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Accelerated pseudo

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This commit is contained in:
Anthony Scemama 2016-10-01 18:04:25 +02:00
parent ac7ae61016
commit 7d320f213f
1 changed files with 75 additions and 23 deletions
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98
src/Integrals_Monoelec/pseudopot.f90
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@ -276,29 +276,17 @@ if(ac.eq.0.d0.and.bc.eq.0.d0)then
do k=1,kmax
do l=0,lmax
ktot=ntot+n_kl(k,l)
if (v_kl(k,l) == 0.d0) cycle
do m=-l,l
prod=bigI(0,0,l,m,n_a(1),n_a(2),n_a(3))
if (prod == 0.d0) cycle
prodp=bigI(0,0,l,m,n_b(1),n_b(2),n_b(3))
if (prodp == 0.d0) cycle
accu=accu+prod*prodp*v_kl(k,l)*int_prod_bessel(ktot+2,g_a+g_b+dz_kl(k,l),0,0,areal,breal,arg)
enddo
enddo
enddo
! do k=1,kmax
! do l=0,lmax
! ktot=ntot+n_kl(k,l)
! do m=-l,l
! prod =bigI(0,0,l,m,n_a(1),n_a(2),n_a(3))*v_kl(k,l)
! prodp=bigI(0,0,l,m,n_b(1),n_b(2),n_b(3))*prod
! if (dabs (prodp) < 1.d-15) then
! cycle
! endif
!
! accu=accu+prodp*int_prod_bessel(ktot+2,g_a+g_b+dz_kl(k,l),0,0,areal,breal,arg)
!
! enddo
! enddo
! enddo
!=!=!=!=!
! E n d !
@ -385,14 +373,17 @@ else if(ac.ne.0.d0.and.bc.ne.0.d0)then
enddo
do k3=0,n_a(3)
if (array_coefs_A(k3,3) == 0.d0) cycle
do k2=0,n_a(2)
if (array_coefs_A(k2,2) == 0.d0) cycle
do k1=0,n_a(1)
if (array_coefs_A(k1,1) == 0.d0) cycle
do lambda=0,l+ntotA
do mu=-lambda,lambda
prod=ylm(lambda,mu,theta_AC0,phi_AC0)*array_coefs_A(k1,1)*array_coefs_A(k2,2)*array_coefs_A(k3,3)*array_I_A(mu,lambda,k1,k2,k3)
if (prod == 0.d0) cycle
do k3p=0,n_b(3)
do k2p=0,n_b(2)
@ -404,6 +395,7 @@ else if(ac.ne.0.d0.and.bc.ne.0.d0)then
array_coefs_B(k1p,1)*array_coefs_B(k2p,2)*array_coefs_B(k3p,3)* &
array_I_B(mup,lambdap,k1p,k2p,k3p)
if (prodp == 0.d0) cycle
do k=1,kmax
ktot=k1+k2+k3+k1p+k2p+k3p+n_kl(k,l)
accu=accu+prodp*v_kl(k,l)*array_R(k,ktot,l,lambda,lambdap)
@ -489,13 +481,18 @@ else if(ac.eq.0.d0.and.bc.ne.0.d0)then
prod=bigI(0,0,l,m,n_a(1),n_a(2),n_a(3))
do k3p=0,n_b(3)
if (array_coefs_B(k3p,3) == 0.d0) cycle
do k2p=0,n_b(2)
if (array_coefs_B(k2p,2) == 0.d0) cycle
do k1p=0,n_b(1)
if (array_coefs_B(k1p,1) == 0.d0) cycle
do lambdap=0,l+ntotB
do mup=-lambdap,lambdap
prodp=prod*array_coefs_B(k1p,1)*array_coefs_B(k2p,2)*array_coefs_B(k3p,3)*ylm(lambdap,mup,theta_BC0,phi_BC0)*array_I_B(mup,lambdap,k1p,k2p,k3p)
if (prodp == 0.d0) cycle
do k=1,kmax
ktot=ntotA+k1p+k2p+k3p+n_kl(k,l)
