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  25 <div class="section">
  26 <div class="titlepage"><div><div><h3 class="title">
  27 <a name="math_toolkit.internals.test_data"></a><a class="link" href="test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">Graphing, Profiling,
  28       and Generating Test Data for Special Functions</a>
  29 </h3></div></div></div>
  30 <p>
  31         The class <code class="computeroutput"><span class="identifier">test_data</span></code> and associated
  32         helper functions are designed so that in just a few lines of code you should
  33         be able to:
  34       </p>
  35 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
  36 <li class="listitem">
  37             Profile a continued fraction, or infinite series for convergence and
  38             accuracy.
  39           </li>
  40 <li class="listitem">
  41             Generate csv data from a special function that can be imported into your
  42             favorite graphing program (or spreadsheet) for further analysis.
  43           </li>
  44 <li class="listitem">
  45             Generate high precision test data.
  46           </li>
  47 </ul></div>
  48 <h5>
  49 <a name="math_toolkit.internals.test_data.h0"></a>
  50         <span class="phrase"><a name="math_toolkit.internals.test_data.synopsis"></a></span><a class="link" href="test_data.html#math_toolkit.internals.test_data.synopsis">Synopsis</a>
  51       </h5>
  52 <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_data</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
  53 </pre>
  54 <div class="important"><table border="0" summary="Important">
  55 <tr>
  56 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Important]" src="../../../../../../doc/src/images/important.png"></td>
  57 <th align="left">Important</th>
  58 </tr>
  59 <tr><td align="left" valign="top"><p>
  60           This is a non-core Boost.Math header that is predominantly used for internal
  61           maintenance of the library: as a result the library 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 you will need to
  62           add that directory to your include path in order to use this feature.
  63         </p></td></tr>
  64 </table></div>
  65 <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">tools</span><span class="special">{</span>
  66
  67 <span class="keyword">enum</span> <span class="identifier">parameter_type</span>
  68 <span class="special">{</span>
  69    <span class="identifier">random_in_range</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span>
  70    <span class="identifier">periodic_in_range</span> <span class="special">=</span> <span class="number">1</span><span class="special">,</span>
  71    <span class="identifier">power_series</span> <span class="special">=</span> <span class="number">2</span><span class="special">,</span>
  72    <span class="identifier">dummy_param</span> <span class="special">=</span> <span class="number">0x80</span><span class="special">,</span>
  73 <span class="special">};</span>
  74
  75 <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>
  76 <span class="keyword">struct</span> <span class="identifier">parameter_info</span><span class="special">;</span>
  77
  78 <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>
  79 <span class="identifier">parameter_info</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">make_random_param</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">start_range</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">end_range</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">n_points</span><span class="special">);</span>
  80
  81 <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>
  82 <span class="identifier">parameter_info</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">make_periodic_param</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">start_range</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">end_range</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">n_points</span><span class="special">);</span>
  83
  84 <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>
  85 <span class="identifier">parameter_info</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">make_power_param</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">basis</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">start_exponent</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">end_exponent</span><span class="special">);</span>
  86
  87 <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>
  88 <span class="keyword">bool</span> <span class="identifier">get_user_parameter_info</span><span class="special">(</span><span class="identifier">parameter_info</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">info</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">param_name</span><span class="special">);</span>
  89
  90 <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>
  91 <span class="keyword">class</span> <span class="identifier">test_data</span>
  92 <span class="special">{</span>
  93 <span class="keyword">public</span><span class="special">:</span>
  94    <span class="keyword">typedef</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">row_type</span><span class="special">;</span>
  95    <span class="keyword">typedef</span> <span class="identifier">row_type</span> <span class="identifier">value_type</span><span class="special">;</span>
  96 <span class="keyword">private</span><span class="special">:</span>
  97    <span class="keyword">typedef</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">set</span><span class="special">&lt;</span><span class="identifier">row_type</span><span class="special">&gt;</span> <span class="identifier">container_type</span><span class="special">;</span>
  98 <span class="keyword">public</span><span class="special">:</span>
  99    <span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">container_type</span><span class="special">::</span><span class="identifier">reference</span> <span class="identifier">reference</span><span class="special">;</span>
 100    <span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">container_type</span><span class="special">::</span><span class="identifier">const_reference</span> <span class="identifier">const_reference</span><span class="special">;</span>
 101    <span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">container_type</span><span class="special">::</span><span class="identifier">iterator</span> <span class="identifier">iterator</span><span class="special">;</span>
 102    <span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">container_type</span><span class="special">::</span><span class="identifier">const_iterator</span> <span class="identifier">const_iterator</span><span class="special">;</span>
 103    <span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">container_type</span><span class="special">::</span><span class="identifier">difference_type</span> <span class="identifier">difference_type</span><span class="special">;</span>
 104    <span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">container_type</span><span class="special">::</span><span class="identifier">size_type</span> <span class="identifier">size_type</span><span class="special">;</span>
 105
 106    <span class="comment">// creation:</span>
 107    <span class="identifier">test_data</span><span class="special">(){}</span>
 108    <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">&gt;</span>
 109    <span class="identifier">test_data</span><span class="special">(</span><span class="identifier">F</span> <span class="identifier">func</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">parameter_info</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">arg1</span><span class="special">);</span>
 110
 111    <span class="comment">// insertion:</span>
 112    <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">&gt;</span>
