# Optimisation with Normalisation Constraint

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## Optimisation with Normalisation Constraint

 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 ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: Optimisation with Normalisation Constraint

 I recommend posting this on a mathematics discussion forum like Stack Exchange and (re-)reading the Posting Guide for this mailing list. I think you are going to need to re-write your model function to algebraically combine your original model along with the constraint, and then use the original model alone for prediction... but I haven't tried it so might be quite far off the mark. On June 20, 2018 8:50:48 AM PDT, Lorenzo Isella <[hidden email]> wrote: >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 > >______________________________________________ >[hidden email] mailing list -- To UNSUBSCRIBE and more, see >https://stat.ethz.ch/mailman/listinfo/r-help>PLEASE do read the posting guide >http://www.R-project.org/posting-guide.html>and provide commented, minimal, self-contained, reproducible code. -- Sent from my phone. Please excuse my brevity. ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.