! ---
subroutine get_j1e_coef_fit_ao(dim_fit, coef_fit)
implicit none
integer , intent(in) :: dim_fit
double precision, intent(out) :: coef_fit(dim_fit)
integer :: i, ipoint
double precision :: g
double precision :: t0, t1
double precision, allocatable :: A(:,:), b(:), A_inv(:,:)
double precision, allocatable :: Pa(:,:), Pb(:,:), Pt(:,:)
double precision, allocatable :: u1e_tmp(:)
PROVIDE j1e_type
PROVIDE int2_u2e_ao
PROVIDE elec_alpha_num elec_beta_num elec_num
PROVIDE mo_coef
PROVIDE ao_overlap
call wall_time(t0)
print*, ' PROVIDING the representation of 1e-Jastrow in AOs ... '
! --- --- ---
! get u1e(r)
allocate(Pa(ao_num,ao_num), Pb(ao_num,ao_num), Pt(ao_num,ao_num))
call dgemm( 'N', 'T', ao_num, ao_num, elec_alpha_num, 1.d0 &
, mo_coef, size(mo_coef, 1), mo_coef, size(mo_coef, 1) &
, 0.d0, Pa, size(Pa, 1))
if(elec_alpha_num .eq. elec_beta_num) then
Pb = Pa
else
call dgemm( 'N', 'T', ao_num, ao_num, elec_beta_num, 1.d0 &
, mo_coef, size(mo_coef, 1), mo_coef, size(mo_coef, 1) &
, 0.d0, Pb, size(Pb, 1))
endif
Pt = Pa + Pb
allocate(u1e_tmp(n_points_final_grid))
g = -0.5d0 * (dble(elec_num) - 1.d0) / dble(elec_num)
call dgemv("T", ao_num*ao_num, n_points_final_grid, g, int2_u2e_ao, ao_num*ao_num, Pt, 1, 0.d0, u1e_tmp, 1)
FREE int2_u2e_ao
deallocate(Pa, Pb, Pt)
! --- --- ---
! get A & b
allocate(A(ao_num,ao_num), b(ao_num))
A(1:ao_num,1:ao_num) = ao_overlap(1:ao_num,1:ao_num)
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i, ipoint) &
!$OMP SHARED (n_points_final_grid, ao_num, &
!$OMP final_weight_at_r_vector, aos_in_r_array_transp, u1e_tmp, b)
!$OMP DO SCHEDULE (static)
do i = 1, ao_num
b(i) = 0.d0
do ipoint = 1, n_points_final_grid
b(i) = b(i) + final_weight_at_r_vector(ipoint) * aos_in_r_array_transp(ipoint,i) * u1e_tmp(ipoint)
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
deallocate(u1e_tmp)
! --- --- ---
! solve Ax = b
allocate(A_inv(ao_num,ao_num))
call get_inverse(A, ao_num, ao_num, A_inv, ao_num)
! coef_fit = A_inv x b
call dgemv("N", ao_num, ao_num, 1.d0, A_inv, ao_num, b, 1, 0.d0, coef_fit, 1)
integer :: j
double precision :: tmp, acc, nrm
acc = 0.d0
nrm = 0.d0
print *, ' check A_inv'
do i = 1, ao_num
tmp = 0.d0
do j = 1, ao_num
tmp += ao_overlap(i,j) * coef_fit(j)
enddo
tmp = tmp - b(i)
if(dabs(tmp) .gt. 1d-8) then
print*, ' problem found in fitting 1e-Jastrow'
print*, i, tmp
endif
acc += dabs(tmp)
nrm += dabs(b(i))
enddo
print *, ' Relative Error (%) =', 100.d0*acc/nrm
deallocate(A, A_inv, b)
call wall_time(t1)
print*, ' END after (min) ', (t1-t0)/60.d0
return
end
! ---
