/* generate Aj coefficient */
double coeff_a(double j, double n, vector<double>& points, vector<double>& values){
  double aj   = 0;
  double a    = 2 / n;
  double sum  = 0;

  for(int k = 0; k < n; k++){
    double yk = values[k];
    double xk = points[k] * j;
    double cosine = cos(xk);
    double product = yk * cosine;
    sum += product;
  }

  aj = a * sum;

  return aj;
}

/* generate Bj coefficient */
double coeff_b(double j, double n, vector<double>& points, vector<double>& values){
  double bj   = 0;
  double a    = 2 / n;
  double sum  = 0;

  for(int k = 0; k < n; k++){
    double yk = values[k];
    double xk = points[k] * j;
    double sine = sin(xk);
    double product = yk * sine;
    sum += product;
  }

  bj = a * sum;

  return bj;
}