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

In DierckxSpline: R companion to "Curve and Surface Fitting with Splines"

Description

Translate a spline object of another class into DierckxSpline (class dierckx) format.

Usage

as.dierckx(x)
## S3 method for class 'fd'
as.dierckx(x)

Arguments

x	an object to be converted to class dierckx.

Details

The behavior depends on the class and nature of x. In particular, the DierckxSpline package only supports splines of order between 2 and 6, degree between 1 and 5, for linear through quintic splines. Other packages, e.g., fda support splines over a wider range and non-spline basis functions such as finite Fourier series. When these are encountered, as.dierckx throws an error.

• as.dierckx.fd The following describes how the components of a dierckx object are constructed from a spline object of a different class:

  • xRestored from the knots.

  • y Restored from spline predictions at the restored values of knot locations '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).

  • g stored 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"]]

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.

See Also

as.fd fd curfit

Examples

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)
curfit.xy <- curfit(x, y, s=0)

if(require(fda)) {
#  as.fd was not exported;  now it is,
#  but I need fda:::as.fd temporarily
  curfit.fd <- fda:::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.


  all.equal(knots(curfit.xy, FALSE), knots(curfit.fd, FALSE))


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


  curfit2 <- as.dierckx(curfit.fd)
  pred.y2 <- predict(curfit2, x.)
  sum(abs(pred.y-pred.y2))/(sum(abs(pred.y)+abs(pred.y2))/2)
# 1.3e-7


  all.equal(knots(curfit.xy, FALSE), knots(curfit2, FALSE))

# TRUE
  all.equal(coef(curfit.xy), coef(curfit2))
# "Mean relative  difference: 4.5e-7

  preserved <- c("from", "to", "n", "g", "periodic", "xlim","ylim")
  all.equal(curfit.xy[preserved], curfit2[preserved])
# TRUE
# Other components are NOT preserved in translation
# and so can NOT be restored.
}

DierckxSpline documentation built on May 2, 2019, 6:30 p.m.