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  25 <div class="refentry">
  26 <a name="boost.numeric.odeint.adams_bashforth_moulton"></a><div class="titlepage"></div>
  27 <div class="refnamediv">
  28 <h2><span class="refentrytitle">Class template adams_bashforth_moulton</span></h2>
  29 <p>boost::numeric::odeint::adams_bashforth_moulton &#8212; The Adams-Bashforth-Moulton 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: &lt;<a class="link" href="../../../header/boost/numeric/odeint/stepper/adams_bashforth_moulton_hpp.html" title="Header &lt;boost/numeric/odeint/stepper/adams_bashforth_moulton.hpp&gt;">boost/numeric/odeint/stepper/adams_bashforth_moulton.hpp</a>&gt;
  33
  34 </span><span class="keyword">template</span><span class="special">&lt;</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">&lt;</span> <span class="identifier">State</span> <span class="special">&gt;</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">&lt;</span> <span class="identifier">State</span> <span class="special">&gt;</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="runge_kutta4.html" title="Class template runge_kutta4">runge_kutta4</a><span class="special">&lt;</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">&gt;</span> <span class="special">&gt;</span>
  40 <span class="keyword">class</span> <a class="link" href="adams_bashforth_moulton.html" title="Class template adams_bashforth_moulton">adams_bashforth_moulton</a> <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_moulton.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">&lt;</span> <span class="identifier">state_type</span> <span class="special">&gt;</span> <a name="boost.numeric.odeint.adams_bashforth_moulton.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_moulton.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_moulton.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">&lt;</span> <span class="identifier">deriv_type</span> <span class="special">&gt;</span> <a name="boost.numeric.odeint.adams_bashforth_moulton.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_moulton.time_type"></a><span class="identifier">time_type</span><span class="special">;</span>
  49   <span class="keyword">typedef</span> <span class="identifier">Algebra</span>                     <a name="boost.numeric.odeint.adams_bashforth_moulton.algebra_type"></a><span class="identifier">algebra_type</span><span class="special">;</span>
  50   <span class="keyword">typedef</span> <span class="identifier">Operations</span>                  <a name="boost.numeric.odeint.adams_bashforth_moulton.operations_type"></a><span class="identifier">operations_type</span><span class="special">;</span>
  51   <span class="keyword">typedef</span> <span class="identifier">Resizer</span>                     <a name="boost.numeric.odeint.adams_bashforth_moulton.resizer_type"></a><span class="identifier">resizer_type</span><span class="special">;</span>
  52   <span class="keyword">typedef</span> <span class="identifier">stepper_tag</span>                 <a name="boost.numeric.odeint.adams_bashforth_moulton.stepper_category"></a><span class="identifier">stepper_category</span><span class="special">;</span>
  53   <span class="keyword">typedef</span> <span class="identifier">InitializingStepper</span>         <a name="boost.numeric.odeint.adams_bashforth_moulton.initializing_stepper_type"></a><span class="identifier">initializing_stepper_type</span><span class="special">;</span>
  54   <span class="keyword">typedef</span> <span class="keyword">unsigned</span> <span class="keyword">short</span>              <a name="boost.numeric.odeint.adams_bashforth_moulton.order_type"></a><span class="identifier">order_type</span><span class="special">;</span>
  55
  56   <span class="comment">// <a class="link" href="adams_bashforth_moulton.html#boost.numeric.odeint.adams_bashforth_moultonconstruct-copy-destruct">construct/copy/destruct</a></span>
  57   <a class="link" href="adams_bashforth_moulton.html#idm45853740354752-bb"><span class="identifier">adams_bashforth_moulton</span></a><span class="special">(</span><span class="keyword">void</span><span class="special">)</span><span class="special">;</span>
  58   <a class="link" href="adams_bashforth_moulton.html#idm45853740352752-bb"><span class="identifier">adams_bashforth_moulton</span></a><span class="special">(</span><span class="keyword">const</span> <span class="identifier">algebra_type</span> <span class="special">&amp;</span><span class="special">)</span><span class="special">;</span>
  59
  60   <span class="comment">// <a class="link" href="adams_bashforth_moulton.html#idm45853740411568-bb">public member functions</a></span>
