ceph/src/boost/libs/numeric/odeint/doc/details_iterators.qbk

   1 [/============================================================================
   2   Boost.odeint
   3
   4   Copyright 2012-2013 Karsten Ahnert
   5   Copyright 2012-2013 Mario Mulansky
   6   Copyright 2012 Sylwester Arabas
   7
   8   Use, modification and distribution is subject to the Boost Software License,
   9   Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
  10   http://www.boost.org/LICENSE_1_0.txt)
  11 =============================================================================/]
  12
  13
  14 [section Iterators and Ranges]
  15
  16 [section Examples]
  17
  18 odeint supports iterators that iterate along an approximate solution of an ordinary differential equation. Iterators offer you an alternative to the integrate functions. Furthermore, many of the standard algorithms in the C++ standard library and Boost.Range can be used with the odeint's iterators.
  19
  20 [import ../examples/const_step_iterator.cpp]
  21
  22 Several iterator types are provided, in consistence with the
  23 __integrate_functions. Hence there are `const_step_iterator`,
  24 `adaptive_step_iterator`, `n_step_iterator` and `times_iterator` -- each of
  25 them in two versions: either with only the `state` or with a
  26 `std::pair<state,time>` as value type.  They are all single pass iterators. In
  27 the following, we show a few examples of how to use those iterators together
  28 with std algorithms.
  29
  30 [const_step_iterator_accumulate]
  31
  32 In this example all x-values of the solution are accumulated. Note, how
  33 dereferencing the iterator gives the current state `x` of the ODE (the second
  34 argument of the accumulate lambda). The iterator
  35 itself does not occur directly in this example but it is generated by the
  36 factory functions `make_const_step_iterator_begin` and
  37 `make_const_step_iterator_end`. odeint also supports Boost.Range, that allows
  38 to write the above example in a more compact form with the factory function
  39 `make_const_step_range`, but now using `boost::accumulate` from __bost_range:
  40
  41 [const_step_iterator_accumulate_range]
  42
  43 The second iterator type is also a iterator with const step size. But the value type of this iterator consists here of a pair of the time and the state of the solution of the ODE. An example is
  44
  45 [const_step_time_iterator_accumulate_range]
  46
  47 The factory functions are now `make_const_step_time_iterator_begin`,
  48 `make_const_step_time_iterator_end` and `make_const_step_time_range`.
  49 Note, how the lambda now expects a `std::pair` as this is the value type of
  50 the `const_step_time_iterator`'s.
  51
  52
  53 [import ../examples/adaptive_iterator.cpp]
  54
  55 Next, we discuss the adaptive iterators which are completely
  56 analogous to the const step iterators, but are based on adaptive stepper
  57 routines and thus adjust the step size during the iteration. Examples are
  58
  59 [adaptive_iterator_accumulate_range]
  60
  61 [adaptive_time_iterator_accumulate_range]
  62
  63 [note 'adaptive_iterator` and `adaptive_time_iterator' can only be used with
  64 __controlled_stepper or __dense_output_stepper.]
  65
  66 In general one can say that iterating over a range of a `const_step_iterator`
  67 behaves like an `integrate_const` function call, and similarly for
  68 `adaptive_iterator` and `integrate_adaptive`, `n_step_iterator` and
  69 `integrate_n_steps`, and finally `times_iterator` and `integrate_times`.
  70
  71 Below we list the most important properties of the exisiting iterators:
  72
  73 [endsect]
  74
  75 [section const_step_iterator]
  76
  77 * Definition: `const_step_iterator< Stepper , System , State >`
  78 * `value_type` is `State`
  79 * `reference_type` is `State const&`
  80 * Factory functions
  81   * `make_const_step_iterator_begin( stepper , system , state , t_start , t_end , dt )`
  82   * `make_const_step_iterator_end( stepper , system , state )`
  83   * `make_const_step_range( stepper , system , state , t_start , t_end , dt )`
  84 * This stepper works with all steppers fulfilling the Stepper concept or the DenseOutputStepper concept.
  85 * The value of `state` is the current state of the ODE during the iteration.
  86
  87 [endsect]
  88
  89 [section const_step_time_iterator]
  90
  91 * Definition: `const_step_time_iterator< Stepper , System , State >`
  92 * `value_type` is `std::pair< State , Stepper::time_type >`
  93 * `reference_type` is `std::pair< State const& , Stepper::time_type > const&`
  94 * Factory functions
  95   * `make_const_step_time_iterator_begin( stepper , system , state , t_start , t_end , dt )`
  96   * `make_const_step_time_iterator_end( stepper , system , state )`
  97   * `make_const_step_time_range( stepper , system , state , t_start , t_end , dt )`
  98 * This stepper works with all steppers fulfilling the Stepper concept or the DenseOutputStepper concept.
  99 * This stepper updates the value of `state`. The value of `state` is the current state of the ODE during the iteration.
