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working on aos debug

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This commit is contained in:
Abdallah Ammar 2024-05-07 01:56:14 +02:00
parent bd8d45b99b
commit 2a8b9e544b
2 changed files with 285 additions and 239 deletions
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16
plugins/local/non_h_ints_mu/deb_aos.irp.f
View File

@ -31,12 +31,14 @@ subroutine print_aos()
integer :: i, ipoint integer :: i, ipoint
double precision :: r(3) double precision :: r(3)
double precision :: ao_val, ao_der(3), ao_lap double precision :: ao_val, ao_der(3), ao_lap
double precision :: mo_val, mo_der(3), mo_lap
PROVIDE final_grid_points aos_in_r_array aos_grad_in_r_array aos_lapl_in_r_array PROVIDE final_grid_points aos_in_r_array aos_grad_in_r_array aos_lapl_in_r_array
write(1000, *) n_points_final_grid
do ipoint = 1, n_points_final_grid do ipoint = 1, n_points_final_grid
r(:) = final_grid_points(:,ipoint) r(:) = final_grid_points(:,ipoint)
print*, r write(1000, '(3(f15.7, 3X))') r
enddo enddo
do ipoint = 1, n_points_final_grid do ipoint = 1, n_points_final_grid
@ -45,7 +47,17 @@ subroutine print_aos()
ao_val = aos_in_r_array (i,ipoint) ao_val = aos_in_r_array (i,ipoint)
ao_der(:) = aos_grad_in_r_array(i,ipoint,:) ao_der(:) = aos_grad_in_r_array(i,ipoint,:)
ao_lap = aos_lapl_in_r_array(1,i,ipoint) + aos_lapl_in_r_array(2,i,ipoint) + aos_lapl_in_r_array(3,i,ipoint) ao_lap = aos_lapl_in_r_array(1,i,ipoint) + aos_lapl_in_r_array(2,i,ipoint) + aos_lapl_in_r_array(3,i,ipoint)
write(*, '(5(f15.7, 3X))') ao_val, ao_der, ao_lap write(1010, '(5(f15.7, 3X))') ao_val, ao_der, ao_lap
enddo
enddo
do ipoint = 1, n_points_final_grid
r(:) = final_grid_points(:,ipoint)
do i = 1, mo_num
mo_val = mos_in_r_array (i,ipoint)
mo_der(:) = mos_grad_in_r_array(i,ipoint,:)
mo_lap = mos_lapl_in_r_array(i,ipoint,1) + mos_lapl_in_r_array(i,ipoint,2) + mos_lapl_in_r_array(i,ipoint,3)
write(2010, '(5(f15.7, 3X))') mo_val, mo_der, mo_lap
enddo enddo
enddo enddo

282
src/ao_basis/aos_in_r.irp.f
View File

@ -1,29 +1,35 @@
double precision function ao_value(i,r)
implicit none
BEGIN_DOC
! Returns the value of the i-th ao at point $\textbf{r}$
END_DOC
double precision, intent(in) :: r(3)
integer, intent(in) :: i
integer :: m,num_ao ! ---
double precision function ao_value(i, r)
BEGIN_DOC
! Returns the value of the i-th ao at point $\textbf{r}$
END_DOC
implicit none
integer, intent(in) :: i
double precision, intent(in) :: r(3)
integer :: m, num_ao
integer :: power_ao(3)
double precision :: center_ao(3) double precision :: center_ao(3)
double precision :: beta double precision :: beta
integer :: power_ao(3) double precision :: accu, dx, dy, dz, r2
double precision :: accu,dx,dy,dz,r2
num_ao = ao_nucl(i) num_ao = ao_nucl(i)
power_ao(1:3)= ao_power(i,1:3) power_ao(1:3) = ao_power(i,1:3)
center_ao(1:3) = nucl_coord(num_ao,1:3) center_ao(1:3) = nucl_coord(num_ao,1:3)
dx = (r(1) - center_ao(1)) dx = r(1) - center_ao(1)
dy = (r(2) - center_ao(2)) dy = r(2) - center_ao(2)
dz = (r(3) - center_ao(3)) dz = r(3) - center_ao(3)
r2 = dx*dx + dy*dy + dz*dz r2 = dx*dx + dy*dy + dz*dz
