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- </div>
- <div class="section">
- <div class="titlepage"><div><div><h3 class="title">
- <a name="boost_numeric_odeint.concepts.state_algebra_operations"></a><a class="link" href="state_algebra_operations.html" title="State Algebra Operations">State
- Algebra Operations</a>
- </h3></div></div></div>
- <div class="toc"><dl class="toc">
- <dt><span class="section"><a href="state_algebra_operations.html#boost_numeric_odeint.concepts.state_algebra_operations.operations">Operations</a></span></dt>
- <dt><span class="section"><a href="state_algebra_operations.html#boost_numeric_odeint.concepts.state_algebra_operations.algebra">Algebra</a></span></dt>
- <dt><span class="section"><a href="state_algebra_operations.html#boost_numeric_odeint.concepts.state_algebra_operations.pre_defined_implementations">Pre-Defined
- implementations</a></span></dt>
- <dt><span class="section"><a href="state_algebra_operations.html#boost_numeric_odeint.concepts.state_algebra_operations.example_expressions">Example
- expressions</a></span></dt>
- </dl></div>
- <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 following does not apply to implicit steppers like implicit_euler or
- Rosenbrock 4 as there the <code class="computeroutput"><span class="identifier">state_type</span></code>
- can not be changed from <code class="computeroutput"><span class="identifier">ublas</span><span class="special">::</span><span class="identifier">vector</span></code>
- and no algebra/operations are used.
- </p></td></tr>
- </table></div>
- <h5>
- <a name="boost_numeric_odeint.concepts.state_algebra_operations.h0"></a>
- <span class="phrase"><a name="boost_numeric_odeint.concepts.state_algebra_operations.description"></a></span><a class="link" href="state_algebra_operations.html#boost_numeric_odeint.concepts.state_algebra_operations.description">Description</a>
- </h5>
- <p>
- The <code class="computeroutput"><span class="identifier">State</span></code>, <code class="computeroutput"><span class="identifier">Algebra</span></code> and <code class="computeroutput"><span class="identifier">Operations</span></code>
- together define a concept describing how the mathematical vector operations
- required for the stepper algorithms are performed. The typical vector operation
- done within steppers is
- </p>
- <p>
- <span class="emphasis"><em><span class="bold"><strong>y</strong></span> = Σ α<sub>i</sub> <span class="bold"><strong>x<sub>i</sub></strong></span></em></span>.
- </p>
- <p>
- The <code class="computeroutput"><span class="identifier">State</span></code> represents the
- state variable of an ODE, usually denoted with <span class="emphasis"><em>x</em></span>. Algorithmically,
- the state is often realized as a <code class="computeroutput"><span class="identifier">vector</span><span class="special"><</span> <span class="keyword">double</span> <span class="special">></span></code> or <code class="computeroutput"><span class="identifier">array</span><span class="special"><</span> <span class="keyword">double</span> <span class="special">,</span> <span class="identifier">N</span> <span class="special">></span></code>,
- however, the genericity of odeint enables you to basically use anything as
- a state type. The algorithmic counterpart of such mathematical expressions
- is divided into two parts. First, the <code class="computeroutput"><span class="identifier">Algebra</span></code>
- is used to account for the vector character of the equation. In the case
- of a <code class="computeroutput"><span class="identifier">vector</span></code> as state type
- this means the <code class="computeroutput"><span class="identifier">Algebra</span></code> is
- responsible for iteration over all vector elements. Second, the <code class="computeroutput"><span class="identifier">Operations</span></code> are used to represent the actual
- operation applied to each of the vector elements. So the <code class="computeroutput"><span class="identifier">Algebra</span></code>
- iterates over all elements of the <code class="computeroutput"><span class="identifier">State</span></code>s
- and calls an operation taken from the <code class="computeroutput"><span class="identifier">Operations</span></code>
- for each element. This is where <code class="computeroutput"><span class="identifier">State</span></code>,
- <code class="computeroutput"><span class="identifier">Algebra</span></code> and <code class="computeroutput"><span class="identifier">Operations</span></code> have to work together to make
- odeint running. Please have a look at the <code class="computeroutput"><span class="identifier">range_algebra</span></code>
- and <code class="computeroutput"><span class="identifier">default_operations</span></code> to
- see an example how this is implemented.
