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| <div class="titlepage"><div><div><h3 class="title"> |
| <a name="boost_numeric_odeint.odeint_in_detail.iterators_and_ranges"></a><a class="link" href="iterators_and_ranges.html" title="Iterators and Ranges">Iterators |
| and Ranges</a> |
| </h3></div></div></div> |
| <div class="toc"><dl class="toc"> |
| <dt><span class="section"><a href="iterators_and_ranges.html#boost_numeric_odeint.odeint_in_detail.iterators_and_ranges.examples">Examples</a></span></dt> |
| <dt><span class="section"><a href="iterators_and_ranges.html#boost_numeric_odeint.odeint_in_detail.iterators_and_ranges.const_step_iterator">const_step_iterator</a></span></dt> |
| <dt><span class="section"><a href="iterators_and_ranges.html#boost_numeric_odeint.odeint_in_detail.iterators_and_ranges.const_step_time_iterator">const_step_time_iterator</a></span></dt> |
| <dt><span class="section"><a href="iterators_and_ranges.html#boost_numeric_odeint.odeint_in_detail.iterators_and_ranges.adaptive_step_iterator">adaptive_step_iterator</a></span></dt> |
| <dt><span class="section"><a href="iterators_and_ranges.html#boost_numeric_odeint.odeint_in_detail.iterators_and_ranges.adaptive_step_time_iterator">adaptive_step_time_iterator</a></span></dt> |
| <dt><span class="section"><a href="iterators_and_ranges.html#boost_numeric_odeint.odeint_in_detail.iterators_and_ranges.n_step_iterator">n_step_iterator</a></span></dt> |
| <dt><span class="section"><a href="iterators_and_ranges.html#boost_numeric_odeint.odeint_in_detail.iterators_and_ranges.n_step_time_iterator">n_step_time_iterator</a></span></dt> |
| <dt><span class="section"><a href="iterators_and_ranges.html#boost_numeric_odeint.odeint_in_detail.iterators_and_ranges.times_iterator">times_iterator</a></span></dt> |
| <dt><span class="section"><a href="iterators_and_ranges.html#boost_numeric_odeint.odeint_in_detail.iterators_and_ranges.times_time_iterator">times_time_iterator</a></span></dt> |
| </dl></div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="boost_numeric_odeint.odeint_in_detail.iterators_and_ranges.examples"></a><a class="link" href="iterators_and_ranges.html#boost_numeric_odeint.odeint_in_detail.iterators_and_ranges.examples" title="Examples">Examples</a> |
| </h4></div></div></div> |
| <p> |
| 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. |
| </p> |
| <p> |
| Several iterator types are provided, in consistence with the <a class="link" href="integrate_functions.html" title="Integrate functions">integrate |
| functions</a>. Hence there are <code class="computeroutput"><span class="identifier">const_step_iterator</span></code>, |
| <code class="computeroutput"><span class="identifier">adaptive_step_iterator</span></code>, |
| <code class="computeroutput"><span class="identifier">n_step_iterator</span></code> and <code class="computeroutput"><span class="identifier">times_iterator</span></code> -- each of them in two |
| versions: either with only the <code class="computeroutput"><span class="identifier">state</span></code> |
| or with a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="identifier">state</span><span class="special">,</span><span class="identifier">time</span><span class="special">></span></code> |
| as value type. They are all single pass iterators. In the following, we |
| show a few examples of how to use those iterators together with std algorithms. |
| </p> |
| <p> |
| </p> |
| <pre class="programlisting"><span class="identifier">runge_kutta4</span><span class="special"><</span> <span class="identifier">state_type</span> <span class="special">></span> <span class="identifier">stepper</span><span class="special">;</span> |
| <span class="identifier">state_type</span> <span class="identifier">x</span> <span class="special">=</span> <span class="special">{{</span> <span class="number">10.0</span> <span class="special">,</span> <span class="number">10.0</span> <span class="special">,</span> <span class="number">10.0</span> <span class="special">}};</span> |
| <span class="keyword">double</span> <span class="identifier">res</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">accumulate</span><span class="special">(</span> <span class="identifier">make_const_step_iterator_begin</span><span class="special">(</span> <span class="identifier">stepper</span> <span class="special">,</span> <span class="identifier">lorenz</span><span class="special">()</span> <span class="special">,</span> <span class="identifier">x</span> <span class="special">,</span> <span class="number">0.0</span> <span class="special">,</span> <span class="number">1.0</span> <span class="special">,</span> <span class="number">0.01</span> <span class="special">)</span> <span class="special">,</span> |
| <span class="identifier">make_const_step_iterator_end</span><span class="special">(</span> <span class="identifier">stepper</span> <span class="special">,</span> <span class="identifier">lorenz</span><span class="special">()</span> <span class="special">,</span> <span class="identifier">x</span> <span class="special">)</span> <span class="special">,</span> |
| <span class="number">0.0</span> <span class="special">,</span> |
| <span class="special">[](</span> <span class="keyword">double</span> <span class="identifier">sum</span> <span class="special">,</span> <span class="keyword">const</span> <span class="identifier">state_type</span> <span class="special">&</span><span class="identifier">x</span> <span class="special">)</span> <span class="special">{</span> |
| <span class="keyword">return</span> <span class="identifier">sum</span> <span class="special">+</span> <span class="identifier">x</span><span class="special">[</span><span class="number">0</span><span class="special">];</span> <span class="special">}</span> <span class="special">);</span> |
