norm.fdata

Approximates Lp-norm for functional data.

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

Keywords
math
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.

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

Aliases
  • norm.fdata
  • norm.fd
Examples
# NOT RUN {
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)
# }
# NOT RUN {
# }
Documentation reproduced from package fda.usc, version 2.0.1, License: GPL-2

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