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  25 <div class="refentry">
  26 <a name="boost.numeric.odeint.velocity_verlet"></a><div class="titlepage"></div>
  27 <div class="refnamediv">
  28 <h2><span class="refentrytitle">Class template velocity_verlet</span></h2>
  29 <p>boost::numeric::odeint::velocity_verlet &#8212; The Velocity-Verlet 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/velocity_verlet_hpp.html" title="Header &lt;boost/numeric/odeint/stepper/velocity_verlet.hpp&gt;">boost/numeric/odeint/stepper/velocity_verlet.hpp</a>&gt;
  33
  34 </span><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> Coor<span class="special">,</span> <span class="keyword">typename</span> Velocity <span class="special">=</span> <span class="identifier">Coor</span><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> Acceleration <span class="special">=</span> <span class="identifier">Coor</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> TimeSq <span class="special">=</span> <span class="identifier">Time</span><span class="special">,</span>
  37          <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">Coor</span> <span class="special">&gt;</span><span class="special">::</span><span class="identifier">algebra_type</span><span class="special">,</span>
  38          <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">Coor</span> <span class="special">&gt;</span><span class="special">::</span><span class="identifier">operations_type</span><span class="special">,</span>
  39          <span class="keyword">typename</span> Resizer <span class="special">=</span> <span class="identifier">initially_resizer</span><span class="special">&gt;</span>
  40 <span class="keyword">class</span> <a class="link" href="velocity_verlet.html" title="Class template velocity_verlet">velocity_verlet</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">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.velocity_verlet.algebra_stepper_base_type"></a><span class="identifier">algebra_stepper_base_type</span><span class="special">;</span>
  44   <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.velocity_verlet.algebra_type"></a><span class="identifier">algebra_type</span><span class="special">;</span>
  45   <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.velocity_verlet.operations_type"></a><span class="identifier">operations_type</span><span class="special">;</span>
  46   <span class="keyword">typedef</span> <span class="identifier">Coor</span>                                          <a name="boost.numeric.odeint.velocity_verlet.coor_type"></a><span class="identifier">coor_type</span><span class="special">;</span>
  47   <span class="keyword">typedef</span> <span class="identifier">Velocity</span>                                      <a name="boost.numeric.odeint.velocity_verlet.velocity_type"></a><span class="identifier">velocity_type</span><span class="special">;</span>
  48   <span class="keyword">typedef</span> <span class="identifier">Acceleration</span>                                  <a name="boost.numeric.odeint.velocity_verlet.acceleration_type"></a><span class="identifier">acceleration_type</span><span class="special">;</span>
  49   <span class="keyword">typedef</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span> <span class="identifier">coor_type</span><span class="special">,</span> <span class="identifier">velocity_type</span> <span class="special">&gt;</span>         <a name="boost.numeric.odeint.velocity_verlet.state_type"></a><span class="identifier">state_type</span><span class="special">;</span>
  50   <span class="keyword">typedef</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span> <span class="identifier">velocity_type</span><span class="special">,</span> <span class="identifier">acceleration_type</span> <span class="special">&gt;</span> <a name="boost.numeric.odeint.velocity_verlet.deriv_type"></a><span class="identifier">deriv_type</span><span class="special">;</span>
  51   <span class="keyword">typedef</span> <span class="identifier">state_wrapper</span><span class="special">&lt;</span> <span class="identifier">acceleration_type</span> <span class="special">&gt;</span>            <a name="boost.numeric.odeint.velocity_verlet.wrapped_acceleration_type"></a><span class="identifier">wrapped_acceleration_type</span><span class="special">;</span>
