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| <div class="refentry"> |
| <a name="boost.numeric.odeint.adams_bashforth_moulton"></a><div class="titlepage"></div> |
| <div class="refnamediv"> |
| <h2><span class="refentrytitle">Class template adams_bashforth_moulton</span></h2> |
| <p>boost::numeric::odeint::adams_bashforth_moulton — The Adams-Bashforth-Moulton multistep algorithm. </p> |
| </div> |
| <h2 xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="refsynopsisdiv-title">Synopsis</h2> |
| <div xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="refsynopsisdiv"><pre class="synopsis"><span class="comment">// In header: <<a class="link" href="../../../header/boost/numeric/odeint/stepper/adams_bashforth_moulton_hpp.html" title="Header <boost/numeric/odeint/stepper/adams_bashforth_moulton.hpp>">boost/numeric/odeint/stepper/adams_bashforth_moulton.hpp</a>> |
| |
| </span><span class="keyword">template</span><span class="special"><</span><span class="identifier">size_t</span> Steps<span class="special">,</span> <span class="keyword">typename</span> State<span class="special">,</span> <span class="keyword">typename</span> Value <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span> |
| <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> |
| <span class="keyword">typename</span> Algebra <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">algebra_dispatcher</span><span class="special"><</span> <span class="identifier">State</span> <span class="special">></span><span class="special">::</span><span class="identifier">algebra_type</span><span class="special">,</span> |
| <span class="keyword">typename</span> Operations <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">operations_dispatcher</span><span class="special"><</span> <span class="identifier">State</span> <span class="special">></span><span class="special">::</span><span class="identifier">operations_type</span><span class="special">,</span> |
| <span class="keyword">typename</span> Resizer <span class="special">=</span> <span class="identifier">initially_resizer</span><span class="special">,</span> |
| <span class="keyword">typename</span> InitializingStepper <span class="special">=</span> <a class="link" href="runge_kutta4.html" title="Class template runge_kutta4">runge_kutta4</a><span class="special"><</span> <span class="identifier">State</span> <span class="special">,</span> <span class="identifier">Value</span> <span class="special">,</span> <span class="identifier">Deriv</span> <span class="special">,</span> <span class="identifier">Time</span> <span class="special">,</span> <span class="identifier">Algebra</span> <span class="special">,</span> <span class="identifier">Operations</span><span class="special">,</span> <span class="identifier">Resizer</span> <span class="special">></span> <span class="special">></span> |
| <span class="keyword">class</span> <a class="link" href="adams_bashforth_moulton.html" title="Class template adams_bashforth_moulton">adams_bashforth_moulton</a> <span class="special">{</span> |
| <span class="keyword">public</span><span class="special">:</span> |
| <span class="comment">// types</span> |
| <span class="keyword">typedef</span> <span class="identifier">State</span> <a name="boost.numeric.odeint.adams_bashforth_moulton.state_type"></a><span class="identifier">state_type</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">state_wrapper</span><span class="special"><</span> <span class="identifier">state_type</span> <span class="special">></span> <a name="boost.numeric.odeint.adams_bashforth_moulton.wrapped_state_type"></a><span class="identifier">wrapped_state_type</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">Value</span> <a name="boost.numeric.odeint.adams_bashforth_moulton.value_type"></a><span class="identifier">value_type</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">Deriv</span> <a name="boost.numeric.odeint.adams_bashforth_moulton.deriv_type"></a><span class="identifier">deriv_type</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">state_wrapper</span><span class="special"><</span> <span class="identifier">deriv_type</span> <span class="special">></span> <a name="boost.numeric.odeint.adams_bashforth_moulton.wrapped_deriv_type"></a><span class="identifier">wrapped_deriv_type</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">Time</span> <a name="boost.numeric.odeint.adams_bashforth_moulton.time_type"></a><span class="identifier">time_type</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">Algebra</span> <a name="boost.numeric.odeint.adams_bashforth_moulton.algebra_type"></a><span class="identifier">algebra_type</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">Operations</span> <a name="boost.numeric.odeint.adams_bashforth_moulton.operations_type"></a><span class="identifier">operations_type</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">Resizer</span> <a