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Vectorizing numerical integrals

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This commit is contained in:
Anthony Scemama 2022-11-20 03:01:06 +01:00
parent e3a91d7823
commit b2f79e2581
10 changed files with 1476 additions and 847 deletions
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141
src/ao_many_one_e_ints/ao_gaus_gauss.irp.f
View File

@ -22,15 +22,15 @@ subroutine overlap_gauss_xyz_r12_ao(D_center,delta,i,j,gauss_ints)
power_B(1:3)= ao_power(j,1:3)
B_center(1:3) = nucl_coord(num_B,1:3)
do l=1,ao_prim_num(i)
alpha = ao_expo_ordered_transp(l,i)
alpha = ao_expo_ordered_transp(l,i)
do k=1,ao_prim_num(j)
beta = ao_expo_ordered_transp(k,j)
beta = ao_expo_ordered_transp(k,j)
call overlap_gauss_xyz_r12(D_center,delta,A_center,B_center,power_A,power_B,alpha,beta,gauss_ints_tmp)
do m = 1, 3
gauss_ints(m) += gauss_ints_tmp(m) * ao_coef_normalized_ordered_transp(l,i) &
* ao_coef_normalized_ordered_transp(k,j)
* ao_coef_normalized_ordered_transp(k,j)
enddo
enddo
enddo
enddo
end
@ -61,13 +61,13 @@ double precision function overlap_gauss_xyz_r12_ao_specific(D_center,delta,i,j,m
power_B(1:3)= ao_power(j,1:3)
B_center(1:3) = nucl_coord(num_B,1:3)
do l=1,ao_prim_num(i)
alpha = ao_expo_ordered_transp(l,i)
alpha = ao_expo_ordered_transp(l,i)
do k=1,ao_prim_num(j)
beta = ao_expo_ordered_transp(k,j)
beta = ao_expo_ordered_transp(k,j)
gauss_int = overlap_gauss_xyz_r12_specific(D_center,delta,A_center,B_center,power_A,power_B,alpha,beta,mx)
overlap_gauss_xyz_r12_ao_specific = gauss_int * ao_coef_normalized_ordered_transp(l,i) &
* ao_coef_normalized_ordered_transp(k,j)
enddo
* ao_coef_normalized_ordered_transp(k,j)
enddo
enddo
end
@ -90,13 +90,13 @@ subroutine overlap_gauss_r12_all_ao(D_center,delta,aos_ints)
power_B(1:3)= ao_power(j,1:3)
B_center(1:3) = nucl_coord(num_B,1:3)
do l=1,ao_prim_num(i)
alpha = ao_expo_ordered_transp(l,i)
alpha = ao_expo_ordered_transp(l,i)
do k=1,ao_prim_num(j)
beta = ao_expo_ordered_transp(k,j)
beta = ao_expo_ordered_transp(k,j)
analytical_j = overlap_gauss_r12(D_center,delta,A_center,B_center,power_A,power_B,alpha,beta)
aos_ints(j,i) += analytical_j * ao_coef_normalized_ordered_transp(l,i) &
* ao_coef_normalized_ordered_transp(k,j)
enddo
* ao_coef_normalized_ordered_transp(k,j)
enddo
enddo
enddo
enddo
@ -114,7 +114,7 @@ double precision function overlap_gauss_r12_ao(D_center, delta, i, j)
implicit none
integer, intent(in) :: i, j
double precision, intent(in) :: D_center(3), delta
integer :: power_A(3), power_B(3), l, k
double precision :: A_center(3), B_center(3), alpha, beta, coef, coef1, analytical_j
@ -133,19 +133,19 @@ double precision function overlap_gauss_r12_ao(D_center, delta, i, j)
B_center(1:3) = nucl_coord(ao_nucl(j),1:3)
do l = 1, ao_prim_num(i)
alpha = ao_expo_ordered_transp (l,i)
coef1 = ao_coef_normalized_ordered_transp(l,i)
alpha = ao_expo_ordered_transp (l,i)
coef1 = ao_coef_normalized_ordered_transp(l,i)
do k = 1, ao_prim_num(j)
beta = ao_expo_ordered_transp(k,j)
coef = coef1 * ao_coef_normalized_ordered_transp(k,j)
coef = coef1 * ao_coef_normalized_ordered_transp(k,j)
if(dabs(coef) .lt. 1d-12) cycle
analytical_j = overlap_gauss_r12(D_center, delta, A_center, B_center, power_A, power_B, alpha, beta)
overlap_gauss_r12_ao += coef * analytical_j
enddo
enddo
enddo
end function overlap_gauss_r12_ao
@ -163,14 +163,13 @@ double precision function overlap_gauss_r12_ao_with1s(B_center, beta, D_center,
implicit none
integer, intent(in) :: i, j
double precision, intent(in) :: B_center(3), beta, D_center(3), delta
integer :: power_A1(3), power_A2(3), l, k
double precision :: A1_center(3), A2_center(3), alpha1, alpha2, coef1, coef12, analytical_j
double precision :: G_center(3), gama, fact_g, gama_inv
double precision, external :: overlap_gauss_r12, overlap_gauss_r12_ao
ASSERT(beta .gt. 0.d0)
if(beta .lt. 1d-10) then
overlap_gauss_r12_ao_with1s = overlap_gauss_r12_ao(D_center, delta, i, j)
return
@ -204,22 +203,120 @@ double precision function overlap_gauss_r12_ao_with1s(B_center, beta, D_center,
A2_center(1:3) = nucl_coord(ao_nucl(j),1:3)
do l = 1, ao_prim_num(i)
alpha1 = ao_expo_ordered_transp (l,i)
alpha1 = ao_expo_ordered_transp (l,i)
coef1 = fact_g * ao_coef_normalized_ordered_transp(l,i)
if(dabs(coef1) .lt. 1d-12) cycle
do k = 1, ao_prim_num(j)
alpha2 = ao_expo_ordered_transp (k,j)
coef12 = coef1 * ao_coef_normalized_ordered_transp(k,j)
coef12 = coef1 * ao_coef_normalized_ordered_transp(k,j)
if(dabs(coef12) .lt. 1d-12) cycle
analytical_j = overlap_gauss_r12(G_center, gama, A1_center, A2_center, power_A1, power_A2, alpha1, alpha2)
overlap_gauss_r12_ao_with1s += coef12 * analytical_j
enddo
enddo
enddo
end function overlap_gauss_r12_ao_with1s
! ---
subroutine overlap_gauss_r12_ao_with1s_v(B_center, beta, D_center, delta, i, j, resv, n_points)
BEGIN_DOC
!
! \int dr AO_i(r) AO_j(r) e^{-beta |r-B_center^2|} e^{-delta |r-D_center|^2}
! using an array of D_centers.
!
END_DOC
implicit none
integer, intent(in) :: i, j, n_points
double precision, intent(in) :: B_center(3), beta, D_center(3,n_points), delta
double precision, intent(out) :: resv(n_points)
integer :: power_A1(3), power_A2(3), l, k
double precision :: A1_center(3), A2_center(3), alpha1, alpha2, coef1
double precision :: coef12, coef12f
double precision :: gama, gama_inv
double precision :: bg, dg, bdg
double precision, external :: overlap_gauss_r12, overlap_gauss_r12_ao
double precision, external :: overlap_gauss_r12_ao_with1s
integer :: ipoint
double precision, allocatable :: fact_g(:), G_center(:,:), analytical_j(:)
if(ao_overlap_abs(j,i) .lt. 1.d-12) then
return
endif
ASSERT(beta .gt. 0.d0)
if(beta .lt. 1d-10) then
do ipoint=1,n_points
resv(ipoint) = overlap_gauss_r12_ao(D_center(1,ipoint), delta, i, j)
enddo
return
endif
resv(:) = 0.d0
! e^{-beta |r-B_center^2|} e^{-delta |r-D_center|^2} = fact_g e^{-gama |r - G|^2}
gama = beta + delta
gama_inv = 1.d0 / gama
power_A1(1:3) = ao_power(i,1:3)
power_A2(1:3) = ao_power(j,1:3)
A1_center(1:3) = nucl_coord(ao_nucl(i),1:3)
A2_center(1:3) = nucl_coord(ao_nucl(j),1:3)
allocate (fact_g(n_points), G_center(3,n_points), analytical_j(n_points) )
bg = beta * gama_inv
dg = delta * gama_inv
bdg = bg * delta
do ipoint=1,n_points
G_center(1,ipoint) = bg * B_center(1) + dg * D_center(1,ipoint)
G_center(2,ipoint) = bg * B_center(2) + dg * D_center(2,ipoint)
G_center(3,ipoint) = bg * B_center(3) + dg * D_center(3,ipoint)
fact_g(ipoint) = bdg * ( &
(B_center(1) - D_center(1,ipoint)) * (B_center(1) - D_center(1,ipoint)) &
+ (B_center(2) - D_center(2,ipoint)) * (B_center(2) - D_center(2,ipoint)) &
+ (B_center(3) - D_center(3,ipoint)) * (B_center(3) - D_center(3,ipoint)) )
if(fact_g(ipoint) < 10d0) then
fact_g(ipoint) = dexp(-fact_g(ipoint))
else
fact_g(ipoint) = 0.d0
endif
enddo
! ---
do l = 1, ao_prim_num(i)
alpha1 = ao_expo_ordered_transp (l,i)
coef1 = ao_coef_normalized_ordered_transp(l,i)
do k = 1, ao_prim_num(j)
alpha2 = ao_expo_ordered_transp (k,j)
coef12 = coef1 * ao_coef_normalized_ordered_transp(k,j)
if(dabs(coef12) .lt. 1d-12) cycle
call overlap_gauss_r12_v(G_center, gama, A1_center,&
A2_center, power_A1, power_A2, alpha1, alpha2, analytical_j, n_points)
do ipoint=1,n_points
coef12f = coef12 * fact_g(ipoint)
resv(ipoint) += coef12f * analytical_j(ipoint)
end do
enddo
enddo
end

