boost odeint：使用自定义 class 和矢量 space 代数控制步进器

Question

我正在使用 boost odeint 来演化一个微分方程。时间和值由围绕普通数字的包装器 class 给出（进行高斯误差传播）。

using Time = Number<double>;
using Value = Number<double>;

状态及其导数由带有声明

的自定义class给出

class State : boost::addable<State>, boost::multipliable<State, Time>, boost::dividable<State>
{
public:
    void Add(Group const& group, Value alpha);
    Value Get(Group const& group) const;
    State& operator*=(Time const& time);
    State& operator+=(State const& state);
    State& operator/=(State const& state);
    State abs() const;
    Value norm_inf() const;
private:
    std::map<Group, Value> map_;
};

State abs(State const& state);

namespace boost
{
namespace numeric
{
namespace odeint
{
template<>
struct boost::numeric::odeint::vector_space_norm_inf<State> {
    using result_type = Value;
    result_type operator()(State const& state) const;
};
}
}
}

using Derivative = State;

我将 Runge-Kutta-Dopri-5 步进器与矢量 space 代数一起使用

using Stepper = boost::numeric::odeint::runge_kutta_dopri5<State, Value, Derivative, Time, boost::numeric::odeint::vector_space_algebra>;

而且我整个人都这么想

auto start_state = GetStart();
auto system = GetSystem();
auto min = GetMin();
auto max = GetMax();
auto dt = GetDt;
auto observer = GetObserver();
auto stepper = boost::numeric::odeint::make_controlled<Stepper>(1e-6, 1e-6);
boost::numeric::odeint::integrate_adaptive(Stepper(), system, start_state, min, max, dt, observer);

这很有魅力。但是您可能会注意到，我没有使用我在倒数第二行中定义的受控步进器，而是使用默认步进器。当我尝试在最后一行中使用 stepper 变量而不是默认的 Stepper() 时，出现以下编译错误：

