ppBspline {fda}

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

References

Ramsay, James O., Hooker, Giles, and Graves, Spencer (2009), Functional data analysis with R and Matlab, Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2005), Functional Data Analysis, 2nd ed., Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2002), Applied Functional Data Analysis, Springer, New York.

See Also

bsplineS

Examples

  ppBspline(1:5)