@ -572,13 +569,19 @@ else if(ac.ne.0.d0.and.bc.eq.0.d0)then
enddo
do k3=0,n_a(3)
if (array_coefs_A(k3,3) == 0.d0) cycle
do k2=0,n_a(2)
if (array_coefs_A(k2,2) == 0.d0) cycle
do k1=0,n_a(1)
if (array_coefs_A(k1,1) == 0.d0) cycle
do lambda=0,l+ntotA
do mu=-lambda,lambda
prod=array_coefs_A(k1,1)*array_coefs_A(k2,2)*array_coefs_A(k3,3)*ylm(lambda,mu,theta_AC0,phi_AC0)*array_I_A(mu,lambda,k1,k2,k3)
if (prod == 0.d0) cycle
prodp=prod*bigI(0,0,l,m,n_b(1),n_b(2),n_b(3))
if (prodp == 0.d0) cycle
do k=1,kmax
ktot=k1+k2+k3+ntotB+n_kl(k,l)
@ -811,18 +814,22 @@ double precision int_prod_bessel_loc,binom_func,accu,prod,ylm,bigI,arg
phi_DC0=datan2(d(2)/d2,d(1)/d2)
do k=1,klocmax
if (v_k(k) == 0.d0) cycle
do k1=0,n_a(1)
do k2=0,n_a(2)
do k3=0,n_a(3)
do k1p=0,n_b(1)
do k2p=0,n_b(2)
do k3p=0,n_b(3)
if (array_coefs(k1,k2,k3,k1p,k2p,k3p) == 0.d0) cycle
do l=0,ntot
do m=-l,l
coef=ylm(l,m,theta_DC0,phi_DC0)
if (coef == 0.d0) cycle
ktot=k1+k2+k3+k1p+k2p+k3p+n_k(k)
if (array_R_loc(ktot,k,l) == 0.d0) cycle
prod=coef*array_coefs(k1,k2,k3,k1p,k2p,k3p) &
*bigI(l,m,0,0,k1+k1p,k2+k2p,k3+k3p)
ktot=k1+k2+k3+k1p+k2p+k3p+n_k(k)
accu=accu+prod*v_k(k)*array_R_loc(ktot,k,l)
enddo
enddo
@ -863,18 +870,24 @@ double precision pi,sum,factor1,factor2,cylm,cylmp,bigA,binom_func,fact,coef_pm
double precision sgn, sgnp
pi=dacos(-1.d0)
bigI=0.d0
if(mu.gt.0.and.m.gt.0)then
sum=0.d0
factor1=dsqrt((2*lambda+1)*fact(lambda-iabs(mu))/(2.d0*pi*fact(lambda+iabs(mu))))
if (factor1== 0.d0) return
factor2=dsqrt((2*l+1)*fact(l-iabs(m))/(2.d0*pi*fact(l+iabs(m))))
if (factor2== 0.d0) return
sgn = 1.d0
do k=0,mu/2
do i=0,lambda-mu
if (coef_pm(lambda,i+mu) == 0.d0) cycle
sgnp = 1.d0
do kp=0,m/2
do ip=0,l-m
cylm=sgn*factor1*binom_func(mu,2*k)*fact(mu+i)/fact(i)*coef_pm(lambda,i+mu)
if (cylm == 0.d0) cycle
cylmp=sgnp*factor2*binom_func(m,2*kp)*fact(m+ip)/fact(ip)*coef_pm(l,ip+m)
if (cylmp == 0.d0) cycle
sum=sum+cylm*cylmp*bigA(mu-2*k+m-2*kp+k1,2*k+2*kp+k2,i+ip+k3)
enddo
sgnp = -sgnp
@ -888,12 +901,16 @@ endif
if(mu.eq.0.and.m.eq.0)then
factor1=dsqrt((2*lambda+1)/(4.d0*pi))
if (factor1== 0.d0) return
factor2=dsqrt((2*l+1)/(4.d0*pi))
if (factor2== 0.d0) return
sum=0.d0
do i=0,lambda
do ip=0,l
cylm=factor1*coef_pm(lambda,i)
if (cylm == 0.d0) cycle
cylmp=factor2*coef_pm(l,ip)
if (cylmp == 0.d0) cycle
sum=sum+cylm*cylmp*bigA(k1,k2,i+ip+k3)
enddo
enddo
@ -903,14 +920,18 @@ endif
if(mu.eq.0.and.m.gt.0)then
factor1=dsqrt((2*lambda+1)/(4.d0*pi))
if (factor1== 0.d0) return
factor2=dsqrt((2*l+1)*fact(l-iabs(m))/(2.d0*pi*fact(l+iabs(m))))
