[/============================================================================
  Boost.odeint

  Copyright 2012 Karsten Ahnert
  Copyright 2012 Mario Mulansky
  Copyright 2012 Sylwester Arabas

  Use, modification and distribution is subject to the Boost Software License,
  Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
  http://www.boost.org/LICENSE_1_0.txt)
=============================================================================/]

[section Generation functions]

[import ../examples/generation_functions.cpp]

In the __tutorial we have learned how we can use the generation functions `make_controlled` and `make_dense_output` to create controlled and dense output stepper from a simple stepper or an error stepper. The syntax of these two functions is very simple:

[generation_functions_syntax_auto]

The first two parameters are the absolute and the relative error tolerances and the third parameter is the stepper. Additionally, a second version exists where additionally a maximal step size is supplied which ensures the the step size is not increased above this value.
 In C++03 you can infer the type from the `result_of` mechanism:

[generation_functions_syntax_result_of]

To use your own steppers with the `make_controlled` or `make_dense_output` you need to specialize two class templates. Suppose your steppers are called `custom_stepper`, `custom_controller` and `custom_dense_output`. Then, the first class you need to specialize is `boost::numeric::get_controller`, a meta function returning the type of the controller:

[generation_functions_get_controller]

The second one is a factory class `boost::numeric::odeint::controller_factory` which constructs the controller from the tolerances and the stepper. In our dummy implementation this class is

[generation_functions_controller_factory]

This is all to use the `make_controlled` mechanism. Now you can use your controller via

[generation_functions_example_custom_controller]

For the dense_output_stepper everything works similar. Here you have to specialize `boost::numeric::odeint::get_dense_output` and `boost::numeric::odeint::dense_output_factory`. These two classes have the same syntax as their relatives `get_controller` and `controller_factory`.

All controllers and dense-output steppers in odeint can be used with these mechanisms. In the table below you will find, which steppers is constructed from `make_controlled` or `make_dense_output` if applied on a stepper from odeint:

[include make_controlled_table.qbk]
[include make_dense_output_table.qbk]

[endsect]
