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| <div class="titlepage"><div><div><h3 class="title"> |
| <a name="math_toolkit.internals2.error_test"></a><a class="link" href="error_test.html" title="Relative Error and Testing">Relative Error and |
| Testing</a> |
| </h3></div></div></div> |
| <h5> |
| <a name="math_toolkit.internals2.error_test.h0"></a> |
| <span class="phrase"><a name="math_toolkit.internals2.error_test.synopsis"></a></span><a class="link" href="error_test.html#math_toolkit.internals2.error_test.synopsis">Synopsis</a> |
| </h5> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">test</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| </pre> |
| <div class="important"><table border="0" summary="Important"> |
| <tr> |
| <td rowspan="2" align="center" valign="top" width="25"><img alt="[Important]" src="../../../../../../doc/src/images/important.png"></td> |
| <th align="left">Important</th> |
| </tr> |
| <tr><td align="left" valign="top"><p> |
| The header <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">test</span><span class="special">.</span><span class="identifier">hpp</span></code> is located under <code class="computeroutput"><span class="identifier">libs</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">include_private</span></code> |
| and is not installed to the usual locations by default, you will need to |
| add <code class="computeroutput"><span class="identifier">libs</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">include_private</span></code> to your compiler's include |
| path in order to use this header. |
| </p></td></tr> |
| </table></div> |
| <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> |
| <span class="identifier">T</span> <span class="identifier">relative_error</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">b</span><span class="special">);</span> |
| |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">A</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">F1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">F2</span><span class="special">></span> |
| <span class="identifier">test_result</span><span class="special"><</span><span class="identifier">see</span><span class="special">-</span><span class="identifier">below</span><span class="special">></span> <span class="identifier">test</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">A</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">F1</span> <span class="identifier">test_func</span><span class="special">,</span> <span class="identifier">F2</span> <span class="identifier">expect_func</span><span class="special">);</span> |
| </pre> |
| <h5> |
| <a name="math_toolkit.internals2.error_test.h1"></a> |
| <span class="phrase"><a name="math_toolkit.internals2.error_test.description"></a></span><a class="link" href="error_test.html#math_toolkit.internals2.error_test.description">Description</a> |
| </h5> |
| <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> |
| <span class="identifier">T</span> <span class="identifier">relative_error</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">v</span><span class="special">);</span> |
| </pre> |
| <p> |
| Returns the relative error between <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>v</em></span> |
| using the usual formula: |
| </p> |
| <p> |
| <span class="inlinemediaobject"><img src="../../../equations/error1.svg"></span> |
| </p> |
| <p> |
| In addition the value returned is zero if: |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> |
| <li class="listitem"> |
| Both <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>v</em></span> are infinite. |
| </li> |
| <li class="listitem"> |
| Both <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>v</em></span> are denormalised |
| numbers or zero. |
| </li> |
| </ul></div> |
| <p> |
| Otherwise if only one of <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>v</em></span> |
| is zero then the value returned is 1. |
| </p> |
| <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">A</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">F1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">F2</span><span class="special">></span> |
| <span class="identifier">test_result</span><span class="special"><</span><span class="identifier">see</span><span class="special">-</span><span class="identifier">below</span><span class="special">></span> <span class="identifier">test</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">A</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">F1</span> <span class="identifier">test_func</span><span class="special">,</span> <span class="identifier">F2</span> <span class="identifier">expect_func</span><span class="special">);</span> |
| </pre> |
| <p> |
| This function is used for testing a function against tabulated test data. |
| </p> |
| <p> |
| The return type contains statistical data on the relative errors (max, mean, |
| variance, and the number of test cases etc), as well as the row of test data |
| that caused the largest relative error. Public members of type test_result |
| are: |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl class="variablelist"> |
| <dt><span class="term"><code class="computeroutput"><span class="keyword">unsigned</span> <span class="identifier">worst</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span></code></span></dt> |
