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772 lines
26 KiB
Fortran
772 lines
26 KiB
Fortran
subroutine give_all_erf_kl_ao(integrals_ao,mu_in,C_center)
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implicit none
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BEGIN_DOC
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! Subroutine that returns all integrals over $r$ of type
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! $\frac{ \erf(\mu * | r - R_C | ) }{ | r - R_C | }$
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END_DOC
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double precision, intent(in) :: mu_in,C_center(3)
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double precision, intent(out) :: integrals_ao(ao_num,ao_num)
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double precision :: NAI_pol_mult_erf_ao
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integer :: i,j,l,k,m
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do k = 1, ao_num
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do m = 1, ao_num
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integrals_ao(m,k) = NAI_pol_mult_erf_ao(m,k,mu_in,C_center)
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enddo
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enddo
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end
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double precision function NAI_pol_mult_erf_ao(i_ao,j_ao,mu_in,C_center)
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implicit none
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BEGIN_DOC
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! Computes the following integral :
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! $\int_{-\infty}^{infty} dr \chi_i(r) \chi_j(r) \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
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END_DOC
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integer, intent(in) :: i_ao,j_ao
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double precision, intent(in) :: mu_in, C_center(3)
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integer :: i,j,num_A,num_B, power_A(3), power_B(3), n_pt_in
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double precision :: A_center(3), B_center(3),integral, alpha,beta
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double precision :: NAI_pol_mult_erf
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num_A = ao_nucl(i_ao)
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power_A(1:3)= ao_power(i_ao,1:3)
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A_center(1:3) = nucl_coord(num_A,1:3)
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num_B = ao_nucl(j_ao)
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power_B(1:3)= ao_power(j_ao,1:3)
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B_center(1:3) = nucl_coord(num_B,1:3)
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n_pt_in = n_pt_max_integrals
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NAI_pol_mult_erf_ao = 0.d0
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do i = 1, ao_prim_num(i_ao)
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alpha = ao_expo_ordered_transp(i,i_ao)
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do j = 1, ao_prim_num(j_ao)
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beta = ao_expo_ordered_transp(j,j_ao)
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integral = NAI_pol_mult_erf(A_center,B_center,power_A,power_B,alpha,beta,C_center,n_pt_in,mu_in)
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NAI_pol_mult_erf_ao += integral * ao_coef_normalized_ordered_transp(j,j_ao)*ao_coef_normalized_ordered_transp(i,i_ao)
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enddo
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enddo
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end
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double precision function NAI_pol_mult_erf(A_center, B_center, power_A, power_B, alpha, beta, C_center, n_pt_in, mu_in)
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BEGIN_DOC
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!
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! Computes the following integral :
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!
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! .. math::
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!
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! \int dr (x-A_x)^a (x-B_x)^b \exp(-\alpha (x-A_x)^2 - \beta (x-B_x)^2 )
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! \frac{\erf(\mu |r - R_C |)}{| r - R_C |}$.
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!
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END_DOC
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include 'utils/constants.include.F'
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implicit none
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integer, intent(in) :: n_pt_in
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integer, intent(in) :: power_A(3), power_B(3)
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double precision, intent(in) :: C_center(3), A_center(3), B_center(3), alpha, beta, mu_in
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integer :: i, n_pt, n_pt_out
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double precision :: P_center(3)
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double precision :: d(0:n_pt_in), coeff, dist, const, factor
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double precision :: const_factor, dist_integral
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double precision :: accu, p_inv, p, rho, p_inv_2
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double precision :: p_new
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double precision :: rint
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p = alpha + beta
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p_inv = 1.d0 / p
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p_inv_2 = 0.5d0 * p_inv
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rho = alpha * beta * p_inv
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dist = 0.d0
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dist_integral = 0.d0
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do i = 1, 3
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P_center(i) = (alpha * A_center(i) + beta * B_center(i)) * p_inv
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dist += (A_center(i) - B_center(i)) * (A_center(i) - B_center(i))
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dist_integral += (P_center(i) - C_center(i)) * (P_center(i) - C_center(i))
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enddo
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const_factor = dist * rho
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if(const_factor > 80.d0) then
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NAI_pol_mult_erf = 0.d0
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return
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endif
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p_new = mu_in / dsqrt(p + mu_in * mu_in)
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factor = dexp(-const_factor)
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coeff = dtwo_pi * factor * p_inv * p_new
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n_pt = 2 * ( (power_A(1) + power_B(1)) + (power_A(2) + power_B(2)) + (power_A(3) + power_B(3)) )
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const = p * dist_integral * p_new * p_new
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if(n_pt == 0) then
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NAI_pol_mult_erf = coeff * rint(0, const)
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return
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endif
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do i = 0, n_pt_in
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d(i) = 0.d0
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enddo
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! call give_polynomial_mult_center_one_e_erf(A_center,B_center,alpha,beta,power_A,power_B,C_center,n_pt_in,d,n_pt_out,mu_in)
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p_new = p_new * p_new
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call give_polynomial_mult_center_one_e_erf_opt(A_center, B_center, power_A, power_B, C_center, n_pt_in, d, n_pt_out, p_inv_2, p_new, P_center)
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if(n_pt_out < 0) then
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NAI_pol_mult_erf = 0.d0
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return
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endif
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! sum of integrals of type : int {t,[0,1]} exp-(rho.(P-Q)^2 * t^2) * t^i
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accu = 0.d0
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do i = 0, n_pt_out, 2
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accu += d(i) * rint(i/2, const)
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enddo
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NAI_pol_mult_erf = accu * coeff
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end function NAI_pol_mult_erf
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! ---
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double precision function NAI_pol_mult_erf_ao_with1s(i_ao, j_ao, beta, B_center, mu_in, C_center)
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BEGIN_DOC
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!