- </p>
- <p>
- In the following we describe how <code class="computeroutput"><span class="identifier">State</span></code>,
- <code class="computeroutput"><span class="identifier">Algebra</span></code> and <code class="computeroutput"><span class="identifier">Operations</span></code> are used together within the
- stepper implementations.
- </p>
- <div class="section">
- <div class="titlepage"><div><div><h4 class="title">
- <a name="boost_numeric_odeint.concepts.state_algebra_operations.operations"></a><a class="link" href="state_algebra_operations.html#boost_numeric_odeint.concepts.state_algebra_operations.operations" title="Operations">Operations</a>
- </h4></div></div></div>
- <h6>
- <a name="boost_numeric_odeint.concepts.state_algebra_operations.operations.h0"></a>
- <span class="phrase"><a name="boost_numeric_odeint.concepts.state_algebra_operations.operations.notation"></a></span><a class="link" href="state_algebra_operations.html#boost_numeric_odeint.concepts.state_algebra_operations.operations.notation">Notation</a>
- </h6>
- <div class="variablelist">
- <p class="title"><b></b></p>
- <dl class="variablelist">
- <dt><span class="term"><code class="computeroutput"><span class="identifier">Operations</span></code></span></dt>
- <dd><p>
- The operations type
- </p></dd>
- <dt><span class="term"><code class="computeroutput"><span class="identifier">Value1</span></code>, ... ,
- <code class="computeroutput"><span class="identifier">ValueN</span></code></span></dt>
- <dd><p>
- Types representing the value or time type of stepper
- </p></dd>
- <dt><span class="term"><code class="computeroutput"><span class="identifier">Scale</span></code></span></dt>
- <dd><p>
- Type of the scale operation
- </p></dd>
- <dt><span class="term"><code class="computeroutput"><span class="identifier">scale</span></code></span></dt>
- <dd><p>
- Object of type <code class="computeroutput"><span class="identifier">Scale</span></code>
- </p></dd>
- <dt><span class="term"><code class="literal">ScaleSum<span class="emphasis"><em>N</em></span></code></span></dt>
- <dd><p>
- Type that represents a general scale_sum operation, <code class="literal"><span class="emphasis"><em>N</em></span></code>
- should be replaced by a number from 1 to 14.
- </p></dd>
- <dt><span class="term"><code class="literal">scale_sum<span class="emphasis"><em>N</em></span></code></span></dt>
- <dd><p>
- Object of type <code class="literal">ScaleSum<span class="emphasis"><em>N</em></span></code>,
- <code class="literal"><span class="emphasis"><em>N</em></span></code> should be replaced by a
- number from 1 to 14.
- </p></dd>
- <dt><span class="term"><code class="computeroutput"><span class="identifier">ScaleSumSwap2</span></code></span></dt>
- <dd><p>
- Type of the scale sum swap operation
- </p></dd>
- <dt><span class="term"><code class="computeroutput"><span class="identifier">scale_sum_swap2</span></code></span></dt>
- <dd><p>
- Object of type <code class="computeroutput"><span class="identifier">ScaleSumSwap2</span></code>
- </p></dd>
- <dt><span class="term"><code class="computeroutput"><span class="identifier">a1</span><span class="special">,</span>
- <span class="identifier">a2</span><span class="special">,</span>
- <span class="special">...</span></code></span></dt>
- <dd><p>
- Objects of type <code class="computeroutput"><span class="identifier">Value1</span></code>,
- <code class="computeroutput"><span class="identifier">Value2</span></code>, ...
