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<title>Dense Output Stepper</title>
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<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
        &lt;= t' &lt;= 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">&amp;</span><span class="identifier">lt</span><span class="special">;</span> <span class="keyword">double</span> <span class="special">&amp;</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">&lt;</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">&gt;</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 &lt;=
                  t<sub>inter</sub> &lt;= 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">&amp;</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">&amp;</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">&amp;</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">&lt;</span> <span class="identifier">controlled_error_stepper_fsal</span><span class="special">&lt;</span> <span class="identifier">runge_kutta_dopri5</span>
            <span class="special">&gt;</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 &#169; 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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