fda.usc (version 1.2.3)

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

Description

Aproximates 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.

fdobj

Functional data or curves of fd class.

metric

Metric function, by default metric.lp.

...

Further arguments passed to or from other methods.

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.

See Also

See also metric.lp and norm Alternative method: inprod of fda-package

Examples

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)