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| <div class="titlepage"><div><div><h3 class="title"> |
| <a name="boost_numeric_odeint.tutorial.using_boost__units"></a><a class="link" href="using_boost__units.html" title="Using boost::units">Using |
| boost::units</a> |
| </h3></div></div></div> |
| <p> |
| odeint also works well with <a href="http://www.boost.org/doc/libs/release/libs/units/" target="_top">Boost.Units</a> |
| - a library for compile time unit and dimension analysis. It works by decoding |
| unit information into the types of values. For a one-dimensional unit you |
| can just use the Boost.Unit types as state type, deriv type and time type |
| and hand the <code class="computeroutput"><span class="identifier">vector_space_algebra</span></code> |
| to the stepper definition and everything works just fine: |
| </p> |
| <p> |
| </p> |
| <pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">units</span><span class="special">::</span><span class="identifier">quantity</span><span class="special"><</span> <span class="identifier">si</span><span class="special">::</span><span class="identifier">time</span> <span class="special">,</span> <span class="keyword">double</span> <span class="special">></span> <span class="identifier">time_type</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">units</span><span class="special">::</span><span class="identifier">quantity</span><span class="special"><</span> <span class="identifier">si</span><span class="special">::</span><span class="identifier">length</span> <span class="special">,</span> <span class="keyword">double</span> <span class="special">></span> <span class="identifier">length_type</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">units</span><span class="special">::</span><span class="identifier">quantity</span><span class="special"><</span> <span class="identifier">si</span><span class="special">::</span><span class="identifier">velocity</span> <span class="special">,</span> <span class="keyword">double</span> <span class="special">></span> <span class="identifier">velocity_type</span><span class="special">;</span> |
| |
| <span class="keyword">typedef</span> <span class="identifier">runge_kutta4</span><span class="special"><</span> <span class="identifier">length_type</span> <span class="special">,</span> <span class="keyword">double</span> <span class="special">,</span> <span class="identifier">velocity_type</span> <span class="special">,</span> <span class="identifier">time_type</span> <span class="special">,</span> |
| <span class="identifier">vector_space_algebra</span> <span class="special">></span> <span class="identifier">stepper_type</span><span class="special">;</span> |
| </pre> |
| <p> |
| </p> |
| <p> |
| If you want to solve more-dimensional problems the individual entries typically |
| have different units. That means that the <code class="computeroutput"><span class="identifier">state_type</span></code> |
| is now possibly heterogeneous, meaning that every entry might have a different |
| type. To solve this problem, compile-time sequences from <a href="http://www.boost.org/doc/libs/release/libs/fusion/" target="_top">Boost.Fusion</a> |
| can be used. |
| </p> |
| <p> |
| To illustrate how odeint works with <a href="http://www.boost.org/doc/libs/release/libs/units/" target="_top">Boost.Units</a> |
| we use the harmonic oscillator as primary example. We start with defining |
| all quantities |
| </p> |
| <p> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">numeric</span><span class="special">/</span><span class="identifier">odeint</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">numeric</span><span class="special">/</span><span class="identifier">odeint</span><span class="special">/</span><span class="identifier">algebra</span><span class="special">/</span><span class="identifier">fusion_algebra</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">numeric</span><span class="special">/</span><span class="identifier">odeint</span><span class="special">/</span><span class="identifier">algebra</span><span class="special">/</span><span class="identifier">fusion_algebra_dispatcher</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| |
| <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">units</span><span class="special">/</span><span class="identifier">systems</span><span class="special">/</span><span class="identifier">si</span><span class="special">/</span><span class="identifier">length</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">units</span><span class="special">/</span><span class="identifier">systems</span><span class="special">/</span><span class="identifier">si</span><span class="special">/</span><span class="identifier">time</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">units</span><span class="special">/</span><span class="identifier">systems</span><span class="special">/</span><span class="identifier">si</span><span class="special">/</span><span class="identifier">velocity</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">units</span><span class="special">/</span><span class="identifier">systems</span><span class="special">/</span><span class="identifier">si</span><span class="special">/</span><span class="identifier">acceleration</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">units</span><span class="special">/</span><span class="identifier">systems</span><span class="special">/</span><span class="identifier">si</span><span class="special">/</span><span class="identifier">io</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| |
