ppBspline: Convert a B-spline function to piece-wise polynomial form

In fda: Functional Data Analysis

Description

The B-spline basis functions of order k = length(t) - 1 defined by the knot sequence in argument t each consist of polynomial segments with the same order joined end-to-end over the successive gaps in the knot sequence. This function computes the k coefficients of these polynomial segments in the rows of the output matrix coeff, with each row corresponding to a B-spline basis function that is positive over the interval spanned by the values in t. The elements of the output vector index indicate where in the sequence t we find the knots. Note that we assume t[1] < t[k+1], i.e. t is not a sequence of the same knot.

Usage

  ppBspline(t)

Arguments

t	numeric vector = knot sequence of length norder+1 where norder = the order of the B-spline. The knot sequence must contain at least one gap.

Value

a list object containing components

Coeff	a matrix with rows corresponding to B-spline basis functions positive over the interval spanned by t and columns corresponding to the terms 1, x, x^2, ... in the polynomial representation.
index	indices indicating where in the sequence t the knots are to be found

See Also

bsplineS

Examples

  ppBspline(1:5)

Example output

Loading required package: splines
Loading required package: Matrix

Attaching package: 'fda'

The following object is masked from 'package:graphics':

    matplot

[[1]]
           [,1] [,2] [,3]      [,4]
[1,]  0.1666667  0.0  0.0 0.0000000
[2,] -0.5000000  0.5  0.5 0.1666667
[3,]  0.5000000 -1.0  0.0 0.6666667
[4,] -0.1666667  0.5 -0.5 0.1666667

[[2]]
[1] 1 2 3 4

fda documentation built on May 2, 2019, 5:12 p.m.