- </p></dd>
- <dt><span class="term"><code class="computeroutput"><span class="identifier">y</span><span class="special">,</span>
- <span class="identifier">x1</span><span class="special">,</span>
- <span class="identifier">x2</span><span class="special">,</span>
- <span class="special">...</span></code></span></dt>
- <dd><p>
- Objects of <code class="computeroutput"><span class="identifier">State</span></code>'s
- value type
- </p></dd>
- </dl>
- </div>
- <h6>
- <a name="boost_numeric_odeint.concepts.state_algebra_operations.operations.h1"></a>
- <span class="phrase"><a name="boost_numeric_odeint.concepts.state_algebra_operations.operations.valid_expressions"></a></span><a class="link" href="state_algebra_operations.html#boost_numeric_odeint.concepts.state_algebra_operations.operations.valid_expressions">Valid
- Expressions</a>
- </h6>
- <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 scale operation
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">Operations</span><span class="special">::</span><span class="identifier">scale</span><span class="special"><</span>
- <span class="identifier">Value</span> <span class="special">></span></code>
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">Scale</span></code>
- </p>
- </td>
- <td>
- <p>
- Get <code class="computeroutput"><span class="identifier">Scale</span></code> from
- <code class="computeroutput"><span class="identifier">Operations</span></code>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">Scale</span></code> constructor
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">Scale</span><span class="special"><</span>
- <span class="identifier">Value</span> <span class="special">>(</span>
- <span class="identifier">a</span> <span class="special">)</span></code>
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">Scale</span></code>
- </p>
- </td>
- <td>
- <p>
- Constructs a <code class="computeroutput"><span class="identifier">Scale</span></code>
- object
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">Scale</span></code> operation
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">scale</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>
- Calculates <code class="computeroutput"><span class="identifier">x</span> <span class="special">*=</span> <span class="identifier">a</span></code>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Get general <code class="computeroutput"><span class="identifier">scale_sum</span></code>
- operation
- </p>
- </td>
- <td>
- <p>
- <code class="literal">Operations::scale_sum<span class="emphasis"><em>N</em></span>< Value1
- , ... , ValueN ></code>
- </p>
- </td>
- <td>
- <p>
- <code class="literal">ScaleSum<span class="emphasis"><em>N</em></span></code>
- </p>
- </td>
- <td>
- <p>
- Get the <code class="literal">ScaleSum<span class="emphasis"><em>N</em></span></code> type
- from <code class="computeroutput"><span class="identifier">Operations</span></code>,
- <code class="literal"><span class="emphasis"><em>N</em></span></code> should be replaced
- by a number from 1 to 14.
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">scale_sum</span></code> constructor
- </p>
- </td>
- <td>
- <p>
- <code class="literal">ScaleSum<span class="emphasis"><em>N</em></span>< Value1 , ... , ValueN
- >( a1 , ... , aN )</code>
- </p>
- </td>
- <td>
- <p>
- <code class="literal">ScaleSum<span class="emphasis"><em>N</em></span></code>
- </p>
- </td>
- <td>
- <p>
- Constructs a <code class="computeroutput"><span class="identifier">scale_sum</span></code>
- object given <code class="literal"><span class="emphasis"><em>N</em></span></code> parameter
- values with <code class="literal"><span class="emphasis"><em>N</em></span></code> between
- 1 and 14.
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">scale_sum</span></code> operation
- </p>
- </td>
- <td>
- <p>
- <code class="literal">scale_sum<span class="emphasis"><em>N</em></span>( y , x1 , ... , xN )</code>
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="keyword">void</span></code>
- </p>
- </td>
- <td>
- <p>
- Calculates <code class="computeroutput"><span class="identifier">y</span> <span class="special">=</span> <span class="identifier">a1</span><span class="special">*</span><span class="identifier">x1</span>
- <span class="special">+</span> <span class="identifier">a2</span><span class="special">*</span><span class="identifier">x2</span>
- <span class="special">+</span> <span class="special">...</span>
- <span class="special">+</span> <span class="identifier">aN</span><span class="special">*</span><span class="identifier">xN</span></code>.
- Note that this is an <code class="literal"><span class="emphasis"><em>N</em></span>+1</code>-ary
- function call.