  61   <span class="identifier">order_type</span> <a class="link" href="adams_bashforth_moulton.html#idm45853740411008-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>
  62   <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateInOut<span class="special">&gt;</span>
  63     <span class="keyword">void</span> <a class="link" href="adams_bashforth_moulton.html#idm45853740407856-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">&amp;</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>
  64   <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateInOut<span class="special">&gt;</span>
  65     <span class="keyword">void</span> <a class="link" href="adams_bashforth_moulton.html#idm45853740400192-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">&amp;</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>
  66   <span class="keyword">template</span><span class="special">&lt;</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">&gt;</span>
  67     <span class="keyword">void</span> <a class="link" href="adams_bashforth_moulton.html#idm45853740394816-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">&amp;</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">&amp;</span><span class="special">,</span>
  68                  <span class="identifier">time_type</span><span class="special">)</span><span class="special">;</span>
  69   <span class="keyword">template</span><span class="special">&lt;</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">&gt;</span>
  70     <span class="keyword">void</span> <a class="link" href="adams_bashforth_moulton.html#idm45853740385456-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">&amp;</span><span class="special">,</span> <span class="identifier">time_type</span><span class="special">,</span> <span class="identifier">StateOut</span> <span class="special">&amp;</span><span class="special">,</span> <span class="identifier">time_type</span><span class="special">)</span><span class="special">;</span>
  71   <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> StateType<span class="special">&gt;</span> <span class="keyword">void</span> <a class="link" href="adams_bashforth_moulton.html#idm45853740378832-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">&amp;</span><span class="special">)</span><span class="special">;</span>
  72   <span class="keyword">template</span><span class="special">&lt;</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">&gt;</span>
  73     <span class="keyword">void</span> <a class="link" href="adams_bashforth_moulton.html#idm45853740375216-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">&amp;</span><span class="special">,</span> <span class="identifier">time_type</span> <span class="special">&amp;</span><span class="special">,</span>
  74                     <span class="identifier">time_type</span><span class="special">)</span><span class="special">;</span>
  75   <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateIn<span class="special">&gt;</span>
  76     <span class="keyword">void</span> <a class="link" href="adams_bashforth_moulton.html#idm45853740365200-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">&amp;</span><span class="special">,</span> <span class="identifier">time_type</span> <span class="special">&amp;</span><span class="special">,</span> <span class="identifier">time_type</span><span class="special">)</span><span class="special">;</span>
  77   <span class="keyword">void</span> <a class="link" href="adams_bashforth_moulton.html#idm45853740356768-bb"><span class="identifier">reset</span></a><span class="special">(</span><span class="keyword">void</span><span class="special">)</span><span class="special">;</span>
  78
  79   <span class="comment">// <a class="link" href="adams_bashforth_moulton.html#idm45853740349808-bb">private member functions</a></span>
  80   <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateInOut<span class="special">&gt;</span>
  81     <span class="keyword">void</span> <a class="link" href="adams_bashforth_moulton.html#idm45853740349232-bb"><span class="identifier">do_step_impl1</span></a><span class="special">(</span><span class="identifier">System</span><span class="special">,</span> <span class="identifier">StateInOut</span> <span class="special">&amp;</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>
  82   <span class="keyword">template</span><span class="special">&lt;</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> StateInOut<span class="special">&gt;</span>
  83     <span class="keyword">void</span> <a class="link" href="adams_bashforth_moulton.html#idm45853740344224-bb"><span class="identifier">do_step_impl2</span></a><span class="special">(</span><span class="identifier">System</span><span class="special">,</span> <span class="identifier">StateIn</span> <span class="keyword">const</span> <span class="special">&amp;</span><span class="special">,</span> <span class="identifier">time_type</span><span class="special">,</span> <span class="identifier">StateInOut</span> <span class="special">&amp;</span><span class="special">,</span>
