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616 lines
17 KiB
Fortran
616 lines
17 KiB
Fortran
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subroutine give_explicit_poly_and_gaussian_x(P_new,P_center,p,fact_k,iorder,alpha,beta,a,b,A_center,B_center,dim)
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BEGIN_DOC
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! Transform the product of
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! (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)
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! into
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! fact_k (x-x_P)^iorder(1) (y-y_P)^iorder(2) (z-z_P)^iorder(3) exp(-p(r-P)^2)
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END_DOC
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implicit none
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include 'constants.include.F'
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integer, intent(in) :: dim
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integer, intent(in) :: a,b ! powers : (x-xa)**a_x = (x-A(1))**a(1)
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double precision, intent(in) :: alpha, beta ! exponents
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double precision, intent(in) :: A_center ! A center
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double precision, intent(in) :: B_center ! B center
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double precision, intent(out) :: P_center ! new center
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double precision, intent(out) :: p ! new exponent
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double precision, intent(out) :: fact_k ! constant factor
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double precision, intent(out) :: P_new(0:max_dim) ! polynomial
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integer, intent(out) :: iorder ! order of the polynomials
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double precision :: P_a(0:max_dim), P_b(0:max_dim)
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integer :: n_new,i,j
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double precision :: p_inv,ab,d_AB
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!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: P_a, P_b
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! Do the gaussian product to get the new center and the new exponent
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P_new = 0.d0
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p = alpha+beta
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p_inv = 1.d0/p
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ab = alpha * beta
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d_AB = (A_center - B_center) * (A_center - B_center)
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P_center = (alpha * A_center + beta * B_center) * p_inv
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fact_k = exp(-ab*p_inv * d_AB)
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! Recenter the polynomials P_a and P_b on x
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!DIR$ FORCEINLINE
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call recentered_poly2(P_a(0),A_center,P_center,a,P_b(0),B_center,P_center,b)
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n_new = 0
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!DIR$ FORCEINLINE
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call multiply_poly(P_a(0),a,P_b(0),b,P_new(0),n_new)
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iorder = a + b
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end
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subroutine give_explicit_poly_and_gaussian(P_new,P_center,p,fact_k,iorder,alpha,beta,a,b,A_center,B_center,dim)
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BEGIN_DOC
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! Transforms the product of
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! (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)
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! into
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! 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 )
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! * [ 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 )
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! * [ 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 )
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END_DOC
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implicit none
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include 'constants.include.F'
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integer, intent(in) :: dim
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integer, intent(in) :: a(3),b(3) ! powers : (x-xa)**a_x = (x-A(1))**a(1)
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double precision, intent(in) :: alpha, beta ! exponents
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double precision, intent(in) :: A_center(3) ! A center
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double precision, intent(in) :: B_center (3) ! B center
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double precision, intent(out) :: P_center(3) ! new center
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double precision, intent(out) :: p ! new exponent
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double precision, intent(out) :: fact_k ! constant factor
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double precision, intent(out) :: P_new(0:max_dim,3)! polynomial
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integer, intent(out) :: iorder(3) ! i_order(i) = order of the polynomials
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double precision :: P_a(0:max_dim,3), P_b(0:max_dim,3)
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integer :: n_new,i,j
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!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: P_a, P_b
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iorder(1) = 0
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iorder(2) = 0
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iorder(3) = 0
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P_new(0,1) = 0.d0
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P_new(0,2) = 0.d0
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P_new(0,3) = 0.d0
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!DIR$ FORCEINLINE
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call gaussian_product(alpha,A_center,beta,B_center,fact_k,p,P_center)
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if (fact_k < thresh) then
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fact_k = 0.d0
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return
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endif
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!DIR$ FORCEINLINE
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call recentered_poly2(P_a(0,1),A_center(1),P_center(1),a(1),P_b(0,1),B_center(1),P_center(1),b(1))
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iorder(1) = a(1) + b(1)
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do i=0,iorder(1)
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P_new(i,1) = 0.d0