| <span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">res</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> |
| </pre> |
| <p> |
| </p> |
| <p> |
| In this example all x-values of the solution are accumulated. Note, how |
| dereferencing the iterator gives the current state <code class="computeroutput"><span class="identifier">x</span></code> |
| of the ODE (the second argument of the accumulate lambda). The iterator |
| itself does not occur directly in this example but it is generated by the |
| factory functions <code class="computeroutput"><span class="identifier">make_const_step_iterator_begin</span></code> |
| and <code class="computeroutput"><span class="identifier">make_const_step_iterator_end</span></code>. |
| odeint also supports Boost.Range, that allows to write the above example |
| in a more compact form with the factory function <code class="computeroutput"><span class="identifier">make_const_step_range</span></code>, |
| but now using <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">accumulate</span></code> from __bost_range: |
| </p> |
| <p> |
| </p> |
| <pre class="programlisting"><span class="identifier">runge_kutta4</span><span class="special"><</span> <span class="identifier">state_type</span> <span class="special">></span> <span class="identifier">stepper</span><span class="special">;</span> |
| <span class="identifier">state_type</span> <span class="identifier">x</span> <span class="special">=</span> <span class="special">{{</span> <span class="number">10.0</span> <span class="special">,</span> <span class="number">10.0</span> <span class="special">,</span> <span class="number">10.0</span> <span class="special">}};</span> |
| <span class="keyword">double</span> <span class="identifier">res</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">accumulate</span><span class="special">(</span> <span class="identifier">make_const_step_range</span><span class="special">(</span> <span class="identifier">stepper</span> <span class="special">,</span> <span class="identifier">lorenz</span><span class="special">()</span> <span class="special">,</span> <span class="identifier">x</span> <span class="special">,</span> <span class="number">0.0</span> <span class="special">,</span> <span class="number">1.0</span> <span class="special">,</span> <span class="number">0.01</span> <span class="special">)</span> <span class="special">,</span> <span class="number">0.0</span> <span class="special">,</span> |
| <span class="special">[](</span> <span class="keyword">double</span> <span class="identifier">sum</span> <span class="special">,</span> <span class="keyword">const</span> <span class="identifier">state_type</span> <span class="special">&</span><span class="identifier">x</span> <span class="special">)</span> <span class="special">{</span> |
| <span class="keyword">return</span> <span class="identifier">sum</span> <span class="special">+</span> <span class="identifier">x</span><span class="special">[</span><span class="number">0</span><span class="special">];</span> <span class="special">}</span> <span class="special">);</span> |
| <span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">res</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> |
| </pre> |
| <p> |
| </p> |
| <p> |
| 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 |
| </p> |
| <p> |
| </p> |
| <pre class="programlisting"><span class="identifier">runge_kutta4</span><span class="special"><</span> <span class="identifier">state_type</span> <span class="special">></span> <span class="identifier">stepper</span><span class="special">;</span> |
| <span class="identifier">state_type</span> <span class="identifier">x</span> <span class="special">=</span> <span class="special">{{</span> <span class="number">10.0</span> <span class="special">,</span> <span class="number">10.0</span> <span class="special">,</span> <span class="number">10.0</span> <span class="special">}};</span> |
| <span class="keyword">double</span> <span class="identifier">res</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">accumulate</span><span class="special">(</span> <span class="identifier">make_const_step_time_range</span><span class="special">(</span> <span class="identifier">stepper</span> <span class="special">,</span> <span class="identifier">lorenz</span><span class="special">()</span> <span class="special">,</span> <span class="identifier">x</span> <span class="special">,</span> <span class="number">0.0</span> <span class="special">,</span> <span class="number">1.0</span> <span class="special">,</span> <span class="number">0.01</span> <span class="special">)</span> <span class="special">,</span> <span class="number">0.0</span> <span class="special">,</span> |
| <span class="special">[](</span> <span class="keyword">double</span> <span class="identifier">sum</span> <span class="special">,</span> <span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span> <span class="keyword">const</span> <span class="identifier">state_type</span> <span class="special">&,</span> <span class="keyword">double</span> <span class="special">></span> <span class="special">&</span><span class="identifier">x</span> <span class="special">)</span> <span class="special">{</span> |
| <span class="keyword">return</span> <span class="identifier">sum</span> <span class="special">+</span> <span class="identifier">x</span><span class="special">.</span><span class="identifier">first</span><span class="special">[</span><span class="number">0</span><span class="special">];</span> <span class="special">}</span> <span class="special">);</span> |
| <span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">res</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> |
| </pre> |
| <p> |
| </p> |
| <p> |
| The factory functions are now <code class="computeroutput"><span class="identifier">make_const_step_time_iterator_begin</span></code>, |
