fda (version 6.2.0)

bsplineS: 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, returnMatrix=FALSE)

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.

Arguments

x

A vector of argument values at which the B-spline basis functions are to be 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.

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.

returnMatrix

logical: If TRUE, a two-dimensional is returned using a special class from the Matrix package.

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.

Examples

# Minimal example:  A B-spline of order 1 (i.e., a step function)
# with 0 interior knots:
bS <- bsplineS(seq(0, 1, .2), 0:1, 1, 0)

# check
stopifnot(
all.equal(bS, matrix(1, 6))
)

#  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)