subroutine get_j1e_coef_fit_ao2(dim_fit, coef_fit)
implicit none
integer , intent(in) :: dim_fit
double precision, intent(out) :: coef_fit(dim_fit,dim_fit)
integer :: i, j, k, l, ipoint
integer :: ij, kl, mn
integer :: info, n_svd, LWORK
double precision :: g
double precision :: t0, t1, svd_t0, svd_t1
double precision :: cutoff_svd, D1_inv
double precision, allocatable :: diff(:)
double precision, allocatable :: A(:,:,:,:), b(:), A_tmp(:,:,:,:)
double precision, allocatable :: Pa(:,:), Pb(:,:), Pt(:,:)
double precision, allocatable :: u1e_tmp(:), tmp(:,:,:)
double precision, allocatable :: tmp1(:,:,:), tmp2(:,:,:)
double precision, allocatable :: U(:,:), D(:), Vt(:,:), work(:)
PROVIDE j1e_type
PROVIDE int2_u2e_ao
PROVIDE elec_alpha_num elec_beta_num elec_num
PROVIDE mo_coef
cutoff_svd = 1d-10
call wall_time(t0)
print*, ' PROVIDING the representation of 1e-Jastrow in AOs x AOs ... '
! --- --- ---
! get u1e(r)
allocate(Pa(ao_num,ao_num), Pb(ao_num,ao_num), Pt(ao_num,ao_num))
call dgemm( 'N', 'T', ao_num, ao_num, elec_alpha_num, 1.d0 &
, mo_coef, size(mo_coef, 1), mo_coef, size(mo_coef, 1) &
, 0.d0, Pa, size(Pa, 1))
if(elec_alpha_num .eq. elec_beta_num) then
Pb = Pa
else
call dgemm( 'N', 'T', ao_num, ao_num, elec_beta_num, 1.d0 &
, mo_coef, size(mo_coef, 1), mo_coef, size(mo_coef, 1) &
, 0.d0, Pb, size(Pb, 1))
endif
Pt = Pa + Pb
allocate(u1e_tmp(n_points_final_grid))
g = -0.5d0 * (dble(elec_num) - 1.d0) / dble(elec_num)
call dgemv("T", ao_num*ao_num, n_points_final_grid, g, int2_u2e_ao, ao_num*ao_num, Pt, 1, 0.d0, u1e_tmp, 1)
FREE int2_u2e_ao
deallocate(Pa, Pb, Pt)
! --- --- ---
! get A
allocate(tmp1(n_points_final_grid,ao_num,ao_num), tmp2(n_points_final_grid,ao_num,ao_num))
allocate(A(ao_num,ao_num,ao_num,ao_num))
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i, j, ipoint) &
!$OMP SHARED (n_points_final_grid, ao_num, final_weight_at_r_vector, aos_in_r_array_transp, tmp1, tmp2)
!$OMP DO COLLAPSE(2)
do j = 1, ao_num
do i = 1, ao_num
do ipoint = 1, n_points_final_grid
tmp1(ipoint,i,j) = final_weight_at_r_vector(ipoint) * aos_in_r_array_transp(ipoint,i) * aos_in_r_array_transp(ipoint,j)
tmp2(ipoint,i,j) = aos_in_r_array_transp(ipoint,i) * aos_in_r_array_transp(ipoint,j)
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
call dgemm( "T", "N", ao_num*ao_num, ao_num*ao_num, n_points_final_grid, 1.d0 &
, tmp1(1,1,1), n_points_final_grid, tmp2(1,1,1), n_points_final_grid &
, 0.d0, A(1,1,1,1), ao_num*ao_num)
allocate(A_tmp(ao_num,ao_num,ao_num,ao_num))
A_tmp = A
! --- --- ---
! get b
allocate(b(ao_num*ao_num))