dx = dx**power_ao(1) dx = dx**power_ao(1)
dy = dy**power_ao(2) dy = dy**power_ao(2)
dz = dz**power_ao(3) dz = dz**power_ao(3)
accu = 0.d0 accu = 0.d0
do m=1,ao_prim_num(i) do m = 1, ao_prim_num(i)
beta = ao_expo_ordered_transp(m,i) beta = ao_expo_ordered_transp(m,i)
accu += ao_coef_normalized_ordered_transp(m,i) * dexp(-beta*r2) accu += ao_coef_normalized_ordered_transp(m,i) * dexp(-beta*r2)
enddo enddo
@ -32,33 +38,36 @@ double precision function ao_value(i,r)
end end
double precision function primitive_value(i,j,r) double precision function primitive_value(i, j, r)
implicit none
BEGIN_DOC
! Returns the value of the j-th primitive of the i-th |AO| at point $\textbf{r}
! **without the coefficient**
END_DOC
double precision, intent(in) :: r(3)
integer, intent(in) :: i,j
integer :: m,num_ao BEGIN_DOC
! Returns the value of the j-th primitive of the i-th |AO| at point $\textbf{r}
! **without the coefficient**
END_DOC
implicit none
integer, intent(in) :: i, j
double precision, intent(in) :: r(3)
integer :: m, num_ao
integer :: power_ao(3)
double precision :: center_ao(3) double precision :: center_ao(3)
double precision :: beta double precision :: beta
integer :: power_ao(3) double precision :: accu, dx, dy, dz, r2
double precision :: accu,dx,dy,dz,r2
num_ao = ao_nucl(i) num_ao = ao_nucl(i)
power_ao(1:3)= ao_power(i,1:3) power_ao(1:3)= ao_power(i,1:3)
center_ao(1:3) = nucl_coord(num_ao,1:3) center_ao(1:3) = nucl_coord(num_ao,1:3)
dx = (r(1) - center_ao(1)) dx = r(1) - center_ao(1)
dy = (r(2) - center_ao(2)) dy = r(2) - center_ao(2)
dz = (r(3) - center_ao(3)) dz = r(3) - center_ao(3)
r2 = dx*dx + dy*dy + dz*dz r2 = dx*dx + dy*dy + dz*dz
dx = dx**power_ao(1) dx = dx**power_ao(1)
dy = dy**power_ao(2) dy = dy**power_ao(2)
dz = dz**power_ao(3) dz = dz**power_ao(3)
accu = 0.d0 accu = 0.d0
m=j m = j
beta = ao_expo_ordered_transp(m,i) beta = ao_expo_ordered_transp(m,i)
accu += dexp(-beta*r2) accu += dexp(-beta*r2)
primitive_value = accu * dx * dy * dz primitive_value = accu * dx * dy * dz
@ -104,9 +113,9 @@ subroutine give_all_aos_at_r(r, tmp_array)
dz2 = dz**p_ao(3) dz2 = dz**p_ao(3)
tmp_array(k) = 0.d0 tmp_array(k) = 0.d0
do l = 1,ao_prim_num(k) do l = 1, ao_prim_num(k)
beta = ao_expo_ordered_transp_per_nucl(l,j,i) beta = ao_expo_ordered_transp_per_nucl(l,j,i)
if(dabs(beta*r2).gt.40.d0) cycle if(beta*r2.gt.50.d0) cycle
tmp_array(k) += ao_coef_normalized_ordered_transp_per_nucl(l,j,i) * dexp(-beta*r2) tmp_array(k) += ao_coef_normalized_ordered_transp_per_nucl(l,j,i) * dexp(-beta*r2)
enddo enddo
@ -120,116 +129,138 @@ end
! --- ! ---
subroutine give_all_aos_and_grad_at_r(r,aos_array,aos_grad_array) subroutine give_all_aos_and_grad_at_r(r, aos_array, aos_grad_array)
implicit none
BEGIN_DOC BEGIN_DOC
! input : r(1) ==> r(1) = x, r(2) = y, r(3) = z !
! ! input : r(1) ==> r(1) = x, r(2) = y, r(3) = z
! output : !
! ! output :
! * aos_array(i) = ao(i) evaluated at ro !
! * aos_grad_array(1,i) = gradient X of the ao(i) evaluated at $\textbf{r}$ ! * aos_array(i) = ao(i) evaluated at ro
! ! * aos_grad_array(1,i) = gradient X of the ao(i) evaluated at $\textbf{r}$
!
