import vector:*;
import io:*;

/*****************************
 *  Functions
 ****************************/

/***************************
 *  dot(vec u, vec v)
 *
 *    This returns the dot product
 *  of two vectors.  This is equivalent
 *  to multiplying the components of the
 *  vector element by element, and then summing
 *  the resulting vector.
 *
 ***************************/

template<T> |T| dot(|vector<T>| u, |vector<T>| v)
{
  if(u.size < v.size) 
  {
    println("Error: Vectors not of same size");
    print("Vector a is of size: ");
    println(u.size);
    print("Vector b is of size: ");
    println(v.size);
  }
  
  |T| ans = 0; 

  for(|int| i = 0; i < lesser<int>(u.size, v.size); i++;)
  {
    ans = ans + u.at(i) * v.at(i); 
  }
  
  println(ans);

  return ans;
}//end dot function 

/***************
 * Norm2(vec r)
 *
 *    This takes a vector,
 *  and finds the norm squared, or 
 *  the sum of all the components squared.
 *  
 *  This is equivalent to dot(r,r)
 *
 **************/
template<J> |J| norm2(|vector<J>| r)
{
  return(dot<J>(r,r)); 
}//end norm function