781 lines
19 KiB
Fortran
781 lines
19 KiB
Fortran
|
|
! ---
|
|
|
|
subroutine give_explicit_cpoly_and_cgaussian_x(P_new, P_center, p, fact_k, iorder, alpha, beta, a, b, A_center, B_center, dim)
|
|
|
|
BEGIN_DOC
|
|
! Transform the product of
|
|
! (x-x_A)^a (x-x_B)^b exp(-(r-A)^2 alpha) exp(-(r-B)^2 beta)
|
|
! into
|
|
! fact_k \sum_{i=0}^{iorder} (x-x_P)^i exp(-p(r-P)^2)
|
|
END_DOC
|
|
|
|
implicit none
|
|
include 'constants.include.F'
|
|
|
|
integer, intent(in) :: dim
|
|
integer, intent(in) :: a, b
|
|
complex*16, intent(in) :: alpha, beta, A_center, B_center
|
|
integer, intent(out) :: iorder
|
|
complex*16, intent(out) :: p, P_center, fact_k
|
|
complex*16, intent(out) :: P_new(0:max_dim)
|
|
|
|
integer :: n_new, i, j
|
|
double precision :: tmp_mod
|
|
complex*16 :: P_a(0:max_dim), P_b(0:max_dim)
|
|
complex*16 :: p_inv, ab, d_AB, tmp
|
|
|
|
!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: P_a, P_b
|
|
|
|
P_new = (0.d0, 0.d0)
|
|
|
|
! new exponent
|
|
p = alpha + beta
|
|
|
|
! new center
|
|
p_inv = (1.d0, 0.d0) / p
|
|
ab = alpha * beta
|
|
P_center = (alpha * A_center + beta * B_center) * p_inv
|
|
|
|
! get the factor
|
|
d_AB = (A_center - B_center) * (A_center - B_center)
|
|
tmp = ab * p_inv * d_AB
|
|
tmp_mod = dsqrt(REAL(tmp)*REAL(tmp) + AIMAG(tmp)*AIMAG(tmp))
|
|
if(tmp_mod .lt. 50.d0) then
|
|
fact_k = zexp(-tmp)
|
|
else
|
|
fact_k = (0.d0, 0.d0)
|
|
endif
|
|
|
|
! Recenter the polynomials P_a and P_b on P_center
|
|
!DIR$ FORCEINLINE
|
|
call recentered_cpoly2(P_a(0), A_center, P_center, a, P_b(0), B_center, P_center, b)
|
|
n_new = 0
|
|
|
|
!DIR$ FORCEINLINE
|
|
call multiply_cpoly(P_a(0), a, P_b(0), b, P_new(0), n_new)
|
|
iorder = a + b
|
|
|
|
end subroutine give_explicit_cpoly_and_cgaussian_x
|
|
|
|
! ---
|
|
|
|
subroutine give_explicit_cpoly_and_cgaussian(P_new, P_center, p, fact_k, iorder, alpha, beta, a, b, A_center, B_center, dim)
|
|
|
|
BEGIN_DOC
|
|
! Transforms the product of
|
|
! (x-x_A)^a(1) (x-x_B)^b(1) (y-y_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) :: dim, a(3), b(3)
|
|
complex*16, intent(in) :: alpha, beta, A_center(3), B_center(3)
|
|
integer, intent(out) :: iorder(3)
|
|
complex*16, intent(out) :: p, P_center(3), fact_k, P_new(0:max_dim,3)
|
|
|
|
integer :: n_new, i, j
|
|
double precision :: tmp_mod
|
|
complex*16 :: P_a(0:max_dim,3), P_b(0:max_dim,3)
|
|
!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: P_a, P_b
|
|
|
|
iorder(1) = 0
|
|
iorder(2) = 0
|
|
iorder(3) = 0
|
|
|
|
P_new(0,1) = (0.d0, 0.d0)
|
|
P_new(0,2) = (0.d0, 0.d0)
|
|
P_new(0,3) = (0.d0, 0.d0)
|
|
|
|
!DIR$ FORCEINLINE
|
|
call cgaussian_product(alpha, A_center, beta, B_center, fact_k, p, P_center)
|
|
|
|
! IF fact_k is too smal then: returns a "s" function centered in zero
|
|
! with an inifinite exponent and a zero polynom coef
|
|
tmp_mod = dsqrt(REAL(fact_k)*REAL(fact_k) + AIMAG(fact_k)*AIMAG(fact_k))
|
|
if(tmp_mod < 1d-14) then
|
|
iorder = 0
|
|
p = (1.d+14, 0.d0)
