123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240 |
- <html>
- <head>
- <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
- <title>Relative Error and Testing</title>
- <link rel="stylesheet" href="../../math.css" type="text/css">
- <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
- <link rel="home" href="../../index.html" title="Math Toolkit 2.11.0">
- <link rel="up" href="../internals.html" title="Internal tools">
- <link rel="prev" href="minimax.html" title="Minimax Approximations and the Remez Algorithm">
- <link rel="next" href="test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">
- </head>
- <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
- <table cellpadding="2" width="100%"><tr>
- <td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
- <td align="center"><a href="../../../../../../index.html">Home</a></td>
- <td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td>
- <td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
- <td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
- <td align="center"><a href="../../../../../../more/index.htm">More</a></td>
- </tr></table>
- <hr>
- <div class="spirit-nav">
- <a accesskey="p" href="minimax.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../internals.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="test_data.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h3 class="title">
- <a name="math_toolkit.internals.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.internals.error_test.h0"></a>
- <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>
- </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.internals.error_test.h1"></a>
- <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>
- </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>
- <div class="blockquote"><blockquote class="blockquote"><p>
- <span class="inlinemediaobject"><img src="../../../equations/error1.svg"></span>
- </p></blockquote></div>
- <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.internals.error_test.h2"></a>
- <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>
- </h5>
- <p>
- Suppose we want to test the <code class="computeroutput"><span class="identifier">tgamma</span></code>
- and <code class="computeroutput"><span class="identifier">lgamma</span></code> 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 <code class="computeroutput"><span class="identifier">tgamma</span></code> and <code class="computeroutput"><span class="identifier">lgamma</span></code> 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 © 2006-2019 Nikhar
- Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
- Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
- Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, 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>
- </tr></table>
- <hr>
- <div class="spirit-nav">
- <a accesskey="p" href="minimax.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../internals.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="test_data.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
- </div>
- </body>
- </html>
|