gradientDescent <- function(X, y, theta, alpha, num_iters){
  
  #   Performs gradient descent to learn theta
  #
  #   theta, J_history <- gradientDescent(X, y, theta, alpha, num_iters) 
  #   updates theta by taking num_iters gradient steps with learning rate alpha
  
  #   Initialize some useful values
  m <- length(y) # number of training examples
  J_history <- rep(0, num_iters)
  
  for (iter in 1:num_iters){
  
    # ====================== YOUR CODE HERE ========================
    # Instructions: Perform a single gradient step on the parameter
    #               vector theta. 
    #
    # Hint: While debugging, it can be useful to print out the values
    #       of the cost function (computeCost) and gradient here.
    #
    
    
    
    # ==============================================================
    
    # Save the cost J in every iteration    
    J_history[iter] <- computeCost(X, y, theta)
    
  }

  return(list(theta = theta, J_history = J_history))
}