111
src/ao_many_one_e_ints/grad2_jmu_modif.irp.f
View File

@ -16,54 +16,55 @@ BEGIN_PROVIDER [ double precision, int2_grad1u2_grad2u2_j1b2, (ao_num, ao_num, n
double precision :: tmp
double precision :: wall0, wall1
double precision, allocatable :: int_fit_v(:)
double precision, external :: overlap_gauss_r12_ao_with1s
provide mu_erf final_grid_points j1b_pen
call wall_time(wall0)
int2_grad1u2_grad2u2_j1b2 = 0.d0
allocate(int_fit_v(n_points_final_grid))
int2_grad1u2_grad2u2_j1b2(:,:,:) = 0.d0
!$OMP PARALLEL DEFAULT (NONE) &
!$OMP PRIVATE (ipoint, i, j, i_1s, i_fit, r, coef, beta, B_center, &
!$OMP coef_fit, expo_fit, int_fit, tmp) &
!$OMP SHARED (n_points_final_grid, ao_num, List_all_comb_b3_size, &
!$OMP final_grid_points, n_max_fit_slat, &
!$OMP expo_gauss_1_erf_x_2, coef_gauss_1_erf_x_2, &
!$OMP List_all_comb_b3_coef, List_all_comb_b3_expo, &
!$OMP List_all_comb_b3_cent, int2_grad1u2_grad2u2_j1b2)
!$OMP DO
!do ipoint = 1, 10
do ipoint = 1, n_points_final_grid
r(1) = final_grid_points(1,ipoint)
r(2) = final_grid_points(2,ipoint)
r(3) = final_grid_points(3,ipoint)
!$OMP PARALLEL DEFAULT (NONE) &
!$OMP PRIVATE (ipoint, i, j, i_1s, i_fit, r, coef, beta, B_center,&
!$OMP coef_fit, expo_fit, int_fit_v, tmp) &
!$OMP SHARED (n_points_final_grid, ao_num, List_all_comb_b3_size,&
!$OMP final_grid_points, n_max_fit_slat, &
!$OMP expo_gauss_1_erf_x_2, coef_gauss_1_erf_x_2, &
!$OMP List_all_comb_b3_coef, List_all_comb_b3_expo, &
!$OMP List_all_comb_b3_cent, int2_grad1u2_grad2u2_j1b2,&
!$OMP ao_overlap_abs)
!$OMP DO SCHEDULE(dynamic)
do i = 1, ao_num
do j = i, ao_num
do i = 1, ao_num
do j = i, ao_num
if(ao_overlap_abs(j,i) .lt. 1.d-12) then
cycle
endif
tmp = 0.d0
do i_1s = 1, List_all_comb_b3_size
do i_1s = 1, List_all_comb_b3_size
coef = List_all_comb_b3_coef (i_1s)
beta = List_all_comb_b3_expo (i_1s)
B_center(1) = List_all_comb_b3_cent(1,i_1s)
B_center(2) = List_all_comb_b3_cent(2,i_1s)
B_center(3) = List_all_comb_b3_cent(3,i_1s)
coef = List_all_comb_b3_coef (i_1s)
beta = List_all_comb_b3_expo (i_1s)
B_center(1) = List_all_comb_b3_cent(1,i_1s)
B_center(2) = List_all_comb_b3_cent(2,i_1s)
B_center(3) = List_all_comb_b3_cent(3,i_1s)
do i_fit = 1, n_max_fit_slat
do i_fit = 1, n_max_fit_slat
expo_fit = expo_gauss_1_erf_x_2(i_fit)
coef_fit = coef_gauss_1_erf_x_2(i_fit)
int_fit = overlap_gauss_r12_ao_with1s(B_center, beta, r, expo_fit, i, j)
expo_fit = expo_gauss_1_erf_x_2(i_fit)
coef_fit = -0.25d0 * coef_gauss_1_erf_x_2(i_fit) * coef
tmp += -0.25d0 * coef * coef_fit * int_fit
enddo
enddo
call overlap_gauss_r12_ao_with1s_v(B_center, beta, final_grid_points, expo_fit, i, j, int_fit_v, n_points_final_grid)
int2_grad1u2_grad2u2_j1b2(j,i,ipoint) = tmp
enddo
enddo
enddo
do ipoint = 1, n_points_final_grid
int2_grad1u2_grad2u2_j1b2(j,i,ipoint) += coef_fit * int_fit_v(ipoint)
enddo
enddo
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
@ -78,7 +79,7 @@ BEGIN_PROVIDER [ double precision, int2_grad1u2_grad2u2_j1b2, (ao_num, ao_num, n
call wall_time(wall1)
print*, ' wall time for int2_grad1u2_grad2u2_j1b2', wall1 - wall0
END_PROVIDER
END_PROVIDER
! ---
@ -105,11 +106,11 @@ BEGIN_PROVIDER [ double precision, int2_u2_j1b2, (ao_num, ao_num, n_points_final
!$OMP PARALLEL DEFAULT (NONE) &
!$OMP PRIVATE (ipoint, i, j, i_1s, i_fit, r, coef, beta, B_center, &
!$OMP coef_fit, expo_fit, int_fit, tmp) &
!$OMP SHARED (n_points_final_grid, ao_num, List_all_comb_b3_size, &
!$OMP coef_fit, expo_fit, int_fit, tmp) &
!$OMP SHARED (n_points_final_grid, ao_num, List_all_comb_b3_size, &
!$OMP final_grid_points, n_max_fit_slat, &
!$OMP expo_gauss_j_mu_x_2, coef_gauss_j_mu_x_2, &
!$OMP List_all_comb_b3_coef, List_all_comb_b3_expo, &
!$OMP List_all_comb_b3_coef, List_all_comb_b3_expo, &
!$OMP List_all_comb_b3_cent, int2_u2_j1b2)
!$OMP DO
!do ipoint = 1, 10
@ -158,7 +159,7 @@ BEGIN_PROVIDER [ double precision, int2_u2_j1b2, (ao_num, ao_num, n_points_final
call wall_time(wall1)
print*, ' wall time for int2_u2_j1b2', wall1 - wall0
END_PROVIDER
END_PROVIDER
! ---
@ -186,12 +187,12 @@ BEGIN_PROVIDER [ double precision, int2_u_grad1u_x_j1b2, (3, ao_num, ao_num, n_p
!$OMP PARALLEL DEFAULT (NONE) &
!$OMP PRIVATE (ipoint, i, j, i_1s, i_fit, r, coef, beta, B_center, &
!$OMP coef_fit, expo_fit, int_fit, alpha_1s, dist, &
!$OMP alpha_1s_inv, centr_1s, expo_coef_1s, coef_tmp, &
!$OMP tmp_x, tmp_y, tmp_z) &
!$OMP SHARED (n_points_final_grid, ao_num, List_all_comb_b3_size, &
!$OMP alpha_1s_inv, centr_1s, expo_coef_1s, coef_tmp, &
!$OMP tmp_x, tmp_y, tmp_z) &
!$OMP SHARED (n_points_final_grid, ao_num, List_all_comb_b3_size, &
!$OMP final_grid_points, n_max_fit_slat, &
!$OMP expo_gauss_j_mu_1_erf, coef_gauss_j_mu_1_erf, &
!$OMP List_all_comb_b3_coef, List_all_comb_b3_expo, &
!$OMP List_all_comb_b3_coef, List_all_comb_b3_expo, &
!$OMP List_all_comb_b3_cent, int2_u_grad1u_x_j1b2)
!$OMP DO
do ipoint = 1, n_points_final_grid
@ -214,7 +215,7 @@ BEGIN_PROVIDER [ double precision, int2_u_grad1u_x_j1b2, (3, ao_num, ao_num, n_p
B_center(3) = List_all_comb_b3_cent(3,i_1s)
dist = (B_center(1) - r(1)) * (B_center(1) - r(1)) &
+ (B_center(2) - r(2)) * (B_center(2) - r(2)) &
+ (B_center(3) - r(3)) * (B_center(3) - r(3))
+ (B_center(3) - r(3)) * (B_center(3) - r(3))
do i_fit = 1, n_max_fit_slat
@ -222,17 +223,17 @@ BEGIN_PROVIDER [ double precision, int2_u_grad1u_x_j1b2, (3, ao_num, ao_num, n_p
coef_fit = coef_gauss_j_mu_1_erf(i_fit)
alpha_1s = beta + expo_fit
alpha_1s_inv = 1.d0 / alpha_1s
alpha_1s_inv = 1.d0 / alpha_1s
centr_1s(1) = alpha_1s_inv * (beta * B_center(1) + expo_fit * r(1))
centr_1s(2) = alpha_1s_inv * (beta * B_center(2) + expo_fit * r(2))
centr_1s(3) = alpha_1s_inv * (beta * B_center(3) + expo_fit * r(3))
expo_coef_1s = beta * expo_fit * alpha_1s_inv * dist
expo_coef_1s = beta * expo_fit * alpha_1s_inv * dist
!if(expo_coef_1s .gt. 80.d0) cycle
coef_tmp = coef * coef_fit * dexp(-expo_coef_1s)
!if(dabs(coef_tmp) .lt. 1d-10) cycle
call NAI_pol_x_mult_erf_ao_with1s(i, j, alpha_1s, centr_1s, 1.d+9, r, int_fit)
tmp_x += coef_tmp * int_fit(1)
@ -263,7 +264,7 @@ BEGIN_PROVIDER [ double precision, int2_u_grad1u_x_j1b2, (3, ao_num, ao_num, n_p
call wall_time(wall1)
print*, ' wall time for int2_u_grad1u_x_j1b2', wall1 - wall0
END_PROVIDER
END_PROVIDER
! ---
@ -291,11 +292,11 @@ BEGIN_PROVIDER [ double precision, int2_u_grad1u_j1b2, (ao_num, ao_num, n_points
!$OMP PARALLEL DEFAULT (NONE) &
!$OMP PRIVATE (ipoint, i, j, i_1s, i_fit, r, coef, beta, B_center, &
!$OMP coef_fit, expo_fit, int_fit, tmp, alpha_1s, dist, &
!$OMP alpha_1s_inv, centr_1s, expo_coef_1s, coef_tmp) &
!$OMP SHARED (n_points_final_grid, ao_num, List_all_comb_b3_size, &
!$OMP alpha_1s_inv, centr_1s, expo_coef_1s, coef_tmp) &
!$OMP SHARED (n_points_final_grid, ao_num, List_all_comb_b3_size, &
!$OMP final_grid_points, n_max_fit_slat, &
!$OMP expo_gauss_j_mu_1_erf, coef_gauss_j_mu_1_erf, &
!$OMP List_all_comb_b3_coef, List_all_comb_b3_expo, &
!$OMP List_all_comb_b3_coef, List_all_comb_b3_expo, &
!$OMP List_all_comb_b3_cent, int2_u_grad1u_j1b2)
!$OMP DO
do ipoint = 1, n_points_final_grid
@ -323,7 +324,7 @@ BEGIN_PROVIDER [ double precision, int2_u_grad1u_j1b2, (ao_num, ao_num, n_points
coef_fit = coef_gauss_j_mu_1_erf(i_fit)
alpha_1s = beta + expo_fit
alpha_1s_inv = 1.d0 / alpha_1s
alpha_1s_inv = 1.d0 / alpha_1s
centr_1s(1) = alpha_1s_inv * (beta * B_center(1) + expo_fit * r(1))
centr_1s(2) = alpha_1s_inv * (beta * B_center(2) + expo_fit * r(2))
centr_1s(3) = alpha_1s_inv * (beta * B_center(3) + expo_fit * r(3))
@ -332,7 +333,7 @@ BEGIN_PROVIDER [ double precision, int2_u_grad1u_j1b2, (ao_num, ao_num, n_points
!if(expo_coef_1s .gt. 80.d0) cycle
coef_tmp = coef * coef_fit * dexp(-expo_coef_1s)
!if(dabs(coef_tmp) .lt. 1d-10) cycle
int_fit = NAI_pol_mult_erf_ao_with1s(i, j, alpha_1s, centr_1s, 1.d+9, r)
tmp += coef_tmp * int_fit
@ -357,7 +358,7 @@ BEGIN_PROVIDER [ double precision, int2_u_grad1u_j1b2, (ao_num, ao_num, n_points
call wall_time(wall1)
print*, ' wall time for int2_u_grad1u_j1b2', wall1 - wall0
END_PROVIDER
END_PROVIDER
! ---

1
src/ao_many_one_e_ints/listj1b.irp.f
View File

@ -63,7 +63,6 @@ END_PROVIDER
tmp_cent_z += tmp_alphaj * nucl_coord(j,3)
enddo
ASSERT(List_all_comb_b2_expo(i) .gt. 0d0)
if(List_all_comb_b2_expo(i) .lt. 1d-10) cycle
List_all_comb_b2_cent(1,i) = tmp_cent_x / List_all_comb_b2_expo(i)

