Generate orthonormal eigenfunctions
This function calculates M (orthonormal) basis functions on a given interval, that can be interpreted as the first M eigenfunctions of an appropriate data generating process of functional data.
eFun(argvals, M, ignoreDeg = NULL, type)
argvals |
A vector of numerics, defining a (fine) grid on the interval for which the basis functions are computed. |
M |
An integer, specifying the number of functions that are calculated. |
ignoreDeg |
A vector of numerics, specifying the degrees to be ignored
for type |
type |
A character string, specifying the type of functions that are calculated. See Details. |
The function implements three families of orthonormal basis functions plus
variations of them. The parameter type, that specifies the functions
to be calculated, can have the following values:
"Poly": Calculate orthonormal Legendre polynomials of degree
0,...,M-1.
"PolyHigh": Calculate M orthonormal Legendre
Polynomials of higher degree. The vector of indices ignoreDeg
specifies the functions to be ignored. If ignoreDeg is not specified,
the function returns an error.
"Fourier": Calculate the first
M Fourier basis functions.
"FourierLin": Calculate the
first M-1 Fourier basis functions plus the linear function,
orthonormalized to the previous functions via Gram-Schmidts method. This type
is currently implemented for functions on the unit interval [0,1] only.
If the function is called with other argvals, an error is thrown.
"Wiener": Calculate the first M orthonormal eigenfunctions
of the Wiener process.
A univariate functional data object of class
funData containing the basis functions on the given
interval.
oldPar <- par(no.readonly = TRUE) argvals <- seq(0,1,0.01) par(mfrow = c(3,2)) plot(eFun(argvals, M = 4, type = "Poly"), main = "Poly", ylim = c(-3,3)) plot(eFun(argvals, M = 4, ignoreDeg = 1:2, type = "PolyHigh"), main = "PolyHigh", ylim = c(-3,3)) plot(eFun(argvals, M = 4, type = "Fourier"), main = "Fourier", ylim = c(-3,3)) plot(eFun(argvals, M = 4, type = "FourierLin"), main = "FourierLin", ylim = c(-3,3)) plot(eFun(argvals, M = 4, type = "Wiener"), main = "Wiener", ylim = c(-3,3)) par(oldPar)
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