| <html> |
| <head> |
| <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> |
| <title>Graphing, Profiling, and Generating Test Data for Special Functions</title> |
| <link rel="stylesheet" href="../../../../../../../../doc/src/boostbook.css" type="text/css"> |
| <meta name="generator" content="DocBook XSL Stylesheets V1.74.0"> |
| <link rel="home" href="../../../index.html" title="Math Toolkit"> |
| <link rel="up" href="../internals2.html" title="Testing and Development"> |
| <link rel="prev" href="error_test.html" title="Relative Error and Testing"> |
| <link rel="next" href="../../using_udt.html" title="Use with User-Defined Floating-Point Types"> |
| </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="error_test.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../internals2.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="../../using_udt.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> |
| </div> |
| <div class="section" lang="en"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="math_toolkit.toolkit.internals2.test_data"></a><a class="link" href="test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions"> Graphing, |
| Profiling, and Generating Test Data for Special Functions</a> |
| </h4></div></div></div> |
| <p> |
| The class <code class="computeroutput"><span class="identifier">test_data</span></code> and |
| associated helper functions are designed so that in just a few lines of |
| code you should be able to: |
| </p> |
| <div class="itemizedlist"><ul type="disc"> |
| <li> |
| Profile a continued fraction, or infinite series for convergence and |
| accuracy. |
| </li> |
| <li> |
| Generate csv data from a special function that can be imported into |
| your favorite graphing program (or spreadsheet) for further analysis. |
| </li> |
| <li> |
| Generate high precision test data. |
| </li> |
| </ul></div> |
| <a name="math_toolkit.toolkit.internals2.test_data.synopsis"></a><h5> |
| <a name="id1220365"></a> |
| <a class="link" href="test_data.html#math_toolkit.toolkit.internals2.test_data.synopsis">Synopsis</a> |
| </h5> |
| <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> |
| |
| <span class="keyword">enum</span> <span class="identifier">parameter_type</span> |
| <span class="special">{</span> |
| <span class="identifier">random_in_range</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> |
| <span class="identifier">periodic_in_range</span> <span class="special">=</span> <span class="number">1</span><span class="special">,</span> |
| <span class="identifier">power_series</span> <span class="special">=</span> <span class="number">2</span><span class="special">,</span> |
| <span class="identifier">dummy_param</span> <span class="special">=</span> <span class="number">0x80</span><span class="special">,</span> |
| <span class="special">};</span> |
| |
| <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="keyword">struct</span> <span class="identifier">parameter_info</span><span class="special">;</span> |
| |
| <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">parameter_info</span><span class="special"><</span><span class="identifier">T</span><span class="special">></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> |
| |
| <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">parameter_info</span><span class="special"><</span><span class="identifier">T</span><span class="special">></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> |
| |
| <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">parameter_info</span><span class="special"><</span><span class="identifier">T</span><span class="special">></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> |
| |
| <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="keyword">bool</span> <span class="identifier">get_user_parameter_info</span><span class="special">(</span><span class="identifier">parameter_info</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</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> |
| |
| <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="keyword">class</span> <span class="identifier">test_data</span> |
| <span class="special">{</span> |
| <span class="keyword">public</span><span class="special">:</span> |
| <span class="keyword">typedef</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">row_type</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">row_type</span> <span class="identifier">value_type</span><span class="special">;</span> |
| <span class="keyword">private</span><span class="special">:</span> |
| <span class="keyword">typedef</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">set</span><span class="special"><</span><span class="identifier">row_type</span><span class="special">></span> <span class="identifier">container_type</span><span class="special">;</span> |
| <span class="keyword">public</span><span class="special">:</span> |
| <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> |
| <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> |
| <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> |
| <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> |
| <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> |
| <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> |
| |
| <span class="comment">// creation: |
| </span> <span class="identifier">test_data</span><span class="special">(){}</span> |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">></span> |
| <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"><</span><span class="identifier">T</span><span class="special">>&</span> <span class="identifier">arg1</span><span class="special">);</span> |
| |
| <span class="comment">// insertion: |
| </span> <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">></span> |
| <span class="identifier">test_data</span><span class="special">&</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"><</span><span class="identifier">T</span><span class="special">>&</span> <span class="identifier">arg1</span><span class="special">);</span> |
| |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">></span> |
| <span class="identifier">test_data</span><span class="special">&</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"><</span><span class="identifier">T</span><span class="special">>&</span> <span class="identifier">arg1</span><span class="special">,</span> |
