ceph/src/boost/libs/math/doc/html/math_toolkit/internals/error_test.html

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  26 <div class="titlepage"><div><div><h3 class="title">
  27 <a name="math_toolkit.internals.error_test"></a><a class="link" href="error_test.html" title="Relative Error and Testing">Relative Error and
  28       Testing</a>
  29 </h3></div></div></div>
  30 <h5>
  31 <a name="math_toolkit.internals.error_test.h0"></a>
  32         <span class="phrase"><a name="math_toolkit.internals.error_test.synopsis"></a></span><a class="link" href="error_test.html#math_toolkit.internals.error_test.synopsis">Synopsis</a>
  33       </h5>
  34 <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</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">&gt;</span>
  35 </pre>
  36 <div class="important"><table border="0" summary="Important">
  37 <tr>
  38 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Important]" src="../../../../../../doc/src/images/important.png"></td>
  39 <th align="left">Important</th>
  40 </tr>
  41 <tr><td align="left" valign="top"><p>
  42           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>
  43           and is not installed to the usual locations by default, you will need to
  44           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
  45           path in order to use this header.
  46         </p></td></tr>
  47 </table></div>
  48 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
  49 <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>
  50
  51 <span class="keyword">template</span> <span class="special">&lt;</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">&gt;</span>
  52 <span class="identifier">test_result</span><span class="special">&lt;</span><span class="identifier">see</span><span class="special">-</span><span class="identifier">below</span><span class="special">&gt;</span> <span class="identifier">test</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">A</span><span class="special">&amp;</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>
  53 </pre>
  54 <h5>
  55 <a name="math_toolkit.internals.error_test.h1"></a>
  56         <span class="phrase"><a name="math_toolkit.internals.error_test.description"></a></span><a class="link" href="error_test.html#math_toolkit.internals.error_test.description">Description</a>
  57       </h5>
  58 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
  59 <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>
  60 </pre>
  61 <p>
  62         Returns the relative error between <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>v</em></span>
  63         using the usual formula:
  64       </p>
  65 <p>
  66         <span class="inlinemediaobject"><img src="../../../equations/error1.svg"></span>
  67       </p>
  68 <p>
  69         In addition the value returned is zero if:
  70       </p>
  71 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
  72 <li class="listitem">
  73             Both <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>v</em></span> are infinite.
  74           </li>
  75 <li class="listitem">
  76             Both <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>v</em></span> are denormalised
  77             numbers or zero.
  78           </li>
  79 </ul></div>
  80 <p>
  81         Otherwise if only one of <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>v</em></span>
  82         is zero then the value returned is 1.
  83       </p>
  84 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</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">&gt;</span>
  85 <span class="identifier">test_result</span><span class="special">&lt;</span><span class="identifier">see</span><span class="special">-</span><span class="identifier">below</span><span class="special">&gt;</span> <span class="identifier">test</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">A</span><span class="special">&amp;</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>
  86 </pre>
  87 <p>
  88         This function is used for testing a function against tabulated test data.
  89       </p>
  90 <p>
  91         The return type contains statistical data on the relative errors (max, mean,
  92         variance, and the number of test cases etc), as well as the row of test data
  93         that caused the largest relative error. Public members of type test_result
  94         are:
  95       </p>
  96 <div class="variablelist">
  97 <p class="title"><b></b></p>
  98 <dl class="variablelist">
  99 <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>
 100 <dd><p>
 101               Returns the row at which the worst error occurred.
 102             </p></dd>
 103 <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>
 104 <dd><p>
 105               Returns the smallest relative error found.
 106             </p></dd>
 107 <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>
 108 <dd><p>
 109               Returns the largest relative error found.
 110             </p></dd>
 111 <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>
 112 <dd><p>
 113               Returns the mean error found.
 114             </p></dd>
 115 <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>
 116 <dd><p>
 117               Returns the number of test cases.
 118             </p></dd>
 119 <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>
 120 <dd><p>
 121               Returns the variance of the errors found.
 122             </p></dd>
 123 <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>
 124 <dd><p>
 125               Returns the unbiased variance of the errors found.
 126             </p></dd>
 127 <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>
 128 <dd><p>
 129               Returns the Root Mean Square, or quadratic mean of the errors.
 130             </p></dd>
 131 <dt><span class="term"><code class="computeroutput"><span class="identifier">test_result</span><span class="special">&amp;</span>
 132           <span class="keyword">operator</span><span class="special">+=(</span><span class="keyword">const</span> <span class="identifier">test_result</span><span class="special">&amp;</span> <span class="identifier">t</span><span class="special">)</span></code></span></dt>
 133 <dd><p>
 134               Combines two test_result's into a single result.
 135             </p></dd>
 136 </dl>
 137 </div>
 138 <p>
 139         The template parameter of test_result, is the same type as the values in
 140         the two dimensional array passed to function <span class="emphasis"><em>test</em></span>, roughly
 141         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>.