  52   <span class="keyword">typedef</span> <span class="identifier">Value</span>                                         <a name="boost.numeric.odeint.velocity_verlet.value_type"></a><span class="identifier">value_type</span><span class="special">;</span>
  53   <span class="keyword">typedef</span> <span class="identifier">Time</span>                                          <a name="boost.numeric.odeint.velocity_verlet.time_type"></a><span class="identifier">time_type</span><span class="special">;</span>
  54   <span class="keyword">typedef</span> <span class="identifier">TimeSq</span>                                        <a name="boost.numeric.odeint.velocity_verlet.time_square_type"></a><span class="identifier">time_square_type</span><span class="special">;</span>
  55   <span class="keyword">typedef</span> <span class="identifier">Resizer</span>                                       <a name="boost.numeric.odeint.velocity_verlet.resizer_type"></a><span class="identifier">resizer_type</span><span class="special">;</span>
  56   <span class="keyword">typedef</span> <span class="identifier">stepper_tag</span>                                   <a name="boost.numeric.odeint.velocity_verlet.stepper_category"></a><span class="identifier">stepper_category</span><span class="special">;</span>
  57   <span class="keyword">typedef</span> <span class="keyword">unsigned</span> <span class="keyword">short</span>                                <a name="boost.numeric.odeint.velocity_verlet.order_type"></a><span class="identifier">order_type</span><span class="special">;</span>
  58
  59   <span class="comment">// <a class="link" href="velocity_verlet.html#boost.numeric.odeint.velocity_verletconstruct-copy-destruct">construct/copy/destruct</a></span>
  60   <a class="link" href="velocity_verlet.html#idm45853738341648-bb"><span class="identifier">velocity_verlet</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>
  61
  62   <span class="comment">// <a class="link" href="velocity_verlet.html#idm45853738398192-bb">public member functions</a></span>
  63   <span class="identifier">order_type</span> <a class="link" href="velocity_verlet.html#idm45853738397632-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>
  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="velocity_verlet.html#idm45853738394816-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>
  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> StateInOut<span class="special">&gt;</span>
  67     <span class="keyword">void</span> <a class="link" href="velocity_verlet.html#idm45853738386256-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>
  68   <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> CoorIn<span class="special">,</span> <span class="keyword">typename</span> VelocityIn<span class="special">,</span>
  69            <span class="keyword">typename</span> AccelerationIn<span class="special">,</span> <span class="keyword">typename</span> CoorOut<span class="special">,</span> <span class="keyword">typename</span> VelocityOut<span class="special">,</span>
  70            <span class="keyword">typename</span> AccelerationOut<span class="special">&gt;</span>
  71     <span class="keyword">void</span> <a class="link" href="velocity_verlet.html#idm45853738377696-bb"><span class="identifier">do_step</span></a><span class="special">(</span><span class="identifier">System</span><span class="special">,</span> <span class="identifier">CoorIn</span> <span class="keyword">const</span> <span class="special">&amp;</span><span class="special">,</span> <span class="identifier">VelocityIn</span> <span class="keyword">const</span> <span class="special">&amp;</span><span class="special">,</span>
  72                  <span class="identifier">AccelerationIn</span> <span class="keyword">const</span> <span class="special">&amp;</span><span class="special">,</span> <span class="identifier">CoorOut</span> <span class="special">&amp;</span><span class="special">,</span> <span class="identifier">VelocityOut</span> <span class="special">&amp;</span><span class="special">,</span>
  73                  <span class="identifier">AccelerationOut</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>
  74   <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> StateIn<span class="special">&gt;</span> <span class="keyword">void</span> <a class="link" href="velocity_verlet.html#idm45853738363152-bb"><span class="identifier">adjust_size</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>