name="boost.numeric.odeint.adams_bashforth_moulton.resizer_type"></a><span class="identifier">resizer_type</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">stepper_tag</span> <a name="boost.numeric.odeint.adams_bashforth_moulton.stepper_category"></a><span class="identifier">stepper_category</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">InitializingStepper</span> <a name="boost.numeric.odeint.adams_bashforth_moulton.initializing_stepper_type"></a><span class="identifier">initializing_stepper_type</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="keyword">unsigned</span> <span class="keyword">short</span> <a name="boost.numeric.odeint.adams_bashforth_moulton.order_type"></a><span class="identifier">order_type</span><span class="special">;</span> |
| |
| <span class="comment">// <a class="link" href="adams_bashforth_moulton.html#boost.numeric.odeint.adams_bashforth_moultonconstruct-copy-destruct">construct/copy/destruct</a></span> |
| <a class="link" href="adams_bashforth_moulton.html#idp39982528-bb"><span class="identifier">adams_bashforth_moulton</span></a><span class="special">(</span><span class="keyword">void</span><span class="special">)</span><span class="special">;</span> |
| <a class="link" href="adams_bashforth_moulton.html#idp39984528-bb"><span class="identifier">adams_bashforth_moulton</span></a><span class="special">(</span><span class="keyword">const</span> <span class="identifier">algebra_type</span> <span class="special">&</span><span class="special">)</span><span class="special">;</span> |
| |
| <span class="comment">// <a class="link" href="adams_bashforth_moulton.html#idp39927888-bb">public member functions</a></span> |
| <span class="identifier">order_type</span> <a class="link" href="adams_bashforth_moulton.html#idp39928448-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> |
| <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateInOut<span class="special">></span> |
| <span class="keyword">void</span> <a class="link" href="adams_bashforth_moulton.html#idp39931440-bb"><span class="identifier">do_step</span></a><span class="special">(</span><span class="identifier">System</span><span class="special">,</span> <span class="identifier">StateInOut</span> <span class="special">&</span><span class="special">,</span> <span class="identifier">time_type</span><span class="special">,</span> <span class="identifier">time_type</span><span class="special">)</span><span class="special">;</span> |
| <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateInOut<span class="special">></span> |
| <span class="keyword">void</span> <a class="link" href="adams_bashforth_moulton.html#idp39939104-bb"><span class="identifier">do_step</span></a><span class="special">(</span><span class="identifier">System</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">StateInOut</span> <span class="special">&</span><span class="special">,</span> <span class="identifier">time_type</span><span class="special">,</span> <span class="identifier">time_type</span><span class="special">)</span><span class="special">;</span> |
| <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateIn<span class="special">,</span> <span class="keyword">typename</span> StateOut<span class="special">></span> |
| <span class="keyword">void</span> <a class="link" href="adams_bashforth_moulton.html#idp39944480-bb"><span class="identifier">do_step</span></a><span class="special">(</span><span class="identifier">System</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">StateIn</span> <span class="special">&</span><span class="special">,</span> <span class="identifier">time_type</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">StateOut</span> <span class="special">&</span><span class="special">,</span> |
| <span class="identifier">time_type</span><span class="special">)</span><span class="special">;</span> |
| <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateIn<span class="special">,</span> <span class="keyword">typename</span> StateOut<span class="special">></span> |
| <span class="keyword">void</span> <a class="link" href="adams_bashforth_moulton.html#idp39953840-bb"><span class="identifier">do_step</span></a><span class="special">(</span><span class="identifier">System</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">StateIn</span> <span class="special">&</span><span class="special">,</span> <span class="identifier">time_type</span><span class="special">,</span> <span class="identifier">StateOut</span> <span class="special">&</span><span class="special">,</span> <span class="identifier">time_type</span><span class="special">)</span><span class="special">;</span> |
| <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> StateType<span class="special">></span> <span class="keyword">void</span> <a class="link" href="adams_bashforth_moulton.html#idp39960464-bb"><span class="identifier">adjust_size</span></a><span class="special">(</span><span class="keyword">const</span> <span class="identifier">StateType</span> <span class="special">&</span><span class="special">)</span><span class="special">;</span> |
