is.splinets: Diagnostics of splines and their generic correction
In Splinets: Functional Data Analysis using Splines and Orthogonal Spline Bases

is.splinets

R Documentation

Diagnostics of splines and their generic correction

Description

The method performs verification of the properties of SLOTS of an object belonging to the Splinets–class. In the case when all the properties are satisfied the logical TRUE is returned. Otherwise, FALSE is returned together with suggested corrections.

Usage

is.splinets(object)

Arguments

object

Splinets object, the object to be diagnosed; For this object to be corrected properly each support interval has to have at least 2*smorder+4 knots.

Value

A list made of: a logical value is, a Splinets object robject, and a numeric value Er.

The logical value is indicates if all the condtions for the elements of Splinets object to be a collection of valid splines are satisfied, additional diagnostic messages are printed out.
The object robject is a modified input object that has all SLOT fields modified so the conditions/restrictions to be a proper spline are satisfied.
The numeric value Er is giving the total squared error of deviation of the input matrix of derivative from the conditions required for a spline.

References

Liu, X., Nassar, H., Podgorski, 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>.

Podgorski, K. (2021) "Splinets – splines through the Taylor expansion, their support sets and orthogonal bases." <arXiv:2102.00733>.

Nassar, H., Podgorski, K. (2023) "Splinets 1.5.0 – Periodic Splinets." <arXiv:2302.07552>

Examples

#-----------------------------------------------------#
#--------Diagnostics of simple Splinets objects-------#
#-----------------------------------------------------#
#----------Full support equidistant cases-------------#
#-----------------------------------------------------#
#Zero order splines, equidistant case, full support
n=20; xi=seq(0,1,by=1/(n+1))
sp=new("Splinets",knots=xi) 
sp@equid #equidistance flag
#Diagnostic of 'Splinets' object 'sp'
is.splinets(sp)

IS=is.splinets(sp)
IS[[1]] #informs if the object is a spline
IS$is   #equivalent to the above

#Third order splines with a noisy matrix of the derivative
set.seed(5)
k=3; sp@smorder=k; sp@der[[1]]=matrix(rnorm((n+2)*(k+1)),ncol=(k+1))

IS=is.splinets(sp)
IS[[2]]@taylor #corrections
sp@taylor
IS[[2]]@der #corrections
sp@der

is.splinets(IS[[2]]) #The output object is a valid splinet

#-----------------------------------------------------#
#--------Full support non-equidistant cases-----------#
#-----------------------------------------------------#
#Zero order splines, non-equidistant case, full support
set.seed(5)
n=17; xi=sort(runif(n+2))
xi[1]=0 ;xi[n+1]=1 #The last knot is not in the order.
          #It will be reported and corrected in the output.  
sp=new("Splinets",knots=xi) 

xi #original knots
sp@knots #vs. corrected ones
sp@taylor

#Diagnostic of 'Splinets' object 'sp'
is.splinets(sp)

IS=is.splinets(sp)
 
nsp=IS$robject #the output spline -- a corrected version of the input
nsp@der
sp@der

#Third order splines
nsp@smorder=3
IS=is.splinets(nsp)

IS[[2]]@taylor #corrections
nsp@taylor
IS[[2]]@der #corrections
nsp@der
is.splinets(IS[[2]]) #verification that the correction is a valid object

#Randomly assigning the derivative -- a very 'unstable' function.
set.seed(5)
k=nsp@smorder; S=matrix(rnorm((n+2)*(k+1)),ncol=(k+1)); nsp@der[[1]]=S

IS=is.splinets(nsp) #the 2nd element of 'IS' is a spline obtained by correcting 'S'
nsp=is.splinets(IS[[2]])
nsp$is #The 'Splinets' object is correct, alternatively use 'nsp$[[1]]'.
nsp$robject #A correct spline object, alternatively use 'nsp$[[2]]'.

#-----------------------------------------------------#
#-----Splinets objects with varying support sets------#
#-----------------------------------------------------#
#-----------------Eequidistant cases------------------#
#-----------------------------------------------------#
#Zero order splines, equidistant case, support with three components
n=20; xi=seq(0,1,by=1/(n+1))
support=list(matrix(c(2,5,6,8,12,18),ncol=2,byrow = TRUE)) 
sp=new("Splinets",knots=xi,supp=support) 
is.splinets(sp)

IS=is.splinets(sp)

sum(sp@supp[[1]][,2]-sp@supp[[1]][,1]+1) #the number of knots in the support
dim(IS[[2]]@der[[1]])[1]  #the number of rows in the derivative matrix
IS[[2]]@der[[1]] #the corrected object
sp@der #the input derivative matrix

#Third order splines
n=40; xi=seq(0,1,by=1/(n+1)); k=3; 
support=list(matrix(c(2,12,15,27,30,40),ncol=2,byrow = TRUE))
m=sum(support[[1]][,2]-support[[1]][,1]+1) #the number of knots in the support
SS=list(matrix(rnorm(m*(k+1)),ncol=(k+1))) #the derivative matrix at random

sp=new("Splinets",knots=xi,smorder=k,supp=support,der=SS) 

IS=is.splinets(sp)

m=sum(sp@supp[[1]][,2]-sp@supp[[1]][,1]+1) #the number of knots in the support
sp@der=list(matrix(rnorm(m*(k+1)),ncol=(k+1))) #the derivative matrix at random

IS=is.splinets(sp) #Comparison of the corrected and the original 'der' matrices
sp@der
IS[[2]]@der
is.splinets(IS[[2]]) #verification

#-----------------------------------------------------#
#----------------Non-equidistant cases----------------#
#-----------------------------------------------------#
#Zero order splines, non-equidistant case, support with three components
set.seed(5)
n=43; xi=seq(0,1,by=1/(n+1)); k=3; xi=sort(runif(n+2)); xi[1]=0; xi[n+2]=1;
support=list(matrix(c(2,14,17,30,32,43),ncol=2,byrow = TRUE))

ssp=new("Splinets",knots=xi,supp=support) #with partial support
nssp=is.splinets(ssp)$robject
nssp@supp
nssp@der

#Third order splines
nssp@smorder=3 #changing the order of the 'Splinets' object
set.seed(5)
m=sum(nssp@supp[[1]][,2]-nssp@supp[[1]][,1]+1) #the number of knots in the support
nssp@der=list(matrix(rnorm(m*(k+1)),ncol=(k+1)))  #the derivative matrix at random
IS=is.splinets(nssp) 
IS$robject@der
is.splinets(IS$robject)$is #verification of the corrected output object

Splinets documentation built on March 7, 2023, 8:24 p.m.