Description Usage Arguments Details Value Author(s) See Also Examples
Convert B-Spline coefficients into a local Taylor series representation expanded about the midpoint between each pair of distinct knots.
1 2 3 4 5 6 7 | TaylorSpline(object, ...)
## S3 method for class 'fd'
TaylorSpline(object, ...)
## S3 method for class 'fdPar'
TaylorSpline(object, ...)
## S3 method for class 'fdSmooth'
TaylorSpline(object, ...)
|
object |
a spline object possibly of some other class |
... |
optional arguments |
1. Is object
a spline object with a B-spline basis? If no,
throw an error.
2. Find knots
and midpoints
.
3. Obtain coef(object).
4. Determine the number of dimensions of coef(object) and create
empty coef
and deriv
arrays to match. Then fill the
arrays.
a list with the following components:
knots |
a numeric vector of knots(object, interior=FALSE) |
midpoints |
midpoints of intervals defined by unique(knots) |
coef |
A matrix of dim = c(nKnots-1, norder) containing the coeffients of a polynomial in (x-midpoints[i]) for interval i, where nKnots = length(unique(knots)). |
deriv |
A matrix of dim = c(nKnots-1, norder) containing the derivatives
of the spline evaluated at |
Spencer Graves
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 | ##
## The simplest b-spline basis: order 1, degree 0, zero interior knots:
## a single step function
##
bspl1.1 <- create.bspline.basis(norder=1, breaks=0:1)
# ... jump to pi to check the code
fd.bspl1.1pi <- fd(pi, basisobj=bspl1.1)
bspl1.1pi <- TaylorSpline(fd.bspl1.1pi)
##
## Cubic spline: 4 basis functions
##
bspl4 <- create.bspline.basis(nbasis=4)
plot(bspl4)
parab4.5 <- fd(c(3, -1, -1, 3)/3, bspl4)
# = 4*(x-.5)
TaylorSpline(parab4.5)
##
## A more realistic example
##
data(titanium)
# Cubic spline with 5 interior knots (6 segments)
# do not run this example on CRAN to save test time
#if(!CRAN()){
#titan10 <- with(titanium, curfit.free.knot(x, y))
#(titan10T <- TaylorSpline(titan10) )
#}
|
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