[R] Calculate x-values from a spline

[Simon Wood]

On Friday 28 July 2006 13:31, Cuvelier Etienne wrote:
> Gunther Höning a écrit :
> > Hello,
> >
> > I calculate splines from messured points(x,y) of an unknown function
> > f(x). e.g.
> > x <- c(0.004115, 0.012345, 0.037037, 0.111110, 0.333330, 1.000000)
> > y <- c(37, 50, 45, 60, 50, 66)
> > w <- c(0.8540541, 0.8320000, 0.8822222, 0.7983333, 0.8220000, 0.8151515)
> > as weights
> > f <- smooth.spline(x,y,w)
> >
> > Now I have y-values and want to calculate the x-value(s) from this
> > spline. There is no further limitation to the spline, like monotonicity
> > or anything else..
> >
> > Does anyone know how to do this ?
>
> Perhaps this ?
>
> finv = splinefun(f$y,f$x)
>
I think this solution is a bit unstable, unless the spline is monotonic. For 
example...

set.seed(1)
x <- sort(runif(100)) ## divide this by 2 to get case where it works
y <- x*(1-x)+rnorm(100)*.01
par(mfrow=c(1,2))
plot(x,y,main="data and spline")
f <- smooth.spline(x,y) ## fit spline to simulated non-monotonic data
lines(x,fitted(f),col=2) ## plot fit
finv <- splinefun(f$y,f$x) ## "inverse function"
xx <- seq(0,0.25,length=1000) 
plot(xx,finv(xx),type="l",main="inverse!") ## plot of "inverse"
abline(0,0);abline(1,0) # plot range that x should lie in

The problem is that you can't really avoid dealing with the fact that the 
problem doesn't have a unique solution if the spline is not monotonic.

Simon

> > Gunther
> >
> >
> >
> > gunther.hoening at ukmainz.de
> >
> > ______________________________________________
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-- 
> Simon Wood, Mathematical Sciences, University of Bath, Bath, BA2 7AY UK
> +44 1225 386603  www.maths.bath.ac.uk/~sw283