#####   R-code for making Figure 5.14.

en = seq(-10,10,0.1)
n=length(en)

la=0.1
u1=2
u2=4
u3=6

eta11=rep(0,n)
eta12=rep(0,n)
eta13=rep(0,n)

for(i in 1:n){

   if(en[i] < -u1){ 
      eta11[i] = en[i]+(1-la)*u1
   }
   else if (abs(en[i]) <= u1){
      eta11[i] = la*en[i]
   }
   else {
      eta11[i] = en[i]-(1-la)*u1
   }

   if(en[i] < -u2){ 
      eta12[i] = en[i]+(1-la)*u2
   }
   else if (abs(en[i]) <= u2){
      eta12[i] = la*en[i]
   }
   else {
      eta12[i] = en[i]-(1-la)*u2
   }

   if(en[i] < -u3){ 
      eta13[i] = en[i]+(1-la)*u3
   }
   else if (abs(en[i]) <= u3){
      eta13[i] = la*en[i]
   }
   else {
      eta13[i] = en[i]-(1-la)*u3
   }

}

eta21=rep(0,n)
eta22=rep(0,n)
eta23=rep(0,n)

for(i in 1:n){

   if(abs(en[i]) <= u1){ 
      eta21[i] = en[i]*(1-(1-la)*(1-(en[i]/u1)^2)^2)
   }
   else {
      eta21[i] = en[i]
   }

   if(abs(en[i]) <= u2){ 
      eta22[i] = en[i]*(1-(1-la)*(1-(en[i]/u2)^2)^2)
   }
   else {
      eta22[i] = en[i]
   }

   if(abs(en[i]) <= u3){ 
      eta23[i] = en[i]*(1-(1-la)*(1-(en[i]/u3)^2)^2)
   }
   else {
      eta23[i] = en[i]
   }

}

w11=eta11/en
w12=eta12/en
w13=eta13/en

w21=eta21/en
w22=eta22/en
w23=eta23/en

postscript("fig514.ps",width=7,height=7.5,horizontal=F)

par(mfrow=c(2,2), mar=c(4,4,2,2))

plot(en,eta11,type="l",lty=1,xlab=expression(e[n]),
     ylab=expression(eta[1](e[n])),mgp=c(2,1,0),xlim=c(-10,10), 
     ylim=c(-10,10),cex=0.8)
lines(en,eta12,lty=2,cex=0.8)
lines(en,eta13,lty=3,cex=0.8)
lines(en,en,lty=4,cex=0.8)
lines(en,la*en,lty=5,cex=0.8)
legend(-10,10,legend=c("u=2","u=4","u=6"),lty=1:3,cex=0.7)
title(xlab="(a)",cex=0.9)

plot(en,w11,type="l",lty=1,xlab=expression(e[n]),
     ylab=expression(w[1](e[n])),mgp=c(2,1,0),xlim=c(-10,10), 
     ylim=c(0,1),cex=0.8)
lines(en,w12,lty=2,cex=0.8)
lines(en,w13,lty=3,cex=0.8)
lines(en,rep(1,n),lty=4,cex=0.8)
lines(en,rep(la,n),lty=5,cex=0.8)
legend(-2.5,0.9,legend=c("u=2","u=4","u=6"),lty=1:3,cex=0.7)
title(xlab="(b)",cex=0.9)

plot(en,eta21,type="l",lty=1,xlab=expression(e[n]),
     ylab=expression(eta[2](e[n])),mgp=c(2,1,0),xlim=c(-10,10), 
     ylim=c(-10,10),cex=0.8)
lines(en,eta22,lty=2,cex=0.8)
lines(en,eta23,lty=3,cex=0.8)
lines(en,en,lty=4,cex=0.8)
lines(en,la*en,lty=5,cex=0.8)
legend(-10,10,legend=c("u=2","u=4","u=6"),lty=1:3,cex=0.7)
title(xlab="(c)",cex=0.9)

plot(en,w21,type="l",lty=1,xlab=expression(e[n]),
     ylab=expression(w[2](e[n])),mgp=c(2,1,0),xlim=c(-10,10), 
     ylim=c(0,1),cex=0.8)
lines(en,w22,lty=2,cex=0.8)
lines(en,w23,lty=3,cex=0.8)
lines(en,rep(1,n),lty=4,cex=0.8)
lines(en,rep(la,n),lty=5,cex=0.8)
legend(-10,0.6,legend=c("u=2","u=4","u=6"),lty=1:3,cex=0.7)
title(xlab="(d)",cex=0.9)

graphics.off()