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! Computes the following integral :
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! $\int_{-\infty}^{infty} dr \chi_i(r) \chi_j(r) e^{-\beta (r - B_center)^2} \frac{\erf(\mu |r - R_C|)}{|r - R_C|}$.
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!
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END_DOC
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implicit none
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integer, intent(in) :: i_ao, j_ao
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double precision, intent(in) :: beta, B_center(3)
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double precision, intent(in) :: mu_in, C_center(3)
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integer :: i, j, power_A1(3), power_A2(3), n_pt_in
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double precision :: A1_center(3), A2_center(3), alpha1, alpha2, coef12, coef1, integral
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double precision, external :: NAI_pol_mult_erf_with1s, NAI_pol_mult_erf_ao
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ASSERT(beta .ge. 0.d0)
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if(beta .lt. 1d-10) then
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NAI_pol_mult_erf_ao_with1s = NAI_pol_mult_erf_ao(i_ao, j_ao, mu_in, C_center)
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return
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endif
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power_A1(1:3) = ao_power(i_ao,1:3)
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power_A2(1:3) = ao_power(j_ao,1:3)
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A1_center(1:3) = nucl_coord(ao_nucl(i_ao),1:3)
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A2_center(1:3) = nucl_coord(ao_nucl(j_ao),1:3)
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n_pt_in = n_pt_max_integrals
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NAI_pol_mult_erf_ao_with1s = 0.d0
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do i = 1, ao_prim_num(i_ao)
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alpha1 = ao_expo_ordered_transp (i,i_ao)
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coef1 = ao_coef_normalized_ordered_transp(i,i_ao)
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do j = 1, ao_prim_num(j_ao)
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alpha2 = ao_expo_ordered_transp(j,j_ao)
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coef12 = coef1 * ao_coef_normalized_ordered_transp(j,j_ao)
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if(dabs(coef12) .lt. 1d-14) cycle
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integral = NAI_pol_mult_erf_with1s( A1_center, A2_center, power_A1, power_A2, alpha1, alpha2 &
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, beta, B_center, C_center, n_pt_in, mu_in )
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NAI_pol_mult_erf_ao_with1s += integral * coef12
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enddo
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enddo
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end function NAI_pol_mult_erf_ao_with1s
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subroutine NAI_pol_mult_erf_with1s_v(A1_center, A2_center, power_A1, power_A2, alpha1, alpha2, beta, B_center, LD_B, C_center, LD_C, n_pt_in, mu_in, res_v, LD_resv, n_points)
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BEGIN_DOC
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!
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! Computes the following integral :
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!
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! .. math ::
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!
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! \int dx (x - A1_x)^a_1 (x - B1_x)^a_2 \exp(-\alpha_1 (x - A1_x)^2 - \alpha_2 (x - A2_x)^2)
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! \int dy (y - A1_y)^b_1 (y - B1_y)^b_2 \exp(-\alpha_1 (y - A1_y)^2 - \alpha_2 (y - A2_y)^2)
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! \int dz (x - A1_z)^c_1 (z - B1_z)^c_2 \exp(-\alpha_1 (z - A1_z)^2 - \alpha_2 (z - A2_z)^2)
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! \exp(-\beta (r - B)^2)
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! \frac{\erf(\mu |r - R_C|)}{|r - R_C|}$.
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!
