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

In fda: Functional Data Analysis

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

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)

fda documentation built on May 31, 2023, 9:19 p.m.