 142       </p>
 143 <p>
 144         Parameter <span class="emphasis"><em>a</em></span> is a matrix of test data: and must be a
 145         standard library Sequence type, that contains another Sequence type: typically
 146         it will be a two dimensional instance of <code class="literal">boost::array</code>.
 147         Each row of <span class="emphasis"><em>a</em></span> should contain all the parameters that
 148         are passed to the function under test as well as the expected result.
 149       </p>
 150 <p>
 151         Parameter <span class="emphasis"><em>test_func</em></span> is the function under test, it is
 152         invoked with each row of test data in <span class="emphasis"><em>a</em></span>. Typically type
 153         F1 is created with Boost.Lambda: see the example below.
 154       </p>
 155 <p>
 156         Parameter <span class="emphasis"><em>expect_func</em></span> is a functor that extracts the
 157         expected result from a row of test data in <span class="emphasis"><em>a</em></span>. Typically
 158         type F2 is created with Boost.Lambda: see the example below.
 159       </p>
 160 <p>
 161         If the function under test returns a non-finite value when a finite result
 162         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>,
 163         and a call to BOOST_ERROR() made (which means that including this header
 164         requires you use Boost.Test). This is mainly a debugging/development aid
 165         (and a good place for a breakpoint).
 166       </p>
 167 <h5>
 168 <a name="math_toolkit.internals.error_test.h2"></a>
 169         <span class="phrase"><a name="math_toolkit.internals.error_test.example"></a></span><a class="link" href="error_test.html#math_toolkit.internals.error_test.example">Example</a>
 170       </h5>
 171 <p>
 172         Suppose we want to test the tgamma and lgamma functions, we can create a
 173         two dimensional matrix of test data, each row is one test case, and contains
 174         three elements: the input value, and the expected results for the tgamma
 175         and lgamma functions respectively.
 176       </p>
 177 <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">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span><span class="special">&lt;</span><span class="identifier">TestType</span><span class="special">,</span> <span class="number">3</span><span class="special">&gt;,</span> <span class="identifier">NumberOfTests</span><span class="special">&gt;</span>
 178    <span class="identifier">factorials</span> <span class="special">=</span> <span class="special">{</span>
 179       <span class="comment">/* big array of test data goes here */</span>
 180    <span class="special">};</span>
 181 </pre>
 182 <p>
 183         Now we can invoke the test function to test tgamma:
 184       </p>
 185 <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>
 186 <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>
 187
 188 <span class="comment">// get a pointer to the function under test:</span>
 189 <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>
 190
 191 <span class="comment">// declare something to hold the result:</span>
 192 <span class="identifier">test_result</span><span class="special">&lt;</span><span class="identifier">TestType</span><span class="special">&gt;</span> <span class="identifier">result</span><span class="special">;</span>
 193 <span class="comment">//</span>
 194 <span class="comment">// and test tgamma against data:</span>
 195 <span class="comment">//</span>
 196 <span class="identifier">result</span> <span class="special">=</span> <span class="identifier">test</span><span class="special">(</span>
 197    <span class="identifier">factorials</span><span class="special">,</span>
 198    <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">&lt;</span><span class="identifier">TestType</span><span class="special">&gt;(</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>
 199    <span class="identifier">ret</span><span class="special">&lt;</span><span class="identifier">TestType</span><span class="special">&gt;(</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>
 200 <span class="special">);</span>
 201 <span class="comment">//</span>
 202 <span class="comment">// Print out some results:</span>
 203 <span class="comment">//</span>
 204 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"The Mean was "</span> <span class="special">&lt;&lt;</span> <span class="identifier">result</span><span class="special">.</span><span class="identifier">mean</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
 205 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"The worst error was "</span> <span class="special">&lt;&lt;</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">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
 206 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"The worst error was at row "</span> <span class="special">&lt;&lt;</span> <span class="identifier">result</span><span class="special">.</span><span class="identifier">worst_case</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
 207 <span class="comment">//</span>
 208 <span class="comment">// same again with lgamma this time:</span>
 209 <span class="comment">//</span>
 210 <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>
 211 <span class="identifier">result</span> <span class="special">=</span> <span class="identifier">test</span><span class="special">(</span>
 212    <span class="identifier">factorials</span><span class="special">,</span>
 213    <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">&lt;</span><span class="identifier">TestType</span><span class="special">&gt;(</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>
 214    <span class="identifier">ret</span><span class="special">&lt;</span><span class="identifier">TestType</span><span class="special">&gt;(</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>
 215 <span class="special">);</span>
 216 <span class="comment">//</span>
 217 <span class="comment">// etc ...</span>
 218 <span class="comment">//</span>
 219 </pre>
 220 </div>
 221 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 222 <td align="left"></td>
 223 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
 224       Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
 225       Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam Sewani,
 226       Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
 227         Distributed under the Boost Software License, Version 1.0. (See accompanying
 228         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>)
 229       </p>
 230 </div></td>
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