plot,Splinets-method {Splinets}

Plotting splines

Description

The method provides graphical visualization of a Splinets-class object. The method plot a Splinets in a cartesian or a polar coordinate if it is a regular splines or a periodic splines, respectively.

Usage

## S4 method for signature 'Splinets'
plot(
  object,
  x = NULL,
  sID = NULL,
  vknots = TRUE,
  type = "stnd",
  mrgn = 2,
  lwd = 2,
  ...
)

Arguments

object

Splinets object;

x

vector, specifying where the splines will be evaluated for the plots;

sID

vector, specifying indices of the splines to be plotted;

vknots

logic, indicates if auxiliary vertical lines will be added to highlight the positions of knots; The default is TRUE.

type

string, controls the layout of graphs; The following options are available

• "stnd" – if object@type="dspnt" or ="spnt", then the plots are over the dyadic net of supports, other types of the bases are on a single plot with information about the basis printed out,

• "simple" – all the objects are plotted in a single plot,

• "dyadic" – if object@type="sp" is not true (unstructured collection of splines), then the plot is over the dyadic net of supports.

mrgn

number, specifying the margin size in the dyadic structure plot;

lwd

positive integer, the line width;

...

other standard graphical parameters can be passed;

Details

The standard method of plotting splines in a Splinet-object. It plots a single graph with all splines in the object except if the field type of the object represents a splinet. In the latter case, the default is the (dyadic) net plot of the basis. The string argument type can overide this to produce a plot that does not use the dyadic net. Most of the standard graphical parameters can be passed to this function.

Value

A plot visualizing a Splinet object. The entire set of splines will be displayed in a plot.

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

evspline for manually evaluating splines in a Splinet-object; Splinets-class for the definition of the Splinet-class; lines,Splinets-method for adding graphs to existing plots;

Examples

#-----------------------------------------------------#
#-------------------Ploting splinets------------------#
#-----------------------------------------------------#
#Constructed splines

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
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')
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

plot(spl)
  plot(spl,sID=c(1,3))
plot(spl,sID=2)
t = seq(0,0.5,length.out = 1000)
plot(spl, t, sID = 1)

#Random splines
n=17; k=4; xi=sort(runif(n+2)); xi[1]=0; xi[n+2]=1 
S=matrix(rnorm((n+2)*(k+1)),ncol=(k+1))
spl=construct(xi,k,S) 
plot(spl,main="Mean Spline",lty=2,lwd=2,xlab='')

RS=rspline(spl,5)
plot(RS,main="Random splines around the mean spline",ylim=3*range(spl@der[[1]][,1]) )
lines(spl,col='red',lwd=4,lty=2)

#Periodic splines
xi = seq(0, 1, length.out = 25)
so = splinet(xi, periodic = TRUE) 

plot(so$bs)
plot(so$os)
plot(so$bs,type= "dyadic")
plot(so$bs, sID=c(4,6))
plot(so$os, type="simple",sID=c(4,6))