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enddo
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n_new=0
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!DIR$ FORCEINLINE
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call multiply_poly(P_a(0,1),a(1),P_b(0,1),b(1),P_new(0,1),n_new)
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!DIR$ FORCEINLINE
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call recentered_poly2(P_a(0,2),A_center(2),P_center(2),a(2),P_b(0,2),B_center(2),P_center(2),b(2))
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iorder(2) = a(2) + b(2)
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do i=0,iorder(2)
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P_new(i,2) = 0.d0
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enddo
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n_new=0
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!DIR$ FORCEINLINE
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call multiply_poly(P_a(0,2),a(2),P_b(0,2),b(2),P_new(0,2),n_new)
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!DIR$ FORCEINLINE
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call recentered_poly2(P_a(0,3),A_center(3),P_center(3),a(3),P_b(0,3),B_center(3),P_center(3),b(3))
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iorder(3) = a(3) + b(3)
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do i=0,iorder(3)
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P_new(i,3) = 0.d0
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enddo
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n_new=0
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!DIR$ FORCEINLINE
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call multiply_poly(P_a(0,3),a(3),P_b(0,3),b(3),P_new(0,3),n_new)
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end
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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)
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BEGIN_DOC
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! Transforms the product of
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! (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)
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! exp(-(r-A)^2 alpha) exp(-(r-B)^2 beta) exp(-(r-Nucl_center)^2 gama
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!
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! into
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! 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 )
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! * [ 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 )
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! * [ 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 )
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END_DOC
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implicit none
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include 'constants.include.F'
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integer, intent(in) :: dim
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integer, intent(in) :: a(3),b(3) ! powers : (x-xa)**a_x = (x-A(1))**a(1)
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double precision, intent(in) :: alpha, beta, gama ! exponents
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double precision, intent(in) :: A_center(3) ! A center
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double precision, intent(in) :: B_center (3) ! B center
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double precision, intent(in) :: Nucl_center(3) ! B center
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double precision, intent(out) :: P_center(3) ! new center
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double precision, intent(out) :: p ! new exponent
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double precision, intent(out) :: fact_k ! constant factor
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double precision, intent(out) :: P_new(0:max_dim,3)! polynomial
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integer , intent(out) :: iorder(3) ! i_order(i) = order of the polynomials
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double precision :: P_center_tmp(3) ! new center
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double precision :: p_tmp ! new exponent
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double precision :: fact_k_tmp,fact_k_bis ! constant factor
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double precision :: P_new_tmp(0:max_dim,3)! polynomial
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integer :: i,j
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double precision :: binom_func
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! First you transform the two primitives into a sum of primitive with the same center P_center_tmp and gaussian exponent p_tmp
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call give_explicit_poly_and_gaussian(P_new_tmp,P_center_tmp,p_tmp,fact_k_tmp,iorder,alpha,beta,a,b,A_center,B_center,dim)
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! Then you create the new gaussian from the product of the new one per the Nuclei one
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call gaussian_product(p_tmp,P_center_tmp,gama,Nucl_center,fact_k_bis,p,P_center)
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fact_k = fact_k_bis * fact_k_tmp
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! Then you build the coefficient of the new polynom
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do i = 0, iorder(1)
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P_new(i,1) = 0.d0
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do j = i,iorder(1)
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P_new(i,1) = P_new(i,1) + P_new_tmp(j,1) * binom_func(j,j-i) * (P_center(1) - P_center_tmp(1))**(j-i)
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enddo
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enddo
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do i = 0, iorder(2)
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P_new(i,2) = 0.d0
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do j = i,iorder(2)
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P_new(i,2) = P_new(i,2) + P_new_tmp(j,2) * binom_func(j,j-i) * (P_center(2) - P_center_tmp(2))**(j-i)
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enddo
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enddo
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do i = 0, iorder(3)
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P_new(i,3) = 0.d0
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do j = i,iorder(3)
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P_new(i,3) = P_new(i,3) + P_new_tmp(j,3) * binom_func(j,j-i) * (P_center(3) - P_center_tmp(3))**(j-i)
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enddo
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enddo
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end
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subroutine gaussian_product(a,xa,b,xb,k,p,xp)
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implicit none
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BEGIN_DOC
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! Gaussian product in 1D.