  84                        <span class="identifier">time_type</span><span class="special">)</span><span class="special">;</span>
  85   <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> StateIn<span class="special">&gt;</span> <span class="keyword">bool</span> <a class="link" href="adams_bashforth_moulton.html#idm45853740337968-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">&amp;</span><span class="special">)</span><span class="special">;</span>
  86
  87   <span class="comment">// public data members</span>
  88   <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>
  89   <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>
  90 <span class="special">}</span><span class="special">;</span></pre></div>
  91 <div class="refsect1">
  92 <a name="idm45221365619872"></a><h2>Description</h2>
  93 <p>The Adams-Bashforth method is a multi-step predictor-corrector 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>
  94 <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>
  95 <p>
  96 </p>
  97 <div class="refsect2">
  98 <a name="idm45221365617344"></a><h3>Template Parameters</h3>
  99 <div class="orderedlist"><ol class="orderedlist" type="1">
 100 <li class="listitem">
 101 <pre class="literallayout"><span class="identifier">size_t</span> Steps</pre>
 102 <p>The number of steps (maximal 8). </p>
 103 </li>
 104 <li class="listitem">
 105 <pre class="literallayout"><span class="keyword">typename</span> State</pre>
 106 <p>The state type. </p>
 107 </li>
 108 <li class="listitem">
 109 <pre class="literallayout"><span class="keyword">typename</span> Value <span class="special">=</span> <span class="keyword">double</span></pre>
 110 <p>The value type. </p>
 111 </li>
 112 <li class="listitem">
 113 <pre class="literallayout"><span class="keyword">typename</span> Deriv <span class="special">=</span> <span class="identifier">State</span></pre>
 114 <p>The type representing the time derivative of the state. </p>
 115 </li>
 116 <li class="listitem">
 117 <pre class="literallayout"><span class="keyword">typename</span> Time <span class="special">=</span> <span class="identifier">Value</span></pre>
 118 <p>The time representing the independent variable - the time. </p>
 119 </li>
 120 <li class="listitem">
 121 <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">&lt;</span> <span class="identifier">State</span> <span class="special">&gt;</span><span class="special">::</span><span class="identifier">algebra_type</span></pre>
 122 <p>The algebra type. </p>
 123 </li>
 124 <li class="listitem">
 125 <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">&lt;</span> <span class="identifier">State</span> <span class="special">&gt;</span><span class="special">::</span><span class="identifier">operations_type</span></pre>
 126 <p>The operations type. </p>
 127 </li>
 128 <li class="listitem">
 129 <pre class="literallayout"><span class="keyword">typename</span> Resizer <span class="special">=</span> <span class="identifier">initially_resizer</span></pre>
 130 <p>The resizer policy type. </p>
 131 </li>
 132 <li class="listitem">
 133 <pre class="literallayout"><span class="keyword">typename</span> InitializingStepper <span class="special">=</span> <a class="link" href="runge_kutta4.html" title="Class template runge_kutta4">runge_kutta4</a><span class="special">&lt;</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">&gt;</span></pre>
 134 <p>The stepper for the first two steps. </p>
 135 </li>
 136 </ol></div>
 137 </div>
 138 <div class="refsect2">
 139 <a name="idm45221365571584"></a><h3>
 140 <a name="boost.numeric.odeint.adams_bashforth_moultonconstruct-copy-destruct"></a><code class="computeroutput">adams_bashforth_moulton</code>
 141         public
 142        construct/copy/destruct</h3>
 143 <div class="orderedlist"><ol class="orderedlist" type="1">
 144 <li class="listitem">
 145 <pre class="literallayout"><a name="idm45853740354752-bb"></a><span class="identifier">adams_bashforth_moulton</span><span class="special">(</span><span class="keyword">void</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. </li>
 146 <li class="listitem">
 147 <pre class="literallayout"><a name="idm45853740352752-bb"></a><span class="identifier">adams_bashforth_moulton</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">algebra_type</span> <span class="special">&amp;</span> algebra<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>
 148 </p>
 149 <div class="variablelist"><table border="0" class="variablelist compact">
 150 <colgroup>
