// Copyright (c) 2020 Marcus Valtonen Örnhag
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in all
// copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
// SOFTWARE.

#include "roots.hpp"
#include <Eigen/Core>
#include <Eigen/Eigenvalues>

namespace HomLib {
    Eigen::VectorXcd roots(const Eigen::VectorXd& coeffs) {
        // Create companion matrix
        int N = coeffs.size() - 1;
        Eigen::MatrixXd companion_mat(N, N);
        companion_mat.setZero();

        for (int i = 0; i < N; i++) {
             for (int j = 0; j < N; j++) {
                if (i == j + 1) {
                    companion_mat(i, j) = 1.0;
                }
                if (j == N - 1) {
                    companion_mat(i, j) = -coeffs[N - i] / coeffs[0];
                }
            }
        }

        // Compute roots via eigenvalues of companion matrix
        Eigen::VectorXcd eigvals = companion_mat.eigenvalues();

        return eigvals;
    }
}  // namespace HomLib