  75   <span class="keyword">void</span> <a class="link" href="velocity_verlet.html#idm45853738359536-bb"><span class="identifier">reset</span></a><span class="special">(</span><span class="keyword">void</span><span class="special">)</span><span class="special">;</span>
  76   <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> AccelerationIn<span class="special">&gt;</span> <span class="keyword">void</span> <a class="link" href="velocity_verlet.html#idm45853738357152-bb"><span class="identifier">initialize</span></a><span class="special">(</span><span class="keyword">const</span> <span class="identifier">AccelerationIn</span> <span class="special">&amp;</span><span class="special">)</span><span class="special">;</span>
  77   <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> CoorIn<span class="special">,</span> <span class="keyword">typename</span> VelocityIn<span class="special">&gt;</span>
  78     <span class="keyword">void</span> <a class="link" href="velocity_verlet.html#idm45853738354032-bb"><span class="identifier">initialize</span></a><span class="special">(</span><span class="identifier">System</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">CoorIn</span> <span class="special">&amp;</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">VelocityIn</span> <span class="special">&amp;</span><span class="special">,</span> <span class="identifier">time_type</span><span class="special">)</span><span class="special">;</span>
  79   <span class="keyword">bool</span> <a class="link" href="velocity_verlet.html#idm45853738344624-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>
  80
  81   <span class="comment">// <a class="link" href="velocity_verlet.html#idm45853738338416-bb">private member functions</a></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> CoorIn<span class="special">,</span> <span class="keyword">typename</span> VelocityIn<span class="special">&gt;</span>
  83     <span class="keyword">void</span> <a class="link" href="velocity_verlet.html#idm45853738337840-bb"><span class="identifier">initialize_acc</span></a><span class="special">(</span><span class="identifier">System</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">CoorIn</span> <span class="special">&amp;</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">VelocityIn</span> <span class="special">&amp;</span><span class="special">,</span> <span class="identifier">time_type</span><span class="special">)</span><span class="special">;</span>
  84   <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>
  85     <span class="keyword">void</span> <a class="link" href="velocity_verlet.html#idm45853738332272-bb"><span class="identifier">do_step_v1</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>
  86   <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="velocity_verlet.html#idm45853738327264-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>
  87   <span class="identifier">acceleration_type</span> <span class="special">&amp;</span> <a class="link" href="velocity_verlet.html#idm45853738324880-bb"><span class="identifier">get_current_acc</span></a><span class="special">(</span><span class="keyword">void</span><span class="special">)</span><span class="special">;</span>
  88   <span class="keyword">const</span> <span class="identifier">acceleration_type</span> <span class="special">&amp;</span> <a class="link" href="velocity_verlet.html#idm45853738323344-bb"><span class="identifier">get_current_acc</span></a><span class="special">(</span><span class="keyword">void</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
  89   <span class="identifier">acceleration_type</span> <span class="special">&amp;</span> <a class="link" href="velocity_verlet.html#idm45853738321520-bb"><span class="identifier">get_old_acc</span></a><span class="special">(</span><span class="keyword">void</span><span class="special">)</span><span class="special">;</span>
  90   <span class="keyword">const</span> <span class="identifier">acceleration_type</span> <span class="special">&amp;</span> <a class="link" href="velocity_verlet.html#idm45853738319984-bb"><span class="identifier">get_old_acc</span></a><span class="special">(</span><span class="keyword">void</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
