Class template modified_midpoint

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## Class template modified_midpoint

boost::numeric::odeint::modified_midpoint

## Synopsis

    // In header: <boost/numeric/odeint/stepper/modified_midpoint.hpp>

    template<typename State, typename Value = double, typename Deriv = State,
             typename Time = Value,
             typename Algebra = typename algebra_dispatcher< State >::algebra_type,
             typename Operations = typename operations_dispatcher< State >::operations_type,
             typename Resizer = initially_resizer>
    class modified_midpoint : public explicit_stepper_base {
    public:
      // types
      typedef explicit_stepper_base< modified_midpoint< State, Value, Deriv, Time, Algebra, Operations, Resizer >, 2, State, Value, Deriv, Time, Algebra, Operations, Resizer > stepper_base_type;
      typedef stepper_base_type::state_type                                                                                                                                     state_type;
      typedef stepper_base_type::wrapped_state_type                                                                                                                             wrapped_state_type;
      typedef stepper_base_type::value_type                                                                                                                                     value_type;
      typedef stepper_base_type::deriv_type                                                                                                                                     deriv_type;
      typedef stepper_base_type::wrapped_deriv_type                                                                                                                             wrapped_deriv_type;
      typedef stepper_base_type::time_type                                                                                                                                      time_type;
      typedef stepper_base_type::algebra_type                                                                                                                                   algebra_type;
      typedef stepper_base_type::operations_type                                                                                                                                operations_type;
      typedef stepper_base_type::resizer_type                                                                                                                                   resizer_type;
      typedef stepper_base_type::stepper_type                                                                                                                                   stepper_type;

      // construct/copy/destruct
      modified_midpoint(unsigned short = 2, const algebra_type & = algebra_type());

      // public member functions
      template<typename System, typename StateIn, typename DerivIn,
               typename StateOut>
        void do_step_impl(System, const StateIn &, const DerivIn &, time_type,
                          StateOut &, time_type);
      void set_steps(unsigned short);
      unsigned short steps(void) const;
      template<typename StateIn> void adjust_size(const StateIn &);

      // private member functions
      template<typename StateIn> bool resize_impl(const StateIn &);
    };

## Description

Implementation of the modified midpoint method with a configurable number of intermediate steps. This class is used by the Bulirsch-Stoer algorithm and is not meant for direct usage.

### `modified_midpoint` public construct/copy/destruct

1.     modified_midpoint(unsigned short steps = 2,
                         const algebra_type & algebra = algebra_type());

### `modified_midpoint` public member functions

1.     template<typename System, typename StateIn, typename DerivIn,
                typename StateOut>
         void do_step_impl(System system, const StateIn & in, const DerivIn & dxdt,
                           time_type t, StateOut & out, time_type dt);

2.     void set_steps(unsigned short steps);

3.     unsigned short steps(void) const;

4.     template<typename StateIn> void adjust_size(const StateIn & x);

### `modified_midpoint` private member functions

1.     template<typename StateIn> bool resize_impl(const StateIn & x);