1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>Class template adams_bashforth</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="../../../header/boost/numeric/odeint/stepper/adams_bashforth_hpp.html" title="Header <boost/numeric/odeint/stepper/adams_bashforth.hpp>"> 9<link rel="prev" href="../../../header/boost/numeric/odeint/stepper/adams_bashforth_hpp.html" title="Header <boost/numeric/odeint/stepper/adams_bashforth.hpp>"> 10<link rel="next" href="order_helper.html" title="Struct template order_helper"> 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 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29<p>boost::numeric::odeint::adams_bashforth — The Adams-Bashforth multistep algorithm. </p> 30</div> 31<h2 xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="refsynopsisdiv-title">Synopsis</h2> 32<div xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="refsynopsisdiv"><pre class="synopsis"><span class="comment">// In header: <<a class="link" href="../../../header/boost/numeric/odeint/stepper/adams_bashforth_hpp.html" title="Header <boost/numeric/odeint/stepper/adams_bashforth.hpp>">boost/numeric/odeint/stepper/adams_bashforth.hpp</a>> 33 34</span><span class="keyword">template</span><span class="special"><</span><span class="identifier">size_t</span> Steps<span class="special">,</span> <span class="keyword">typename</span> State<span class="special">,</span> <span class="keyword">typename</span> Value <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span> 35 <span class="keyword">typename</span> Deriv <span class="special">=</span> <span class="identifier">State</span><span class="special">,</span> <span class="keyword">typename</span> Time <span class="special">=</span> <span class="identifier">Value</span><span class="special">,</span> 36 <span class="keyword">typename</span> Algebra <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">algebra_dispatcher</span><span class="special"><</span> <span class="identifier">State</span> <span class="special">></span><span class="special">::</span><span class="identifier">algebra_type</span><span class="special">,</span> 37 <span class="keyword">typename</span> Operations <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">operations_dispatcher</span><span class="special"><</span> <span class="identifier">State</span> <span class="special">></span><span class="special">::</span><span class="identifier">operations_type</span><span class="special">,</span> 38 <span class="keyword">typename</span> Resizer <span class="special">=</span> <span class="identifier">initially_resizer</span><span class="special">,</span> 39 <span class="keyword">typename</span> InitializingStepper <span class="special">=</span> <a class="link" href="extrapolation_stepper.html" title="Class template extrapolation_stepper">extrapolation_stepper</a><span class="special"><</span> <span class="identifier">order_helper</span><span class="special"><</span><span class="identifier">Steps</span><span class="special">></span><span class="special">::</span><span class="identifier">value</span><span class="special">,</span> <span class="identifier">State</span><span class="special">,</span> <span class="identifier">Value</span><span class="special">,</span> <span class="identifier">Deriv</span><span class="special">,</span> <span class="identifier">Time</span><span class="special">,</span> <span class="identifier">Algebra</span><span class="special">,</span> <span class="identifier">Operations</span><span class="special">,</span> <span class="identifier">Resizer</span> <span class="special">></span> <span class="special">></span> 40<span class="keyword">class</span> <a class="link" href="adams_bashforth.html" title="Class template adams_bashforth">adams_bashforth</a> <span class="special">:</span> <span class="keyword">public</span> <span class="identifier">algebra_stepper_base</span><span class="special"><</span> <span class="identifier">Algebra</span><span class="special">,</span> <span class="identifier">Operations</span> <span class="special">></span> <span class="special">{</span> 41<span class="keyword">public</span><span class="special">:</span> 42 <span class="comment">// types</span> 43 <span class="keyword">typedef</span> <span class="identifier">State</span> <a name="boost.numeric.odeint.adams_bashforth.state_type"></a><span class="identifier">state_type</span><span class="special">;</span> 44 <span class="keyword">typedef</span> <span class="identifier">state_wrapper</span><span class="special"><</span> <span class="identifier">state_type</span> <span class="special">></span> <a name="boost.numeric.odeint.adams_bashforth.wrapped_state_type"></a><span class="identifier">wrapped_state_type</span><span class="special">;</span> 45 <span class="keyword">typedef</span> <span class="identifier">Value</span> <a name="boost.numeric.odeint.adams_bashforth.value_type"></a><span class="identifier">value_type</span><span class="special">;</span> 46 <span class="keyword">typedef</span> <span class="identifier">Deriv</span> <a name="boost.numeric.odeint.adams_bashforth.deriv_type"></a><span class="identifier">deriv_type</span><span class="special">;</span> 47 <span class="keyword">typedef</span> <span class="identifier">state_wrapper</span><span class="special"><</span> <span