fda (version 6.1.8)

polygpen: Polygonal Penalty Matrix

Description

Computes the matrix defining the roughness penalty for functions expressed in terms of a polygonal basis.

Usage

polygpen(basisobj, Lfdobj=int2Lfd(1))

Value

a symmetric matrix of order equal to the number of basis functions defined by the polygonal basis object. Each element is the inner product of two polygonal basis functions after applying the derivative or linear differential operator defined by Lfdobj.

Arguments

basisobj

a polygonal functional basis object.

Lfdobj

either an integer that is either 0 or 1, or a linear differential operator object of degree 0 or 1.

Details

a roughness penalty for a function $ x(t) $ is defined by integrating the square of either the derivative of $ x(t) $ or, more generally, the result of applying a linear differential operator $ L $ to it. The only roughness penalty possible aside from penalizing the size of the function itself is the integral of the square of the first derivative, and this is the default. To apply this roughness penalty, the matrix of inner products produced by this function is necessary.

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

create.polygonal.basis, polyg

Examples

#  set up a sequence of 11 argument values
argvals <- seq(0,1,0.1)
#  set up the polygonal basis
basisobj <- create.polygonal.basis(argvals)
#  compute the 11 by 11 penalty matrix

penmat <- polygpen(basisobj)