|
|
fact_k = (0.d0 , 0.d0)
|
|
P_new(0:max_dim,1:3) = (0.d0 , 0.d0)
|
|
P_center(1:3) = (0.d0 , 0.d0)
|
|
return
|
|
endif
|
|
|
|
!DIR$ FORCEINLINE
|
|
call recentered_cpoly2(P_a(0,1), A_center(1), P_center(1), a(1), P_b(0,1), B_center(1), P_center(1), b(1))
|
|
iorder(1) = a(1) + b(1)
|
|
do i = 0, iorder(1)
|
|
P_new(i,1) = 0.d0
|
|
enddo
|
|
n_new = 0
|
|
!DIR$ FORCEINLINE
|
|
call multiply_cpoly(P_a(0,1), a(1), P_b(0,1), b(1), P_new(0,1), n_new)
|
|
|
|
!DIR$ FORCEINLINE
|
|
call recentered_cpoly2(P_a(0,2), A_center(2), P_center(2), a(2), P_b(0,2), B_center(2), P_center(2), b(2))
|
|
iorder(2) = a(2) + b(2)
|
|
do i = 0, iorder(2)
|
|
P_new(i,2) = 0.d0
|
|
enddo
|
|
n_new = 0
|
|
!DIR$ FORCEINLINE
|
|
call multiply_cpoly(P_a(0,2), a(2), P_b(0,2), b(2), P_new(0,2), n_new)
|
|
|
|
!DIR$ FORCEINLINE
|
|
call recentered_cpoly2(P_a(0,3), A_center(3), P_center(3), a(3), P_b(0,3), B_center(3), P_center(3), b(3))
|
|
iorder(3) = a(3) + b(3)
|
|
do i = 0, iorder(3)
|
|
P_new(i,3) = 0.d0
|
|
enddo
|
|
n_new = 0
|
|
!DIR$ FORCEINLINE
|
|
call multiply_cpoly(P_a(0,3), a(3), P_b(0,3), b(3), P_new(0,3), n_new)
|
|
|
|
end subroutine give_explicit_cpoly_and_cgaussian
|
|
|
|
! ---
|
|
|
|
!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
|
|
! ! 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) exp(-(r-Nucl_center)^2 gama
|
|
! !
|
|
! ! 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 )
|
|
! END_DOC
|
|
! implicit none
|
|
! include 'constants.include.F'
|
|
! integer, intent(in) :: dim
|
|
! integer, intent(in) :: a(3),b(3) ! powers : (x-xa)**a_x = (x-A(1))**a(1)
|
|
! double precision, intent(in) :: alpha, beta, gama ! exponents
|
|
! double precision, intent(in) :: A_center(3) ! A center
|
|
! double precision, intent(in) :: B_center (3) ! B center
|
|
! double precision, intent(in) :: Nucl_center(3) ! B center
|
|
! double precision, intent(out) :: P_center(3) ! new center
|
|
! double precision, intent(out) :: p ! new exponent
|
|
! double precision, intent(out) :: fact_k ! constant factor
|
|
! double precision, intent(out) :: P_new(0:max_dim,3)! polynomial
|
|
! integer , intent(out) :: iorder(3) ! i_order(i) = order of the polynomials
|
|
!
|
|
! double precision :: P_center_tmp(3) ! new center
|
|
! double precision :: p_tmp ! new exponent
|
|
! double precision :: fact_k_tmp,fact_k_bis ! constant factor
|
|
! double precision :: P_new_tmp(0:max_dim,3)! polynomial
|
|
! integer :: i,j
|
|
! double precision :: binom_func
|
|
!
|
|
! ! First you transform the two primitives into a sum of primitive with the same center P_center_tmp and gaussian exponent p_tmp
|
|
! call give_explicit_cpoly_and_cgaussian(P_new_tmp,P_center_tmp,p_tmp,fact_k_tmp,iorder,alpha,beta,a,b,A_center,B_center,dim)
|
|
! ! Then you create the new gaussian from the product of the new one per the Nuclei one
|
|
! call cgaussian_product(p_tmp,P_center_tmp,gama,Nucl_center,fact_k_bis,p,P_center)
|
|
! fact_k = fact_k_bis * fact_k_tmp
|
|
!
