1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>Stepper</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="../concepts.html" title="Concepts"> 9<link rel="prev" href="implicit_system.html" title="Implicit System"> 10<link rel="next" href="error_stepper.html" title="Error Stepper"> 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="implicit_system.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../concepts.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="error_stepper.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.concepts.stepper"></a><a class="link" href="stepper.html" title="Stepper">Stepper</a> 28</h3></div></div></div> 29<p> 30 This concepts specifies the interface a simple stepper has to fulfill to 31 be used within the <a class="link" href="../odeint_in_detail/integrate_functions.html" title="Integrate functions">integrate 32 functions</a>. 33 </p> 34<h5> 35<a name="boost_numeric_odeint.concepts.stepper.h0"></a> 36 <span class="phrase"><a name="boost_numeric_odeint.concepts.stepper.description"></a></span><a class="link" href="stepper.html#boost_numeric_odeint.concepts.stepper.description">Description</a> 37 </h5> 38<p> 39 The basic stepper concept. A basic stepper following this Stepper concept 40 is able to perform a single step of the solution <span class="emphasis"><em>x(t)</em></span> 41 of an ODE to obtain <span class="emphasis"><em>x(t+dt)</em></span> using a given step size 42 <span class="emphasis"><em>dt</em></span>. Basic steppers can be Runge-Kutta steppers, symplectic 43 steppers as well as implicit steppers. Depending on the actual stepper, the 44 ODE is defined as <a class="link" href="system.html" title="System">System</a>, 45 <a class="link" href="symplectic_system.html" title="Symplectic System">Symplectic 46 System</a>, <a class="link" href="simple_symplectic_system.html" title="Simple Symplectic System">Simple 47 Symplectic System</a> or <a class="link" href="implicit_system.html" title="Implicit System">Implicit 48 System</a>. Note that all error steppers are also basic steppers. 49 </p> 50<h5> 51<a name="boost_numeric_odeint.concepts.stepper.h1"></a> 52 <span class="phrase"><a name="boost_numeric_odeint.concepts.stepper.refinement_of"></a></span><a class="link" href="stepper.html#boost_numeric_odeint.concepts.stepper.refinement_of">Refinement 53 of</a> 54 </h5> 55<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> 56<li class="listitem"> 57 DefaultConstructable 58 </li> 59<li class="listitem"> 60 CopyConstructable 61 </li> 62</ul></div> 63<h5> 64<a name="boost_numeric_odeint.concepts.stepper.h2"></a> 65 <span class="phrase"><a name="boost_numeric_odeint.concepts.stepper.associated_types"></a></span><a class="link" href="stepper.html#boost_numeric_odeint.concepts.stepper.associated_types">Associated 66 types</a> 67 </h5> 68<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> 69<li class="listitem"> 70 <p><span class="bold"><strong>state_type</strong></span></p> 71<p><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">state_type</span></code></p> 72<p>The 73 type characterizing the state of the ODE, hence <span class="emphasis"><em>x</em></span>.</p> 74 </li> 75<li class="listitem"> 76 <p><span class="bold"><strong>deriv_type</strong></span></p> 77<p><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">deriv_type</span></code></p> 78<p>The 79 type characterizing the derivative of the ODE, hence <span class="emphasis"><em>d x/dt</em></span>.</p> 80 </li> 81<li class="listitem"> 82 <p><span class="bold"><strong>time_type</strong></span></p> 83<p><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">time_type</span></code></p> 84<p>The 85 type characterizing the dependent variable of the ODE, hence the time 86 <span class="emphasis"><em>t</em></span>.</p> 87 </li> 88<li class="listitem"> 89 <p><span class="bold"><strong>value_type</strong></span></p> 90<p><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">value_type</span></code></p> 91<p>The 92 numerical data type which is used within the stepper, something like 93 <code class="computeroutput"><span class="keyword">float</span></code>, <code class="computeroutput"><span class="keyword">double</span></code>, 94 <code class="computeroutput"><span class="identifier">complex</span><span class="special">&</span><span class="identifier">lt</span><span class="special">;</span> <span class="keyword">double</span> <span class="special">&</span><span class="identifier">gt</span><span class="special">;</span></code>.</p> 95 </li> 96<li class="listitem"> 97 <p><span class="bold"><strong>order_type</strong></span></p> 98<p><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">order_type</span></code></p> 99<p>The 100 type characterizing the order of the ODE, typically <code class="computeroutput"><span class="keyword">unsigned</span> 101 <span class="keyword">short</span></code>.</p> 102 </li> 103<li class="listitem"> 104 <p><span class="bold"><strong>stepper_category</strong></span></p> 105<p><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">stepper_category</span></code></p> 106<p>A 107 tag type characterizing the category of the stepper. This type must be 108 convertible to <code class="computeroutput"><span class="identifier">stepper_tag</span></code>.