186
src/ao_many_one_e_ints/prim_int_gauss_gauss.irp.f
View File

@ -1,67 +1,139 @@
double precision function overlap_gauss_r12(D_center,delta,A_center,B_center,power_A,power_B,alpha,beta)
BEGIN_DOC
! Computes the following integral :
!
! .. math::
!
! .. math ::
!
! \int dr exp(-delta (r - D)^2 ) (x-A_x)^a (x-B_x)^b \exp(-\alpha (x-A_x)^2 - \beta (x-B_x)^2 )
!
END_DOC
implicit none
implicit none
include 'constants.include.F'
double precision, intent(in) :: D_center(3), delta ! pure gaussian "D"
double precision, intent(in) :: A_center(3),B_center(3),alpha,beta ! gaussian/polynoms "A" and "B"
integer, intent(in) :: power_A(3),power_B(3)
double precision, intent(in) :: D_center(3), delta ! pure gaussian "D"
double precision, intent(in) :: A_center(3),B_center(3),alpha,beta ! gaussian/polynoms "A" and "B"
integer, intent(in) :: power_A(3),power_B(3)
double precision :: overlap_x,overlap_y,overlap_z,overlap
! First you multiply the usual gaussian "A" with the gaussian exp(-delta (r - D)^2 )
double precision :: A_new(0:max_dim,3)! new polynom
double precision :: A_center_new(3) ! new center
integer :: iorder_a_new(3) ! i_order(i) = order of the new polynom ==> should be equal to power_A
double precision :: alpha_new ! new exponent
double precision :: fact_a_new ! constant factor
double precision :: accu,coefx,coefy,coefz,coefxy,coefxyz,thr
integer :: d(3),i,lx,ly,lz,iorder_tmp(3),dim1
dim1=100
thr = 1.d-10
d = 0 ! order of the polynom for the gaussian exp(-delta (r - D)^2 ) == 0
double precision :: overlap_x,overlap_y,overlap_z,overlap
! First you multiply the usual gaussian "A" with the gaussian exp(-delta (r - D)^2 )
double precision :: A_new(0:max_dim,3)! new polynom
double precision :: A_center_new(3) ! new center
integer :: iorder_a_new(3) ! i_order(i) = order of the new polynom ==> should be equal to power_A
double precision :: alpha_new ! new exponent
double precision :: fact_a_new ! constant factor
double precision :: accu,coefx,coefy,coefz,coefxy,coefxyz,thr
integer :: d(3),i,lx,ly,lz,iorder_tmp(3),dim1
dim1=100
thr = 1.d-10
d(:) = 0 ! order of the polynom for the gaussian exp(-delta (r - D)^2 ) == 0
! New gaussian/polynom defined by :: new pol new center new expo cst fact new order
call give_explicit_poly_and_gaussian(A_new , A_center_new , alpha_new, fact_a_new , iorder_a_new , &
delta,alpha,d,power_A,D_center,A_center,n_pt_max_integrals)
! The new gaussian exp(-delta (r - D)^2 ) (x-A_x)^a \exp(-\alpha (x-A_x)^2
accu = 0.d0
do lx = 0, iorder_a_new(1)
coefx = A_new(lx,1)
if(dabs(coefx).lt.thr)cycle
iorder_tmp(1) = lx
do ly = 0, iorder_a_new(2)
coefy = A_new(ly,2)
coefxy = coefx * coefy
if(dabs(coefxy).lt.thr)cycle
iorder_tmp(2) = ly
do lz = 0, iorder_a_new(3)
coefz = A_new(lz,3)
coefxyz = coefxy * coefz
if(dabs(coefxyz).lt.thr)cycle
iorder_tmp(3) = lz
call overlap_gaussian_xyz(A_center_new,B_center,alpha_new,beta,iorder_tmp,power_B,overlap_x,overlap_y,overlap_z,overlap,dim1)
accu += coefxyz * overlap
enddo
! New gaussian/polynom defined by :: new pol new center new expo cst fact new order
call give_explicit_poly_and_gaussian(A_new , A_center_new , alpha_new, fact_a_new , iorder_a_new ,&
delta,alpha,d,power_A,D_center,A_center,n_pt_max_integrals)
! The new gaussian exp(-delta (r - D)^2 ) (x-A_x)^a \exp(-\alpha (x-A_x)^2
accu = 0.d0
do lx = 0, iorder_a_new(1)
coefx = A_new(lx,1)
if(dabs(coefx).lt.thr)cycle
iorder_tmp(1) = lx
do ly = 0, iorder_a_new(2)
coefy = A_new(ly,2)
coefxy = coefx * coefy
if(dabs(coefxy).lt.thr)cycle
iorder_tmp(2) = ly
do lz = 0, iorder_a_new(3)
coefz = A_new(lz,3)
coefxyz = coefxy * coefz
if(dabs(coefxyz).lt.thr)cycle
iorder_tmp(3) = lz
call overlap_gaussian_xyz(A_center_new,B_center,alpha_new,beta,iorder_tmp,power_B,overlap_x,overlap_y,overlap_z,overlap,dim1)
accu += coefxyz * overlap
enddo
enddo
enddo
enddo
overlap_gauss_r12 = fact_a_new * accu
overlap_gauss_r12 = fact_a_new * accu
end
!---
subroutine overlap_gauss_r12_v(D_center,delta,A_center,B_center,power_A,power_B,alpha,beta,rvec,n_points)
BEGIN_DOC
! Computes the following integral :
!
! .. math ::
!
! \int dr exp(-delta (r - D)^2 ) (x-A_x)^a (x-B_x)^b \exp(-\alpha (x-A_x)^2 - \beta (x-B_x)^2 )
! using an array of D_centers
!
END_DOC
implicit none
include 'constants.include.F'
integer, intent(in) :: n_points
double precision, intent(in) :: D_center(3,n_points), delta ! pure gaussian "D"
double precision, intent(in) :: A_center(3),B_center(3),alpha,beta ! gaussian/polynoms "A" and "B"
integer, intent(in) :: power_A(3),power_B(3)
double precision, intent(out) :: rvec(n_points)
double precision :: overlap_x,overlap_y,overlap_z,overlap
integer :: maxab
integer, allocatable :: iorder_a_new(:)
double precision, allocatable :: A_new(:,:,:), A_center_new(:,:)
double precision, allocatable :: fact_a_new(:)
double precision :: alpha_new
double precision :: accu,coefx,coefy,coefz,coefxy,coefxyz,thr
integer :: d(3),i,lx,ly,lz,iorder_tmp(3),dim1, ipoint
dim1=100
thr = 1.d-10
d(:) = 0
! maxab = maxval(d(1:3))
maxab = max_dim
allocate (A_new(0:maxab, 3, n_points), A_center_new(3, n_points), &
fact_a_new(n_points), iorder_a_new(3))
call give_explicit_poly_and_gaussian_v(A_new, maxab, A_center_new, &
alpha_new, fact_a_new, iorder_a_new , delta, alpha, d, power_A, &
D_center, A_center, n_points)
do ipoint=1,n_points
! The new gaussian exp(-delta (r - D)^2 ) (x-A_x)^a \exp(-\alpha (x-A_x)^2
accu = 0.d0
do lx = 0, iorder_a_new(1)
coefx = A_new(lx,1,ipoint)
if(dabs(coefx).lt.thr)cycle
iorder_tmp(1) = lx
do ly = 0, iorder_a_new(2)
coefy = A_new(ly,2,ipoint)
coefxy = coefx * coefy
if(dabs(coefxy).lt.thr)cycle
iorder_tmp(2) = ly
do lz = 0, iorder_a_new(3)
coefz = A_new(lz,3,ipoint)
coefxyz = coefxy * coefz
if(dabs(coefxyz).lt.thr)cycle
iorder_tmp(3) = lz
call overlap_gaussian_xyz(A_center_new(1,ipoint),B_center,alpha_new,beta,iorder_tmp,power_B,overlap_x,overlap_y,overlap_z,overlap,dim1)
accu += coefxyz * overlap
enddo
enddo
enddo
rvec(ipoint) = fact_a_new(ipoint) * accu
end do
end
!---
!---
subroutine overlap_gauss_xyz_r12(D_center,delta,A_center,B_center,power_A,power_B,alpha,beta,gauss_ints)
BEGIN_DOC
! Computes the following integral :
!
! .. math::
!
!
! gauss_ints(m) = \int dr exp(-delta (r - D)^2 ) * x/y/z (x-A_x)^a (x-B_x)^b \exp(-\alpha (x-A_x)^2 - \beta (x-B_x)^2 )
!
! with m == 1 ==> x, m == 2 ==> y, m == 3 ==> z
@ -69,14 +141,14 @@ subroutine overlap_gauss_xyz_r12(D_center,delta,A_center,B_center,power_A,power_
implicit none
include 'constants.include.F'
double precision, intent(in) :: D_center(3), delta ! pure gaussian "D"
double precision, intent(in) :: D_center(3), delta ! pure gaussian "D"
double precision, intent(in) :: A_center(3),B_center(3),alpha,beta ! gaussian/polynoms "A" and "B"
integer, intent(in) :: power_A(3),power_B(3)
double precision, intent(out) :: gauss_ints(3)
double precision :: overlap_x,overlap_y,overlap_z,overlap
! First you multiply the usual gaussian "A" with the gaussian exp(-delta (r - D)^2 )
double precision :: A_new(0:max_dim,3)! new polynom
double precision :: A_new(0:max_dim,3)! new polynom
double precision :: A_center_new(3) ! new center
integer :: iorder_a_new(3) ! i_order(i) = order of the new polynom ==> should be equal to power_A
integer :: power_B_new(3)
@ -88,8 +160,8 @@ subroutine overlap_gauss_xyz_r12(D_center,delta,A_center,B_center,power_A,power_
thr = 1.d-10
d = 0 ! order of the polynom for the gaussian exp(-delta (r - D)^2 ) == 0
! New gaussian/polynom defined by :: new pol new center new expo cst fact new order
call give_explicit_poly_and_gaussian(A_new , A_center_new , alpha_new, fact_a_new , iorder_a_new , &
! New gaussian/polynom defined by :: new pol new center new expo cst fact new order
call give_explicit_poly_and_gaussian(A_new , A_center_new , alpha_new, fact_a_new , iorder_a_new , &
delta,alpha,d,power_A,D_center,A_center,n_pt_max_integrals)
! The new gaussian exp(-delta (r - D)^2 ) (x-A_x)^a \exp(-\alpha (x-A_x)^2
gauss_ints = 0.d0
@ -99,12 +171,12 @@ subroutine overlap_gauss_xyz_r12(D_center,delta,A_center,B_center,power_A,power_
iorder_tmp(1) = lx
do ly = 0, iorder_a_new(2)
coefy = A_new(ly,2)
coefxy = coefx * coefy
coefxy = coefx * coefy
if(dabs(coefxy).lt.thr)cycle
iorder_tmp(2) = ly
do lz = 0, iorder_a_new(3)
coefz = A_new(lz,3)
coefxyz = coefxy * coefz
coefxyz = coefxy * coefz
if(dabs(coefxyz).lt.thr)cycle
iorder_tmp(3) = lz
do m = 1, 3
@ -129,7 +201,7 @@ double precision function overlap_gauss_xyz_r12_specific(D_center,delta,A_center
! Computes the following integral :
!
! .. math::
!
!
! \int dr exp(-delta (r - D)^2 ) * x/y/z (x-A_x)^a (x-B_x)^b \exp(-\alpha (x-A_x)^2 - \beta (x-B_x)^2 )
!
! with mx == 1 ==> x, mx == 2 ==> y, mx == 3 ==> z
@ -137,13 +209,13 @@ double precision function overlap_gauss_xyz_r12_specific(D_center,delta,A_center
implicit none
include 'constants.include.F'
double precision, intent(in) :: D_center(3), delta ! pure gaussian "D"
double precision, intent(in) :: D_center(3), delta ! pure gaussian "D"
double precision, intent(in) :: A_center(3),B_center(3),alpha,beta ! gaussian/polynoms "A" and "B"
integer, intent(in) :: power_A(3),power_B(3),mx
double precision :: overlap_x,overlap_y,overlap_z,overlap
! First you multiply the usual gaussian "A" with the gaussian exp(-delta (r - D)^2 )
double precision :: A_new(0:max_dim,3)! new polynom
double precision :: A_new(0:max_dim,3)! new polynom
double precision :: A_center_new(3) ! new center
integer :: iorder_a_new(3) ! i_order(i) = order of the new polynom ==> should be equal to power_A
integer :: power_B_new(3)
@ -155,8 +227,8 @@ double precision function overlap_gauss_xyz_r12_specific(D_center,delta,A_center
thr = 1.d-10
d = 0 ! order of the polynom for the gaussian exp(-delta (r - D)^2 ) == 0
! New gaussian/polynom defined by :: new pol new center new expo cst fact new order
call give_explicit_poly_and_gaussian(A_new , A_center_new , alpha_new, fact_a_new , iorder_a_new , &
! New gaussian/polynom defined by :: new pol new center new expo cst fact new order
call give_explicit_poly_and_gaussian(A_new , A_center_new , alpha_new, fact_a_new , iorder_a_new , &
delta,alpha,d,power_A,D_center,A_center,n_pt_max_integrals)
! The new gaussian exp(-delta (r - D)^2 ) (x-A_x)^a \exp(-\alpha (x-A_x)^2
overlap_gauss_xyz_r12_specific = 0.d0
@ -166,12 +238,12 @@ double precision function overlap_gauss_xyz_r12_specific(D_center,delta,A_center
iorder_tmp(1) = lx
do ly = 0, iorder_a_new(2)
coefy = A_new(ly,2)
coefxy = coefx * coefy
coefxy = coefx * coefy
if(dabs(coefxy).lt.thr)cycle
iorder_tmp(2) = ly
do lz = 0, iorder_a_new(3)
coefz = A_new(lz,3)
coefxyz = coefxy * coefz
coefxyz = coefxy * coefz
if(dabs(coefxyz).lt.thr)cycle
iorder_tmp(3) = lz
m = mx