  91   <span class="keyword">void</span> <a class="link" href="velocity_verlet.html#idm45853738318160-bb"><span class="identifier">toggle_current_acc</span></a><span class="special">(</span><span class="keyword">void</span><span class="special">)</span><span class="special">;</span>
  92
  93   <span class="comment">// public data members</span>
  94   <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>
  95 <span class="special">}</span><span class="special">;</span></pre></div>
  96 <div class="refsect1">
  97 <a name="idm45221353693056"></a><h2>Description</h2>
  98 <p><a href="http://en.wikipedia.org/wiki/Verlet_integration" target="_top">The Velocity-Verlet algorithm</a> is a method for simulation of molecular dynamics systems. It solves the ODE a=f(r,v',t) where r are the coordinates, v are the velocities and a are the accelerations, hence v = dr/dt, a=dv/dt.</p>
  99 <p>
 100 </p>
 101 <div class="refsect2">
 102 <a name="idm45221353691312"></a><h3>Template Parameters</h3>
 103 <div class="orderedlist"><ol class="orderedlist" type="1">
 104 <li class="listitem">
 105 <pre class="literallayout"><span class="keyword">typename</span> Coor</pre>
 106 <p>The type representing the coordinates. </p>
 107 </li>
 108 <li class="listitem">
 109 <pre class="literallayout"><span class="keyword">typename</span> Velocity <span class="special">=</span> <span class="identifier">Coor</span></pre>
 110 <p>The type representing the velocities. </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 type value type. </p>
 115 </li>
 116 <li class="listitem">
 117 <pre class="literallayout"><span class="keyword">typename</span> Acceleration <span class="special">=</span> <span class="identifier">Coor</span></pre>
 118 <p>The type representing the acceleration. </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> TimeSq <span class="special">=</span> <span class="identifier">Time</span></pre>
 126 <p>The time representing the square of the time. </p>
 127 </li>
 128 <li class="listitem">
 129 <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">Coor</span> <span class="special">&gt;</span><span class="special">::</span><span class="identifier">algebra_type</span></pre>
 130 <p>The algebra. </p>
 131 </li>
 132 <li class="listitem">
 133 <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">Coor</span> <span class="special">&gt;</span><span class="special">::</span><span class="identifier">operations_type</span></pre>
 134 <p>The operations type. </p>
 135 </li>
 136 <li class="listitem">
 137 <pre class="literallayout"><span class="keyword">typename</span> Resizer <span class="special">=</span> <span class="identifier">initially_resizer</span></pre>
 138 <p>The resizer policy type. </p>
 139 </li>
 140 </ol></div>
 141 </div>
 142 <div class="refsect2">
 143 <a name="idm45221353654336"></a><h3>
 144 <a name="boost.numeric.odeint.velocity_verletconstruct-copy-destruct"></a><code class="computeroutput">velocity_verlet</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="idm45853738341648-bb"></a><span class="identifier">velocity_verlet</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="velocity_verlet.html" title="Class template velocity_verlet">velocity_verlet</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="idm45221353639248"></a><h3>
 173 <a name="idm45853738398192-bb"></a><code class="computeroutput">velocity_verlet</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="idm45853738397632-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>
 177 <p>
 178 </p>
 179 <div class="variablelist"><table border="0" class="variablelist compact">
 180 <colgroup>
 181 <col align="left" valign="top">
 182 <col>
 183 </colgroup>
 184 <tbody><tr>
 185 <td><p><span class="term">Returns:</span></p></td>
 186 <td><p>Returns the order of the stepper. </p></td>
 187 </tr></tbody>
 188 </table></div>
 189 </li>
 190 <li class="listitem">
 191 <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>
 192   <span class="keyword">void</span> <a name="idm45853738394816-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>It can be used like </p>
 193 <pre class="programlisting"><span class="identifier">pair</span><span class="special">&lt;</span> <span class="identifier">coordinates</span> <span class="special">,</span> <span class="identifier">velocities</span> <span class="special">&gt;</span> <span class="identifier">state</span><span class="special">;</span>