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Get scale sum swap operation
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">Operations</span><span class="special">::</span><span class="identifier">scale_sum_swap2</span><span class="special"><</span>
- <span class="identifier">Value1</span> <span class="special">,</span>
- <span class="identifier">Value2</span> <span class="special">></span></code>
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">ScaleSumSwap2</span></code>
- </p>
- </td>
- <td>
- <p>
- Get scale sum swap from operations
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">ScaleSumSwap2</span></code>
- constructor
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">ScaleSumSwap2</span><span class="special"><</span> <span class="identifier">Value1</span>
- <span class="special">,</span> <span class="identifier">Value2</span>
- <span class="special">>(</span> <span class="identifier">a1</span>
- <span class="special">,</span> <span class="identifier">a2</span>
- <span class="special">)</span></code>
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">ScaleSumSwap2</span></code>
- </p>
- </td>
- <td>
- <p>
- Constructor
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">ScaleSumSwap2</span></code>
- operation
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">scale_sum_swap2</span><span class="special">(</span> <span class="identifier">x1</span>
- <span class="special">,</span> <span class="identifier">x2</span>
- <span class="special">,</span> <span class="identifier">x3</span>
- <span class="special">)</span></code>
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="keyword">void</span></code>
- </p>
- </td>
- <td>
- <p>
- Calculates <code class="computeroutput"><span class="identifier">tmp</span> <span class="special">=</span> <span class="identifier">x1</span></code>,
- <code class="computeroutput"><span class="identifier">x1</span> <span class="special">=</span>
- <span class="identifier">a1</span><span class="special">*</span><span class="identifier">x2</span> <span class="special">+</span>
- <span class="identifier">a2</span><span class="special">*</span><span class="identifier">x3</span></code> and <code class="computeroutput"><span class="identifier">x2</span>
- <span class="special">=</span> <span class="identifier">tmp</span></code>.
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h4 class="title">
- <a name="boost_numeric_odeint.concepts.state_algebra_operations.algebra"></a><a class="link" href="state_algebra_operations.html#boost_numeric_odeint.concepts.state_algebra_operations.algebra" title="Algebra">Algebra</a>
- </h4></div></div></div>
- <h6>
- <a name="boost_numeric_odeint.concepts.state_algebra_operations.algebra.h0"></a>
- <span class="phrase"><a name="boost_numeric_odeint.concepts.state_algebra_operations.algebra.notation"></a></span><a class="link" href="state_algebra_operations.html#boost_numeric_odeint.concepts.state_algebra_operations.algebra.notation">Notation</a>
- </h6>
- <div class="variablelist">
- <p class="title"><b></b></p>
- <dl class="variablelist">
- <dt><span class="term"><code class="computeroutput"><span class="identifier">State</span></code></span></dt>
- <dd><p>
- The state type
- </p></dd>
- <dt><span class="term"><code class="computeroutput"><span class="identifier">Algebra</span></code></span></dt>
- <dd><p>
- The algebra type
- </p></dd>
- <dt><span class="term"><code class="literal">Operation<span class="emphasis"><em>N</em></span></code></span></dt>
- <dd><p>
- An <code class="literal"><span class="emphasis"><em>N</em></span></code>-ary operation type,
- <code class="literal"><span class="emphasis"><em>N</em></span></code> should be a number from
- 1 to 14.
- </p></dd>
- <dt><span class="term"><code class="computeroutput"><span class="identifier">algebra</span></code></span></dt>
- <dd><p>
- Object of type <code class="computeroutput"><span class="identifier">Algebra</span></code>
- </p></dd>
- <dt><span class="term"><code class="literal">operation<span class="emphasis"><em>N</em></span></code></span></dt>
- <dd><p>
- Object of type <code class="literal">Operation<span class="emphasis"><em>N</em></span></code>
- </p></dd>
- <dt><span class="term"><code class="computeroutput"><span class="identifier">y</span><span class="special">,</span>
- <span class="identifier">x1</span><span class="special">,</span>
- <span class="identifier">x2</span><span class="special">,</span>
- <span class="special">...</span></code></span></dt>
- <dd><p>
- Objects of type <code class="computeroutput"><span class="identifier">State</span></code>
- </p></dd>
- </dl>
- </div>
- <h6>
- <a name="boost_numeric_odeint.concepts.state_algebra_operations.algebra.h1"></a>
- <span class="phrase"><a name="boost_numeric_odeint.concepts.state_algebra_operations.algebra.valid_expressions"></a></span><a class="link" href="state_algebra_operations.html#boost_numeric_odeint.concepts.state_algebra_operations.algebra.valid_expressions">Valid
- Expressions</a>
- </h6>
- <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>
- Vector Operation with arity 2
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">algebra</span><span class="special">.</span><span class="identifier">for_each2</span><span class="special">(</span>
- <span class="identifier">y</span> <span class="special">,</span>
- <span class="identifier">x</span> <span class="special">,</span>
- <span class="identifier">operation2</span> <span class="special">)</span></code>
- </p>
- </td>
- <td>
- <p>
- void
- </p>
- </td>
- <td>
- <p>
- Calls <code class="computeroutput"><span class="identifier">operation2</span><span class="special">(</span> <span class="identifier">y_i</span>
- <span class="special">,</span> <span class="identifier">x_i</span>
- <span class="special">)</span></code> for each element <code class="computeroutput"><span class="identifier">y_i</span></code> of <code class="computeroutput"><span class="identifier">y</span></code>
- and <code class="computeroutput"><span class="identifier">x_i</span></code> of <code class="computeroutput"><span class="identifier">x</span></code>.
