# Classes "SplineBasis" and "OrthogonalSplineBasis"

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### Description

Contains the matrix representation for spline basis functions. The OrthongonalSplineBasis class has the basis functions orthogonalized.

### Objects from the Class

Objects can be created by calls of the form SplineBasis(knots, order) or to generate orthogonal spline basis functions directly OrthogonalSplineBasis(knots, order) or the short version OBasis(knots,order).

### Slots

transformation:

Object of class "matrix" Only applicable on OrthogonalSplineBasis Class, shows the transformation matrix use to get from regular basis functions to orthogonal basis functions.

knots:

Object of class "numeric"

order:

Object of class "integer"

Matrices:

Object of class "array"

### Methods

deriv

signature(expr = "SplineBasis"): Computes the derivative of the basis functions. Returns an object of class SplineBasis.

dim

signature(x = "SplineBasis"): gives the dim as the order and number of basis functions. Returns numeric of length 2.

evaluate

signature(object = "SplineBasis", x = "numeric"): Evaluates the basis functions and the points provided in x. Returns a matrix with length(x) rows and dim(object)[2] columns.

integrate

signature(object = "SplineBasis"): computes the integral of the basis functions defined by \int\limits_{k_0}^x b(t)dt where k_0 is the first knot. Returns an object of class SplineBasis.

orthogonalize

signature(object = "SplineBasis"): Takes in a SplinesBasis object, computes the orthogonalization transformation and returns an object of class OrthogonalSplineBasis.

plot

signature(x = "SplineBasis", y = "missing"): Takes an object of class SplineBasis and plots the basis functions for the domain defined by the knots in object.

plot

signature(x = "SplineBasis", y = "vector"): Interprets y as a vector of coefficients and plots the resulting curve.

plot

signature(x = "SplineBasis", y = "matrix"): Interprets y as a matrix of coefficients and plots the resulting curves.

### Author(s)

Andrew Redd <aredd at stat.tamu.edu>

### References

General matrix representations for Bsplines Kaihuai Qin, The Visual Computer 2000 16:177–186

SplineBasis
 1 2 3 4 5 6 7 showClass("SplineBasis") knots<-c(0,0,0,0:5,5,5,5) (base <-SplineBasis(knots)) (obase<-OBasis(knots)) plot(base) plot(obase)