 113    <span class="identifier">test_data</span><span class="special">&amp;</span> <span class="identifier">insert</span><span class="special">(</span><span class="identifier">F</span> <span class="identifier">func</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">parameter_info</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">arg1</span><span class="special">);</span>
 114
 115    <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">&gt;</span>
 116    <span class="identifier">test_data</span><span class="special">&amp;</span> <span class="identifier">insert</span><span class="special">(</span><span class="identifier">F</span> <span class="identifier">func</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">parameter_info</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">arg1</span><span class="special">,</span>
 117                      <span class="keyword">const</span> <span class="identifier">parameter_info</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">arg2</span><span class="special">);</span>
 118
 119    <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">&gt;</span>
 120    <span class="identifier">test_data</span><span class="special">&amp;</span> <span class="identifier">insert</span><span class="special">(</span><span class="identifier">F</span> <span class="identifier">func</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">parameter_info</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">arg1</span><span class="special">,</span>
 121                      <span class="keyword">const</span> <span class="identifier">parameter_info</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">arg2</span><span class="special">,</span>
 122                      <span class="keyword">const</span> <span class="identifier">parameter_info</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">arg3</span><span class="special">);</span>
 123
 124    <span class="keyword">void</span> <span class="identifier">clear</span><span class="special">();</span>
 125
 126    <span class="comment">// access:</span>
 127    <span class="identifier">iterator</span> <span class="identifier">begin</span><span class="special">();</span>
 128    <span class="identifier">iterator</span> <span class="identifier">end</span><span class="special">();</span>
 129    <span class="identifier">const_iterator</span> <span class="identifier">begin</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
 130    <span class="identifier">const_iterator</span> <span class="identifier">end</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
 131    <span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">==(</span><span class="keyword">const</span> <span class="identifier">test_data</span><span class="special">&amp;</span> <span class="identifier">d</span><span class="special">)</span><span class="keyword">const</span><span class="special">;</span>
 132    <span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">!=(</span><span class="keyword">const</span> <span class="identifier">test_data</span><span class="special">&amp;</span> <span class="identifier">d</span><span class="special">)</span><span class="keyword">const</span><span class="special">;</span>
 133    <span class="keyword">void</span> <span class="identifier">swap</span><span class="special">(</span><span class="identifier">test_data</span><span class="special">&amp;</span> <span class="identifier">other</span><span class="special">);</span>
 134    <span class="identifier">size_type</span> <span class="identifier">size</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
 135    <span class="identifier">size_type</span> <span class="identifier">max_size</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
 136    <span class="keyword">bool</span> <span class="identifier">empty</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
 137
 138    <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">&lt;</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">test_data</span><span class="special">&amp;</span> <span class="identifier">dat</span><span class="special">)</span><span class="keyword">const</span><span class="special">;</span>
 139    <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">&lt;=</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">test_data</span><span class="special">&amp;</span> <span class="identifier">dat</span><span class="special">)</span><span class="keyword">const</span><span class="special">;</span>
 140    <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">&gt;</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">test_data</span><span class="special">&amp;</span> <span class="identifier">dat</span><span class="special">)</span><span class="keyword">const</span><span class="special">;</span>
 141    <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">&gt;=</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">test_data</span><span class="special">&amp;</span> <span class="identifier">dat</span><span class="special">)</span><span class="keyword">const</span><span class="special">;</span>
 142 <span class="special">};</span>
 143
 144 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">charT</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">traits</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
 145 <span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span> <span class="identifier">traits</span><span class="special">&gt;&amp;</span> <span class="identifier">write_csv</span><span class="special">(</span>
 146             <span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span> <span class="identifier">traits</span><span class="special">&gt;&amp;</span> <span class="identifier">os</span><span class="special">,</span>
 147             <span class="keyword">const</span> <span class="identifier">test_data</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">data</span><span class="special">);</span>
 148
 149 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">charT</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">traits</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
 150 <span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span> <span class="identifier">traits</span><span class="special">&gt;&amp;</span> <span class="identifier">write_csv</span><span class="special">(</span>
 151             <span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span> <span class="identifier">traits</span><span class="special">&gt;&amp;</span> <span class="identifier">os</span><span class="special">,</span>
 152             <span class="keyword">const</span> <span class="identifier">test_data</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">data</span><span class="special">,</span>
 153             <span class="keyword">const</span> <span class="identifier">charT</span><span class="special">*</span> <span class="identifier">separator</span><span class="special">);</span>
 154
 155 <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>
 156 <span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream</span><span class="special">&amp;</span> <span class="identifier">write_code</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream</span><span class="special">&amp;</span> <span class="identifier">os</span><span class="special">,</span>
 157                          <span class="keyword">const</span> <span class="identifier">test_data</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">data</span><span class="special">,</span>
 158                          <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">name</span><span class="special">);</span>
 159
 160 <span class="special">}}}</span> <span class="comment">// namespaces</span>
 161 </pre>
 162 <h5>
 163 <a name="math_toolkit.internals.test_data.h1"></a>
 164         <span class="phrase"><a name="math_toolkit.internals.test_data.description"></a></span><a class="link" href="test_data.html#math_toolkit.internals.test_data.description">Description</a>