class="identifier">deriv_type</span> <span class="special">></span> <a name="boost.numeric.odeint.adams_bashforth.wrapped_deriv_type"></a><span class="identifier">wrapped_deriv_type</span><span class="special">;</span> 48 <span class="keyword">typedef</span> <span class="identifier">Time</span> <a name="boost.numeric.odeint.adams_bashforth.time_type"></a><span class="identifier">time_type</span><span class="special">;</span> 49 <span class="keyword">typedef</span> <span class="identifier">Resizer</span> <a name="boost.numeric.odeint.adams_bashforth.resizer_type"></a><span class="identifier">resizer_type</span><span class="special">;</span> 50 <span class="keyword">typedef</span> <span class="identifier">stepper_tag</span> <a name="boost.numeric.odeint.adams_bashforth.stepper_category"></a><span class="identifier">stepper_category</span><span class="special">;</span> 51 <span class="keyword">typedef</span> <span class="identifier">InitializingStepper</span> <a name="boost.numeric.odeint.adams_bashforth.initializing_stepper_type"></a><span class="identifier">initializing_stepper_type</span><span class="special">;</span> 52 <span class="keyword">typedef</span> <span class="identifier">algebra_stepper_base</span><span class="special"><</span> <span class="identifier">Algebra</span><span class="special">,</span> <span class="identifier">Operations</span> <span class="special">></span> <a name="boost.numeric.odeint.adams_bashforth.algebra_stepper_base_type"></a><span class="identifier">algebra_stepper_base_type</span><span class="special">;</span> 53 <span class="keyword">typedef</span> <span class="identifier">algebra_stepper_base_type</span><span class="special">::</span><span class="identifier">algebra_type</span> <a name="boost.numeric.odeint.adams_bashforth.algebra_type"></a><span class="identifier">algebra_type</span><span class="special">;</span> 54 <span class="keyword">typedef</span> <span class="identifier">algebra_stepper_base_type</span><span class="special">::</span><span class="identifier">operations_type</span> <a name="boost.numeric.odeint.adams_bashforth.operations_type"></a><span class="identifier">operations_type</span><span class="special">;</span> 55 <span class="keyword">typedef</span> <span class="keyword">unsigned</span> <span class="keyword">short</span> <a name="boost.numeric.odeint.adams_bashforth.order_type"></a><span class="identifier">order_type</span><span class="special">;</span> 56 <span class="keyword">typedef</span> <span class="emphasis"><em><span class="identifier">unspecified</span></em></span> <a name="boost.numeric.odeint.adams_bashforth.step_storage_type"></a><span class="identifier">step_storage_type</span><span class="special">;</span> 57 58 <span class="comment">// <a class="link" href="adams_bashforth.html#boost.numeric.odeint.adams_bashforthconstruct-copy-destruct">construct/copy/destruct</a></span> 59 <a class="link" href="adams_bashforth.html#idm45875527501888-bb"><span class="identifier">adams_bashforth</span></a><span class="special">(</span><span class="keyword">const</span> <span class="identifier">algebra_type</span> <span class="special">&</span> <span class="special">=</span> <span class="identifier">algebra_type</span><span class="special">(</span><span class="special">)</span><span class="special">)</span><span class="special">;</span> 60 61 <span class="comment">// <a class="link" href="adams_bashforth.html#idm45875527573152-bb">public member functions</a></span> 62 <span class="identifier">order_type</span> <a class="link" href="adams_bashforth.html#idm45875527572592-bb"><span class="identifier">order</span></a><span class="special">(</span><span class="keyword">void</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span> 63 <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateInOut<span class="special">></span> 64 <span class="keyword">void</span> <a class="link" href="adams_bashforth.html#idm45875527569440-bb"><span class="identifier">do_step</span></a><span class="special">(</span><span class="identifier">System</span><span class="special">,</span> <span class="identifier">StateInOut</span> <span class="special">&</span><span class="special">,</span> <span class="identifier">time_type</span><span class="special">,</span> <span class="identifier">time_type</span><span class="special">)</span><span class="special">;</span> 65 <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateInOut<span class="special">></span> 66 <span class="keyword">void</span> <a class="link" href="adams_bashforth.html#idm45875527561776-bb"><span class="identifier">do_step</span></a><span class="special">(</span><span class="identifier">System</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">StateInOut</span> <span class="special">&</span><span class="special">,</span> <span class="identifier">time_type</span><span class="special">,</span> <span class="identifier">time_type</span><span class="special">)</span><span class="special">;</span> 67 <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateIn<span class="special">,</span> <span class="keyword">typename</span> StateOut<span class="special">></span> 68 <span class="keyword">void</span> <a class="link" href="adams_bashforth.html#idm45875527556400-bb"><span class="identifier">do_step</span></a><span