Convert a spline object to class 'fd'
Translate a spline object of another class into the
Functional Data (class fd) format.
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, ...)
x |
an object to be converted to class |
... |
optional arguments passed to specific methods, currently unused. |
The behavior depends on the class and nature of x.
as.fd.fdSmoothextract 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.
Spencer Graves
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
https://en.wikipedia.org/wiki/Spline_(mathematics)
## ## 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)
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