 194 <span class="identifier">stepper</span><span class="special">.</span><span class="identifier">do_step</span><span class="special">(</span> <span class="identifier">sys</span> <span class="special">,</span> <span class="identifier">x</span> <span class="special">,</span> <span class="identifier">t</span> <span class="special">,</span> <span class="identifier">dt</span> <span class="special">)</span><span class="special">;</span>
 195 </pre>
 196 <p>
 197 </p>
 198 <div class="variablelist"><table border="0" class="variablelist compact">
 199 <colgroup>
 200 <col align="left" valign="top">
 201 <col>
 202 </colgroup>
 203 <tbody><tr>
 204 <td><p><span class="term">Parameters:</span></p></td>
 205 <td><div class="variablelist"><table border="0" class="variablelist compact">
 206 <colgroup>
 207 <col align="left" valign="top">
 208 <col>
 209 </colgroup>
 210 <tbody>
 211 <tr>
 212 <td><p><span class="term"><code class="computeroutput">dt</code></span></p></td>
 213 <td><p>The step size. </p></td>
 214 </tr>
 215 <tr>
 216 <td><p><span class="term"><code class="computeroutput">system</code></span></p></td>
 217 <td><p>The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Second Order System concept. </p></td>
 218 </tr>
 219 <tr>
 220 <td><p><span class="term"><code class="computeroutput">t</code></span></p></td>
 221 <td><p>The value of the time, at which the step should be performed. </p></td>
 222 </tr>
 223 <tr>
 224 <td><p><span class="term"><code class="computeroutput">x</code></span></p></td>
 225 <td><p>The state of the ODE which should be solved. The state is pair of Coor and Velocity. </p></td>
 226 </tr>
 227 </tbody>
 228 </table></div></td>
 229 </tr></tbody>
 230 </table></div>
 231 </li>
 232 <li class="listitem">
 233 <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>
 234   <span class="keyword">void</span> <a name="idm45853738386256-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>This method performs one step. It transforms the result in-place. <p>It can be used like </p>
 235 <pre class="programlisting"><span class="identifier">pair</span><span class="special">&lt;</span> <span class="identifier">coordinates</span> <span class="special">,</span> <span class="identifier">velocities</span> <span class="special">&gt;</span> <span class="identifier">state</span><span class="special">;</span>
 236 <span class="identifier">stepper</span><span class="special">.</span><span class="identifier">do_step</span><span class="special">(</span> <span class="identifier">sys</span> <span class="special">,</span> <span class="identifier">x</span> <span class="special">,</span> <span class="identifier">t</span> <span class="special">,</span> <span class="identifier">dt</span> <span class="special">)</span><span class="special">;</span>
 237 </pre>
 238 <p>
 239 </p>
 240 <div class="variablelist"><table border="0" class="variablelist compact">
 241 <colgroup>
 242 <col align="left" valign="top">
 243 <col>
 244 </colgroup>
 245 <tbody><tr>
 246 <td><p><span class="term">Parameters:</span></p></td>
 247 <td><div class="variablelist"><table border="0" class="variablelist compact">
 248 <colgroup>
 249 <col align="left" valign="top">
 250 <col>
 251 </colgroup>
 252 <tbody>
 253 <tr>
 254 <td><p><span class="term"><code class="computeroutput">dt</code></span></p></td>
 255 <td><p>The step size. </p></td>
 256 </tr>
 257 <tr>
 258 <td><p><span class="term"><code class="computeroutput">system</code></span></p></td>
 259 <td><p>The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Second Order System concept. </p></td>
 260 </tr>
 261 <tr>
 262 <td><p><span class="term"><code class="computeroutput">t</code></span></p></td>
 263 <td><p>The value of the time, at which the step should be performed. </p></td>
 264 </tr>
 265 <tr>
 266 <td><p><span class="term"><code class="computeroutput">x</code></span></p></td>
 267 <td><p>The state of the ODE which should be solved. The state is pair of Coor and Velocity. </p></td>
 268 </tr>
 269 </tbody>
 270 </table></div></td>
 271 </tr></tbody>
 272 </table></div>
 273 </li>
 274 <li class="listitem">
 275 <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> CoorIn<span class="special">,</span> <span class="keyword">typename</span> VelocityIn<span class="special">,</span>