class="special">(</span><span class="identifier">System</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">StateIn</span> <span class="special">&</span><span class="special">,</span> <span class="identifier">time_type</span><span class="special">,</span> <span class="identifier">StateOut</span> <span class="special">&</span><span class="special">,</span> <span class="identifier">time_type</span><span class="special">)</span><span class="special">;</span> 69 <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateIn<span class="special">,</span> <span class="keyword">typename</span> StateOut<span class="special">></span> 70 <span class="keyword">void</span> <a class="link" href="adams_bashforth.html#idm45875527547040-bb"><span class="identifier">do_step</span></a><span class="special">(</span><span class="identifier">System</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">StateIn</span> <span class="special">&</span><span class="special">,</span> <span class="identifier">time_type</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">StateOut</span> <span class="special">&</span><span class="special">,</span> 71 <span class="identifier">time_type</span><span class="special">)</span><span class="special">;</span> 72 <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> StateType<span class="special">></span> <span class="keyword">void</span> <a class="link" href="adams_bashforth.html#idm45875527540416-bb"><span class="identifier">adjust_size</span></a><span class="special">(</span><span class="keyword">const</span> <span class="identifier">StateType</span> <span class="special">&</span><span class="special">)</span><span class="special">;</span> 73 <span class="keyword">const</span> <span class="identifier">step_storage_type</span> <span class="special">&</span> <a class="link" href="adams_bashforth.html#idm45875527536800-bb"><span class="identifier">step_storage</span></a><span class="special">(</span><span class="keyword">void</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span> 74 <span class="identifier">step_storage_type</span> <span class="special">&</span> <a class="link" href="adams_bashforth.html#idm45875527533648-bb"><span class="identifier">step_storage</span></a><span class="special">(</span><span class="keyword">void</span><span class="special">)</span><span class="special">;</span> 75 <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> ExplicitStepper<span class="special">,</span> <span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateIn<span class="special">></span> 76 <span class="keyword">void</span> <a class="link" href="adams_bashforth.html#idm45875527530784-bb"><span class="identifier">initialize</span></a><span class="special">(</span><span class="identifier">ExplicitStepper</span><span class="special">,</span> <span class="identifier">System</span><span class="special">,</span> <span class="identifier">StateIn</span> <span class="special">&</span><span class="special">,</span> <span class="identifier">time_type</span> <span class="special">&</span><span class="special">,</span> 77 <span class="identifier">time_type</span><span class="special">)</span><span class="special">;</span> 78 <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateIn<span class="special">></span> 79 <span class="keyword">void</span> <a class="link" href="adams_bashforth.html#idm45875527521376-bb"><span class="identifier">initialize</span></a><span class="special">(</span><span class="identifier">System</span><span class="special">,</span> <span class="identifier">StateIn</span> <span class="special">&</span><span class="special">,</span> <span class="identifier">time_type</span> <span class="special">&</span><span class="special">,</span> <span class="identifier">time_type</span><span class="special">)</span><span class="special">;</span> 80 <span class="keyword">void</span> <a class="link" href="adams_bashforth.html#idm45875527513056-bb"><span class="identifier">reset</span></a><span class="special">(</span><span class="keyword">void</span><span class="special">)</span><span class="special">;</span> 81 <span class="keyword">bool</span> <a class="link" href="adams_bashforth.html#idm45875527511200-bb"><span class="identifier">is_initialized</span></a><span class="special">(</span><span class="keyword">void</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span> 82 <span class="keyword">const</span> <span class="identifier">initializing_stepper_type</span> <span class="special">&</span> <a class="link" href="adams_bashforth.html#idm45875527508048-bb"><span class="identifier">initializing_stepper</span></a><span class="special">(</span><span class="keyword">void</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span> 83 <span class="identifier">initializing_stepper_type</span> <span class="special">&</span> <a class="link" href="adams_bashforth.html#idm45875527504912-bb"><span class="identifier">initializing_stepper</span></a><span class="special">(</span><span class="keyword">void</span><span class="special">)</span><span class="special">;</span> 84 85 <span class="comment">// <a class="link" href="adams_bashforth.html#idm45875527498656-bb">private member functions</a></span> 86 <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateIn<span class="special">,</span> <span