 165       </h5>
 166 <p>
 167         This tool is best illustrated with the following series of examples.
 168       </p>
 169 <p>
 170         The functionality of test_data is split into the following parts:
 171       </p>
 172 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 173 <li class="listitem">
 174             A functor that implements the function for which data is being generated:
 175             this is the bit you have to write.
 176           </li>
 177 <li class="listitem">
 178             One of more parameters that are to be passed to the functor, these are
 179             described in fairly abstract terms: give me N points distributed like
 180             <span class="emphasis"><em>this</em></span> etc.
 181           </li>
 182 <li class="listitem">
 183             The class test_data, that takes the functor and descriptions of the parameters
 184             and computes how ever many output points have been requested, these are
 185             stored in a sorted container.
 186           </li>
 187 <li class="listitem">
 188             Routines to iterate over the test_data container and output the data
 189             in either csv format, or as C++ source code (as a table using Boost.Array).
 190           </li>
 191 </ul></div>
 192 <h6>
 193 <a name="math_toolkit.internals.test_data.h2"></a>
 194         <span class="phrase"><a name="math_toolkit.internals.test_data.example_1_output_data_for_graph_"></a></span><a class="link" href="test_data.html#math_toolkit.internals.test_data.example_1_output_data_for_graph_">Example
 195         1: Output Data for Graph Plotting</a>
 196       </h6>
 197 <p>
 198         For example, lets say we want to graph the lgamma function between -3 and
 199         100, one could do this like so:
 200       </p>
 201 <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_data</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
 202 <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">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
 203
 204 <span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
 205 <span class="special">{</span>
 206    <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>
 207
 208    <span class="comment">// create an object to hold the data:</span>
 209    <span class="identifier">test_data</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">data</span><span class="special">;</span>
 210
 211    <span class="comment">// insert 500 points at uniform intervals between just after -3 and 100:</span>
 212    <span class="keyword">double</span> <span class="special">(*</span><span class="identifier">pf</span><span class="special">)(</span><span class="keyword">double</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">lgamma</span><span class="special">;</span>
 213    <span class="identifier">data</span><span class="special">.</span><span class="identifier">insert</span><span class="special">(</span><span class="identifier">pf</span><span class="special">,</span> <span class="identifier">make_periodic_param</span><span class="special">(-</span><span class="number">3.0</span> <span class="special">+</span> <span class="number">0.00001</span><span class="special">,</span> <span class="number">100.0</span><span class="special">,</span> <span class="number">500</span><span class="special">));</span>
 214
 215    <span class="comment">// print out in csv format:</span>
 216    <span class="identifier">write_csv</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="identifier">data</span><span class="special">,</span> <span class="string">", "</span><span class="special">);</span>
 217    <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
 218 <span class="special">}</span>
 219 </pre>
 220 <p>
 221         Which, when plotted, results in:
 222       </p>
 223 <div class="blockquote"><blockquote class="blockquote"><p>
 224           <span class="inlinemediaobject"><img src="../../../graphs/lgamma.svg" align="middle"></span>
 225
 226         </p></blockquote></div>
 227 <h6>
 228 <a name="math_toolkit.internals.test_data.h3"></a>
 229         <span class="phrase"><a name="math_toolkit.internals.test_data.example_2_creating_test_data"></a></span><a class="link" href="test_data.html#math_toolkit.internals.test_data.example_2_creating_test_data">Example
 230         2: Creating Test Data</a>
 231       </h6>
 232 <p>
 233         As a second example, let's suppose we want to create highly accurate test
 234         data for a special function. Since many special functions have two or more
 235         independent parameters, it's very hard to effectively cover all of the possible
 236         parameter space without generating gigabytes of data at great computational
 237         expense. A second best approach is to provide the tools by which a user (or
 238         the library maintainer) can quickly generate more data on demand to probe
 239         the function over a particular domain of interest.