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! e^{-a (x-x_A)^2} e^{-b (x-x_B)^2} = K_{ab}^x e^{-p (x-x_P)^2}
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END_DOC
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double precision, intent(in) :: a,b ! Exponents
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double precision, intent(in) :: xa(3),xb(3) ! Centers
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double precision, intent(out) :: p ! New exponent
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double precision, intent(out) :: xp(3) ! New center
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double precision, intent(out) :: k ! Constant
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double precision :: p_inv
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ASSERT (a>0.)
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ASSERT (b>0.)
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double precision :: xab(3), ab
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!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: xab
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p = a+b
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p_inv = 1.d0/(a+b)
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ab = a*b
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xab(1) = xa(1)-xb(1)
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xab(2) = xa(2)-xb(2)
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xab(3) = xa(3)-xb(3)
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ab = ab*p_inv
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k = ab*(xab(1)*xab(1)+xab(2)*xab(2)+xab(3)*xab(3))
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if (k > 40.d0) then
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k=0.d0
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return
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endif
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k = dexp(-k)
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xp(1) = (a*xa(1)+b*xb(1))*p_inv
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xp(2) = (a*xa(2)+b*xb(2))*p_inv
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xp(3) = (a*xa(3)+b*xb(3))*p_inv
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end subroutine
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subroutine gaussian_product_x(a,xa,b,xb,k,p,xp)
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implicit none
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BEGIN_DOC
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! Gaussian product in 1D.
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! e^{-a (x-x_A)^2} e^{-b (x-x_B)^2} = K_{ab}^x e^{-p (x-x_P)^2}
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END_DOC
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double precision , intent(in) :: a,b ! Exponents
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double precision , intent(in) :: xa,xb ! Centers
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double precision , intent(out) :: p ! New exponent
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double precision , intent(out) :: xp ! New center
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double precision , intent(out) :: k ! Constant
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double precision :: p_inv
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ASSERT (a>0.)
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ASSERT (b>0.)
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double precision :: xab, ab
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p = a+b
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p_inv = 1.d0/(a+b)
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ab = a*b
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xab = xa-xb
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ab = ab*p_inv
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k = ab*xab*xab
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if (k > 40.d0) then
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k=0.d0
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return
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endif
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k = exp(-k)
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xp = (a*xa+b*xb)*p_inv
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end subroutine
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subroutine multiply_poly(b,nb,c,nc,d,nd)
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implicit none
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BEGIN_DOC
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! Multiply two polynomials
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! D(t) += B(t)*C(t)
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END_DOC
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integer, intent(in) :: nb, nc
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integer, intent(out) :: nd
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double precision, intent(in) :: b(0:nb), c(0:nc)
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double precision, intent(inout) :: d(0:nb+nc)
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integer :: ndtmp
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integer :: ib, ic, id, k
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if(ior(nc,nb) >= 0) then ! True if nc>=0 and nb>=0
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continue
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else
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return
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endif
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ndtmp = nb+nc
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do ic = 0,nc
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d(ic) = d(ic) + c(ic) * b(0)
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enddo
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do ib=1,nb
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d(ib) = d(ib) + c(0) * b(ib)
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do ic = 1,nc
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d(ib+ic) = d(ib+ic) + c(ic) * b(ib)
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enddo
