# ZBsplineBasis: ZB-spline basis In robCompositions: Compositional Data Analysis

## Description

Spline basis system having zero-integral on I=[a,b] of the L^2_0 space (called ZB-splines) has been proposed for an basis representation of fcenLR transformed probability density functions. The ZB-spline basis functions can be back transformed to Bayes spaces using inverse of fcenLR transformation, resulting in compositional B-splines (CB-splines), and forming a basis system of the Bayes spaces.

## Usage

 `1` ```ZBsplineBasis(t, knots, order, basis.plot = FALSE) ```

## Arguments

 `t` a vector of argument values at which the ZB-spline basis functions are to be evaluated `knots` sequence of knots `order` order of the ZB-splines (i.e., degree + 1) `basis.plot` if TRUE, the ZB-spline basis system is plotted

## Value

 `ZBsplineBasis` matrix of ZB-spline basis functions evaluated at a vector of argument values t `nbasis` number of ZB-spline basis functions

## Author(s)

J. Machalova jitka.machalova@upol.cz, R. Talska talskarenata@seznam.cz

## References

Machalova, J., Talska, R., Hron, K. Gaba, A. Compositional splines for representation of density functions. Comput Stat (2020). https://doi.org/10.1007/s00180-020-01042-7

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21``` ```# Example: ZB-spline basis functions evaluated at a vector of argument values t t = seq(0,20,l=500) knots = c(0,2,5,9,14,20) order = 4 ZBsplineBasis.out = ZBsplineBasis(t,knots,order, basis.plot=TRUE) # Back-transformation of ZB-spline basis functions from L^2_0 to Bayes space -> # CB-spline basis functions CBsplineBasis=NULL for (i in 1:ZBsplineBasis.out\$nbasis) { CB_spline = fcenLRinv(t,diff(t)[1:2],ZBsplineBasis.out\$ZBsplineBasis[,i]) CBsplineBasis = cbind(CBsplineBasis,CB_spline) } matplot(t,CBsplineBasis, type="l",lty=1, las=1, col=rainbow(ZBsplineBasis.out\$nbasis), xlab="t", ylab="CB-spline basis", cex.lab=1.2,cex.axis=1.2) abline(v=knots, col="gray", lty=2) ```

robCompositions documentation built on Jan. 13, 2021, 10:07 p.m.