 240       </p>
 241 <p>
 242         In this example we'll generate test data for the beta function using <a href="http://shoup.net/ntl/doc/RR.txt" target="_top">NTL::RR</a> at 1000 bit precision.
 243         Rather than call our generic version of the beta function, we'll implement
 244         a deliberately naive version of the beta function using lgamma, and rely
 245         on the high precision of the data type used to get results accurate to at
 246         least 128-bit precision. In this way our test data is independent of whatever
 247         clever tricks we may wish to use inside the our beta function.
 248       </p>
 249 <p>
 250         To start with then, here's the function object that creates the test data:
 251       </p>
 252 <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">ntl</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
 253 <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">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
 254 <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_data</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
 255 <span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">fstream</span><span class="special">&gt;</span>
 256
 257 <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_data</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
 258
 259 <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>
 260
 261 <span class="keyword">struct</span> <span class="identifier">beta_data_generator</span>
 262 <span class="special">{</span>
 263    <span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span> <span class="identifier">b</span><span class="special">)</span>
 264    <span class="special">{</span>
 265       <span class="comment">//</span>
 266       <span class="comment">// If we throw a domain error then test_data will</span>
 267       <span class="comment">// ignore this input point. We'll use this to filter</span>
 268       <span class="comment">// out all cases where a &lt; b since the beta function</span>
 269       <span class="comment">// is symmetrical in a and b:</span>
 270       <span class="comment">//</span>
 271       <span class="keyword">if</span><span class="special">(</span><span class="identifier">a</span> <span class="special">&lt;</span> <span class="identifier">b</span><span class="special">)</span>
 272          <span class="keyword">throw</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">domain_error</span><span class="special">(</span><span class="string">""</span><span class="special">);</span>
 273
 274       <span class="comment">// very naively calculate spots with lgamma:</span>
 275       <span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span> <span class="identifier">g1</span><span class="special">,</span> <span class="identifier">g2</span><span class="special">,</span> <span class="identifier">g3</span><span class="special">;</span>
 276       <span class="keyword">int</span> <span class="identifier">s1</span><span class="special">,</span> <span class="identifier">s2</span><span class="special">,</span> <span class="identifier">s3</span><span class="special">;</span>
 277       <span class="identifier">g1</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">a</span><span class="special">,</span> <span class="special">&amp;</span><span class="identifier">s1</span><span class="special">);</span>
 278       <span class="identifier">g2</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">b</span><span class="special">,</span> <span class="special">&amp;</span><span class="identifier">s2</span><span class="special">);</span>
 279       <span class="identifier">g3</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">a</span><span class="special">+</span><span class="identifier">b</span><span class="special">,</span> <span class="special">&amp;</span><span class="identifier">s3</span><span class="special">);</span>
 280       <span class="identifier">g1</span> <span class="special">+=</span> <span class="identifier">g2</span> <span class="special">-</span> <span class="identifier">g3</span><span class="special">;</span>
 281       <span class="identifier">g1</span> <span class="special">=</span> <span class="identifier">exp</span><span class="special">(</span><span class="identifier">g1</span><span class="special">);</span>
 282       <span class="identifier">g1</span> <span class="special">*=</span> <span class="identifier">s1</span> <span class="special">*</span> <span class="identifier">s2</span> <span class="special">*</span> <span class="identifier">s3</span><span class="special">;</span>
 283       <span class="keyword">return</span> <span class="identifier">g1</span><span class="special">;</span>
 284    <span class="special">}</span>
 285 <span class="special">};</span>
 286 </pre>
 287 <p>
 288         To create the data, we'll need to input the domains for a and b for which
 289         the function will be tested: the function <code class="computeroutput"><span class="identifier">get_user_parameter_info</span></code>
 290         is designed for just that purpose. The start of main will look something
 291         like:
 292       </p>
 293 <pre class="programlisting"><span class="comment">// Set the precision on RR:</span>
 294 <span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span><span class="special">::</span><span class="identifier">SetPrecision</span><span class="special">(</span><span class="number">1000</span><span class="special">);</span> <span class="comment">// bits.</span>
 295 <span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span><span class="special">::</span><span class="identifier">SetOutputPrecision</span><span class="special">(</span><span class="number">40</span><span class="special">);</span> <span class="comment">// decimal digits.</span>
 296
 297 <span class="identifier">parameter_info</span><span class="special">&lt;</span><span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span><span class="special">&gt;</span> <span class="identifier">arg1</span><span class="special">,</span> <span class="identifier">arg2</span><span class="special">;</span>
 298 <span class="identifier">test_data</span><span class="special">&lt;</span><span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span><span class="special">&gt;</span> <span class="identifier">data</span><span class="special">;</span>
 299
 300 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Welcome.\n"</span>
 301    <span class="string">"This program will generate spot tests for the beta function:\n"</span>
 302    <span class="string">"  beta(a, b)\n\n"</span><span class="special">;</span>
 303
 304 <span class="keyword">bool</span> <span class="identifier">cont</span><span class="special">;</span>
 305 <span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">line</span><span class="special">;</span>
 306
 307 <span class="keyword">do</span><span class="special">{</span>
 308    <span class="comment">// prompt the user for the domain of a and b to test:</span>