if (factor2== 0.d0) return
sum=0.d0
do i=0,lambda
sgnp = 1.d0
do kp=0,m/2
do ip=0,l-m
cylm=factor1*coef_pm(lambda,i)
if (cylm == 0.d0) cycle
cylmp=sgnp*factor2*binom_func(m,2*kp)*fact(m+ip)/fact(ip)*coef_pm(l,ip+m)
if (cylmp == 0.d0) cycle
sum=sum+cylm*cylmp*bigA(m-2*kp+k1,2*kp+k2,i+ip+k3)
enddo
sgnp = -sgnp
@ -923,13 +944,18 @@ endif
if(mu.gt.0.and.m.eq.0)then
sum=0.d0
factor1=dsqrt((2*lambda+1)*fact(lambda-iabs(mu))/(2.d0*pi*fact(lambda+iabs(mu))))
if (factor1== 0.d0) return
factor2=dsqrt((2*l+1)/(4.d0*pi))
if (factor2== 0.d0) return
sgn = 1.d0
do k=0,mu/2
do i=0,lambda-mu
if (coef_pm(lambda,i+mu) == 0.d0) cycle
do ip=0,l
cylm=sgn*factor1*binom_func(mu,2*k)*fact(mu+i)/fact(i)*coef_pm(lambda,i+mu)
if (cylm == 0.d0) cycle
cylmp=factor2*coef_pm(l,ip)
if (cylmp == 0.d0) cycle
sum=sum+cylm*cylmp*bigA(mu-2*k +k1,2*k +k2,i+ip +k3)
enddo
enddo
@ -943,16 +969,22 @@ if(mu.lt.0.and.m.lt.0)then
mu=-mu
m=-m
factor1=dsqrt((2*lambda+1)*fact(lambda-iabs(mu))/(2.d0*pi*fact(lambda+iabs(mu))))
if (factor1== 0.d0) return
factor2=dsqrt((2*l+1)*fact(l-iabs(m))/(2.d0*pi*fact(l+iabs(m))))
if (factor2== 0.d0) return
sum=0.d0
sgn = 1.d0
do k=0,(mu-1)/2
do i=0,lambda-mu
if (coef_pm(lambda,i+mu) == 0.d0) cycle
sgnp = 1.d0
do kp=0,(m-1)/2
do ip=0,l-m
if (coef_pm(l,ip+m) == 0.d0) cycle
cylm=sgn*factor1*binom_func(mu,2*k+1)*fact(mu+i)/fact(i)*coef_pm(lambda,i+mu)
if (cylm == 0.d0) cycle
cylmp=sgnp*factor2*binom_func(m,2*kp+1)*fact(m+ip)/fact(ip)*coef_pm(l,ip+m)
if (cylmp == 0.d0) cycle
sum=sum+cylm*cylmp*bigA(mu-(2*k+1)+m-(2*kp+1)+k1,(2*k+1)+(2*kp+1)+k2,i+ip+k3)
enddo
sgnp = -sgnp
@ -969,14 +1001,18 @@ endif
if(mu.eq.0.and.m.lt.0)then
m=-m
factor1=dsqrt((2*lambda+1)/(4.d0*pi))
if (factor1 == 0.d0) return
factor2=dsqrt((2*l+1)*fact(l-iabs(m))/(2.d0*pi*fact(l+iabs(m))))
if (factor2 == 0.d0) return
sum=0.d0
do i=0,lambda
sgnp = 1.d0
do kp=0,(m-1)/2
do ip=0,l-m
cylm=factor1*coef_pm(lambda,i)
if (cylm == 0.d0) cycle
cylmp=sgnp*factor2*binom_func(m,2*kp+1)*fact(m+ip)/fact(ip)*coef_pm(l,ip+m)
if (cylmp == 0.d0) cycle
sum=sum+cylm*cylmp*bigA(m-(2*kp+1)+k1,2*kp+1+k2,i+ip+k3)
enddo
sgnp = -sgnp
@ -991,13 +1027,17 @@ if(mu.lt.0.and.m.eq.0)then
sum=0.d0
mu=-mu
factor1=dsqrt((2*lambda+1)*fact(lambda-iabs(mu))/(2.d0*pi*fact(lambda+iabs(mu))))
if (factor1== 0.d0) return
factor2=dsqrt((2*l+1)/(4.d0*pi))
if (factor2== 0.d0) return
sgn = 1.d0
do k=0,(mu-1)/2
do i=0,lambda-mu
do ip=0,l