do ipoint = 1, n_points_final_grid
u1e_tmp(ipoint) = u1e_tmp(ipoint)
enddo
call dgemv("T", n_points_final_grid, ao_num*ao_num, 1.d0, tmp1(1,1,1), n_points_final_grid, u1e_tmp(1), 1, 0.d0, b(1), 1)
deallocate(u1e_tmp)
deallocate(tmp1, tmp2)
! --- --- ---
! solve Ax = b
allocate(D(ao_num*ao_num), U(ao_num*ao_num,ao_num*ao_num), Vt(ao_num*ao_num,ao_num*ao_num))
call wall_time(svd_t0)
allocate(work(1))
lwork = -1
call dgesvd( 'S', 'A', ao_num*ao_num, ao_num*ao_num, A(1,1,1,1), ao_num*ao_num &
, D(1), U(1,1), ao_num*ao_num, Vt(1,1), ao_num*ao_num, work, lwork, info)
if(info /= 0) then
print *, info, ': SVD failed'
stop
endif
LWORK = max(5*ao_num*ao_num, int(WORK(1)))
deallocate(work)
allocate(work(lwork))
call dgesvd( 'S', 'A', ao_num*ao_num, ao_num*ao_num, A(1,1,1,1), ao_num*ao_num &
, D(1), U(1,1), ao_num*ao_num, Vt(1,1), ao_num*ao_num, work, lwork, info)
if(info /= 0) then
print *, info, ':: SVD failed'
stop 1
endif
deallocate(work)
call wall_time(svd_t1)
print*, ' SVD time (min) ', (svd_t1-svd_t0)/60.d0
if(D(1) .lt. 1d-14) then
print*, ' largest singular value is very small:', D(1)
n_svd = 1
else
n_svd = 0
D1_inv = 1.d0 / D(1)
do ij = 1, ao_num*ao_num
if(D(ij)*D1_inv > cutoff_svd) then
D(ij) = 1.d0 / D(ij)
n_svd = n_svd + 1
else
D(ij) = 0.d0
endif
enddo
endif
print*, ' n_svd = ', n_svd
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (ij, kl) &
!$OMP SHARED (ao_num, n_svd, D, Vt)
!$OMP DO
do kl = 1, ao_num*ao_num
do ij = 1, n_svd
Vt(ij,kl) = Vt(ij,kl) * D(ij)
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
! A = A_inv
call dgemm( "N", "N", ao_num*ao_num, ao_num*ao_num, n_svd, 1.d0 &
, U(1,1), ao_num*ao_num, Vt(1,1), ao_num*ao_num &
, 0.d0, A(1,1,1,1), ao_num*ao_num)
deallocate(D, U, Vt)
! ---
! coef_fit = A_inv x b
call dgemv("N", ao_num*ao_num, ao_num*ao_num, 1.d0, A(1,1,1,1), ao_num*ao_num, b(1), 1, 0.d0, coef_fit(1,1), 1)
! ---
allocate(diff(ao_num*ao_num))
call dgemv("N", ao_num*ao_num, ao_num*ao_num, 1.d0, A_tmp(1,1,1,1), ao_num*ao_num, coef_fit(1,1), 1, 0.d0, diff(1), 1)
print*, ' accu total on Ax = b (%) = ', 100.d0*sum(dabs(diff-b))/sum(dabs(b))
deallocate(diff)
deallocate(A_tmp)
! ---
deallocate(A, b)
call wall_time(t1)
print*, ' END after (min) ', (t1-t0)/60.d0
return
end
! ---
subroutine get_j1e_coef_fit_ao3(dim_fit, coef_fit)
implicit none
integer , intent(in) :: dim_fit
double precision, intent(out) :: coef_fit(dim_fit,3)
integer :: i, d, ipoint
double precision :: g
double precision :: t0, t1
double precision, allocatable :: A(:,:), b(:,:), A_inv(:,:)
double precision, allocatable :: Pa(:,:), Pb(:,:), Pt(:,:)