| <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> ExplicitStepper<span class="special">,</span> <span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateIn<span class="special">></span> |
| <span class="keyword">void</span> <a class="link" href="adams_bashforth_moulton.html#idp39964080-bb"><span class="identifier">initialize</span></a><span class="special">(</span><span class="identifier">ExplicitStepper</span><span class="special">,</span> <span class="identifier">System</span><span class="special">,</span> <span class="identifier">StateIn</span> <span class="special">&</span><span class="special">,</span> <span class="identifier">time_type</span> <span class="special">&</span><span class="special">,</span> |
| <span class="identifier">time_type</span><span class="special">)</span><span class="special">;</span> |
| <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateIn<span class="special">></span> |
| <span class="keyword">void</span> <a class="link" href="adams_bashforth_moulton.html#idp39973936-bb"><span class="identifier">initialize</span></a><span class="special">(</span><span class="identifier">System</span><span class="special">,</span> <span class="identifier">StateIn</span> <span class="special">&</span><span class="special">,</span> <span class="identifier">time_type</span> <span class="special">&</span><span class="special">,</span> <span class="identifier">time_type</span><span class="special">)</span><span class="special">;</span> |
| |
| <span class="comment">// <a class="link" href="adams_bashforth_moulton.html#idp39987472-bb">private member functions</a></span> |
| <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateInOut<span class="special">></span> |
| <span class="keyword">void</span> <a class="link" href="adams_bashforth_moulton.html#idp39988048-bb"><span class="identifier">do_step_impl1</span></a><span class="special">(</span><span class="identifier">System</span><span class="special">,</span> <span class="identifier">StateInOut</span> <span class="special">&</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> |
| <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateIn<span class="special">,</span> <span class="keyword">typename</span> StateInOut<span class="special">></span> |
| <span class="keyword">void</span> <a class="link" href="adams_bashforth_moulton.html#idp39993056-bb"><span class="identifier">do_step_impl2</span></a><span class="special">(</span><span class="identifier">System</span><span class="special">,</span> <span class="identifier">StateIn</span> <span class="keyword">const</span> <span class="special">&</span><span class="special">,</span> <span class="identifier">time_type</span><span class="special">,</span> <span class="identifier">StateInOut</span> <span class="special">&</span><span class="special">,</span> |
| <span class="identifier">time_type</span><span class="special">)</span><span class="special">;</span> |
| <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> StateIn<span class="special">></span> <span class="keyword">bool</span> <a class="link" href="adams_bashforth_moulton.html#idp39999312-bb"><span class="identifier">resize_impl</span></a><span class="special">(</span><span class="keyword">const</span> <span class="identifier">StateIn</span> <span class="special">&</span><span class="special">)</span><span class="special">;</span> |
| |
| <span class="comment">// public data members</span> |
| <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> |
| <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> |
| <span class="special">}</span><span class="special">;</span></pre></div> |
| <div class="refsect1"> |
| <a name="idp109383472"></a><h2>Description</h2> |
| <p>The Adams-Bashforth method is a multi-step predictor-corrector algorithm with configurable step number. The step number is specified as template parameter Steps and it then uses the result from the previous Steps steps. See also <a href="http://en.wikipedia.org/wiki/Linear_multistep_method" target="_top">en.wikipedia.org/wiki/Linear_multistep_method</a>. Currently, a maximum of Steps=8 is supported. The method is explicit and fulfills the Stepper concept. Step size control or continuous output are not provided.</p> |
| <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> |
| <p> |
| </p> |
| <div class="refsect2"> |
| <a name="idp109386000"></a><h3>Template Parameters</h3> |
| <div class="orderedlist"><ol class="orderedlist" type="1"> |
| <li class="listitem"> |
| <pre class="literallayout"><span class="identifier">size_t</span> Steps</pre> |
| <p>The number of steps (maximal 8). </p> |
| </li> |
| <li class="listitem"> |
| <pre class="literallayout"><span class="keyword">typename</span> State</pre> |
| <p>The state type. </p> |
| </li> |
