// Copyright (c) 2020, Viktor Larsson
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#pragma once

#include <Eigen/Dense>

namespace poselib {
namespace qep {

// Helper functions for solving quadratic eigenvalue problems
// (Currently only 4x4 problems are implemented)
// Note: The impl. assumes that fourth element of eigenvector is non-zero.
// The return eigenvectors are only the first three elements (fourth is normalized to 1)

// Solves the QEP by reduction to normal eigenvalue problem
int qep_linearize(const Eigen::Matrix<double, 4, 4> &A, const Eigen::Matrix<double, 4, 4> &B,
                  const Eigen::Matrix<double, 4, 4> &C, double eig_vals[8], Eigen::Matrix<double, 3, 8> *eig_vecs);

// Solves the QEP by sturm bracketing on det(lambda^2*A + lambda*B + C)
int qep_sturm(const Eigen::Matrix<double, 4, 4> &A, const Eigen::Matrix<double, 4, 4> &B,
              const Eigen::Matrix<double, 4, 4> &C, double eig_vals[8], Eigen::Matrix<double, 3, 8> *eig_vecs);

// Solves the QEP by solving det(lambda^2*A + lambda*B + C) where we know that (1+lambda^2) is a factor.
// This is the case in the upright solvers from Sweeney et al.
// The roots are found using sturm bracketing.
int qep_sturm_div_1_q2(const Eigen::Matrix<double, 4, 4> &A, const Eigen::Matrix<double, 4, 4> &B,
                       const Eigen::Matrix<double, 4, 4> &C, double eig_vals[6], Eigen::Matrix<double, 3, 6> *eig_vecs);

// Solves the QEP by sturm bracketing on det(lambda^2*A + lambda*B + C)
int qep_sturm(const Eigen::Matrix<double, 3, 3> &A, const Eigen::Matrix<double, 3, 3> &B,
              const Eigen::Matrix<double, 3, 3> &C, double eig_vals[6], Eigen::Matrix<double, 3, 6> *eig_vecs);

// Solves the QEP by solving det(lambda^2*A + lambda*B + C) where we know that (1+lambda^2) is a factor.
// This is the case in the upright solvers from Sweeney et al.
// The roots are found using the closed form solver for the quartic.
int qep_div_1_q2(const Eigen::Matrix<double, 3, 3> &A, const Eigen::Matrix<double, 3, 3> &B,
                 const Eigen::Matrix<double, 3, 3> &C, double eig_vals[4], Eigen::Matrix<double, 3, 4> *eig_vecs);

} // namespace qep
} // namespace poselib