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enddo
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do nd = ndtmp,0,-1
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if (d(nd) == 0.d0) then
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cycle
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endif
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exit
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enddo
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end
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subroutine add_poly(b,nb,c,nc,d,nd)
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implicit none
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BEGIN_DOC
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! Add two polynomials
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! D(t) += B(t)+C(t)
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END_DOC
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integer, intent(inout) :: nb, nc
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integer, intent(out) :: nd
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double precision, intent(in) :: b(0:nb), c(0:nc)
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double precision, intent(out) :: d(0:nb+nc)
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nd = nb+nc
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integer :: ib, ic, id
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do ib=0,max(nb,nc)
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d(ib) = d(ib) + c(ib) + b(ib)
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enddo
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do while ( (d(nd) == 0.d0).and.(nd>=0) )
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nd -= 1
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if (nd < 0) then
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exit
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endif
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enddo
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end
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subroutine add_poly_multiply(b,nb,cst,d,nd)
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implicit none
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BEGIN_DOC
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! Add a polynomial multiplied by a constant
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! D(t) += cst * B(t)
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END_DOC
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integer, intent(in) :: nb
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integer, intent(inout) :: nd
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double precision, intent(in) :: b(0:nb),cst
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double precision, intent(inout) :: d(0:max(nb,nd))
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nd = max(nd,nb)
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if (nd /= -1) then
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integer :: ib, ic, id
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do ib=0,nb
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d(ib) = d(ib) + cst*b(ib)
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enddo
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do while ( d(nd) == 0.d0 )
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nd -= 1
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if (nd < 0) then
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exit
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endif
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enddo
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endif
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end
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subroutine recentered_poly2(P_new,x_A,x_P,a,P_new2,x_B,x_Q,b)
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implicit none
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BEGIN_DOC
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! Recenter two polynomials
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END_DOC
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integer, intent(in) :: a,b
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|
double precision, intent(in) :: x_A,x_P,x_B,x_Q
|
||
|
double precision, intent(out) :: P_new(0:a),P_new2(0:b)
|
||
|
double precision :: pows_a(-2:a+b+4), pows_b(-2:a+b+4)
|
||
|
double precision :: binom_func
|
||
|
integer :: i,j,k,l, minab, maxab
|
||
|
if ((a<0).or.(b<0) ) return
|
||
|
maxab = max(a,b)
|
||
|
minab = max(min(a,b),0)
|
||
|
pows_a(0) = 1.d0
|
||
|
pows_a(1) = (x_P - x_A)
|
||
|
pows_b(0) = 1.d0
|
||
|
pows_b(1) = (x_Q - x_B)
|
||
|
do i = 2,maxab
|
||
|
pows_a(i) = pows_a(i-1)*pows_a(1)
|
||
|
pows_b(i) = pows_b(i-1)*pows_b(1)
|
||
|
enddo
|
||
|
P_new (0) = pows_a(a)
|
||
|
P_new2(0) = pows_b(b)
|
||
|
do i = 1,min(minab,20)
|
||
|
P_new (i) = binom_transp(a-i,a) * pows_a(a-i)
|
||
|
P_new2(i) = binom_transp(b-i,b) * pows_b(b-i)
|
||
|
enddo
|
||
|
do i = minab+1,min(a,20)
|
||
|
P_new (i) = binom_transp(a-i,a) * pows_a(a-i)
|
||
|
enddo
|
||
|
do i = minab+1,min(b,20)
|
||
|
P_new2(i) = binom_transp(b-i,b) * pows_b(b-i)
|
||
|
enddo
|
||
|
do i = 101,a
|
||
|
P_new(i) = binom_func(a,a-i) * pows_a(a-i)
|
||
|
enddo
|
||
|
do i = 101,b
|
||
|
P_new2(i) = binom_func(b,b-i) * pows_b(b-i)
|
||
|
enddo
|
||
|
end
|
||
|
|
||
|
|
||
|
|
||
|
|
||
|
double precision function F_integral(n,p)
|
||
|
BEGIN_DOC
|
||
|
! function that calculates the following integral
|
||
|
! \int_{\-infty}^{+\infty} x^n \exp(-p x^2) dx
|
||
|
END_DOC
|
||
|
implicit none
|
||
|
integer :: n
|
||
|
double precision :: p
|
||
|
integer :: i,j
|
||
|
double precision :: accu,sqrt_p,fact_ratio,tmp,fact
|
||
|
include 'constants.include.F'
|
||
|
if(n < 0)then
|
||
|
F_integral = 0.d0
|
||
|
endif
|
||
|
if(iand(n,1).ne.0)then
|
||
|
F_integral = 0.d0
|
||
|
return
|
||
|
endif
|
||
|
sqrt_p = 1.d0/dsqrt(p)
|
||
|
if(n==0)then
|
||
|
F_integral = sqpi * sqrt_p
|
||
|
return
|
||
|
endif
|
||
|
F_integral = sqpi * 0.5d0**n * sqrt_p**(n+1) * fact(n)/fact(shiftr(n,1))
|
||
|
end
|
||
|
|
||
|
|
||
|
|
||
|
double precision function rint(n,rho)
|
||
|
implicit none
|
||
|
BEGIN_DOC
|
||
|
!.. math::
|
||
|
!