END_DOC END_DOC
implicit none
double precision, intent(in) :: r(3) double precision, intent(in) :: r(3)
double precision, intent(out) :: aos_array(ao_num) double precision, intent(out) :: aos_array(ao_num)
double precision, intent(out) :: aos_grad_array(3,ao_num) double precision, intent(out) :: aos_grad_array(3,ao_num)
integer :: power_ao(3) integer :: power_ao(3)
integer :: i,j,k,l,m integer :: i, j, k, l, m
double precision :: dx,dy,dz,r2 double precision :: dx, dy, dz, r2
double precision :: dx2,dy2,dz2 double precision :: dx1, dy1, dz1
double precision :: dx1,dy1,dz1 double precision :: dx2, dy2, dz2
double precision :: center_ao(3) double precision :: center_ao(3)
double precision :: beta,accu_1,accu_2,contrib double precision :: beta, accu_1, accu_2, contrib
do i = 1, nucl_num do i = 1, nucl_num
center_ao(1:3) = nucl_coord(i,1:3) center_ao(1:3) = nucl_coord(i,1:3)
dx = (r(1) - center_ao(1))
dy = (r(2) - center_ao(2)) dx = r(1) - center_ao(1)
dz = (r(3) - center_ao(3)) dy = r(2) - center_ao(2)
dz = r(3) - center_ao(3)
r2 = dx*dx + dy*dy + dz*dz r2 = dx*dx + dy*dy + dz*dz
do j = 1,Nucl_N_Aos(i)
do j = 1, Nucl_N_Aos(i)
k = Nucl_Aos_transposed(j,i) ! index of the ao in the ordered format k = Nucl_Aos_transposed(j,i) ! index of the ao in the ordered format
aos_array(k) = 0.d0 aos_array(k) = 0.d0
aos_grad_array(1,k) = 0.d0 aos_grad_array(1,k) = 0.d0
aos_grad_array(2,k) = 0.d0 aos_grad_array(2,k) = 0.d0
aos_grad_array(3,k) = 0.d0 aos_grad_array(3,k) = 0.d0
power_ao(1:3)= ao_power_ordered_transp_per_nucl(1:3,j,i)
power_ao(1:3) = ao_power_ordered_transp_per_nucl(1:3,j,i)
dx2 = dx**power_ao(1) dx2 = dx**power_ao(1)
dy2 = dy**power_ao(2) dy2 = dy**power_ao(2)
dz2 = dz**power_ao(3) dz2 = dz**power_ao(3)
if(power_ao(1) .ne. 0)then
dx1 = dble(power_ao(1)) * dx**(power_ao(1)-1)
else
dx1 = 0.d0 dx1 = 0.d0
if(power_ao(1) .ne. 0) then
dx1 = dble(power_ao(1)) * dx**(power_ao(1)-1)
endif endif
if(power_ao(2) .ne. 0)then
dy1 = dble(power_ao(2)) * dy**(power_ao(2)-1)
else
dy1 = 0.d0 dy1 = 0.d0
if(power_ao(2) .ne. 0) then
dy1 = dble(power_ao(2)) * dy**(power_ao(2)-1)
endif endif
if(power_ao(3) .ne. 0)then
dz1 = dble(power_ao(3)) * dz**(power_ao(3)-1)
else
dz1 = 0.d0 dz1 = 0.d0
if(power_ao(3) .ne. 0) then
dz1 = dble(power_ao(3)) * dz**(power_ao(3)-1)
endif endif
accu_1 = 0.d0 accu_1 = 0.d0
accu_2 = 0.d0 accu_2 = 0.d0
do l = 1,ao_prim_num(k) do l = 1, ao_prim_num(k)
beta = ao_expo_ordered_transp_per_nucl(l,j,i) beta = ao_expo_ordered_transp_per_nucl(l,j,i)
contrib = 0.d0 if(beta*r2.gt.50.d0) cycle
if(beta*r2.gt.50.d0)cycle
contrib = ao_coef_normalized_ordered_transp_per_nucl(l,j,i) * dexp(-beta*r2) contrib = ao_coef_normalized_ordered_transp_per_nucl(l,j,i) * dexp(-beta*r2)
