[R] smooth.spline

Sun Jul 20 05:43:04 CEST 2008

Fair enough. FOr a spline interpolation I can do the following:

> n <- 9
> x <- 1:n
> y <- rnorm(n)
> plot(x, y, main = paste("spline[fun](.) through", n, "points"))
> lines(spline(x, y))

Then look at the coefficients generated as:

> f <- splinefun(x, y)
> ls(envir = environment(f))
[1] "ties" "ux"   "z"   
> splinecoef <- get("z", envir = environment(f))
> slinecoef
$method
[1] 3

$n
[1] 9

$x
[1] 1 2 3 4 5 6 7 8 9

$y
[1]  0.93571604  0.44240485  0.45451903 -0.96207396 -1.13246522 -0.60032698
[7] -1.77506105 -0.09171419 -0.23262573

$b
[1] -1.53673409  0.22775629 -0.81788209 -1.16966436  0.73558677 -0.68744178
[7]  0.08639287  1.86770869 -2.92992167

$c
[1]  1.3657783  0.3987121 -1.4443504  1.0925682  0.8126830 -2.2357115  3.0095462
[8] -1.2282303 -3.5694000

$d
[1] -0.32235542 -0.61435416  0.84563953 -0.09329507 -1.01613149  1.74841922
[7] -1.41259217 -0.78038989 -0.78038989

WHen I look at ?spline there is even an example of "manually" using these coefficeients:

## Manual spline evaluation --- demo the coefficients :
.x <- get("ux", envir = environment(f))
u <- seq(3,6, by = 0.25)
(ii <- findInterval(u, .x))
dx <- u - .x[ii]
f.u <- with(splinecoef,
            y[ii] + dx*(b[ii] + dx*(c[ii] + dx* d[ii])))
stopifnot(all.equal(f(u), f.u))

For the smooth.spline as

spl <- smooth.spline(x,y)

I can also look at the coefficients:

spl$fit
$knot
 [1] 0.000 0.000 0.000 0.000 0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000
[13] 1.000 1.000 1.000

$nk
[1] 11

$min
[1] 1

$range
[1] 8

$coef
 [1]  0.90345898  0.73823276  0.40777431 -0.08046715 -0.54625461 -0.85205147
 [7] -0.96233408 -0.91373830 -0.66529714 -0.47674774 -0.38246971

attr(,"class")
[1] "smooth.spline.fit"

But there isn't an example on how to "manual" use these coefficients. This is what I was asking about. Once I hae the coefficients how do I "manually" interpolate using the coefficients given and x.

Thank you.

Kevin

---- Spencer Graves <spencer.graves at pdf.com> wrote: 
>       PLEASE do read the posting guide 
> http://www.R-project.org/posting-guide.html and provide commented, 
> minimal, self-contained, reproducible code.
> 
>       I do NOT know how to do what you want, but with a self-contained 
> example, I suspect many people on this list -- probably including me -- 
> could easily solve the problem.  Without such an example, there is a 
> high probability that any answer might (a) not respond to your need, and 
> (b) take more time to develop, just because we don't know enough of what 
> you are asking. 
> 
>       Spencer
> 
> rkevinburton at charter.net wrote:
> > Like I indicated. I understand the coefficients in a B-spline context. If I use the the 'spline' or 'splinefun' I can get the coefficients and they are grouped as 'a', 'b', 'c', and 'd' coefficients. But the coefficients for smooth.spline is just an array. I basically want to take these coefficients and outside of 'R' use them to form an interpolation. In other words I want 'R' to do the hard work and then export the results so they can be used else where.
> >
> > Thank you.
> >
> > Kevin
> >   
> 
> Spencer Graves wrote:
> >      I believe that a short answer to your question is that the 
> > "smooth" is a linear combination of B-spline basis functions, and the 
> > coefficients are the weights assigned to the different B-splines in 
> > that basis.
> >      Before offering a much longer answer, I would want to know what 
> > problem you are trying to solve and why you want to know.  For a brief 
> > description of B-splines, see 
> > "http://en.wikipedia.org/wiki/B-spline".  For a slightly longer 
> > commentary on them I suggest the "scripts\ch01.R" in the DierckxSpline 
> > package:  That script computes and displays some B-splines using 
> > "splineDesign", "spline.des" in the 'splines' package plus comparable 
> > functions in the 'fda' package.  For more info on this, I found the 
> > first chapter of Paul Dierckx (1993) Curve and Surface Fitting with 
> > Splines (Oxford U. Pr.).  Beyond that, I've learned a lot from the 
> > 'fda' package and the two companion volumes by Ramsay and Silverman 
> > (2006) Functional Data Analysis, 2nd ed. and (2002) Applied Functional 
> > Data Analysis (both Springer).
> >      If you'd like more help from this listserve, PLEASE do read the 
> > posting guide http://www.R-project.org/posting-guide.html and provide 
> > commented, minimal, self-contained, reproducible code.
> >         Hope this helps.      Spencer Graves
> >
> > rkevinburton at charter.net wrote:
> >> I like what smooth.spline does but I am unclear on the output. I can 
> >> see from the documentation that there are fit.coef but I am unclear 
> >> what those coeficients are applied to.With spline I understand the 
> >> "noraml" coefficients applied to a cubic polynomial. But these 
> >> coefficients I am not sure how to interpret. If I had a description 
> >> of the algorithm maybe I could figure it out but as it is I have this 
> >> question. Any help?
> >>
> >> Kevin
> >>
> >> ______________________________________________
> >> R-help at r-project.org mailing list
> >> https://stat.ethz.ch/mailman/listinfo/r-help
> >> PLEASE do read the posting guide 
> >> http://www.R-project.org/posting-guide.html
> >> and provide commented, minimal, self-contained, reproducible code.
> >>   
> >