|
||
|
! \int_0^1 dx \exp(-p x^2) x^n
|
||
|
!
|
||
|
END_DOC
|
||
|
include 'constants.include.F'
|
||
|
double precision :: rho,u,rint1,v,val0,rint_large_n,u_inv
|
||
|
integer :: n,k
|
||
|
double precision :: two_rho_inv
|
||
|
|
||
|
if(n.eq.0)then
|
||
|
if(rho == 0.d0)then
|
||
|
rint=1.d0
|
||
|
else
|
||
|
u_inv=1.d0/dsqrt(rho)
|
||
|
u=rho*u_inv
|
||
|
rint=0.5d0*u_inv*sqpi*erf(u)
|
||
|
endif
|
||
|
return
|
||
|
endif
|
||
|
if(rho.lt.1.d0)then
|
||
|
rint=rint1(n,rho)
|
||
|
else
|
||
|
if(n.le.20)then
|
||
|
u_inv=1.d0/dsqrt(rho)
|
||
|
if(rho.gt.80.d0)then
|
||
|
v=0.d0
|
||
|
else
|
||
|
v=dexp(-rho)
|
||
|
endif
|
||
|
u=rho*u_inv
|
||
|
two_rho_inv = 0.5d0*u_inv*u_inv
|
||
|
val0=0.5d0*u_inv*sqpi*erf(u)
|
||
|
rint=(val0-v)*two_rho_inv
|
||
|
do k=2,n
|
||
|
rint=(rint*dfloat(k+k-1)-v)*two_rho_inv
|
||
|
enddo
|
||
|
else
|
||
|
rint=rint_large_n(n,rho)
|
||
|
endif
|
||
|
endif
|
||
|
end
|
||
|
|
||
|
|
||
|
|
||
|
double precision function rint_sum(n_pt_out,rho,d1)
|
||
|
implicit none
|
||
|
BEGIN_DOC
|
||
|
! Needed for the calculation of two-electron integrals.
|
||
|
END_DOC
|
||
|
include 'constants.include.F'
|
||
|
integer, intent(in) :: n_pt_out
|
||
|
double precision, intent(in) :: rho,d1(0:n_pt_out)
|
||
|
double precision :: u,rint1,v,val0,rint_large_n,u_inv
|
||
|
integer :: n,k,i
|
||
|
double precision :: two_rho_inv, rint_tmp, di
|
||
|
|
||
|
|
||
|
if(rho < 1.d0)then
|
||
|
|
||
|
if(rho == 0.d0)then
|
||
|
rint_sum=d1(0)
|
||
|
else
|
||
|
u_inv=1.d0/dsqrt(rho)
|
||
|
u=rho*u_inv
|
||
|
rint_sum=0.5d0*u_inv*sqpi*erf(u) *d1(0)
|
||
|
endif
|
||
|
|
||
|
do i=2,n_pt_out,2
|
||
|
n = shiftr(i,1)
|
||
|
rint_sum = rint_sum + d1(i)*rint1(n,rho)
|
||
|
enddo
|
||
|
|
||
|
else
|
||
|
|
||
|
if(rho.gt.80.d0)then
|
||
|
v=0.d0
|
||
|
else
|
||
|
v=dexp(-rho)
|
||
|
endif
|
||
|
|
||
|
u_inv=1.d0/dsqrt(rho)
|
||
|
u=rho*u_inv
|
||
|
two_rho_inv = 0.5d0*u_inv*u_inv
|
||
|
val0=0.5d0*u_inv*sqpi*erf(u)
|
||
|
rint_sum=val0*d1(0)
|
||
|
rint_tmp=(val0-v)*two_rho_inv
|
||
|
di = 3.d0
|
||
|
do i=2,min(n_pt_out,40),2
|
||
|
rint_sum = rint_sum + d1(i)*rint_tmp
|
||
|