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Vector Operation with arity 3
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">algebra</span><span class="special">.</span><span class="identifier">for_each3</span><span class="special">(</span>
- <span class="identifier">y</span> <span class="special">,</span>
- <span class="identifier">x1</span> <span class="special">,</span>
- <span class="identifier">x2</span> <span class="special">,</span>
- <span class="identifier">operation3</span> <span class="special">)</span></code>
- </p>
- </td>
- <td>
- <p>
- void
- </p>
- </td>
- <td>
- <p>
- Calls <code class="computeroutput"><span class="identifier">operation3</span><span class="special">(</span> <span class="identifier">y_i</span>
- <span class="special">,</span> <span class="identifier">x1_i</span>
- <span class="special">,</span> <span class="identifier">x2_i</span>
- <span class="special">)</span></code> for each element <code class="computeroutput"><span class="identifier">y_i</span></code> of <code class="computeroutput"><span class="identifier">y</span></code>
- and <code class="computeroutput"><span class="identifier">x1_i</span></code> of
- <code class="computeroutput"><span class="identifier">x1</span></code> and <code class="computeroutput"><span class="identifier">x2_i</span></code> of <code class="computeroutput"><span class="identifier">x2</span></code>.
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Vector Operation with arity <code class="literal"><span class="emphasis"><em>N</em></span></code>
- </p>
- </td>
- <td>
- <p>
- <code class="literal">algebra.for_each<span class="emphasis"><em>N</em></span>( y , x1 , ...
- , xN , operation<span class="emphasis"><em>N</em></span> )</code>
- </p>
- </td>
- <td>
- <p>
- void
- </p>
- </td>
- <td>
- <p>
- Calls <code class="literal">operation<span class="emphasis"><em>N</em></span>( y_i , x1_i ,
- ... , xN_i )</code> for each element <code class="computeroutput"><span class="identifier">y_i</span></code>
- of <code class="computeroutput"><span class="identifier">y</span></code> and <code class="computeroutput"><span class="identifier">x1_i</span></code> of <code class="computeroutput"><span class="identifier">x1</span></code>
- and so on. <code class="literal"><span class="emphasis"><em>N</em></span></code> should be
- replaced by a number between 1 and 14.
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h4 class="title">
- <a name="boost_numeric_odeint.concepts.state_algebra_operations.pre_defined_implementations"></a><a class="link" href="state_algebra_operations.html#boost_numeric_odeint.concepts.state_algebra_operations.pre_defined_implementations" title="Pre-Defined implementations">Pre-Defined
- implementations</a>
- </h4></div></div></div>
- <p>
- As standard configuration odeint uses the <code class="computeroutput"><span class="identifier">range_algebra</span></code>
- and <code class="computeroutput"><span class="identifier">default_operations</span></code>
- which suffices most situations. However, a few more possibilities exist
- either to gain better performance or to ensure interoperability with other
- libraries. In the following we list the existing <code class="computeroutput"><span class="identifier">Algebra</span></code>/<code class="computeroutput"><span class="identifier">Operations</span></code> configurations that can be
- used in the steppers.
