Calculate x-values from a spline

Gunther H?ning a ?crit :

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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