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<div class="titlepage"><div><div><h4 class="title">
<a name="math_toolkit.toolkit.internals2.error_test"></a><a class="link" href="error_test.html" title="Relative Error and Testing"> Relative
Error and Testing</a>
</h4></div></div></div>
<a name="math_toolkit.toolkit.internals2.error_test.synopsis"></a><h5>
<a name="id1216523"></a>
<a class="link" href="error_test.html#math_toolkit.toolkit.internals2.error_test.synopsis">Synopsis</a>
</h5>
<p>
</p>
<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>
</pre>
<p>
</p>
<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>
<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">&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>
<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>
</pre>
<a name="math_toolkit.toolkit.internals2.error_test.description"></a><h5>
<a name="id1216779"></a>
<a class="link" href="error_test.html#math_toolkit.toolkit.internals2.error_test.description">Description</a>
</h5>
<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>
<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.png"></span>
</p>
<p>
In addition the value returned is zero if:
</p>
<div class="itemizedlist"><ul type="disc">
<li>
Both <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>v</em></span> are infinite.
</li>
<li>
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">&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>
<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>
</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>
<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">&amp;</span>
<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>
<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>
<a name="math_toolkit.toolkit.internals2.error_test.example"></a><h5>
<a name="id1219562"></a>
<a class="link" href="error_test.html#math_toolkit.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">&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>
<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">&lt;</span><span class="identifier">TestType</span><span class="special">&gt;</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">&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> <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><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">&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>
<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>
<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>
<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">&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> <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><span class="special">);</span>
<span class="comment">//
</span><span class="comment">// etc ...
</span><span class="comment">//
</span></pre>
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<td align="right"><div class="copyright-footer">Copyright &#169; 2006 , 2007, 2008, 2009, 2010 John Maddock, Paul A. Bristow,
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan R&#229;de, Gautam Sewani and
Thijs van den Berg<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>)
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