 100
 101
 102 [endsect]
 103
 104
 105 [section adaptive_step_iterator]
 106
 107 * Definition: `adaptive_iterator< Stepper , System , State >`
 108 * `value_type` is `State`
 109 * `reference_type` is `State const&`
 110 * Factory functions
 111   * `make_adaptive_iterator_begin( stepper , system , state , t_start , t_end , dt )`
 112   * `make_adaptive_iterator_end( stepper , system , state )`
 113   * `make_adaptive_range( stepper , system , state , t_start , t_end , dt )`
 114 * This stepper works with all steppers fulfilling the ControlledStepper concept or the DenseOutputStepper concept.
 115 * For steppers fulfilling the ControlledStepper concept `state` is modified according to the current state of the ODE. For DenseOutputStepper the state is not modified due to performance optimizations, but the steppers itself.
 116
 117
 118 [endsect]
 119
 120 [section adaptive_step_time_iterator]
 121
 122 * Definition: `adaptive_iterator< Stepper , System , State >`
 123 * `value_type` is `std::pair< State , Stepper::time_type >`
 124 * `reference_type` is `std::pair< State const& , Stepper::time_type > const&`
 125 * Factory functions
 126   * `make_adaptive_time_iterator_begin( stepper , system , state , t_start , t_end , dt )`
 127   * `make_adaptive_time_iterator_end( stepper , system , state )`
 128   * `make_adaptive_time_range( stepper , system , state , t_start , t_end , dt )`
 129 * This stepper works with all steppers fulfilling the ControlledStepper concept or the DenseOutputStepper concept.
 130 * For steppers fulfilling the ControlledStepper concept `state` is modified according to the current state of the ODE. For DenseOutputStepper the state is not modified due to performance optimizations, but the stepper itself.
 131
 132
 133 [endsect]
 134
 135
 136 [section n_step_iterator]
 137
 138 * Definition: `n_step_iterator< Stepper , System , State >`
 139 * `value_type` is `State`
 140 * `reference_type` is `State const&`
 141 * Factory functions
 142   * `make_n_step_iterator_begin( stepper , system , state , t_start , dt , num_of_steps )`
 143   * `make_n_step_iterator_end( stepper , system , state )`
 144   * `make_n_step_range( stepper , system , state , t_start , dt , num_of_steps )`
 145 * This stepper works with all steppers fulfilling the Stepper concept or the DenseOutputStepper concept.
 146 * The value of `state` is the current state of the ODE during the iteration.
 147
 148 [endsect]
 149
 150 [section n_step_time_iterator]
 151
 152 * Definition: `n_step_time_iterator< Stepper , System , State >`
 153 * `value_type` is `std::pair< State , Stepper::time_type >`
 154 * `reference_type` is `std::pair< State const& , Stepper::time_type > const&`
 155 * Factory functions
 156   * `make_n_step_time_iterator_begin( stepper , system , state , t_start , dt , num_of_steps )`
 157   * `make_n_step_time_iterator_end( stepper , system , state )`
 158   * `make_n_step_time_range( stepper , system , state , t_start , dt , num_of_steps )`
 159 * This stepper works with all steppers fulfilling the Stepper concept or the DenseOutputStepper concept.
 160 * This stepper updates the value of `state`. The value of `state` is the current state of the ODE during the iteration.
 161
 162
 163 [endsect]
 164
 165
 166 [section times_iterator]
 167
 168 * Definition: `times_iterator< Stepper , System , State , TimeIterator >`
 169 * `value_type` is `State`
 170 * `reference_type` is `State const&`
 171 * Factory functions
 172   * `make_times_iterator_begin( stepper , system , state , t_start , t_end , dt )`
 173   * `make_times_iterator_end( stepper , system , state )`
 174   * `make_times_range( stepper , system , state , t_start , t_end , dt )`
 175 * This stepper works with all steppers fulfilling the Stepper concept, the ControlledStepper concept or the DenseOutputStepper concept.
 176 * The value of `state` is the current state of the ODE during the iteration.
 177
 178 [endsect]
 179
 180 [section times_time_iterator]
 181
 182 * Definition: `times_time_iterator< Stepper , System , State , TimeIterator>`
 183 * `value_type` is `std::pair< State , Stepper::time_type >`
 184 * `reference_type` is `std::pair< State const& , Stepper::time_type > const&`
 185 * Factory functions
 186   * `make_times_time_iterator_begin( stepper , system , state , t_start , t_end , dt )`
 187   * `make_times_time_step_iterator_end( stepper , system , state )`
 188   * `make_times_time_range( stepper , system , state , t_start , t_end , dt )`
 189 * This stepper works with all steppers fulfilling the Stepper concept, the ControlledStepper concept or the DenseOutputStepper concept.
 190 * This stepper updates the value of `state`. The value of `state` is the current state of the ODE during the iteration.
 191
 192 [endsect]
 193
 194
 195 [endsect]