| <li class="listitem"> |
| <pre class="literallayout"><span class="keyword">typename</span> Value <span class="special">=</span> <span class="keyword">double</span></pre> |
| <p>The value type. </p> |
| </li> |
| <li class="listitem"> |
| <pre class="literallayout"><span class="keyword">typename</span> Deriv <span class="special">=</span> <span class="identifier">State</span></pre> |
| <p>The type representing the time derivative of the state. </p> |
| </li> |
| <li class="listitem"> |
| <pre class="literallayout"><span class="keyword">typename</span> Time <span class="special">=</span> <span class="identifier">Value</span></pre> |
| <p>The time representing the independent variable - the time. </p> |
| </li> |
| <li class="listitem"> |
| <pre class="literallayout"><span class="keyword">typename</span> Algebra <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">algebra_dispatcher</span><span class="special"><</span> <span class="identifier">State</span> <span class="special">></span><span class="special">::</span><span class="identifier">algebra_type</span></pre> |
| <p>The algebra type. </p> |
| </li> |
| <li class="listitem"> |
| <pre class="literallayout"><span class="keyword">typename</span> Operations <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">operations_dispatcher</span><span class="special"><</span> <span class="identifier">State</span> <span class="special">></span><span class="special">::</span><span class="identifier">operations_type</span></pre> |
| <p>The operations type. </p> |
| </li> |
| <li class="listitem"> |
| <pre class="literallayout"><span class="keyword">typename</span> Resizer <span class="special">=</span> <span class="identifier">initially_resizer</span></pre> |
| <p>The resizer policy type. </p> |
| </li> |
| <li class="listitem"> |
| <pre class="literallayout"><span class="keyword">typename</span> InitializingStepper <span class="special">=</span> <a class="link" href="runge_kutta4.html" title="Class template runge_kutta4">runge_kutta4</a><span class="special"><</span> <span class="identifier">State</span> <span class="special">,</span> <span class="identifier">Value</span> <span class="special">,</span> <span class="identifier">Deriv</span> <span class="special">,</span> <span class="identifier">Time</span> <span class="special">,</span> <span class="identifier">Algebra</span> <span class="special">,</span> <span class="identifier">Operations</span><span class="special">,</span> <span class="identifier">Resizer</span> <span class="special">></span></pre> |
| <p>The stepper for the first two steps. </p> |
| </li> |
| </ol></div> |
| </div> |
| <div class="refsect2"> |
| <a name="idp109431760"></a><h3> |
| <a name="boost.numeric.odeint.adams_bashforth_moultonconstruct-copy-destruct"></a><code class="computeroutput">adams_bashforth_moulton</code> |
| public |
| construct/copy/destruct</h3> |
| <div class="orderedlist"><ol class="orderedlist" type="1"> |
| <li class="listitem"> |
| <pre class="literallayout"><a name="idp39982528-bb"></a><span class="identifier">adams_bashforth_moulton</span><span class="special">(</span><span class="keyword">void</span><span class="special">)</span><span class="special">;</span></pre>Constructs the <code class="computeroutput"><a class="link" href="adams_bashforth.html" title="Class template adams_bashforth">adams_bashforth</a></code> class. </li> |
| <li class="listitem"> |
| <pre class="literallayout"><a name="idp39984528-bb"></a><span class="identifier">adams_bashforth_moulton</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">algebra_type</span> <span class="special">&</span> algebra<span class="special">)</span><span class="special">;</span></pre>Constructs the <code class="computeroutput"><a class="link" href="adams_bashforth.html" title="Class template adams_bashforth">adams_bashforth</a></code> class. This constructor can be used as a default constructor if the algebra has a default constructor. <p> |
| </p> |
| <div class="variablelist"><table border="0" class="variablelist compact"> |
| <colgroup> |
| <col align="left" valign="top"> |
| <col> |
| </colgroup> |
| <tbody><tr> |
| <td><p><span class="term">Parameters:</span></p></td> |
| <td><div class="variablelist"><table border="0" class="variablelist compact"> |
| <colgroup> |
| <col align="left" valign="top"> |
| <col> |
| </colgroup> |
| <tbody><tr> |
| <td><p><span class="term"><code class="computeroutput">algebra</code></span></p></td> |
| <td><p>A copy of algebra is made and stored. </p></td> |
| </tr></tbody> |
| </table></div></td> |
| </tr></tbody> |
| </table></div> |
| </li> |
| </ol></div> |
| </div> |
| <div class="refsect2"> |
| <a name="idp109450256"></a><h3> |
| <a name="idp39927888-bb"></a><code class="computeroutput">adams_bashforth_moulton</code> public member functions</h3> |
| <div class="orderedlist"><ol class="orderedlist" type="1"> |
| <li class="listitem"> |
