 0.d0 do i = 1, nn do j = 1, nn overlopU = 0.d0 do ii = 1, mm overlopU += Uref(ii,j) * Uref(ii,i) enddo overlopU_mat += overlopU overlopV = 0.d0 do ii = 1, nn overlopV += Vref(ii,j) * Vref(ii,i) enddo overlopV_mat += overlopV enddo enddo print *, 'overlop U =', overlopU_mat print *, 'overlop V =', overlopV_mat deallocate( U_newsvd, V_newsvd, Vt_newsvd, D_newsvd, A_newsvd ) return end subroutine perform_newSVD subroutine perform_newpostSVD(n_selected, n_selected2, psi_postsvd, Uref, Vref, Dref) USE OMP_LIB integer, intent(in) :: n_selected, n_selected2 double precision, intent(in) :: psi_postsvd(n_selected2) 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, na, nb double precision :: err0, err_norm, err_tmp, norm_tmp double precision :: overlopU_mat, overlopV_mat, overlopU, overlopV 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(mm,n_selected) , V_svd(nn,n_selected) , S_mat(n_selected,n_selected) ) U_svd(:,:) = Uref(:,1:n_selected) V_svd(:,:) = Vref(:,1:n_selected) S_mat(:,:) = 0.d0 do i = 1, n_selected ii = (i-1)*n_selected do j = 1, n_selected jj = ii + j S_mat(i,j) = psi_postsvd(jj) enddo enddo ! first compute S_mat x transpose(V_svd) allocate( SxVt(n_selected,nn) ) call dgemm( 'N', 'T', n_selected, nn, n_selected, 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, n_selected, 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 *, ' +++ 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, n_selected 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, n_selected Dref(l) = D_newsvd(l) Uref(:,l) = U_newsvd(:,l) Vref(:,l) = V_newsvd(:,l) enddo ! print *, Dref(:) overlopU_mat = 0.d0 overlopV_mat = 0.d0 do i = 1, nn do j = 1, nn overlopU = 0.d0 do ii = 1, mm overlopU += Uref(ii,j) * Uref(ii,i) enddo overlopU_mat += overlopU overlopV = 0.d0 do ii = 1, nn overlopV += Vref(ii,j) * Vref(ii,i) enddo overlopV_mat += overlopV enddo enddo print *, 'overlop U =', overlopU_mat print *, 'overlop V =', overlopV_mat deallocate( U_newsvd, V_newsvd, Vt_newsvd, D_newsvd, A_newsvd ) return end subroutine perform_newpostSVD