 309    <span class="identifier">get_user_parameter_info</span><span class="special">(</span><span class="identifier">arg1</span><span class="special">,</span> <span class="string">"a"</span><span class="special">);</span>
 310    <span class="identifier">get_user_parameter_info</span><span class="special">(</span><span class="identifier">arg2</span><span class="special">,</span> <span class="string">"b"</span><span class="special">);</span>
 311
 312    <span class="comment">// create the data:</span>
 313    <span class="identifier">data</span><span class="special">.</span><span class="identifier">insert</span><span class="special">(</span><span class="identifier">beta_data_generator</span><span class="special">(),</span> <span class="identifier">arg1</span><span class="special">,</span> <span class="identifier">arg2</span><span class="special">);</span>
 314
 315    <span class="comment">// see if the user want's any more domains tested:</span>
 316    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Any more data [y/n]?"</span><span class="special">;</span>
 317    <span class="identifier">std</span><span class="special">::</span><span class="identifier">getline</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">cin</span><span class="special">,</span> <span class="identifier">line</span><span class="special">);</span>
 318    <span class="identifier">boost</span><span class="special">::</span><span class="identifier">algorithm</span><span class="special">::</span><span class="identifier">trim</span><span class="special">(</span><span class="identifier">line</span><span class="special">);</span>
 319    <span class="identifier">cont</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">line</span> <span class="special">==</span> <span class="string">"y"</span><span class="special">);</span>
 320 <span class="special">}</span><span class="keyword">while</span><span class="special">(</span><span class="identifier">cont</span><span class="special">);</span>
 321 </pre>
 322 <div class="caution"><table border="0" summary="Caution">
 323 <tr>
 324 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../../doc/src/images/caution.png"></td>
 325 <th align="left">Caution</th>
 326 </tr>
 327 <tr><td align="left" valign="top"><p>
 328           At this point one potential stumbling block should be mentioned: test_data&lt;&gt;::insert
 329           will create a matrix of test data when there are two or more parameters,
 330           so if we have two parameters and we're asked for a thousand points on each,
 331           that's a <span class="emphasis"><em>million test points in total</em></span>. Don't say you
 332           weren't warned!
 333         </p></td></tr>
 334 </table></div>
 335 <p>
 336         There's just one final step now, and that's to write the test data to file:
 337       </p>
 338 <pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Enter name of test data file [default=beta_data.ipp]"</span><span class="special">;</span>
 339 <span class="identifier">std</span><span class="special">::</span><span class="identifier">getline</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">cin</span><span class="special">,</span> <span class="identifier">line</span><span class="special">);</span>
 340 <span class="identifier">boost</span><span class="special">::</span><span class="identifier">algorithm</span><span class="special">::</span><span class="identifier">trim</span><span class="special">(</span><span class="identifier">line</span><span class="special">);</span>
 341 <span class="keyword">if</span><span class="special">(</span><span class="identifier">line</span> <span class="special">==</span> <span class="string">""</span><span class="special">)</span>
 342    <span class="identifier">line</span> <span class="special">=</span> <span class="string">"beta_data.ipp"</span><span class="special">;</span>
 343 <span class="identifier">std</span><span class="special">::</span><span class="identifier">ofstream</span> <span class="identifier">ofs</span><span class="special">(</span><span class="identifier">line</span><span class="special">.</span><span class="identifier">c_str</span><span class="special">());</span>
 344 <span class="identifier">write_code</span><span class="special">(</span><span class="identifier">ofs</span><span class="special">,</span> <span class="identifier">data</span><span class="special">,</span> <span class="string">"beta_data"</span><span class="special">);</span>
 345 </pre>
 346 <p>
 347         The format of the test data looks something like:
 348       </p>
 349 <pre class="programlisting"><span class="preprocessor">#define</span> <span class="identifier">SC_</span><span class="special">(</span><span class="identifier">x</span><span class="special">)</span> <span class="keyword">static_cast</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="identifier">BOOST_JOIN</span><span class="special">(</span><span class="identifier">x</span><span class="special">,</span> <span class="identifier">L</span><span class="special">))</span>
 350    <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">T</span><span class="special">,</span> <span class="number">3</span><span class="special">&gt;,</span> <span class="number">1830</span><span class="special">&gt;</span>
 351    <span class="identifier">beta_med_data</span> <span class="special">=</span> <span class="special">{</span>
 352       <span class="identifier">SC_</span><span class="special">(</span><span class="number">0.4883005917072296142578125</span><span class="special">),</span>
 353       <span class="identifier">SC_</span><span class="special">(</span><span class="number">0.4883005917072296142578125</span><span class="special">),</span>
 354       <span class="identifier">SC_</span><span class="special">(</span><span class="number">3.245912809500479157065104747353807392371</span><span class="special">),</span>
 355       <span class="identifier">SC_</span><span class="special">(</span><span class="number">3.5808107852935791015625</span><span class="special">),</span>
 356       <span class="identifier">SC_</span><span class="special">(</span><span class="number">0.4883005917072296142578125</span><span class="special">),</span>
 357       <span class="identifier">SC_</span><span class="special">(</span><span class="number">1.007653173802923954909901438393379243537</span><span class="special">),</span>
 358       <span class="comment">/* ... lots of rows skipped */</span>
 359 <span class="special">};</span>
 360 </pre>
 361 <p>
 362         The first two values in each row are the input parameters that were passed
 363         to our functor and the last value is the return value from the functor. Had
 364         our functor returned a <a class="link" href="tuples.html" title="Tuples">boost::math::tuple</a>
 365         rather than a value, then we would have had one entry for each element in
 366         the tuple in addition to the input parameters.