|
|
! ! Then you build the coefficient of the new polynom
|
|
! do i = 0, iorder(1)
|
|
! P_new(i,1) = 0.d0
|
|
! do j = i,iorder(1)
|
|
! 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)
|
|
! enddo
|
|
! enddo
|
|
! do i = 0, iorder(2)
|
|
! P_new(i,2) = 0.d0
|
|
! do j = i,iorder(2)
|
|
! 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)
|
|
! enddo
|
|
! enddo
|
|
! do i = 0, iorder(3)
|
|
! P_new(i,3) = 0.d0
|
|
! do j = i,iorder(3)
|
|
! 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)
|
|
! enddo
|
|
! enddo
|
|
!
|
|
!end
|
|
|
|
! ---
|
|
|
|
subroutine cgaussian_product(a, xa, b, xb, k, p, xp)
|
|
|
|
BEGIN_DOC
|
|
! complex Gaussian product
|
|
! e^{-a (r-r_A)^2} e^{-b (r-r_B)^2} = k e^{-p (r-r_P)^2}
|
|
END_DOC
|
|
|
|
implicit none
|
|
complex*16, intent(in) :: a, b, xa(3), xb(3)
|
|
complex*16, intent(out) :: p, k, xp(3)
|
|
|
|
double precision :: tmp_mod
|
|
complex*16 :: p_inv, xab(3), ab
|
|
|
|
!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: xab
|
|
|
|
ASSERT (REAL(a) > 0.)
|
|
ASSERT (REAL(b) > 0.)
|
|
|
|
! new exponent
|
|
p = a + b
|
|
|
|
xab(1) = xa(1) - xb(1)
|
|
xab(2) = xa(2) - xb(2)
|
|
xab(3) = xa(3) - xb(3)
|
|
|
|
p_inv = (1.d0, 0.d0) / p
|
|
ab = a * b * p_inv
|
|
|
|
k = ab * (xab(1)*xab(1) + xab(2)*xab(2) + xab(3)*xab(3))
|
|
tmp_mod = dsqrt(REAL(k)*REAL(k) + AIMAG(k)*AIMAG(k))
|
|
if(tmp_mod .gt. 40.d0) then
|
|
k = (0.d0, 0.d0)
|
|
xp(1:3) = (0.d0, 0.d0)
|
|
return
|
|
endif
|
|
|
|
k = zexp(-k)
|
|
xp(1) = ( a * xa(1) + b * xb(1) ) * p_inv
|
|
xp(2) = ( a * xa(2) + b * xb(2) ) * p_inv
|
|
xp(3) = ( a * xa(3) + b * xb(3) ) * p_inv
|
|
|
|
end subroutine cgaussian_product
|
|
|
|
! ---
|
|
|
|
subroutine cgaussian_product_x(a, xa, b, xb, k, p, xp)
|
|
|
|
BEGIN_DOC
|
|
! complex Gaussian product in 1D.
|
|
! e^{-a (x-x_A)^2} e^{-b (x-x_B)^2} = K e^{-p (x-x_P)^2}
|
|
END_DOC
|
|
|
|
implicit none
|
|
complex*16, intent(in) :: a, b, xa, xb
|
|
complex*16, intent(out) :: p, k, xp
|
|
|
|
double precision :: tmp_mod
|
|
complex*16 :: p_inv
|
|
complex*16 :: xab, ab
|
|
|
|
ASSERT (REAL(a) > 0.)
|
|
ASSERT (REAL(b) > 0.)
