我正在尝试使用 boost / odeint 实施一些事件检测。我首先尝试获取示例“ find_crossing.cpp”，该示例随 odeint 一起使用。
1>d:\github\vcpkg\installed\x64-windows\include\boost\numeric\odeint\util\stepper_traits.hpp(47): error C2039: 'stepper_category': is not a member of 'std::reference_wrapper<boost::numeric::odeint::dense_output_runge_kutta<boost::numeric::odeint::controlled_runge_kutta<boost::numeric::odeint::runge_kutta_dopri5<state_type,double,State,Value,boost::numeric::odeint::algebra_dispatcher_sfinae<StateType,void>::algebra_type,boost::numeric::odeint::operations_dispatcher_sfinae<StateType,void>::operations_type,boost::numeric::odeint::initially_resizer>,boost::numeric::odeint::default_error_checker<Value,boost::numeric::odeint::range_algebra,boost::numeric::odeint::default_operations>,boost::numeric::odeint::default_step_adjuster<Value,double>,boost::numeric::odeint::initially_resizer,boost::numeric::odeint::explicit_error_stepper_fsal_base<boost::numeric::odeint::runge_kutta_dopri5<State,Value,State,Value,boost::numeric::odeint::algebra_dispatcher_sfinae<StateType,void>::algebra_type,boost::numeric::odeint::operations_dispatcher_sfinae<StateType,void>::operations_type,boost::numeric::odeint::initially_resizer>,5,5,4,State,Value,Deriv,Time,Algebra,Operations,Resizer>::stepper_category>,boost::numeric::odeint::controlled_runge_kutta<boost::numeric::odeint::runge_kutta_dopri5<State,Value,Deriv,Time,Algebra,Operations,Resizer>,boost::numeric::odeint::default_error_checker<Value,Algebra,Operations>,boost::numeric::odeint::default_step_adjuster<Value,Time>,Resizer,boost::numeric::odeint::explicit_error_stepper_fsal_base<boost::numeric::odeint::runge_kutta_dopri5<State,Value,Deriv,Time,Algebra,Operations,Resizer>,5,5,4,State,Value,Deriv,Time,Algebra,Operations,Resizer>::stepper_category>::stepper_category>>'
我认为，这是最相关的路线。因为如果我将'std :: ref（stepper）'替换为'boost :: ref（stepper）'，它将进行编译。
我所指的'std :: ref'的使用位于文件的第74行，链接如下。
Link to GitHub: find_crossing.cpp
/*
* find_crossing.cpp
*
* Finds the energy threshold crossing for a damped oscillator.
* The algorithm uses a dense out stepper with find_if to first find an
* interval containing the threshold crossing and the utilizes the dense out
* functionality with a bisection to further refine the interval until some
* desired precision is reached.
*
* Copyright 2015 Mario Mulansky
*
* 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)
*/
#include <iostream>
#include <utility>
#include <algorithm>
#include <array>
#include <boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp>
#include <boost/numeric/odeint/stepper/generation.hpp>
#include <boost/numeric/odeint/iterator/adaptive_iterator.hpp>
namespace odeint = boost::numeric::odeint;
typedef std::array<double, 2> state_type;
const double gam = 1.0; // damping strength
void damped_osc(const state_type &x, state_type &dxdt, const double /*t*/)
{
dxdt[0] = x[1];
dxdt[1] = -x[0] - gam * x[1];
}
struct energy_condition {
// defines the threshold crossing in terms of a boolean functor
double m_min_energy;
energy_condition(const double min_energy)
: m_min_energy(min_energy) { }
double energy(const state_type &x) {
return 0.5 * x[1] * x[1] + 0.5 * x[0] * x[0];
}
bool operator()(const state_type &x) {
// becomes true if the energy becomes smaller than the threshold
return energy(x) <= m_min_energy;
}
};
template<class System, class Condition>
std::pair<double, state_type>
find_condition(state_type &x0, System sys, Condition cond,
const double t_start, const double t_end, const double dt,
const double precision = 1E-6) {
// integrates an ODE until some threshold is crossed
// returns time and state at the point of the threshold crossing
// if no threshold crossing is found, some time > t_end is returned
auto stepper = odeint::make_dense_output(1.0e-6, 1.0e-6,
odeint::runge_kutta_dopri5<state_type>());
auto ode_range = odeint::make_adaptive_range(std::ref(stepper), sys, x0,
t_start, t_end, dt);
// find the step where the condition changes
auto found_iter = std::find_if(ode_range.first, ode_range.second, cond);
if(found_iter == ode_range.second)
{
// no threshold crossing -> return time after t_end and ic
return std::make_pair(t_end + dt, x0);
}
// the dense out stepper now covers the interval where the condition changes
// improve the solution by bisection
double t0 = stepper.previous_time();
double t1 = stepper.current_time();
double t_m;
state_type x_m;
// use odeint's resizing functionality to allocate memory for x_m
odeint::adjust_size_by_resizeability(x_m, x0,
typename odeint::is_resizeable<state_type>::type());
while(std::abs(t1 - t0) > precision) {
t_m = 0.5 * (t0 + t1); // get the mid point time
stepper.calc_state(t_m, x_m); // obtain the corresponding state
if (cond(x_m))
t1 = t_m; // condition changer lies before midpoint
else
t0 = t_m; // condition changer lies after midpoint
}
// we found the interval of size eps, take it's midpoint as final guess
t_m = 0.5 * (t0 + t1);
stepper.calc_state(t_m, x_m);
return std::make_pair(t_m, x_m);
}
int main(int argc, char **argv)
{
state_type x0 = {{10.0, 0.0}};
const double t_start = 0.0;
const double t_end = 10.0;
const double dt = 0.1;
const double threshold = 0.1;
energy_condition cond(threshold);
state_type x_cond;
double t_cond;
std::tie(t_cond, x_cond) = find_condition(x0, damped_osc, cond,
t_start, t_end, dt, 1E-6);
if(t_cond > t_end)
{
// time after t_end -> no threshold crossing within [t_start, t_end]
std::cout << "No threshold crossing found." << std::endl;
} else
{
std::cout.precision(16);
std::cout << "Time of energy threshold crossing: " << t_cond << std::endl;
std::cout << "State: [" << x_cond[0] << " , " << x_cond[1] << "]" << std::endl;
std::cout << "Energy: " << cond.energy(x_cond) << std::endl;
}
}
Windows / Visual Studio 2017