text: #include "tools.h"
  #include <iostream>
  
  using Eigen::VectorXd;
  using Eigen::MatrixXd;
  using std::vector;
  using namespace std;
  
  Tools::Tools() {}
  
  Tools::~Tools() {}
  
  VectorXd Tools::CalculateRMSE(const vector<VectorXd> &estimations,
                                const vector<VectorXd> &ground_truth) {
    /**
     * TODO: 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) {
    /**
     * TODO:
     * 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;
  }
  