</p> 109 </li> 110</ul></div> 111<h5> 112<a name="boost_numeric_odeint.concepts.stepper.h3"></a> 113 <span class="phrase"><a name="boost_numeric_odeint.concepts.stepper.notation"></a></span><a class="link" href="stepper.html#boost_numeric_odeint.concepts.stepper.notation">Notation</a> 114 </h5> 115<div class="variablelist"> 116<p class="title"><b></b></p> 117<dl class="variablelist"> 118<dt><span class="term"><code class="computeroutput"><span class="identifier">Stepper</span></code></span></dt> 119<dd><p> 120 A type that is a model of Stepper 121 </p></dd> 122<dt><span class="term"><code class="computeroutput"><span class="identifier">State</span></code></span></dt> 123<dd><p> 124 A type representing the state <span class="emphasis"><em>x</em></span> of the ODE 125 </p></dd> 126<dt><span class="term"><code class="computeroutput"><span class="identifier">Time</span></code></span></dt> 127<dd><p> 128 A type representing the time <span class="emphasis"><em>t</em></span> of the ODE 129 </p></dd> 130<dt><span class="term"><code class="computeroutput"><span class="identifier">stepper</span></code></span></dt> 131<dd><p> 132 An object of type <code class="computeroutput"><span class="identifier">Stepper</span></code> 133 </p></dd> 134<dt><span class="term"><code class="computeroutput"><span class="identifier">x</span></code></span></dt> 135<dd><p> 136 Object of type <code class="computeroutput"><span class="identifier">State</span></code> 137 </p></dd> 138<dt><span class="term"><code class="computeroutput"><span class="identifier">t</span></code>, <code class="computeroutput"><span class="identifier">dt</span></code></span></dt> 139<dd><p> 140 Objects of type <code class="computeroutput"><span class="identifier">Time</span></code> 141 </p></dd> 142<dt><span class="term"><code class="computeroutput"><span class="identifier">sys</span></code></span></dt> 143<dd><p> 144 An object defining the ODE. Depending on the Stepper this might be 145 a model of <a class="link" href="system.html" title="System">System</a>, 146 <a class="link" href="symplectic_system.html" title="Symplectic System">Symplectic 147 System</a>, <a class="link" href="simple_symplectic_system.html" title="Simple Symplectic System">Simple 148 Symplectic System</a> or <a class="link" href="implicit_system.html" title="Implicit System">Implicit 149 System</a> 150 </p></dd> 151</dl> 152</div> 153<h5> 154<a name="boost_numeric_odeint.concepts.stepper.h4"></a> 155 <span class="phrase"><a name="boost_numeric_odeint.concepts.stepper.valid_expressions"></a></span><a class="link" href="stepper.html#boost_numeric_odeint.concepts.stepper.valid_expressions">Valid Expressions</a> 156 </h5> 157<div class="informaltable"><table class="table"> 158<colgroup> 159<col> 160<col> 161<col> 162<col> 163</colgroup> 164<thead><tr> 165<th> 166 <p> 167 Name 168 </p> 169 </th> 170<th> 171 <p> 172 Expression 173 </p> 174 </th> 175<th> 176 <p> 177 Type 178 </p> 179 </th> 180<th> 181 <p> 182 Semantics 183 </p> 184 </th> 185</tr></thead> 186<tbody> 187<tr> 188<td> 189 <p> 190 Get the order 191 </p> 192 </td> 193<td> 194 <p> 195 <code class="computeroutput"><span class="identifier">stepper</span><span class="special">.</span><span class="identifier">order</span><span class="special">()</span></code> 196 </p> 197 </td> 198<td> 199 <p> 200 <code class="computeroutput"><span class="identifier">order_type</span></code> 201 </p> 202 </td> 203<td> 204 <p> 205 Returns the order of the stepper. 206 </p> 207 </td> 208</tr> 209<tr> 210<td> 211 <p> 212 Do step 213 </p> 214 </td> 215<td> 216 <p> 217 <code class="computeroutput"><span class="identifier">stepper</span><span class="special">.</span><span class="identifier">do_step</span><span class="special">(</span> 218 <span class="identifier">sys</span> <span class="special">,</span> 219 <span class="identifier">x</span> <span class="special">,</span> 220 <span class="identifier">t</span> <span class="special">,</span> 221 <span class="identifier">dt</span> <span class="special">)</span></code> 222 </p> 223 </td> 224<td> 225 <p> 226 <code class="computeroutput"><span class="keyword">void</span></code> 227 </p> 228 </td> 229<td> 230 <p> 231 Performs one step of step size <code class="computeroutput"><span class="identifier">dt</span></code>. 232 The newly obtained state is written in place in <code class="computeroutput"><span class="identifier">x</span></code>. 233 </p> 234 </td> 235</tr> 236</tbody> 237</table></div> 238<h5> 239<a name="boost_numeric_odeint.concepts.stepper.h5"></a> 240 <span class="phrase"><a name="boost_numeric_odeint.concepts.stepper.models"></a></span><a class="link" href="stepper.html#boost_numeric_odeint.concepts.stepper.models">Models</a> 241 </h5> 242<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> 243<li class="listitem"> 244 <code class="computeroutput"><span class="identifier">runge_kutta4</span></code> 245 </li> 246<li class="listitem"> 247 <code class="computeroutput"><span class="identifier">euler</span></code> 248 </li> 249<li class="listitem"> 250 <code class="computeroutput"><span class="identifier">runge_kutta_cash_karp54</span></code> 251 </li> 252<li class="listitem"> 253 <code class="computeroutput"><span class="identifier">runge_kutta_dopri5</span></code> 254 </li> 255<li class="listitem"> 256 <code class="computeroutput"><span class="identifier">runge_kutta_fehlberg78</span></code> 257 </li> 258<li class="listitem"> 259 <code class="computeroutput"><span class="identifier">modified_midpoint</span></code> 260 </li> 261<li class="listitem"> 262 <code class="computeroutput"><span class="identifier">rosenbrock4</span></code> 263 </li> 264</ul></div> 265</div> 266<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 267<td align="left"></td> 268<td align="right"><div class="copyright-footer">Copyright © 2009-2015 Karsten Ahnert and Mario Mulansky<p> 269 Distributed under the Boost Software License, Version 1.0. (See accompanying 270 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>) 271 </p> 272</div></td> 273</tr></table> 274<hr> 275<div class="spirit-nav"> 276<a accesskey="p" href="implicit_system.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../concepts.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="error_stepper.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> 277</div> 278</body> 279</html> 280