|
|
|
|
! new center
|
|
p = a + b
|
|
|
|
xab = xa - xb
|
|
|
|
p_inv = (1.d0, 0.d0) / p
|
|
ab = a * b * p_inv
|
|
|
|
k = ab * xab*xab
|
|
tmp_mod = dsqrt(REAL(k)*REAL(k) + AIMAG(k)*AIMAG(k))
|
|
if(tmp_mod > 40.d0) then
|
|
k = (0.d0, 0.d0)
|
|
xp = (0.d0, 0.d0)
|
|
return
|
|
endif
|
|
|
|
k = zexp(-k)
|
|
xp = (a*xa + b*xb) * p_inv
|
|
|
|
end subroutine cgaussian_product_x
|
|
|
|
! ---
|
|
|
|
subroutine multiply_cpoly(b, nb, c, nc, d, nd)
|
|
|
|
BEGIN_DOC
|
|
! Multiply two complex polynomials
|
|
! D(t) += B(t) * C(t)
|
|
END_DOC
|
|
|
|
implicit none
|
|
|
|
integer, intent(in) :: nb, nc
|
|
complex*16, intent(in) :: b(0:nb), c(0:nc)
|
|
complex*16, intent(inout) :: d(0:nb+nc)
|
|
integer, intent(out) :: nd
|
|
|
|
integer :: ndtmp, ib, ic
|
|
double precision :: tmp_mod
|
|
complex*16 :: tmp
|
|
|
|
if(ior(nc, nb) >= 0) then ! True if nc>=0 and nb>=0
|
|
continue
|
|
else
|
|
return
|
|
endif
|
|
|
|
ndtmp = nb + nc
|
|
|
|
do ic = 0, nc
|
|
d(ic) = d(ic) + c(ic) * b(0)
|
|
enddo
|
|
|
|
do ib = 1, nb
|
|
d(ib) = d(ib) + c(0) * b(ib)
|
|
do ic = 1, nc
|
|
d(ib+ic) = d(ib+ic) + c(ic) * b(ib)
|
|
enddo
|
|
enddo
|
|
|
|
do nd = ndtmp, 0, -1
|
|
tmp = d(nd)
|
|
tmp_mod = dsqrt(REAL(tmp)*REAL(tmp) + AIMAG(tmp)*AIMAG(tmp))
|
|
if(tmp_mod .lt. 1.d-15) cycle
|
|
exit
|
|
enddo
|
|
|
|
end subroutine multiply_cpoly
|
|
|
|
! ---
|
|
|
|
subroutine add_cpoly(b, nb, c, nc, d, nd)
|
|
|
|
BEGIN_DOC
|
|
! Add two complex polynomials
|
|
! D(t) += B(t) + C(t)
|
|
END_DOC
|
|
|
|
implicit none
|
|
complex*16, intent(in) :: b(0:nb), c(0:nc)
|
|
integer, intent(inout) :: nb, nc
|
|
integer, intent(out) :: nd
|
|
complex*16, intent(out) :: d(0:nb+nc)
|
|
|
|
integer :: ib
|
|
double precision :: tmp_mod
|
|
complex*16 :: tmp
|
|
|
|
nd = nb + nc
|
|
do ib = 0, max(nb, nc)
|
|
d(ib) = d(ib) + c(ib) + b(ib)
|
|
enddo
|
|
|
|
tmp = d(nd)
|
|
tmp_mod = dsqrt(REAL(tmp)*REAL(tmp) + AIMAG(tmp)*AIMAG(tmp))
|
|
do while( (tmp_mod .lt. 1.d-15) .and. (nd >= 0) )
|
|
nd -= 1
|
|
tmp = d(nd)
|
|
tmp_mod = dsqrt(REAL(tmp)*REAL(tmp) + AIMAG(tmp)*AIMAG(tmp))
|
|
if(nd < 0) exit
|
|
enddo
|
|
|
|
end subroutine add_cpoly
|
|
|
|
! ---
|
|
|
|
subroutine add_cpoly_multiply(b, nb, cst, d, nd)
|
|
|
|
BEGIN_DOC
|
|
! Add a complex polynomial multiplied by a complex constant
|
|
! D(t) += cst * B(t)
|
|
END_DOC
|
|
|
|
implicit none
|
|
|
|
integer, intent(in) :: nb
|
|
complex*16, intent(in) :: b(0:nb), cst
|
|
integer, intent(inout) :: nd
|
|
complex*16, intent(inout) :: d(0:max(nb, nd))
|
|
|
|
integer :: ib
|
|
double precision :: tmp_mod
|
|
complex*16 :: tmp
|
|
|
|
nd = max(nd, nb)
|
|
if(nd /= -1) then
|
|
|
|
do ib = 0, nb
|
|
d(ib) = d(ib) + cst * b(ib)
|
|
enddo
|
|
|
|
tmp = d(nd)
|
|
tmp_mod = dsqrt(REAL(tmp)*REAL(tmp) + AIMAG(tmp)*AIMAG(tmp))
|
|
do while(tmp_mod .lt. 1.d-15)
|
|
nd -= 1
|
|
if(nd < 0) exit
|
|
tmp = d(nd)
|
|
tmp_mod = dsqrt(REAL(tmp)*REAL(tmp) + AIMAG(tmp)*AIMAG(tmp))
|
|
enddo
|
|
|
|
endif
|
|
|
|
end subroutine add_cpoly_multiply
|
|
|
|
! ---
|
|
|
|
subroutine recentered_cpoly2(P_A, x_A, x_P, a, P_B, x_B, x_Q, b)
|
|
|
|
BEGIN_DOC
|
|
!