| <pre class="literallayout"><span class="identifier">order_type</span> <a name="idp39928448-bb"></a><span class="identifier">order</span><span class="special">(</span><span class="keyword">void</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span></pre>Returns the order of the algorithm, which is equal to the number of steps+1. <p> |
| </p> |
| <div class="variablelist"><table border="0" class="variablelist compact"> |
| <colgroup> |
| <col align="left" valign="top"> |
| <col> |
| </colgroup> |
| <tbody><tr> |
| <td><p><span class="term">Returns:</span></p></td> |
| <td><p>order of the method. </p></td> |
| </tr></tbody> |
| </table></div> |
| </li> |
| <li class="listitem"> |
| <pre class="literallayout"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateInOut<span class="special">></span> |
| <span class="keyword">void</span> <a name="idp39931440-bb"></a><span class="identifier">do_step</span><span class="special">(</span><span class="identifier">System</span> system<span class="special">,</span> <span class="identifier">StateInOut</span> <span class="special">&</span> x<span class="special">,</span> <span class="identifier">time_type</span> t<span class="special">,</span> <span class="identifier">time_type</span> dt<span class="special">)</span><span class="special">;</span></pre>This method performs one step. It transforms the result in-place. <p> |
| </p> |
| <div class="variablelist"><table border="0" class="variablelist compact"> |
| <colgroup> |
| <col align="left" valign="top"> |
| <col> |
| </colgroup> |
| <tbody><tr> |
| <td><p><span class="term">Parameters:</span></p></td> |
| <td><div class="variablelist"><table border="0" class="variablelist compact"> |
| <colgroup> |
| <col align="left" valign="top"> |
| <col> |
| </colgroup> |
| <tbody> |
| <tr> |
| <td><p><span class="term"><code class="computeroutput">dt</code></span></p></td> |
| <td><p>The step size. </p></td> |
| </tr> |
| <tr> |
| <td><p><span class="term"><code class="computeroutput">system</code></span></p></td> |
| <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> |
| </tr> |
| <tr> |
| <td><p><span class="term"><code class="computeroutput">t</code></span></p></td> |
| <td><p>The value of the time, at which the step should be performed. </p></td> |
| </tr> |
| <tr> |
| <td><p><span class="term"><code class="computeroutput">x</code></span></p></td> |
| <td><p>The state of the ODE which should be solved. After calling do_step the result is updated in x. </p></td> |
| </tr> |
| </tbody> |
| </table></div></td> |
| </tr></tbody> |
| </table></div> |
| </li> |
| <li class="listitem"> |
| <pre class="literallayout"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateInOut<span class="special">></span> |
| <span class="keyword">void</span> <a name="idp39939104-bb"></a><span class="identifier">do_step</span><span class="special">(</span><span class="identifier">System</span> system<span class="special">,</span> <span class="keyword">const</span> <span class="identifier">StateInOut</span> <span class="special">&</span> x<span class="special">,</span> <span class="identifier">time_type</span> t<span class="special">,</span> <span class="identifier">time_type</span> dt<span class="special">)</span><span class="special">;</span></pre>Second version to solve the forwarding problem, can be called with Boost.Range as StateInOut. </li> |
| <li class="listitem"> |
| <pre class="literallayout"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateIn<span class="special">,</span> <span class="keyword">typename</span> StateOut<span class="special">></span> |
| <span class="keyword">void</span> <a name="idp39944480-bb"></a><span class="identifier">do_step</span><span class="special">(</span><span class="identifier">System</span> system<span class="special">,</span> <span class="keyword">const</span> <span class="identifier">StateIn</span> <span class="special">&</span> in<span class="special">,</span> <span class="identifier">time_type</span> t<span class="special">,</span> |
| <span class="keyword">const</span> <span class="identifier">StateOut</span> <span class="special">&</span> out<span class="special">,</span> <span class="identifier">time_type</span> dt<span class="special">)</span><span class="special">;</span></pre>The method performs one step with the stepper passed by Stepper. The state of the ODE is updated out-of-place. <p> |
| </p> |
| <div class="variablelist"><table border="0" class="variablelist compact"> |
| <colgroup> |
| <col align="left" valign="top"> |
| <col> |
| </colgroup> |
| <tbody><tr> |
| <td><p><span class="term">Parameters:</span></p></td> |
| <td><div class="variablelist"><table border="0" class="variablelist compact"> |
| <colgroup> |
| <col align="left" valign="top"> |
| <col> |
| </colgroup> |
| <tbody> |
| <tr> |
| <td><p><span class="term"><code class="computeroutput">dt</code></span></p></td> |
| <td><p>The step size. </p></td> |
| </tr> |
| <tr> |
