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25 | <div class="section"> | |
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"><</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> | |
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"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></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"><</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> | |
52 | <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> | |
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"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></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"><</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> | |
85 | <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> | |
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">&</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">&</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"><</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> | |
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"><</span><span class="identifier">TestType</span><span class="special">></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"><</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> | |
199 | <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> | |
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"><<</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> | |
205 | <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> | |
206 | <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> | |
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"><</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> | |
214 | <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> | |
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 © 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 Råde, 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> | |
231 | </tr></table> | |
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