fda (version 2.4.0)

as.fd: 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 'dierckx':
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.

Value

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

item

• as.fd.function
• as.fd.smooth.spline

code

smooth.spline

Details

The behavior depends on the class and nature of x.

• as.fd.fdSmooth

{extract 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)):

• x

{lost. Restored from the knots.} y{ lost. Restored from spline predictions at the restored values of 'x'. } w{lost. Restored as rep(1, length(x)).} from, to{fd[["basis"]][["rangeval"]] } k{ coded indirectly as fd[["basis"]][["nbasis"]] - length(fd[["basis"]][["params"]]) - 1. } s{lost, restored as 0.} nest{lost, 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"]]. } fp{lost. Restored as 0.} wrk, lwrk, iwrk{ lost. Restore by refitting to the knots. } ier{lost. Restored as 0.} message{lost. Restored as character(0).} g{stored indirectly as length(fd[["basis"]][["params"]]).} method{lost. Restored as "ss".} periodic{ 'dierckx2fd' only translates 'dierckx' objects with coincident boundary knots. Therefore, 'periodic' is restored as FALSE. } routine{lost. Restored as 'curfit.default'.} xlab{fd[["fdnames"]][["args"]]} ylab{fd[["fdnames"]][["funs"]]} }

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

as.dierckx curfit 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.dierckx
##
x <- 0:24
y <- c(1.0,1.0,1.4,1.1,1.0,1.0,4.0,9.0,13.0,
       13.4,12.8,13.1,13.0,14.0,13.0,13.5,
       10.0,2.0,3.0,2.5,2.5,2.5,3.0,4.0,3.5)
library(DierckxSpline)
curfit.xy <- curfit(x, y, s=0)

curfit.fd <- as.fd(curfit.xy)
plot(curfit.fd) # as an 'fd' object
points(x, y) # Curve goes through the points.

x. <- seq(0, 24, length=241)
pred.y <- predict(curfit.xy, x.)
lines(x., pred.y, lty="dashed", lwd=3, col="blue")
# dierckx and fd objects match.

stopifnot(
all.equal(knots(curfit.xy, FALSE), knots(curfit.fd, FALSE))
)
stopifnot(
all.equal(coef(curfit.xy), as.vector(coef(curfit.fd)))
)

##
## 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)

# 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
##
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)