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

 ZBsplineBasis R Documentation

## ZB-spline basis

### 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

``````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

``````# 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 Aug. 25, 2023, 5:13 p.m.