cylm=sgn*factor1*binom_func(mu,2*k+1)*fact(mu+i)/fact(i)*coef_pm(lambda,i+mu)
if (cylm == 0.d0) cycle
cylmp=factor2*coef_pm(l,ip)
if (cylmp == 0.d0) cycle
sum=sum+cylm*cylmp*bigA(mu-(2*k+1)+k1,2*k+1+k2,i+ip+k3)
enddo
enddo
@ -1011,16 +1051,22 @@ endif
if(mu.gt.0.and.m.lt.0)then
sum=0.d0
factor1=dsqrt((2*lambda+1)*fact(lambda-iabs(mu))/(2.d0*pi*fact(lambda+iabs(mu))))
if (factor1== 0.d0) return
factor2=dsqrt((2*l+1)*fact(l-iabs(m))/(2.d0*pi*fact(l+iabs(m))))
if (factor2== 0.d0) return
m=-m
sgn=1.d0
do k=0,mu/2
do i=0,lambda-mu
if (coef_pm(lambda,i+mu) == 0.d0) cycle
sgnp=1.d0
do kp=0,(m-1)/2
do ip=0,l-m
if (coef_pm(l,ip+m) == 0.d0) cycle
cylm =sgn *factor1*binom_func(mu,2*k)*fact(mu+i)/fact(i)*coef_pm(lambda,i+mu)
if (cylm == 0.d0) cycle
cylmp=sgnp*factor2*binom_func(m,2*kp+1)*fact(m+ip)/fact(ip)*coef_pm(l,ip+m)
if (cylmp == 0.d0) cycle
sum=sum+cylm*cylmp*bigA(mu-2*k+m-(2*kp+1)+k1,2*k+2*kp+1+k2,i+ip+k3)
enddo
sgnp = -sgnp
@ -1036,16 +1082,22 @@ endif
if(mu.lt.0.and.m.gt.0)then
mu=-mu
factor1=dsqrt((2*lambda+1)*fact(lambda-iabs(mu))/(2.d0*pi*fact(lambda+iabs(mu))))
if (factor1== 0.d0) return
factor2=dsqrt((2*l+1)*fact(l-iabs(m))/(2.d0*pi*fact(l+iabs(m))))
if (factor2== 0.d0) return
sum=0.d0
sgn = 1.d0
do k=0,(mu-1)/2
do i=0,lambda-mu
if (coef_pm(lambda,i+mu) == 0.d0) cycle
sgnp = 1.d0
do kp=0,m/2
do ip=0,l-m
if (coef_pm(l,ip+m) == 0.d0) cycle
cylm=sgn*factor1 *binom_func(mu,2*k+1)*fact(mu+i)/fact(i)*coef_pm(lambda,i+mu)
if (cylm == 0.d0) cycle
cylmp=sgnp*factor2*binom_func(m,2*kp)*fact(m+ip)/fact(ip)*coef_pm(l,ip+m)
if (cylmp == 0.d0) cycle
sum=sum+cylm*cylmp*bigA(mu-(2*k+1)+m-2*kp+k1,2*k+1+2*kp+k2,i+ip+k3)
enddo
sgnp = -sgnp
@ -1543,7 +1595,7 @@ end
r=(i-1)*dr
x1=delta1*r
x2=delta2*r
sum=sum+dr*r**(n+2)*dexp(-cc*r**2)*bessel_mod(x1,lambda)*bessel_mod(x2,lambdap)
sum=sum+dr*r**(n+2)*dexp(-cc*r*r)*bessel_mod(x1,lambda)*bessel_mod(x2,lambdap)
enddo
bigR=sum*factor
end
@ -1568,8 +1620,8 @@ end
return
endif
if(n.eq.0)a=dsinh(x)/x
if(n.eq.1)a=(x*dcosh(x)-dsinh(x))/x**2
if(n.ge.2)a=bessel_mod_recur(n-2,x)-(2*n-1)/x*bessel_mod_recur(n-1,x)
if(n.eq.1)a=(x*dcosh(x)-dsinh(x))/(x*x)
if(n.ge.2)a=bessel_mod_recur(n-2,x)-(n+n-1)/x*bessel_mod_recur(n-1,x)
end
double precision function bessel_mod_exp(n,x)
@ -1578,8 +1630,8 @@ end
double precision x,coef,accu,fact,dble_fact
accu=0.d0
do k=0,10
coef=1.d0/fact(k)/dble_fact(2*(n+k)+1)
accu=accu+(x**2/2.d0)**k*coef
coef=1.d0/(fact(k)*dble_fact(2*(n+k)+1))
accu=accu+(0.5d0*x*x)**k*coef
enddo
bessel_mod_exp=x**n*accu
end