accu_1 += contrib accu_1 += contrib
accu_2 += contrib * beta accu_2 += contrib * beta
enddo enddo
aos_array(k) = accu_1 * dx2 * dy2 * dz2 aos_array(k) = accu_1 * dx2 * dy2 * dz2
aos_grad_array(1,k) = accu_1 * dx1 * dy2 * dz2- 2.d0 * dx2 * dx * dy2 * dz2 * accu_2 aos_grad_array(1,k) = accu_1 * dx1 * dy2 * dz2 - 2.d0 * dx2 * dx * dy2 * dz2 * accu_2
aos_grad_array(2,k) = accu_1 * dx2 * dy1 * dz2- 2.d0 * dx2 * dy2 * dy * dz2 * accu_2 aos_grad_array(2,k) = accu_1 * dx2 * dy1 * dz2 - 2.d0 * dx2 * dy2 * dy * dz2 * accu_2
aos_grad_array(3,k) = accu_1 * dx2 * dy2 * dz1- 2.d0 * dx2 * dy2 * dz2 * dz * accu_2 aos_grad_array(3,k) = accu_1 * dx2 * dy2 * dz1 - 2.d0 * dx2 * dy2 * dz2 * dz * accu_2
enddo enddo
enddo enddo
end end
! ---
subroutine give_all_aos_and_grad_and_lapl_at_r(r, aos_array, aos_grad_array, aos_lapl_array)
subroutine give_all_aos_and_grad_and_lapl_at_r(r,aos_array,aos_grad_array,aos_lapl_array)
implicit none
BEGIN_DOC BEGIN_DOC
! input : r(1) ==> r(1) = x, r(2) = y, r(3) = z !
! ! input : r(1) ==> r(1) = x, r(2) = y, r(3) = z
! output : !
! ! output :
! * aos_array(i) = ao(i) evaluated at $\textbf{r}$ !
! * aos_grad_array(1,i) = $\nabla_x$ of the ao(i) evaluated at $\textbf{r}$ ! * aos_array(i) = ao(i) evaluated at $\textbf{r}$
! * aos_grad_array(1,i) = $\nabla_x$ of the ao(i) evaluated at $\textbf{r}$
!
END_DOC END_DOC
implicit none
double precision, intent(in) :: r(3) double precision, intent(in) :: r(3)
double precision, intent(out) :: aos_array(ao_num) double precision, intent(out) :: aos_array(ao_num)
double precision, intent(out) :: aos_grad_array(3,ao_num) double precision, intent(out) :: aos_grad_array(3,ao_num)
double precision, intent(out) :: aos_lapl_array(3,ao_num) double precision, intent(out) :: aos_lapl_array(3,ao_num)
integer :: power_ao(3) integer :: power_ao(3)
integer :: i,j,k,l,m integer :: i, j, k, l, m
double precision :: dx,dy,dz,r2 double precision :: dx, dy, dz, r2
double precision :: dx2,dy2,dz2 double precision :: dx1, dy1, dz1
double precision :: dx1,dy1,dz1 double precision :: dx2, dy2, dz2
double precision :: dx3,dy3,dz3 double precision :: dx3, dy3, dz3
double precision :: dx4,dy4,dz4 double precision :: dx4, dy4, dz4
double precision :: dx5,dy5,dz5 double precision :: dx5, dy5, dz5
double precision :: center_ao(3) double precision :: center_ao(3)
double precision :: beta,accu_1,accu_2,accu_3,contrib double precision :: beta, accu_1, accu_2, accu_3, contrib
do i = 1, nucl_num do i = 1, nucl_num
center_ao(1:3) = nucl_coord(i,1:3) center_ao(1:3) = nucl_coord(i,1:3)
dx = (r(1) - center_ao(1))
dy = (r(2) - center_ao(2)) dx = r(1) - center_ao(1)
dz = (r(3) - center_ao(3)) dy = r(2) - center_ao(2)