class="keyword">typename</span> StateOut<span class="special">></span> 87 <span class="keyword">void</span> <a class="link" href="adams_bashforth.html#idm45875527498080-bb"><span class="identifier">do_step_impl</span></a><span class="special">(</span><span class="identifier">System</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">StateIn</span> <span class="special">&</span><span class="special">,</span> <span class="identifier">time_type</span><span class="special">,</span> <span class="identifier">StateOut</span> <span class="special">&</span><span class="special">,</span> 88 <span class="identifier">time_type</span><span class="special">)</span><span class="special">;</span> 89 <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> StateIn<span class="special">></span> <span class="keyword">bool</span> <a class="link" href="adams_bashforth.html#idm45875527491824-bb"><span class="identifier">resize_impl</span></a><span class="special">(</span><span class="keyword">const</span> <span class="identifier">StateIn</span> <span class="special">&</span><span class="special">)</span><span class="special">;</span> 90 91 <span class="comment">// public data members</span> 92 <span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">size_t</span> <span class="identifier">steps</span><span class="special">;</span> 93 <span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">order_type</span> <span class="identifier">order_value</span><span class="special">;</span> 94<span class="special">}</span><span class="special">;</span></pre></div> 95<div class="refsect1"> 96<a name="idm45600380025920"></a><h2>Description</h2> 97<p>The Adams-Bashforth method is a multi-step algorithm with configurable step number. The step number is specified as template parameter Steps and it then uses the result from the previous Steps steps. See also <a href="http://en.wikipedia.org/wiki/Linear_multistep_method" target="_top">en.wikipedia.org/wiki/Linear_multistep_method</a>. Currently, a maximum of Steps=8 is supported. The method is explicit and fulfills the Stepper concept. Step size control or continuous output are not provided.</p> 98<p>This class derives from algebra_base and inherits its interface via CRTP (current recurring template pattern). For more details see algebra_stepper_base.</p> 99<p> 100</p> 101<div class="refsect2"> 102<a name="idm45600380023408"></a><h3>Template Parameters</h3> 103<div class="orderedlist"><ol class="orderedlist" type="1"> 104<li class="listitem"> 105<pre class="literallayout"><span class="identifier">size_t</span> Steps</pre> 106<p>The number of steps (maximal 8). </p> 107</li> 108<li class="listitem"> 109<pre class="literallayout"><span class="keyword">typename</span> State</pre> 110<p>The state type. </p> 111</li> 112<li class="listitem"> 113<pre class="literallayout"><span class="keyword">typename</span> Value <span class="special">=</span> <span class="keyword">double</span></pre> 114<p>The value type. </p> 115</li> 116<li class="listitem"> 117<pre class="literallayout"><span class="keyword">typename</span> Deriv <span class="special">=</span> <span class="identifier">State</span></pre> 118<p>The type representing the time derivative of the state. </p> 119</li> 120<li class="listitem"> 121<pre class="literallayout"><span class="keyword">typename</span> Time <span class="special">=</span> <span class="identifier">Value</span></pre> 122<p>The time representing the independent variable - the time. </p> 123</li> 124<li class="listitem"> 125<pre class="literallayout"><span class="keyword">typename</span> Algebra <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">algebra_dispatcher</span><span class="special"><</span> <span class="identifier">State</span> <span class="special">></span><span class="special">::</span><span class="identifier">algebra_type</span></pre> 126<p>The algebra type. </p> 127</li> 128<li class="listitem"> 129<pre class="literallayout"><span class="keyword">typename</span> Operations <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">operations_dispatcher</span><span class="special"><</span> <span class="identifier">State</span> <span class="special">></span><span class="special">::</span><span class="identifier">operations_type</span></pre> 130<p>The operations type. </p> 131</li> 132<li class="listitem"> 133<pre class="literallayout"><span class="keyword">typename</span> Resizer <span class="special">=</span> <span class="identifier">initially_resizer</span></pre> 134<p>The resizer policy type. </p> 135</li> 136<li class="listitem"> 137<pre class="literallayout"><span class="keyword">typename</span> InitializingStepper <span class="special">=</span> <a class="link" href="extrapolation_stepper.html" title="Class template extrapolation_stepper">extrapolation_stepper</a><span class="special"><</span> <span class="identifier">order_helper</span><span class="special"><</span><span class="identifier">Steps</span><span class="special">></span><span class="special">::</span><span class="identifier">value</span><span class="special">,</span> <span class="identifier">State</span><span class="special">,</span> <span class="identifier">Value</span><span class="special">,</span> <span class="identifier">Deriv</span><span class="special">,</span> <span