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<div class="section">
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<div class="titlepage"><div><div><h3 class="title">
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<a name="math_toolkit.internals.error_test"></a><a class="link" href="error_test.html" title="Relative Error and Testing">Relative Error and
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Testing</a>
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</h3></div></div></div>
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<h5>
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<a name="math_toolkit.internals.error_test.h0"></a>
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<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>
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</h5>
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<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>
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</pre>
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<div class="important"><table border="0" summary="Important">
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<tr>
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<td rowspan="2" align="center" valign="top" width="25"><img alt="[Important]" src="../../../../../../doc/src/images/important.png"></td>
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<th align="left">Important</th>
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</tr>
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<tr><td align="left" valign="top"><p>
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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>
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and is NOT installed to the usual locations by default; you will need to
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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
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path in order to use this header.
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</p></td></tr>
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</table></div>
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<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>
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<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>
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<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>
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<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>
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</pre>
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<h5>
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<a name="math_toolkit.internals.error_test.h1"></a>
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<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>
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</h5>
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<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>
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<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>
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</pre>
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<p>
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Returns the relative error between <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>v</em></span>
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using the usual formula:
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</p>
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<div class="blockquote"><blockquote class="blockquote"><p>
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<span class="inlinemediaobject"><img src="../../../equations/error1.svg"></span>
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</p></blockquote></div>
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<p>
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In addition the value returned is zero if:
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</p>
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<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
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<li class="listitem">
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Both <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>v</em></span> are infinite.
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</li>
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<li class="listitem">
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Both <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>v</em></span> are denormalised
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numbers or zero.
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</li>
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</ul></div>
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<p>
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Otherwise if only one of <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>v</em></span>
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is zero then the value returned is 1.
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</p>
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<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>
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<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>
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</pre>
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<p>
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This function is used for testing a function against tabulated test data.
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</p>
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<p>
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The return type contains statistical data on the relative errors (max, mean,
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variance, and the number of test cases etc), as well as the row of test data
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that caused the largest relative error. Public members of type test_result
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are:
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</p>
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<div class="variablelist">
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<p class="title"><b></b></p>
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<dl class="variablelist">
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<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>
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<dd><p>
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Returns the row at which the worst error occurred.
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</p></dd>
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<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>
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<dd><p>
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Returns the smallest relative error found.
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</p></dd>
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<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>
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<dd><p>
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Returns the largest relative error found.
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</p></dd>
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<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>
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<dd><p>
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Returns the mean error found.
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</p></dd>
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<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>
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<dd><p>
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Returns the number of test cases.
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</p></dd>
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<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>
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<dd><p>
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Returns the variance of the errors found.
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</p></dd>
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<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>
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<dd><p>
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Returns the unbiased variance of the errors found.
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</p></dd>
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<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>
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<dd><p>
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Returns the Root Mean Square, or quadratic mean of the errors.
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</p></dd>
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<dt><span class="term"><code class="computeroutput"><span class="identifier">test_result</span><span class="special">&</span>
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<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>
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<dd><p>
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Combines two test_result's into a single result.
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</p></dd>
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</dl>
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</div>
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<p>
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The template parameter of test_result, is the same type as the values in
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the two dimensional array passed to function <span class="emphasis"><em>test</em></span>, roughly
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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>.
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</p>
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<p>
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Parameter <span class="emphasis"><em>a</em></span> is a matrix of test data: and must be a
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standard library Sequence type, that contains another Sequence type: typically
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it will be a two dimensional instance of <code class="literal">boost::array</code>.
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Each row of <span class="emphasis"><em>a</em></span> should contain all the parameters that
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are passed to the function under test as well as the expected result.
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</p>
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<p>
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Parameter <span class="emphasis"><em>test_func</em></span> is the function under test, it is
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invoked with each row of test data in <span class="emphasis"><em>a</em></span>. Typically type
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F1 is created with Boost.Lambda: see the example below.
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</p>
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<p>
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Parameter <span class="emphasis"><em>expect_func</em></span> is a functor that extracts the
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expected result from a row of test data in <span class="emphasis"><em>a</em></span>. Typically
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type F2 is created with Boost.Lambda: see the example below.
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</p>
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<p>
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If the function under test returns a non-finite value when a finite result
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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>,
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and a call to BOOST_ERROR() made (which means that including this header
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requires you use Boost.Test). This is mainly a debugging/development aid
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(and a good place for a breakpoint).
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</p>
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<h5>
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<a name="math_toolkit.internals.error_test.h2"></a>
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<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>
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</h5>
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<p>
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Suppose we want to test the <code class="computeroutput"><span class="identifier">tgamma</span></code>
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and <code class="computeroutput"><span class="identifier">lgamma</span></code> functions, we
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can create a two-dimensional matrix of test data, each row is one test case,
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and contains three elements: the input value, and the expected results for
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the <code class="computeroutput"><span class="identifier">tgamma</span></code> and <code class="computeroutput"><span class="identifier">lgamma</span></code> functions respectively.
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</p>
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<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>
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<span class="identifier">factorials</span> <span class="special">=</span> <span class="special">{</span>
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<span class="comment">/* big array of test data goes here */</span>
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<span class="special">};</span>
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</pre>
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<p>
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Now we can invoke the test function to test tgamma:
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</p>
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<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>
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<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>
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<span class="comment">// get a pointer to the function under test:</span>
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<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>
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<span class="comment">// declare something to hold the result:</span>
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<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>
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<span class="comment">//</span>
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<span class="comment">// and test tgamma against data:</span>
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<span class="comment">//</span>
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<span class="identifier">result</span> <span class="special">=</span> <span class="identifier">test</span><span class="special">(</span>
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<span class="identifier">factorials</span><span class="special">,</span>
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<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>
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<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>
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<span class="special">);</span>
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<span class="comment">//</span>
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<span class="comment">// Print out some results:</span>
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<span class="comment">//</span>
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<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>
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<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>
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<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>
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<span class="comment">//</span>
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<span class="comment">// same again with lgamma this time:</span>
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<span class="comment">//</span>
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<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>
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<span class="identifier">result</span> <span class="special">=</span> <span class="identifier">test</span><span class="special">(</span>
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<span class="identifier">factorials</span><span class="special">,</span>
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<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>
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<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>
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<span class="special">);</span>
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<span class="comment">//</span>
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<span class="comment">// etc ...</span>
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<span class="comment">//</span>
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</pre>
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</div>
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="left"></td>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2019 Nikhar
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Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
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Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
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Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
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Daryle Walker and Xiaogang Zhang<p>
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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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>)
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</p>
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</div></td>
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</tr></table>
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