subsample {Splinets}

Subsampling from a set of splines

Description

The function constructs a Splinets-object that is made of subsampled elements of the input Splinets-object. The input objects have to be of the same order and over the same knots.

Usage

subsample(Sp, ss)

Arguments

Sp

Splinets-object, a collection of s splines;

ss

vector of integers, the coordinates from 1:s;

Details

The output Splinet-object made of subsampled splines is always is of the regular type, i.e. SLOT type='sp'.

Value

An Splinets-object containing length(ss) splines that are selected from the input object./

References

Liu, X., Nassar, H., Podg\mbox{\'o}rski, K. "Dyadic diagonalization of positive definite band matrices and efficient B-spline orthogonalization." Journal of Computational and Applied Mathematics (2022) <https://doi.org/10.1016/j.cam.2022.114444>.

Podg\mbox{\'o}rski, K. (2021) "Splinets – splines through the Taylor expansion, their support sets and orthogonal bases." <arXiv:2102.00733>.

Nassar, H., Podg\mbox{\'o}rski, K. (2023) "Splinets 1.5.0 – Periodic Splinets." <arXiv:2302.07552>

See Also

is.splinets for diagnostic of Splinets-objects; construct for constructing such a Splinets-object; gather for combining Splinets-objects; refine for refinment of a spline to a larger number of knots; plot,Splinets-method for plotting Splinets-objects;

Examples

#-----------------------------------------------------#
#---------------------Subsampling---------------------#
#-----------------------------------------------------#

#Example with different support ranges, the 3rd order
n=25; xi=sort(runif(n+2)); xi[1]=0; xi[n+2]=1; k=3
supp=list(t(c(2,12)),t(c(4,20)),t(c(6,25))) #defining support ranges for three splines

#Initial random matrices of the derivative for each spline
set.seed(5)
SS1=matrix(rnorm((supp[[1]][1,2]-supp[[1]][1,1]+1)*(k+1)),ncol=(k+1)) 
SS2=matrix(rnorm((supp[[2]][1,2]-supp[[2]][1,1]+1)*(k+1)),ncol=(k+1)) 
SS3=matrix(rnorm((supp[[3]][1,2]-supp[[3]][1,1]+1)*(k+1)),ncol=(k+1)) 

spl=construct(xi,k,SS1,supp[[1]]) #constructing the first correct spline
nspl=construct(xi,k,SS2,supp[[2]],'CRFC')

#See 'gather' function for more details on what follows
spl=gather(spl,nspl) #the second and the first ones
nspl=construct(xi,k,SS3,supp[[3]],'CRLC')
spl=gather(spl,nspl) #the third is added

#Replicating by subsampling with replacement
sz=length(spl@der)
ss=sample(1:sz,size=10,rep=TRUE)

spl=subsample(spl,ss)
is.splinets(spl)[[1]]

spl@supp
spl@der

#Subsampling without replacements
ss=c(3,8,1)
sspl=subsample(spl,ss)

sspl@supp
sspl@der

is.splinets(sspl)[[1]]

#A single spline sampled from a 'Splinets' object
is.splinets(subsample(sspl,1))