fda (version 2.4.0)

fd: Define a Functional Data Object

Description

This is the constructor function for objects of the fd class. Each function that sets up an object of this class must call this function. This includes functions Data2fd, smooth.basis, density.fd, and so forth that estimate functional data objects that smooth or otherwise represent data. Ordinarily, users of the functional data analysis software will not need to call this function directly, but these notes are valuable to understanding the components of a list of class fd.

Usage

fd(coef=NULL, basisobj=NULL, fdnames=NULL)

Arguments

coef

a vector, matrix, or three-dimensional array of coefficients.

The first dimension (or elements of a vector) corresponds to basis functions.

A second dimension corresponds to the number of functional observations, curves or replicates. I

basisobj

a functional basis object defining the basis

if(is.null(basisobj)){ if(is.null(coef)) basisobj <- basisfd() else { rc <- range(coef) if(diff(rc)==0) rc <- rc+0:1 nb <- max(4, nrow(coef)) basisobj <- create.bspline.basis(rc, nbasis

fdnames

A list of length 3, each member being a string vector containing labels for the levels of the corresponding dimension of the discrete data. The first dimension is for argument values, and is given the default name "time", the second is for re

Value

• A functional data object (i.e., having class fd), which is a list with components named coefs, basis, and fdnames.

source

Ramsay, James O., and Silverman, Bernard W. (2006), Functional Data Analysis, 2nd ed., Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2002), Applied Functional Data Analysis, Springer, New York

Details

To check that an object is of this class, use function is.fd.

Normally only developers of new functional data analysis functions will actually need to use this function.

See Also

smooth.basis smooth.basisPar Data2fd density.fd create.bspline.basis arithmetic.fd

Examples

##
## default
##
fd()

##
## The simplest b-spline basis:  order 1, degree 0, zero interior knots:
##       a single step function
##
bspl1.1 <- create.bspline.basis(norder=1, breaks=0:1)
fd.bspl1.1 <- fd(0, basisobj=bspl1.1)

fd.bspl1.1a <- fd(basisobj=bspl1.1)
stopifnot(
all.equal(fd.bspl1.1, fd.bspl1.1a)
)
# TRUE

fd.bspl1.1b <- fd(0)
Error in fd(0) :
  Number of coefficients does not match number of basis functions.

... because fd by default wants to create a cubic spline
##
## Cubic spline:  4  basis functions
##
bspl4 <- create.bspline.basis(nbasis=4)
plot(bspl4)
parab4.5 <- fd(c(3, -1, -1, 3)/3, bspl4)
# = 4*(x-.5)^2
plot(parab4.5)

##
## Fourier basis
##
f3 <- fd(c(0,0,1), create.fourier.basis())
plot(f3)
# range over +/-sqrt(2), because
# integral from 0 to 1 of cos^2 = 1/2
# so multiply by sqrt(2) to get
# its square to integrate to 1.

##
## subset of an fd object
##
gaitbasis3 <- create.fourier.basis(nbasis=5)
gaitfd3    <- Data2fd(gait, basisobj=gaitbasis3)
gaitfd3[1]