fourierpen | Language Reference for FDA Library
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fourierpen(basisobj, Lfdobj=2)
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 most common roughness penalty is the integral of the square of the second derivative, and this is the default. To apply this roughness penalty, the matrix of inner products of the basis functions (possibly after applying the linear differential operator to them) defining this function is necessary. This function just calls the roughness penalty evaluation function specific to the basis involved.
# set up a Fourier basis with 13 basis functions # and and period 1.0. basisobj <- create.fourier.basis(c(0,1),13) # compute the 13 by 13 matrix of inner products # of second derivatives penmat <- fourierpen(basisobj)