# Classes "SplineBasis" and "OrthogonalSplineBasis"

### 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

### See Also

`SplineBasis`

### Examples

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