| <dd><p> |
| Returns the row at which the worst error occurred. |
| </p></dd> |
| <dt><span class="term"><code class="computeroutput"><span class="identifier">T</span> <span class="identifier">min</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span></code></span></dt> |
| <dd><p> |
| Returns the smallest relative error found. |
| </p></dd> |
| <dt><span class="term"><code class="computeroutput"><span class="identifier">T</span> <span class="identifier">max</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span></code></span></dt> |
| <dd><p> |
| Returns the largest relative error found. |
| </p></dd> |
| <dt><span class="term"><code class="computeroutput"><span class="identifier">T</span> <span class="identifier">mean</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span></code></span></dt> |
| <dd><p> |
| Returns the mean error found. |
| </p></dd> |
| <dt><span class="term"><code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span> <span class="identifier">count</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span></code></span></dt> |
| <dd><p> |
| Returns the number of test cases. |
| </p></dd> |
| <dt><span class="term"><code class="computeroutput"><span class="identifier">T</span> <span class="identifier">variance</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span></code></span></dt> |
| <dd><p> |
| Returns the variance of the errors found. |
| </p></dd> |
| <dt><span class="term"><code class="computeroutput"><span class="identifier">T</span> <span class="identifier">variance1</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span></code></span></dt> |
| <dd><p> |
| Returns the unbiased variance of the errors found. |
| </p></dd> |
| <dt><span class="term"><code class="computeroutput"><span class="identifier">T</span> <span class="identifier">rms</span><span class="special">()</span><span class="keyword">const</span></code></span></dt> |
| <dd><p> |
| Returns the Root Mean Square, or quadratic mean of the errors. |
| </p></dd> |
| <dt><span class="term"><code class="computeroutput"><span class="identifier">test_result</span><span class="special">&</span> |
| <span class="keyword">operator</span><span class="special">+=(</span><span class="keyword">const</span> <span class="identifier">test_result</span><span class="special">&</span> <span class="identifier">t</span><span class="special">)</span></code></span></dt> |
| <dd><p> |
| Combines two test_result's into a single result. |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| The template parameter of test_result, is the same type as the values in |
| the two dimensional array passed to function <span class="emphasis"><em>test</em></span>, roughly |
| that's <code class="computeroutput"><span class="identifier">A</span><span class="special">::</span><span class="identifier">value_type</span><span class="special">::</span><span class="identifier">value_type</span></code>. |
| </p> |
| <p> |
| Parameter <span class="emphasis"><em>a</em></span> is a matrix of test data: and must be a |
| standard library Sequence type, that contains another Sequence type: typically |
| it will be a two dimensional instance of <code class="literal">boost::array</code>. |
| Each row of <span class="emphasis"><em>a</em></span> should contain all the parameters that |
| are passed to the function under test as well as the expected result. |
| </p> |
| <p> |
| Parameter <span class="emphasis"><em>test_func</em></span> is the function under test, it is |
| invoked with each row of test data in <span class="emphasis"><em>a</em></span>. Typically type |
| F1 is created with Boost.Lambda: see the example below. |
| </p> |
| <p> |
| Parameter <span class="emphasis"><em>expect_func</em></span> is a functor that extracts the |
| expected result from a row of test data in <span class="emphasis"><em>a</em></span>. Typically |
| type F2 is created with Boost.Lambda: see the example below. |
| </p> |
| <p> |
| If the function under test returns a non-finite value when a finite result |
| is expected, or if a gross error is found, then a message is sent to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cerr</span></code>, |
| and a call to BOOST_ERROR() made (which means that including this header |
| requires you use Boost.Test). This is mainly a debugging/development aid |
| (and a good place for a breakpoint). |
| </p> |
| <h5> |
| <a name="math_toolkit.internals2.error_test.h2"></a> |
| <span class="phrase"><a name="math_toolkit.internals2.error_test.example"></a></span><a class="link" href="error_test.html#math_toolkit.internals2.error_test.example">Example</a> |
| </h5> |
| <p> |
| Suppose we want to test the tgamma and lgamma functions, we can create a |
| two dimensional matrix of test data, each row is one test case, and contains |
| three elements: the input value, and the expected results for the tgamma |
| and lgamma functions respectively. |
| </p> |
| <pre class="programlisting"><span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span><span class="special"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span><span class="special"><</span><span class="identifier">TestType</span><span class="special">,</span> <span class="number">3</span><span class="special">>,</span> <span class="identifier">NumberOfTests</span><span class="special">></span> |
