ZB-spline basis
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.
ZBsplineBasis(t, knots, order, basis.plot = FALSE)
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 |
|
matrix of ZB-spline basis functions evaluated at a vector of argument values t |
|
number of ZB-spline basis functions |
J. Machalova jitka.machalova@upol.cz, R. Talska talskarenata@seznam.cz
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
# 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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.