 151 <col align="left" valign="top">
 152 <col>
 153 </colgroup>
 154 <tbody><tr>
 155 <td><p><span class="term">Parameters:</span></p></td>
 156 <td><div class="variablelist"><table border="0" class="variablelist compact">
 157 <colgroup>
 158 <col align="left" valign="top">
 159 <col>
 160 </colgroup>
 161 <tbody><tr>
 162 <td><p><span class="term"><code class="computeroutput">algebra</code></span></p></td>
 163 <td><p>A copy of algebra is made and stored. </p></td>
 164 </tr></tbody>
 165 </table></div></td>
 166 </tr></tbody>
 167 </table></div>
 168 </li>
 169 </ol></div>
 170 </div>
 171 <div class="refsect2">
 172 <a name="idm45221365553152"></a><h3>
 173 <a name="idm45853740411568-bb"></a><code class="computeroutput">adams_bashforth_moulton</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="idm45853740411008-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+1. <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">&lt;</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateInOut<span class="special">&gt;</span>
 191   <span class="keyword">void</span> <a name="idm45853740407856-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">&amp;</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">&lt;</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateInOut<span class="special">&gt;</span>
 229   <span class="keyword">void</span> <a name="idm45853740400192-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">&amp;</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">&lt;</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">&gt;</span>
 232   <span class="keyword">void</span> <a name="idm45853740394816-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">&amp;</span> in<span class="special">,</span> <span class="identifier">time_type</span> t<span class="special">,</span>
 233                <span class="keyword">const</span> <span class="identifier">StateOut</span> <span class="special">&amp;</span> out<span class="special">,</span> <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">&lt;</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">&gt;</span>
 275   <span class="keyword">void</span> <a name="idm45853740385456-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">&amp;</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">&amp;</span> out<span class="special">,</span>
 276                <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">&lt;</span><span class="keyword">typename</span> StateType<span class="special">&gt;</span> <span class="keyword">void</span> <a name="idm45853740378832-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">&amp;</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">template</span><span class="special">&lt;</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">&gt;</span>
 302   <span class="keyword">void</span> <a name="idm45853740375216-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>
 303                   <span class="identifier">StateIn</span> <span class="special">&amp;</span> x<span class="special">,</span> <span class="identifier">time_type</span> <span class="special">&amp;</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. <div class="note"><table border="0" summary="Note">
 304 <tr>
 305 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../../doc/src/images/note.png"></td>
 306 <th align="left">Note</th>
 307 </tr>
 308 <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>
 309 </table></div>
 310 <p>
 311
 312 </p>
 313 <div class="variablelist"><table border="0" class="variablelist compact">
 314 <colgroup>
 315 <col align="left" valign="top">
 316 <col>
 317 </colgroup>
 318 <tbody><tr>
 319 <td><p><span class="term">Parameters:</span></p></td>
 320 <td><div class="variablelist"><table border="0" class="variablelist compact">
 321 <colgroup>
 322 <col align="left" valign="top">
 323 <col>
 324 </colgroup>
 325 <tbody>
 326 <tr>
 327 <td><p><span class="term"><code class="computeroutput">dt</code></span></p></td>
 328 <td><p>The step size. </p></td>
 329 </tr>
 330 <tr>
 331 <td><p><span class="term"><code class="computeroutput">explicit_stepper</code></span></p></td>
 332 <td><p>the stepper used to fill the buffer of previous step results </p></td>
 333 </tr>
 334 <tr>
 335 <td><p><span class="term"><code class="computeroutput">system</code></span></p></td>
 336 <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>
 337 </tr>
 338 <tr>
 339 <td><p><span class="term"><code class="computeroutput">t</code></span></p></td>
 340 <td><p>The initial time, updated in this method. </p></td>
 341 </tr>
 342 <tr>
 343 <td><p><span class="term"><code class="computeroutput">x</code></span></p></td>
 344 <td><p>The initial state of the ODE which should be solved, updated after in this method. </p></td>
