Using Boost::odeint with Eigen::Matrix as state vector

Question

I'm trying to utilize the ODE integration capabilities of Boost using the Matrix class from Eigen 3 as my state vector, but I'm running into problems deep into Boost that I don't understand how to address.

A minimal example of what I'm trying to do:

#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;
}

If I coment out the call to stepper.do_step everything compiles and runs just fine, but of course doesn't do anything interesting. If I don't, Boost vomits compile errors over my terminal, the first of which is

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;

I tried to dig into the Boost header where the error occurs, but I didn't understand enough of what's going on to be able to fix my code. Since the odeint library documentation 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.

I believe this shouldn't be too hard to get working even if odeint doesn't support Eigen natively.

Answer 1

You only need to replace the definition of the stepper by

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

Eigen should work out of the Box with the vector_space_algebra but you need to specify them manually. In the next odeint version we have a mechanism for automatically detecting the algebra.

Btw. youe definition of the ODE is not correct, you need a reference for the derivatve

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

Answer 2

This solution does not seem to work for adaptive integrator

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;)