# [R] how to fit gauss beam?

From: Thomas Hunger <hto_at_arcor.de>
Date: Mon 04 Sep 2006 - 14:14:50 GMT

Hello,

\$ w(z) = w0 * sqrt(1+(z/z0)**2)
\$ fit w(z) 'before_eom.txt' using 1:2 via w0, z0

to obtain w0 and z0. Now I want to do the same in R. I tried a linear model like this (r = radius, z = distance):

beam <- function(z) {
sum(sqrt(1 + z**2))
}

lm(r ~ I(beam(z)), data = before_eom)

Then I tried a nonlinear model:

```d <- read.table ("before_eom.tab", header=T)
z <- d\$d
r <- d\$minor * 1e-6

```

beam<- function(p) {
M <- 1.1
sum((r-M*p*sqrt(1 + (z/p)**2))^2)
}

out <- nlm(beam, p=c(400, 0.1), hessian=TRUE) out\$estimate

This is very sensitive to the starting values and gives nonsensical answers as well...

Is there a simple way to translate the gnuplot fit into R?

Thanks,
Thomas

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