exponpen | Language Reference for FDA Library
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exponpen(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 an exponential basis with 3 basis functions ratevec <- c(0, -1, -5) basisobj <- create.exponential.basis(c(0,1),3,ratevec) # compute the 3 by 3 matrix of inner products of # second derivatives penmat <- exponpen(basisobj)