splineUpdate {ivmte}

Constructing higher order splines

Description

This function recursively constructs the higher order splines basis. Note that the function does not take into consideration the order of the final basis function. The dimensions of the inputs dicate this, and are updated in each iteration of the recursion. The recursion ends once the row number of argument bmat reaches 1. This function was coded in accordance to Carl de Boor's set of notes on splines, "B(asic)-Spline Basics".

Usage

splineUpdate(x, bmat, knots, i, current.order)

Arguments

x

vector, the values at which to evaluate the basis function.

bmat

matrix. Each column of bmat corresponds to an element of argument x. Each row corresponds to the evaluation of basis component i, i + 1, .... The recursive nature of splines requires that we initially evaluate the basis functions for components i, ..., i + degree of spline. Each iteration of the recursion reduces the row of bmat by 1. The recursion terminates once bmat has only a single row.

knots

vector, the internal knots.

i

integer, the basis component of interest.

current.order

integer, the current order associated with the argument bmat.

Value

vector, the evaluation of the spline at each value in vector x.