 345 </tr>
 346 </tbody>
 347 </table></div></td>
 348 </tr></tbody>
 349 </table></div>
 350 </li>
 351 <li class="listitem">
 352 <pre class="literallayout"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateIn<span class="special">&gt;</span>
 353   <span class="keyword">void</span> <a name="idm45853740365200-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">&amp;</span> x<span class="special">,</span> <span class="identifier">time_type</span> <span class="special">&amp;</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 using the standard initializing stepper of the underlying <code class="computeroutput"><a class="link" href="adams_bashforth.html" title="Class template adams_bashforth">adams_bashforth</a></code> stepper. <p>
 354 </p>
 355 <div class="variablelist"><table border="0" class="variablelist compact">
 356 <colgroup>
 357 <col align="left" valign="top">
 358 <col>
 359 </colgroup>
 360 <tbody><tr>
 361 <td><p><span class="term">Parameters:</span></p></td>
 362 <td><div class="variablelist"><table border="0" class="variablelist compact">
 363 <colgroup>
 364 <col align="left" valign="top">
 365 <col>
 366 </colgroup>
 367 <tbody>
 368 <tr>
 369 <td><p><span class="term"><code class="computeroutput">dt</code></span></p></td>
 370 <td><p>The step size. </p></td>
 371 </tr>
 372 <tr>
 373 <td><p><span class="term"><code class="computeroutput">system</code></span></p></td>
 374 <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>
 375 </tr>
 376 <tr>
 377 <td><p><span class="term"><code class="computeroutput">t</code></span></p></td>
 378 <td><p>The value of the time, at which the step should be performed. </p></td>
 379 </tr>
 380 <tr>
 381 <td><p><span class="term"><code class="computeroutput">x</code></span></p></td>
 382 <td><p>The state of the ODE which should be solved. After calling do_step the result is updated in x. </p></td>
 383 </tr>
 384 </tbody>
 385 </table></div></td>
 386 </tr></tbody>
 387 </table></div>
 388 </li>
 389 <li class="listitem">
 390 <pre class="literallayout"><span class="keyword">void</span> <a name="idm45853740356768-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 buffers of the stepper. </li>
 391 </ol></div>
 392 </div>
 393 <div class="refsect2">
 394 <a name="idm45221365396496"></a><h3>
 395 <a name="idm45853740349808-bb"></a><code class="computeroutput">adams_bashforth_moulton</code> private member functions</h3>
 396 <div class="orderedlist"><ol class="orderedlist" type="1">
 397 <li class="listitem"><pre class="literallayout"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateInOut<span class="special">&gt;</span>
 398   <span class="keyword">void</span> <a name="idm45853740349232-bb"></a><span class="identifier">do_step_impl1</span><span class="special">(</span><span class="identifier">System</span> system<span class="special">,</span> <span class="identifier">StateInOut</span> <span class="special">&amp;</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></li>
 399 <li class="listitem"><pre class="literallayout"><span class="keyword">template</span><span class="special">&lt;</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> StateInOut<span class="special">&gt;</span>
 400   <span class="keyword">void</span> <a name="idm45853740344224-bb"></a><span class="identifier">do_step_impl2</span><span class="special">(</span><span class="identifier">System</span> system<span class="special">,</span> <span class="identifier">StateIn</span> <span class="keyword">const</span> <span class="special">&amp;</span> in<span class="special">,</span> <span class="identifier">time_type</span> t<span class="special">,</span>
 401                      <span class="identifier">StateInOut</span> <span class="special">&amp;</span> out<span class="special">,</span> <span class="identifier">time_type</span> dt<span class="special">)</span><span class="special">;</span></pre></li>
 402 <li class="listitem"><pre class="literallayout"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> StateIn<span class="special">&gt;</span> <span class="keyword">bool</span> <a name="idm45853740337968-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">&amp;</span> x<span class="special">)</span><span class="special">;</span></pre></li>
 403 </ol></div>
 404 </div>
 405 </div>
 406 </div>
 407 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 408 <td align="left"></td>
 409 <td align="right"><div class="copyright-footer">Copyright &#169; 2009-2015 Karsten Ahnert and Mario Mulansky<p>
 410         Distributed under the Boost Software License, Version 1.0. (See accompanying
 411         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>)
 412       </p>
 413 </div></td>
 414 </tr></table>
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