Question

我尝试使用ODE integration capabilities of Boost作为我的状态向量来使用Matrix class from Eigen 3，但我遇到了Boost的深层问题，我不明白解决。

我尝试做的最小例子：

#include <Eigen/Core>
#include <boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp>
#include <iostream>

using namespace Eigen;
using namespace boost::numeric::odeint;

template<size_t N>
using vector = Matrix<double, N, 1>;

typedef vector<3> state;

int main() {

    state X0;
    X0 << 1., 2., 3.;
    state xout = X0;

    runge_kutta_dopri5<state> stepper;

    // If I remove these lines, everything compiles fine
    stepper.do_step([](const state x, state dxdt, const double t) -> void { 
        dxdt = x;
    }, X0, 0.0, xout, 0.01);

    std::cout << xout << std::endl;
}

如果我打电话给stepper.do_step，那么所有内容都会编译并运行得很好，但当然不会做任何有趣的事情。如果我没有，请提升vomits compile errors over my terminal，其中第一个是

In file included from /usr/include/boost/mpl/aux_/begin_end_impl.hpp:20:0,
                 from /usr/include/boost/mpl/begin_end.hpp:18,
                 from /usr/include/boost/mpl/is_sequence.hpp:19,
                 from /usr/include/boost/fusion/support/detail/is_mpl_sequence.hpp:12,
                 from /usr/include/boost/fusion/support/tag_of.hpp:13,
                 from /usr/include/boost/fusion/support/is_sequence.hpp:11,
                 from /usr/include/boost/fusion/sequence/intrinsic_fwd.hpp:12,
                 from /usr/include/boost/fusion/sequence/intrinsic/front.hpp:10,
                 from /usr/include/boost/fusion/include/front.hpp:10,
                 from /usr/include/boost/numeric/odeint/util/is_resizeable.hpp:26,
                 from /usr/include/boost/numeric/odeint/util/state_wrapper.hpp:25,
                 from /usr/include/boost/numeric/odeint/stepper/base/explicit_error_stepper_fsal_base.hpp:27,
                 from /usr/include/boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp:24,
                 from /home/tlycken/exjobb/Code/alpha-orbit-follower/test/algebra/algebra-tests.cpp:2:
/usr/include/boost/mpl/eval_if.hpp: In instantiation of ‘struct boost::mpl::eval_if_c<true, boost::range_const_iterator<Eigen::Matrix<double, 3, 1> >, boost::range_mutable_iterator<const Eigen::Matrix<double, 3, 1> > >’:
/usr/include/boost/range/iterator.hpp:63:63:   required from ‘struct boost::range_iterator<const Eigen::Matrix<double, 3, 1> >’
/usr/include/boost/range/begin.hpp:112:61:   required by substitution of ‘template<class T> typename boost::range_iterator<const T>::type boost::range_adl_barrier::begin(const T&) [with T = Eigen::Matrix<double, 3, 1>]’
/usr/include/boost/numeric/odeint/algebra/range_algebra.hpp:52:45:   required from ‘static void boost::numeric::odeint::range_algebra::for_each3(S1&, S2&, S3&, Op) [with S1 = Eigen::Matrix<double, 3, 1>; S2 = const Eigen::Matrix<double, 3, 1>; S3 = const Eigen::Matrix<double, 3, 1>; Op = boost::numeric::odeint::default_operations::scale_sum2<double, double>]’
/usr/include/boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp:128:9:   required from ‘void boost::numeric::odeint::runge_kutta_dopri5<State, Value, Deriv, Time, Algebra, Operations, Resizer>::do_step_impl(System, const StateIn&, const DerivIn&, boost::numeric::odeint::runge_kutta_dopri5<State, Value, Deriv, Time, Algebra, Operations, Resizer>::time_type, StateOut&, DerivOut&, boost::numeric::odeint::runge_kutta_dopri5<State, Value, Deriv, Time, Algebra, Operations, Resizer>::time_type) [with System = main()::__lambda0; StateIn = Eigen::Matrix<double, 3, 1>; DerivIn = Eigen::Matrix<double, 3, 1>; StateOut = Eigen::Matrix<double, 3, 1>; DerivOut = Eigen::Matrix<double, 3, 1>; State = Eigen::Matrix<double, 3, 1>; Value = double; Deriv = Eigen::Matrix<double, 3, 1>; Time = double; Algebra = boost::numeric::odeint::range_algebra; Operations = boost::numeric::odeint::default_operations; Resizer = boost::numeric::odeint::initially_resizer; boost::numeric::odeint::runge_kutta_dopri5<State, Value, Deriv, Time, Algebra, Operations, Resizer>::time_type = double]’
/usr/include/boost/numeric/odeint/stepper/base/explicit_error_stepper_fsal_base.hpp:167:9:   required from ‘typename boost::disable_if<boost::is_same<StateInOut, Time>, void>::type boost::numeric::odeint::explicit_error_stepper_fsal_base<Stepper, Order, StepperOrder, ErrorOrder, State, Value, Deriv, Time, Algebra, Operations, Resizer>::do_step(System, const StateIn&, boost::numeric::odeint::explicit_error_stepper_fsal_base<Stepper, Order, StepperOrder, ErrorOrder, State, Value, Deriv, Time, Algebra, Operations, Resizer>::time_type, StateOut&, boost::numeric::odeint::explicit_error_stepper_fsal_base<Stepper, Order, StepperOrder, ErrorOrder, State, Value, Deriv, Time, Algebra, Operations, Resizer>::time_type) [with System = main()::__lambda0; StateIn = Eigen::Matrix<double, 3, 1>; StateOut = Eigen::Matrix<double, 3, 1>; Stepper = boost::numeric::odeint::runge_kutta_dopri5<Eigen::Matrix<double, 3, 1> >; short unsigned int Order = 5u; short unsigned int StepperOrder = 5u; short unsigned int ErrorOrder = 4u; State = Eigen::Matrix<double, 3, 1>; Value = double; Deriv = Eigen::Matrix<double, 3, 1>; Time = double; Algebra = boost::numeric::odeint::range_algebra; Operations = boost::numeric::odeint::default_operations; Resizer = boost::numeric::odeint::initially_resizer; typename boost::disable_if<boost::is_same<StateInOut, Time>, void>::type = void; boost::numeric::odeint::explicit_error_stepper_fsal_base<Stepper, Order, StepperOrder, ErrorOrder, State, Value, Deriv, Time, Algebra, Operations, Resizer>::time_type = double]’
/home/tlycken/exjobb/Code/alpha-orbit-follower/test/algebra/algebra-tests.cpp:21:137:   required from here
/usr/include/boost/mpl/eval_if.hpp:60:31: error: no type named ‘type’ in ‘boost::mpl::eval_if_c<true, boost::range_const_iterator<Eigen::Matrix<double, 3, 1> >, boost::range_mutable_iterator<const Eigen::Matrix<double, 3, 1> > >::f_ {aka struct boost::range_const_iterator<Eigen::Matrix<double, 3, 1> >}’
     typedef typename f_::type type;