296
src/utils/integration.irp.f
View File

@ -56,7 +56,7 @@ subroutine give_explicit_poly_and_gaussian(P_new,P_center,p,fact_k,iorder,alpha,
! * [ sum (l_y = 0,i_order(2)) P_new(l_y,2) * (y-P_center(2))^l_y ] exp (- p (y-P_center(2))^2 )
! * [ sum (l_z = 0,i_order(3)) P_new(l_z,3) * (z-P_center(3))^l_z ] exp (- p (z-P_center(3))^2 )
!
! WARNING ::: IF fact_k is too smal then:
! WARNING ::: IF fact_k is too smal then:
! returns a "s" function centered in zero
! with an inifinite exponent and a zero polynom coef
END_DOC
@ -86,13 +86,11 @@ subroutine give_explicit_poly_and_gaussian(P_new,P_center,p,fact_k,iorder,alpha,
!DIR$ FORCEINLINE
call gaussian_product(alpha,A_center,beta,B_center,fact_k,p,P_center)
if (fact_k < thresh) then
! IF fact_k is too smal then:
! IF fact_k is too smal then:
! returns a "s" function centered in zero
! with an inifinite exponent and a zero polynom coef
P_center = 0.d0
p = 1.d+15
P_new = 0.d0
iorder = 0
fact_k = 0.d0
return
endif
@ -129,6 +127,89 @@ subroutine give_explicit_poly_and_gaussian(P_new,P_center,p,fact_k,iorder,alpha,
end
!---
subroutine give_explicit_poly_and_gaussian_v(P_new, ldp, P_center,p,fact_k,iorder,alpha,beta,a,b,A_center,B_center,n_points)
BEGIN_DOC
! Transforms the product of
! (x-x_A)^a(1) (x-x_B)^b(1) (x-x_A)^a(2) (y-y_B)^b(2) (z-z_A)^a(3) (z-z_B)^b(3) exp(-(r-A)^2 alpha) exp(-(r-B)^2 beta)
! into
! fact_k * [ sum (l_x = 0,i_order(1)) P_new(l_x,1) * (x-P_center(1))^l_x ] exp (- p (x-P_center(1))^2 )
! * [ sum (l_y = 0,i_order(2)) P_new(l_y,2) * (y-P_center(2))^l_y ] exp (- p (y-P_center(2))^2 )
! * [ sum (l_z = 0,i_order(3)) P_new(l_z,3) * (z-P_center(3))^l_z ] exp (- p (z-P_center(3))^2 )
!
! WARNING :: : IF fact_k is too smal then:
! returns a "s" function centered in zero
! with an inifinite exponent and a zero polynom coef
END_DOC
implicit none
include 'constants.include.F'
integer, intent(in) :: n_points, ldp
integer, intent(in) :: a(3),b(3) ! powers : (x-xa)**a_x = (x-A(1))**a(1)
double precision, intent(in) :: alpha, beta ! exponents
double precision, intent(in) :: A_center(3,n_points) ! A center
double precision, intent(in) :: B_center (3) ! B center
double precision, intent(out) :: P_center(3,n_points) ! new center
double precision, intent(out) :: p ! new exponent
double precision, intent(out) :: fact_k(n_points) ! constant factor
double precision, intent(out) :: P_new(0:ldp,3,n_points)! polynomial
integer, intent(out) :: iorder(3) ! i_order(i) = order of the polynomials
double precision, allocatable :: P_a(:,:,:), P_b(:,:,:)
integer :: n_new,i,j, ipoint, lda, ldb, xyz
call gaussian_product_v(alpha,A_center,beta,B_center,fact_k,p,P_center,n_points)
if ( ior(ior(b(1),b(2)),b(3)) == 0 ) then ! b == (0,0,0)
lda = maxval(a)
ldb = 0
allocate(P_a(0:lda,3,n_points),P_b(0:0,3,n_points))
call recentered_poly2_v0(P_a,lda,A_center,P_center,a,P_b,B_center,P_center,n_points)
iorder(1:3) = a(1:3)
do ipoint=1,n_points
do xyz=1,3
P_new(0,xyz,ipoint) = P_b(0,xyz,ipoint) * P_a(0,xyz,ipoint)
do i=1,a(xyz)
P_new(i,xyz,ipoint) = P_new(i,xyz,ipoint) + P_b(0,xyz,ipoint) * P_a(i,xyz,ipoint)
enddo
enddo
enddo
return
endif
lda = maxval(a)
ldb = maxval(b)
allocate(P_a(0:lda,3,n_points),P_b(0:ldb,3,n_points))
call recentered_poly2_v(P_a,lda,A_center,P_center,a,P_b,ldb,B_center,P_center,b,n_points)
iorder(1:3) = a(1:3) + b(1:3)
do xyz=1,3
if (b(xyz) == 0) then
do ipoint=1,n_points
P_new(0,xyz,ipoint) = P_b(0,xyz,ipoint) * P_a(0,xyz,ipoint)
do i=1,a(xyz)
P_new(i,xyz,ipoint) = P_new(i,xyz,ipoint) + P_b(0,xyz,ipoint) * P_a(i,xyz,ipoint)
enddo
enddo
else
do ipoint=1,n_points
do i=0,iorder(xyz)
P_new(i,xyz,ipoint) = 0.d0
enddo
n_new=0
call multiply_poly(P_a(0,xyz,ipoint),a(xyz),P_b(0,xyz,ipoint),b(xyz),P_new(0,xyz,ipoint),n_new)
enddo
endif
enddo
end
!-
subroutine give_explicit_poly_and_gaussian_double(P_new,P_center,p,fact_k,iorder,alpha,beta,gama,a,b,A_center,B_center,Nucl_center,dim)
BEGIN_DOC
@ -231,6 +312,59 @@ subroutine gaussian_product(a,xa,b,xb,k,p,xp)
xp(3) = (a*xa(3)+b*xb(3))*p_inv
end subroutine
!---
subroutine gaussian_product_v(a,xa,b,xb,k,p,xp,n_points)
implicit none
BEGIN_DOC
! Gaussian product in 1D.
! e^{-a (x-x_A)^2} e^{-b (x-x_B)^2} = K_{ab}^x e^{-p (x-x_P)^2}
! Using multiple A centers
END_DOC
integer, intent(in) :: n_points
double precision, intent(in) :: a,b ! Exponents
double precision, intent(in) :: xa(3,n_points),xb(3) ! Centers
double precision, intent(out) :: p ! New exponent
double precision, intent(out) :: xp(3,n_points) ! New center
double precision, intent(out) :: k(n_points) ! Constant
double precision :: p_inv
integer :: ipoint
ASSERT (a>0.)
ASSERT (b>0.)
double precision :: xab(3), ab, ap, bp, bpxb(3)
!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: xab
p = a+b
p_inv = 1.d0/(a+b)
ab = a*b*p_inv
ap = a*p_inv
bp = b*p_inv
bpxb(1) = bp*xb(1)
bpxb(2) = bp*xb(2)
bpxb(3) = bp*xb(3)
do ipoint=1,n_points
xab(1) = xa(1,ipoint)-xb(1)
xab(2) = xa(2,ipoint)-xb(2)
xab(3) = xa(3,ipoint)-xb(3)
k(ipoint) = ab*(xab(1)*xab(1)+xab(2)*xab(2)+xab(3)*xab(3))
if (k(ipoint) > 40.d0) then
k(ipoint)=0.d0
xp(1,ipoint) = 0.d0
xp(2,ipoint) = 0.d0
xp(3,ipoint) = 0.d0
else
k(ipoint) = dexp(-k(ipoint))
xp(1,ipoint) = ap*xa(1,ipoint)+bpxb(1)
xp(2,ipoint) = ap*xa(2,ipoint)+bpxb(2)
xp(3,ipoint) = ap*xa(3,ipoint)+bpxb(3)
endif
enddo
end subroutine
@ -404,22 +538,152 @@ subroutine recentered_poly2(P_new,x_A,x_P,a,P_new2,x_B,x_Q,b)
do i = minab+1,min(b,20)
P_new2(i) = binom_transp(b-i,b) * pows_b(b-i)
enddo
do i = 101,a
do i = 21,a
P_new(i) = binom_func(a,a-i) * pows_a(a-i)
enddo
do i = 101,b
do i = 21,b
P_new2(i) = binom_func(b,b-i) * pows_b(b-i)
enddo
end
subroutine pol_modif_center(A_center, B_center, iorder, A_pol, B_pol)
!-
subroutine recentered_poly2_v(P_new,lda,x_A,x_P,a,P_new2,ldb,x_B,x_Q,b,n_points)
implicit none
BEGIN_DOC
! Recenter two polynomials
END_DOC
integer, intent(in) :: a(3),b(3), n_points, lda, ldb
double precision, intent(in) :: x_A(3,n_points),x_P(3,n_points),x_B(3),x_Q(3,n_points)
double precision, intent(out) :: P_new(0:lda,3,n_points),P_new2(0:ldb,3,n_points)
double precision :: binom_func
integer :: i,j,k,l, minab(3), maxab(3),ipoint, xyz
double precision, allocatable :: pows_a(:,:), pows_b(:,:)
double precision :: fa, fb
maxab(1:3) = max(a(1:3),b(1:3))
minab(1:3) = max(min(a(1:3),b(1:3)),(/0,0,0/))
allocate( pows_a(n_points,-2:maxval(maxab)+4), pows_b(n_points,-2:maxval(maxab)+4) )
do xyz=1,3
if ((a(xyz)<0).or.(b(xyz)<0) ) cycle
do ipoint=1,n_points
pows_a(ipoint,0) = 1.d0
pows_a(ipoint,1) = (x_P(xyz,ipoint) - x_A(xyz,ipoint))
pows_b(ipoint,0) = 1.d0
pows_b(ipoint,1) = (x_Q(xyz,ipoint) - x_B(xyz))
enddo
do i = 2,maxab(xyz)
do ipoint=1,n_points
pows_a(ipoint,i) = pows_a(ipoint,i-1)*pows_a(ipoint,1)
pows_b(ipoint,i) = pows_b(ipoint,i-1)*pows_b(ipoint,1)
enddo
enddo
do ipoint=1,n_points
P_new (0,xyz,ipoint) = pows_a(ipoint,a(xyz))
P_new2(0,xyz,ipoint) = pows_b(ipoint,b(xyz))
enddo
do i = 1,min(minab(xyz),20)
fa = binom_transp(a(xyz)-i,a(xyz))
fb = binom_transp(b(xyz)-i,b(xyz))
do ipoint=1,n_points
P_new (i,xyz,ipoint) = fa * pows_a(ipoint,a(xyz)-i)
P_new2(i,xyz,ipoint) = fb * pows_b(ipoint,b(xyz)-i)
enddo
enddo
do i = minab(xyz)+1,min(a(xyz),20)
fa = binom_transp(a(xyz)-i,a(xyz))
do ipoint=1,n_points
P_new (i,xyz,ipoint) = fa * pows_a(ipoint,a(xyz)-i)
enddo
enddo
do i = minab(xyz)+1,min(b(xyz),20)
fb = binom_transp(b(xyz)-i,b(xyz))
do ipoint=1,n_points
P_new2(i,xyz,ipoint) = fb * pows_b(ipoint,b(xyz)-i)
enddo
enddo
do i = 21,a(xyz)
fa = binom_func(a(xyz),a(xyz)-i)
do ipoint=1,n_points
P_new (i,xyz,ipoint) = fa * pows_a(ipoint,a(xyz)-i)
enddo
enddo
do i = 21,b(xyz)
fb = binom_func(b(xyz),b(xyz)-i)
do ipoint=1,n_points
P_new2(i,xyz,ipoint) = fb * pows_b(ipoint,b(xyz)-i)
enddo
enddo
enddo
end
subroutine recentered_poly2_v0(P_new,lda,x_A,x_P,a,P_new2,x_B,x_Q,n_points)
implicit none
BEGIN_DOC
! Recenter two polynomials. Special case for b=(0,0,0)
END_DOC
integer, intent(in) :: a(3), n_points, lda
double precision, intent(in) :: x_A(3,n_points),x_P(3,n_points),x_B(3),x_Q(3,n_points)
double precision, intent(out) :: P_new(0:lda,3,n_points),P_new2(3,n_points)
double precision :: binom_func
integer :: i,j,k,l, xyz, ipoint, maxab(3)
double precision, allocatable :: pows_a(:,:), pows_b(:,:)
double precision :: fa
maxab(1:3) = max(a(1:3),(/0,0,0/))
allocate( pows_a(n_points,-2:maxval(maxab)+4), pows_b(n_points,-2:maxval(maxab)+4) )
do xyz=1,3
if (a(xyz)<0) cycle
do ipoint=1,n_points
pows_a(ipoint,0) = 1.d0
pows_a(ipoint,1) = (x_P(xyz,ipoint) - x_A(xyz,ipoint))
pows_b(ipoint,0) = 1.d0
pows_b(ipoint,1) = (x_Q(xyz,ipoint) - x_B(xyz))
enddo
do i = 2,maxab(xyz)
do ipoint=1,n_points
pows_a(ipoint,i) = pows_a(ipoint,i-1)*pows_a(ipoint,1)
pows_b(ipoint,i) = pows_b(ipoint,i-1)*pows_b(ipoint,1)
enddo
enddo
do ipoint=1,n_points
P_new (0,xyz,ipoint) = pows_a(ipoint,a(xyz))
P_new2(xyz,ipoint) = pows_b(ipoint,0)
enddo
do i = 1,min(a(xyz),20)
fa = binom_transp(a(xyz)-i,a(xyz))
do ipoint=1,n_points
P_new (i,xyz,ipoint) = fa * pows_a(ipoint,a(xyz)-i)
enddo
enddo
do i = 21,a(xyz)
fa = binom_func(a(xyz),a(xyz)-i)
do ipoint=1,n_points
P_new (i,xyz,ipoint) = fa * pows_a(ipoint,a(xyz)-i)
enddo
enddo
enddo !xyz
deallocate(pows_a, pows_b)
end
!--
!--
subroutine pol_modif_center(A_center, B_center, iorder, A_pol, B_pol)
BEGIN_DOC
!
!
! Transform the pol centerd on A:
! [ \sum_i ax_i (x-x_A)^i ] [ \sum_j ay_j (y-y_A)^j ] [ \sum_k az_k (z-z_A)^k ]
! [ \sum_i ax_i (x-x_A)^i ] [ \sum_j ay_j (y-y_A)^j ] [ \sum_k az_k (z-z_A)^k ]
! to a pol centered on B
! [ \sum_i bx_i (x-x_B)^i ] [ \sum_j by_j (y-y_B)^j ] [ \sum_k bz_k (z-z_B)^k ]
! [ \sum_i bx_i (x-x_B)^i ] [ \sum_j by_j (y-y_B)^j ] [ \sum_k bz_k (z-z_B)^k ]
!
END_DOC
@ -437,7 +701,7 @@ subroutine pol_modif_center(A_center, B_center, iorder, A_pol, B_pol)
do i = 1, 3
Lmax = iorder(i)
call pol_modif_center_x( A_center(i), B_center(i), Lmax, A_pol(0:Lmax, i), B_pol(0:Lmax, i) )
call pol_modif_center_x( A_center(i), B_center(i), Lmax, A_pol(0:Lmax, i), B_pol(0:Lmax, i) )
enddo
return
@ -445,14 +709,14 @@ end subroutine pol_modif_center
subroutine pol_modif_center_x(A_center, B_center, iorder, A_pol, B_pol)
subroutine pol_modif_center_x(A_center, B_center, iorder, A_pol, B_pol)
BEGIN_DOC
!
!
! Transform the pol centerd on A:
! [ \sum_i ax_i (x-x_A)^i ]
! [ \sum_i ax_i (x-x_A)^i ]
! to a pol centered on B
! [ \sum_i bx_i (x-x_B)^i ]
! [ \sum_i bx_i (x-x_B)^i ]
!
! bx_i = \sum_{j=i}^{iorder} ax_j (x_B - x_A)^(j-i) j! / [ i! (j-i)! ]
! = \sum_{j=i}^{iorder} ax_j (x_B - x_A)^(j-i) binom_func(j,i)
@ -591,7 +855,7 @@ double precision function rint_sum(n_pt_out,rho,d1)
u_inv=1.d0/dsqrt(rho)
u=rho*u_inv
rint_sum=0.5d0*u_inv*sqpi*derf(u) *d1(0)
! print *, 0, d1(0), 0.5d0*u_inv*sqpi*derf(u)
! print *, 0, d1(0), 0.5d0*u_inv*sqpi*derf(u)
endif
do i=2,n_pt_out,2

