bls<-function(x0,x,y){
  x0%*%solve(t(x)%*%x,t(x)%*%y)
}
knn<-function(x0,x,y,k){
      x=as.matrix(x)
      p=dim(x)[2]	
      n=dim(x)[1]        
      dis=rep(0,n)
      for(i in 1:p){
        dis= (x0[i]-x[,i])^2+dis
      }
      ind=order(dis)[1:k]
      mean(y[ind])
}

loess0<-function(x0,x,y,kern,lam){
  x=as.matrix(x)
  p=dim(x)[2]
  n=dim(x)[1]        
  dis=rep(0,n)
  for(i in 1:p){
    dis= (x0[i]-x[,i])^2+dis
  }
  
  ##My code is below
  w = kern(dis,lam)
  return (sum(w*y)/sum(w))
  ##Your code here
  
}

loess1<-function(x0,x,y,kern,lam){
  x=as.matrix(x)
  p=dim(x)[2]	
  n=dim(x)[1]        
  dis=rep(0,n)
  for(i in 1:p){
    dis= (x0[i]-x[,i])^2+dis
  }
  ##My code is below
  w = kern(dis,lam)
  ## below we calculate the teta1
  ky = sum(w*y)
  kx = sum(w*x)
  kxy = sum(w*x*y)
  k = sum(w)
  kxx = sum(w*x*x)
  teta1 = (kxy*k - kx*ky)/(kxx*k - kx*kx)
  ## below we calculate the teta0
  teta0 = (ky*kxx - kxy*kx)/(k*kxx - kx*kx)

  return(teta1*x0 + teta0)
  ##Your code here
}

kern<-function(x,lam){
  exp(-x/lam)/lam
}
######
## sin(x) Regression Example
######
set.seed(100)
x=runif(100,0,2*pi)
y=sin(x)+rnorm(100,,0.1)

xgrid=seq(0,2*pi,length=500)
n=length(xgrid)
ygrid=vector(length=n)
k=15
lam=0.01
for(i in 1:n){
  ##ygrid[i]= loess0(xgrid[i],x,y,kern,lam) ##loess d=0 , d=1
  ygrid[i]= loess1(xgrid[i],x,y,kern,lam) ##loess d=0 , d=1
}
plot(x,y,pch=16)
lines(xgrid,ygrid,col=c("red"))
lines(xgrid,sin(xgrid),col=c("blue"))