1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 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 V1.79.1"> 7<link rel="home" href="../../index.html" title="Chapter 1. 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="comment">// or with max step size limit:</span> 41<span class="comment">// auto stepper1 = make_controlled( 1.0e-6 , 1.0e-6 , 0.01, stepper_type() );</span> 42 43<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> 44</pre> 45<p> 46 </p> 47<p> 48 The first two parameters are the absolute and the relative error tolerances 49 and the third parameter is the stepper. Additionally, a second version exists 50 where additionally a maximal step size is supplied which ensures the the 51 step size is not increased above this value. In C++03 you can infer the type 52 from the <code class="computeroutput"><span class="identifier">result_of</span></code> mechanism: 53 </p> 54<p> 55</p> 56<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"><</span> <span class="identifier">stepper_type</span> <span class="special">>::</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> 57<span class="special">(</span><span class="keyword">void</span><span class="special">)</span><span class="identifier">stepper3</span><span class="special">;</span> 58<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"><</span> <span class="identifier">stepper_type</span> <span class="special">>::</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> 59<span class="special">(</span><span class="keyword">void</span><span class="special">)</span><span class="identifier">stepper4</span><span class="special">;</span> 60</pre> 61<p> 62 </p> 63<p> 64 To use your own steppers with the <code class="computeroutput"><span class="identifier">make_controlled</span></code> 65 or <code class="computeroutput"><span class="identifier">make_dense_output</span></code> you 66 need to specialize two class templates. Suppose your steppers are called 67 <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>. 68 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>, 69 a meta function returning the type of the controller: 70 </p> 71<p> 72</p> 73<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> 74 75<span class="keyword">template</span><span class="special"><></span> 76<span class="keyword">struct</span> <span class="identifier">get_controller</span><span class="special"><</span> <span class="identifier">custom_stepper</span> <span class="special">></span> 77<span class="special">{</span> 78 <span class="keyword">typedef</span> <span class="identifier">custom_controller</span> <span class="identifier">type</span><span class="special">;</span> 79<span class="special">};</span> 80 81<span class="special">}</span> <span class="special">}</span> <span class="special">}</span> 82</pre> 83<p> 84 </p> 85<p> 86 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> 87 which constructs the controller from the tolerances and the stepper. In our 88 dummy implementation this class is 89 </p> 90<p> 91</p> 92<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> 93 94<span class="keyword">template</span><span class="special"><></span> 95<span class="keyword">struct</span> <span class="identifier">controller_factory</span><span class="special"><</span> <span class="identifier">custom_stepper</span> <span class="special">,</span> <span class="identifier">custom_controller</span> <span class="special">></span> 96<span class="special">{</span> 97 <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">&</span> <span class="special">)</span> <span class="keyword">const</span> 98 <span class="special">{</span> 99 <span class="keyword">return</span> <span class="identifier">custom_controller</span><span class="special">();</span> 100 <span class="special">}</span> 101 102 <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">double</span> <span class="identifier">max_dt</span> <span class="special">,</span> 103 <span class="keyword">const</span> <span class="identifier">custom_stepper</span> <span class="special">&</span> <span class="special">)</span> <span class="keyword">const</span> 104 <span class="special">{</span> 105 <span class="comment">// version with maximal allowed step size max_dt</span> 106 <span class="keyword">return</span> <span class="identifier">custom_controller</span><span class="special">();</span> 107 <span class="special">}</span> 108<span class="special">};</span> 109 110<span class="special">}</span> <span class="special">}</span> <span class="special">}</span> 111</pre> 112<p> 113 </p> 114<p> 115 This is all to use the <code class="computeroutput"><span class="identifier">make_controlled</span></code> 116 mechanism. Now you can use your controller via 117 </p> 118<p> 119</p> 120<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> 121</pre> 122<p> 123 </p> 124<p> 125 For the dense_output_stepper everything works similar. Here you have to specialize 126 <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>. 127 These two classes have the same syntax as their relatives <code class="computeroutput"><span class="identifier">get_controller</span></code> 128 and <code class="computeroutput"><span class="identifier">controller_factory</span></code>. 