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## Class template explicit_generic_rk

boost::numeric::odeint::explicit_generic_rk — A generic implementation of explicit Runge-Kutta algorithms. This class is as a base class for all explicit Runge-Kutta steppers.

## Synopsis

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

    template<size_t StageCount, size_t Order, typename State, typename Value,
             typename Deriv, typename Time, typename Algebra, typename Operations,
             typename Resizer>
    class explicit_generic_rk : public boost::numeric::odeint::explicit_stepper_base< Stepper, Order, State, Value, Deriv, Time, Algebra, Operations, Resizer >
    {
    public:
      // types
      typedef explicit_stepper_base< ... >          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 unspecified                           rk_algorithm_type;
      typedef rk_algorithm_type::coef_a_type        coef_a_type;
      typedef rk_algorithm_type::coef_b_type        coef_b_type;
      typedef rk_algorithm_type::coef_c_type        coef_c_type;

      // construct/copy/destruct
      explicit_generic_rk(const coef_a_type &, const coef_b_type &,
                          const coef_c_type &,
                          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);
      template<typename StateIn> void adjust_size(const StateIn &);
      template<typename System, typename StateInOut>
        void do_step(System, StateInOut &, time_type, time_type);
      template<typename System, typename StateInOut>
        void do_step(System, const StateInOut &, time_type, time_type);
      template<typename System, typename StateInOut, typename DerivIn>
        boost::disable_if< boost::is_same< DerivIn, time_type >, void >::type
        do_step(System, StateInOut &, const DerivIn &, time_type, time_type);
      template<typename System, typename StateIn, typename StateOut>
        void do_step(System, const StateIn &, time_type, StateOut &, time_type);
      template<typename System, typename StateIn, typename DerivIn,
               typename StateOut>
        void do_step(System, const StateIn &, const DerivIn &, time_type,
                     StateOut &, time_type);
      const algebra_type & algebra() const;

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

## Description

This class implements the explicit Runge-Kutta algorithms without error estimation in a generic way. The Butcher tableau is passed to the stepper which constructs the stepper scheme with the help of a template-metaprogramming algorithm. ToDo : Add example!

This class derives explicit_stepper_base which provides the stepper interface.

### Template Parameters

1.     size_t StageCount

   The number of stages of the Runge-Kutta algorithm.

2.     size_t Order

   The order of the stepper.

3.     typename State

   The type representing the state of the ODE.

4.     typename Value

   The floating point type which is used in the computations.

5.     typename Deriv

6.     typename Time

   The type representing the independent variable - the time - of the ODE.

7.     typename Algebra

   The algebra type.

8.     typename Operations

   The operations type.

9.     typename Resizer

   The resizer policy type.

### `explicit_generic_rk` public construct/copy/destruct

1.     explicit_generic_rk(const coef_a_type & a, const coef_b_type & b,
                           const coef_c_type & c,
                           const algebra_type & algebra = algebra_type());

   Constructs the `explicit_generic_rk` class. See examples section for details on the coefficients.

   Parameters: |
   `a` | Triangular matrix of parameters b in the Butcher tableau.
   `algebra` | A copy of algebra is made and stored inside `explicit_stepper_base`.
   `b` | Last row of the butcher tableau.
   `c` | Parameters to calculate the time points in the Butcher tableau.

### `explicit_generic_rk` 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);

   This method performs one step. The derivative `dxdt` of `in` at the time `t` is passed to the method. The result is updated out of place, hence the input is in `in` and the output in `out`. Access to this step functionality is provided by `explicit_stepper_base` and `do_step_impl` should not be called directly.

   Parameters: |
   `dt` | The step size.
   `dxdt` | The derivative of x at t.
   `in` | The state of the ODE which should be solved. in is not modified in this method
   `out` | The result of the step is written in out.
   `system` | The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.
   `t` | The value of the time, at which the step should be performed.

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

   Adjust the size of all temporaries in the stepper manually.

   Parameters: |
   `x` | A state from which the size of the temporaries to be resized is deduced.

3.     template<typename System, typename StateInOut>
         void do_step(System system, StateInOut & x, time_type t, time_type dt);

   This method performs one step. It transforms the result in-place.

   Parameters: |
   `dt` | The step size.
   `system` | The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Simple System concept.
   `t` | The value of the time, at which the step should be performed.
   `x` | The state of the ODE which should be solved. After calling do_step the result is updated in x.

4.     template<typename System, typename StateInOut>
         void do_step(System system, const StateInOut & x, time_type t, time_type dt);

   Second version to solve the forwarding problem, can be called with Boost.Range as StateInOut.

5.     template<typename System, typename StateInOut, typename DerivIn>
         boost::disable_if< boost::is_same< DerivIn, time_type >, void >::type
         do_step(System system, StateInOut & x, const DerivIn & dxdt, time_type t,
                 time_type dt);

   The method performs one step. Additionally to the other method the derivative of x is also passed to this method. It is supposed to be used in the following way:

       * sys( x , dxdt , t );
       * stepper.do_step( sys , x , dxdt , t , dt );
       *

   The result is updated in place in x. This method is disabled if Time and Deriv are of the same type. In this case the method could not be distinguished from other `do_step` versions.

   | Note
   This method does not solve the forwarding problem.

   Parameters: |
   `dt` | The step size.
   `dxdt` | The derivative of x at t.
   `system` | The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.
   `t` | The value of the time, at which the step should be performed.
   `x` | The state of the ODE which should be solved. After calling do_step the result is updated in x.

6.     template<typename System, typename StateIn, typename StateOut>
         void do_step(System system, const StateIn & in, time_type t, StateOut & out,
                      time_type dt);

   The method performs one step. The state of the ODE is updated out-of-place.

   | Note
   This method does not solve the forwarding problem.

   Parameters: |
   `dt` | The step size.
   `in` | The state of the ODE which should be solved. in is not modified in this method
   `out` | The result of the step is written in out.
   `system` | The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.
   `t` | The value of the time, at which the step should be performed.

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

   The method performs one step. The state of the ODE is updated out-of-place. Furthermore, the derivative of x at t is passed to the stepper. It is supposed to be used in the following way:

       * sys( in , dxdt , t );
       * stepper.do_step( sys , in , dxdt , t , out , dt );
       *

   | Note
   This method does not solve the forwarding problem.

   Parameters: |
   `dt` | The step size.
   `dxdt` | The derivative of x at t.
   `in` | The state of the ODE which should be solved. in is not modified in this method
   `out` | The result of the step is written in out.
   `system` | The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.
   `t` | The value of the time, at which the step should be performed.

8.     const algebra_type & algebra() const;

   Returns: | A reference to the algebra which is held by this class. A const reference to the algebra which is held by this class.

### `explicit_generic_rk` private member functions

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