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qp_plugins_scemama/devel/svdwf/buildpsi_diagSVDit_v0.irp.f

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2021-07-28 17:19:18 +02:00
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
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