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END_DOC
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include 'utils/constants.include.F'
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implicit none
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integer, intent(in) :: n_pt_in, LD_B, LD_C, LD_resv, n_points
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integer, intent(in) :: power_A1(3), power_A2(3)
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double precision, intent(in) :: A1_center(3), A2_center(3)
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double precision, intent(in) :: C_center(LD_C,3), B_center(LD_B,3)
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double precision, intent(in) :: alpha1, alpha2, beta, mu_in
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double precision, intent(out) :: res_v(LD_resv)
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integer :: i, n_pt, n_pt_out, ipoint
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double precision :: alpha12, alpha12_inv, alpha12_inv_2, rho12, A12_center(3), dist12, const_factor12
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double precision :: p, p_inv, p_inv_2, rho, P_center(3), dist, const_factor
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double precision :: dist_integral
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double precision :: d(0:n_pt_in), coeff, const, factor
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double precision :: accu
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double precision :: p_new, p_new2, coef_tmp, cons_tmp
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double precision :: rint
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res_V(1:LD_resv) = 0.d0
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! e^{-alpha1 (r - A1)^2} e^{-alpha2 (r - A2)^2} = e^{-K12} e^{-alpha12 (r - A12)^2}
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alpha12 = alpha1 + alpha2
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alpha12_inv = 1.d0 / alpha12
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alpha12_inv_2 = 0.5d0 * alpha12_inv
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rho12 = alpha1 * alpha2 * alpha12_inv
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A12_center(1) = (alpha1 * A1_center(1) + alpha2 * A2_center(1)) * alpha12_inv
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A12_center(2) = (alpha1 * A1_center(2) + alpha2 * A2_center(2)) * alpha12_inv
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A12_center(3) = (alpha1 * A1_center(3) + alpha2 * A2_center(3)) * alpha12_inv
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dist12 = (A1_center(1) - A2_center(1)) * (A1_center(1) - A2_center(1))&
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+ (A1_center(2) - A2_center(2)) * (A1_center(2) - A2_center(2))&
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+ (A1_center(3) - A2_center(3)) * (A1_center(3) - A2_center(3))
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const_factor12 = dist12 * rho12
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if(const_factor12 > 80.d0) then
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return
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endif
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! e^{-K12} e^{-alpha12 (r - A12)^2} e^{-beta (r - B)^2} = e^{-K} e^{-p (r - P)^2}
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p = alpha12 + beta
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p_inv = 1.d0 / p
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p_inv_2 = 0.5d0 * p_inv
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rho = alpha12 * beta * p_inv
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p_new = mu_in / dsqrt(p + mu_in * mu_in)
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p_new2 = p_new * p_new
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coef_tmp = dtwo_pi * p_inv * p_new
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cons_tmp = p * p_new2
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n_pt = 2 * (power_A1(1) + power_A2(1) + power_A1(2) + power_A2(2) + power_A1(3) + power_A2(3) )
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if(n_pt == 0) then
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do ipoint = 1, n_points
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dist = (A12_center(1) - B_center(ipoint,1)) * (A12_center(1) - B_center(ipoint,1))&
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+ (A12_center(2) - B_center(ipoint,2)) * (A12_center(2) - B_center(ipoint,2))&
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+ (A12_center(3) - B_center(ipoint,3)) * (A12_center(3) - B_center(ipoint,3))
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const_factor = const_factor12 + dist * rho
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if(const_factor > 80.d0) cycle
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coeff = coef_tmp * dexp(-const_factor)
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P_center(1) = (alpha12 * A12_center(1) + beta * B_center(ipoint,1)) * p_inv
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P_center(2) = (alpha12 * A12_center(2) + beta * B_center(ipoint,2)) * p_inv
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P_center(3) = (alpha12 * A12_center(3) + beta * B_center(ipoint,3)) * p_inv
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dist_integral = (P_center(1) - C_center(ipoint,1)) * (P_center(1) - C_center(ipoint,1))&
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+ (P_center(2) - C_center(ipoint,2)) * (P_center(2) - C_center(ipoint,2))&
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+ (P_center(3) - C_center(ipoint,3)) * (P_center(3) - C_center(ipoint,3))
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const = cons_tmp * dist_integral
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res_v(ipoint) = coeff * rint(0, const)
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enddo
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else
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do ipoint = 1, n_points
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dist = (A12_center(1) - B_center(ipoint,1)) * (A12_center(1) - B_center(ipoint,1))&
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+ (A12_center(2) - B_center(ipoint,2)) * (A12_center(2) - B_center(ipoint,2))&
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+ (A12_center(3) - B_center(ipoint,3)) * (A12_center(3) - B_center(ipoint,3))
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const_factor = const_factor12 + dist * rho
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if(const_factor > 80.d0) cycle
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coeff = coef_tmp * dexp(-const_factor)
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P_center(1) = (alpha12 * A12_center(1) + beta * B_center(ipoint,1)) * p_inv
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P_center(2) = (alpha12 * A12_center(2) + beta * B_center(ipoint,2)) * p_inv
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P_center(3) = (alpha12 * A12_center(3) + beta * B_center(ipoint,3)) * p_inv
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dist_integral = (P_center(1) - C_center(ipoint,1)) * (P_center(1) - C_center(ipoint,1))&
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+ (P_center(2) - C_center(ipoint,2)) * (P_center(2) - C_center(ipoint,2))&
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+ (P_center(3) - C_center(ipoint,3)) * (P_center(3) - C_center(ipoint,3))
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const = cons_tmp * dist_integral
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do i = 0, n_pt_in
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d(i) = 0.d0
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enddo
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!TODO: VECTORIZE HERE
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call give_polynomial_mult_center_one_e_erf_opt(A1_center, A2_center, power_A1, power_A2, C_center(ipoint,1:3), n_pt_in, d, n_pt_out, p_inv_2, p_new2, P_center)
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if(n_pt_out < 0) then
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cycle
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endif
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! sum of integrals of type : int {t,[0,1]} exp-(rho.(P-Q)^2 * t^2) * t^i
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accu = 0.d0
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do i = 0, n_pt_out, 2
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accu += d(i) * rint(i/2, const)
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enddo
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res_v(ipoint) = accu * coeff
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enddo
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endif
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end subroutine NAI_pol_mult_erf_with1s_v
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! ---
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subroutine give_polynomial_mult_center_one_e_erf_opt(A_center, B_center, power_A, power_B, C_center, n_pt_in, d, n_pt_out, p_inv_2, p_new, P_center)
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BEGIN_DOC
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! Returns the explicit polynomial in terms of the $t$ variable of the
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! following polynomial:
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!
