rhoOpt = function(r,c)
{
n = length(r)
rho = rep(0,n)
h0 = 1.792
h2 = -.972
h4 = .432
h6 = -.052
h8 = .002
c2 = c^2
k = c/3
k2 = k^2
for(i in 1:n)
{
x = r[i]/k
x2 = x^2
x4 = x^4
x6 = x^6
x8 = x^8
if((abs(x)>2) & (abs(x)<=3))
{rho[i] = k2*(h0+h2*x2+h4*x4+h6*x6+h8*x8)}
else
{if(abs(x)<=2)
{rho[i] = .5*r[i]^2} else {rho[i] = 3.25*k2}}
}
rho
}
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