hwk 3 prob 5 a

gistfile1.txt

norm <- function(x) {
  norm <- sqrt(sum(x^2))
  return(norm)
}

x.1 <- c(-2,1,0)
x.2 <- c(1,-1,1)

y.1 <- c(0,1,0)
y.2 <- c(1,1,2)

#making lines into planes, finding normal vector between them
x.1 <- c(-2,1,0)
x.2 <- c(1,-1,1)

y.1 <- c(0,1,0)
y.2 <- c(1,1,2)

#find normal vector
mm<-cbind(x.2,y.2)
N <- sapply(1:3,function(x)det(mm[-x,])*(2*(x%%2)-1))

xy <- x.1 - y.1
dist <- norm(t(xy)%*%N)/norm(N)


#minimizing the distance function
linesDist <- function(x1, x2, y1, y2) {   

        dist <- function(s1, s2) {   

               d <- sqrt(t(x1 + s1*x2 - (y1 + s2*y2)) %*% (x1 + s1*x2 - (y1 + s2*y2))) 

        return(d)}  

   start <- cbind(seq(-100,100,.01),seq(-100,100,.01)) 

   m<-min(mapply(function(s1,s2) nlm(dist,s1,s2)$minimum,start[,1],start[,2]))

return(m)}

linesDist(x.1,x.2,y.1,y.2)
#[1] 1.603579
dist
# 1.603567