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.
ppBspline(t)a list object containing components
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.
indices indicating where in the sequence t the knots are to be found
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.
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.
bsplineS