mirror of
https://github.com/QuantumPackage/qp2.git
synced 2024-12-23 12:03:30 +01:00
439 lines
12 KiB
Fortran
439 lines
12 KiB
Fortran
|
|
! ---
|
|
|
|
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
|
|
|
|
! ---
|
|
|