|
|
! write two complex polynomials (x-x_A)^a (x-x_B)^b
|
|
! as P_A(x-x_P) and P_B(x-x_Q)
|
|
!
|
|
END_DOC
|
|
|
|
implicit none
|
|
|
|
integer, intent(in) :: a, b
|
|
complex*16, intent(in) :: x_A, x_P, x_B, x_Q
|
|
complex*16, intent(out) :: P_A(0:a), P_B(0:b)
|
|
|
|
integer :: i, minab, maxab
|
|
complex*16 :: pows_a(-2:a+b+4), pows_b(-2:a+b+4)
|
|
|
|
double precision :: binom_func
|
|
|
|
if((a<0) .or. (b<0)) return
|
|
|
|
maxab = max(a, b)
|
|
minab = max(min(a, b), 0)
|
|
|
|
pows_a(0) = (1.d0, 0.d0)
|
|
pows_a(1) = x_P - x_A
|
|
|
|
pows_b(0) = (1.d0, 0.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_A(0) = pows_a(a)
|
|
P_B(0) = pows_b(b)
|
|
|
|
do i = 1, min(minab, 20)
|
|
P_A(i) = binom_transp(a-i,a) * pows_a(a-i)
|
|
P_B(i) = binom_transp(b-i,b) * pows_b(b-i)
|
|
enddo
|
|
|
|
do i = minab+1, min(a, 20)
|
|
P_A(i) = binom_transp(a-i,a) * pows_a(a-i)
|
|
enddo
|
|
do i = minab+1, min(b, 20)
|
|
P_B(i) = binom_transp(b-i,b) * pows_b(b-i)
|
|
enddo
|
|
|
|
do i = 101, a
|
|
P_A(i) = binom_func(a,a-i) * pows_a(a-i)
|
|
enddo
|
|
do i = 101, b
|
|
P_B(i) = binom_func(b,b-i) * pows_b(b-i)
|
|
enddo
|
|
|
|
end subroutine recentered_cpoly2
|
|
|
|
! ---
|
|
|
|
complex*16 function Fc_integral(n, inv_sq_p)
|
|
|
|
BEGIN_DOC
|
|
! function that calculates the following integral
|
|
! \int_{\-infty}^{+\infty} x^n \exp(-p x^2) dx
|
|
! for complex valued p
|
|
END_DOC
|
|
|
|
implicit none
|
|
include 'constants.include.F'
|
|
|
|
integer, intent(in) :: n
|
|
complex*16, intent(in) :: inv_sq_p
|
|
|
|
! (n)!
|
|
double precision :: fact
|
|
|
|
if(n < 0) then
|
|
Fc_integral = (0.d0, 0.d0)
|
|
return
|
|
endif
|
|
|
|
! odd n
|
|
if(iand(n, 1) .ne. 0) then
|
|
Fc_integral = (0.d0, 0.d0)
|
|
return
|
|
endif
|
|
|
|
if(n == 0) then
|
|
Fc_integral = sqpi * inv_sq_p
|
|
return
|
|
endif
|
|
|
|
Fc_integral = sqpi * 0.5d0**n * inv_sq_p**dble(n+1) * fact(n) / fact(shiftr(n, 1))
|
|
|
|
end function Fc_integral
|
|
|
|
! ---
|
|
|
|
complex*16 function crint(n, rho)
|
|
|
|
implicit none
|
|
include 'constants.include.F'
|
|
|
|
integer, intent(in) :: n
|
|
complex*16, intent(in) :: rho
|
|
|
|
integer :: i, mmax
|
|
double precision :: rho_mod, rho_re, rho_im
|
|
double precision :: sq_rho_re, sq_rho_im
|
|
double precision :: n_tmp
|
|
complex*16 :: sq_rho, rho_inv, rho_exp
|
|
|
|
complex*16 :: crint_smallz, cpx_erf
|
|
|
|
rho_re = REAL (rho)
|
|
rho_im = AIMAG(rho)
|
|
rho_mod = dsqrt(rho_re*rho_re + rho_im*rho_im)
|
|
|
|
if(rho_mod < 10.d0) then
|
|
! small z
|
|
|
|
if(rho_mod .lt. 1.d-10) then
|
|
crint = 1.d0 / dble(n + n + 1)
|
|
else
|
|
crint = crint_smallz(n, rho)
|
|
endif
|
|
|
|
else
|
|
! large z
|
|
|
|
if(rho_mod .gt. 40.d0) then
|
|
|
|
n_tmp = dble(n) + 0.5d0
|
|
crint = 0.5d0 * gamma(n_tmp) / (rho**n_tmp)
|
|
|
|
else
|
|
|
|
! get \sqrt(rho)
|
|
sq_rho_re = sq_op5 * dsqrt(rho_re + rho_mod)
|
|
sq_rho_im = 0.5d0 * rho_im / sq_rho_re
|
|
sq_rho = sq_rho_re + (0.d0, 1.d0) * sq_rho_im
|
|
|
|
rho_exp = 0.5d0 * zexp(-rho)
|
|
rho_inv = (1.d0, 0.d0) / rho
|
|
|
|
crint = 0.5d0 * sqpi * cpx_erf(sq_rho_re, sq_rho_im) / sq_rho
|
|
mmax = n
|
|
if(mmax .gt. 0) then
|
|
do i = 0, mmax-1
|
|
crint = ((dble(i) + 0.5d0) * crint - rho_exp) * rho_inv
|
|
enddo
|
|
endif
|
|
|
|
! ***
|
|
|
|
endif
|
|
|
|
endif
|
|
|
|
! print *, n, real(rho), real(crint)
|
|
|
|
end function crint
|
|
|
|
! ---
|
|
|
|
complex*16 function crint_sum(n_pt_out, rho, d1)
|
|
|
|
implicit none
|
|
include 'constants.include.F'
|
|
|
|
integer, intent(in) :: n_pt_out
|
|
complex*16, intent(in) :: rho, d1(0:n_pt_out)
|
|
|
|
integer :: n, i, mmax
|
|
double precision :: rho_mod, rho_re, rho_im
|
|
double precision :: sq_rho_re, sq_rho_im
|
|
complex*16 :: sq_rho, F0
|
|
complex*16 :: rho_tmp, rho_inv, rho_exp
|
|
complex*16, allocatable :: Fm(:)
|
|
|
|
complex*16 :: crint_smallz, cpx_erf
|
|
|
|
rho_re = REAL (rho)
|
|
rho_im = AIMAG(rho)
|
|
rho_mod = dsqrt(rho_re*rho_re + rho_im*rho_im)
|
|
|
|
if(rho_mod < 10.d0) then
|
|
! small z
|
|
|
|
if(rho_mod .lt. 1.d-10) then
|
|
|
|
! print *, ' 111'
|
|
! print *, ' rho = ', rho
|
|
|
|
crint_sum = d1(0)
|
|
! print *, 0, 1
|
|
|
|
do i = 2, n_pt_out, 2
|
|
|
|
n = shiftr(i, 1)
|
|
crint_sum = crint_sum + d1(i) / dble(n+n+1)
|
|
|
|
! print *, n, 1.d0 / dble(n+n+1)
|
|
enddo
|
|
|
|
! ***
|
|
|
|
else
|
|
|
|
! print *, ' 222'
|
|
! print *, ' rho = ', real(rho)
|
|
! if(abs(aimag(rho)) .gt. 1d-15) then
|
|
! print *, ' complex rho', rho
|
|
! stop
|
|
! endif
|
|
|
|
crint_sum = d1(0) * crint_smallz(0, rho)
|
|
|
|
! print *, 0, real(d1(0)), real(crint_smallz(0, rho))
|
|
! if(abs(aimag(d1(0))) .gt. 1d-15) then
|
|
! print *, ' complex d1(0)', d1(0)
|
|
! stop
|
|
! endif
|
|
|
|
do i = 2, n_pt_out, 2
|
|
n = shiftr(i, 1)
|
|
crint_sum = crint_sum + d1(i) * crint_smallz(n, rho)
|
|
|
|
! print *, n, real(d1(i)), real(crint_smallz(n, rho))
|
|
! if(abs(aimag(d1(i))) .gt. 1d-15) then
|
|
! print *, ' complex d1(i)', i, d1(i)
|
|
! stop
|
|
! endif
|
|
|
|
enddo
|
|
|
|
! print *, 'sum = ', real(crint_sum)
|
|
