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

In fda: Functional Data Analysis

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.fdSmoothextract the fd component

• as.fd.dierckx The 'fda' package (as of version 2.0.0) supports B-splines with coincident boundary knots. For periodic phenomena, the DierckxSpline packages uses periodic spines, while fda recommends finite Fourier series. Accordingly, as.fd.dierckx if x[["periodic"]] is TRUE.

  The following describes how the components of a dierckx object are handled by as.dierckx(as.fd(x)):

  • xlost. Restored from the knots.

  • y lost. Restored from spline predictions at the restored values of 'x'.

  • wlost. Restored as rep(1, length(x)).

  • from, tofd[["basis"]][["rangeval"]]

  • k coded indirectly as fd[["basis"]][["nbasis"]] - length(fd[["basis"]][["params"]]) - 1.

  • slost, restored as 0.

  • nestlost, restored as length(x) + k + 1

  • n coded indirectly as 2*fd[["basis"]][["nbasis"]] - length(fd[["basis"]][["params"]]).

  • knots The end knots are stored (unreplicated) in fd[["basis"]][["rangeval"]], while the interior knots are stored in fd[["basis"]][["params"]].

  • fplost. Restored as 0.

  • wrk, lwrk, iwrk lost. Restore by refitting to the knots.

  • ierlost. Restored as 0.

  • messagelost. Restored as character(0).

  • gstored indirectly as length(fd[["basis"]][["params"]]).

  • methodlost. Restored as "ss".

  • periodic 'dierckx2fd' only translates 'dierckx' objects with coincident boundary knots. Therefore, 'periodic' is restored as FALSE.

  • routinelost. Restored as 'curfit.default'.

  • xlabfd[["fdnames"]][["args"]]

  • ylabfd[["fdnames"]][["funs"]]

• 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 coindicent 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.

Value

as.fd.dierckx converts an object of class 'dierckx' into one of class fd.

Author(s)

Spencer Graves

References

Dierckx, P. (1991) Curve and Surface Fitting with Splines, Oxford Science Publications.

Ramsay, James O., and Silverman, Bernard W. (2006), 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 http://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)
f <- splinefun(x2, y2)
fd. <- as.fd(f)
x. <- seq(1, 7, .02)
fx. <- f(x.)
fdx. <- eval.fd(x., fd.)

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

rfdx <- range(fdx.)

plot(range(x2), range(y2, fx., rfdx), type='n')
points(x2, y2)
lines(x., sin((x.-0.5)*pi), lty='dashed')
lines(x., f(x.), 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)

## Not run: 
# 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.


## End(Not run)

##
## as.fd.smooth.spline
##
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)

fda documentation built on May 2, 2019, 5:12 p.m.