fda (version 6.2.0)

deriv.fd: Compute a Derivative of a Functional Data Object

Description

A derivative of a functional data object, or the result of applying a linear differential operator to a functional data object, is then converted to a functional data object. This is intended for situations where a derivative is to be manipulated as a functional data object rather than simply evaluated.

Usage

# S3 method for fd
deriv(expr, Lfdobj=int2Lfd(1), ...)

Value

a functional data object for the derivative

Arguments

expr

a functional data object. It is assumed that the basis for representing the object can support the order of derivative to be computed. For B-spline bases, this means that the order of the spline must be at least one larger than the order of the derivative to be computed.

Lfdobj

either a positive integer or a linear differential operator object.

...

Other arguments to match generic for 'deriv'

Details

Typically, a derivative has more high frequency variation or detail than the function itself. The basis defining the function is used, and therefore this must have enough basis functions to represent the variation in the derivative satisfactorily.

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

getbasismatrix, eval.basis deriv

Examples

#  Estimate the acceleration functions for growth curves
#  See the analyses of the growth data.
#  Set up the ages of height measurements for Berkeley data
age <- c( seq(1, 2, 0.25), seq(3, 8, 1), seq(8.5, 18, 0.5))
#  Range of observations
rng <- c(1,18)
#  Set up a B-spline basis of order 6 with knots at ages
knots  <- age
norder <- 6
nbasis <- length(knots) + norder - 2
hgtbasis <- create.bspline.basis(rng, nbasis, norder, knots)
#  Set up a functional parameter object for estimating
#  growth curves.  The 4th derivative is penalyzed to
#  ensure a smooth 2nd derivative or acceleration.
Lfdobj <- 4
lambda <- 10^(-0.5)   #  This value known in advance.
growfdPar <- fdPar(fd(matrix(0,nbasis,1),hgtbasis), Lfdobj, lambda)
#  Smooth the data.  The data for the boys and girls
#  are in matrices hgtm and hgtf, respectively.
hgtmfd <- smooth.basis(age, growth$hgtm, growfdPar)$fd
hgtffd <- smooth.basis(age, growth$hgtf, growfdPar)$fd
#  Compute the acceleration functions
accmfd <- deriv.fd(hgtmfd, 2)
accffd <- deriv.fd(hgtffd, 2)
#  Plot the two sets of curves
oldpar <- par(mfrow=c(2,1))
plot(accmfd)
plot(accffd)
par(oldpar)