| <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">fusion</span><span class="special">/</span><span class="identifier">container</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| |
| <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">std</span><span class="special">;</span> |
| <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">odeint</span><span class="special">;</span> |
| <span class="keyword">namespace</span> <span class="identifier">fusion</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">fusion</span><span class="special">;</span> |
| <span class="keyword">namespace</span> <span class="identifier">units</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">units</span><span class="special">;</span> |
| <span class="keyword">namespace</span> <span class="identifier">si</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">units</span><span class="special">::</span><span class="identifier">si</span><span class="special">;</span> |
| |
| <span class="keyword">typedef</span> <span class="identifier">units</span><span class="special">::</span><span class="identifier">quantity</span><span class="special"><</span> <span class="identifier">si</span><span class="special">::</span><span class="identifier">time</span> <span class="special">,</span> <span class="keyword">double</span> <span class="special">></span> <span class="identifier">time_type</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">units</span><span class="special">::</span><span class="identifier">quantity</span><span class="special"><</span> <span class="identifier">si</span><span class="special">::</span><span class="identifier">length</span> <span class="special">,</span> <span class="keyword">double</span> <span class="special">></span> <span class="identifier">length_type</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">units</span><span class="special">::</span><span class="identifier">quantity</span><span class="special"><</span> <span class="identifier">si</span><span class="special">::</span><span class="identifier">velocity</span> <span class="special">,</span> <span class="keyword">double</span> <span class="special">></span> <span class="identifier">velocity_type</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">units</span><span class="special">::</span><span class="identifier">quantity</span><span class="special"><</span> <span class="identifier">si</span><span class="special">::</span><span class="identifier">acceleration</span> <span class="special">,</span> <span class="keyword">double</span> <span class="special">></span> <span class="identifier">acceleration_type</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">units</span><span class="special">::</span><span class="identifier">quantity</span><span class="special"><</span> <span class="identifier">si</span><span class="special">::</span><span class="identifier">frequency</span> <span class="special">,</span> <span class="keyword">double</span> <span class="special">></span> <span class="identifier">frequency_type</span><span class="special">;</span> |
| |
| <span class="keyword">typedef</span> <span class="identifier">fusion</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><</span> <span class="identifier">length_type</span> <span class="special">,</span> <span class="identifier">velocity_type</span> <span class="special">></span> <span class="identifier">state_type</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">fusion</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><</span> <span class="identifier">velocity_type</span> <span class="special">,</span> <span class="identifier">acceleration_type</span> <span class="special">></span> <span class="identifier">deriv_type</span><span class="special">;</span> |
| </pre> |
| <p> |
| </p> |
| <p> |
| Note, that the <code class="computeroutput"><span class="identifier">state_type</span></code> |
| and the <code class="computeroutput"><span class="identifier">deriv_type</span></code> are now |
| a compile-time fusion sequences. <code class="computeroutput"><span class="identifier">deriv_type</span></code> |
| represents <span class="emphasis"><em>x'</em></span> and is now different from the state type |
| as it has different unit definitions. Next, we define the ordinary differential |
| equation which is completely equivalent to the example in <a class="link" href="harmonic_oscillator.html" title="Harmonic oscillator">Harmonic |
| Oscillator</a>: |
| </p> |
| <p> |
| </p> |
| <pre class="programlisting"><span class="keyword">struct</span> <span class="identifier">oscillator</span> |
| <span class="special">{</span> |
| <span class="identifier">frequency_type</span> <span class="identifier">m_omega</span><span class="special">;</span> |
| |
| <span class="identifier">oscillator</span><span class="special">(</span> <span class="keyword">const</span> <span class="identifier">frequency_type</span> <span class="special">&</span><span class="identifier">omega</span> <span class="special">=</span> <span class="number">1.0</span> <span class="special">*</span> <span class="identifier">si</span><span class="special">::</span><span class="identifier">hertz</span> <span class="special">)</span> <span class="special">:</span> <span class="identifier">m_omega</span><span class="special">(</span> <span class="identifier">omega</span> <span class="special">)</span> <span class="special">{</span> <span class="special">}</span> |
| |
| <span class="keyword">void</span> <span class="keyword">operator</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="identifier">deriv_type</span> <span class="special">&</span><span class="identifier">dxdt</span> <span class="special">,</span> <span class="identifier">time_type</span> <span class="identifier">t</span> <span class="special">)</span> <span class="keyword">const</span> |
| <span class="special">{</span> |
| <span class="identifier">fusion</span><span class="special">::</span><span class="identifier">at_c</span><span class="special"><</span> <span class="number">0</span> <span class="special">>(</span> <span class="identifier">dxdt</span> <span class="special">)</span> <span class="special">=</span> <span class="identifier">fusion</span><span class="special">::</span><span class="identifier">at_c</span><span class="special"><</span> <span class="number">1</span> <span class="special">>(</span> <span class="identifier">x</span> <span class="special">);</span> |
| <span class="identifier">fusion</span><span class="special">::</span><span class="identifier">at_c</span><span class="special"><</span> <span class="number">1</span> <span class="special">>(</span> <span class="identifier">dxdt</span> <span class="special">)</span> <span class="special">=</span> <span class="special">-</span> <span class="identifier">m_omega</span> <span class="special">*</span> <span class="identifier">m_omega</span> <span class="special">*</span> <span class="identifier">fusion</span><span class="special">::</span><span class="identifier">at_c</span><span class="special"><</span> <span class="number">0</span> <span class="special">>(</span> <span class="identifier">x</span> <span class="special">);</span> |
| <span class="special">}</span> |
| <span class="special">};</span> |
| </pre> |
| <p> |
| </p> |
| <p> |
| Next, we instantiate an appropriate stepper. We must explicitly parametrize |
| the stepper with the <code class="computeroutput"><span class="identifier">state_type</span></code>, |
| <code class="computeroutput"><span class="identifier">deriv_type</span></code>, <code class="computeroutput"><span class="identifier">time_type</span></code>. |
| </p> |
| <p> |
| </p> |
| <pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">runge_kutta_dopri5</span><span class="special"><</span> <span class="identifier">state_type</span> <span class="special">,</span> <span class="keyword">double</span> <span class="special">,</span> <span class="identifier">deriv_type</span> <span class="special">,</span> <span class="identifier">time_type</span> <span class="special">></span> <span class="identifier">stepper_type</span><span class="special">;</span> |
| |
| <span class="identifier">state_type</span> <span class="identifier">x</span><span class="special">(</span> <span class="number">1.0</span> <span class="special">*</span> <span class="identifier">si</span><span class="special">::</span><span class="identifier">meter</span> <span class="special">,</span> <span class="number">0.0</span> <span class="special">*</span> <span class="identifier">si</span><span class="special">::</span><span class="identifier">meter_per_second</span> <span class="special">);</span> |
| |
| <span class="identifier">integrate_const</span><span class="special">(</span> <span class="identifier">make_dense_output</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">stepper_type</span><span class="special">()</span> <span class="special">)</span> <span class="special">,</span> <span class="identifier">oscillator</span><span class="special">(</span> <span class="number">2.0</span> <span class="special">*</span> <span class="identifier">si</span><span class="special">::</span><span class="identifier">hertz</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="identifier">si</span><span class="special">::</span><span class="identifier">second</span> <span class="special">,</span> <span class="number">100.0</span> <span class="special">*</span> <span class="identifier">si</span><span class="special">::</span><span class="identifier">second</span> <span class="special">,</span> <span class="number">0.1</span> <span class="special">*</span> <span class="identifier">si</span><span class="special">::</span><span class="identifier">second</span> <span class="special">,</span> <span class="identifier">streaming_observer</span><span class="special">(</span> <span class="identifier">cout</span> <span class="special">)</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> |
| When using compile-time sequences, the iteration over vector elements is |
| done by the <code class="computeroutput"><span class="identifier">fusion_algebra</span></code>, |
| which is automatically chosen by odeint. For more on the state types / |
