Roots.hpp

// Reaktoro is a unified framework for modeling chemically reactive systems.
//
// Copyright (C) 2014-2018 Allan Leal
//
// This library is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
//
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
// Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public License
// along with this library. If not, see <http://www.gnu.org/licenses/>.
 
#pragma once
 
// C++ includes
#include <complex>
#include <functional>
#include <tuple>
 
// Reaktoro includes
#include <Reaktoro/Math/Matrix.hpp>
 
namespace Reaktoro {
 
using CubicRoots = std::tuple<std::complex<double>, std::complex<double>, std::complex<double>>;
 
using SquareRoots = std::tuple<double, double>;
 
auto cardano(double a, double b, double c, double d) -> CubicRoots;
 
auto newton(const std::function<std::tuple<double,double>(double)>& f,
            double x0, double epsilon, unsigned maxiter) -> double;
 
auto newton(const std::function<void(VectorConstRef, VectorRef, MatrixRef)>& f,
            VectorConstRef x0, double epsilon, unsigned maxiter) -> Vector;
 
auto realRoots(const CubicRoots& roots)->std::vector<double>;
 
} // namespace Reaktoro