norm.fdata: Approximates Lp-norm for functional data.

Description

Approximates Lp-norm for functional data (fdata) object using metric or semimetric functions. Norm for functional data using by default Lp-metric.

Usage

norm.fdata(fdataobj, metric = metric.lp, ...)
norm.fd(fdobj)

Arguments

fdataobj: fdata class object.
metric: Metric function, by default metric.lp.
...: Further arguments passed to or from other methods.
fdobj: Functional data or curves of fd class.

Author

Manuel Febrero-Bande, Manuel Oviedo de la Fuente manuel.oviedo@udc.es

Details

By default it computes the L2-norm with p = 2 and weights w with length=(m-1). $$Let \ \ f(x)= fdataobj(x)\ $$ $$\left\|f\right\|_p=\left ( \frac{1}{\int_{a}^{b}w(x)dx} \int_{a}^{b} \left|f(x)\right|^{p}w(x)dx \right)^{1/p}$$

The observed points on each curve are equally spaced (by default) or not.

Examples

Run this code

if (FALSE) {
x<-seq(0,2*pi,length=1001)
fx1<-sin(x)/sqrt(pi)
fx2<-cos(x)/sqrt(pi)
argv<-seq(0,2*pi,len=1001)
fdat0<-fdata(rep(0,len=1001),argv,range(argv))
fdat1<-fdata(fx1,x,range(x))
metric.lp(fdat1)
metric.lp(fdat1,fdat0)
norm.fdata(fdat1)
# The same
integrate(function(x){(abs(sin(x)/sqrt(pi))^2)},0,2*pi)
integrate(function(x){(abs(cos(x)/sqrt(pi))^2)},0,2*pi)

bspl1<- create.bspline.basis(c(0,2*pi),21)
fd.bspl1 <- fd(basisobj=bspl1)
fd.bspl2<-fdata2fd(fdat1,nbasis=21)
norm.fd(fd.bspl1)
norm.fd(fd.bspl2)
}