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! $I_{x1}(a_x, d_x,p,q) \times I_{x1}(a_y, d_y,p,q) \times I_{x1}(a_z, d_z,p,q)$.
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END_DOC
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implicit none
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integer, intent(in) :: n_pt_in
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integer, intent(in) :: power_A(3), power_B(3)
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double precision, intent(in) :: A_center(3), B_center(3), C_center(3), p_inv_2, p_new, P_center(3)
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integer, intent(out) :: n_pt_out
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double precision, intent(out) :: d(0:n_pt_in)
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integer :: a_x, b_x, a_y, b_y, a_z, b_z
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integer :: n_pt1, n_pt2, n_pt3, dim, i
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integer :: n_pt_tmp
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double precision :: d1(0:n_pt_in)
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double precision :: d2(0:n_pt_in)
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double precision :: d3(0:n_pt_in)
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double precision :: accu
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double precision :: R1x(0:2), B01(0:2), R1xp(0:2), R2x(0:2)
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accu = 0.d0
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ASSERT (n_pt_in > 1)
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R1x(0) = (P_center(1) - A_center(1))
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R1x(1) = 0.d0
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R1x(2) = -(P_center(1) - C_center(1))* p_new
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! R1x = (P_x - A_x) - (P_x - C_x) ( t * mu/sqrt(p+mu^2) )^2
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R1xp(0) = (P_center(1) - B_center(1))
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R1xp(1) = 0.d0
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R1xp(2) =-(P_center(1) - C_center(1))* p_new
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!R1xp = (P_x - B_x) - (P_x - C_x) ( t * mu/sqrt(p+mu^2) )^2
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R2x(0) = p_inv_2
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R2x(1) = 0.d0
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R2x(2) = -p_inv_2 * p_new
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!R2x = 0.5 / p - 0.5/p ( t * mu/sqrt(p+mu^2) )^2
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do i = 0, n_pt_in
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d (i) = 0.d0
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d1(i) = 0.d0
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d2(i) = 0.d0
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d3(i) = 0.d0
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enddo
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n_pt1 = n_pt_in
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n_pt2 = n_pt_in
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n_pt3 = n_pt_in
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a_x = power_A(1)
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b_x = power_B(1)
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call I_x1_pol_mult_one_e(a_x, b_x, R1x, R1xp, R2x, d1, n_pt1, n_pt_in)
|
|
if(n_pt1<0)then
|
|
n_pt_out = -1
|
|
do i = 0,n_pt_in
|
|
d(i) = 0.d0
|
|
enddo
|
|
return
|
|
endif
|
|
|
|
R1x(0) = (P_center(2) - A_center(2))
|
|
R1x(1) = 0.d0
|
|
R1x(2) = -(P_center(2) - C_center(2))* p_new
|
|
! R1x = (P_x - A_x) - (P_x - C_x) ( t * mu/sqrt(p+mu^2) )^2
|
|
R1xp(0) = (P_center(2) - B_center(2))
|
|
R1xp(1) = 0.d0
|
|
R1xp(2) =-(P_center(2) - C_center(2))* p_new
|
|
!R1xp = (P_x - B_x) - (P_x - C_x) ( t * mu/sqrt(p+mu^2) )^2
|
|
a_y = power_A(2)
|
|
b_y = power_B(2)
|
|
call I_x1_pol_mult_one_e(a_y, b_y, R1x, R1xp, R2x, d2, n_pt2, n_pt_in)
