It works fine for me. Since you don’t give example data, I generated some:
fx(x) = 1.5 - 1.3 / (1. + (x/0.7)^1.3)
xdata = range(0,3,length=50)
ydata = fx.(xdata).*(1 .+0.1randn(50))
plot(xdata,ydata,legend=:bottomright)
leads to:
Next, doing model fitting:
julia> @. H(x,p) = p[1] - (p[1]-p[2]) / ( 1. + (x/p[3])^p[4] )
julia> Hfit = LsqFit.curve_fit(H,xdata,ydata,[1.,0.,0.5,1.],lower=[0.,0.,0.,1.])
julia> par = coef(Hfit)
4-element Array{Float64,1}:
1.4779674751492053
0.21988771220240352
0.6945565635031009
1.6532411388662613
julia> plot(xdata,ydata,label="data")
julia> plot!(xdata,x-> par[1] - (par[1]-par[2])/(1+(x/par[3])^par[4]),label="fitted model",legend=:bottomright)
leads to:
Of course, if you have negative elements in xdata, you will have problems as x/p[3] will be negative, and raising this to a number that is not an even integer will produce a complex number.
Another problem is that you allow p[3] to have zero as lower bound, hence allows the fitting algorithm to divide by zero in x/p[3].
So, I’d check the minimal value in xdata, and change the lower value of p[3] to 1e-2 or something.
You do indicate that xdata contains concentrations, which should be positive at the outset. Maybe there are some errors in the measurements so that some of them are (slightly) negative??