dz = r(3) - center_ao(3)
r2 = dx*dx + dy*dy + dz*dz r2 = dx*dx + dy*dy + dz*dz
do j = 1,Nucl_N_Aos(i)
do j = 1, Nucl_N_Aos(i)
k = Nucl_Aos_transposed(j,i) ! index of the ao in the ordered format k = Nucl_Aos_transposed(j,i) ! index of the ao in the ordered format
aos_array(k) = 0.d0 aos_array(k) = 0.d0
aos_grad_array(1,k) = 0.d0 aos_grad_array(1,k) = 0.d0
aos_grad_array(2,k) = 0.d0 aos_grad_array(2,k) = 0.d0
aos_grad_array(3,k) = 0.d0 aos_grad_array(3,k) = 0.d0
aos_lapl_array(1,k) = 0.d0 aos_lapl_array(1,k) = 0.d0
aos_lapl_array(2,k) = 0.d0 aos_lapl_array(2,k) = 0.d0
aos_lapl_array(3,k) = 0.d0 aos_lapl_array(3,k) = 0.d0
@ -238,18 +269,20 @@ subroutine give_all_aos_and_grad_and_lapl_at_r(r,aos_array,aos_grad_array,aos_la
dx2 = dx**power_ao(1) dx2 = dx**power_ao(1)
dy2 = dy**power_ao(2) dy2 = dy**power_ao(2)
dz2 = dz**power_ao(3) dz2 = dz**power_ao(3)
if(power_ao(1) .ne. 0)then
dx1 = dble(power_ao(1)) * dx**(power_ao(1)-1) ! ---
else
dx1 = 0.d0 dx1 = 0.d0
if(power_ao(1) .ne. 0) then
dx1 = dble(power_ao(1)) * dx**(power_ao(1)-1)
endif endif
! For the Laplacian
if(power_ao(1) .ge. 2)then
dx3 = dble(power_ao(1)) * dble((power_ao(1)-1)) * dx**(power_ao(1)-2)
else
dx3 = 0.d0 dx3 = 0.d0
if(power_ao(1) .ge. 2) then
dx3 = dble(power_ao(1)) * dble((power_ao(1)-1)) * dx**(power_ao(1)-2)
endif endif
if(power_ao(1) .ge. 1)then
if(power_ao(1) .ge. 1) then
dx4 = dble((2 * power_ao(1) + 1)) * dx**(power_ao(1)) dx4 = dble((2 * power_ao(1) + 1)) * dx**(power_ao(1))
else else
dx4 = dble((power_ao(1) + 1)) * dx**(power_ao(1)) dx4 = dble((power_ao(1) + 1)) * dx**(power_ao(1))
@ -257,19 +290,19 @@ subroutine give_all_aos_and_grad_and_lapl_at_r(r,aos_array,aos_grad_array,aos_la
dx5 = dx**(power_ao(1)+2) dx5 = dx**(power_ao(1)+2)
if(power_ao(2) .ne. 0)then ! ---
dy1 = dble(power_ao(2)) * dy**(power_ao(2)-1)
else
dy1 = 0.d0 dy1 = 0.d0
endif if(power_ao(2) .ne. 0) then
! For the Laplacian dy1 = dble(power_ao(2)) * dy**(power_ao(2)-1)
if(power_ao(2) .ge. 2)then
dy3 = dble(power_ao(2)) * dble((power_ao(2)-1)) * dy**(power_ao(2)-2)
else
dy3 = 0.d0
endif endif
if(power_ao(2) .ge. 1)then dy3 = 0.d0
if(power_ao(2) .ge. 2) then
dy3 = dble(power_ao(2)) * dble((power_ao(2)-1)) * dy**(power_ao(2)-2)
endif
if(power_ao(2) .ge. 1) then
dy4 = dble((2 * power_ao(2) + 1)) * dy**(power_ao(2)) dy4 = dble((2 * power_ao(2) + 1)) * dy**(power_ao(2))
else else
dy4 = dble((power_ao(2) + 1)) * dy**(power_ao(2)) dy4 = dble((power_ao(2) + 1)) * dy**(power_ao(2))
@ -277,20 +310,19 @@ subroutine give_all_aos_and_grad_and_lapl_at_r(r,aos_array,aos_grad_array,aos_la
dy5 = dy**(power_ao(2)+2) dy5 = dy**(power_ao(2)+2)
! ---
if(power_ao(3) .ne. 0)then
dz1 = dble(power_ao(3)) * dz**(power_ao(3)-1)
