c++ - 使用 Boost::odeint 和 Eigen::Matrix 作为状态 vector

Question

我正在尝试使用 ODE integration capabilities of Boost使用 Matrix class from Eigen 3作为我的状态 vector ，但我在 Boost 中遇到了我不知道如何解决的问题。

我正在尝试做的一个最小示例:

#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;
}

如果我取消对 stepper.do_step 的调用，一切都会编译并运行得很好，但当然不会做任何有趣的事情。如果我不这样做，请 boost 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 ，但我对能够修复我的代码的情况还不够了解。由于 odeint 库文档 clearly states

The main focus of odeint is to provide numerical methods implemented in a way where the algorithm is completely independent on the data structure used to represent the state x.

我相信即使 odeint 本身不支持 Eigen，这也不难实现。

Answer 1

只需将步进器的定义替换为

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。

顺便说一句。您对 ODE 的定义不正确，您需要派生的引用

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