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qp2/src/utils/cgtos_utils.irp.f
AbdAmmar 3589688254 few opt in cgtos integrals
2024-10-20 11:18:28 +02:00

471 lines
11 KiB
Fortran
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! ---
subroutine give_explicit_cpoly_and_cgaussian_x(P_new, P_center, p, fact_k, iorder, &
alpha, beta, a, b, Ae_center, Be_center, Ap_center, Bp_center, dim)
BEGIN_DOC
!
! Transform the product of
!
! (x - x_Ap)^a (x - x_Bp)^b exp(-alpha (r - Ae)^2) exp(-beta (r - Be)^2)
!
! 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, Ae_center, Ap_center
complex*16, intent(in) :: beta, Be_center, Bp_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
complex*16 :: P_a(0:max_dim), P_b(0:max_dim)
complex*16 :: p_inv, ab, d_AB, tmp
!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: P_a, P_b
P_new = (0.d0, 0.d0)
! new exponent
p = alpha + beta
! new center
p_inv = (1.d0, 0.d0) / p
ab = alpha * beta
P_center = (alpha * Ae_center + beta * Be_center) * p_inv
! get the factor
d_AB = (Ae_center - Be_center) * (Ae_center - Be_center)
tmp = ab * p_inv * d_AB
if(zabs(tmp) .lt. 50.d0) then
fact_k = zexp(-tmp)
else
fact_k = (0.d0, 0.d0)
endif
! Recenter the polynomials P_a and P_b on P_center
!DIR$ FORCEINLINE
call recentered_cpoly2(P_a(0), Ap_center, P_center, a, P_b(0), Bp_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(P_new, P_center, p, fact_k, iorder, &
alpha, beta, a, b, Ae_center, Be_center, Ap_center, Bp_center, dim)
BEGIN_DOC
!
! Transforms the product of
!
! (x - x_Ap)^a(1) (x - x_Bp)^b(1) exp(-alpha (x - x_Ae)^2) exp(-beta (x - x_Be)^2) x
! (y - y_Ap)^a(2) (y - y_Bp)^b(2) exp(-alpha (y - y_Ae)^2) exp(-beta (y - y_Be)^2) x
! (z - z_Ap)^a(3) (z - z_Bp)^b(3) exp(-alpha (z - z_Ae)^2) exp(-beta (z - z_Be)^2)
!
! 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, Ae_center(3), Ap_center(3)
complex*16, intent(in) :: beta, Be_center(3), Bp_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
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, Ae_center, beta, Be_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
if(zabs(fact_k) < 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), Ap_center(1), P_center(1), a(1), P_b(0,1), Bp_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), Ap_center(2), P_center(2), a(2), P_b(0,2), Bp_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), Ap_center(3), P_center(3), a(3), P_b(0,3), Bp_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 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)
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))
if(real(k) .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
return
end
! ---
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
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
if(real(k) > 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 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
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
if(abs(d(nd)) .lt. 1.d-15) cycle
exit
enddo
end
! ---
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
complex*16 :: tmp
nd = nb + nc
do ib = 0, max(nb, nc)
d(ib) = d(ib) + c(ib) + b(ib)
enddo
tmp = d(nd)
do while( (zabs(tmp) .lt. 1.d-15) .and. (nd >= 0) )
nd -= 1
tmp = d(nd)
if(nd < 0) exit
enddo
end
! ---
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
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)
do while(zabs(tmp) .lt. 1.d-15)
nd -= 1
if(nd < 0) exit
tmp = d(nd)
enddo
endif
end
! ---
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
integer :: maxbinom
complex*16 :: pows_a(0:a+b+2), pows_b(0:a+b+2)
double precision :: binom_func
if((a < 0) .or. (b < 0)) return
maxbinom = size(binom_transp, 1)
pows_a(0) = (1.d0, 0.d0)
pows_a(1) = x_P - x_A
do i = 2, a
pows_a(i) = pows_a(i-1) * pows_a(1)
enddo
pows_b(0) = (1.d0, 0.d0)
pows_b(1) = x_Q - x_B
do i = 2, b
pows_b(i) = pows_b(i-1) * pows_b(1)
enddo
P_A(0) = pows_a(a)
do i = 1, min(a, maxbinom)
P_A(i) = binom_transp(i,a) * pows_a(a-i)
enddo
do i = maxbinom+1, a
P_A(i) = binom_func(a, i) * pows_a(a-i)
enddo
P_B(0) = pows_b(b)
do i = 1, min(b, maxbinom)
P_B(i) = binom_transp(i,b) * pows_b(b-i)
enddo
do i = maxbinom+1, b
P_B(i) = binom_func(b, i) * pows_b(b-i)
enddo
end
! ---
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
complex*16 :: inv_sq_p2, inv_sq_p3, inv_sq_p4
! (n)!
double precision, external :: 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
select case(n)
case(0)
Fc_integral = sqpi * inv_sq_p
case(2)
Fc_integral = 0.5d0 * sqpi * inv_sq_p * inv_sq_p * inv_sq_p
case(4)
inv_sq_p2 = inv_sq_p * inv_sq_p
Fc_integral = 0.75d0 * sqpi * inv_sq_p * inv_sq_p2 * inv_sq_p2
case(6)
inv_sq_p3 = inv_sq_p * inv_sq_p * inv_sq_p
Fc_integral = 1.875d0 * sqpi * inv_sq_p * inv_sq_p3 * inv_sq_p3
case(8)
inv_sq_p3 = inv_sq_p * inv_sq_p * inv_sq_p
Fc_integral = 6.5625d0 * sqpi * inv_sq_p3 * inv_sq_p3 * inv_sq_p3
case(10)
inv_sq_p2 = inv_sq_p * inv_sq_p
inv_sq_p4 = inv_sq_p2 * inv_sq_p2
Fc_integral = 29.53125d0 * sqpi * inv_sq_p * inv_sq_p2 * inv_sq_p4 * inv_sq_p4
case default
Fc_integral = 2.d0 * sqpi * (0.5d0 * inv_sq_p)**(n+1) * fact(n) / fact(shiftr(n, 1))
end select
return
end
! ---
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