 367       </p>
 368 <p>
 369         The first #define serves two purposes:
 370       </p>
 371 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 372 <li class="listitem">
 373             It reduces the file sizes considerably: all those <code class="computeroutput"><span class="keyword">static_cast</span></code>'s
 374             add up to a lot of bytes otherwise (they are needed to suppress compiler
 375             warnings when <code class="computeroutput"><span class="identifier">T</span></code> is narrower
 376             than a <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>).
 377           </li>
 378 <li class="listitem">
 379             It provides a useful customisation point: for example if we were testing
 380             a user-defined type that has more precision than a <code class="computeroutput"><span class="keyword">long</span>
 381             <span class="keyword">double</span></code> we could change it to:
 382           </li>
 383 </ul></div>
 384 <p>
 385         <code class="literal">#define SC_(x) lexical_cast&lt;T&gt;(BOOST_STRINGIZE(x))</code>
 386       </p>
 387 <p>
 388         in order to ensure that no truncation of the values occurs prior to conversion
 389         to <code class="computeroutput"><span class="identifier">T</span></code>. Note that this isn't
 390         used by default as it's rather hard on the compiler when the table is large.
 391       </p>
 392 <h6>
 393 <a name="math_toolkit.internals.test_data.h4"></a>
 394         <span class="phrase"><a name="math_toolkit.internals.test_data.example_3_profiling_a_continued_"></a></span><a class="link" href="test_data.html#math_toolkit.internals.test_data.example_3_profiling_a_continued_">Example
 395         3: Profiling a Continued Fraction for Convergence and Accuracy</a>
 396       </h6>
 397 <p>
 398         Alternatively, lets say we want to profile a continued fraction for convergence
 399         and error. As an example, we'll use the continued fraction for the upper
 400         incomplete gamma function, the following function object returns the next
 401         a<sub>N </sub> and b<sub>N </sub> of the continued fraction each time it's invoked:
 402       </p>
 403 <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>
 404 <span class="keyword">struct</span> <span class="identifier">upper_incomplete_gamma_fract</span>
 405 <span class="special">{</span>
 406 <span class="keyword">private</span><span class="special">:</span>
 407    <span class="identifier">T</span> <span class="identifier">z</span><span class="special">,</span> <span class="identifier">a</span><span class="special">;</span>
 408    <span class="keyword">int</span> <span class="identifier">k</span><span class="special">;</span>
 409 <span class="keyword">public</span><span class="special">:</span>
 410    <span class="keyword">typedef</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">result_type</span><span class="special">;</span>
 411
 412    <span class="identifier">upper_incomplete_gamma_fract</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">a1</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">z1</span><span class="special">)</span>
 413       <span class="special">:</span> <span class="identifier">z</span><span class="special">(</span><span class="identifier">z1</span><span class="special">-</span><span class="identifier">a1</span><span class="special">+</span><span class="number">1</span><span class="special">),</span> <span class="identifier">a</span><span class="special">(</span><span class="identifier">a1</span><span class="special">),</span> <span class="identifier">k</span><span class="special">(</span><span class="number">0</span><span class="special">)</span>
 414    <span class="special">{</span>
 415    <span class="special">}</span>
 416
 417    <span class="identifier">result_type</span> <span class="keyword">operator</span><span class="special">()()</span>
 418    <span class="special">{</span>
 419       <span class="special">++</span><span class="identifier">k</span><span class="special">;</span>
 420       <span class="identifier">z</span> <span class="special">+=</span> <span class="number">2</span><span class="special">;</span>
 421       <span class="keyword">return</span> <span class="identifier">result_type</span><span class="special">(</span><span class="identifier">k</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">a</span> <span class="special">-</span> <span class="identifier">k</span><span class="special">),</span> <span class="identifier">z</span><span class="special">);</span>
 422    <span class="special">}</span>
 423 <span class="special">};</span>
 424 </pre>
 425 <p>
 426         We want to measure both the relative error, and the rate of convergence of
 427         this fraction, so we'll write a functor that returns both as a <a class="link" href="tuples.html" title="Tuples">boost::math::tuple</a>:
 428         class test_data will unpack the tuple for us, and create one column of data
 429         for each element in the tuple (in addition to the input parameters):
 430       </p>
 431 <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_data</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
 432 <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>
 433 <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">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
 434 <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">ntl</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
 435 <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">tuple</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
 436
 437 <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>
 438 <span class="keyword">struct</span> <span class="identifier">profile_gamma_fraction</span>
 439 <span class="special">{</span>
 440    <span class="keyword">typedef</span> <a class="link" href="tuples.html" title="Tuples">boost::math::tuple</a><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">result_type</span><span class="special">;</span>
