fs.test {mgcv} R Documentation

## FELSPLINE test function

### Description

Implements a finite area test function based on one proposed by Tim Ramsay (2002).

### Usage

```
fs.test(x,y,r0=.1,r=.5,l=3,b=1,exclude=TRUE)
fs.boundary(r0=.1,r=.5,l=3,n.theta=20)
```

### Arguments

 `x,y` Points at which to evaluate the test function. `r0` The test domain is a sort of bent sausage. This is the radius of the inner bend `r` The radius of the curve at the centre of the sausage. `l` The length of an arm of the sausage. `b` The rate at which the function increases per unit increase in distance along the centre line of the sausage. `exclude` Should exterior points be set to `NA`? `n.theta` How many points to use in a piecewise linear representation of a quarter of a circle, when generating the boundary curve.

### Details

The function details are not given in the source article: but this is pretty close. The function is modified from Ramsay (2002), in that it bulges, rather than being flat: this makes a better test of the smoother.

### Value

`fs.test` returns function evaluations, or `NA`s for points outside the boundary. `fs.boundary` returns a list of `x,y` points to be jointed up in order to define/draw the boundary.

### Author(s)

Simon N. Wood simon.wood@r-project.org

### References

Tim Ramsay (2002) "Spline smoothing over difficult regions" J.R.Statist. Soc. B 64(2):307-319

### Examples

```require(mgcv)
## plot the function, and its boundary...
fsb <- fs.boundary()
m<-300;n<-150
xm <- seq(-1,4,length=m);yn<-seq(-1,1,length=n)
xx <- rep(xm,n);yy<-rep(yn,rep(m,n))
tru <- matrix(fs.test(xx,yy),m,n) ## truth
image(xm,yn,tru,col=heat.colors(100),xlab="x",ylab="y")
lines(fsb\$x,fsb\$y,lwd=3)