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| <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 © 2009-2012 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> |
| <hr> |
| <div class="spirit-nav"> |
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