| <code class="computeroutput"><span class="identifier">make_const_step_time_iterator_end</span></code> |
| and <code class="computeroutput"><span class="identifier">make_const_step_time_range</span></code>. |
| Note, how the lambda now expects a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span></code> |
| as this is the value type of the <code class="computeroutput"><span class="identifier">const_step_time_iterator</span></code>'s. |
| </p> |
| <p> |
| Next, we discuss the adaptive iterators which are completely analogous |
| to the const step iterators, but are based on adaptive stepper routines |
| and thus adjust the step size during the iteration. Examples are |
| </p> |
| <p> |
| </p> |
| <pre class="programlisting"><span class="keyword">auto</span> <span class="identifier">stepper</span> <span class="special">=</span> <span class="identifier">make_controlled</span><span class="special">(</span> <span class="number">1.0e-6</span> <span class="special">,</span> <span class="number">1.0e-6</span> <span class="special">,</span> <span class="identifier">runge_kutta_cash_karp54</span><span class="special"><</span> <span class="identifier">state_type</span> <span class="special">>()</span> <span class="special">);</span> |
| <span class="identifier">state_type</span> <span class="identifier">x</span> <span class="special">=</span> <span class="special">{{</span> <span class="number">10.0</span> <span class="special">,</span> <span class="number">10.0</span> <span class="special">,</span> <span class="number">10.0</span> <span class="special">}};</span> |
| <span class="keyword">double</span> <span class="identifier">res</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">accumulate</span><span class="special">(</span> <span class="identifier">make_adaptive_range</span><span class="special">(</span> <span class="identifier">stepper</span> <span class="special">,</span> <span class="identifier">lorenz</span><span class="special">()</span> <span class="special">,</span> <span class="identifier">x</span> <span class="special">,</span> <span class="number">0.0</span> <span class="special">,</span> <span class="number">1.0</span> <span class="special">,</span> <span class="number">0.01</span> <span class="special">)</span> <span class="special">,</span> <span class="number">0.0</span> <span class="special">,</span> |
| <span class="special">[](</span> <span class="keyword">double</span> <span class="identifier">sum</span> <span class="special">,</span> <span class="keyword">const</span> <span class="identifier">state_type</span><span class="special">&</span> <span class="identifier">x</span> <span class="special">)</span> <span class="special">{</span> |
| <span class="keyword">return</span> <span class="identifier">sum</span> <span class="special">+</span> <span class="identifier">x</span><span class="special">[</span><span class="number">0</span><span class="special">];</span> <span class="special">}</span> <span class="special">);</span> |
| <span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">res</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> |
| </pre> |
| <p> |
| </p> |
| <p> |
| </p> |
| <pre class="programlisting"><span class="keyword">auto</span> <span class="identifier">stepper</span> <span class="special">=</span> <span class="identifier">make_controlled</span><span class="special">(</span> <span class="number">1.0e-6</span> <span class="special">,</span> <span class="number">1.0e-6</span> <span class="special">,</span> <span class="identifier">runge_kutta_cash_karp54</span><span class="special"><</span> <span class="identifier">state_type</span> <span class="special">>()</span> <span class="special">);</span> |
| <span class="identifier">state_type</span> <span class="identifier">x</span> <span class="special">=</span> <span class="special">{{</span> <span class="number">10.0</span> <span class="special">,</span> <span class="number">10.0</span> <span class="special">,</span> <span class="number">10.0</span> <span class="special">}};</span> |
| <span class="keyword">double</span> <span class="identifier">res</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">accumulate</span><span class="special">(</span> <span class="identifier">make_adaptive_time_range</span><span class="special">(</span> <span class="identifier">stepper</span> <span class="special">,</span> <span class="identifier">lorenz</span><span class="special">()</span> <span class="special">,</span> <span class="identifier">x</span> <span class="special">,</span> <span class="number">0.0</span> <span class="special">,</span> <span class="number">1.0</span> <span class="special">,</span> <span class="number">0.01</span> <span class="special">)</span> <span class="special">,</span> <span class="number">0.0</span> <span class="special">,</span> |
| <span class="special">[](</span> <span class="keyword">double</span> <span class="identifier">sum</span> <span class="special">,</span> <span class="keyword">const</span> <span class="identifier">pair</span><span class="special"><</span> <span class="keyword">const</span> <span class="identifier">state_type</span><span class="special">&</span> <span class="special">,</span> <span class="keyword">double</span> <span class="special">></span> <span class="special">&</span><span class="identifier">x</span> <span class="special">)</span> <span class="special">{</span> |
| <span class="keyword">return</span> <span class="identifier">sum</span> <span class="special">+</span> <span class="identifier">x</span><span class="special">.</span><span class="identifier">first</span><span class="special">[</span><span class="number">0</span><span class="special">];</span> <span class="special">}</span> <span class="special">);</span> |
| <span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">res</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> |
| </pre> |