 276          <span class="keyword">typename</span> AccelerationIn<span class="special">,</span> <span class="keyword">typename</span> CoorOut<span class="special">,</span> <span class="keyword">typename</span> VelocityOut<span class="special">,</span>
 277          <span class="keyword">typename</span> AccelerationOut<span class="special">&gt;</span>
 278   <span class="keyword">void</span> <a name="idm45853738377696-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">CoorIn</span> <span class="keyword">const</span> <span class="special">&amp;</span> qin<span class="special">,</span> <span class="identifier">VelocityIn</span> <span class="keyword">const</span> <span class="special">&amp;</span> pin<span class="special">,</span>
 279                <span class="identifier">AccelerationIn</span> <span class="keyword">const</span> <span class="special">&amp;</span> ain<span class="special">,</span> <span class="identifier">CoorOut</span> <span class="special">&amp;</span> qout<span class="special">,</span>
 280                <span class="identifier">VelocityOut</span> <span class="special">&amp;</span> pout<span class="special">,</span> <span class="identifier">AccelerationOut</span> <span class="special">&amp;</span> aout<span class="special">,</span> <span class="identifier">time_type</span> t<span class="special">,</span>
 281                <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. Additionally to the other methods the coordinates, velocities and accelerations are passed directly to do_step and they are transformed out-of-place. <p>It can be used like </p>
 282 <pre class="programlisting"><span class="identifier">coordinates</span> <span class="identifier">qin</span> <span class="special">,</span> <span class="identifier">qout</span><span class="special">;</span>
 283 <span class="identifier">velocities</span> <span class="identifier">pin</span> <span class="special">,</span> <span class="identifier">pout</span><span class="special">;</span>
 284 <span class="identifier">accelerations</span> <span class="identifier">ain</span><span class="special">,</span> <span class="identifier">aout</span><span class="special">;</span>
 285 <span class="identifier">stepper</span><span class="special">.</span><span class="identifier">do_step</span><span class="special">(</span> <span class="identifier">sys</span> <span class="special">,</span> <span class="identifier">qin</span> <span class="special">,</span> <span class="identifier">pin</span> <span class="special">,</span> <span class="identifier">ain</span> <span class="special">,</span> <span class="identifier">qout</span> <span class="special">,</span> <span class="identifier">pout</span> <span class="special">,</span> <span class="identifier">aout</span> <span class="special">,</span> <span class="identifier">t</span> <span class="special">,</span> <span class="identifier">dt</span> <span class="special">)</span><span class="special">;</span>
 286 </pre>
 287 <p>
 288 </p>
 289 <div class="variablelist"><table border="0" class="variablelist compact">
 290 <colgroup>
 291 <col align="left" valign="top">
 292 <col>
 293 </colgroup>
 294 <tbody><tr>
 295 <td><p><span class="term">Parameters:</span></p></td>
 296 <td><div class="variablelist"><table border="0" class="variablelist compact">
 297 <colgroup>
 298 <col align="left" valign="top">
 299 <col>
 300 </colgroup>
 301 <tbody>
 302 <tr>
 303 <td><p><span class="term"><code class="computeroutput">dt</code></span></p></td>
 304 <td><p>The step size. </p></td>
 305 </tr>
 306 <tr>
 307 <td><p><span class="term"><code class="computeroutput">system</code></span></p></td>
 308 <td><p>The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Second Order System concept. </p></td>
 309 </tr>
 310 <tr>
 311 <td><p><span class="term"><code class="computeroutput">t</code></span></p></td>
 312 <td><p>The value of the time, at which the step should be performed. </p></td>
 313 </tr>
 314 </tbody>
 315 </table></div></td>
 316 </tr></tbody>
 317 </table></div>
 318 </li>
 319 <li class="listitem">
 320 <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">void</span> <a name="idm45853738363152-bb"></a><span class="identifier">adjust_size</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>Adjust the size of all temporaries in the stepper manually. <p>
 321 </p>
