Evaluate Monomial Roughness Penalty Matrix
monomialpen
Language Reference for FDA Library

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)

REQUIRED ARGUMENTS:

basisobj
a monomial basis object.

OPTIONAL ARGUMENTS:

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)