# bsplineS: B-spline Basis Function Values In fda: Functional Data Analysis

 bsplineS R Documentation

## 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)
```

### 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.

### 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

```# 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

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)
```

fda documentation built on April 27, 2022, 1:07 a.m.