| <span class="identifier">factorials</span> <span class="special">=</span> <span class="special">{</span> |
| <span class="comment">/* big array of test data goes here */</span> |
| <span class="special">};</span> |
| </pre> |
| <p> |
| Now we can invoke the test function to test tgamma: |
| </p> |
| <pre class="programlisting"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">;</span> |
| <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">lambda</span><span class="special">;</span> |
| |
| <span class="comment">// get a pointer to the function under test:</span> |
| <span class="identifier">TestType</span> <span class="special">(*</span><span class="identifier">funcp</span><span class="special">)(</span><span class="identifier">TestType</span><span class="special">)</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">;</span> |
| |
| <span class="comment">// declare something to hold the result:</span> |
| <span class="identifier">test_result</span><span class="special"><</span><span class="identifier">TestType</span><span class="special">></span> <span class="identifier">result</span><span class="special">;</span> |
| <span class="comment">//</span> |
| <span class="comment">// and test tgamma against data:</span> |
| <span class="comment">//</span> |
| <span class="identifier">result</span> <span class="special">=</span> <span class="identifier">test</span><span class="special">(</span> |
| <span class="identifier">factorials</span><span class="special">,</span> |
| <span class="identifier">bind</span><span class="special">(</span><span class="identifier">funcp</span><span class="special">,</span> <span class="identifier">ret</span><span class="special"><</span><span class="identifier">TestType</span><span class="special">>(</span><span class="identifier">_1</span><span class="special">[</span><span class="number">0</span><span class="special">])),</span> <span class="comment">// calls tgamma with factorials[row][0]</span> |
| <span class="identifier">ret</span><span class="special"><</span><span class="identifier">TestType</span><span class="special">>(</span><span class="identifier">_1</span><span class="special">[</span><span class="number">1</span><span class="special">])</span> <span class="comment">// extracts the expected result from factorials[row][1]</span> |
| <span class="special">);</span> |
| <span class="comment">//</span> |
| <span class="comment">// Print out some results:</span> |
| <span class="comment">//</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"The Mean was "</span> <span class="special"><<</span> <span class="identifier">result</span><span class="special">.</span><span class="identifier">mean</span><span class="special">()</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"The worst error was "</span> <span class="special"><<</span> <span class="special">(</span><span class="identifier">result</span><span class="special">.</span><span class="identifier">max</span><span class="special">)()</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"The worst error was at row "</span> <span class="special"><<</span> <span class="identifier">result</span><span class="special">.</span><span class="identifier">worst_case</span><span class="special">()</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> |
| <span class="comment">//</span> |
| <span class="comment">// same again with lgamma this time:</span> |
| <span class="comment">//</span> |
| <span class="identifier">funcp</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">lgamma</span><span class="special">;</span> |
| <span class="identifier">result</span> <span class="special">=</span> <span class="identifier">test</span><span class="special">(</span> |
| <span class="identifier">factorials</span><span class="special">,</span> |
| <span class="identifier">bind</span><span class="special">(</span><span class="identifier">funcp</span><span class="special">,</span> <span class="identifier">ret</span><span class="special"><</span><span class="identifier">TestType</span><span class="special">>(</span><span class="identifier">_1</span><span class="special">[</span><span class="number">0</span><span class="special">])),</span> <span class="comment">// calls tgamma with factorials[row][0]</span> |
| <span class="identifier">ret</span><span class="special"><</span><span class="identifier">TestType</span><span class="special">>(</span><span class="identifier">_1</span><span class="special">[</span><span class="number">2</span><span class="special">])</span> <span class="comment">// extracts the expected result from factorials[row][2]</span> |
| <span class="special">);</span> |
| <span class="comment">//</span> |
| <span class="comment">// etc ...</span> |
| <span class="comment">//</span> |
| </pre> |
| </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 © 2006-2010, 2012-2014 Nikhar Agrawal, |
| Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert |
| Holin, Bruno Lalande, John Maddock, Johan Råde, Gautam Sewani, Benjamin Sobotta, |
| Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p> |
| Distributed under the Boost Software License, Version 1.0. (See accompanying |
| file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) |
| </p> |
| </div></td> |
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