In file included from /home/me/Integrate.cpp:2:
In file included from /usr/include/boost/numeric/odeint.hpp:35:
/usr/include/boost/numeric/odeint/stepper/controlled_runge_kutta.hpp:85:17: error: no matching constructor for initialization of 'typename operations_type::rel_error<value_type>' (aka 'rel_error<me::Number<double> >')
                typename operations_type::template rel_error< value_type >( m_eps_abs , m_eps_rel , m_a_x , m_a_dxdt * abs(get_unit_value( dt )) ) );
                ^                                                           ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/boost/numeric/odeint/stepper/controlled_runge_kutta.hpp:768:50: note: in instantiation of function template specialization 'odeint::default_error_checker<me::Number<double>, odeint::vector_space_algebra, odeint::default_operations>::error<me::State, me::State, me::State, me::Number<double> >' requested here
        value_type max_rel_err = m_error_checker.error( m_stepper.algebra() , in , dxdt_in , m_xerr.m_v , dt );
                                                 ^
/usr/include/boost/numeric/odeint/stepper/controlled_runge_kutta.hpp:716:38: note: in instantiation of function template specialization 'odeint::controlled_runge_kutta<odeint::runge_kutta_dopri5<me::State, me::Number<double>, me::State, me::Number<double>, odeint::vector_space_algebra, odeint::default_operations, odeint::initially_resizer>, odeint::default_error_checker<me::Number<double>, odeint::vector_space_algebra, odeint::default_operations>, odeint::default_step_adjuster<me::Number<double>, me::Number<double> >, odeint::initially_resizer, odeint::explicit_error_stepper_fsal_tag>::try_step<(lambda at /home/me/Integrate.cpp:28:19), me::State, me::State, me::State, me::State>' requested here
        controlled_step_result res = try_step( system , x , dxdt , t , m_xnew.m_v , m_dxdtnew.m_v , dt );
                                     ^
/usr/include/boost/numeric/odeint/stepper/controlled_runge_kutta.hpp:899:16: note: in instantiation of function template specialization 'odeint::controlled_runge_kutta<odeint::runge_kutta_dopri5<me::State, me::Number<double>, me::State, me::Number<double>, odeint::vector_space_algebra, odeint::default_operations, odeint::initially_resizer>, odeint::default_error_checker<me::Number<double>, odeint::vector_space_algebra, odeint::default_operations>, odeint::default_step_adjuster<me::Number<double>, me::Number<double> >, odeint::initially_resizer, odeint::explicit_error_stepper_fsal_tag>::try_step<(lambda at /home/me/Integrate.cpp:28:19), me::State, me::State>' requested here
        return try_step( system , x , m_dxdt.m_v , t , dt );
               ^
/usr/include/boost/numeric/odeint/stepper/controlled_runge_kutta.hpp:617:16: note: in instantiation of function template specialization 'odeint::controlled_runge_kutta<odeint::runge_kutta_dopri5<me::State, me::Number<double>, me::State, me::Number<double>, odeint::vector_space_algebra, odeint::default_operations, odeint::initially_resizer>, odeint::default_error_checker<me::Number<double>, odeint::vector_space_algebra, odeint::default_operations>, odeint::default_step_adjuster<me::Number<double>, me::Number<double> >, odeint::initially_resizer, odeint::explicit_error_stepper_fsal_tag>::try_step_v1<(lambda at /home/me/Integrate.cpp:28:19), me::State>' requested here
        return try_step_v1( system , x , t , dt );
               ^
/usr/include/boost/numeric/odeint/integrate/detail/integrate_adaptive.hpp:103:22: note: in instantiation of function template specialization 'odeint::controlled_runge_kutta<odeint::runge_kutta_dopri5<me::State, me::Number<double>, me::State, me::Number<double>, odeint::vector_space_algebra, odeint::default_operations, odeint::initially_resizer>, odeint::default_error_checker<me::Number<double>, odeint::vector_space_algebra, odeint::default_operations>, odeint::default_step_adjuster<me::Number<double>, me::Number<double> >, odeint::initially_resizer, odeint::explicit_error_stepper_fsal_tag>::try_step<(lambda at /home/me/Integrate.cpp:28:19), me::State>' requested here
            res = st.try_step( system , start_state , start_time , dt );
                     ^
/usr/include/boost/numeric/odeint/integrate/integrate_adaptive.hpp:42:20: note: in instantiation of function template specialization 'odeint::detail::integrate_adaptive<odeint::controlled_runge_kutta<odeint::runge_kutta_dopri5<me::State, me::Number<double>, me::State, me::Number<double>, odeint::vector_space_algebra, odeint::default_operations, odeint::initially_resizer>, odeint::default_error_checker<me::Number<double>, odeint::vector_space_algebra, odeint::default_operations>, odeint::default_step_adjuster<me::Number<double>, me::Number<double> >, odeint::initially_resizer, odeint::explicit_error_stepper_fsal_tag>, (lambda at /home/me/Integrate.cpp:28:19), me::State, me::Number<double>, (lambda at /home/me/Integrate.cpp:48:21)>' requested here
    return detail::integrate_adaptive(
                   ^
/usr/include/boost/numeric/odeint/algebra/default_operations.hpp:435:9: note: candidate constructor not viable: no known conversion from 'me::State' to 'me::Number<double>' for 4th argument
        rel_error( Fac1 eps_abs , Fac1 eps_rel , Fac1 a_x , Fac1 a_dxdt )
        ^
/usr/include/boost/numeric/odeint/algebra/default_operations.hpp:431:12: note: candidate constructor (the implicit move constructor) not viable: requires 1 argument, but 4 were provided
    struct rel_error
           ^
/usr/include/boost/numeric/odeint/algebra/default_operations.hpp:431:12: note: candidate constructor (the implicit copy constructor) not viable: requires 1 argument, but 4 were provided

我可以看到 odeint::rel_error<me::Number<double>> 应该是 Number 类型，但是乘积 m_a_dxdt * abs(get_unit_value( dt )) 用作 rel_error 的第 4 个参数构造函数是 State 类型。我假设我在为 State class 实现向量 space 代数时犯了一个错误，但我找不到我在哪里犯了错误。

如果我用普通 double 替换时间和值类型，错误检查器将再次工作。

Answer 1

odeint指令好像有错误。如果 abs 函数的 return 类型是 Value 而不是人们天真地认为它是 State ，那么编译错误就会消失。

boost odeint：使用自定义 class 和矢量 space 代数控制步进器

boost odeint: controlled stepper with custom class and vector space algebra

c++

boost

odeint