| <p> |
| </p> |
| <div class="note"><table border="0" summary="Note"> |
| <tr> |
| <td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../doc/src/images/note.png"></td> |
| <th align="left">Note</th> |
| </tr> |
| <tr><td align="left" valign="top"><p> |
| 'adaptive_iterator<code class="computeroutput"> <span class="keyword">and</span> </code>adaptive_time_iterator' |
| can only be used with <a class="link" href="../concepts/controlled_stepper.html" title="Controlled Stepper">Controlled |
| Stepper</a> or <a class="link" href="../concepts/dense_output_stepper.html" title="Dense Output Stepper">Dense |
| Output Stepper</a>. |
| </p></td></tr> |
| </table></div> |
| <p> |
| In general one can say that iterating over a range of a <code class="computeroutput"><span class="identifier">const_step_iterator</span></code> |
| behaves like an <code class="computeroutput"><span class="identifier">integrate_const</span></code> |
| function call, and similarly for <code class="computeroutput"><span class="identifier">adaptive_iterator</span></code> |
| and <code class="computeroutput"><span class="identifier">integrate_adaptive</span></code>, |
| <code class="computeroutput"><span class="identifier">n_step_iterator</span></code> and <code class="computeroutput"><span class="identifier">integrate_n_steps</span></code>, and finally <code class="computeroutput"><span class="identifier">times_iterator</span></code> and <code class="computeroutput"><span class="identifier">integrate_times</span></code>. |
| </p> |
| <p> |
| Below we list the most important properties of the exisiting iterators: |
| </p> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="boost_numeric_odeint.odeint_in_detail.iterators_and_ranges.const_step_iterator"></a><a class="link" href="iterators_and_ranges.html#boost_numeric_odeint.odeint_in_detail.iterators_and_ranges.const_step_iterator" title="const_step_iterator">const_step_iterator</a> |
| </h4></div></div></div> |
| <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> |
| <li class="listitem"> |
| Definition: <code class="computeroutput"><span class="identifier">const_step_iterator</span><span class="special"><</span> <span class="identifier">Stepper</span> |
| <span class="special">,</span> <span class="identifier">System</span> |
| <span class="special">,</span> <span class="identifier">State</span> |
| <span class="special">></span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">value_type</span></code> is <code class="computeroutput"><span class="identifier">State</span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">reference_type</span></code> is |
| <code class="computeroutput"><span class="identifier">State</span> <span class="keyword">const</span><span class="special">&</span></code> |
| </li> |
| <li class="listitem"> |
| Factory functions |
| <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: circle; "> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">make_const_step_iterator_begin</span><span class="special">(</span> <span class="identifier">stepper</span> |
| <span class="special">,</span> <span class="identifier">system</span> |
| <span class="special">,</span> <span class="identifier">state</span> |
| <span class="special">,</span> <span class="identifier">t_start</span> |
| <span class="special">,</span> <span class="identifier">t_end</span> |
| <span class="special">,</span> <span class="identifier">dt</span> |
| <span class="special">)</span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">make_const_step_iterator_end</span><span class="special">(</span> <span class="identifier">stepper</span> |
| <span class="special">,</span> <span class="identifier">system</span> |
| <span class="special">,</span> <span class="identifier">state</span> |
| <span class="special">)</span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">make_const_step_range</span><span class="special">(</span> <span class="identifier">stepper</span> |
| <span class="special">,</span> <span class="identifier">system</span> |
| <span class="special">,</span> <span class="identifier">state</span> |
| <span class="special">,</span> <span class="identifier">t_start</span> |
| <span class="special">,</span> <span class="identifier">t_end</span> |
| <span class="special">,</span> <span class="identifier">dt</span> |
| <span class="special">)</span></code> |
| </li> |
| </ul></div> |
| </li> |
| <li class="listitem"> |
| This stepper works with all steppers fulfilling the Stepper concept |
| or the DenseOutputStepper concept. |
| </li> |
| <li class="listitem"> |
| The value of <code class="computeroutput"><span class="identifier">state</span></code> |
| is the current state of the ODE during the iteration. |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="boost_numeric_odeint.odeint_in_detail.iterators_and_ranges.const_step_time_iterator"></a><a class="link" href="iterators_and_ranges.html#boost_numeric_odeint.odeint_in_detail.iterators_and_ranges.const_step_time_iterator" title="const_step_time_iterator">const_step_time_iterator</a> |
| </h4></div></div></div> |
| <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> |
| <li class="listitem"> |
| Definition: <code class="computeroutput"><span class="identifier">const_step_time_iterator</span><span class="special"><</span> <span class="identifier">Stepper</span> |
| <span class="special">,</span> <span class="identifier">System</span> |
| <span class="special">,</span> <span class="identifier">State</span> |
| <span class="special">></span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">value_type</span></code> is <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span> |
| <span class="identifier">State</span> <span class="special">,</span> |
| <span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">time_type</span> <span class="special">></span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">reference_type</span></code> is |
