fda (version 2.2.7)

monomialpen: Evaluate Monomial Roughness Penalty Matrix

Description

The roughness penalty matrix is the set of inner products of all pairs of a derivative of integer powers of the argument.

Usage

monomialpen(basisobj, Lfdobj=int2Lfd(2),
            rng=basisobj$rangeval)

Arguments

basisobj

a monomial basis object.

Lfdobj

either a nonnegative integer specifying an order of derivative or a linear differential operator object.

rng

the inner product may be computed over a range that is contained within the range defined in the basis object. This is a vector or length two defining the range.

Value

• a symmetric matrix of order equal to the number of monomial basis functions.

See Also

polynompen, exponpen, fourierpen, bsplinepen, polygpen

Examples

# set up a monomial basis for the first five powers
nbasis   <- 5
basisobj <- create.monomial.basis(c(-1,1),nbasis)
#  evaluate the rougness penalty matrix for the
#  second derivative.
penmat <- monomialpen(basisobj, 2)