我试图深入研究the Boost header where the error occurs，但我还没有完全了解能够修复代码的内容。自odeint库文档clearly states

以来

odeint的主要焦点是提供数值方法，其方法是算法完全独立于用于表示状态x的数据结构。

我相信即使odeint本身并不支持Eigen，这也不会太难实现。

Answer 1

您只需要通过

替换步进器的定义

runge_kutta_dopri5<state,double,state,double,vector_space_algebra> stepper;

Eigen应该使用vector_space_algebra开箱即用，但您需要手动指定它们。在下一个odeint版本中，我们有一个自动检测代数的机制。

顺便说一下。你定义的ODE不正确，你需要一个衍生物的参考

stepper.do_step([](const state &x, state &dxdt, const double t) -> void { 
    dxdt = x;
}, X0, 0.0, xout, 0.01);

Answer 2

此解决方案似乎不适用于自适应积分器

typedef runge_kutta_dopri5<state,double,state,double,vector_space_algebra> stepper_type;
auto rhs = [](const state &x, state &dxdt, const double t) -> void { dxdt = x;}
integrate_adaptive( make_controlled<stepper_type>( 1E-12 , 1E-12 ), rhs , X0 , 0. , xout , 0.01;)

使用带有Eigen :: Matrix的Boost :: odeint作为状态向量

2 个答案: