1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>Using boost::units</title> 5<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css"> 6<meta name="generator" content="DocBook XSL Stylesheets V1.79.1"> 7<link rel="home" href="../../index.html" title="Chapter 1. Boost.Numeric.Odeint"> 8<link rel="up" href="../tutorial.html" title="Tutorial"> 9<link rel="prev" href="ensembles_of_oscillators.html" title="Ensembles of oscillators"> 10<link rel="next" href="using_matrices_as_state_types.html" title="Using matrices as state types"> 11</head> 12<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> 13<table cellpadding="2" width="100%"><tr> 14<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../logo.jpg"></td> 15<td align="center"><a href="../../../../../../../index.html">Home</a></td> 16<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td> 17<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> 18<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> 19<td align="center"><a href="../../../../../../../more/index.htm">More</a></td> 20</tr></table> 21<hr> 22<div class="spirit-nav"> 23<a accesskey="p" href="ensembles_of_oscillators.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tutorial.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="using_matrices_as_state_types.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> 24</div> 25<div class="section"> 26<div class="titlepage"><div><div><h3 class="title"> 27<a name="boost_numeric_odeint.tutorial.using_boost__units"></a><a class="link" href="using_boost__units.html" title="Using boost::units">Using 28 boost::units</a> 29</h3></div></div></div> 30<p> 31 odeint also works well with <a href="http://www.boost.org/doc/libs/release/libs/units/" target="_top">Boost.Units</a> 32 - a library for compile time unit and dimension analysis. It works by decoding 33 unit information into the types of values. For a one-dimensional unit you 34 can just use the Boost.Unit types as state type, deriv type and time type 35 and hand the <code class="computeroutput"><span class="identifier">vector_space_algebra</span></code> 36 to the stepper definition and everything works just fine: 37 </p> 38<p> 39</p> 40<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> 41<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> 42<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> 43 44<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> 45 <span class="identifier">vector_space_algebra</span> <span class="special">></span> <span class="identifier">stepper_type</span><span class="special">;</span> 46</pre> 47<p> 48 </p> 49<p> 50 If you want to solve more-dimensional problems the individual entries typically 51 have different units. That means that the <code class="computeroutput"><span class="identifier">state_type</span></code> 52 is now possibly heterogeneous, meaning that every entry might have a different 53 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> 54 can be used. 55 </p> 56<p> 57 To illustrate how odeint works with <a href="http://www.boost.org/doc/libs/release/libs/units/" target="_top">Boost.Units</a> 58 we use the harmonic oscillator as primary example. We start with defining 59 all quantities 60 </p> 61<p> 62</p> 63<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> 64<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> 65<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> 66 67<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> 68<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> 69<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> 70<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> 71<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> 72 73<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> 74 75<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">std</span><span class="special">;</span> 76<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> 77<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> 78<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> 79<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> 80 81<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> 82<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> 83<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> 84<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> 85<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> 86 87<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> 88<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> 89</pre> 90<p> 91 </p> 92<p> 93 Note, that the <code class="computeroutput"><span class="identifier">state_type</span></code> 94 and the <code class="computeroutput"><span class="identifier">deriv_type</span></code> are now 95 a compile-time fusion sequences. <code class="computeroutput"><span class="identifier">deriv_type</span></code> 96 represents <span class="emphasis"><em>x'</em></span> and is now different from the state type 97 as it has different unit definitions. Next, we define the ordinary differential 98 equation which is completely equivalent to the example in <a class="link" href="harmonic_oscillator.html" title="Harmonic oscillator">Harmonic 99 Oscillator</a>: 100 </p> 101<p> 102</p> 103<pre class="programlisting"><span class="keyword">struct</span> <span class="identifier">oscillator</span> 104<span class="special">{</span> 105 <span class="identifier">frequency_type</span> <span class="identifier">m_omega</span><span class="special">;</span> 106 107 <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> 108 109 <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> 110 <span class="special">{</span> 111 <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> 112 <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> 113 <span class="special">}</span> 114<span class="special">};</span> 115</pre> 116<p> 117 </p> 118<p> 119 Next, we instantiate an appropriate stepper. We must explicitly parametrize 120 the stepper with the <code class="computeroutput"><span class="identifier">state_type</span></code>, 121 <code class="computeroutput"><span class="identifier">deriv_type</span></code>, <code class="computeroutput"><span class="identifier">time_type</span></code>. 122 </p> 123<p> 124</p> 125<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> 126 127<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> 128 129<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> 130 <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> 131</pre> 132<p> 133 </p> 134<div class="note"><table border="0" summary="Note"> 135<tr> 136<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../doc/src/images/note.png"></td> 137<th align="left">Note</th> 138</tr> 139<tr><td align="left" valign="top"><p> 140 When using compile-time sequences, the iteration over vector elements is 141 done by the <code class="computeroutput"><span class="identifier">fusion_algebra</span></code>, 142 which is automatically chosen by odeint. For more on the state types / 143 algebras see chapter <a class="link" href="../odeint_in_detail/state_types__algebras_and_operations.html" title="State types, algebras and operations">Adapt 144 your own state types</a>. 145 </p></td></tr> 146</table></div> 147<p> 148 It is quite easy but the compilation time might take very long. Furthermore, 149 the observer is defined a bit different 150 </p> 151<p> 152</p> 153<pre class="programlisting"><span class="keyword">struct</span> <span class="identifier">streaming_observer</span> 154<span class="special">{</span> 155 <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> 156 157 <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> 158 159 <span class="keyword">struct</span> <span class="identifier">write_element</span> 160 <span class="special">{</span> 161 <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> 162 <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> 163 164 <span class="keyword">template</span><span class="special"><</span> <span class="keyword">class</span> <span class="identifier">T</span> <span class="special">></span> 165 <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> 166 <span class="special">{</span> 167 <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> 168 <span class="special">}</span> 169 <span class="special">};</span> 170 171 <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> 172 <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> 173 <span class="special">{</span> 174 <span class="identifier">m_out</span> <span class="special"><<</span> <span class="identifier">t</span><span class="special">;</span> 175 <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> 176 <span class="identifier">m_out</span> <span class="special"><<</span> <span class="string">"\n"</span><span class="special">;</span> 177 <span class="special">}</span> 178<span class="special">};</span> 179</pre> 180<p> 181 </p> 182<div class="caution"><table border="0" summary="Caution"> 183<tr> 184<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../../../doc/src/images/caution.png"></td> 185<th align="left">Caution</th> 186</tr> 187<tr><td align="left" valign="top"><p> 188 Using <a href="http://www.boost.org/doc/libs/release/libs/units/" target="_top">Boost.Units</a> 189 works nicely but compilation can be very time and memory consuming. For 190 example the unit test for the usage of <a href="http://www.boost.org/doc/libs/release/libs/units/" target="_top">Boost.Units</a> 191 in odeint take up to 4 GB of memory at compilation. 192 </p></td></tr> 193</table></div> 194<p> 195 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>. 196 </p> 197</div> 198<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 199<td align="left"></td> 200<td align="right"><div class="copyright-footer">Copyright © 2009-2015 Karsten Ahnert and Mario Mulansky<p> 201 Distributed under the Boost Software License, Version 1.0. (See accompanying 202 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>) 203 </p> 204</div></td> 205</tr></table> 206<hr> 207<div class="spirit-nav"> 208<a accesskey="p" href="ensembles_of_oscillators.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tutorial.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="using_matrices_as_state_types.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> 209</div> 210</body> 211</html> 212