 322 <div class="variablelist"><table border="0" class="variablelist compact">
 323 <colgroup>
 324 <col align="left" valign="top">
 325 <col>
 326 </colgroup>
 327 <tbody><tr>
 328 <td><p><span class="term">Parameters:</span></p></td>
 329 <td><div class="variablelist"><table border="0" class="variablelist compact">
 330 <colgroup>
 331 <col align="left" valign="top">
 332 <col>
 333 </colgroup>
 334 <tbody><tr>
 335 <td><p><span class="term"><code class="computeroutput">x</code></span></p></td>
 336 <td><p>A state from which the size of the temporaries to be resized is deduced. </p></td>
 337 </tr></tbody>
 338 </table></div></td>
 339 </tr></tbody>
 340 </table></div>
 341 </li>
 342 <li class="listitem">
 343 <pre class="literallayout"><span class="keyword">void</span> <a name="idm45853738359536-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 state of this stepper. After calling this method it is safe to use all <code class="computeroutput">do_step</code> method without explicitly initializing the stepper. </li>
 344 <li class="listitem">
 345 <pre class="literallayout"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> AccelerationIn<span class="special">&gt;</span> <span class="keyword">void</span> <a name="idm45853738357152-bb"></a><span class="identifier">initialize</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">AccelerationIn</span> <span class="special">&amp;</span> ain<span class="special">)</span><span class="special">;</span></pre>Initializes the internal state of the stepper. <p>
 346 </p>
 347 </li>
 348 <li class="listitem">
 349 <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> CoorIn<span class="special">,</span> <span class="keyword">typename</span> VelocityIn<span class="special">&gt;</span>
 350   <span class="keyword">void</span> <a name="idm45853738354032-bb"></a><span class="identifier">initialize</span><span class="special">(</span><span class="identifier">System</span> system<span class="special">,</span> <span class="keyword">const</span> <span class="identifier">CoorIn</span> <span class="special">&amp;</span> qin<span class="special">,</span> <span class="keyword">const</span> <span class="identifier">VelocityIn</span> <span class="special">&amp;</span> pin<span class="special">,</span>
 351                   <span class="identifier">time_type</span> t<span class="special">)</span><span class="special">;</span></pre>Initializes the internal state of the stepper. <p>This method is equivalent to </p>
 352 <pre class="programlisting"><span class="identifier">Acceleration</span> <span class="identifier">a</span><span class="special">;</span>
 353 <span class="identifier">system</span><span class="special">(</span> <span class="identifier">qin</span> <span class="special">,</span> <span class="identifier">pin</span> <span class="special">,</span> <span class="identifier">a</span> <span class="special">,</span> <span class="identifier">t</span> <span class="special">)</span><span class="special">;</span>
 354 <span class="identifier">stepper</span><span class="special">.</span><span class="identifier">initialize</span><span class="special">(</span> <span class="identifier">a</span> <span class="special">)</span><span class="special">;</span>
 355 </pre>
 356 <p>
 357 </p>
 358 <div class="variablelist"><table border="0" class="variablelist compact">
 359 <colgroup>
 360 <col align="left" valign="top">
 361 <col>
 362 </colgroup>
 363 <tbody><tr>
 364 <td><p><span class="term">Parameters:</span></p></td>
 365 <td><div class="variablelist"><table border="0" class="variablelist compact">
 366 <colgroup>
 367 <col align="left" valign="top">
 368 <col>
 369 </colgroup>
 370 <tbody>
 371 <tr>
 372 <td><p><span class="term"><code class="computeroutput">pin</code></span></p></td>
 373 <td><p>The current velocities of the ODE. </p></td>
 374 </tr>
 375 <tr>
 376 <td><p><span class="term"><code class="computeroutput">qin</code></span></p></td>
 377 <td><p>The current coordinates of the ODE. </p></td>
 378 </tr>
 379 <tr>
 380 <td><p><span class="term"><code class="computeroutput">system</code></span></p></td>
 381 <td><p>The system function for the next calls of <code class="computeroutput">do_step</code>. </p></td>
 382 </tr>
 383 <tr>
 384 <td><p><span class="term"><code class="computeroutput">t</code></span></p></td>
 385 <td><p>The current time of the ODE. </p></td>
