w=matrix(0,nrow=101,ncol=9)
s=seq(0,10,by=.1)
for(i in 1:9) w[,i]=dnorm(s-i)

x=rnorm(9)
z=w%*%x
plot(s,z,type="l",ylim=c(min(min(z),min(x)*dnorm(0)),max(max(z),max(x)*dnorm(0))),lwd=2)
for(i in 1:9) {
  lines(s,x[i]*w[,i],col=8)
  lines(c(i,i),c(0,x[i]*dnorm(0)))
}

# examples of changing kernel width
par(mfrow=c(3,1))
w2=matrix(0,nrow=101,ncol=9)
s=seq(0,10,by=.1)
for(i in 1:9) w2[,i]=dnorm(s-i,sd=0.4)
z=w2%*%x
plot(s,z,type="l",lwd=2)
for(i in 1:9) {
  lines(s,x[i]*w2[,i],col=8,lwd=2)
  lines(c(i,i),c(0,x[i]*dnorm(0,sd=0.4)))
}
w2=matrix(0,nrow=101,ncol=9)
s=seq(0,10,by=.1)
for(i in 1:9) w2[,i]=dnorm(s-i,sd=0.6)
z=w2%*%x
plot(s,z,type="l",lwd=2)
for(i in 1:9) {
  lines(s,x[i]*w2[,i],col=8,lwd=2)
  lines(c(i,i),c(0,x[i]*dnorm(0,sd=0.6)))
}
w2=matrix(0,nrow=101,ncol=9)
s=seq(0,10,by=.1)
for(i in 1:9) w2[,i]=dnorm(s-i,sd=2)
z=w2%*%x
plot(s,z,type="l",lwd=2)
for(i in 1:9) {
  lines(s,x[i]*w2[,i],col=8,lwd=2)
  lines(c(i,i),c(0,x[i]*dnorm(0,sd=2)))
}

# examples of changing kernel shape
par(mfrow=c(3,1))
matern1.fun=function(x) return(1.0*abs(x)^0.5*besselK(1.0*abs(x),0.5)/(2*1.253189))
w2=matrix(0,nrow=101,ncol=9)
s=seq(0,10.0001,by=.100001)
for(i in 1:9) {
  for(j in 1:101) w2[j,i]=matern1.fun(s[j]-i)
}
z=w2%*%x
plot(s,z,type="l",lwd=2)
for(i in 1:9) {
  lines(s,x[i]*w2[,i],col=8,lwd=2)
  lines(c(i,i),c(0,x[i]*matern1.fun(0.00001)))
}
#matern with lambda=2, nu=1.5
matern2.fun=function(x) return((2.0^0.5)*abs(x)^1.5*besselK((2.0^0.5)*abs(x),1.5)/(2*1.490345))
w2=matrix(0,nrow=101,ncol=9)
s=seq(0,10.0001,by=.100001)
for(i in 1:9) {
  for(j in 1:101) w2[j,i]=matern2.fun(s[j]-i)
}
z=w2%*%x
plot(s,z,type="l",lwd=2)
for(i in 1:9) {
  lines(s,x[i]*w2[,i],col=8,lwd=2)
  lines(c(i,i),c(0,x[i]*matern2.fun(0.00001)))
}
#tricube kernel
tricube.fun=function(x) return(0.328*(abs(x)<2.635)*(1-(abs(x)/2.635)^3)^3)
w2=matrix(0,nrow=101,ncol=9)
s=seq(0,10,by=.1)
for(i in 1:9) {
  for(j in 1:101) w2[j,i]=tricube.fun(s[j]-i)
}
z=w2%*%x
plot(s,z,type="l",lwd=2)
for(i in 1:9) {
  lines(s,x[i]*w2[,i],col=8,lwd=2)
  lines(c(i,i),c(0,x[i]*0.328))
}