robCompositions (version 2.4.1)

ZBsplineBasis: 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)

Value

ZBsplineBasis

matrix of ZB-spline basis functions evaluated at a vector of argument values t

nbasis

number of ZB-spline basis functions

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

Author

J. Machalova , R. Talska

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)