6
src/utils/map_module.f90
View File

@ -238,11 +238,11 @@ subroutine cache_map_sort(map)
iorder(i) = i
enddo
if (cache_key_kind == 2) then
call i2radix_sort(map%key,iorder,map%n_elements,-1)
call i2sort(map%key,iorder,map%n_elements,-1)
else if (cache_key_kind == 4) then
call iradix_sort(map%key,iorder,map%n_elements,-1)
call isort(map%key,iorder,map%n_elements,-1)
else if (cache_key_kind == 8) then
call i8radix_sort(map%key,iorder,map%n_elements,-1)
call i8sort(map%key,iorder,map%n_elements,-1)
endif
if (integral_kind == 4) then
call set_order(map%value,iorder,map%n_elements)

373
src/utils/qsort.c Normal file
View File

@ -0,0 +1,373 @@
/* [[file:~/qp2/src/utils/qsort.org::*Generated%20C%20file][Generated C file:1]] */
#include <stdlib.h>
#include <stdint.h>
struct int16_t_comp {
int16_t x;
int32_t i;
};
int compare_int16_t( const void * l, const void * r )
{
const int16_t * restrict _l= l;
const int16_t * restrict _r= r;
if( *_l > *_r ) return 1;
if( *_l < *_r ) return -1;
return 0;
}
void qsort_int16_t(int16_t* restrict A_in, int32_t* restrict iorder, int32_t isize) {
struct int16_t_comp* A = malloc(isize * sizeof(struct int16_t_comp));
if (A == NULL) return;
for (int i=0 ; i<isize ; ++i) {
A[i].x = A_in[i];
A[i].i = iorder[i];
}
qsort( (void*) A, (size_t) isize, sizeof(struct int16_t_comp), compare_int16_t);
for (int i=0 ; i<isize ; ++i) {
A_in[i] = A[i].x;
iorder[i] = A[i].i;
}
free(A);
}
void qsort_int16_t_noidx(int16_t* A, int32_t isize) {
qsort( (void*) A, (size_t) isize, sizeof(int16_t), compare_int16_t);
}
struct int16_t_comp_big {
int16_t x;
int64_t i;
};
int compare_int16_t_big( const void * l, const void * r )
{
const int16_t * restrict _l= l;
const int16_t * restrict _r= r;
if( *_l > *_r ) return 1;
if( *_l < *_r ) return -1;
return 0;
}
void qsort_int16_t_big(int16_t* restrict A_in, int64_t* restrict iorder, int64_t isize) {
struct int16_t_comp_big* A = malloc(isize * sizeof(struct int16_t_comp_big));
if (A == NULL) return;
for (int i=0 ; i<isize ; ++i) {
A[i].x = A_in[i];
A[i].i = iorder[i];
}
qsort( (void*) A, (size_t) isize, sizeof(struct int16_t_comp_big), compare_int16_t_big);
for (int i=0 ; i<isize ; ++i) {
A_in[i] = A[i].x;
iorder[i] = A[i].i;
}
free(A);
}
void qsort_int16_t_noidx_big(int16_t* A, int64_t isize) {
qsort( (void*) A, (size_t) isize, sizeof(int16_t), compare_int16_t_big);
}
struct int32_t_comp {
int32_t x;
int32_t i;
};
int compare_int32_t( const void * l, const void * r )
{
const int32_t * restrict _l= l;
const int32_t * restrict _r= r;
if( *_l > *_r ) return 1;
if( *_l < *_r ) return -1;
return 0;
}
void qsort_int32_t(int32_t* restrict A_in, int32_t* restrict iorder, int32_t isize) {
struct int32_t_comp* A = malloc(isize * sizeof(struct int32_t_comp));
if (A == NULL) return;
for (int i=0 ; i<isize ; ++i) {
A[i].x = A_in[i];
A[i].i = iorder[i];
}
qsort( (void*) A, (size_t) isize, sizeof(struct int32_t_comp), compare_int32_t);
for (int i=0 ; i<isize ; ++i) {
A_in[i] = A[i].x;
iorder[i] = A[i].i;
}
free(A);
}
void qsort_int32_t_noidx(int32_t* A, int32_t isize) {
qsort( (void*) A, (size_t) isize, sizeof(int32_t), compare_int32_t);
}
struct int32_t_comp_big {
int32_t x;
int64_t i;
};
int compare_int32_t_big( const void * l, const void * r )
{
const int32_t * restrict _l= l;
const int32_t * restrict _r= r;
if( *_l > *_r ) return 1;
if( *_l < *_r ) return -1;
return 0;
}
void qsort_int32_t_big(int32_t* restrict A_in, int64_t* restrict iorder, int64_t isize) {
struct int32_t_comp_big* A = malloc(isize * sizeof(struct int32_t_comp_big));
if (A == NULL) return;
for (int i=0 ; i<isize ; ++i) {
A[i].x = A_in[i];
A[i].i = iorder[i];
}
qsort( (void*) A, (size_t) isize, sizeof(struct int32_t_comp_big), compare_int32_t_big);
for (int i=0 ; i<isize ; ++i) {
A_in[i] = A[i].x;
iorder[i] = A[i].i;
}
free(A);
}
void qsort_int32_t_noidx_big(int32_t* A, int64_t isize) {
qsort( (void*) A, (size_t) isize, sizeof(int32_t), compare_int32_t_big);
}
struct int64_t_comp {
int64_t x;
int32_t i;
};
int compare_int64_t( const void * l, const void * r )
{
const int64_t * restrict _l= l;
const int64_t * restrict _r= r;
if( *_l > *_r ) return 1;
if( *_l < *_r ) return -1;
return 0;
}
void qsort_int64_t(int64_t* restrict A_in, int32_t* restrict iorder, int32_t isize) {
struct int64_t_comp* A = malloc(isize * sizeof(struct int64_t_comp));
if (A == NULL) return;
for (int i=0 ; i<isize ; ++i) {
A[i].x = A_in[i];
A[i].i = iorder[i];
}
qsort( (void*) A, (size_t) isize, sizeof(struct int64_t_comp), compare_int64_t);
for (int i=0 ; i<isize ; ++i) {
A_in[i] = A[i].x;
iorder[i] = A[i].i;
}
free(A);
}
void qsort_int64_t_noidx(int64_t* A, int32_t isize) {
qsort( (void*) A, (size_t) isize, sizeof(int64_t), compare_int64_t);
}
struct int64_t_comp_big {
int64_t x;
int64_t i;
};
int compare_int64_t_big( const void * l, const void * r )
{
const int64_t * restrict _l= l;
const int64_t * restrict _r= r;
if( *_l > *_r ) return 1;
if( *_l < *_r ) return -1;
return 0;
}
void qsort_int64_t_big(int64_t* restrict A_in, int64_t* restrict iorder, int64_t isize) {
struct int64_t_comp_big* A = malloc(isize * sizeof(struct int64_t_comp_big));
if (A == NULL) return;
for (int i=0 ; i<isize ; ++i) {
A[i].x = A_in[i];
A[i].i = iorder[i];
}
qsort( (void*) A, (size_t) isize, sizeof(struct int64_t_comp_big), compare_int64_t_big);
for (int i=0 ; i<isize ; ++i) {
A_in[i] = A[i].x;
iorder[i] = A[i].i;
}
free(A);
}
void qsort_int64_t_noidx_big(int64_t* A, int64_t isize) {
qsort( (void*) A, (size_t) isize, sizeof(int64_t), compare_int64_t_big);
}
struct double_comp {
double x;
int32_t i;
};
int compare_double( const void * l, const void * r )
{
const double * restrict _l= l;
const double * restrict _r= r;
if( *_l > *_r ) return 1;
if( *_l < *_r ) return -1;
return 0;
}
void qsort_double(double* restrict A_in, int32_t* restrict iorder, int32_t isize) {
struct double_comp* A = malloc(isize * sizeof(struct double_comp));
if (A == NULL) return;
for (int i=0 ; i<isize ; ++i) {
A[i].x = A_in[i];
A[i].i = iorder[i];
}
qsort( (void*) A, (size_t) isize, sizeof(struct double_comp), compare_double);
for (int i=0 ; i<isize ; ++i) {
A_in[i] = A[i].x;
iorder[i] = A[i].i;
}
free(A);
}
void qsort_double_noidx(double* A, int32_t isize) {
qsort( (void*) A, (size_t) isize, sizeof(double), compare_double);
}
struct double_comp_big {
double x;
int64_t i;
};
int compare_double_big( const void * l, const void * r )
{
const double * restrict _l= l;
const double * restrict _r= r;
if( *_l > *_r ) return 1;
if( *_l < *_r ) return -1;
return 0;
}
void qsort_double_big(double* restrict A_in, int64_t* restrict iorder, int64_t isize) {
struct double_comp_big* A = malloc(isize * sizeof(struct double_comp_big));
if (A == NULL) return;
for (int i=0 ; i<isize ; ++i) {
A[i].x = A_in[i];
A[i].i = iorder[i];
}
qsort( (void*) A, (size_t) isize, sizeof(struct double_comp_big), compare_double_big);
for (int i=0 ; i<isize ; ++i) {
A_in[i] = A[i].x;
iorder[i] = A[i].i;
}
free(A);
}
void qsort_double_noidx_big(double* A, int64_t isize) {
qsort( (void*) A, (size_t) isize, sizeof(double), compare_double_big);
}
struct float_comp {
float x;
int32_t i;
};
int compare_float( const void * l, const void * r )
{
const float * restrict _l= l;
const float * restrict _r= r;
if( *_l > *_r ) return 1;
if( *_l < *_r ) return -1;
return 0;
}
void qsort_float(float* restrict A_in, int32_t* restrict iorder, int32_t isize) {
struct float_comp* A = malloc(isize * sizeof(struct float_comp));
if (A == NULL) return;
for (int i=0 ; i<isize ; ++i) {
A[i].x = A_in[i];
A[i].i = iorder[i];
}
qsort( (void*) A, (size_t) isize, sizeof(struct float_comp), compare_float);
for (int i=0 ; i<isize ; ++i) {
A_in[i] = A[i].x;
iorder[i] = A[i].i;
}
free(A);
}
void qsort_float_noidx(float* A, int32_t isize) {
qsort( (void*) A, (size_t) isize, sizeof(float), compare_float);
}
struct float_comp_big {
float x;
int64_t i;
};
int compare_float_big( const void * l, const void * r )
{
const float * restrict _l= l;
const float * restrict _r= r;
if( *_l > *_r ) return 1;
if( *_l < *_r ) return -1;
return 0;
}
void qsort_float_big(float* restrict A_in, int64_t* restrict iorder, int64_t isize) {
struct float_comp_big* A = malloc(isize * sizeof(struct float_comp_big));
if (A == NULL) return;
for (int i=0 ; i<isize ; ++i) {
A[i].x = A_in[i];
A[i].i = iorder[i];
}
qsort( (void*) A, (size_t) isize, sizeof(struct float_comp_big), compare_float_big);
for (int i=0 ; i<isize ; ++i) {
A_in[i] = A[i].x;
iorder[i] = A[i].i;
}
free(A);
}
void qsort_float_noidx_big(float* A, int64_t isize) {
qsort( (void*) A, (size_t) isize, sizeof(float), compare_float_big);
}
/* Generated C file:1 ends here */

