ode: tutorial 1

#include "pressio/ode_advancers.hpp"
#include "pressio/ode_steppers_explicit.hpp"
#include <Eigen/Core>

template<class ScalarType>
class SimpleSystem{
public:
  using independent_variable_type = ScalarType;
  using state_type                = Eigen::Matrix<ScalarType,-1,1>;
  using rhs_type	          = state_type;

  state_type createState() const{
    auto s = state_type(3);
    s.setConstant(0);
    return s;
  };

  rhs_type createRhs() const{
    auto v = rhs_type(3);
    v.setConstant(0);
    return v;
  };

  void rhs(const state_type & state,
	   const independent_variable_type timeIn,
	   rhs_type & rhs) const
  {
    constexpr ScalarType ten{10};
    rhs(0) = ten * state(0);
    rhs(1) = ten * state(1);
    rhs(2) = ten * state(2);
  };
};

int main(int argc, char *argv[])
{
  pressio::log::initialize(pressio::logto::terminal);

  using scalar_type = double;
  SimpleSystem<scalar_type> problem;

  auto y = problem.createState();

  namespace pode = pressio::ode;
  constexpr auto scheme = pode::StepScheme::ForwardEuler;
  auto stepperObj = pode::create_explicit_stepper(scheme, problem);

  {
    /*
      run a fixed number of steps
    */
    y(0) = 1.; y(1) = 2.; y(2) = 3.;
    const scalar_type dt{0.1};
    const scalar_type startTime{0.0};
    pode::advance_n_steps(stepperObj, y, startTime, dt, pode::StepCount{1});
    // check solution
    std::cout << "Computed solution: ["
	      << y(0) << " " << y(1) << " " << y(2) << "] "
	      << "Expected solution: [2,4,6] \n";
  }
  std::cout << std::endl;

  {
    /*
      run until target time
    */
    y(0) = 1.; y(1) = 2.; y(2) = 3.;
    const scalar_type startTime{0.0};
    const scalar_type finalTime{1.0};
    pode::advance_to_target_point(stepperObj, y, startTime, finalTime,
				  [](const pode::StepCount & /*unused*/,
				     const pode::StepStartAt<scalar_type> & /*unused*/,
				     pode::StepSize<scalar_type> & dt)
				  {
				    dt = 0.1;
				  });
    // check solution
    std::cout << "Computed solution: ["
	      << y(0) << " " << y(1) << " " << y(2) << "] "
	      << "Expected solution: [1024, 2048, 3074] \n";
  }

  pressio::log::finalize();
  return 0;
}