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subroutine spline(r,start,n,db,db2)
c spline calculates the cubic spline interpolation of the density
c together with subroutine splint.
c the main ideas are "stolen" from "numerical recipes", cambridge
c university press (1992).
c input r : position coordinate (array)
c input start : index, r(start) = starting point of the spline
c input n : index, r(n) = r_max
c input db : spin up and down density. (array)
c output db2 : second derivative of db (array)
implicit logical (a-z)
double precision r,db,db2,u,sig,p,qn,un
integer spin,start,n,i
dimension r(561),db(2,561),db2(2,561),u(561)
do 100 spin = 1,2
db2(spin,start) = 0.d0
u(start) = 0.d0
do 10 i = start+1,n-1
sig = (r(i)-r(i-1))/(r(i+1)-r(i-1))
p = sig*db2(spin,i-1)+2.d0
db2(spin,i) = (sig-1.d0)/p
u(i) = (6.d0*((db(spin,i+1)-db(spin,i))/(r(i+1)-r(i))-
j (db(spin,i)-db(spin,i-1))/(r(i)-r(i-1)))/
j (r(i+1)-r(i-1))-sig*u(i-1))/p
10 continue
qn = 0.d0
un = 0.d0
db2(spin,n) = (un-qn*u(n-1))/(qn*db2(spin,n-1)+1.d0)
do 20 i = n-1,start,-1
db2(spin,i) = db2(spin,i)*db2(spin,i+1)+u(i)
20 continue
100 continue
return
end
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