class="identifier">Time</span><span class="special">,</span> <span class="identifier">Algebra</span><span class="special">,</span> <span class="identifier">Operations</span><span class="special">,</span> <span class="identifier">Resizer</span> <span class="special">></span></pre> 138<p>The stepper for the first two steps. </p> 139</li> 140</ol></div> 141</div> 142<div class="refsect2"> 143<a name="idm45600379974208"></a><h3> 144<a name="boost.numeric.odeint.adams_bashforthconstruct-copy-destruct"></a><code class="computeroutput">adams_bashforth</code> 145 public 146 construct/copy/destruct</h3> 147<div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"> 148<pre class="literallayout"><a name="idm45875527501888-bb"></a><span class="identifier">adams_bashforth</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">algebra_type</span> <span class="special">&</span> algebra <span class="special">=</span> <span class="identifier">algebra_type</span><span class="special">(</span><span class="special">)</span><span class="special">)</span><span class="special">;</span></pre>Constructs the <code class="computeroutput"><a class="link" href="adams_bashforth.html" title="Class template adams_bashforth">adams_bashforth</a></code> class. This constructor can be used as a default constructor if the algebra has a default constructor. <p> 149</p> 150<div class="variablelist"><table border="0" class="variablelist compact"> 151<colgroup> 152<col align="left" valign="top"> 153<col> 154</colgroup> 155<tbody><tr> 156<td><p><span class="term">Parameters:</span></p></td> 157<td><div class="variablelist"><table border="0" class="variablelist compact"> 158<colgroup> 159<col align="left" valign="top"> 160<col> 161</colgroup> 162<tbody><tr> 163<td><p><span class="term"><code class="computeroutput">algebra</code></span></p></td> 164<td><p>A copy of algebra is made and stored. </p></td> 165</tr></tbody> 166</table></div></td> 167</tr></tbody> 168</table></div> 169</li></ol></div> 170</div> 171<div class="refsect2"> 172<a name="idm45600379959120"></a><h3> 173<a name="idm45875527573152-bb"></a><code class="computeroutput">adams_bashforth</code> public member functions</h3> 174<div class="orderedlist"><ol class="orderedlist" type="1"> 175<li class="listitem"> 176<pre class="literallayout"><span class="identifier">order_type</span> <a name="idm45875527572592-bb"></a><span class="identifier">order</span><span class="special">(</span><span class="keyword">void</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span></pre>Returns the order of the algorithm, which is equal to the number of steps. <p> 177</p> 178<div class="variablelist"><table border="0" class="variablelist compact"> 179<colgroup> 180<col align="left" valign="top"> 181<col> 182</colgroup> 183<tbody><tr> 184<td><p><span class="term">Returns:</span></p></td> 185<td><p>order of the method. </p></td> 186</tr></tbody> 187</table></div> 188</li> 189<li class="listitem"> 190<pre class="literallayout"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateInOut<span class="special">></span> 191 <span class="keyword">void</span> <a name="idm45875527569440-bb"></a><span class="identifier">do_step</span><span class="special">(</span><span class="identifier">System</span> system<span class="special">,</span> <span class="identifier">StateInOut</span> <span class="special">&</span> x<span class="special">,</span> <span class="identifier">time_type</span> t<span class="special">,</span> <span class="identifier">time_type</span> dt<span class="special">)</span><span class="special">;</span></pre>This method performs one step. It transforms the result in-place. <p> 192</p> 193<div class="variablelist"><table border="0" class="variablelist compact"> 194<colgroup> 195<col align="left" valign="top"> 196<col> 197</colgroup> 198<tbody><tr> 199<td><p><span class="term">Parameters:</span></p></td> 200<td><div class="variablelist"><table border="0" class="variablelist compact"> 201<colgroup> 202<col align="left" valign="top"> 203<col> 204</colgroup> 205<tbody> 206<tr> 207<td><p><span class="term"><code class="computeroutput">dt</code></span></p></td> 208<td><p>The step size. </p></td> 209</tr> 210<tr> 211<td><p><span class="term"><code class="computeroutput">system</code></span></p></td> 212<td><p>The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Simple System concept. </p></td> 213</tr> 214<tr> 215<td><p><span class="term"><code class="computeroutput">t</code></span></p></td> 216<td><p>The value of the time, at which the step should be performed. </p></td> 217</tr> 218<tr> 219<td><p><span class="term"><code class="computeroutput">x</code></span></p></td> 220<td><p>The state of the ODE which should be solved. After calling do_step the result is updated in x. </p></td> 221</tr> 222</tbody> 223</table></div></td> 224</tr></tbody> 225</table></div> 226</li> 227<li class="listitem"> 228<pre class="literallayout"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateInOut<span class="special">></span> 229 <span class="keyword">void</span> <a name="idm45875527561776-bb"></a><span class="identifier">do_step</span><span class="special">(</span><span class="identifier">System</span> system<span class="special">,</span> <span class="keyword">const</span> <span class="identifier">StateInOut</span> <span