monomialpen function

Evaluate Monomial Roughness Penalty Matrix

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

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.

Returns

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

References

Ramsay, James O., Hooker, Giles, and Graves, Spencer (2009), Functional data analysis with R and Matlab, Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2005), Functional Data Analysis, 2nd ed., Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2002), Applied Functional Data Analysis, Springer, New York.

See Also

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)

##
## with rng of class Date and POSIXct
##
# Date
invasion1 <- as.Date('1775-09-04')
invasion2 <- as.Date('1812-07-12')
earlyUS.Canada <- c(invasion1, invasion2)
BspInvade1 <- create.monomial.basis(earlyUS.Canada)
invadmat <- monomialpen(BspInvade1)

# POSIXct
AmRev.ct <- as.POSIXct1970(c('1776-07-04', '1789-04-30'))
BspRev1.ct <- create.monomial.basis(AmRev.ct)
revmat <- monomialpen(BspRev1.ct)