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| <div class="titlepage"><div><div><h3 class="title"> |
| <a name="boost_numeric_odeint.concepts.stepper"></a><a class="link" href="stepper.html" title="Stepper">Stepper</a> |
| </h3></div></div></div> |
| <p> |
| This concepts specifies the interface a simple stepper has to fulfill to |
| be used within the <a class="link" href="../odeint_in_detail/integrate_functions.html" title="Integrate functions">integrate |
| functions</a>. |
| </p> |
| <h5> |
| <a name="boost_numeric_odeint.concepts.stepper.h0"></a> |
| <span class="phrase"><a name="boost_numeric_odeint.concepts.stepper.description"></a></span><a class="link" href="stepper.html#boost_numeric_odeint.concepts.stepper.description">Description</a> |
| </h5> |
| <p> |
| The basic stepper concept. A basic stepper following this Stepper concept |
| is able to perform a single step of the solution <span class="emphasis"><em>x(t)</em></span> |
| of an ODE to obtain <span class="emphasis"><em>x(t+dt)</em></span> using a given step size |
| <span class="emphasis"><em>dt</em></span>. Basic steppers can be Runge-Kutta steppers, symplectic |
| steppers as well as implicit steppers. Depending on the actual stepper, the |
| ODE is defined as <a class="link" href="system.html" title="System">System</a>, |
| <a class="link" href="symplectic_system.html" title="Symplectic System">Symplectic |
| System</a>, <a class="link" href="simple_symplectic_system.html" title="Simple Symplectic System">Simple |
| Symplectic System</a> or <a class="link" href="implicit_system.html" title="Implicit System">Implicit |
| System</a>. Note that all error steppers are also basic steppers. |
| </p> |
| <h5> |
| <a name="boost_numeric_odeint.concepts.stepper.h1"></a> |
| <span class="phrase"><a name="boost_numeric_odeint.concepts.stepper.refinement_of"></a></span><a class="link" href="stepper.html#boost_numeric_odeint.concepts.stepper.refinement_of">Refinement |
| of</a> |
| </h5> |
| <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> |
| <li class="listitem"> |
| DefaultConstructable |
| </li> |
| <li class="listitem"> |
| CopyConstructable |
| </li> |
| </ul></div> |
| <h5> |
| <a name="boost_numeric_odeint.concepts.stepper.h2"></a> |
| <span class="phrase"><a name="boost_numeric_odeint.concepts.stepper.associated_types"></a></span><a class="link" href="stepper.html#boost_numeric_odeint.concepts.stepper.associated_types">Associated |
| types</a> |
| </h5> |
| <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> |
| <li class="listitem"> |
| <p><span class="bold"><strong>state_type</strong></span></p> |
| <p><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">state_type</span></code></p> |
| <p>The |
| type characterizing the state of the ODE, hence <span class="emphasis"><em>x</em></span>.</p> |
| </li> |
| <li class="listitem"> |
| <p><span class="bold"><strong>deriv_type</strong></span></p> |
| <p><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">deriv_type</span></code></p> |
| <p>The |
| type characterizing the derivative of the ODE, hence <span class="emphasis"><em>d x/dt</em></span>.</p> |
| </li> |
| <li class="listitem"> |
| <p><span class="bold"><strong>time_type</strong></span></p> |
| <p><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">time_type</span></code></p> |
| <p>The |
| type characterizing the dependent variable of the ODE, hence the time |
| <span class="emphasis"><em>t</em></span>.</p> |
| </li> |
| <li class="listitem"> |
| <p><span class="bold"><strong>value_type</strong></span></p> |
| <p><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">value_type</span></code></p> |
| <p>The |
| numerical data type which is used within the stepper, something like |
| <code class="computeroutput"><span class="keyword">float</span></code>, <code class="computeroutput"><span class="keyword">double</span></code>, |
| <code class="computeroutput"><span class="identifier">complex</span><span class="special">&</span><span class="identifier">lt</span><span class="special">;</span> <span class="keyword">double</span> <span class="special">&</span><span class="identifier">gt</span><span class="special">;</span></code>.</p> |
| </li> |
| <li class="listitem"> |
| <p><span class="bold"><strong>order_type</strong></span></p> |
| <p><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">order_type</span></code></p> |
| <p>The |
| type characterizing the order of the ODE, typically <code class="computeroutput"><span class="keyword">unsigned</span> |
| <span class="keyword">short</span></code>.</p> |
| </li> |
| <li class="listitem"> |
| <p><span class="bold"><strong>stepper_category</strong></span></p> |
| <p><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">stepper_category</span></code></p> |
| <p>A |
| tag type characterizing the category of the stepper. This type must be |
| convertible to <code class="computeroutput"><span class="identifier">stepper_tag</span></code>.</p> |