169
src/utils/qsort.org Normal file
View File

@ -0,0 +1,169 @@
#+TITLE: Quick sort binding for Fortran
* C template
#+NAME: c_template
#+BEGIN_SRC c
struct TYPE_comp_big {
TYPE x;
int32_t i;
};
int compare_TYPE_big( const void * l, const void * r )
{
const TYPE * restrict _l= l;
const TYPE * restrict _r= r;
if( *_l > *_r ) return 1;
if( *_l < *_r ) return -1;
return 0;
}
void qsort_TYPE_big(TYPE* restrict A_in, int32_t* restrict iorder, int32_t isize) {
struct TYPE_comp_big* A = malloc(isize * sizeof(struct TYPE_comp_big));
if (A == NULL) return;
for (int i=0 ; i<isize ; ++i) {
A[i].x = A_in[i];
A[i].i = iorder[i];
}
qsort( (void*) A, (size_t) isize, sizeof(struct TYPE_comp_big), compare_TYPE_big);
for (int i=0 ; i<isize ; ++i) {
A_in[i] = A[i].x;
iorder[i] = A[i].i;
}
free(A);
}
void qsort_TYPE_noidx_big(TYPE* A, int32_t isize) {
qsort( (void*) A, (size_t) isize, sizeof(TYPE), compare_TYPE_big);
}
#+END_SRC
* Fortran template
#+NAME:f_template
#+BEGIN_SRC f90
subroutine Lsort_big_c(A, iorder, isize) bind(C, name="qsort_TYPE_big")
use iso_c_binding
integer(c_int32_t), value :: isize
integer(c_int32_t) :: iorder(isize)
real (c_TYPE) :: A(isize)
end subroutine Lsort_big_c
subroutine Lsort_noidx_big_c(A, isize) bind(C, name="qsort_TYPE_noidx_big")
use iso_c_binding
integer(c_int32_t), value :: isize
real (c_TYPE) :: A(isize)
end subroutine Lsort_noidx_big_c
#+END_SRC
#+NAME:f_template2
#+BEGIN_SRC f90
subroutine Lsort_big(A, iorder, isize)
use qsort_module
use iso_c_binding
integer(c_int32_t) :: isize
integer(c_int32_t) :: iorder(isize)
real (c_TYPE) :: A(isize)
call Lsort_big_c(A, iorder, isize)
end subroutine Lsort_big
subroutine Lsort_noidx_big(A, isize)
use iso_c_binding
use qsort_module
integer(c_int32_t) :: isize
real (c_TYPE) :: A(isize)
call Lsort_noidx_big_c(A, isize)
end subroutine Lsort_noidx_big
#+END_SRC
* Python scripts for type replacements
#+NAME: replaced
#+begin_src python :results output :noweb yes
data = """
<<c_template>>
"""
for typ in ["int16_t", "int32_t", "int64_t", "double", "float"]:
print( data.replace("TYPE", typ).replace("_big", "") )
print( data.replace("int32_t", "int64_t").replace("TYPE", typ) )
#+end_src
#+NAME: replaced_f
#+begin_src python :results output :noweb yes
data = """
<<f_template>>
"""
c1 = {
"int16_t": "i2",
"int32_t": "i",
"int64_t": "i8",
"double": "d",
"float": ""
}
c2 = {
"int16_t": "integer",
"int32_t": "integer",
"int64_t": "integer",
"double": "real",
"float": "real"
}
for typ in ["int16_t", "int32_t", "int64_t", "double", "float"]:
print( data.replace("real",c2[typ]).replace("L",c1[typ]).replace("TYPE", typ).replace("_big", "") )
print( data.replace("real",c2[typ]).replace("L",c1[typ]).replace("int32_t", "int64_t").replace("TYPE", typ) )
#+end_src
#+NAME: replaced_f2
#+begin_src python :results output :noweb yes
data = """
<<f_template2>>
"""
c1 = {
"int16_t": "i2",
"int32_t": "i",
"int64_t": "i8",
"double": "d",
"float": ""
}
c2 = {
"int16_t": "integer",
"int32_t": "integer",
"int64_t": "integer",
"double": "real",
"float": "real"
}
for typ in ["int16_t", "int32_t", "int64_t", "double", "float"]:
print( data.replace("real",c2[typ]).replace("L",c1[typ]).replace("TYPE", typ).replace("_big", "") )
print( data.replace("real",c2[typ]).replace("L",c1[typ]).replace("int32_t", "int64_t").replace("TYPE", typ) )
#+end_src
* Generated C file
#+BEGIN_SRC c :comments link :tangle qsort.c :noweb yes
#include <stdlib.h>
#include <stdint.h>
<<replaced()>>
#+END_SRC
* Generated Fortran file
#+BEGIN_SRC f90 :tangle qsort_module.f90 :noweb yes
module qsort_module
use iso_c_binding
interface
<<replaced_f()>>
end interface
end module qsort_module
<<replaced_f2()>>
#+END_SRC