| <td><p><span class="term"><code class="computeroutput">in</code></span></p></td> |
| <td><p>The state of the ODE which should be solved. in is not modified in this method </p></td> |
| </tr> |
| <tr> |
| <td><p><span class="term"><code class="computeroutput">out</code></span></p></td> |
| <td><p>The result of the step is written in out. </p></td> |
| </tr> |
| <tr> |
| <td><p><span class="term"><code class="computeroutput">system</code></span></p></td> |
| <td><p>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </p></td> |
| </tr> |
| <tr> |
| <td><p><span class="term"><code class="computeroutput">t</code></span></p></td> |
| <td><p>The value of the time, at which the step should be performed. </p></td> |
| </tr> |
| </tbody> |
| </table></div></td> |
| </tr></tbody> |
| </table></div> |
| </li> |
| <li class="listitem"> |
| <pre class="literallayout"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateIn<span class="special">,</span> <span class="keyword">typename</span> StateOut<span class="special">></span> |
| <span class="keyword">void</span> <a name="idp39953840-bb"></a><span class="identifier">do_step</span><span class="special">(</span><span class="identifier">System</span> system<span class="special">,</span> <span class="keyword">const</span> <span class="identifier">StateIn</span> <span class="special">&</span> in<span class="special">,</span> <span class="identifier">time_type</span> t<span class="special">,</span> <span class="identifier">StateOut</span> <span class="special">&</span> out<span class="special">,</span> |
| <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> |
| <li class="listitem"> |
| <pre class="literallayout"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> StateType<span class="special">></span> <span class="keyword">void</span> <a name="idp39960464-bb"></a><span class="identifier">adjust_size</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">StateType</span> <span class="special">&</span> x<span class="special">)</span><span class="special">;</span></pre>Adjust the size of all temporaries in the stepper manually. <p> |
| </p> |
| <div class="variablelist"><table border="0" class="variablelist compact"> |
| <colgroup> |
| <col align="left" valign="top"> |
| <col> |
| </colgroup> |
| <tbody><tr> |
| <td><p><span class="term">Parameters:</span></p></td> |
| <td><div class="variablelist"><table border="0" class="variablelist compact"> |
| <colgroup> |
| <col align="left" valign="top"> |
| <col> |
| </colgroup> |
| <tbody><tr> |
| <td><p><span class="term"><code class="computeroutput">x</code></span></p></td> |
| <td><p>A state from which the size of the temporaries to be resized is deduced. </p></td> |
| </tr></tbody> |
| </table></div></td> |
| </tr></tbody> |
| </table></div> |
| </li> |
| <li class="listitem"> |
| <pre class="literallayout"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> ExplicitStepper<span class="special">,</span> <span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateIn<span class="special">></span> |
| <span class="keyword">void</span> <a name="idp39964080-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> |
| <span class="identifier">StateIn</span> <span class="special">&</span> x<span class="special">,</span> <span class="identifier">time_type</span> <span class="special">&</span> t<span class="special">,</span> <span class="identifier">time_type</span> dt<span class="special">)</span><span class="special">;</span></pre>Initialized the stepper. Does Steps-1 steps with the explicit_stepper to fill the buffer. <div class="note"><table border="0" summary="Note"> |
| <tr> |
| <td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../../doc/src/images/note.png"></td> |
| <th align="left">Note</th> |
| </tr> |
| <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> |
| </table></div> |
| <p> |
| |
| </p> |
| <div class="variablelist"><table border="0" class="variablelist compact"> |
| <colgroup> |
| <col align="left" valign="top"> |
| <col> |
| </colgroup> |
| <tbody><tr> |
| <td><p><span class="term">Parameters:</span></p></td> |
| <td><div class="variablelist"><table border="0" class="variablelist compact"> |
| <colgroup> |
| <col align="left" valign="top"> |
| <col> |
| </colgroup> |
| <tbody> |
| <tr> |
| <td><p><span class="term"><code class="computeroutput">dt</code></span></p></td> |
| <td><p>The step size. </p></td> |
| </tr> |
| <tr> |
| <td><p><span class="term"><code class="computeroutput">explicit_stepper</code></span></p></td> |
| <td><p>the stepper used to fill the buffer of previous step results </p></td> |
| </tr> |
| <tr> |
| <td><p><span class="term"><code class="computeroutput">system</code></span></p></td> |
| <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> |
| </tr> |
| <tr> |
| <td><p><span class="term"><code class="computeroutput">t</code></span></p></td> |
| <td><p>The initial time, updated in this method. </p></td> |
| </tr> |
| <tr> |