! if(abs(aimag(crint_sum)) .gt. 1d-15) then
|
|
! print *, ' complex crint_sum', crint_sum
|
|
! stop
|
|
! endif
|
|
|
|
! ***
|
|
|
|
endif
|
|
|
|
else
|
|
! large z
|
|
|
|
if(rho_mod .gt. 40.d0) then
|
|
|
|
! print *, ' 333'
|
|
! print *, ' rho = ', rho
|
|
|
|
rho_inv = (1.d0, 0.d0) / rho
|
|
rho_tmp = 0.5d0 * sqpi * zsqrt(rho_inv)
|
|
crint_sum = rho_tmp * d1(0)
|
|
! print *, 0, rho_tmp
|
|
|
|
do i = 2, n_pt_out, 2
|
|
n = shiftr(i, 1)
|
|
rho_tmp = rho_tmp * (dble(n) + 0.5d0) * rho_inv
|
|
crint_sum = crint_sum + rho_tmp * d1(i)
|
|
! print *, n, rho_tmp
|
|
enddo
|
|
|
|
! ***
|
|
|
|
else
|
|
|
|
! print *, ' 444'
|
|
! print *, ' rho = ', rho
|
|
|
|
! get \sqrt(rho)
|
|
sq_rho_re = sq_op5 * dsqrt(rho_re + rho_mod)
|
|
sq_rho_im = 0.5d0 * rho_im / sq_rho_re
|
|
sq_rho = sq_rho_re + (0.d0, 1.d0) * sq_rho_im
|
|
!sq_rho = zsqrt(rho)
|
|
|
|
|
|
F0 = 0.5d0 * sqpi * cpx_erf(sq_rho_re, sq_rho_im) / sq_rho
|
|
crint_sum = F0 * d1(0)
|
|
! print *, 0, F0
|
|
|
|
rho_exp = 0.5d0 * zexp(-rho)
|
|
rho_inv = (1.d0, 0.d0) / rho
|
|
|
|
mmax = shiftr(n_pt_out, 1)
|
|
if(mmax .gt. 0) then
|
|
|
|
allocate( Fm(mmax) )
|
|
Fm(1:mmax) = (0.d0, 0.d0)
|
|
|
|
do n = 0, mmax-1
|
|
F0 = ((dble(n) + 0.5d0) * F0 - rho_exp) * rho_inv
|
|
Fm(n+1) = F0
|
|
! print *, n, F0
|
|
enddo
|
|
|
|
do i = 2, n_pt_out, 2
|
|
n = shiftr(i, 1)
|
|
crint_sum = crint_sum + Fm(n) * d1(i)
|
|
enddo
|
|
deallocate(Fm)
|
|
endif
|
|
|
|
! ***
|
|
|
|
endif
|
|
|
|
endif
|
|
|
|
end function crint_sum
|
|
|
|
! ---
|
|
|
|
complex*16 function crint_smallz(n, rho)
|
|
|
|
BEGIN_DOC
|
|
! Standard version of rint
|
|
END_DOC
|
|
|
|
implicit none
|
|
integer, intent(in) :: n
|
|
complex*16, intent(in) :: rho
|
|
|
|
integer, parameter :: kmax = 40
|
|
double precision, parameter :: eps = 1.d-13
|
|
|
|
integer :: k
|
|
double precision :: delta_mod
|
|
complex*16 :: rho_k, ct, delta_k
|
|
|
|
ct = 0.5d0 * zexp(-rho) * gamma(dble(n) + 0.5d0)
|
|
rho_k = (1.d0, 0.d0)
|
|
crint_smallz = ct * rho_k / gamma(dble(n) + 1.5d0)
|
|
|
|
do k = 1, kmax
|
|
|
|
rho_k = rho_k * rho
|
|
delta_k = ct * rho_k / gamma(dble(n+k) + 1.5d0)
|
|
crint_smallz = crint_smallz + delta_k
|
|
|
|
delta_mod = dsqrt(REAL(delta_k)*REAL(delta_k) + AIMAG(delta_k)*AIMAG(delta_k))
|
|
if(delta_mod .lt. eps) return
|
|
enddo
|
|
|
|
if(delta_mod > eps) then
|
|
write(*,*) ' pb in crint_smallz !'
|
|
write(*,*) ' n, rho = ', n, rho
|
|
write(*,*) ' delta_mod = ', delta_mod
|
|
stop 1
|
|
endif
|
|
|
|
end function crint_smallz
|
|
|
|
! ---
|
|
|