B-spline Basis Function Values
bsplineS |
Language Reference for FDA Library
|
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
-
A nonnegative integer specifying the order of 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)