fda (version 1.2.3)

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(argvals=NULL, dropind=NULL,
                       quadvals=NULL, values=NULL)

Arguments

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 argument values used to approximate an integral using Simpson's rule. The first column contains these argument values. A minimum of 5 values are required for each int

values

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

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.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)