From: <rkevinburton_at_charter.net>

Date: Sat, 19 Jul 2008 20:43:04 -0700

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. Received on Sun 20 Jul 2008 - 03:54:23 GMT

Date: Sat, 19 Jul 2008 20:43:04 -0700

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.**> >>**> >*

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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. Received on Sun 20 Jul 2008 - 03:54:23 GMT

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