R/Examples/ExExsupp.R

In Splinets: Functional Data Analysis using Splines and Orthogonal Spline Bases

#----------------------------------------------------#
#---Correcting support sets in a derivative matrix---#
#----------------------------------------------------#
n=20; k=3; xi=seq(0,1,by=1/(n+1)) #an even number of equally spaced knots 
set.seed(5)
S=matrix(rnorm((n+2)*(k+1)),ncol=(k+1))
spl=construct(xi,k,S) #this spline will be used below to construct a 'sparse' spline
is.splinets(spl) #verification
plot(spl)


xxi=seq(0,20,by=1/(n+1)) #large set of knots for construction of a sparse spline 
nn=length(xxi)-2
spspl=new('Splinets',knots=xxi,smorder=k) #generic object from the 'Splinets'-class
spspl@der[[1]]=matrix(0,ncol=(k+1),nrow=(nn+2)) #starting with zeros everywhere

spspl@der[[1]][1:(n+2),]=sym2one(spl@der[[1]]) #assigning local spline to a sparse spline at 
spspl@der[[1]][nn+3-(1:(n+2)),]=spspl@der[[1]][(n+2):1,] #the beginning and the same at the end
spspl@der[[1]]=sym2one(spspl@der[[1]],inv=TRUE) 
                                #at this point the object does not account for the sparsity

is.splinets(spspl) #a sparse spline on 421 knots with a non-zero terms at the first 22 
                   #and at the last 22 knots, the actual support set is not yet reported
plot(spspl)
plot(spspl,xlim=c(0,1)) #the local part of the sparse spline

exsupp(spspl@der[[1]]) #the actual support of the spline given the sparse derivative matrix

#Expanding the previous spline by building a slightly more complex support set
spspl@der[[1]][(n+1)+(1:(n+2)),]=sym2one(spl@der[[1]]) #double the first component of the
                                              #support because these are tangent supports 
spspl@der[[1]][(2*n+3)+(1:(n+2)),]=sym2one(spl@der[[1]]) #tdetect a single component of
                                                #the support with no internal knots removed
is.splinets(spspl)
plot(spspl)


es=exsupp(spspl@der[[1]])
es[[2]]   #the new support made of three components with the two first ones
          #separated by an interval with no knots in it 
          

spspl@der[[1]]=es[[1]]         #defining the spline on the evaluated actual support
spspl@supp[[1]]=es[[2]]
#Example with reduction of not a full support. 

xi1=seq(0,14/(n+1),by=1/(n+1)); n1=13; #the odd number of equally spaced knots 
S1=matrix(rnorm((n1+2)*(k+1)),ncol=(k+1))
spl1=construct(xi1,k,S1) #construction of a local spline
xi2=seq(16/(n+1),42/(n+1),by=1/(n+1)); n2=25; #the odd number of equally spaced knots 

S2=matrix(rnorm((n2+2)*(k+1)),ncol=(k+1))
spl2=construct(xi2,k,S2) #construction of a local spline

spspl@der[[1]][1:15,]=sym2one(spl1@der[[1]])
spspl@der[[1]][16,]=rep(0,k+1)
spspl@der[[1]][17:43,]=sym2one(spl2@der[[1]])
spspl@der[[1]][1:43,]=sym2one(spspl@der[[1]][1:43,],inv=TRUE)

is.splinets(spspl) #three intervals in the support are repported 

exsupp(spspl@der[[1]],spspl@supp[[1]])