class="special">&</span> x<span class="special">,</span> <span class="identifier">time_type</span> t<span class="special">,</span> <span class="identifier">time_type</span> dt<span class="special">)</span><span class="special">;</span></pre>Second version to solve the forwarding problem, can be called with Boost.Range as StateInOut. </li> 230<li class="listitem"> 231<pre class="literallayout"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateIn<span class="special">,</span> <span class="keyword">typename</span> StateOut<span class="special">></span> 232 <span class="keyword">void</span> <a name="idm45875527556400-bb"></a><span class="identifier">do_step</span><span class="special">(</span><span class="identifier">System</span> system<span class="special">,</span> <span class="keyword">const</span> <span class="identifier">StateIn</span> <span class="special">&</span> in<span class="special">,</span> <span class="identifier">time_type</span> t<span class="special">,</span> <span class="identifier">StateOut</span> <span class="special">&</span> out<span class="special">,</span> 233 <span class="identifier">time_type</span> dt<span class="special">)</span><span class="special">;</span></pre>The method performs one step with the stepper passed by Stepper. The state of the ODE is updated out-of-place. <p> 234</p> 235<div class="variablelist"><table border="0" class="variablelist compact"> 236<colgroup> 237<col align="left" valign="top"> 238<col> 239</colgroup> 240<tbody><tr> 241<td><p><span class="term">Parameters:</span></p></td> 242<td><div class="variablelist"><table border="0" class="variablelist compact"> 243<colgroup> 244<col align="left" valign="top"> 245<col> 246</colgroup> 247<tbody> 248<tr> 249<td><p><span class="term"><code class="computeroutput">dt</code></span></p></td> 250<td><p>The step size. </p></td> 251</tr> 252<tr> 253<td><p><span class="term"><code class="computeroutput">in</code></span></p></td> 254<td><p>The state of the ODE which should be solved. in is not modified in this method </p></td> 255</tr> 256<tr> 257<td><p><span class="term"><code class="computeroutput">out</code></span></p></td> 258<td><p>The result of the step is written in out. </p></td> 259</tr> 260<tr> 261<td><p><span class="term"><code class="computeroutput">system</code></span></p></td> 262<td><p>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </p></td> 263</tr> 264<tr> 265<td><p><span class="term"><code class="computeroutput">t</code></span></p></td> 266<td><p>The value of the time, at which the step should be performed. </p></td> 267</tr> 268</tbody> 269</table></div></td> 270</tr></tbody> 271</table></div> 272</li> 273<li class="listitem"> 274<pre class="literallayout"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateIn<span class="special">,</span> <span class="keyword">typename</span> StateOut<span class="special">></span> 275 <span class="keyword">void</span> <a name="idm45875527547040-bb"></a><span class="identifier">do_step</span><span class="special">(</span><span class="identifier">System</span> system<span class="special">,</span> <span class="keyword">const</span> <span class="identifier">StateIn</span> <span class="special">&</span> in<span class="special">,</span> <span class="identifier">time_type</span> t<span class="special">,</span> 276 <span class="keyword">const</span> <span class="identifier">StateOut</span> <span class="special">&</span> out<span class="special">,</span> <span class="identifier">time_type</span> dt<span class="special">)</span><span class="special">;</span></pre>Second version to solve the forwarding problem, can be called with Boost.Range as StateOut. </li> 277<li class="listitem"> 278<pre class="literallayout"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> StateType<span class="special">></span> <span class="keyword">void</span> <a name="idm45875527540416-bb"></a><span class="identifier">adjust_size</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">StateType</span> <span class="special">&</span> x<span class="special">)</span><span class="special">;</span></pre>Adjust the size of all temporaries in the stepper manually. <p> 279</p> 280<div class="variablelist"><table border="0" class="variablelist compact"> 281<colgroup> 282<col align="left" valign="top"> 283<col> 284</colgroup> 285<tbody><tr> 286<td><p><span class="term">Parameters:</span></p></td> 287<td><div class="variablelist"><table border="0" class="variablelist compact"> 288<colgroup> 289<col align="left" valign="top"> 290<col> 291</colgroup> 292<tbody><tr> 293<td><p><span class="term"><code class="computeroutput">x</code></span></p></td> 294<td><p>A state from which the size of the temporaries to be resized is deduced. </p></td> 295</tr></tbody> 296</table></div></td> 297</tr></tbody> 298</table></div> 299</li> 300<li class="listitem"> 301<pre class="literallayout"><span class="keyword">const</span> <span class="identifier">step_storage_type</span> <span class="special">&</span> <a name="idm45875527536800-bb"></a><span class="identifier">step_storage</span><span class="special">(</span><span class="keyword">void</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span></pre>Returns the storage of intermediate results. <p> 302</p> 303<div class="variablelist"><table border="0" class="variablelist