 441
 442    <span class="identifier">result_type</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">T</span> <span class="identifier">val</span><span class="special">)</span>
 443    <span class="special">{</span>
 444       <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>
 445       <span class="comment">// estimate the true value, using arbitary precision</span>
 446       <span class="comment">// arithmetic and NTL::RR:</span>
 447       <span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span> <span class="identifier">rval</span><span class="special">(</span><span class="identifier">val</span><span class="special">);</span>
 448       <span class="identifier">upper_incomplete_gamma_fract</span><span class="special">&lt;</span><span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span><span class="special">&gt;</span> <span class="identifier">f1</span><span class="special">(</span><span class="identifier">rval</span><span class="special">,</span> <span class="identifier">rval</span><span class="special">);</span>
 449       <span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span> <span class="identifier">true_val</span> <span class="special">=</span> <span class="identifier">continued_fraction_a</span><span class="special">(</span><span class="identifier">f1</span><span class="special">,</span> <span class="number">1000</span><span class="special">);</span>
 450       <span class="comment">//</span>
 451       <span class="comment">// Now get the aproximation at double precision, along with the number of</span>
 452       <span class="comment">// iterations required:</span>
 453       <span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span> <span class="identifier">iters</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">&gt;::</span><span class="identifier">max</span><span class="special">();</span>
 454       <span class="identifier">upper_incomplete_gamma_fract</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">f2</span><span class="special">(</span><span class="identifier">val</span><span class="special">,</span> <span class="identifier">val</span><span class="special">);</span>
 455       <span class="identifier">T</span> <span class="identifier">found_val</span> <span class="special">=</span> <span class="identifier">continued_fraction_a</span><span class="special">(</span><span class="identifier">f2</span><span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">digits</span><span class="special">,</span> <span class="identifier">iters</span><span class="special">);</span>
 456       <span class="comment">//</span>
 457       <span class="comment">// Work out the relative error, as measured in units of epsilon:</span>
 458       <span class="identifier">T</span> <span class="identifier">err</span> <span class="special">=</span> <span class="identifier">real_cast</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="identifier">relative_error</span><span class="special">(</span><span class="identifier">true_val</span><span class="special">,</span> <span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span><span class="special">(</span><span class="identifier">found_val</span><span class="special">))</span> <span class="special">/</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">epsilon</span><span class="special">());</span>
 459       <span class="comment">//</span>
 460       <span class="comment">// now just return the results as a tuple:</span>
 461       <span class="keyword">return</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">make_tuple</span><span class="special">(</span><span class="identifier">err</span><span class="special">,</span> <span class="identifier">iters</span><span class="special">);</span>
 462    <span class="special">}</span>
 463 <span class="special">};</span>
 464 </pre>
 465 <p>
 466         Feeding that functor into test_data allows rapid output of csv data, for
 467         whatever type <code class="computeroutput"><span class="identifier">T</span></code> we may be
 468         interested in:
 469       </p>
 470 <pre class="programlisting"><span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
 471 <span class="special">{</span>
 472    <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>
 473    <span class="comment">// create an object to hold the data:</span>
 474    <span class="identifier">test_data</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">data</span><span class="special">;</span>
 475    <span class="comment">// insert 500 points at uniform intervals between just after 0 and 100:</span>
 476    <span class="identifier">data</span><span class="special">.</span><span class="identifier">insert</span><span class="special">(</span><span class="identifier">profile_gamma_fraction</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;(),</span> <span class="identifier">make_periodic_param</span><span class="special">(</span><span class="number">0.01</span><span class="special">,</span> <span class="number">100.0</span><span class="special">,</span> <span class="number">100</span><span class="special">));</span>
 477    <span class="comment">// print out in csv format:</span>
 478    <span class="identifier">write_csv</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="identifier">data</span><span class="special">,</span> <span class="string">", "</span><span class="special">);</span>
 479    <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
 480 <span class="special">}</span>
 481 </pre>
 482 <p>
 483         This time there's no need to plot a graph, the first few rows are:
 484       </p>
 485 <pre class="programlisting"><span class="identifier">a</span> <span class="keyword">and</span> <span class="identifier">z</span><span class="special">,</span>  <span class="identifier">Error</span><span class="special">/</span><span class="identifier">epsilon</span><span class="special">,</span>  <span class="identifier">Iterations</span> <span class="identifier">required</span>
 486
