libs/numeric/odeint/doc/html/boost_numeric_odeint/odeint_in_detail/generation_functions.html

   1 <html>
   2 <head>
   3 <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
   4 <title>Generation functions</title>
   5 <link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css">
   6 <meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
   7 <link rel="home" href="../../index.html" title="Chapter&#160;1.&#160;Boost.Numeric.Odeint">
   8 <link rel="up" href="../odeint_in_detail.html" title="odeint in detail">
   9 <link rel="prev" href="steppers.html" title="Steppers">
  10 <link rel="next" href="integrate_functions.html" title="Integrate functions">
  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="steppers.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../odeint_in_detail.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="integrate_functions.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.odeint_in_detail.generation_functions"></a><a class="link" href="generation_functions.html" title="Generation functions">Generation
  28       functions</a>
  29 </h3></div></div></div>
  30 <p>
  31         In the <a class="link" href="../tutorial.html" title="Tutorial">Tutorial</a> we have
  32         learned how we can use the generation functions <code class="computeroutput"><span class="identifier">make_controlled</span></code>
  33         and <code class="computeroutput"><span class="identifier">make_dense_output</span></code> to
  34         create controlled and dense output stepper from a simple stepper or an error
  35         stepper. The syntax of these two functions is very simple:
  36       </p>
  37 <p>
  38 </p>
  39 <pre class="programlisting"><span class="keyword">auto</span> <span class="identifier">stepper1</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">stepper_type</span><span class="special">()</span> <span class="special">);</span>
  40 <span class="keyword">auto</span> <span class="identifier">stepper2</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>
  41 </pre>
  42 <p>
  43       </p>
  44 <p>
  45         The first two parameters are the absolute and the relative error tolerances
  46         and the third parameter is the stepper. In C++03 you can infer the type from
  47         the <code class="computeroutput"><span class="identifier">result_of</span></code> mechanism:
  48       </p>
  49 <p>
  50 </p>
  51 <pre class="programlisting"><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">result_of</span><span class="special">::</span><span class="identifier">make_controlled</span><span class="special">&lt;</span> <span class="identifier">stepper_type</span> <span class="special">&gt;::</span><span class="identifier">type</span> <span class="identifier">stepper3</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">stepper_type</span><span class="special">()</span> <span class="special">);</span>
  52 <span class="special">(</span><span class="keyword">void</span><span class="special">)</span><span class="identifier">stepper3</span><span class="special">;</span>
  53 <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">result_of</span><span class="special">::</span><span class="identifier">make_dense_output</span><span class="special">&lt;</span> <span class="identifier">stepper_type</span> <span class="special">&gt;::</span><span class="identifier">type</span> <span class="identifier">stepper4</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>
  54 <span class="special">(</span><span class="keyword">void</span><span class="special">)</span><span class="identifier">stepper4</span><span class="special">;</span>
  55 </pre>
  56 <p>
  57       </p>
  58 <p>
  59         To use your own steppers with the <code class="computeroutput"><span class="identifier">make_controlled</span></code>
  60         or <code class="computeroutput"><span class="identifier">make_dense_output</span></code> you
  61         need to specialize two class templates. Suppose your steppers are called
  62         <code class="computeroutput"><span class="identifier">custom_stepper</span></code>, <code class="computeroutput"><span class="identifier">custom_controller</span></code> and <code class="computeroutput"><span class="identifier">custom_dense_output</span></code>.
  63         Then, the first class you need to specialize is <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">get_controller</span></code>,
  64         a meta function returning the type of the controller:
  65       </p>
  66 <p>
  67 </p>
  68 <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">numeric</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">odeint</span> <span class="special">{</span>
  69
  70 <span class="keyword">template</span><span class="special">&lt;&gt;</span>
  71 <span class="keyword">struct</span> <span class="identifier">get_controller</span><span class="special">&lt;</span> <span class="identifier">custom_stepper</span> <span class="special">&gt;</span>
  72 <span class="special">{</span>
  73     <span class="keyword">typedef</span> <span class="identifier">custom_controller</span> <span class="identifier">type</span><span class="special">;</span>
  74 <span class="special">};</span>
  75
  76 <span class="special">}</span> <span class="special">}</span> <span class="special">}</span>
  77 </pre>
  78 <p>
  79       </p>
  80 <p>
  81         The second one is a factory class <code class="computeroutput"><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">controller_factory</span></code>
  82         which constructs the controller from the tolerances and the stepper. In our