347
src/utils/qsort_module.f90 Normal file
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@ -0,0 +1,347 @@
module qsort_module
use iso_c_binding
interface
subroutine i2sort_c(A, iorder, isize) bind(C, name="qsort_int16_t")
use iso_c_binding
integer(c_int32_t), value :: isize
integer(c_int32_t) :: iorder(isize)
integer (c_int16_t) :: A(isize)
end subroutine i2sort_c
subroutine i2sort_noidx_c(A, isize) bind(C, name="qsort_int16_t_noidx")
use iso_c_binding
integer(c_int32_t), value :: isize
integer (c_int16_t) :: A(isize)
end subroutine i2sort_noidx_c
subroutine i2sort_big_c(A, iorder, isize) bind(C, name="qsort_int16_t_big")
use iso_c_binding
integer(c_int64_t), value :: isize
integer(c_int64_t) :: iorder(isize)
integer (c_int16_t) :: A(isize)
end subroutine i2sort_big_c
subroutine i2sort_noidx_big_c(A, isize) bind(C, name="qsort_int16_t_noidx_big")
use iso_c_binding
integer(c_int64_t), value :: isize
integer (c_int16_t) :: A(isize)
end subroutine i2sort_noidx_big_c
subroutine isort_c(A, iorder, isize) bind(C, name="qsort_int32_t")
use iso_c_binding
integer(c_int32_t), value :: isize
integer(c_int32_t) :: iorder(isize)
integer (c_int32_t) :: A(isize)
end subroutine isort_c
subroutine isort_noidx_c(A, isize) bind(C, name="qsort_int32_t_noidx")
use iso_c_binding
integer(c_int32_t), value :: isize
integer (c_int32_t) :: A(isize)
end subroutine isort_noidx_c
subroutine isort_big_c(A, iorder, isize) bind(C, name="qsort_int32_t_big")
use iso_c_binding
integer(c_int64_t), value :: isize
integer(c_int64_t) :: iorder(isize)
integer (c_int32_t) :: A(isize)
end subroutine isort_big_c
subroutine isort_noidx_big_c(A, isize) bind(C, name="qsort_int32_t_noidx_big")
use iso_c_binding
integer(c_int64_t), value :: isize
integer (c_int32_t) :: A(isize)
end subroutine isort_noidx_big_c
subroutine i8sort_c(A, iorder, isize) bind(C, name="qsort_int64_t")
use iso_c_binding
integer(c_int32_t), value :: isize
integer(c_int32_t) :: iorder(isize)
integer (c_int64_t) :: A(isize)
end subroutine i8sort_c
subroutine i8sort_noidx_c(A, isize) bind(C, name="qsort_int64_t_noidx")
use iso_c_binding
integer(c_int32_t), value :: isize
integer (c_int64_t) :: A(isize)
end subroutine i8sort_noidx_c
subroutine i8sort_big_c(A, iorder, isize) bind(C, name="qsort_int64_t_big")
use iso_c_binding
integer(c_int64_t), value :: isize
integer(c_int64_t) :: iorder(isize)
integer (c_int64_t) :: A(isize)
end subroutine i8sort_big_c
subroutine i8sort_noidx_big_c(A, isize) bind(C, name="qsort_int64_t_noidx_big")
use iso_c_binding
integer(c_int64_t), value :: isize
integer (c_int64_t) :: A(isize)
end subroutine i8sort_noidx_big_c
subroutine dsort_c(A, iorder, isize) bind(C, name="qsort_double")
use iso_c_binding
integer(c_int32_t), value :: isize
integer(c_int32_t) :: iorder(isize)
real (c_double) :: A(isize)
end subroutine dsort_c
subroutine dsort_noidx_c(A, isize) bind(C, name="qsort_double_noidx")
use iso_c_binding
integer(c_int32_t), value :: isize
real (c_double) :: A(isize)
end subroutine dsort_noidx_c
subroutine dsort_big_c(A, iorder, isize) bind(C, name="qsort_double_big")
use iso_c_binding
integer(c_int64_t), value :: isize
integer(c_int64_t) :: iorder(isize)
real (c_double) :: A(isize)
end subroutine dsort_big_c
subroutine dsort_noidx_big_c(A, isize) bind(C, name="qsort_double_noidx_big")
use iso_c_binding
integer(c_int64_t), value :: isize
real (c_double) :: A(isize)
end subroutine dsort_noidx_big_c
subroutine sort_c(A, iorder, isize) bind(C, name="qsort_float")
use iso_c_binding
integer(c_int32_t), value :: isize
integer(c_int32_t) :: iorder(isize)
real (c_float) :: A(isize)
end subroutine sort_c
subroutine sort_noidx_c(A, isize) bind(C, name="qsort_float_noidx")
use iso_c_binding
integer(c_int32_t), value :: isize
real (c_float) :: A(isize)
end subroutine sort_noidx_c
subroutine sort_big_c(A, iorder, isize) bind(C, name="qsort_float_big")
use iso_c_binding
integer(c_int64_t), value :: isize
integer(c_int64_t) :: iorder(isize)
real (c_float) :: A(isize)
end subroutine sort_big_c
subroutine sort_noidx_big_c(A, isize) bind(C, name="qsort_float_noidx_big")
use iso_c_binding
integer(c_int64_t), value :: isize
real (c_float) :: A(isize)
end subroutine sort_noidx_big_c
end interface
end module qsort_module
subroutine i2sort(A, iorder, isize)
use qsort_module
use iso_c_binding
integer(c_int32_t) :: isize
integer(c_int32_t) :: iorder(isize)
integer (c_int16_t) :: A(isize)
call i2sort_c(A, iorder, isize)
end subroutine i2sort
subroutine i2sort_noidx(A, isize)
use iso_c_binding
use qsort_module
integer(c_int32_t) :: isize
integer (c_int16_t) :: A(isize)
call i2sort_noidx_c(A, isize)
end subroutine i2sort_noidx
subroutine i2sort_big(A, iorder, isize)
use qsort_module
use iso_c_binding
integer(c_int64_t) :: isize
integer(c_int64_t) :: iorder(isize)
integer (c_int16_t) :: A(isize)
call i2sort_big_c(A, iorder, isize)
end subroutine i2sort_big
subroutine i2sort_noidx_big(A, isize)
use iso_c_binding
use qsort_module
integer(c_int64_t) :: isize
integer (c_int16_t) :: A(isize)
call i2sort_noidx_big_c(A, isize)
end subroutine i2sort_noidx_big
subroutine isort(A, iorder, isize)
use qsort_module
use iso_c_binding
integer(c_int32_t) :: isize
integer(c_int32_t) :: iorder(isize)
integer (c_int32_t) :: A(isize)
call isort_c(A, iorder, isize)
end subroutine isort
subroutine isort_noidx(A, isize)
use iso_c_binding
use qsort_module
integer(c_int32_t) :: isize
integer (c_int32_t) :: A(isize)
call isort_noidx_c(A, isize)
end subroutine isort_noidx
subroutine isort_big(A, iorder, isize)
use qsort_module
use iso_c_binding
integer(c_int64_t) :: isize
integer(c_int64_t) :: iorder(isize)
integer (c_int32_t) :: A(isize)
call isort_big_c(A, iorder, isize)
end subroutine isort_big
subroutine isort_noidx_big(A, isize)
use iso_c_binding
use qsort_module
integer(c_int64_t) :: isize
integer (c_int32_t) :: A(isize)
call isort_noidx_big_c(A, isize)
end subroutine isort_noidx_big
subroutine i8sort(A, iorder, isize)
use qsort_module
use iso_c_binding
integer(c_int32_t) :: isize
integer(c_int32_t) :: iorder(isize)
integer (c_int64_t) :: A(isize)
call i8sort_c(A, iorder, isize)
end subroutine i8sort
subroutine i8sort_noidx(A, isize)
use iso_c_binding
use qsort_module
integer(c_int32_t) :: isize
integer (c_int64_t) :: A(isize)
call i8sort_noidx_c(A, isize)
end subroutine i8sort_noidx
subroutine i8sort_big(A, iorder, isize)
use qsort_module
use iso_c_binding
integer(c_int64_t) :: isize
integer(c_int64_t) :: iorder(isize)
integer (c_int64_t) :: A(isize)
call i8sort_big_c(A, iorder, isize)
end subroutine i8sort_big
subroutine i8sort_noidx_big(A, isize)
use iso_c_binding
use qsort_module
integer(c_int64_t) :: isize
integer (c_int64_t) :: A(isize)
call i8sort_noidx_big_c(A, isize)
end subroutine i8sort_noidx_big
subroutine dsort(A, iorder, isize)
use qsort_module
use iso_c_binding
integer(c_int32_t) :: isize
integer(c_int32_t) :: iorder(isize)
real (c_double) :: A(isize)
call dsort_c(A, iorder, isize)
end subroutine dsort
subroutine dsort_noidx(A, isize)
use iso_c_binding
use qsort_module
integer(c_int32_t) :: isize
real (c_double) :: A(isize)
call dsort_noidx_c(A, isize)
end subroutine dsort_noidx
subroutine dsort_big(A, iorder, isize)
use qsort_module
use iso_c_binding
integer(c_int64_t) :: isize
integer(c_int64_t) :: iorder(isize)
real (c_double) :: A(isize)
call dsort_big_c(A, iorder, isize)
end subroutine dsort_big
subroutine dsort_noidx_big(A, isize)
use iso_c_binding
use qsort_module
integer(c_int64_t) :: isize
real (c_double) :: A(isize)
call dsort_noidx_big_c(A, isize)
end subroutine dsort_noidx_big
subroutine sort(A, iorder, isize)
use qsort_module
use iso_c_binding
integer(c_int32_t) :: isize
integer(c_int32_t) :: iorder(isize)
real (c_float) :: A(isize)
call sort_c(A, iorder, isize)
end subroutine sort
subroutine sort_noidx(A, isize)
use iso_c_binding
use qsort_module
integer(c_int32_t) :: isize
real (c_float) :: A(isize)
call sort_noidx_c(A, isize)
end subroutine sort_noidx
subroutine sort_big(A, iorder, isize)
use qsort_module
use iso_c_binding
integer(c_int64_t) :: isize
integer(c_int64_t) :: iorder(isize)
real (c_float) :: A(isize)
call sort_big_c(A, iorder, isize)
end subroutine sort_big
subroutine sort_noidx_big(A, isize)
use iso_c_binding
use qsort_module
integer(c_int64_t) :: isize
real (c_float) :: A(isize)
call sort_noidx_big_c(A, isize)
end subroutine sort_noidx_big

