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  25 <div class="refentry">
  26 <a name="boost.numeric.odeint.adams_bashforth"></a><div class="titlepage"></div>
  27 <div class="refnamediv">
  28 <h2><span class="refentrytitle">Class template adams_bashforth</span></h2>
  29 <p>boost::numeric::odeint::adams_bashforth &#8212; 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: &lt;<a class="link" href="../../../header/boost/numeric/odeint/stepper/adams_bashforth_hpp.html" title="Header &lt;boost/numeric/odeint/stepper/adams_bashforth.hpp&gt;">boost/numeric/odeint/stepper/adams_bashforth.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="extrapolation_stepper.html" title="Class template extrapolation_stepper">extrapolation_stepper</a><span class="special">&lt;</span> <span class="identifier">order_helper</span><span class="special">&lt;</span><span class="identifier">Steps</span><span class="special">&gt;</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">&gt;</span> <span class="special">&gt;</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">&lt;</span> <span class="identifier">Algebra</span><span class="special">,</span> <span class="identifier">Operations</span> <span class="special">&gt;</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">&lt;</span> <span class="identifier">state_type</span> <span class="special">&gt;</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">&lt;</span> <span class="identifier">deriv_type</span> <span class="special">&gt;</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">&lt;</span> <span class="identifier">Algebra</span><span class="special">,</span> <span class="identifier">Operations</span> <span class="special">&gt;</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#idm45853740457200-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">&amp;</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#idm45853740528464-bb">public member functions</a></span>
  62   <span class="identifier">order_type</span> <a class="link" href="adams_bashforth.html#idm45853740527904-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">&lt;</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateInOut<span class="special">&gt;</span>
  64     <span class="keyword">void</span> <a class="link" href="adams_bashforth.html#idm45853740524752-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>
  65   <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>
  66     <span class="keyword">void</span> <a class="link" href="adams_bashforth.html#idm45853740517088-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>
  67   <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>
  68     <span class="keyword">void</span> <a class="link" href="adams_bashforth.html#idm45853740511712-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>
  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.html#idm45853740502352-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>
  71                  <span class="identifier">time_type</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> StateType<span class="special">&gt;</span> <span class="keyword">void</span> <a class="link" href="adams_bashforth.html#idm45853740495728-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>
  73   <span class="keyword">const</span> <span class="identifier">step_storage_type</span> <span class="special">&amp;</span> <a class="link" href="adams_bashforth.html#idm45853740492112-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">&amp;</span> <a class="link" href="adams_bashforth.html#idm45853740488960-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">&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>
  76     <span class="keyword">void</span> <a class="link" href="adams_bashforth.html#idm45853740486096-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>
  77                     <span class="identifier">time_type</span><span class="special">)</span><span class="special">;</span>
  78   <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>
  79     <span class="keyword">void</span> <a class="link" href="adams_bashforth.html#idm45853740476688-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>
  80   <span class="keyword">void</span> <a class="link" href="adams_bashforth.html#idm45853740468368-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#idm45853740466512-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">&amp;</span> <a class="link" href="adams_bashforth.html#idm45853740463360-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">&amp;</span> <a class="link" href="adams_bashforth.html#idm45853740460224-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#idm45853740453968-bb">private member functions</a></span>
  86   <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>
  87     <span class="keyword">void</span> <a class="link" href="adams_bashforth.html#idm45853740453392-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">&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>
  88                       <span class="identifier">time_type</span><span class="special">)</span><span class="special">;</span>
  89   <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.html#idm45853740447136-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>
  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="idm45221366229552"></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="idm45221366227040"></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">&lt;</span> <span class="identifier">State</span> <span class="special">&gt;</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">&lt;</span> <span class="identifier">State</span> <span class="special">&gt;</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">&lt;</span> <span class="identifier">order_helper</span><span class="special">&lt;</span><span class="identifier">Steps</span><span class="special">&gt;</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">&gt;</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="idm45221366177840"></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="idm45853740457200-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">&amp;</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="idm45221366162816"></a><h3>
 173 <a name="idm45853740528464-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="idm45853740527904-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">&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="idm45853740524752-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="idm45853740517088-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="idm45853740511712-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>
 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">&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="idm45853740502352-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>
 276                <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>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="idm45853740495728-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">const</span> <span class="identifier">step_storage_type</span> <span class="special">&amp;</span> <a name="idm45853740492112-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">&amp;</span> <a name="idm45853740488960-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">&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>
 330   <span class="keyword">void</span> <a name="idm45853740486096-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">&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. <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">&lt;</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateIn<span class="special">&gt;</span>
 373   <span class="keyword">void</span> <a name="idm45853740476688-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 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="idm45853740468368-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="idm45853740466512-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">&amp;</span> <a name="idm45853740463360-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">&amp;</span> <a name="idm45853740460224-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="idm45221365967584"></a><h3>
 465 <a name="idm45853740453968-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">&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>
 468   <span class="keyword">void</span> <a name="idm45853740453392-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">&amp;</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">&amp;</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">&lt;</span><span class="keyword">typename</span> StateIn<span class="special">&gt;</span> <span class="keyword">bool</span> <a name="idm45853740447136-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>
 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 &#169; 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>
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