| <td><p><span class="term"><code class="computeroutput">x</code></span></p></td> |
| <td><p>The initial state of the ODE which should be solved, updated after in this method. </p></td> |
| </tr> |
| </tbody> |
| </table></div></td> |
| </tr></tbody> |
| </table></div> |
| </li> |
| <li class="listitem"> |
| <pre class="literallayout"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateIn<span class="special">></span> |
| <span class="keyword">void</span> <a name="idp39973936-bb"></a><span class="identifier">initialize</span><span class="special">(</span><span class="identifier">System</span> system<span class="special">,</span> <span class="identifier">StateIn</span> <span class="special">&</span> x<span class="special">,</span> <span class="identifier">time_type</span> <span class="special">&</span> t<span class="special">,</span> <span class="identifier">time_type</span> dt<span class="special">)</span><span class="special">;</span></pre>Initialized the stepper. Does Steps-1 steps using the standard initializing stepper of the underlying <code class="computeroutput"><a class="link" href="adams_bashforth.html" title="Class template adams_bashforth">adams_bashforth</a></code> stepper. <p> |
| </p> |
| <div class="variablelist"><table border="0" class="variablelist compact"> |
| <colgroup> |
| <col align="left" valign="top"> |
| <col> |
| </colgroup> |
| <tbody><tr> |
| <td><p><span class="term">Parameters:</span></p></td> |
| <td><div class="variablelist"><table border="0" class="variablelist compact"> |
| <colgroup> |
| <col align="left" valign="top"> |
| <col> |
| </colgroup> |
| <tbody> |
| <tr> |
| <td><p><span class="term"><code class="computeroutput">dt</code></span></p></td> |
| <td><p>The step size. </p></td> |
| </tr> |
| <tr> |
| <td><p><span class="term"><code class="computeroutput">system</code></span></p></td> |
| <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> |
| </tr> |
| <tr> |
| <td><p><span class="term"><code class="computeroutput">t</code></span></p></td> |
| <td><p>The value of the time, at which the step should be performed. </p></td> |
| </tr> |
| <tr> |
| <td><p><span class="term"><code class="computeroutput">x</code></span></p></td> |
| <td><p>The state of the ODE which should be solved. After calling do_step the result is updated in x. </p></td> |
| </tr> |
| </tbody> |
| </table></div></td> |
| </tr></tbody> |
| </table></div> |
| </li> |
| </ol></div> |
| </div> |
| <div class="refsect2"> |
| <a name="idp109601600"></a><h3> |
| <a name="idp39987472-bb"></a><code class="computeroutput">adams_bashforth_moulton</code> private member functions</h3> |
| <div class="orderedlist"><ol class="orderedlist" type="1"> |
| <li class="listitem"><pre class="literallayout"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateInOut<span class="special">></span> |
| <span class="keyword">void</span> <a name="idp39988048-bb"></a><span class="identifier">do_step_impl1</span><span class="special">(</span><span class="identifier">System</span> system<span class="special">,</span> <span class="identifier">StateInOut</span> <span class="special">&</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> |
| <li class="listitem"><pre class="literallayout"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateIn<span class="special">,</span> <span class="keyword">typename</span> StateInOut<span class="special">></span> |
| <span class="keyword">void</span> <a name="idp39993056-bb"></a><span class="identifier">do_step_impl2</span><span class="special">(</span><span class="identifier">System</span> system<span class="special">,</span> <span class="identifier">StateIn</span> <span class="keyword">const</span> <span class="special">&</span> in<span class="special">,</span> <span class="identifier">time_type</span> t<span class="special">,</span> |
| <span class="identifier">StateInOut</span> <span class="special">&</span> out<span class="special">,</span> <span class="identifier">time_type</span> dt<span class="special">)</span><span class="special">;</span></pre></li> |
| <li class="listitem"><pre class="literallayout"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> StateIn<span class="special">></span> <span class="keyword">bool</span> <a name="idp39999312-bb"></a><span class="identifier">resize_impl</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">StateIn</span> <span class="special">&</span> x<span class="special">)</span><span class="special">;</span></pre></li> |
| </ol></div> |
| </div> |
| </div> |
| </div> |
| <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> |
| <td align="left"></td> |
| <td align="right"><div class="copyright-footer">Copyright © 2009-2012 Karsten |
| Ahnert and Mario Mulansky<p> |
| Distributed under the Boost Software License, Version 1.0. (See accompanying |
| 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>) |
| </p> |
| </div></td> |
| </tr></table> |
| <hr> |
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