Chapter 19: Best basis selection

Figure 1

num<-100  
p<-seq(1,2,1/num)
xlen<-length(p)

d<-2
s2<-seq(0,1/d,1/(d*num))
ylen2<-length(s2)
zn2<-matrix(0,xlen,ylen2)
for (i in 1:xlen){
    for (j in 1:ylen2){
         if (s2[j]<=(1/p[i]-1/2)) zn2[i,j]<--1
         else if ( s2[j]/((2*s2[j]+1)*(s2[j]-1/p[i]+1/2))<=1 ) zn2[i,j]<-1
    }
}

d<-4
s4<-seq(0,1/d,1/(d*num))
ylen4<-length(s4)
zn4<-matrix(0,xlen,ylen4)
for (i in 1:xlen){
    for (j in 1:ylen4){
         if (s4[j]<=(1/p[i]-1/2)) zn4[i,j]<--1
         else if ( s4[j]/((2*s4[j]+1)*(s4[j]-1/p[i]+1/2))<=1 ) zn4[i,j]<-1
    }
}

cex<-1.5

# frame 1
image(p,s2,zn2,ylab=expression(sigma),xlab=expression(p[l]),
cex.axis=1,
cex.lab=cex)
text(1.2,0.1,"A",cex=cex)
text(1.4,0.3,"B",cex=cex)
text(1.8,0.4,"C",cex=cex)

# frame 2
image(p,s4,zn4,ylab=expression(sigma),xlab=expression(p[l]),
cex.axis=1,
cex.lab=cex)
text(1.2,0.1,"A",cex=cex)
text(1.65,0.17,"B",cex=cex)
text(1.9,0.2,"C",cex=cex)