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| <div class="section"> |
| <div class="titlepage"><div><div><h3 class="title"> |
| <a name="boost_numeric_odeint.concepts.controlled_stepper"></a><a class="link" href="controlled_stepper.html" title="Controlled Stepper">Controlled |
| Stepper</a> |
| </h3></div></div></div> |
| <p> |
| This concept specifies the interface a controlled stepper has to fulfill |
| to be used within <a class="link" href="../odeint_in_detail/integrate_functions.html" title="Integrate functions">integrate |
| functions</a>. |
| </p> |
| <h5> |
| <a name="boost_numeric_odeint.concepts.controlled_stepper.h0"></a> |
| <span class="phrase"><a name="boost_numeric_odeint.concepts.controlled_stepper.description"></a></span><a class="link" href="controlled_stepper.html#boost_numeric_odeint.concepts.controlled_stepper.description">Description</a> |
| </h5> |
| <p> |
| A controlled stepper following this Controlled Stepper concept provides the |
| possibility to perform one step of the solution <span class="emphasis"><em>x(t)</em></span> |
| of an ODE with step-size <span class="emphasis"><em>dt</em></span> to obtain <span class="emphasis"><em>x(t+dt)</em></span> |
| with a given step-size <span class="emphasis"><em>dt</em></span>. Depending on an error estimate |
| of the solution the step might be rejected and a smaller step-size is suggested. |
| </p> |
| <h5> |
| <a name="boost_numeric_odeint.concepts.controlled_stepper.h1"></a> |
| <span class="phrase"><a name="boost_numeric_odeint.concepts.controlled_stepper.associated_types"></a></span><a class="link" href="controlled_stepper.html#boost_numeric_odeint.concepts.controlled_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>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">controlled_stepper_tag</span></code>.</p> |
| </li> |
| </ul></div> |
| <h5> |
| <a name="boost_numeric_odeint.concepts.controlled_stepper.h2"></a> |
| <span class="phrase"><a name="boost_numeric_odeint.concepts.controlled_stepper.notation"></a></span><a class="link" href="controlled_stepper.html#boost_numeric_odeint.concepts.controlled_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">ControlledStepper</span></code></span></dt> |
| <dd><p> |
| A type that is a model of Controlled 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">ControlledStepper</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, should 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.controlled_stepper.h3"></a> |
| <span class="phrase"><a name="boost_numeric_odeint.concepts.controlled_stepper.valid_expressions"></a></span><a class="link" href="controlled_stepper.html#boost_numeric_odeint.concepts.controlled_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> |
| Do step |
| </p> |
| </td> |
| <td> |
| <p> |
| </p> |
| <pre xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="table-programlisting"><span class="identifier">stepper</span><span class="special">.</span><span class="identifier">try_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></pre> |
| <p> |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">controlled_step_result</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| Tries one step of step size <code class="computeroutput"><span class="identifier">dt</span></code>. |
| If the step was successful, <code class="computeroutput"><span class="identifier">success</span></code> |
| is returned, the resulting state is written to <code class="computeroutput"><span class="identifier">x</span></code>, |
| the new time is stored in <code class="computeroutput"><span class="identifier">t</span></code> |
| and <code class="computeroutput"><span class="identifier">dt</span></code> now contains |
| a new (possibly larger) step-size for the next step. If the error |
| was too big, <code class="computeroutput"><span class="identifier">rejected</span></code> |
| is returned and the results are neglected - <code class="computeroutput"><span class="identifier">x</span></code> |
| and <code class="computeroutput"><span class="identifier">t</span></code> are unchanged |
| and <code class="computeroutput"><span class="identifier">dt</span></code> now contains |
| a reduced step-size to be used for the next try. |
| </p> |
| </td> |
| </tr></tbody> |
| </table></div> |
| <h5> |
| <a name="boost_numeric_odeint.concepts.controlled_stepper.h4"></a> |
| <span class="phrase"><a name="boost_numeric_odeint.concepts.controlled_stepper.models"></a></span><a class="link" href="controlled_stepper.html#boost_numeric_odeint.concepts.controlled_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">controlled_error_stepper</span><span class="special"><</span> <span class="identifier">runge_kutta_cash_karp54</span> |
| <span class="special">></span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">controlled_error_stepper_fsal</span><span class="special"><</span> <span class="identifier">runge_kutta_dopri5</span> |
| <span class="special">></span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">controlled_error_stepper</span><span class="special"><</span> <span class="identifier">runge_kutta_fehlberg78</span> |
| <span class="special">></span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">rosenbrock4_controller</span></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><span class="identifier">bulirsch_stoer</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> |
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