| <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span> |
| <span class="identifier">State</span> <span class="keyword">const</span><span class="special">&</span> <span class="special">,</span> <span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">time_type</span> <span class="special">></span> |
| <span class="keyword">const</span><span class="special">&</span></code> |
| </li> |
| <li class="listitem"> |
| Factory functions |
| <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: circle; "> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">make_const_step_time_iterator_begin</span><span class="special">(</span> <span class="identifier">stepper</span> |
| <span class="special">,</span> <span class="identifier">system</span> |
| <span class="special">,</span> <span class="identifier">state</span> |
| <span class="special">,</span> <span class="identifier">t_start</span> |
| <span class="special">,</span> <span class="identifier">t_end</span> |
| <span class="special">,</span> <span class="identifier">dt</span> |
| <span class="special">)</span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">make_const_step_time_iterator_end</span><span class="special">(</span> <span class="identifier">stepper</span> |
| <span class="special">,</span> <span class="identifier">system</span> |
| <span class="special">,</span> <span class="identifier">state</span> |
| <span class="special">)</span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">make_const_step_time_range</span><span class="special">(</span> <span class="identifier">stepper</span> |
| <span class="special">,</span> <span class="identifier">system</span> |
| <span class="special">,</span> <span class="identifier">state</span> |
| <span class="special">,</span> <span class="identifier">t_start</span> |
| <span class="special">,</span> <span class="identifier">t_end</span> |
| <span class="special">,</span> <span class="identifier">dt</span> |
| <span class="special">)</span></code> |
| </li> |
| </ul></div> |
| </li> |
| <li class="listitem"> |
| This stepper works with all steppers fulfilling the Stepper concept |
| or the DenseOutputStepper concept. |
| </li> |
| <li class="listitem"> |
| This stepper updates the value of <code class="computeroutput"><span class="identifier">state</span></code>. |
| The value of <code class="computeroutput"><span class="identifier">state</span></code> |
| is the current state of the ODE during the iteration. |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="boost_numeric_odeint.odeint_in_detail.iterators_and_ranges.adaptive_step_iterator"></a><a class="link" href="iterators_and_ranges.html#boost_numeric_odeint.odeint_in_detail.iterators_and_ranges.adaptive_step_iterator" title="adaptive_step_iterator">adaptive_step_iterator</a> |
| </h4></div></div></div> |
| <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> |
| <li class="listitem"> |
| Definition: <code class="computeroutput"><span class="identifier">adaptive_iterator</span><span class="special"><</span> <span class="identifier">Stepper</span> |
| <span class="special">,</span> <span class="identifier">System</span> |
| <span class="special">,</span> <span class="identifier">State</span> |
| <span class="special">></span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">value_type</span></code> is <code class="computeroutput"><span class="identifier">State</span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">reference_type</span></code> is |
| <code class="computeroutput"><span class="identifier">State</span> <span class="keyword">const</span><span class="special">&</span></code> |
| </li> |
| <li class="listitem"> |
| Factory functions |
| <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: circle; "> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">make_adaptive_iterator_begin</span><span class="special">(</span> <span class="identifier">stepper</span> |
| <span class="special">,</span> <span class="identifier">system</span> |
| <span class="special">,</span> <span class="identifier">state</span> |
| <span class="special">,</span> <span class="identifier">t_start</span> |
| <span class="special">,</span> <span class="identifier">t_end</span> |
| <span class="special">,</span> <span class="identifier">dt</span> |
| <span class="special">)</span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">make_adaptive_iterator_end</span><span class="special">(</span> <span class="identifier">stepper</span> |
| <span class="special">,</span> <span class="identifier">system</span> |
| <span class="special">,</span> <span class="identifier">state</span> |
| <span class="special">)</span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">make_adaptive_range</span><span class="special">(</span> <span class="identifier">stepper</span> |
| <span class="special">,</span> <span class="identifier">system</span> |
| <span class="special">,</span> <span class="identifier">state</span> |
| <span class="special">,</span> <span class="identifier">t_start</span> |
| <span class="special">,</span> <span class="identifier">t_end</span> |
| <span class="special">,</span> <span class="identifier">dt</span> |
| <span class="special">)</span></code> |
| </li> |
| </ul></div> |
| </li> |
| <li class="listitem"> |
| This stepper works with all steppers fulfilling the ControlledStepper |
| concept or the DenseOutputStepper concept. |
| </li> |
| <li class="listitem"> |
| For steppers fulfilling the ControlledStepper concept <code class="computeroutput"><span class="identifier">state</span></code> 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. |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="boost_numeric_odeint.odeint_in_detail.iterators_and_ranges.adaptive_step_time_iterator"></a><a class="link" href="iterators_and_ranges.html#boost_numeric_odeint.odeint_in_detail.iterators_and_ranges.adaptive_step_time_iterator" title="adaptive_step_time_iterator">adaptive_step_time_iterator</a> |
