Compute fucntional coefficients from functional data represented in a base of functions

Compute fucntional coefficients from functional data (fdata class object) represented in a basis (fixed of data-driven basis).

Usage

fdata2basis(fdataobj, basis, method = c("grid", "inprod"))

# S3 method for class 'basis.fdata'
summary(object, draw = TRUE, index = NULL, ...)

Arguments

fdataobj: fdata class object.
basis: a functional basis object defining the basis
method: character string, if it is "grid" the fdata object is evaluated in the grid (argvals of fdata), if it is "inprod" the basis representation of functional data is computed by inner product (inprod.fdata(fdataobj,basis)).
object: basis.fdata class object calculated by: fdata2basis
draw: logical, original curves and their basis representation are plotted
index: vector, by default (if NULL) the first n curves are plotted, where n = min(4, length(fdataobj)). Otherwise, index vector indicates taht curvesare plotted.
...: Further arguments passed to or from other methods.

Value

The fdata2basis function returns:

coef: A matrix or two-dimensional array of coefficients.
basis: Basis of fdata class evaluated on the same grid as fdataobj.

And summary function return:

R: a matrix with a measure similar to R-sq for each curve aproximation (by row) and number of basis elements (by column).

Author

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

Examples

if (FALSE) { # \dontrun{
T <- 71
S <- 51
tj <- round(seq(0,1,len=T),3)
si <- round(seq(0,1,len=S),3)
beta1 <- outer(si,tj,function(si,tj){exp(-5*abs((tj-si)/5))})
nbasis.s =7
nbasis.t=11
base.s <- create.fourier.basis(c(0,1),nbasis=nbasis.s)
base.t <- create.fourier.basis(c(0,1),nbasis=nbasis.t)
y1 <- fdata(rbind(log(1+tj),1-5*(tj-0.5)^2),argvals=tj,rangeval=c(0,1))
aa <- fdata2basis(y1,base.t,method="inprod")
summary(aa)
plot(gridfdata(aa$coefs,aa$basis))
lines(y1,lwd=2,col=c(3,4),lty=2)
} # }