#include "mfem.hpp"
#include <cmath>

#include "coeff.h"

/**
 * @brief Computes the xi coefficient function.
 * 
 * @param x Input vector.
 * @return double The computed xi coefficient.
 */
double xi_coeff_func(const mfem::Vector &x)
{
  return std::pow(x(0), 2);
}

/**
 * @brief Computes the vector xi coefficient function.
 * 
 * @param x Input vector.
 * @param v Output vector to store the computed xi coefficient.
 */
void vec_xi_coeff_func(const mfem::Vector &x, mfem::Vector &v)
{
  v.SetSize(1);
  v[0] = -std::pow(x(0), 2);
}

/**
 * @brief Computes the initial guess for theta.
 * 
 * @param x Input vector.
 * @param root Root value used in the computation.
 * @return double The initial guess for theta.
 */
double theta_initial_guess(const mfem::Vector &x, double root)
{
  double xi = x[0];
  return 1 - std::pow(xi / root, 2);
}