| </h4></div></div></div> |
| <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> |
| <li class="listitem"> |
| Definition: <code class="computeroutput"><span class="identifier">adaptive_iterator</span><span class="special"><</span> <span class="identifier">Stepper</span> |
| <span class="special">,</span> <span class="identifier">System</span> |
| <span class="special">,</span> <span class="identifier">State</span> |
| <span class="special">></span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">value_type</span></code> is <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span> |
| <span class="identifier">State</span> <span class="special">,</span> |
| <span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">time_type</span> <span class="special">></span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">reference_type</span></code> is |
| <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span> |
| <span class="identifier">State</span> <span class="keyword">const</span><span class="special">&</span> <span class="special">,</span> <span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">time_type</span> <span class="special">></span> |
| <span class="keyword">const</span><span class="special">&</span></code> |
| </li> |
| <li class="listitem"> |
| Factory functions |
| <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: circle; "> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">make_adaptive_time_iterator_begin</span><span class="special">(</span> <span class="identifier">stepper</span> |
| <span class="special">,</span> <span class="identifier">system</span> |
| <span class="special">,</span> <span class="identifier">state</span> |
| <span class="special">,</span> <span class="identifier">t_start</span> |
| <span class="special">,</span> <span class="identifier">t_end</span> |
| <span class="special">,</span> <span class="identifier">dt</span> |
| <span class="special">)</span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">make_adaptive_time_iterator_end</span><span class="special">(</span> <span class="identifier">stepper</span> |
| <span class="special">,</span> <span class="identifier">system</span> |
| <span class="special">,</span> <span class="identifier">state</span> |
| <span class="special">)</span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">make_adaptive_time_range</span><span class="special">(</span> <span class="identifier">stepper</span> |
| <span class="special">,</span> <span class="identifier">system</span> |
| <span class="special">,</span> <span class="identifier">state</span> |
| <span class="special">,</span> <span class="identifier">t_start</span> |
| <span class="special">,</span> <span class="identifier">t_end</span> |
| <span class="special">,</span> <span class="identifier">dt</span> |
| <span class="special">)</span></code> |
| </li> |
| </ul></div> |
| </li> |
| <li class="listitem"> |
| This stepper works with all steppers fulfilling the ControlledStepper |
| concept or the DenseOutputStepper concept. |
| </li> |
| <li class="listitem"> |
| For steppers fulfilling the ControlledStepper concept <code class="computeroutput"><span class="identifier">state</span></code> 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. |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="boost_numeric_odeint.odeint_in_detail.iterators_and_ranges.n_step_iterator"></a><a class="link" href="iterators_and_ranges.html#boost_numeric_odeint.odeint_in_detail.iterators_and_ranges.n_step_iterator" title="n_step_iterator">n_step_iterator</a> |
| </h4></div></div></div> |
| <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> |
| <li class="listitem"> |
| Definition: <code class="computeroutput"><span class="identifier">n_step_iterator</span><span class="special"><</span> <span class="identifier">Stepper</span> |
| <span class="special">,</span> <span class="identifier">System</span> |
| <span class="special">,</span> <span class="identifier">State</span> |
| <span class="special">></span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">value_type</span></code> is <code class="computeroutput"><span class="identifier">State</span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">reference_type</span></code> is |
| <code class="computeroutput"><span class="identifier">State</span> <span class="keyword">const</span><span class="special">&</span></code> |
| </li> |
| <li class="listitem"> |
| Factory functions |
| <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: circle; "> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">make_n_step_iterator_begin</span><span class="special">(</span> <span class="identifier">stepper</span> |
| <span class="special">,</span> <span class="identifier">system</span> |
| <span class="special">,</span> <span class="identifier">state</span> |
| <span class="special">,</span> <span class="identifier">t_start</span> |
| <span class="special">,</span> <span class="identifier">dt</span> |
| <span class="special">,</span> <span class="identifier">num_of_steps</span> |
| <span class="special">)</span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">make_n_step_iterator_end</span><span class="special">(</span> <span class="identifier">stepper</span> |
| <span class="special">,</span> <span class="identifier">system</span> |
| <span class="special">,</span> <span class="identifier">state</span> |
| <span class="special">)</span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">make_n_step_range</span><span class="special">(</span> <span class="identifier">stepper</span> |
| <span class="special">,</span> <span class="identifier">system</span> |
| <span class="special">,</span> <span class="identifier">state</span> |
