#########################################
# Tutorial on functions
# with vector calculus
#########################################




# vector magnitude
magnitude<-function(x){
  n<-length(x)
  res<-0
  for (i in 1:n){
    res<-res+x[i]^2
  }
  return(sqrt(res))
}

# another way to do it:
# I use R's own sum-function
# is much faster!
# You can try it with a long vector
# and compare the speed of both functions
# with vector x<-rep(1,1000000)

magnitude2<-function(x){
  x<-x*x
  return(sqrt(sum(x)))
}



dotproduct<-function(x,y){
  n<-length(x)
  n2<-length(y)
  if (n2!=n){
    res<-NA
  } else {
    res<-0
    for (i in 1:n){
      res<-res+x[i]*y[i]
    }
  }
  return(res)
}