fda (version 2.4.0)

create.polygonal.basis: Create a Polygonal Basis

Description

A basis is set up for constructing polygonal lines, consisting of straight line segments that join together.

Usage

create.polygonal.basis(rangeval=NULL, argvals=NULL, dropind=NULL,
        quadvals=NULL, values=NULL, basisvalues=NULL, names='polygon',
        axes=NULL)

Arguments

rangeval

a numeric vector of length 2 defining the interval over which the functional data object can be evaluated; default value is if(is.null(argvals)) 0:1 else range(argvals).

If length(rangeval) == 1 and rangeval <

argvals

a strictly increasing vector of argument values at which line segments join to form a polygonal line.

dropind

a vector of integers specifiying the basis functions to be dropped, if any. For example, if it is required that a function be zero at the left boundary, this is achieved by dropping the first basis function, the only one that is nonzero a

quadvals

a matrix with two columns and a number of rows equal to the number of quadrature points for numerical evaluation of the penalty integral. The first column of quadvals contains the quadrature points, and the second column the quad

values

a list containing the basis functions and their derivatives evaluated at the quadrature points contained in the first column of quadvals.

basisvalues

A list of lists, allocated by code such as vector("list",1). This is designed to avoid evaluation of a basis system repeatedly at a set of argument values. Each sublist corresponds to a specific set of argument values, and must have at least

names

either a character vector of the same length as the number of basis functions or a single character string to which 1:nbasis are appended as paste(names, 1:nbasis, sep=''. For example, if nbasis = 4, thi

axes

an optional list used by selected plot functions to create custom axes. If this axes argument is not NULL, functions plot.basisfd, plot.fd, plot.fdSmooth

Value

• a basis object with the type polyg.

Details

The actual basis functions consist of triangles, each with its apex over an argument value. Note that in effect the polygonal basis is identical to a B-spline basis of order 2 and a knot or break value at each argument value. The range of the polygonal basis is set to the interval defined by the smallest and largest argument values.

See Also

basisfd, create.bspline.basis, create.basis, create.constant.basis, create.exponential.basis, create.fourier.basis, create.monomial.basis, create.polynomial.basis, create.power.basis

Examples

#  Create a polygonal basis over the interval [0,1]
#  with break points at 0, 0.1, ..., 0.95, 1
(basisobj <- create.polygonal.basis(seq(0,1,0.1)))
#  plot the basis
plot(basisobj)