 487 <span class="number">0.01</span><span class="special">,</span>     <span class="number">9723.14</span><span class="special">,</span>        <span class="number">4726</span>
 488 <span class="number">1.0099</span><span class="special">,</span>   <span class="number">9.54818</span><span class="special">,</span>        <span class="number">87</span>
 489 <span class="number">2.0098</span><span class="special">,</span>   <span class="number">3.84777</span><span class="special">,</span>        <span class="number">40</span>
 490 <span class="number">3.0097</span><span class="special">,</span>   <span class="number">0.728358</span><span class="special">,</span>       <span class="number">25</span>
 491 <span class="number">4.0096</span><span class="special">,</span>   <span class="number">2.39712</span><span class="special">,</span>        <span class="number">21</span>
 492 <span class="number">5.0095</span><span class="special">,</span>   <span class="number">0.233263</span><span class="special">,</span>       <span class="number">16</span>
 493 </pre>
 494 <p>
 495         So it's pretty clear that this fraction shouldn't be used for small values
 496         of <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>z</em></span>.
 497       </p>
 498 <h5>
 499 <a name="math_toolkit.internals.test_data.h5"></a>
 500         <span class="phrase"><a name="math_toolkit.internals.test_data.reference"></a></span><a class="link" href="test_data.html#math_toolkit.internals.test_data.reference">reference</a>
 501       </h5>
 502 <p>
 503         Most of this tool has been described already in the examples above, we'll
 504         just add the following notes on the non-member functions:
 505       </p>
 506 <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>
 507 <span class="identifier">parameter_info</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">make_random_param</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">start_range</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">end_range</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">n_points</span><span class="special">);</span>
 508 </pre>
 509 <p>
 510         Tells class test_data to test <span class="emphasis"><em>n_points</em></span> random values
 511         in the range [start_range,end_range].
 512       </p>
 513 <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>
 514 <span class="identifier">parameter_info</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">make_periodic_param</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">start_range</span><span class="special">,</span> <span class="identifier">T</span> <span class="identifier">end_range</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">n_points</span><span class="special">);</span>
 515 </pre>
 516 <p>
 517         Tells class test_data to test <span class="emphasis"><em>n_points</em></span> evenly spaced
 518         values in the range [start_range,end_range].
 519       </p>
 520 <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>
 521 <span class="identifier">parameter_info</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">make_power_param</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">basis</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">start_exponent</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">end_exponent</span><span class="special">);</span>
 522 </pre>
 523 <p>
 524         Tells class test_data to test points of the form <span class="emphasis"><em>basis + R * 2<sup>expon</sup></em></span>
 525         for each <span class="emphasis"><em>expon</em></span> in the range [start_exponent, end_exponent],
 526         and <span class="emphasis"><em>R</em></span> a random number in [0.5, 1].
 527       </p>
 528 <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>
 529 <span class="keyword">bool</span> <span class="identifier">get_user_parameter_info</span><span class="special">(</span><span class="identifier">parameter_info</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">info</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">param_name</span><span class="special">);</span>
 530 </pre>
 531 <p>
 532         Prompts the user for the parameter range and form to use.
 533       </p>
 534 <p>
 535         Finally, if we don't want the parameter to be included in the output, we
 536         can tell test_data by setting it a "dummy parameter":
 537       </p>
 538 <pre class="programlisting"><span class="identifier">parameter_info</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">p</span> <span class="special">=</span> <span class="identifier">make_random_param</span><span class="special">(</span><span class="number">2.0</span><span class="special">,</span> <span class="number">5.0</span><span class="special">,</span> <span class="number">10</span><span class="special">);</span>
 539 <span class="identifier">p</span><span class="special">.</span><span class="identifier">type</span> <span class="special">|=</span> <span class="identifier">dummy_param</span><span class="special">;</span>
 540 </pre>
 541 <p>
 542         This is useful when the functor used transforms the parameter in some way
 543         before passing it to the function under test, usually the functor will then
 544         return both the transformed input and the result in a tuple, so there's no
 545         need for the original pseudo-parameter to be included in program output.
 546       </p>
 547 </div>
 548 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 549 <td align="left"></td>
 550 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
 551       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
 552       Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
 553       R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
 554       Daryle Walker and Xiaogang Zhang<p>
 555         Distributed under the Boost Software License, Version 1.0. (See accompanying
 556         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>)
 557       </p>
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