compact"> 304<colgroup> 305<col align="left" valign="top"> 306<col> 307</colgroup> 308<tbody><tr> 309<td><p><span class="term">Returns:</span></p></td> 310<td><p>The storage of intermediate results. </p></td> 311</tr></tbody> 312</table></div> 313</li> 314<li class="listitem"> 315<pre class="literallayout"><span class="identifier">step_storage_type</span> <span class="special">&</span> <a name="idm45875527533648-bb"></a><span class="identifier">step_storage</span><span class="special">(</span><span class="keyword">void</span><span class="special">)</span><span class="special">;</span></pre>Returns the storage of intermediate results. <p> 316</p> 317<div class="variablelist"><table border="0" class="variablelist compact"> 318<colgroup> 319<col align="left" valign="top"> 320<col> 321</colgroup> 322<tbody><tr> 323<td><p><span class="term">Returns:</span></p></td> 324<td><p>The storage of intermediate results. </p></td> 325</tr></tbody> 326</table></div> 327</li> 328<li class="listitem"> 329<pre class="literallayout"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> ExplicitStepper<span class="special">,</span> <span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateIn<span class="special">></span> 330 <span class="keyword">void</span> <a name="idm45875527530784-bb"></a><span class="identifier">initialize</span><span class="special">(</span><span class="identifier">ExplicitStepper</span> explicit_stepper<span class="special">,</span> <span class="identifier">System</span> system<span class="special">,</span> 331 <span class="identifier">StateIn</span> <span class="special">&</span> x<span class="special">,</span> <span class="identifier">time_type</span> <span class="special">&</span> t<span class="special">,</span> <span class="identifier">time_type</span> dt<span class="special">)</span><span class="special">;</span></pre>Initialized the stepper. Does Steps-1 steps with the explicit_stepper to fill the buffer. <p> 332</p> 333<div class="variablelist"><table border="0" class="variablelist compact"> 334<colgroup> 335<col align="left" valign="top"> 336<col> 337</colgroup> 338<tbody><tr> 339<td><p><span class="term">Parameters:</span></p></td> 340<td><div class="variablelist"><table border="0" class="variablelist compact"> 341<colgroup> 342<col align="left" valign="top"> 343<col> 344</colgroup> 345<tbody> 346<tr> 347<td><p><span class="term"><code class="computeroutput">dt</code></span></p></td> 348<td><p>The step size. </p></td> 349</tr> 350<tr> 351<td><p><span class="term"><code class="computeroutput">explicit_stepper</code></span></p></td> 352<td><p>the stepper used to fill the buffer of previous step results </p></td> 353</tr> 354<tr> 355<td><p><span class="term"><code class="computeroutput">system</code></span></p></td> 356<td><p>The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Simple System concept. </p></td> 357</tr> 358<tr> 359<td><p><span class="term"><code class="computeroutput">t</code></span></p></td> 360<td><p>The value of the time, at which the step should be performed. </p></td> 361</tr> 362<tr> 363<td><p><span class="term"><code class="computeroutput">x</code></span></p></td> 364<td><p>The state of the ODE which should be solved. After calling do_step the result is updated in x. </p></td> 365</tr> 366</tbody> 367</table></div></td> 368</tr></tbody> 369</table></div> 370</li> 371<li class="listitem"> 372<pre class="literallayout"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateIn<span class="special">></span> 373 <span class="keyword">void</span> <a name="idm45875527521376-bb"></a><span class="identifier">initialize</span><span class="special">(</span><span class="identifier">System</span> system<span class="special">,</span> <span class="identifier">StateIn</span> <span class="special">&</span> x<span class="special">,</span> <span class="identifier">time_type</span> <span class="special">&</span> t<span class="special">,</span> <span class="identifier">time_type</span> dt<span class="special">)</span><span class="special">;</span></pre>Initialized the stepper. Does Steps-1 steps with an internal instance of InitializingStepper to fill the buffer. <div class="note"><table border="0" summary="Note"> 374<tr> 375<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../../doc/src/images/note.png"></td> 376<th align="left">Note</th> 377</tr> 378<tr><td align="left" valign="top"><p>The state x and time t are updated to the values after Steps-1 initial steps. </p></td></tr> 379</table></div> 380<p> 381 382</p> 383<div class="variablelist"><table border="0" class="variablelist compact"> 384<colgroup> 385<col align="left" valign="top"> 386<col> 387</colgroup> 388<tbody><tr> 389<td><p><span class="term">Parameters:</span></p></td> 390<td><div class="variablelist"><table border="0" class="variablelist compact"> 391<colgroup> 392<col align="left" valign="top"> 393<col> 394</colgroup> 395<tbody> 396<tr> 397<td><p><span class="term"><code class="computeroutput">dt</code></span></p></td> 398<td><p>The step size. </p></td> 399</tr> 400<tr> 401<td><p><span class="term"><code class="computeroutput">system</code></span></p></td> 402<td><p>The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Simple System concept. </p></td> 403</tr> 404<tr> 405<td><p><span class="term"><code