Reaktoro 
A unified framework for modeling chemically reactive systems
Roots.hpp
1 // Reaktoro is a unified framework for modeling chemically reactive systems.
2 //
3 // Copyright (C) 2014-2015 Allan Leal
4 //
5 // This program is free software: you can redistribute it and/or modify
6 // it under the terms of the GNU General Public License as published by
7 // the Free Software Foundation, either version 3 of the License, or
8 // (at your option) any later version.
9 //
10 // This program is distributed in the hope that it will be useful,
11 // but WITHOUT ANY WARRANTY; without even the implied warranty of
12 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
13 // GNU General Public License for more details.
14 //
15 // You should have received a copy of the GNU General Public License
16 // along with this program. If not, see <http://www.gnu.org/licenses/>.
17 
18 #pragma once
19 
20 // C++ includes
21 #include <complex>
22 #include <functional>
23 #include <tuple>
24 
25 // Reaktoro includes
26 #include <Reaktoro/Math/Matrix.hpp>
27 
28 namespace Reaktoro {
29 
31 using CubicRoots = std::tuple<std::complex<double>, std::complex<double>, std::complex<double>>;
32 
45 auto cardano(double a, double b, double c, double d) -> CubicRoots;
46 
52 auto newton(const std::function<std::tuple<double,double>(double)>& f,
53  double x0, double epsilon, unsigned maxiter) -> double;
54 
60 auto newton(const std::function<void(const Vector&, Vector&, Matrix&)>& f,
61  const Vector& x0, double epsilon, unsigned maxiter) -> Vector;
62 
63 } // namespace Reaktoro
Eigen::MatrixXd Matrix
Define an alias to the matrix type of the Eigen library.
Definition: Matrix.hpp:387
Eigen::VectorXd Vector
Define an alias to the vector type of the Eigen library.
Definition: Matrix.hpp:384
std::tuple< std::complex< double >, std::complex< double >, std::complex< double >> CubicRoots
Define a type that describes the roots of a cubic equation.
Definition: Roots.hpp:31
The namespace containing all components of the Reaktoro library.
Definition: ChemicalScalar.hpp:24
auto newton(const std::function< std::tuple< double, double >(double)> &f, double x0, double epsilon, unsigned maxiter) -> double
Calculate the root of a non-linear function using Newton&#39;s method.
Definition: Roots.cpp:76
auto cardano(double a, double b, double c, double d) -> CubicRoots
Calculate the roots of a cubic equation using Cardano&#39;s method.
Definition: Roots.cpp:28