double precision, allocatable :: u1e_tmp(:,:)
PROVIDE j1e_type
PROVIDE int2_grad1_u2e_ao
PROVIDE elec_alpha_num elec_beta_num elec_num
PROVIDE mo_coef
PROVIDE ao_overlap
call wall_time(t0)
print*, ' PROVIDING the representation of 1e-Jastrow in AOs ... '
! --- --- ---
! get u1e(r)
allocate(Pa(ao_num,ao_num), Pb(ao_num,ao_num), Pt(ao_num,ao_num))
call dgemm( 'N', 'T', ao_num, ao_num, elec_alpha_num, 1.d0 &
, mo_coef, size(mo_coef, 1), mo_coef, size(mo_coef, 1) &
, 0.d0, Pa, size(Pa, 1))
if(elec_alpha_num .eq. elec_beta_num) then
Pb = Pa
else
call dgemm( 'N', 'T', ao_num, ao_num, elec_beta_num, 1.d0 &
, mo_coef, size(mo_coef, 1), mo_coef, size(mo_coef, 1) &
, 0.d0, Pb, size(Pb, 1))
endif
Pt = Pa + Pb
allocate(u1e_tmp(n_points_final_grid,3))
g = -0.5d0 * (dble(elec_num) - 1.d0) / dble(elec_num)
do d = 1, 3
call dgemv("T", ao_num*ao_num, n_points_final_grid, g, int2_grad1_u2e_ao(1,1,1,d), ao_num*ao_num, Pt, 1, 0.d0, u1e_tmp(1,d), 1)
enddo
deallocate(Pa, Pb, Pt)
! --- --- ---
! get A & b
allocate(A(ao_num,ao_num), b(ao_num,3))
A(1:ao_num,1:ao_num) = ao_overlap(1:ao_num,1:ao_num)
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i, ipoint) &
!$OMP SHARED (n_points_final_grid, ao_num, &
!$OMP final_weight_at_r_vector, aos_in_r_array_transp, u1e_tmp, b)
!$OMP DO SCHEDULE (static)
do i = 1, ao_num
b(i,1) = 0.d0
b(i,2) = 0.d0
b(i,3) = 0.d0
do ipoint = 1, n_points_final_grid
b(i,1) = b(i,1) + final_weight_at_r_vector(ipoint) * aos_in_r_array_transp(ipoint,i) * u1e_tmp(ipoint,1)
b(i,2) = b(i,2) + final_weight_at_r_vector(ipoint) * aos_in_r_array_transp(ipoint,i) * u1e_tmp(ipoint,2)
b(i,3) = b(i,3) + final_weight_at_r_vector(ipoint) * aos_in_r_array_transp(ipoint,i) * u1e_tmp(ipoint,3)
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
deallocate(u1e_tmp)
! --- --- ---
! solve Ax = b
allocate(A_inv(ao_num,ao_num))
call get_inverse(A, ao_num, ao_num, A_inv, ao_num)
! coef_fit = A_inv x b
do d = 1, 3
call dgemv("N", ao_num, ao_num, 1.d0, A_inv, ao_num, b(1,d), 1, 0.d0, coef_fit(1,d), 1)
enddo
integer :: j
double precision :: tmp, acc, nrm
acc = 0.d0
nrm = 0.d0
print *, ' check A_inv'
do d = 1, 3
do i = 1, ao_num
tmp = 0.d0
do j = 1, ao_num
tmp += ao_overlap(i,j) * coef_fit(j,d)
enddo
tmp = tmp - b(i,d)
if(dabs(tmp) .gt. 1d-8) then
print*, ' problem found in fitting 1e-Jastrow'
print*, d, i, tmp
endif
acc += dabs(tmp)
nrm += dabs(b(i,d))
enddo
enddo
print *, ' Relative Error (%) =', 100.d0*acc/nrm
deallocate(A, A_inv, b)
call wall_time(t1)
print*, ' END after (min) ', (t1-t0)/60.d0
return
end
! ---