| <span class="special">,</span> <span class="identifier">t_start</span> |
| <span class="special">,</span> <span class="identifier">dt</span> |
| <span class="special">,</span> <span class="identifier">num_of_steps</span> |
| <span class="special">)</span></code> |
| </li> |
| </ul></div> |
| </li> |
| <li class="listitem"> |
| This stepper works with all steppers fulfilling the Stepper concept |
| or the DenseOutputStepper concept. |
| </li> |
| <li class="listitem"> |
| The value of <code class="computeroutput"><span class="identifier">state</span></code> |
| is the current state of the ODE during the iteration. |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="boost_numeric_odeint.odeint_in_detail.iterators_and_ranges.n_step_time_iterator"></a><a class="link" href="iterators_and_ranges.html#boost_numeric_odeint.odeint_in_detail.iterators_and_ranges.n_step_time_iterator" title="n_step_time_iterator">n_step_time_iterator</a> |
| </h4></div></div></div> |
| <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> |
| <li class="listitem"> |
| Definition: <code class="computeroutput"><span class="identifier">n_step_time_iterator</span><span class="special"><</span> <span class="identifier">Stepper</span> |
| <span class="special">,</span> <span class="identifier">System</span> |
| <span class="special">,</span> <span class="identifier">State</span> |
| <span class="special">></span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">value_type</span></code> is <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span> |
| <span class="identifier">State</span> <span class="special">,</span> |
| <span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">time_type</span> <span class="special">></span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">reference_type</span></code> is |
| <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span> |
| <span class="identifier">State</span> <span class="keyword">const</span><span class="special">&</span> <span class="special">,</span> <span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">time_type</span> <span class="special">></span> |
| <span class="keyword">const</span><span class="special">&</span></code> |
| </li> |
| <li class="listitem"> |
| Factory functions |
| <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: circle; "> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">make_n_step_time_iterator_begin</span><span class="special">(</span> <span class="identifier">stepper</span> |
| <span class="special">,</span> <span class="identifier">system</span> |
| <span class="special">,</span> <span class="identifier">state</span> |
| <span class="special">,</span> <span class="identifier">t_start</span> |
| <span class="special">,</span> <span class="identifier">dt</span> |
| <span class="special">,</span> <span class="identifier">num_of_steps</span> |
| <span class="special">)</span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">make_n_step_time_iterator_end</span><span class="special">(</span> <span class="identifier">stepper</span> |
| <span class="special">,</span> <span class="identifier">system</span> |
| <span class="special">,</span> <span class="identifier">state</span> |
| <span class="special">)</span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">make_n_step_time_range</span><span class="special">(</span> <span class="identifier">stepper</span> |
| <span class="special">,</span> <span class="identifier">system</span> |
| <span class="special">,</span> <span class="identifier">state</span> |
| <span class="special">,</span> <span class="identifier">t_start</span> |
| <span class="special">,</span> <span class="identifier">dt</span> |
| <span class="special">,</span> <span class="identifier">num_of_steps</span> |
| <span class="special">)</span></code> |
| </li> |
| </ul></div> |
| </li> |
| <li class="listitem"> |
| This stepper works with all steppers fulfilling the Stepper concept |
| or the DenseOutputStepper concept. |
| </li> |
| <li class="listitem"> |
| This stepper updates the value of <code class="computeroutput"><span class="identifier">state</span></code>. |
| The value of <code class="computeroutput"><span class="identifier">state</span></code> |
| is the current state of the ODE during the iteration. |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="boost_numeric_odeint.odeint_in_detail.iterators_and_ranges.times_iterator"></a><a class="link" href="iterators_and_ranges.html#boost_numeric_odeint.odeint_in_detail.iterators_and_ranges.times_iterator" title="times_iterator">times_iterator</a> |
| </h4></div></div></div> |
| <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> |
| <li class="listitem"> |
| Definition: <code class="computeroutput"><span class="identifier">times_iterator</span><span class="special"><</span> <span class="identifier">Stepper</span> |
| <span class="special">,</span> <span class="identifier">System</span> |
| <span class="special">,</span> <span class="identifier">State</span> |
| <span class="special">,</span> <span class="identifier">TimeIterator</span> |
| <span class="special">></span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">value_type</span></code> is <code class="computeroutput"><span class="identifier">State</span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">reference_type</span></code> is |
| <code class="computeroutput"><span class="identifier">State</span> <span class="keyword">const</span><span class="special">&</span></code> |
| </li> |
| <li class="listitem"> |
| Factory functions |
| <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: circle; "> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">make_times_iterator_begin</span><span class="special">(</span> <span class="identifier">stepper</span> |
| <span class="special">,</span> <span class="identifier">system</span> |
