R: ZB-spline basis

ZBsplineBasis {robCompositions} | 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)

[Package robCompositions version 2.3.1 Index]