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- <title>Dense Output Stepper</title>
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- <div class="section">
- <div class="titlepage"><div><div><h3 class="title">
- <a name="boost_numeric_odeint.concepts.dense_output_stepper"></a><a class="link" href="dense_output_stepper.html" title="Dense Output Stepper">Dense
- Output Stepper</a>
- </h3></div></div></div>
- <p>
- This concept specifies the interface a dense output 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.dense_output_stepper.h0"></a>
- <span class="phrase"><a name="boost_numeric_odeint.concepts.dense_output_stepper.description"></a></span><a class="link" href="dense_output_stepper.html#boost_numeric_odeint.concepts.dense_output_stepper.description">Description</a>
- </h5>
- <p>
- A dense output stepper following this Dense Output Stepper concept provides
- the possibility 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>. The step-size <code class="computeroutput"><span class="identifier">dt</span></code> might be adjusted automatically due
- to error control. Dense output steppers also can interpolate the solution
- to calculate the state <span class="emphasis"><em>x(t')</em></span> at any point <span class="emphasis"><em>t
- <= t' <= t+dt</em></span>.
- </p>
- <h5>
- <a name="boost_numeric_odeint.concepts.dense_output_stepper.h1"></a>
- <span class="phrase"><a name="boost_numeric_odeint.concepts.dense_output_stepper.associated_types"></a></span><a class="link" href="dense_output_stepper.html#boost_numeric_odeint.concepts.dense_output_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">dense_output_stepper_tag</span></code>.</p>
- </li>
- </ul></div>
- <h5>
- <a name="boost_numeric_odeint.concepts.dense_output_stepper.h2"></a>
- <span class="phrase"><a name="boost_numeric_odeint.concepts.dense_output_stepper.notation"></a></span><a class="link" href="dense_output_stepper.html#boost_numeric_odeint.concepts.dense_output_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 Dense Output 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">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">x0</span></code>, <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">t0</span></code>, <code class="computeroutput"><span class="identifier">dt0</span></code>, <code class="computeroutput"><span class="identifier">t</span></code></span></dt>
- <dd><p>
- Objects of type <code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">time_type</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.dense_output_stepper.h3"></a>
- <span class="phrase"><a name="boost_numeric_odeint.concepts.dense_output_stepper.valid_expressions"></a></span><a class="link" href="dense_output_stepper.html#boost_numeric_odeint.concepts.dense_output_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>
- Initialize integration
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">stepper</span><span class="special">.</span><span class="identifier">initialize</span><span class="special">(</span>
- <span class="identifier">x0</span> <span class="special">,</span>
- <span class="identifier">t0</span> <span class="special">,</span>
- <span class="identifier">dt0</span> <span class="special">)</span></code>
- </p>
- </td>
- <td>
- <p>
- void
- </p>
- </td>
- <td>
- <p>
- Initializes the stepper with initial values <code class="computeroutput"><span class="identifier">x0</span></code>,
- <code class="computeroutput"><span class="identifier">t0</span></code> and <code class="computeroutput"><span class="identifier">dt0</span></code>.
- </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></code>
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span>
- <span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">time_type</span> <span class="special">,</span>
- <span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">time_type</span> <span class="special">></span></code>
- </p>
- </td>
- <td>
- <p>
- Performs one step using the ODE defined by <code class="computeroutput"><span class="identifier">sys</span></code>.
- The step-size might be changed internally due to error control.
- This function returns a pair containing <code class="computeroutput"><span class="identifier">t</span></code>
- and <code class="computeroutput"><span class="identifier">t</span><span class="special">+</span><span class="identifier">dt</span></code> representing the interval
- for which interpolation can be performed.
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Do interpolation
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">stepper</span><span class="special">.</span><span class="identifier">calc_state</span><span class="special">(</span>
- <span class="identifier">t_inter</span> <span class="special">,</span>
- <span class="identifier">x</span> <span class="special">)</span></code>
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="keyword">void</span></code>
- </p>
- </td>
- <td>
- <p>
- Performs the interpolation to calculate /x(t<sub>inter</sub>/) where /t <=
- t<sub>inter</sub> <= t+dt/.
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Get current time
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">stepper</span><span class="special">.</span><span class="identifier">current_time</span><span class="special">()</span></code>
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="keyword">const</span> <span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">time_type</span><span class="special">&</span></code>
- </p>
- </td>
- <td>
- <p>
- Returns the current time <span class="emphasis"><em>t+dt</em></span> of the stepper,
- that is the end time of the last step and the starting time for
- the next call of <code class="computeroutput"><span class="identifier">do_step</span></code>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Get current state
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">stepper</span><span class="special">.</span><span class="identifier">current_state</span><span class="special">()</span></code>
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="keyword">const</span> <span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">state_type</span><span class="special">&</span></code>
- </p>
- </td>
- <td>
- <p>
- Returns the current state of the stepper, that is <span class="emphasis"><em>x(t+dt)</em></span>,
- the state at the time returned by <code class="computeroutput"><span class="identifier">stepper</span><span class="special">.</span><span class="identifier">current_time</span><span class="special">()</span></code>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Get current time step
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">stepper</span><span class="special">.</span><span class="identifier">current_time_step</span><span class="special">()</span></code>
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="keyword">const</span> <span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">time_type</span><span class="special">&</span></code>
- </p>
- </td>
- <td>
- <p>
- Returns the current step size of the stepper, that is <span class="emphasis"><em>dt</em></span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- <h5>
- <a name="boost_numeric_odeint.concepts.dense_output_stepper.h4"></a>
- <span class="phrase"><a name="boost_numeric_odeint.concepts.dense_output_stepper.models"></a></span><a class="link" href="dense_output_stepper.html#boost_numeric_odeint.concepts.dense_output_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">dense_output_controlled_explicit_fsal</span><span class="special"><</span> <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">bulirsch_stoer_dense_out</span></code>
- </li>
- <li class="listitem">
- <code class="computeroutput"><span class="identifier">rosenbrock4_dense_output</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 © 2009-2015 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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