| <span class="special">,</span> <span class="identifier">state</span> |
| <span class="special">,</span> <span class="identifier">t_start</span> |
| <span class="special">,</span> <span class="identifier">t_end</span> |
| <span class="special">,</span> <span class="identifier">dt</span> |
| <span class="special">)</span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">make_times_iterator_end</span><span class="special">(</span> <span class="identifier">stepper</span> |
| <span class="special">,</span> <span class="identifier">system</span> |
| <span class="special">,</span> <span class="identifier">state</span> |
| <span class="special">)</span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">make_times_range</span><span class="special">(</span> <span class="identifier">stepper</span> |
| <span class="special">,</span> <span class="identifier">system</span> |
| <span class="special">,</span> <span class="identifier">state</span> |
| <span class="special">,</span> <span class="identifier">t_start</span> |
| <span class="special">,</span> <span class="identifier">t_end</span> |
| <span class="special">,</span> <span class="identifier">dt</span> |
| <span class="special">)</span></code> |
| </li> |
| </ul></div> |
| </li> |
| <li class="listitem"> |
| This stepper works with all steppers fulfilling the Stepper concept, |
| the ControlledStepper concept or the DenseOutputStepper concept. |
| </li> |
| <li class="listitem"> |
| The value of <code class="computeroutput"><span class="identifier">state</span></code> |
| is the current state of the ODE during the iteration. |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="boost_numeric_odeint.odeint_in_detail.iterators_and_ranges.times_time_iterator"></a><a class="link" href="iterators_and_ranges.html#boost_numeric_odeint.odeint_in_detail.iterators_and_ranges.times_time_iterator" title="times_time_iterator">times_time_iterator</a> |
| </h4></div></div></div> |
| <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> |
| <li class="listitem"> |
| Definition: <code class="computeroutput"><span class="identifier">times_time_iterator</span><span class="special"><</span> <span class="identifier">Stepper</span> |
| <span class="special">,</span> <span class="identifier">System</span> |
| <span class="special">,</span> <span class="identifier">State</span> |
| <span class="special">,</span> <span class="identifier">TimeIterator</span><span class="special">></span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">value_type</span></code> is <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span> |
| <span class="identifier">State</span> <span class="special">,</span> |
| <span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">time_type</span> <span class="special">></span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">reference_type</span></code> is |
| <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span> |
| <span class="identifier">State</span> <span class="keyword">const</span><span class="special">&</span> <span class="special">,</span> <span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">time_type</span> <span class="special">></span> |
| <span class="keyword">const</span><span class="special">&</span></code> |
| </li> |
| <li class="listitem"> |
| Factory functions |
| <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: circle; "> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">make_times_time_iterator_begin</span><span class="special">(</span> <span class="identifier">stepper</span> |
| <span class="special">,</span> <span class="identifier">system</span> |
| <span class="special">,</span> <span class="identifier">state</span> |
| <span class="special">,</span> <span class="identifier">t_start</span> |
| <span class="special">,</span> <span class="identifier">t_end</span> |
| <span class="special">,</span> <span class="identifier">dt</span> |
| <span class="special">)</span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">make_times_time_step_iterator_end</span><span class="special">(</span> <span class="identifier">stepper</span> |
| <span class="special">,</span> <span class="identifier">system</span> |
| <span class="special">,</span> <span class="identifier">state</span> |
| <span class="special">)</span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">make_times_time_range</span><span class="special">(</span> <span class="identifier">stepper</span> |
| <span class="special">,</span> <span class="identifier">system</span> |
| <span class="special">,</span> <span class="identifier">state</span> |
| <span class="special">,</span> <span class="identifier">t_start</span> |
| <span class="special">,</span> <span class="identifier">t_end</span> |
| <span class="special">,</span> <span class="identifier">dt</span> |
| <span class="special">)</span></code> |
| </li> |
| </ul></div> |
| </li> |
| <li class="listitem"> |
| This stepper works with all steppers fulfilling the Stepper concept, |
| the ControlledStepper concept or the DenseOutputStepper concept. |
| </li> |
| <li class="listitem"> |
| This stepper updates the value of <code class="computeroutput"><span class="identifier">state</span></code>. |
| The value of <code class="computeroutput"><span class="identifier">state</span></code> |
| is the current state of the ODE during the iteration. |
| </li> |
| </ul></div> |
| </div> |
| </div> |
| <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> |
| <td align="left"></td> |
| <td align="right"><div class="copyright-footer">Copyright © 2009-2012 Karsten |
| Ahnert and Mario Mulansky<p> |
| Distributed under the Boost Software License, Version 1.0. (See accompanying |
| file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) |
| </p> |
| </div></td> |
| </tr></table> |
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