else
dz1 = 0.d0 dz1 = 0.d0
endif if(power_ao(3) .ne. 0) then
! For the Laplacian dz1 = dble(power_ao(3)) * dz**(power_ao(3)-1)
if(power_ao(3) .ge. 2)then
dz3 = dble(power_ao(3)) * dble((power_ao(3)-1)) * dz**(power_ao(3)-2)
else
dz3 = 0.d0
endif endif
if(power_ao(3) .ge. 1)then dz3 = 0.d0
if(power_ao(3) .ge. 2) then
dz3 = dble(power_ao(3)) * dble((power_ao(3)-1)) * dz**(power_ao(3)-2)
endif
if(power_ao(3) .ge. 1) then
dz4 = dble((2 * power_ao(3) + 1)) * dz**(power_ao(3)) dz4 = dble((2 * power_ao(3) + 1)) * dz**(power_ao(3))
else else
dz4 = dble((power_ao(3) + 1)) * dz**(power_ao(3)) dz4 = dble((power_ao(3) + 1)) * dz**(power_ao(3))
@ -298,29 +330,31 @@ subroutine give_all_aos_and_grad_and_lapl_at_r(r,aos_array,aos_grad_array,aos_la
dz5 = dz**(power_ao(3)+2) dz5 = dz**(power_ao(3)+2)
! ---
accu_1 = 0.d0 accu_1 = 0.d0
accu_2 = 0.d0 accu_2 = 0.d0
accu_3 = 0.d0 accu_3 = 0.d0
do l = 1,ao_prim_num(k) do l = 1,ao_prim_num(k)
beta = ao_expo_ordered_transp_per_nucl(l,j,i) beta = ao_expo_ordered_transp_per_nucl(l,j,i)
if(beta*r2.gt.50.d0) cycle
contrib = ao_coef_normalized_ordered_transp_per_nucl(l,j,i) * dexp(-beta*r2) contrib = ao_coef_normalized_ordered_transp_per_nucl(l,j,i) * dexp(-beta*r2)
accu_1 += contrib accu_1 += contrib
accu_2 += contrib * beta accu_2 += contrib * beta
accu_3 += contrib * beta**2 accu_3 += contrib * beta**2
enddo enddo
aos_array(k) = accu_1 * dx2 * dy2 * dz2 aos_array(k) = accu_1 * dx2 * dy2 * dz2
aos_grad_array(1,k) = accu_1 * dx1 * dy2 * dz2 - 2.d0 * dx2 * dx * dy2 * dz2 * accu_2
aos_grad_array(1,k) = accu_1 * dx1 * dy2 * dz2- 2.d0 * dx2 * dx * dy2 * dz2 * accu_2 aos_grad_array(2,k) = accu_1 * dx2 * dy1 * dz2 - 2.d0 * dx2 * dy2 * dy * dz2 * accu_2
aos_grad_array(2,k) = accu_1 * dx2 * dy1 * dz2- 2.d0 * dx2 * dy2 * dy * dz2 * accu_2 aos_grad_array(3,k) = accu_1 * dx2 * dy2 * dz1 - 2.d0 * dx2 * dy2 * dz2 * dz * accu_2
aos_grad_array(3,k) = accu_1 * dx2 * dy2 * dz1- 2.d0 * dx2 * dy2 * dz2 * dz * accu_2 aos_lapl_array(1,k) = accu_1 * dx3 * dy2 * dz2 - 2.d0 * dx4 * dy2 * dz2 * accu_2 + 4.d0 * dx5 * dy2 * dz2 * accu_3
aos_lapl_array(2,k) = accu_1 * dx2 * dy3 * dz2 - 2.d0 * dx2 * dy4 * dz2 * accu_2 + 4.d0 * dx2 * dy5 * dz2 * accu_3
aos_lapl_array(1,k) = accu_1 * dx3 * dy2 * dz2- 2.d0 * dx4 * dy2 * dz2* accu_2 +4.d0 * dx5 *dy2 * dz2* accu_3 aos_lapl_array(3,k) = accu_1 * dx2 * dy2 * dz3 - 2.d0 * dx2 * dy2 * dz4 * accu_2 + 4.d0 * dx2 * dy2 * dz5 * accu_3
aos_lapl_array(2,k) = accu_1 * dx2 * dy3 * dz2- 2.d0 * dx2 * dy4 * dz2* accu_2 +4.d0 * dx2 *dy5 * dz2* accu_3
aos_lapl_array(3,k) = accu_1 * dx2 * dy2 * dz3- 2.d0 * dx2 * dy2 * dz4* accu_2 +4.d0 * dx2 *dy2 * dz5* accu_3
enddo enddo
enddo enddo
end end
! ---