| </li> |
| </ul></div> |
| <h5> |
| <a name="boost_numeric_odeint.concepts.stepper.h3"></a> |
| <span class="phrase"><a name="boost_numeric_odeint.concepts.stepper.notation"></a></span><a class="link" href="stepper.html#boost_numeric_odeint.concepts.stepper.notation">Notation</a> |
| </h5> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl class="variablelist"> |
| <dt><span class="term"><code class="computeroutput"><span class="identifier">Stepper</span></code></span></dt> |
| <dd><p> |
| A type that is a model of Stepper |
| </p></dd> |
| <dt><span class="term"><code class="computeroutput"><span class="identifier">State</span></code></span></dt> |
| <dd><p> |
| A type representing the state <span class="emphasis"><em>x</em></span> of the ODE |
| </p></dd> |
| <dt><span class="term"><code class="computeroutput"><span class="identifier">Time</span></code></span></dt> |
| <dd><p> |
| A type representing the time <span class="emphasis"><em>t</em></span> of the ODE |
| </p></dd> |
| <dt><span class="term"><code class="computeroutput"><span class="identifier">stepper</span></code></span></dt> |
| <dd><p> |
| An object of type <code class="computeroutput"><span class="identifier">Stepper</span></code> |
| </p></dd> |
| <dt><span class="term"><code class="computeroutput"><span class="identifier">x</span></code></span></dt> |
| <dd><p> |
| Object of type <code class="computeroutput"><span class="identifier">State</span></code> |
| </p></dd> |
| <dt><span class="term"><code class="computeroutput"><span class="identifier">t</span></code>, <code class="computeroutput"><span class="identifier">dt</span></code></span></dt> |
| <dd><p> |
| Objects of type <code class="computeroutput"><span class="identifier">Time</span></code> |
| </p></dd> |
| <dt><span class="term"><code class="computeroutput"><span class="identifier">sys</span></code></span></dt> |
| <dd><p> |
| An object defining the ODE. Depending on the Stepper this might be |
| a model of <a class="link" href="system.html" title="System">System</a>, |
| <a class="link" href="symplectic_system.html" title="Symplectic System">Symplectic |
| System</a>, <a class="link" href="simple_symplectic_system.html" title="Simple Symplectic System">Simple |
| Symplectic System</a> or <a class="link" href="implicit_system.html" title="Implicit System">Implicit |
| System</a> |
| </p></dd> |
| </dl> |
| </div> |
| <h5> |
| <a name="boost_numeric_odeint.concepts.stepper.h4"></a> |
| <span class="phrase"><a name="boost_numeric_odeint.concepts.stepper.valid_expressions"></a></span><a class="link" href="stepper.html#boost_numeric_odeint.concepts.stepper.valid_expressions">Valid Expressions</a> |
| </h5> |
| <div class="informaltable"><table class="table"> |
| <colgroup> |
| <col> |
| <col> |
| <col> |
| <col> |
| </colgroup> |
| <thead><tr> |
| <th> |
| <p> |
| Name |
| </p> |
| </th> |
| <th> |
| <p> |
| Expression |
| </p> |
| </th> |
| <th> |
| <p> |
| Type |
| </p> |
| </th> |
| <th> |
| <p> |
| Semantics |
| </p> |
| </th> |
| </tr></thead> |
| <tbody> |
| <tr> |
| <td> |
| <p> |
| Get the order |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">stepper</span><span class="special">.</span><span class="identifier">order</span><span class="special">()</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">order_type</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| Returns the order of the stepper. |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| Do step |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="computeroutput"><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></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="keyword">void</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| Performs one step of step size <code class="computeroutput"><span class="identifier">dt</span></code>. |
| The newly obtained state is written in place in <code class="computeroutput"><span class="identifier">x</span></code>. |
| </p> |
| </td> |
| </tr> |
| </tbody> |
| </table></div> |
| <h5> |
| <a name="boost_numeric_odeint.concepts.stepper.h5"></a> |
| <span class="phrase"><a name="boost_numeric_odeint.concepts.stepper.models"></a></span><a class="link" href="stepper.html#boost_numeric_odeint.concepts.stepper.models">Models</a> |
| </h5> |
| <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">runge_kutta4</span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">euler</span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">runge_kutta_cash_karp54</span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">runge_kutta_dopri5</span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">runge_kutta_fehlberg78</span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">modified_midpoint</span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">rosenbrock4</span></code> |
| </li> |
| </ul></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> |
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