|
|
if(n_pt2<0)then
|
|
n_pt_out = -1
|
|
do i = 0,n_pt_in
|
|
d(i) = 0.d0
|
|
enddo
|
|
return
|
|
endif
|
|
|
|
R1x(0) = (P_center(3) - A_center(3))
|
|
R1x(1) = 0.d0
|
|
R1x(2) = -(P_center(3) - C_center(3)) * p_new
|
|
! R1x = (P_x - A_x) - (P_x - C_x) ( t * mu/sqrt(p+mu^2) )^2
|
|
R1xp(0) = (P_center(3) - B_center(3))
|
|
R1xp(1) = 0.d0
|
|
R1xp(2) =-(P_center(3) - C_center(3)) * p_new
|
|
!R2x = 0.5 / p - 0.5/p ( t * mu/sqrt(p+mu^2) )^2
|
|
a_z = power_A(3)
|
|
b_z = power_B(3)
|
|
|
|
call I_x1_pol_mult_one_e(a_z, b_z, R1x, R1xp, R2x, d3, n_pt3, n_pt_in)
|
|
if(n_pt3 < 0) then
|
|
n_pt_out = -1
|
|
do i = 0,n_pt_in
|
|
d(i) = 0.d0
|
|
enddo
|
|
return
|
|
endif
|
|
|
|
n_pt_tmp = 0
|
|
call multiply_poly(d1, n_pt1, d2, n_pt2, d, n_pt_tmp)
|
|
do i = 0, n_pt_tmp
|
|
d1(i) = 0.d0
|
|
enddo
|
|
n_pt_out = 0
|
|
call multiply_poly(d, n_pt_tmp, d3, n_pt3, d1, n_pt_out)
|
|
do i = 0, n_pt_out
|
|
d(i) = d1(i)
|
|
enddo
|
|
|
|
end subroutine give_polynomial_mult_center_one_e_erf_opt
|
|
|
|
! ---
|
|
subroutine NAI_pol_mult_erf_v(A_center, B_center, power_A, power_B, alpha, beta, C_center, LD_C, n_pt_in, mu_in, res_v, LD_resv, n_points)
|
|
|
|
BEGIN_DOC
|
|
!
|
|
! Computes the following integral :
|
|
!
|
|
! .. math::
|
|
!
|
|
! \int dr (x-A_x)^a (x-B_x)^b \exp(-\alpha (x-A_x)^2 - \beta (x-B_x)^2 )
|
|
! \frac{\erf(\mu |r - R_C |)}{| r - R_C |}$.
|
|
!
|
|
END_DOC
|
|
|
|
include 'utils/constants.include.F'
|
|
|
|
implicit none
|
|
|
|
integer, intent(in) :: n_pt_in, n_points, LD_C, LD_resv
|
|
integer, intent(in) :: power_A(3), power_B(3)
|
|
double precision, intent(in) :: A_center(3), B_center(3), alpha, beta, mu_in
|
|
double precision, intent(in) :: C_center(LD_C,3)
|
|
double precision, intent(out) :: res_v(LD_resv)
|
|
|
|
integer :: i, n_pt, n_pt_out, ipoint
|
|
double precision :: P_center(3)
|
|
double precision :: d(0:n_pt_in), coeff, dist, const, factor
|
|
double precision :: const_factor, dist_integral
|
|
double precision :: accu, p_inv, p, rho, p_inv_2
|
|
double precision :: p_new, p_new2, coef_tmp
|
|
|
|
double precision :: rint
|
|
|
|
res_V(1:LD_resv) = 0.d0
|
|
|
|
p = alpha + beta
|
|
p_inv = 1.d0 / p
|
|
p_inv_2 = 0.5d0 * p_inv
|
|
rho = alpha * beta * p_inv
|
|
p_new = mu_in / dsqrt(p + mu_in * mu_in)
|
|
p_new2 = p_new * p_new
|
|
coef_tmp = p * p_new2
|
|
|
|
dist = 0.d0
|
|
do i = 1, 3
|
|
P_center(i) = (alpha * A_center(i) + beta * B_center(i)) * p_inv
|
|
dist += (A_center(i) - B_center(i)) * (A_center(i) - B_center(i))
|
|
enddo
|
|
|
|
const_factor = dist * rho
|
|
if(const_factor > 80.d0) then
|
|
return
|
|
endif
|
|
factor = dexp(-const_factor)
|
|
coeff = dtwo_pi * factor * p_inv * p_new
|
|
|
|
n_pt = 2 * ( power_A(1) + power_B(1) + power_A(2) + power_B(2) + power_A(3) + power_B(3) )
|
|
|
|
if(n_pt == 0) then
|
|
|
|
do ipoint = 1, n_points
|
|
dist_integral = 0.d0
|
|
do i = 1, 3
|
|
dist_integral += (P_center(i) - C_center(ipoint,i)) * (P_center(i) - C_center(ipoint,i))
|
|
enddo
|
|
const = coef_tmp * dist_integral
|
|
|
|
res_v(ipoint) = coeff * rint(0, const)
|
|
enddo
|
|
|
|
else
|
|
|
|
do ipoint = 1, n_points
|
|
dist_integral = 0.d0
|
|
do i = 1, 3
|
|
dist_integral += (P_center(i) - C_center(ipoint,i)) * (P_center(i) - C_center(ipoint,i))
|
|
enddo
|
|
const = coef_tmp * dist_integral
|
|
|
|
do i = 0, n_pt_in
|
|
d(i) = 0.d0
|
|
enddo
|
|
call give_polynomial_mult_center_one_e_erf_opt(A_center, B_center, power_A, power_B, C_center(ipoint,1:3), n_pt_in, d, n_pt_out, p_inv_2, p_new2, P_center)
|
|
|
|
if(n_pt_out < 0) then
|
|
res_v(ipoint) = 0.d0
|
|
cycle
|
|
endif
|
|
|
|
! sum of integrals of type : int {t,[0,1]} exp-(rho.(P-Q)^2 * t^2) * t^i
|
|
accu = 0.d0
|
|
do i = 0, n_pt_out, 2
|
|
accu += d(i) * rint(i/2, const)
|
|
enddo
|
|
|
|
res_v(ipoint) = accu * coeff
|
|
enddo
|
|
|
|
endif
|
|
|
|
end subroutine NAI_pol_mult_erf_v
|
|
|
|
|
|
subroutine give_polynomial_mult_center_one_e_erf(A_center,B_center,alpha,beta,power_A,power_B,C_center,n_pt_in,d,n_pt_out,mu_in)
|
|
|
|
BEGIN_DOC
|
|
! Returns the explicit polynomial in terms of the $t$ variable of the
|
|
! following polynomial:
|
|
!