class="computeroutput">t</code></span></p></td> 406<td><p>The initial value of the time, updated in this method. </p></td> 407</tr> 408<tr> 409<td><p><span class="term"><code class="computeroutput">x</code></span></p></td> 410<td><p>The initial state of the ODE which should be solved, updated in this method. </p></td> 411</tr> 412</tbody> 413</table></div></td> 414</tr></tbody> 415</table></div> 416</li> 417<li class="listitem"> 418<pre class="literallayout"><span class="keyword">void</span> <a name="idm45875527513056-bb"></a><span class="identifier">reset</span><span class="special">(</span><span class="keyword">void</span><span class="special">)</span><span class="special">;</span></pre>Resets the internal buffer of the stepper. </li> 419<li class="listitem"> 420<pre class="literallayout"><span class="keyword">bool</span> <a name="idm45875527511200-bb"></a><span class="identifier">is_initialized</span><span class="special">(</span><span class="keyword">void</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span></pre>Returns true if the stepper has been initialized. <p> 421</p> 422<div class="variablelist"><table border="0" class="variablelist compact"> 423<colgroup> 424<col align="left" valign="top"> 425<col> 426</colgroup> 427<tbody><tr> 428<td><p><span class="term">Returns:</span></p></td> 429<td><p>bool true if stepper is initialized, false otherwise </p></td> 430</tr></tbody> 431</table></div> 432</li> 433<li class="listitem"> 434<pre class="literallayout"><span class="keyword">const</span> <span class="identifier">initializing_stepper_type</span> <span class="special">&</span> <a name="idm45875527508048-bb"></a><span class="identifier">initializing_stepper</span><span class="special">(</span><span class="keyword">void</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span></pre>Returns the internal initializing stepper instance. <p> 435</p> 436<div class="variablelist"><table border="0" class="variablelist compact"> 437<colgroup> 438<col align="left" valign="top"> 439<col> 440</colgroup> 441<tbody><tr> 442<td><p><span class="term">Returns:</span></p></td> 443<td><p>initializing_stepper </p></td> 444</tr></tbody> 445</table></div> 446</li> 447<li class="listitem"> 448<pre class="literallayout"><span class="identifier">initializing_stepper_type</span> <span class="special">&</span> <a name="idm45875527504912-bb"></a><span class="identifier">initializing_stepper</span><span class="special">(</span><span class="keyword">void</span><span class="special">)</span><span class="special">;</span></pre>Returns the internal initializing stepper instance. <p> 449</p> 450<div class="variablelist"><table border="0" class="variablelist compact"> 451<colgroup> 452<col align="left" valign="top"> 453<col> 454</colgroup> 455<tbody><tr> 456<td><p><span class="term">Returns:</span></p></td> 457<td><p>initializing_stepper </p></td> 458</tr></tbody> 459</table></div> 460</li> 461</ol></div> 462</div> 463<div class="refsect2"> 464<a name="idm45600379763760"></a><h3> 465<a name="idm45875527498656-bb"></a><code class="computeroutput">adams_bashforth</code> private member functions</h3> 466<div class="orderedlist"><ol class="orderedlist" type="1"> 467<li class="listitem"><pre class="literallayout"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateIn<span class="special">,</span> <span class="keyword">typename</span> StateOut<span class="special">></span> 468 <span class="keyword">void</span> <a name="idm45875527498080-bb"></a><span class="identifier">do_step_impl</span><span class="special">(</span><span class="identifier">System</span> system<span class="special">,</span> <span class="keyword">const</span> <span class="identifier">StateIn</span> <span class="special">&</span> in<span class="special">,</span> <span class="identifier">time_type</span> t<span class="special">,</span> 469 <span class="identifier">StateOut</span> <span class="special">&</span> out<span class="special">,</span> <span class="identifier">time_type</span> dt<span class="special">)</span><span class="special">;</span></pre></li> 470<li class="listitem"><pre class="literallayout"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> StateIn<span class="special">></span> <span class="keyword">bool</span> <a name="idm45875527491824-bb"></a><span class="identifier">resize_impl</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">StateIn</span> <span class="special">&</span> x<span class="special">)</span><span class="special">;</span></pre></li> 471</ol></div> 472</div> 473</div> 474</div> 475<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 476<td align="left"></td> 477<td align="right"><div class="copyright-footer">Copyright © 2009-2015 Karsten Ahnert and Mario Mulansky<p> 478 Distributed under the Boost Software License, Version 1.0. (See accompanying 479 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>) 480 </p> 481</div></td> 482</tr></table> 483<hr> 484<div class="spirit-nav"> 485<a accesskey="p" href="../../../header/boost/numeric/odeint/stepper/adams_bashforth_hpp.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../../../header/boost/numeric/odeint/stepper/adams_bashforth_hpp.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="order_helper.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> 486</div> 487</body> 488</html> 489
