fda (version 1.1.8)

create.polynomial.basis: Create a Polynomial Basis

Description

Creates a set of basis functions consisting of powers of the argument shifted by a constant.

Usage

create.polynomial.basis(rangeval=c(0, 1), nbasis=2,
                        ctr=midrange, dropind=NULL,
                        quadvals=NULL, values=NULL)

Arguments

rangeval

a vector of length 2 defining the range.

nbasis

the number of basis functions. The default is 2, which defines a basis for straight lines.

ctr

this value is used to shift the argument prior to taking its power.

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 inter

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 polynom.

Details

The only difference between a monomial and a polynomial basis is the use of a shift value. This helps to avoid rounding error when the argument values are a long way from zero.

See Also

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

Examples

#  Create a polynomial basis over the years in the 20th century
#  and center the basis functions on 1950.
basisobj <- create.polynomial.basis(c(1900, 2000), nbasis=3, ctr=1950)
#  plot the basis
plot(basisobj)