129 </p> 130<p> 131 All controllers and dense-output steppers in odeint can be used with these 132 mechanisms. In the table below you will find, which steppers is constructed 133 from <code class="computeroutput"><span class="identifier">make_controlled</span></code> or 134 <code class="computeroutput"><span class="identifier">make_dense_output</span></code> if applied 135 on a stepper from odeint: 136 </p> 137<div class="table"> 138<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 1.7. Generation functions make_controlled( abs_error , rel_error , stepper 139 )</b></p> 140<div class="table-contents"><table class="table" summary="Generation functions make_controlled( abs_error , rel_error , stepper 141 )"> 142<colgroup> 143<col> 144<col> 145<col> 146</colgroup> 147<thead><tr> 148<th> 149 <p> 150 Stepper 151 </p> 152 </th> 153<th> 154 <p> 155 Result of make_controlled 156 </p> 157 </th> 158<th> 159 <p> 160 Remarks 161 </p> 162 </th> 163</tr></thead> 164<tbody> 165<tr> 166<td> 167 <p> 168 <code class="computeroutput"><span class="identifier">runge_kutta_cash_karp54</span></code> 169 </p> 170 </td> 171<td> 172 <p> 173 <code class="computeroutput"><span class="identifier">controlled_runge_kutta</span><span class="special"><</span> <span class="identifier">runge_kutta_cash_karp54</span> 174 <span class="special">,</span> <span class="identifier">default_error_checker</span><span class="special"><...></span> <span class="special">></span></code> 175 </p> 176 </td> 177<td> 178 <p> 179 <span class="emphasis"><em>a<sub>x</sub>=1</em></span>, <span class="emphasis"><em>a<sub>dxdt</sub>=1</em></span> 180 </p> 181 </td> 182</tr> 183<tr> 184<td> 185 <p> 186 <code class="computeroutput"><span class="identifier">runge_kutta_fehlberg78</span></code> 187 </p> 188 </td> 189<td> 190 <p> 191 <code class="computeroutput"><span class="identifier">controlled_runge_kutta</span><span class="special"><</span> <span class="identifier">runge_kutta_fehlberg78</span> 192 <span class="special">,</span> <span class="identifier">default_error_checker</span><span class="special"><...></span> <span class="special">></span></code> 193 </p> 194 </td> 195<td> 196 <p> 197 <span class="emphasis"><em>a<sub>x</sub>=1</em></span>, <span class="emphasis"><em>a<sub>dxdt</sub>=1</em></span> 198 </p> 199 </td> 200</tr> 201<tr> 202<td> 203 <p> 204 <code class="computeroutput"><span class="identifier">runge_kutta_dopri5</span></code> 205 </p> 206 </td> 207<td> 208 <p> 209 <code class="computeroutput"><span class="identifier">controlled_runge_kutta</span><span class="special"><</span> <span class="identifier">runge_kutta_dopri5</span> 210 <span class="special">,</span> <span class="identifier">default_error_checker</span><span class="special"><...></span> <span class="special">></span></code> 211 </p> 212 </td> 213<td> 214 <p> 215 <span class="emphasis"><em>a <sub>x</sub>=1</em></span>, <span class="emphasis"><em>a<sub>dxdt</sub>=1</em></span> 216 </p> 217 </td> 218</tr> 219<tr> 220<td> 221 <p> 222 <code class="computeroutput"><span class="identifier">rosenbrock4</span></code> 223 </p> 224 </td> 225<td> 226 <p> 227 <code class="computeroutput"><span class="identifier">rosenbrock4_controlled</span><span class="special"><</span> <span class="identifier">rosenbrock4</span> 228 <span class="special">></span></code> 229 </p> 230 </td> 231<td> 232 <p> 233 - 234 </p> 235 </td> 236</tr> 237</tbody> 238</table></div> 239</div> 240<br class="table-break"><div class="table"> 241<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 1.8. Generation functions make_dense_output( abs_error , rel_error , stepper 242 )</b></p> 243<div class="table-contents"><table class="table" summary="Generation functions make_dense_output( abs_error , rel_error , stepper 244 )"> 245<colgroup> 246<col> 247<col> 248<col> 249</colgroup> 250<thead><tr> 251<th> 252 <p> 253 Stepper 254 </p> 255 </th> 256<th> 257 <p> 258 Result of make_dense_output 259 </p> 260 </th> 261<th> 262 <p> 263 Remarks 264 </p> 265 </th> 266</tr></thead> 267<tbody> 268<tr> 269<td> 270 <p> 271 <code class="computeroutput"><span class="identifier">runge_kutta_dopri5</span></code> 272 </p> 273 </td> 274<td> 275 <p> 276 <code class="computeroutput"><span class="identifier">dense_output_runge_kutta</span><span class="special"><</span> <span class="identifier">controlled_runge_kutta</span><span class="special"><</span> <span class="identifier">runge_kutta_dopri5</span> 277 <span class="special">,</span> <span class="identifier">default_error_checker</span><span class="special"><...></span> <span class="special">></span> 278 <span class="special">></span></code> 279 </p> 280 </td> 281<td> 282 <p> 283 <span class="emphasis"><em>a <sub>x</sub>=1</em></span>, <span class="emphasis"><em>a<sub>dxdt</sub>=1</em></span> 284 </p> 285 </td> 286</tr> 287<tr> 288<td> 289 <p> 290 <code class="computeroutput"><span class="identifier">rosenbrock4</span></code> 291 </p> 292 </td> 293<td> 294 <p> 295 <code class="computeroutput"><span class="identifier">rosenbrock4_dense_output</span><span class="special"><</span> <span class="identifier">rosenbrock4_controller</span><span class="special"><</span> <span class="identifier">rosenbrock4</span> 296 <span class="special">></span> <span class="special">></span></code> 297 </p> 298 </td> 299<td> 300 <p> 301 - 302 </p> 303 </td> 304</tr> 305</tbody> 306</table></div> 307</div> 308<br class="table-break"> 309</div> 310<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 311<td align="left"></td> 312<td align="right"><div class="copyright-footer">Copyright © 2009-2015 Karsten Ahnert and Mario Mulansky<p> 313 Distributed under the Boost Software License, Version 1.0. (See accompanying 314 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>) 315 </p> 316</div></td> 317</tr></table> 318<hr> 319<div class="spirit-nav"> 320<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> 321</div> 322</body> 323</html> 324
