It is a complex function, functions are quoted frequently, you may read
from bottom up
The independent variable for final fit is q
%%Rg0 is a function of L and b
Rg0sq<-function(L,b)L*b/6*(1-3/2*b/L+3/2*(b/L)^2-3/4*(b/L)^3*(1-exp(-2*L/b)))
%%alpha is a defined function
alpha<-function(x)(1+(x/3.12)^2+(x/8.67)^3)^(0.176/3)
%%w is a defined function
w<-function(x)(1+tanh(x-1.523)/0.1477)/2
%%It is Rg^2
Rgsq<-function(L,b)(alpha(L/b)*Rg0sq(L,b))
%%This is Rg
Rg<-function(L,b)(Rg0sq(L,b))^0.5
%%A debye function of q, the parameters are L and b
PDebye<-function(L,b)2*(exp(-q^2*Rg0sq(L,b))+q^2*Rg0sq(L,b)-1)/q^4/(Rg0sq(L,b))^2
%%Another function of q that quote w, PDebye, Rg, parameters are v, L and
b
Pexv<-function(v,L,b)w(q*Rg(L,b))*PDebye(L,b)+(1-w(q*Rg(L,b)))(1.22*(q*Rg(L,b))^(-1/v)+0.4288*(q*Rg(L,b))^(-2/v)-1.651*(q*Rg(L,b))^(-1/v))
%%Another defined function
cf<-function(L,b,pa,pb)pa/(L/b)^pb
%%A function of q, quote Pexv, Rgsq, cf
Psfcex<-function(v,L,b,pa,pb)Pexv(v,L,b)+cf(L,b,pa,pb)*b/L/15*(4+7/q^2/Rgsq(L,b)-(11+7/q^2/Rgsq(L,b))*exp(-q^2*Rgsq(L,b)))
%%non-linear fit
Pfit<-function(p)sum((I-Psfcex(p[1],p[2],p[3],p[4],p[5]))^2)
wavefit<-nlm(Pfit,c(1.5,500,5,1,0.1),hessian=TRUE)
error code: Error in c(1.5, 500, 5, 1, 0.1) : unused argument(s) (0.1)
the fifth parameter is pb, which goes from Psfcex to cf, actually pa which
only exist in cf is used, why not pb?