B-spline Basis Function Values

B-spline Basis Function Values

DESCRIPTION:

Evaluates a set of B-spline basis functions, or a derivative of these functions, at a set of arguments.

USAGE:

bsplineS(x, breaks, norder=4, nderiv=0)

REQUIRED ARGUMENTS:

x
A vector of argument values at which the B-spline basis functions are to evaluated.
breaks
A strictly increasing set of break values defining the B-spline basis. The argument values
x
should be within the interval spanned by the break values.

OPTIONAL ARGUMENTS:

norder
The order of the B-spline basis functions. The order less one is the degree of the piece-wise polynomials that make up any B-spline function. The default is order 4, meaning piece-wise cubic.
nderiv
The derivative to be evaluated. The derivative must not exceed the order. The default derivative is 0, meaning that the basis functions themselves are evaluated.

VALUE:

A matrix of function values. The number of rows equals the number of arguments, and the number of columns equals the number of basis functions.

EXAMPLES:

#  set up break values at 0.0, 0.2,..., 0.8, 1.0.
breaks <- seq(0,1,0.2)
#  set up a set of 11 argument values
x <- seq(0,1,0.1)
#  the order willl be 4, and the number of basis functions
#  is equal to the number of interior break values (4 here)
#  plus the order, for a total here of 8.
norder <- 4
#  compute the 11 by 8 matrix of basis function values
basismat <- bsplineS(x, breaks, norder)