rint_tmp = (rint_tmp*di-v)*two_rho_inv
|
||
|
di = di+2.d0
|
||
|
enddo
|
||
|
do i=42,n_pt_out,2
|
||
|
n = shiftr(i,1)
|
||
|
rint_sum = rint_sum + d1(i)*rint_large_n(n,rho)
|
||
|
enddo
|
||
|
|
||
|
endif
|
||
|
end
|
||
|
|
||
|
double precision function hermite(n,x)
|
||
|
implicit none
|
||
|
BEGIN_DOC
|
||
|
! Hermite polynomial
|
||
|
END_DOC
|
||
|
integer :: n,k
|
||
|
double precision :: h0,x,h1,h2
|
||
|
h0=1.d0
|
||
|
if(n.eq.0)then
|
||
|
hermite=h0
|
||
|
return
|
||
|
endif
|
||
|
h1=x+x
|
||
|
if(n.eq.1)then
|
||
|
hermite=h1
|
||
|
return
|
||
|
endif
|
||
|
do k=1,n-1
|
||
|
h2=(x+x)*h1-dfloat(k+k)*h0
|
||
|
h0=h1
|
||
|
h1=h2
|
||
|
enddo
|
||
|
hermite=h2
|
||
|
end
|
||
|
|
||
|
double precision function rint_large_n(n,rho)
|
||
|
implicit none
|
||
|
BEGIN_DOC
|
||
|
! Version of rint for large values of n
|
||
|
END_DOC
|
||
|
integer :: n,k,l
|
||
|
double precision :: rho,u,accu,eps,t1,t2,fact,alpha_k,rajout,hermite
|
||
|
u=dsqrt(rho)
|
||
|
accu=0.d0
|
||
|
k=0
|
||
|
eps=1.d0
|
||
|
do while (eps.gt.1.d-15)
|
||
|
t1=1.d0
|
||
|
do l=0,k
|
||
|
t1=t1*(n+n+l+1.d0)
|
||
|
enddo
|
||
|
t2=0.d0
|
||
|
do l=0,k
|
||
|
t2=t2+(-1.d0)**l/(fact(l+1)*fact(k-l))
|
||
|
enddo
|
||
|
alpha_k=t2*fact(k+1)*fact(k)*(-1.d0)**k
|
||
|
alpha_k= alpha_k/t1
|
||
|
rajout=(-1.d0)**k*u**k*hermite(k,u)*alpha_k/fact(k)
|
||
|
accu=accu+rajout
|
||
|
eps=dabs(rajout)/accu
|
||
|
k=k+1
|
||
|
enddo
|
||
|
rint_large_n=dexp(-rho)*accu
|
||
|
end
|
||
|
|
||
|
|
||
|
double precision function rint1(n,rho)
|
||
|
implicit none
|
||
|
BEGIN_DOC
|
||
|
! Standard version of rint
|
||
|
END_DOC
|
||
|
integer, intent(in) :: n
|
||
|
double precision, intent(in) :: rho
|
||
|
double precision, parameter :: eps=1.d-15
|
||
|
double precision :: rho_tmp, diff
|
||
|
integer :: k
|
||
|
rint1=inv_int(n+n+1)
|
||
|
rho_tmp = 1.d0
|
||
|
do k=1,20
|
||
|
rho_tmp = -rho_tmp*rho
|
||
|
diff=rho_tmp*fact_inv(k)*inv_int(shiftl(k+n,1)+1)
|
||
|
rint1=rint1+diff
|
||
|
if (dabs(diff) > eps) then
|
||
|
cycle
|
||
|
endif
|
||
|
return
|
||
|
enddo
|
||
|
write(*,*)'pb in rint1 k too large!'
|
||
|
stop 1
|
||
|
end
|