Lfd | Language Reference for FDA Library
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Lfd(nderiv=0, bwtlist=vector("list", 0))
To check that an object is of this class, use functions
is.Lfd
or
int2Lfd
.
Linear differential operator objects are often used to define roughness penalties for smoothing towards a "hypersmooth" function that is annihilated by the operator. For example, the harmonic acceleration operator used in the analysis of the daily weather data annihilates linear combinations of 1, sin(2 pi t/365) and cos(2 pi t/365), and the larger the smoothing parameter, the closer the smooth function will be to a function of this shape.
Function
pda.fd
estimates a linear differential
operator object that comes as close as possible to annihilating
a functional data object.
A linear differential operator of order m is a linear combination of the derivatives of a functional data object up to order m. The derivatives of orders 0, 1, ..., m-1 can each be multiplied by a weight function b(t) that may or may not vary with argument t.
If the notation D^j is taken to mean "take the derivative of order j", then a linear differental operator L applied to function x has the expression Lx(t) = b_0(t) x(t) + b_1(t)Dx(t) + ... + b_{m-1}(t) D^{m-1} x(t) + D^mx(t).
# Set up the harmonic acceleration operator Lbasis <- create.constant.basis(dayrange); Lcoef <- matrix(c(0,(2*pi/365)^2,0),1,3) bfdobj <- fd(Lcoef,Lbasis) bwtlist <- fd2list(bfdobj) harmaccelLfd <- Lfd(3, bwtlist)