- </p>
- <div class="informaltable"><table class="table">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- <p>
- <code class="computeroutput"><span class="identifier">State</span></code>
- </p>
- </th>
- <th>
- <p>
- <code class="computeroutput"><span class="identifier">Algebra</span></code>
- </p>
- </th>
- <th>
- <p>
- <code class="computeroutput"><span class="identifier">Operations</span></code>
- </p>
- </th>
- <th>
- <p>
- Remarks
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Anything supporting <a href="http://www.boost.org/doc/libs/release/libs/range/" target="_top">Boost.Range</a>,
- like <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span></code>, <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">list</span></code>,
- <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span></code>,... based on a <code class="computeroutput"><span class="identifier">value_type</span></code> that supports operators
- +,* (typically <code class="computeroutput"><span class="keyword">double</span></code>)
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">range_algebra</span></code>
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">default_operations</span></code>
- </p>
- </td>
- <td>
- <p>
- Standard implementation, applicable for most typical situations.
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span></code> based on a <code class="computeroutput"><span class="identifier">value_type</span></code> that supports operators
- +,*
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">array_algebra</span></code>
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">default_operations</span></code>
- </p>
- </td>
- <td>
- <p>
- Special implementation for boost::array with better performance
- than <code class="computeroutput"><span class="identifier">range_algebra</span></code>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Anything that defines operators + within itself and * with scalar
- (Mathematically spoken, anything that is a vector space).
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">vector_space_algebra</span></code>
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">default_operations</span></code>
- </p>
- </td>
- <td>
- <p>
- For the use of <a class="link" href="controlled_stepper.html" title="Controlled Stepper">Controlled
- Stepper</a>, the template <code class="computeroutput"><span class="identifier">vector_space_reduce</span></code>
- has to be instantiated.
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">thrust</span><span class="special">::</span><span class="identifier">device_vector</span></code>, <code class="computeroutput"><span class="identifier">thrust</span><span class="special">::</span><span class="identifier">host_vector</span></code>
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">thrust_algebra</span></code>
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">thrust_operations</span></code>
- </p>
- </td>
- <td>
- <p>
- For running odeint on CUDA devices by using <a href="http://code.google.com/p/thrust/" target="_top">Thrust</a>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Any RandomAccessRange
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">openmp_range_algebra</span></code>
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">default_operations</span></code>
- </p>
- </td>
- <td>
- <p>
- OpenMP-parallelised range algebra
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">openmp_state</span></code>
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">openmp_algebra</span></code>
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">default_operations</span></code>
- </p>
- </td>
- <td>
- <p>
- OpenMP-parallelised algebra for split data
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span></code> or anything which allocates
- the elements in a C-like manner
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">vector_space_algebra</span></code>
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">mkl_operations</span></code>
- </p>
- </td>
- <td>
- <p>
- Using the <a href="http://software.intel.com/en-us/articles/intel-mkl/" target="_top">Intel
- Math Kernel Library</a> in odeint for maximum performance.
- Currently, only the RK4 stepper is supported.
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h4 class="title">
- <a name="boost_numeric_odeint.concepts.state_algebra_operations.example_expressions"></a><a class="link" href="state_algebra_operations.html#boost_numeric_odeint.concepts.state_algebra_operations.example_expressions" title="Example expressions">Example
- expressions</a>
- </h4></div></div></div>
- <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>
- Vector operation
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">algebra</span><span class="special">.</span><span class="identifier">for_each3</span><span class="special">(</span>
- <span class="identifier">y</span> <span class="special">,</span>
- <span class="identifier">x1</span> <span class="special">,</span>
- <span class="identifier">x2</span> <span class="special">,</span>
- <span class="identifier">Operations</span><span class="special">::</span><span class="identifier">scale_sum2</span><span class="special"><</span>
- <span class="identifier">Value1</span> <span class="special">,</span>
- <span class="identifier">Value2</span> <span class="special">>(</span>
- <span class="identifier">a1</span> <span class="special">,</span>
- <span class="identifier">a2</span> <span class="special">)</span>
- <span class="special">)</span></code>
- </p>
- </td>
- <td>
- <p>
- void
- </p>
- </td>
- <td>
- <p>
- Calculates <span class="emphasis"><em><span class="bold"><strong>y</strong></span> = a1
- <span class="bold"><strong>x1</strong></span> + a2 <span class="bold"><strong>x2</strong></span></em></span>
- </p>
- </td>
- </tr></tbody>
- </table></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 © 2009-2015 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>
- <hr>
- <div class="spirit-nav">
- <a accesskey="p" href="dense_output_stepper.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../concepts.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="state_wrapper.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
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