Armadillo's cx_mat and Boost's odeint compilation error

Question

I was going to solve several matrix differential equations, of the form d/dt (X) = F(X) , where X is a large complex matrix, and F denotes some function of it. I tried to use Boost's odeint with state_type as Armadillo's cx_mat . But it produces compilation error for controlled stepper type. My sample code is as follows

#include <armadillo>
#include <iostream>
#include <boost/numeric/odeint.hpp>

using namespace std;
using namespace arma;
using namespace boost::numeric::odeint;

using state_type = arma::cx_mat;


void ode(const state_type& X, state_type& derr, double) {
  derr =  X;  // sample derivative, can be anything else
}

// define resizable and norm_inf
namespace boost { namespace numeric { namespace odeint {

template <>
struct is_resizeable<arma::cx_mat> {
    typedef boost::true_type type;
    const static bool value = type::value;
};

template <>
struct same_size_impl<arma::cx_mat, arma::cx_mat> {
    static bool same_size(const arma::cx_mat& x, const arma::cx_mat& y)
    {
      return arma::size(x) == arma::size(y);
    }
};

template<>
struct resize_impl<arma::cx_mat, arma::cx_mat> {
      static void resize(arma::cx_mat& v1, const arma::cx_mat& v2) {
      v1.resize(arma::size(v2));
    }
};


template<>
 struct vector_space_norm_inf<state_type> {
    typedef double result_type;
    result_type operator()(const state_type& p) const
    {
      return arma::norm(p, "inf");
    }
};



} } } // namespace boost::numeric::odeint





using stepper =  runge_kutta_dopri5<state_type, double, state_type, double, vector_space_algebra>;

int main () {

  cx_mat A = randu<cx_mat>(4, 4);


  integrate_adaptive( make_controlled<stepper>(1E-10, 1E-10),  ode, A, 0.0 , 10.0, 0.1);
}  

This code gives the following compilation error:

/usr/include/armadillo_bits/Mat_meat.hpp:5153:3: error: static assertion failed: error: incorrect or unsupported type
   arma_type_check(( is_same_type< eT, typename T1::elem_type >::no ));

What I can understand that Armadillo does not support copying a real matrix ( mat ) into a complex one ( cx_mat ), like

mat Z = something;
cx_mat Y = Z;  // ERROR

Which happens somewhere in odeint . Right now I am overcoming this by copying whole matrix into std::vector<std::complex<double> > put it into the function ode , then inside the function again copy whole std::vector<std::complex<double> > into cx_mat , calculate F(X) , then copy it into std::vector<std::complex<double> > and return. Obviously, this is very slow and inefficient.

Any simple solution to the problem?? If possible, I may want to shift to Eigen, if that helps.

Answer 1

Hi I know this is quite old but as I did stumble across it facing the same problem I wanted to share my solution to this. I used Eigen and with some minor additions similar to yours in Armadillo it worked for me(tested compilation with icpc and g++). Here a minimal code snipped:

#include<Eigen/Eigen>
#include<boost/numeric/odeint.hpp>
#include<iostream>
#include<complex>
#include<boost/numeric/odeint/external/eigen/eigen_algebra.hpp>

typedef std::complex<double> cdoub;
typedef Eigen::MatrixXcd state_type;

namespace boost {
namespace numeric {
namespace odeint {

template<typename B,int S1,int S2,int O, int M1, int M2>
struct algebra_dispatcher< Eigen::Matrix<B,S1,S2,O,M1,M2> >
{
    typedef vector_space_algebra algebra_type;
};

template<>
 struct vector_space_norm_inf<state_type> {
    typedef double result_type;
    result_type operator()(const state_type& p) const
    {
      return p.lpNorm<Eigen::Infinity>();
    }
};
}}}

namespace Eigen {
template<typename D, int Rows, int Cols>
Matrix<D, Rows, Cols> operator/(const Matrix<D, Rows, Cols>& v1, const Matrix<D, Rows, Cols>& v2)
{
    return v1.array()/v2.array();
}   

template<typename D, int Rows, int Cols>
Matrix<D, Rows, Cols>
abs(Matrix<D, Rows, Cols> const& m) {
    return m.cwiseAbs();
}
}

/* The rhs of x' = f(x) */
void harmonic_oscillator( const state_type &x , state_type &dxdt , const double /* t */ )
{
    dxdt = x;
}
//]

int main() {
    using namespace boost::numeric::odeint;
    state_type X0(3,3);
    X0 = state_type::Random(3,3);
    state_type xout = X0;

    typedef runge_kutta_dopri5<state_type,double,state_type,double,vector_space_algebra> error_stepper_type;
    typedef controlled_runge_kutta< error_stepper_type > controlled_stepper_type;
    controlled_stepper_type controlled_stepper;

    double t =0.0;
    double dt = 0.1;

    controlled_stepper.try_step(harmonic_oscillator, X0, t, dt);

    std::cout << X0 << std::endl;
}

Perhaps the problem has already been solved but as the question came up again here https://gist.github.com/jefftrull/5625b77c0f86c439f29f five days ago I wanted to share it, hopfully it helps:)

Answer 2

Yes, complex valued state types don't play well with adaptive steppers because odeint does not differentiate between state_type and error_type. Ie it uses state_type also to store the error, but this does not work for complex valued state_types, while the error should be double-valued matrix. I'm not sure how well Eigen plays with this, but it might be worth a try. Feel free to file a ticket on https://github.com/headmyshoulder/odeint-v2 , but this will be quite a big change...