693
src/utils/sort.irp.f
View File

@ -1,222 +1,4 @@
BEGIN_TEMPLATE
subroutine insertion_$Xsort (x,iorder,isize)
implicit none
BEGIN_DOC
! Sort array x(isize) using the insertion sort algorithm.
! iorder in input should be (1,2,3,...,isize), and in output
! contains the new order of the elements.
END_DOC
integer,intent(in) :: isize
$type,intent(inout) :: x(isize)
integer,intent(inout) :: iorder(isize)
$type :: xtmp
integer :: i, i0, j, jmax
do i=2,isize
xtmp = x(i)
i0 = iorder(i)
j=i-1
do while (j>0)
if ((x(j) <= xtmp)) exit
x(j+1) = x(j)
iorder(j+1) = iorder(j)
j=j-1
enddo
x(j+1) = xtmp
iorder(j+1) = i0
enddo
end subroutine insertion_$Xsort
subroutine quick_$Xsort(x, iorder, isize)
implicit none
BEGIN_DOC
! Sort array x(isize) using the quicksort algorithm.
! iorder in input should be (1,2,3,...,isize), and in output
! contains the new order of the elements.
END_DOC
integer,intent(in) :: isize
$type,intent(inout) :: x(isize)
integer,intent(inout) :: iorder(isize)
integer, external :: omp_get_num_threads
call rec_$X_quicksort(x,iorder,isize,1,isize,nproc)
end
recursive subroutine rec_$X_quicksort(x, iorder, isize, first, last, level)
implicit none
integer, intent(in) :: isize, first, last, level
integer,intent(inout) :: iorder(isize)
$type, intent(inout) :: x(isize)
$type :: c, tmp
integer :: itmp
integer :: i, j
if(isize<2)return
c = x( shiftr(first+last,1) )
i = first
j = last
do
do while (x(i) < c)
i=i+1
end do
do while (c < x(j))
j=j-1
end do
if (i >= j) exit
tmp = x(i)
x(i) = x(j)
x(j) = tmp
itmp = iorder(i)
iorder(i) = iorder(j)
iorder(j) = itmp
i=i+1
j=j-1
enddo
if ( ((i-first <= 10000).and.(last-j <= 10000)).or.(level<=0) ) then
if (first < i-1) then
call rec_$X_quicksort(x, iorder, isize, first, i-1,level/2)
endif
if (j+1 < last) then
call rec_$X_quicksort(x, iorder, isize, j+1, last,level/2)
endif
else
if (first < i-1) then
call rec_$X_quicksort(x, iorder, isize, first, i-1,level/2)
endif
if (j+1 < last) then
call rec_$X_quicksort(x, iorder, isize, j+1, last,level/2)
endif
endif
end
subroutine heap_$Xsort(x,iorder,isize)
implicit none
BEGIN_DOC
! Sort array x(isize) using the heap sort algorithm.
! iorder in input should be (1,2,3,...,isize), and in output
! contains the new order of the elements.
END_DOC
integer,intent(in) :: isize
$type,intent(inout) :: x(isize)
integer,intent(inout) :: iorder(isize)
integer :: i, k, j, l, i0
$type :: xtemp
l = isize/2+1
k = isize
do while (.True.)
if (l>1) then
l=l-1
xtemp = x(l)
i0 = iorder(l)
else
xtemp = x(k)
i0 = iorder(k)
x(k) = x(1)
iorder(k) = iorder(1)
k = k-1
if (k == 1) then
x(1) = xtemp
iorder(1) = i0
exit
endif
endif
i=l
j = shiftl(l,1)
do while (j<k)
if ( x(j) < x(j+1) ) then
j=j+1
endif
if (xtemp < x(j)) then
x(i) = x(j)
iorder(i) = iorder(j)
i = j
j = shiftl(j,1)
else
j = k+1
endif
enddo
if (j==k) then
if (xtemp < x(j)) then
x(i) = x(j)
iorder(i) = iorder(j)
i = j
j = shiftl(j,1)
else
j = k+1
endif
endif
x(i) = xtemp
iorder(i) = i0
enddo
end subroutine heap_$Xsort
subroutine heap_$Xsort_big(x,iorder,isize)
implicit none
BEGIN_DOC
! Sort array x(isize) using the heap sort algorithm.
! iorder in input should be (1,2,3,...,isize), and in output
! contains the new order of the elements.
! This is a version for very large arrays where the indices need
! to be in integer*8 format
END_DOC
integer*8,intent(in) :: isize
$type,intent(inout) :: x(isize)
integer*8,intent(inout) :: iorder(isize)
integer*8 :: i, k, j, l, i0
$type :: xtemp
l = isize/2+1
k = isize
do while (.True.)
if (l>1) then
l=l-1
xtemp = x(l)
i0 = iorder(l)
else
xtemp = x(k)
i0 = iorder(k)
x(k) = x(1)
iorder(k) = iorder(1)
k = k-1
if (k == 1) then
x(1) = xtemp
iorder(1) = i0
exit
endif
endif
i=l
j = shiftl(l,1)
do while (j<k)
if ( x(j) < x(j+1) ) then
j=j+1
endif
if (xtemp < x(j)) then
x(i) = x(j)
iorder(i) = iorder(j)
i = j
j = shiftl(j,1)
else
j = k+1
endif
enddo
if (j==k) then
if (xtemp < x(j)) then
x(i) = x(j)
iorder(i) = iorder(j)
i = j
j = shiftl(j,1)
else
j = k+1
endif
endif
x(i) = xtemp
iorder(i) = i0
enddo
end subroutine heap_$Xsort_big
subroutine sorted_$Xnumber(x,isize,n)
implicit none
@ -250,220 +32,6 @@ SUBST [ X, type ]
END_TEMPLATE
!---------------------- INTEL
IRP_IF INTEL
BEGIN_TEMPLATE
subroutine $Xsort(x,iorder,isize)
use intel
implicit none
BEGIN_DOC
! Sort array x(isize).
! iorder in input should be (1,2,3,...,isize), and in output
! contains the new order of the elements.
END_DOC
integer,intent(in) :: isize
$type,intent(inout) :: x(isize)
integer,intent(inout) :: iorder(isize)
integer :: n
character, allocatable :: tmp(:)
if (isize < 2) return
call ippsSortRadixIndexGetBufferSize(isize, $ippsz, n)
allocate(tmp(n))
call ippsSortRadixIndexAscend_$ityp(x, $n, iorder, isize, tmp)
deallocate(tmp)
iorder(1:isize) = iorder(1:isize)+1
call $Xset_order(x,iorder,isize)
end
subroutine $Xsort_noidx(x,isize)
use intel
implicit none
BEGIN_DOC
! Sort array x(isize).
! iorder in input should be (1,2,3,...,isize), and in output
! contains the new order of the elements.
END_DOC
integer,intent(in) :: isize
$type,intent(inout) :: x(isize)
integer :: n
character, allocatable :: tmp(:)
if (isize < 2) return
call ippsSortRadixIndexGetBufferSize(isize, $ippsz, n)
allocate(tmp(n))
call ippsSortRadixAscend_$ityp_I(x, isize, tmp)
deallocate(tmp)
end
SUBST [ X, type, ityp, n, ippsz ]
; real ; 32f ; 4 ; 13 ;;
i ; integer ; 32s ; 4 ; 11 ;;
i2 ; integer*2 ; 16s ; 2 ; 7 ;;
END_TEMPLATE
BEGIN_TEMPLATE
subroutine $Xsort(x,iorder,isize)
implicit none
BEGIN_DOC
! Sort array x(isize).
! iorder in input should be (1,2,3,...,isize), and in output
! contains the new order of the elements.
END_DOC
integer,intent(in) :: isize
$type,intent(inout) :: x(isize)
integer,intent(inout) :: iorder(isize)
integer :: n
if (isize < 2) then
return
endif
! call sorted_$Xnumber(x,isize,n)
! if (isize == n) then
! return
! endif
if ( isize < 32) then
call insertion_$Xsort(x,iorder,isize)
else
! call heap_$Xsort(x,iorder,isize)
call quick_$Xsort(x,iorder,isize)
endif
end subroutine $Xsort
SUBST [ X, type ]
d ; double precision ;;
END_TEMPLATE
BEGIN_TEMPLATE
subroutine $Xsort(x,iorder,isize)
implicit none
BEGIN_DOC
! Sort array x(isize).
! iorder in input should be (1,2,3,...,isize), and in output
! contains the new order of the elements.
END_DOC
integer,intent(in) :: isize
$type,intent(inout) :: x(isize)
integer,intent(inout) :: iorder(isize)
integer :: n
if (isize < 2) then
return
endif
call sorted_$Xnumber(x,isize,n)
if (isize == n) then
return
endif
if ( isize < 32) then
call insertion_$Xsort(x,iorder,isize)
else
call $Xradix_sort(x,iorder,isize,-1)
endif
end subroutine $Xsort
SUBST [ X, type ]
i8 ; integer*8 ;;
END_TEMPLATE
!---------------------- END INTEL
IRP_ELSE
!---------------------- NON-INTEL
BEGIN_TEMPLATE
subroutine $Xsort_noidx(x,isize)
implicit none
BEGIN_DOC
! Sort array x(isize).
END_DOC
integer,intent(in) :: isize
$type,intent(inout) :: x(isize)
integer, allocatable :: iorder(:)
integer :: i
allocate(iorder(isize))
do i=1,isize
iorder(i)=i
enddo
call $Xsort(x,iorder,isize)
deallocate(iorder)
end subroutine $Xsort_noidx
SUBST [ X, type ]
; real ;;
d ; double precision ;;
i ; integer ;;
i8 ; integer*8 ;;
i2 ; integer*2 ;;
END_TEMPLATE
BEGIN_TEMPLATE
subroutine $Xsort(x,iorder,isize)
implicit none
BEGIN_DOC
! Sort array x(isize).
! iorder in input should be (1,2,3,...,isize), and in output
! contains the new order of the elements.
END_DOC
integer,intent(in) :: isize
$type,intent(inout) :: x(isize)
integer,intent(inout) :: iorder(isize)
integer :: n
if (isize < 2) then
return
endif
! call sorted_$Xnumber(x,isize,n)
! if (isize == n) then
! return
! endif
if ( isize < 32) then
call insertion_$Xsort(x,iorder,isize)
else
! call heap_$Xsort(x,iorder,isize)
call quick_$Xsort(x,iorder,isize)
endif
end subroutine $Xsort
SUBST [ X, type ]
; real ;;
d ; double precision ;;
END_TEMPLATE
BEGIN_TEMPLATE
subroutine $Xsort(x,iorder,isize)
implicit none
BEGIN_DOC
! Sort array x(isize).
! iorder in input should be (1,2,3,...,isize), and in output
! contains the new order of the elements.
END_DOC
integer,intent(in) :: isize
$type,intent(inout) :: x(isize)
integer,intent(inout) :: iorder(isize)
integer :: n
if (isize < 2) then
return
endif
call sorted_$Xnumber(x,isize,n)
if (isize == n) then
return
endif
if ( isize < 32) then
call insertion_$Xsort(x,iorder,isize)
else
call $Xradix_sort(x,iorder,isize,-1)
endif
end subroutine $Xsort
SUBST [ X, type ]
i ; integer ;;
i8 ; integer*8 ;;
i2 ; integer*2 ;;
END_TEMPLATE
IRP_ENDIF
!---------------------- END NON-INTEL
BEGIN_TEMPLATE
subroutine $Xset_order(x,iorder,isize)
@ -489,47 +57,6 @@ BEGIN_TEMPLATE
deallocate(xtmp)
end
SUBST [ X, type ]
; real ;;
d ; double precision ;;
i ; integer ;;
i8; integer*8 ;;
i2; integer*2 ;;
END_TEMPLATE
BEGIN_TEMPLATE
subroutine insertion_$Xsort_big (x,iorder,isize)
implicit none
BEGIN_DOC
! Sort array x(isize) using the insertion sort algorithm.
! iorder in input should be (1,2,3,...,isize), and in output
! contains the new order of the elements.
! This is a version for very large arrays where the indices need
! to be in integer*8 format
END_DOC
integer*8,intent(in) :: isize
$type,intent(inout) :: x(isize)
integer*8,intent(inout) :: iorder(isize)
$type :: xtmp
integer*8 :: i, i0, j, jmax
do i=2_8,isize
xtmp = x(i)
i0 = iorder(i)
j = i-1_8
do while (j>0_8)
if (x(j)<=xtmp) exit
x(j+1_8) = x(j)
iorder(j+1_8) = iorder(j)
j = j-1_8
enddo
x(j+1_8) = xtmp
iorder(j+1_8) = i0
enddo
end subroutine insertion_$Xsort_big
subroutine $Xset_order_big(x,iorder,isize)
implicit none
BEGIN_DOC
@ -563,223 +90,3 @@ SUBST [ X, type ]
END_TEMPLATE
BEGIN_TEMPLATE
recursive subroutine $Xradix_sort$big(x,iorder,isize,iradix)
implicit none
BEGIN_DOC
! Sort integer array x(isize) using the radix sort algorithm.
! iorder in input should be (1,2,3,...,isize), and in output
! contains the new order of the elements.
! iradix should be -1 in input.
END_DOC
integer*$int_type, intent(in) :: isize
integer*$int_type, intent(inout) :: iorder(isize)
integer*$type, intent(inout) :: x(isize)
integer, intent(in) :: iradix
integer :: iradix_new
integer*$type, allocatable :: x2(:), x1(:)
integer*$type :: i4 ! data type
integer*$int_type, allocatable :: iorder1(:),iorder2(:)
integer*$int_type :: i0, i1, i2, i3, i ! index type
integer*$type :: mask
integer :: err
!DIR$ ATTRIBUTES ALIGN : 128 :: iorder1,iorder2, x2, x1
if (isize < 2) then
return
endif
if (iradix == -1) then ! Sort Positive and negative
allocate(x1(isize),iorder1(isize), x2(isize),iorder2(isize),stat=err)
if (err /= 0) then
print *, irp_here, ': Unable to allocate arrays'
stop
endif
i1=1_$int_type
i2=1_$int_type
do i=1_$int_type,isize
if (x(i) < 0_$type) then
iorder1(i1) = iorder(i)
x1(i1) = -x(i)
i1 = i1+1_$int_type
else
iorder2(i2) = iorder(i)
x2(i2) = x(i)
i2 = i2+1_$int_type
endif
enddo
i1=i1-1_$int_type
i2=i2-1_$int_type
do i=1_$int_type,i2
iorder(i1+i) = iorder2(i)
x(i1+i) = x2(i)
enddo
deallocate(x2,iorder2,stat=err)
if (err /= 0) then
print *, irp_here, ': Unable to deallocate arrays x2, iorder2'
stop
endif
if (i1 > 1_$int_type) then
call $Xradix_sort$big(x1,iorder1,i1,-2)
do i=1_$int_type,i1
x(i) = -x1(1_$int_type+i1-i)
iorder(i) = iorder1(1_$int_type+i1-i)
enddo
endif
if (i2>1_$int_type) then
call $Xradix_sort$big(x(i1+1_$int_type),iorder(i1+1_$int_type),i2,-2)
endif
deallocate(x1,iorder1,stat=err)
if (err /= 0) then
print *, irp_here, ': Unable to deallocate arrays x1, iorder1'
stop
endif
return
else if (iradix == -2) then ! Positive
! Find most significant bit
i0 = 0_$int_type
i4 = maxval(x)
iradix_new = max($integer_size-1-leadz(i4),1)
mask = ibset(0_$type,iradix_new)
allocate(x1(isize),iorder1(isize), x2(isize),iorder2(isize),stat=err)
if (err /= 0) then
print *, irp_here, ': Unable to allocate arrays'
stop
endif
i1=1_$int_type
i2=1_$int_type
do i=1_$int_type,isize
if (iand(mask,x(i)) == 0_$type) then
iorder1(i1) = iorder(i)
x1(i1) = x(i)
i1 = i1+1_$int_type
else
iorder2(i2) = iorder(i)
x2(i2) = x(i)
i2 = i2+1_$int_type
endif
enddo
i1=i1-1_$int_type
i2=i2-1_$int_type
do i=1_$int_type,i1
iorder(i0+i) = iorder1(i)
x(i0+i) = x1(i)
enddo
i0 = i0+i1
i3 = i0
deallocate(x1,iorder1,stat=err)
if (err /= 0) then
print *, irp_here, ': Unable to deallocate arrays x1, iorder1'
stop
endif
do i=1_$int_type,i2
iorder(i0+i) = iorder2(i)
x(i0+i) = x2(i)
enddo
i0 = i0+i2
deallocate(x2,iorder2,stat=err)
if (err /= 0) then
print *, irp_here, ': Unable to deallocate arrays x2, iorder2'
stop
endif
if (i3>1_$int_type) then
call $Xradix_sort$big(x,iorder,i3,iradix_new-1)
endif
if (isize-i3>1_$int_type) then
call $Xradix_sort$big(x(i3+1_$int_type),iorder(i3+1_$int_type),isize-i3,iradix_new-1)
endif
return
endif
ASSERT (iradix >= 0)
if (isize < 48) then
call insertion_$Xsort$big(x,iorder,isize)
return
endif
allocate(x2(isize),iorder2(isize),stat=err)
if (err /= 0) then
print *, irp_here, ': Unable to allocate arrays x1, iorder1'
stop
endif
mask = ibset(0_$type,iradix)
i0=1_$int_type
i1=1_$int_type
do i=1_$int_type,isize
if (iand(mask,x(i)) == 0_$type) then
iorder(i0) = iorder(i)
x(i0) = x(i)
i0 = i0+1_$int_type
else
iorder2(i1) = iorder(i)
x2(i1) = x(i)
i1 = i1+1_$int_type
endif
enddo
i0=i0-1_$int_type
i1=i1-1_$int_type
do i=1_$int_type,i1
iorder(i0+i) = iorder2(i)
x(i0+i) = x2(i)
enddo
deallocate(x2,iorder2,stat=err)
if (err /= 0) then
print *, irp_here, ': Unable to allocate arrays x2, iorder2'
stop
endif
if (iradix == 0) then
return
endif
if (i1>1_$int_type) then
call $Xradix_sort$big(x(i0+1_$int_type),iorder(i0+1_$int_type),i1,iradix-1)
endif
if (i0>1) then
call $Xradix_sort$big(x,iorder,i0,iradix-1)
endif
end
SUBST [ X, type, integer_size, is_big, big, int_type ]
i ; 4 ; 32 ; .False. ; ; 4 ;;
i8 ; 8 ; 64 ; .False. ; ; 4 ;;
i2 ; 2 ; 16 ; .False. ; ; 4 ;;
i ; 4 ; 32 ; .True. ; _big ; 8 ;;
i8 ; 8 ; 64 ; .True. ; _big ; 8 ;;
END_TEMPLATE