|
|
! $I_{x1}(a_x, d_x,p,q) \times I_{x1}(a_y, d_y,p,q) \times I_{x1}(a_z, d_z,p,q)$.
|
|
END_DOC
|
|
|
|
implicit none
|
|
integer, intent(in) :: n_pt_in
|
|
integer,intent(out) :: n_pt_out
|
|
double precision, intent(in) :: A_center(3), B_center(3),C_center(3)
|
|
double precision, intent(in) :: alpha,beta,mu_in
|
|
integer, intent(in) :: power_A(3), power_B(3)
|
|
integer :: a_x,b_x,a_y,b_y,a_z,b_z
|
|
double precision :: d(0:n_pt_in)
|
|
double precision :: d1(0:n_pt_in)
|
|
double precision :: d2(0:n_pt_in)
|
|
double precision :: d3(0:n_pt_in)
|
|
double precision :: accu, pq_inv, p10_1, p10_2, p01_1, p01_2
|
|
double precision :: p,P_center(3),rho,p_inv,p_inv_2
|
|
accu = 0.d0
|
|
ASSERT (n_pt_in > 1)
|
|
p = alpha+beta
|
|
p_inv = 1.d0/p
|
|
p_inv_2 = 0.5d0/p
|
|
do i =1, 3
|
|
P_center(i) = (alpha * A_center(i) + beta * B_center(i)) * p_inv
|
|
enddo
|
|
|
|
double precision :: R1x(0:2), B01(0:2), R1xp(0:2),R2x(0:2)
|
|
R1x(0) = (P_center(1) - A_center(1))
|
|
R1x(1) = 0.d0
|
|
R1x(2) = -(P_center(1) - C_center(1))* mu_in**2 / (p+mu_in*mu_in)
|
|
! R1x = (P_x - A_x) - (P_x - C_x) ( t * mu/sqrt(p+mu^2) )^2
|
|
R1xp(0) = (P_center(1) - B_center(1))
|
|
R1xp(1) = 0.d0
|
|
R1xp(2) =-(P_center(1) - C_center(1))* mu_in**2 / (p+mu_in*mu_in)
|
|
!R1xp = (P_x - B_x) - (P_x - C_x) ( t * mu/sqrt(p+mu^2) )^2
|
|
R2x(0) = p_inv_2
|
|
R2x(1) = 0.d0
|
|
R2x(2) = -p_inv_2* mu_in**2 / (p+mu_in*mu_in)
|
|
!R2x = 0.5 / p - 0.5/p ( t * mu/sqrt(p+mu^2) )^2
|
|
do i = 0,n_pt_in
|
|
d(i) = 0.d0
|
|
enddo
|
|
do i = 0,n_pt_in
|
|
d1(i) = 0.d0
|
|
enddo
|
|
do i = 0,n_pt_in
|
|
d2(i) = 0.d0
|
|
enddo
|
|
do i = 0,n_pt_in
|
|
d3(i) = 0.d0
|
|
enddo
|
|
integer :: n_pt1,n_pt2,n_pt3,dim,i
|
|
n_pt1 = n_pt_in
|
|
n_pt2 = n_pt_in
|
|
n_pt3 = n_pt_in
|
|
a_x = power_A(1)
|
|
b_x = power_B(1)
|
|
call I_x1_pol_mult_one_e(a_x,b_x,R1x,R1xp,R2x,d1,n_pt1,n_pt_in)
|
|
! print*,'passed the first I_x1'
|
|
if(n_pt1<0)then
|
|
n_pt_out = -1
|
|
do i = 0,n_pt_in
|
|
d(i) = 0.d0
|
|
enddo
|
|
return
|
|
endif
|
|
|
|
R1x(0) = (P_center(2) - A_center(2))
|
|
R1x(1) = 0.d0
|
|
R1x(2) = -(P_center(2) - C_center(2))* mu_in**2 / (p+mu_in*mu_in)
