as.fd: Convert a spline object to class 'fd'

In fda: Functional Data Analysis

Convert a spline object to class 'fd'

Description

Translate a spline object of another class into the Functional Data (class fd) format.

Usage

as.fd(x, ...)
## S3 method for class 'fdSmooth'
as.fd(x, ...)
## S3 method for class 'function'
as.fd(x, ...)
## S3 method for class 'smooth.spline'
as.fd(x, ...)

Arguments

x	an object to be converted to class fd.
...	optional arguments passed to specific methods, currently unused.

Details

The behavior depends on the class and nature of x.

as.fd.fdSmooth

extract the fd component

as.fd.function

Create an fd object from a function of the form created by splinefun. This will translate method = 'fmn' and 'natural' but not 'periodic': 'fmn' splines are isomorphic to standard B-splines with coincident boundary knots, which is the basis produced by create.bspline.basis. 'natural' splines occupy a subspace of this space, with the restriction that the second derivative at the end points is zero (as noted in the Wikipedia spline article). 'periodic' splines do not use coincident boundary knots and are not currently supported in fda; instead, fda uses finite Fourier bases for periodic phenomena.

as.fd.smooth.spline

Create an fd object from a smooth.spline object.

Author(s)

Spencer Graves

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.

spline entry in Wikipedia https://en.wikipedia.org/wiki/Spline_(mathematics)

See Also

fd splinefun

Examples

##
## as.fd.fdSmooth
##
girlGrowthSm <- with(growth, 
  smooth.basisPar(argvals=age, y=hgtf, lambda=0.1))
girlGrowth.fd <- as.fd(girlGrowthSm)

##
## as.fd.function(splinefun(...), ...)
##
x2 <- 1:7
y2 <- sin((x2-0.5)*pi)
fd_function <- splinefun(x2, y2)
fd.  <- as.fd(fd_function)
x.   <- seq(1, 7, .02)
fdx. <- fda::eval.fd(x., fd.)

# range(y2, fx., fdx.) generates an error 2012.04.22

rfdx <- range(fdx.)

oldpar <- par(no.readonly= TRUE)
plot(range(x2), range(y2, fdx., rfdx), type='n')
points(x2, y2)
lines(x., sin((x.-0.5)*pi), lty='dashed')
lines(x., fdx., col='blue')
lines(x., eval.fd(x., fd.), col='red', lwd=3, lty='dashed')
# splinefun and as.fd(splineful(...)) are close
# but quite different from the actual function
# apart from the actual 7 points fitted,
# which are fitted exactly
# ... and there is no information in the data
# to support a better fit!

# Translate also a natural spline
fn <- splinefun(x2, y2, method='natural')
fn. <- as.fd(fn)
lines(x., fn(x.), lty='dotted', col='blue')
lines(x., eval.fd(x., fn.), col='green', lty='dotted', lwd=3)

if(!CRAN()) {
# Will NOT translate a periodic spline
# fp <- splinefun(x, y, method='periodic')
# as.fd(fp)
# Error in as.fd.function(fp) :
#  x (fp)  uses periodic B-splines, and as.fd is programmed
#   to translate only B-splines with coincident boundary knots.
}

##
## as.fd.smooth.spline ... this doesn't work (24 January 2024)
##
#cars.spl <- with(cars, smooth.spline(speed, dist))
#cars.fd  <- as.fd(cars.spl)

#plot(dist~speed, cars)
#lines(cars.spl)
#sp. <- with(cars, seq(min(speed), max(speed), len=101))
#d. <- eval.fd(sp., cars.fd)
#lines(sp., d., lty=2, col='red', lwd=3)
par(oldpar)

fda documentation built on Sept. 30, 2024, 9:19 a.m.