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- /*
- * Copyright 2011-2013 Mario Mulansky
- * Copyright 2012 Karsten Ahnert
- *
- * Distributed under the Boost Software License, Version 1.0.
- * (See accompanying file LICENSE_1_0.txt or
- * copy at http://www.boost.org/LICENSE_1_0.txt)
- *
- * Example for the lorenz system with a 3D point type
- */
- #include <iostream>
- #include <cmath>
- #include <boost/operators.hpp>
- #include <boost/numeric/odeint.hpp>
- //[point3D
- class point3D :
- boost::additive1< point3D ,
- boost::additive2< point3D , double ,
- boost::multiplicative2< point3D , double > > >
- {
- public:
- double x , y , z;
- point3D()
- : x( 0.0 ) , y( 0.0 ) , z( 0.0 )
- { }
- point3D( const double val )
- : x( val ) , y( val ) , z( val )
- { }
- point3D( const double _x , const double _y , const double _z )
- : x( _x ) , y( _y ) , z( _z )
- { }
- point3D& operator+=( const point3D &p )
- {
- x += p.x; y += p.y; z += p.z;
- return *this;
- }
- point3D& operator*=( const double a )
- {
- x *= a; y *= a; z *= a;
- return *this;
- }
- };
- //]
- //[point3D_abs_div
- // only required for steppers with error control
- point3D operator/( const point3D &p1 , const point3D &p2 )
- {
- return point3D( p1.x/p2.x , p1.y/p2.y , p1.z/p2.z );
- }
- point3D abs( const point3D &p )
- {
- return point3D( std::abs(p.x) , std::abs(p.y) , std::abs(p.z) );
- }
- //]
- //[point3D_norm
- // also only for steppers with error control
- namespace boost { namespace numeric { namespace odeint {
- template<>
- struct vector_space_norm_inf< point3D >
- {
- typedef double result_type;
- double operator()( const point3D &p ) const
- {
- using std::max;
- using std::abs;
- return max( max( abs( p.x ) , abs( p.y ) ) , abs( p.z ) );
- }
- };
- } } }
- //]
- std::ostream& operator<<( std::ostream &out , const point3D &p )
- {
- out << p.x << " " << p.y << " " << p.z;
- return out;
- }
- //[point3D_main
- const double sigma = 10.0;
- const double R = 28.0;
- const double b = 8.0 / 3.0;
- void lorenz( const point3D &x , point3D &dxdt , const double t )
- {
- dxdt.x = sigma * ( x.y - x.x );
- dxdt.y = R * x.x - x.y - x.x * x.z;
- dxdt.z = -b * x.z + x.x * x.y;
- }
- using namespace boost::numeric::odeint;
- int main()
- {
- point3D x( 10.0 , 5.0 , 5.0 );
- // point type defines it's own operators -> use vector_space_algebra !
- typedef runge_kutta_dopri5< point3D , double , point3D ,
- double , vector_space_algebra > stepper;
- int steps = integrate_adaptive( make_controlled<stepper>( 1E-10 , 1E-10 ) , lorenz , x ,
- 0.0 , 10.0 , 0.1 );
- std::cout << x << std::endl;
- std::cout << "steps: " << steps << std::endl;
- }
- //]
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