fda (version 2.4.7)

ppBspline: 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

Run this code
# NOT RUN {
  ppBspline(1:5)
# }

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