# wrapnlsr: Provides class nls solution to a nonlinear least squares... In nlsr: Functions for Nonlinear Least Squares Solutions

## Description

Given a nonlinear model expressed as an expression of the form `lhs ~ formula_for_rhs` and a start vector where parameters used in the model formula are named, attempts to find the minimum of the residual sum of squares using the Nash variant (Nash, 1979) of the Marquardt algorithm, where the linear sub-problem is solved by a qr method. The resulting solution is fed into the `nls()` function in an attempt to get the nls class solution.

## Usage

 ```1 2``` ``` wrapnlsr(formula, start, trace=FALSE, data, lower=-Inf, upper=Inf, control=list(), ...) ```

## Arguments

 `formula` This is a modeling formula of the form (as in `nls`) lhsvar ~ rhsexpression for example, y ~ b1/(1+b2*exp(-b3*tt)) You may also give this as a string. `start` A named parameter vector. For our example, we could use start=c(b1=1, b2=2.345, b3=0.123) `trace` Logical `TRUE` if we want intermediate progress to be reported. Default is `FALSE`. `data` A data frame containing the data of the variables in the formula. This data may, however, be supplied directly in the parent frame. `lower` Lower bounds on the parameters. If a single number, this will be applied to all parameters. Default `-Inf`. `upper` Upper bounds on the parameters. If a single number, this will be applied to all parameters. Default `Inf`. `control` A list of controls for the algorithm. These are as for `nlxb()`. `...` Any data needed for computation of the residual vector from the expression rhsexpression - lhsvar. Note that this is the negative of the usual residual, but the sum of squares is the same.

## Details

`wrapnlsr` first attempts to solve the nonlinear sum of squares problem by using `nlsmnq`, then takes the parameters from that method to call `nls`.

## Value

An object of type nls.

## Author(s)

John C Nash <nashjc@uottawa.ca>

Function `nls()`, packages `optim` and `optimx`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```cat("See more examples in nlmrt-package.Rd\n") cat("kvanderpoel.R test of wrapnlsr\n") # require(nlsr) x<-c(1,3,5,7) y<-c(37.98,11.68,3.65,3.93) pks28<-data.frame(x=x,y=y) fit0<-try(nls(y~(a+b*exp(1)^(-c*x)), data=pks28, start=c(a=0,b=1,c=1), trace=TRUE)) print(fit0) cat("\n\n") fit1<-nlxb(y~(a+b*exp(-c*x)), data=pks28, start=c(a=0,b=1,c=1), trace = TRUE) print(fit1) cat("\n\nor better\n") fit2<-wrapnlsr(y~(a+b*exp(-c*x)), data=pks28, start=c(a=0,b=1,c=1), lower=-Inf, upper=Inf, trace = TRUE) ```