|
|
! R1x = (P_x - A_x) - (P_x - C_x) ( t * mu/sqrt(p+mu^2) )^2
|
|
R1xp(0) = (P_center(2) - B_center(2))
|
|
R1xp(1) = 0.d0
|
|
R1xp(2) =-(P_center(2) - C_center(2))* mu_in**2 / (p+mu_in*mu_in)
|
|
!R1xp = (P_x - B_x) - (P_x - C_x) ( t * mu/sqrt(p+mu^2) )^2
|
|
a_y = power_A(2)
|
|
b_y = power_B(2)
|
|
call I_x1_pol_mult_one_e(a_y,b_y,R1x,R1xp,R2x,d2,n_pt2,n_pt_in)
|
|
! print*,'passed the second I_x1'
|
|
if(n_pt2<0)then
|
|
n_pt_out = -1
|
|
do i = 0,n_pt_in
|
|
d(i) = 0.d0
|
|
enddo
|
|
return
|
|
endif
|
|
|
|
|
|
R1x(0) = (P_center(3) - A_center(3))
|
|
R1x(1) = 0.d0
|
|
R1x(2) = -(P_center(3) - C_center(3))* mu_in**2 / (p+mu_in*mu_in)
|
|
! R1x = (P_x - A_x) - (P_x - C_x) ( t * mu/sqrt(p+mu^2) )^2
|
|
R1xp(0) = (P_center(3) - B_center(3))
|
|
R1xp(1) = 0.d0
|
|
R1xp(2) =-(P_center(3) - C_center(3))* mu_in**2 / (p+mu_in*mu_in)
|
|
!R2x = 0.5 / p - 0.5/p ( t * mu/sqrt(p+mu^2) )^2
|
|
a_z = power_A(3)
|
|
b_z = power_B(3)
|
|
|
|
! print*,'a_z = ',a_z
|
|
! print*,'b_z = ',b_z
|
|
call I_x1_pol_mult_one_e(a_z,b_z,R1x,R1xp,R2x,d3,n_pt3,n_pt_in)
|
|
! print*,'passed the third I_x1'
|
|
if(n_pt3<0)then
|
|
n_pt_out = -1
|
|
do i = 0,n_pt_in
|
|
d(i) = 0.d0
|
|
enddo
|
|
return
|
|
endif
|
|
integer :: n_pt_tmp
|
|
n_pt_tmp = 0
|
|
call multiply_poly(d1,n_pt1,d2,n_pt2,d,n_pt_tmp)
|
|
do i = 0,n_pt_tmp
|
|
d1(i) = 0.d0
|
|
enddo
|
|
n_pt_out = 0
|
|
call multiply_poly(d ,n_pt_tmp ,d3,n_pt3,d1,n_pt_out)
|
|
do i = 0, n_pt_out
|
|
d(i) = d1(i)
|
|
enddo
|
|
|
|
end
|
|
|
|
double precision function NAI_pol_mult_erf_with1s( A1_center, A2_center, power_A1, power_A2, alpha1, alpha2 &
|
|
, beta, B_center, C_center, n_pt_in, mu_in )
|
|
|
|
BEGIN_DOC
|
|
!
|
|
! Computes the following integral :
|
|
!
|
|
! .. math::
|
|
!
|
|
! \int dx (x - A1_x)^a_1 (x - B1_x)^a_2 \exp(-\alpha_1 (x - A1_x)^2 - \alpha_2 (x - A2_x)^2)
|
|
! \int dy (y - A1_y)^b_1 (y - B1_y)^b_2 \exp(-\alpha_1 (y - A1_y)^2 - \alpha_2 (y - A2_y)^2)
|
|
! \int dz (x - A1_z)^c_1 (z - B1_z)^c_2 \exp(-\alpha_1 (z - A1_z)^2 - \alpha_2 (z - A2_z)^2)
|
|
! \exp(-\beta (r - B)^2)
|
|
! \frac{\erf(\mu |r - R_C|)}{|r - R_C|}$.
|
|
!
