[R] Optimisation with Normalisation Constraint
Lorenzo Isella
lorenzo@i@ell@ @ending from gm@il@com
Wed Jun 20 17:50:48 CEST 2018
Dear All,
I have a problem I haver been struggling with for a while: I need to
carry out a non-linear fit (and this is the
easy part).
I have a set of discrete values {x1,x2...xN} and the corresponding
{y1, y2...yN}. The difficulty is that I would like the linear fit to
preserve the sum of the values y1+y2+...yN.
I give an example below (for which there may even be an analytical
solution, but that is not the point here)
############################################################################
library(minpack.lm)
set.seed(124)
z <- rexp(3000,3)
zf <- z[z<= 0.5 | z>=0.9]
myhist <- hist(zf, plot=FALSE)
df <- data.frame(x=myhist$mids, y=myhist$density)
myfit <- nlsLM(y~(A*exp(-lambda*x))
,data=df, start=list(A=1,lambda=1))
> sum(myhist$density)
[1] 5
> sum(predict(myfit))
[1] 4.931496
############################################################################
I would like sum(predict(myfit)) to be exactly 5 from the start,
without renormalising a posteriori the fit.
Any suggestion is appreciated.
Cheers
Lorenzo
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