FELSPLINE test function
Implements a finite area test function based on one proposed by Tim Ramsay (2002).
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)
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 |
n.theta |
How many points to use in a piecewise linear representation of a quarter of a circle, when generating the boundary curve. |
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.
fs.test returns function evaluations, or NAs 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.
Simon N. Wood simon.wood@r-project.org
Tim Ramsay (2002) "Spline smoothing over difficult regions" J.R.Statist. Soc. B 64(2):307-319
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) contour(xm,yn,tru,levels=seq(-5,5,by=.25),add=TRUE)
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