 386 </tr>
 387 </tbody>
 388 </table></div></td>
 389 </tr></tbody>
 390 </table></div>
 391 </li>
 392 <li class="listitem">
 393 <pre class="literallayout"><span class="keyword">bool</span> <a name="idm45853738344624-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>
 394 <p>
 395 </p>
 396 <div class="variablelist"><table border="0" class="variablelist compact">
 397 <colgroup>
 398 <col align="left" valign="top">
 399 <col>
 400 </colgroup>
 401 <tbody><tr>
 402 <td><p><span class="term">Returns:</span></p></td>
 403 <td><p>Returns if the stepper is initialized. </p></td>
 404 </tr></tbody>
 405 </table></div>
 406 </li>
 407 </ol></div>
 408 </div>
 409 <div class="refsect2">
 410 <a name="idm45221353422048"></a><h3>
 411 <a name="idm45853738338416-bb"></a><code class="computeroutput">velocity_verlet</code> private member functions</h3>
 412 <div class="orderedlist"><ol class="orderedlist" type="1">
 413 <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> CoorIn<span class="special">,</span> <span class="keyword">typename</span> VelocityIn<span class="special">&gt;</span>
 414   <span class="keyword">void</span> <a name="idm45853738337840-bb"></a><span class="identifier">initialize_acc</span><span class="special">(</span><span class="identifier">System</span> system<span class="special">,</span> <span class="keyword">const</span> <span class="identifier">CoorIn</span> <span class="special">&amp;</span> qin<span class="special">,</span>
 415                       <span class="keyword">const</span> <span class="identifier">VelocityIn</span> <span class="special">&amp;</span> pin<span class="special">,</span> <span class="identifier">time_type</span> t<span class="special">)</span><span class="special">;</span></pre></li>
 416 <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>
 417   <span class="keyword">void</span> <a name="idm45853738332272-bb"></a><span class="identifier">do_step_v1</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>
 418 <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="idm45853738327264-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>
 419 <li class="listitem"><pre class="literallayout"><span class="identifier">acceleration_type</span> <span class="special">&amp;</span> <a name="idm45853738324880-bb"></a><span class="identifier">get_current_acc</span><span class="special">(</span><span class="keyword">void</span><span class="special">)</span><span class="special">;</span></pre></li>
 420 <li class="listitem"><pre class="literallayout"><span class="keyword">const</span> <span class="identifier">acceleration_type</span> <span class="special">&amp;</span> <a name="idm45853738323344-bb"></a><span class="identifier">get_current_acc</span><span class="special">(</span><span class="keyword">void</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span></pre></li>
 421 <li class="listitem"><pre class="literallayout"><span class="identifier">acceleration_type</span> <span class="special">&amp;</span> <a name="idm45853738321520-bb"></a><span class="identifier">get_old_acc</span><span class="special">(</span><span class="keyword">void</span><span class="special">)</span><span class="special">;</span></pre></li>
 422 <li class="listitem"><pre class="literallayout"><span class="keyword">const</span> <span class="identifier">acceleration_type</span> <span class="special">&amp;</span> <a name="idm45853738319984-bb"></a><span class="identifier">get_old_acc</span><span class="special">(</span><span class="keyword">void</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span></pre></li>
 423 <li class="listitem"><pre class="literallayout"><span class="keyword">void</span> <a name="idm45853738318160-bb"></a><span class="identifier">toggle_current_acc</span><span class="special">(</span><span class="keyword">void</span><span class="special">)</span><span class="special">;</span></pre></li>
 424 </ol></div>
 425 </div>
 426 </div>
 427 </div>
 428 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 429 <td align="left"></td>
 430 <td align="right"><div class="copyright-footer">Copyright &#169; 2009-2015 Karsten Ahnert and Mario Mulansky<p>
 431         Distributed under the Boost Software License, Version 1.0. (See accompanying
 432         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>)
 433       </p>
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