  83         dummy implementation this class is
  84       </p>
  85 <p>
  86 </p>
  87 <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">numeric</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">odeint</span> <span class="special">{</span>
  88
  89 <span class="keyword">template</span><span class="special">&lt;&gt;</span>
  90 <span class="keyword">struct</span> <span class="identifier">controller_factory</span><span class="special">&lt;</span> <span class="identifier">custom_stepper</span> <span class="special">,</span> <span class="identifier">custom_controller</span> <span class="special">&gt;</span>
  91 <span class="special">{</span>
  92     <span class="identifier">custom_controller</span> <span class="keyword">operator</span><span class="special">()(</span> <span class="keyword">double</span> <span class="identifier">abs_tol</span> <span class="special">,</span> <span class="keyword">double</span> <span class="identifier">rel_tol</span> <span class="special">,</span> <span class="keyword">const</span> <span class="identifier">custom_stepper</span> <span class="special">&amp;</span> <span class="special">)</span> <span class="keyword">const</span>
  93     <span class="special">{</span>
  94         <span class="keyword">return</span> <span class="identifier">custom_controller</span><span class="special">();</span>
  95     <span class="special">}</span>
  96 <span class="special">};</span>
  97
  98 <span class="special">}</span> <span class="special">}</span> <span class="special">}</span>
  99 </pre>
 100 <p>
 101       </p>
 102 <p>
 103         This is all to use the <code class="computeroutput"><span class="identifier">make_controlled</span></code>
 104         mechanism. Now you can use your controller via
 105       </p>
 106 <p>
 107 </p>
 108 <pre class="programlisting"><span class="keyword">auto</span> <span class="identifier">stepper5</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">custom_stepper</span><span class="special">()</span> <span class="special">);</span>
 109 </pre>
 110 <p>
 111       </p>
 112 <p>
 113         For the dense_output_stepper everything works similar. Here you have to specialize
 114         <code class="computeroutput"><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">get_dense_output</span></code> and <code class="computeroutput"><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">dense_output_factory</span></code>.
 115         These two classes have the same syntax as their relatives <code class="computeroutput"><span class="identifier">get_controller</span></code>
 116         and <code class="computeroutput"><span class="identifier">controller_factory</span></code>.
 117       </p>
 118 <p>
 119         All controllers and dense-output steppers in odeint can be used with these
 120         mechanisms. In the table below you will find, which steppers is constructed
 121         from <code class="computeroutput"><span class="identifier">make_controlled</span></code> or
 122         <code class="computeroutput"><span class="identifier">make_dense_output</span></code> if applied
 123         on a stepper from odeint:
 124       </p>
 125 <div class="table">
 126 <a name="boost_numeric_odeint.odeint_in_detail.generation_functions.generation_functions_make_controlled__abs_error___rel_error___stepper__"></a><p class="title"><b>Table&#160;1.7.&#160;Generation functions make_controlled( abs_error , rel_error , stepper
 127         )</b></p>
 128 <div class="table-contents"><table class="table" summary="Generation functions make_controlled( abs_error , rel_error , stepper
 129         )">
 130 <colgroup>
 131 <col>
 132 <col>
 133 <col>
 134 </colgroup>
 135 <thead><tr>
 136 <th>
 137                 <p>
 138                   Stepper
 139                 </p>
 140               </th>
 141 <th>
 142                 <p>
 143                   Result of make_controlled
 144                 </p>
 145               </th>
 146 <th>
 147                 <p>
 148                   Remarks
 149                 </p>
 150               </th>
 151 </tr></thead>
 152 <tbody>
 153 <tr>
 154 <td>
 155                 <p>
 156                   <code class="computeroutput"><span class="identifier">runge_kutta_cash_karp54</span></code>
 157                 </p>
 158               </td>
 159 <td>
 160                 <p>
 161                   <code class="computeroutput"><span class="identifier">controlled_runge_kutta</span><span class="special">&lt;</span> <span class="identifier">runge_kutta_cash_karp54</span>
 162                   <span class="special">,</span> <span class="identifier">default_error_checker</span><span class="special">&lt;...&gt;</span> <span class="special">&gt;</span></code>
 163                 </p>
 164               </td>
 165 <td>
 166                 <p>
 167                   <span class="emphasis"><em>a<sub>x</sub>=1</em></span>, <span class="emphasis"><em>a<sub>dxdt</sub>=1</em></span>
 168                 </p>
 169               </td>
 170 </tr>
 171 <tr>
 172 <td>
 173                 <p>
 174                   <code class="computeroutput"><span class="identifier">runge_kutta_fehlberg78</span></code>
 175                 </p>
 176               </td>
 177 <td>
 178                 <p>
 179                   <code class="computeroutput"><span class="identifier">controlled_runge_kutta</span><span class="special">&lt;</span> <span class="identifier">runge_kutta_fehlberg78</span>
 180                   <span class="special">,</span> <span class="identifier">default_error_checker</span><span class="special">&lt;...&gt;</span> <span class="special">&gt;</span></code>
