nls when the data is a convoluted spectra (variable number of variables)

Question

I have some spectrum data that looks like one of the multiplets when is plotted: http://journals.prous.com/journals/dof/19982303/html/df230301/images/keiferf3.gif

How it is seen in the image, all the peaks are realy close among each other, so I would like to do some deconvolution using nls function, like it was posted before (R: Fitting Gaussian peaks to density plot data using nls), but using a Lorentzian function instead:

y <- 1/(pi*a*(1+((x-x0)/a)^2))

In my case, x0 is the peak maximum (and length(x0) is the number of peaks), so I only need to optimize 'a'.

However, my problem is not related to perform that, but in writing a robust script that would deconvolute any spectrum, taking the number of peaks as input information.

My first idea was to write the lorentzian function and leave the 'a' as a vector (to apply thereafter a sum of all lorentzian curves), but R doesn't recognize this structure:

for (i in 1:length(x0)) {
    f[i]<-function(a) { y <- 1/(pi*a[i]*(1+((x-x0[i])/a[i])^2)) }
}

fit <- nls(sum(f[1:length(x0)]), start=list(a=rep(1, times=length(x0))))

Update:

This is my sample, in .csv format (https://drive.google.com/file/d/0B66EHLI5AufhbjlWcW9rYXl1UFk/edit?usp=sharing). Data is filled in 2 rows. The first one has the frequency (in ppm), and the second the intensity. For this data, I will pick 5 peaks, so I would do 'nls' on formula=f[1]+f[2]+f[3]+f[4]+f[5] and I would have 5 parametres (a[1:5]) to evaluate.

Answer 1

I've found the 'as.formula' command, which allows to convert any character string to formula. Therefore, I manage to create a for loop that creates the sum of lorentzian curves. In my example, parameters a[1:5] are now defined as a-e, but with sprintf I can use the vector nomenclature as well.

cac<-"abcdefghijklmnopqrstuvwxyz"
for (i in 1:length(x0)) {
    letter<-substr(cac, i,i)
    formulae[i]<-sprintf("1/(pi*%s*(1+((spectra[1,]-%f)/%s)^2))", letter,x0[i],letter)
    coeff[i]<-sprintf("%s=1", letter)
}
formula2<-paste(formulae, collapse="+")
formulo<-paste("spectra[2,] ~", formula2, sep="")
coeffs<-paste(coeff, collapse=",")

fit<-as.formula(paste("nls(",formulo,",start=list(",coeffs,"))", sep=""))

So, all this code brings me the following formula for the posted example:

"nls(spectra[2,] ~1/(pi*a*(1+((spectra[1,]-2.156460)/a)^2))+1/(pi*b*(1+((spectra[1,]-2.170150)/b)^2))+1/(pi*c*(1+((spectra[1,]-2.184820)/c)^2))+1/(pi*d*(1+((spectra[1,]-2.163550)/d)^2))+1/(pi*e*(1+((spectra[1,]-2.142040)/e)^2)), start=list(a=1,b=1,c=1,d=1,e=1))

However, it seems that the formula does not work, but this wasn't the aim of this thread, so I can say now it's closed (I opened a new one to try to solve it).