| algebras see chapter <a class="link" href="../odeint_in_detail/state_types__algebras_and_operations.html" title="State types, algebras and operations">Adapt |
| your own state types</a>. |
| </p></td></tr> |
| </table></div> |
| <p> |
| It is quite easy but the compilation time might take very long. Furthermore, |
| the observer is defined a bit different |
| </p> |
| <p> |
| </p> |
| <pre class="programlisting"><span class="keyword">struct</span> <span class="identifier">streaming_observer</span> |
| <span class="special">{</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream</span><span class="special">&</span> <span class="identifier">m_out</span><span class="special">;</span> |
| |
| <span class="identifier">streaming_observer</span><span class="special">(</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream</span> <span class="special">&</span><span class="identifier">out</span> <span class="special">)</span> <span class="special">:</span> <span class="identifier">m_out</span><span class="special">(</span> <span class="identifier">out</span> <span class="special">)</span> <span class="special">{</span> <span class="special">}</span> |
| |
| <span class="keyword">struct</span> <span class="identifier">write_element</span> |
| <span class="special">{</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream</span> <span class="special">&</span><span class="identifier">m_out</span><span class="special">;</span> |
| <span class="identifier">write_element</span><span class="special">(</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream</span> <span class="special">&</span><span class="identifier">out</span> <span class="special">)</span> <span class="special">:</span> <span class="identifier">m_out</span><span class="special">(</span> <span class="identifier">out</span> <span class="special">)</span> <span class="special">{</span> <span class="special">};</span> |
| |
| <span class="keyword">template</span><span class="special"><</span> <span class="keyword">class</span> <span class="identifier">T</span> <span class="special">></span> |
| <span class="keyword">void</span> <span class="keyword">operator</span><span class="special">()(</span> <span class="keyword">const</span> <span class="identifier">T</span> <span class="special">&</span><span class="identifier">t</span> <span class="special">)</span> <span class="keyword">const</span> |
| <span class="special">{</span> |
| <span class="identifier">m_out</span> <span class="special"><<</span> <span class="string">"\t"</span> <span class="special"><<</span> <span class="identifier">t</span><span class="special">;</span> |
| <span class="special">}</span> |
| <span class="special">};</span> |
| |
| <span class="keyword">template</span><span class="special"><</span> <span class="keyword">class</span> <span class="identifier">State</span> <span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Time</span> <span class="special">></span> |
| <span class="keyword">void</span> <span class="keyword">operator</span><span class="special">()(</span> <span class="keyword">const</span> <span class="identifier">State</span> <span class="special">&</span><span class="identifier">x</span> <span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Time</span> <span class="special">&</span><span class="identifier">t</span> <span class="special">)</span> <span class="keyword">const</span> |
| <span class="special">{</span> |
| <span class="identifier">m_out</span> <span class="special"><<</span> <span class="identifier">t</span><span class="special">;</span> |
| <span class="identifier">fusion</span><span class="special">::</span><span class="identifier">for_each</span><span class="special">(</span> <span class="identifier">x</span> <span class="special">,</span> <span class="identifier">write_element</span><span class="special">(</span> <span class="identifier">m_out</span> <span class="special">)</span> <span class="special">);</span> |
| <span class="identifier">m_out</span> <span class="special"><<</span> <span class="string">"\n"</span><span class="special">;</span> |
| <span class="special">}</span> |
| <span class="special">};</span> |
| </pre> |
| <p> |
| </p> |
| <div class="caution"><table border="0" summary="Caution"> |
| <tr> |
| <td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../../../doc/src/images/caution.png"></td> |
| <th align="left">Caution</th> |
| </tr> |
| <tr><td align="left" valign="top"><p> |
| Using <a href="http://www.boost.org/doc/libs/release/libs/units/" target="_top">Boost.Units</a> |
| works nicely but compilation can be very time and memory consuming. For |
| example the unit test for the usage of <a href="http://www.boost.org/doc/libs/release/libs/units/" target="_top">Boost.Units</a> |
| in odeint take up to 4 GB of memory at compilation. |
| </p></td></tr> |
| </table></div> |
| <p> |
| The full cpp file for this example can be found here <a href="https://github.com/headmyshoulder/odeint-v2/blob/master/examples/harmonic_oscillator_units.cpp" target="_top">harmonic_oscillator_units.cpp</a>. |
| </p> |
| </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 |
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| Distributed under the Boost Software License, Version 1.0. (See accompanying |
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