 181                 </p>
 182               </td>
 183 <td>
 184                 <p>
 185                   <span class="emphasis"><em>a<sub>x</sub>=1</em></span>, <span class="emphasis"><em>a<sub>dxdt</sub>=1</em></span>
 186                 </p>
 187               </td>
 188 </tr>
 189 <tr>
 190 <td>
 191                 <p>
 192                   <code class="computeroutput"><span class="identifier">runge_kutta_dopri5</span></code>
 193                 </p>
 194               </td>
 195 <td>
 196                 <p>
 197                   <code class="computeroutput"><span class="identifier">controlled_runge_kutta</span><span class="special">&lt;</span> <span class="identifier">runge_kutta_dopri5</span>
 198                   <span class="special">,</span> <span class="identifier">default_error_checker</span><span class="special">&lt;...&gt;</span> <span class="special">&gt;</span></code>
 199                 </p>
 200               </td>
 201 <td>
 202                 <p>
 203                   <span class="emphasis"><em>a <sub>x</sub>=1</em></span>, <span class="emphasis"><em>a<sub>dxdt</sub>=1</em></span>
 204                 </p>
 205               </td>
 206 </tr>
 207 <tr>
 208 <td>
 209                 <p>
 210                   <code class="computeroutput"><span class="identifier">rosenbrock4</span></code>
 211                 </p>
 212               </td>
 213 <td>
 214                 <p>
 215                   <code class="computeroutput"><span class="identifier">rosenbrock4_controlled</span><span class="special">&lt;</span> <span class="identifier">rosenbrock4</span>
 216                   <span class="special">&gt;</span></code>
 217                 </p>
 218               </td>
 219 <td>
 220                 <p>
 221                   -
 222                 </p>
 223               </td>
 224 </tr>
 225 </tbody>
 226 </table></div>
 227 </div>
 228 <br class="table-break"><div class="table">
 229 <a name="boost_numeric_odeint.odeint_in_detail.generation_functions.generation_functions_make_dense_output__abs_error___rel_error___stepper__"></a><p class="title"><b>Table&#160;1.8.&#160;Generation functions make_dense_output( abs_error , rel_error , stepper
 230         )</b></p>
 231 <div class="table-contents"><table class="table" summary="Generation functions make_dense_output( abs_error , rel_error , stepper
 232         )">
 233 <colgroup>
 234 <col>
 235 <col>
 236 <col>
 237 </colgroup>
 238 <thead><tr>
 239 <th>
 240                 <p>
 241                   Stepper
 242                 </p>
 243               </th>
 244 <th>
 245                 <p>
 246                   Result of make_dense_output
 247                 </p>
 248               </th>
 249 <th>
 250                 <p>
 251                   Remarks
 252                 </p>
 253               </th>
 254 </tr></thead>
 255 <tbody>
 256 <tr>
 257 <td>
 258                 <p>
 259                   <code class="computeroutput"><span class="identifier">runge_kutta_dopri5</span></code>
 260                 </p>
 261               </td>
 262 <td>
 263                 <p>
 264                   <code class="computeroutput"><span class="identifier">dense_output_runge_kutta</span><span class="special">&lt;</span> <span class="identifier">controlled_runge_kutta</span><span class="special">&lt;</span> <span class="identifier">runge_kutta_dopri5</span>
 265                   <span class="special">,</span> <span class="identifier">default_error_checker</span><span class="special">&lt;...&gt;</span> <span class="special">&gt;</span>
 266                   <span class="special">&gt;</span></code>
 267                 </p>
 268               </td>
 269 <td>
 270                 <p>
 271                   <span class="emphasis"><em>a <sub>x</sub>=1</em></span>, <span class="emphasis"><em>a<sub>dxdt</sub>=1</em></span>
 272                 </p>
 273               </td>
 274 </tr>
 275 <tr>
 276 <td>
 277                 <p>
 278                   <code class="computeroutput"><span class="identifier">rosenbrock4</span></code>
 279                 </p>
 280               </td>
 281 <td>
 282                 <p>
 283                   <code class="computeroutput"><span class="identifier">rosenbrock4_dense_output</span><span class="special">&lt;</span> <span class="identifier">rosenbrock4_controller</span><span class="special">&lt;</span> <span class="identifier">rosenbrock4</span>
 284                   <span class="special">&gt;</span> <span class="special">&gt;</span></code>
 285                 </p>
 286               </td>
 287 <td>
 288                 <p>
 289                   -
 290                 </p>
 291               </td>
 292 </tr>
 293 </tbody>
 294 </table></div>
 295 </div>
 296 <br class="table-break">
 297 </div>
 298 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 299 <td align="left"></td>
 300 <td align="right"><div class="copyright-footer">Copyright &#169; 2009-2012 Karsten
 301       Ahnert and Mario Mulansky<p>
 302         Distributed under the Boost Software License, Version 1.0. (See accompanying
 303         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>)
 304       </p>
 305 </div></td>
 306 </tr></table>
 307 <hr>
 308 <div class="spirit-nav">
 309 <a accesskey="p" href="steppers.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../odeint_in_detail.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="integrate_functions.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
 310 </div>
 311 </body>
 312 </html>