|
|
END_DOC
|
|
|
|
include 'utils/constants.include.F'
|
|
|
|
implicit none
|
|
integer, intent(in) :: n_pt_in
|
|
integer, intent(in) :: power_A1(3), power_A2(3)
|
|
double precision, intent(in) :: C_center(3), A1_center(3), A2_center(3), B_center(3)
|
|
double precision, intent(in) :: alpha1, alpha2, beta, mu_in
|
|
|
|
integer :: i, n_pt, n_pt_out
|
|
double precision :: alpha12, alpha12_inv, alpha12_inv_2, rho12, A12_center(3), dist12, const_factor12
|
|
double precision :: p, p_inv, p_inv_2, rho, P_center(3), dist, const_factor
|
|
double precision :: dist_integral
|
|
double precision :: d(0:n_pt_in), coeff, const, factor
|
|
double precision :: accu
|
|
double precision :: p_new
|
|
|
|
double precision :: rint
|
|
|
|
|
|
! e^{-alpha1 (r - A1)^2} e^{-alpha2 (r - A2)^2} = e^{-K12} e^{-alpha12 (r - A12)^2}
|
|
alpha12 = alpha1 + alpha2
|
|
alpha12_inv = 1.d0 / alpha12
|
|
alpha12_inv_2 = 0.5d0 * alpha12_inv
|
|
rho12 = alpha1 * alpha2 * alpha12_inv
|
|
A12_center(1) = (alpha1 * A1_center(1) + alpha2 * A2_center(1)) * alpha12_inv
|
|
A12_center(2) = (alpha1 * A1_center(2) + alpha2 * A2_center(2)) * alpha12_inv
|
|
A12_center(3) = (alpha1 * A1_center(3) + alpha2 * A2_center(3)) * alpha12_inv
|
|
dist12 = (A1_center(1) - A2_center(1)) * (A1_center(1) - A2_center(1)) &
|
|
+ (A1_center(2) - A2_center(2)) * (A1_center(2) - A2_center(2)) &
|
|
+ (A1_center(3) - A2_center(3)) * (A1_center(3) - A2_center(3))
|
|
|
|
const_factor12 = dist12 * rho12
|
|
if(const_factor12 > 80.d0) then
|
|
NAI_pol_mult_erf_with1s = 0.d0
|
|
return
|
|
endif
|
|
|
|
! ---
|
|
|
|
! e^{-K12} e^{-alpha12 (r - A12)^2} e^{-beta (r - B)^2} = e^{-K} e^{-p (r - P)^2}
|
|
p = alpha12 + beta
|
|
p_inv = 1.d0 / p
|
|
p_inv_2 = 0.5d0 * p_inv
|
|
rho = alpha12 * beta * p_inv
|
|
P_center(1) = (alpha12 * A12_center(1) + beta * B_center(1)) * p_inv
|
|
P_center(2) = (alpha12 * A12_center(2) + beta * B_center(2)) * p_inv
|
|
P_center(3) = (alpha12 * A12_center(3) + beta * B_center(3)) * p_inv
|
|
dist = (A12_center(1) - B_center(1)) * (A12_center(1) - B_center(1)) &
|
|
+ (A12_center(2) - B_center(2)) * (A12_center(2) - B_center(2)) &
|
|
+ (A12_center(3) - B_center(3)) * (A12_center(3) - B_center(3))
|
|
|
|
const_factor = const_factor12 + dist * rho
|
|
if(const_factor > 80.d0) then
|
|
NAI_pol_mult_erf_with1s = 0.d0
|
|
return
|
|
endif
|
|
|
|
dist_integral = (P_center(1) - C_center(1)) * (P_center(1) - C_center(1)) &
|
|
+ (P_center(2) - C_center(2)) * (P_center(2) - C_center(2)) &
|
|
+ (P_center(3) - C_center(3)) * (P_center(3) - C_center(3))
|
|
|
|
! ---
|
|
|
|
p_new = mu_in / dsqrt(p + mu_in * mu_in)
|
|
factor = dexp(-const_factor)
|
|
coeff = dtwo_pi * factor * p_inv * p_new
|
|
|
|
n_pt = 2 * ( (power_A1(1) + power_A2(1)) + (power_A1(2) + power_A2(2)) + (power_A1(3) + power_A2(3)) )
|
|
const = p * dist_integral * p_new * p_new
|
|
if(n_pt == 0) then
|
|
NAI_pol_mult_erf_with1s = coeff * rint(0, const)
|
|
return
|
|
endif
|
|
|
|
do i = 0, n_pt_in
|
|
d(i) = 0.d0
|
|
enddo
|
|
p_new = p_new * p_new
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call give_polynomial_mult_center_one_e_erf_opt( A1_center, A2_center, power_A1, power_A2, C_center, n_pt_in, d, n_pt_out, p_inv_2, p_new, P_center)
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if(n_pt_out < 0) then
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NAI_pol_mult_erf_with1s = 0.d0
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return
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endif
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! sum of integrals of type : int {t,[0,1]} exp-(rho.(P-Q)^2 * t^2) * t^i
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accu = 0.d0
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do i = 0, n_pt_out, 2
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accu += d(i) * rint(i/2, const)
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enddo
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NAI_pol_mult_erf_with1s = accu * coeff
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end function NAI_pol_mult_erf_with1s
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