text: #include <iostream>
  #include "tools.h"
  
  using Eigen::VectorXd;
  using Eigen::MatrixXd;
  using std::vector;
  
  Tools::Tools() {}
  
  Tools::~Tools() {}
  
  VectorXd Tools::CalculateRMSE(const vector<VectorXd> &estimations,
                                const vector<VectorXd> &ground_truth) {
  	/**
  
  	    * Calculate the RMSE here.
  	 */
  
  	VectorXd rmse(4);
  
  	rmse << 0,0,0,0;
  
  	// check the validity of the following inputs:
  	//  * the estimation vector size should not be zero
  	//  * the estimation vector size should equal ground truth vector size
  	if(estimations.size() != ground_truth.size() || estimations.size() == 0){
  
  		cout << "Invalid estimation or ground_truth data" << endl;
  		return rmse;
  	}
  
  	//accumulate squared residuals
  	for(unsigned int i=0; i < estimations.size(); ++i){
  
  		VectorXd residual = estimations[i] - ground_truth[i];
  
  		//coefficient-wise multiplication
  		residual = residual.array()*residual.array();
  		rmse += residual;
  	}
  
  	//calculate the mean
  	rmse = rmse/estimations.size();
  
  	//calculate the squared root
  	rmse = rmse.array().sqrt();
  
  	//return the result
  	return rmse;
  
  }
  
  MatrixXd Tools::CalculateJacobian(const VectorXd& x_state) {
  
  	/**
  
  	    * Calculate a Jacobian here.
  	  */
  
  	MatrixXd Hj(3,4);
  	//recover state parameters
  	float px = x_state(0);
  	float py = x_state(1);
  	float vx = x_state(2);
  	float vy = x_state(3);
  
  	//pre-compute a set of terms to avoid repeated calculation
  	float c1 = px*px+py*py;
  	float c2 = sqrt(c1);
  	float c3 = (c1*c2);
  
  	//check division by zero
  	if(fabs(c1) < 0.0001){
  		cout << "CalculateJacobian () - Error - Division by Zero" << endl;
  		return Hj;
  	}
  
  	//compute the Jacobian matrix
  	Hj << (px/c2), (py/c2), 0, 0,
  			 -(py/c1), (px/c1), 0, 0,
  			 py*(vx*py - vy*px)/c3, px*(px*vy - py*vx)/c3, px/c2, py/c2;
  
  	return Hj;
  
  }
  