| <span class="keyword">const</span> <span class="identifier">parameter_info</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <span class="identifier">arg2</span><span class="special">);</span> |
| |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">F</span><span class="special">></span> |
| <span class="identifier">test_data</span><span class="special">&</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"><</span><span class="identifier">T</span><span class="special">>&</span> <span class="identifier">arg1</span><span class="special">,</span> |
| <span class="keyword">const</span> <span class="identifier">parameter_info</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <span class="identifier">arg2</span><span class="special">,</span> |
| <span class="keyword">const</span> <span class="identifier">parameter_info</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <span class="identifier">arg3</span><span class="special">);</span> |
| |
| <span class="keyword">void</span> <span class="identifier">clear</span><span class="special">();</span> |
| |
| <span class="comment">// access: |
| </span> <span class="identifier">iterator</span> <span class="identifier">begin</span><span class="special">();</span> |
| <span class="identifier">iterator</span> <span class="identifier">end</span><span class="special">();</span> |
| <span class="identifier">const_iterator</span> <span class="identifier">begin</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> |
| <span class="identifier">const_iterator</span> <span class="identifier">end</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> |
| <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">&</span> <span class="identifier">d</span><span class="special">)</span><span class="keyword">const</span><span class="special">;</span> |
| <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">&</span> <span class="identifier">d</span><span class="special">)</span><span class="keyword">const</span><span class="special">;</span> |
| <span class="keyword">void</span> <span class="identifier">swap</span><span class="special">(</span><span class="identifier">test_data</span><span class="special">&</span> <span class="identifier">other</span><span class="special">);</span> |
| <span class="identifier">size_type</span> <span class="identifier">size</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> |
| <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> |
| <span class="keyword">bool</span> <span class="identifier">empty</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> |
| |
| <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special"><</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">test_data</span><span class="special">&</span> <span class="identifier">dat</span><span class="special">)</span><span class="keyword">const</span><span class="special">;</span> |
| <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special"><=</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">test_data</span><span class="special">&</span> <span class="identifier">dat</span><span class="special">)</span><span class="keyword">const</span><span class="special">;</span> |
| <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">></span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">test_data</span><span class="special">&</span> <span class="identifier">dat</span><span class="special">)</span><span class="keyword">const</span><span class="special">;</span> |
| <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">>=</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">test_data</span><span class="special">&</span> <span class="identifier">dat</span><span class="special">)</span><span class="keyword">const</span><span class="special">;</span> |
| <span class="special">};</span> |
| |
| <span class="keyword">template</span> <span class="special"><</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">></span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span> <span class="identifier">traits</span><span class="special">>&</span> <span class="identifier">write_csv</span><span class="special">(</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span> <span class="identifier">traits</span><span class="special">>&</span> <span class="identifier">os</span><span class="special">,</span> |
| <span class="keyword">const</span> <span class="identifier">test_data</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <span class="identifier">data</span><span class="special">);</span> |
| |
| <span class="keyword">template</span> <span class="special"><</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">></span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span> <span class="identifier">traits</span><span class="special">>&</span> <span class="identifier">write_csv</span><span class="special">(</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special"><</span><span class="identifier">charT</span><span class="special">,</span> <span class="identifier">traits</span><span class="special">>&</span> <span class="identifier">os</span><span class="special">,</span> |
| <span class="keyword">const</span> <span class="identifier">test_data</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <span class="identifier">data</span><span class="special">,</span> |
| <span class="keyword">const</span> <span class="identifier">charT</span><span class="special">*</span> <span class="identifier">separator</span><span class="special">);</span> |
| |
| <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">std</span><span class="special">::</span><span class="identifier">ostream</span><span class="special">&</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">&</span> <span class="identifier">os</span><span class="special">,</span> |
| <span class="keyword">const</span> <span class="identifier">test_data</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</span> <span class="identifier">data</span><span class="special">,</span> |
| <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">name</span><span class="special">);</span> |
| |
| <span class="special">}}}</span> <span class="comment">// namespaces |
| </span></pre> |
| <a name="math_toolkit.toolkit.internals2.test_data.description"></a><h5> |
| <a name="id1223079"></a> |
| <a class="link" href="test_data.html#math_toolkit.toolkit.internals2.test_data.description">Description</a> |
| </h5> |
| <p> |
| This tool is best illustrated with the following series of examples. |
| </p> |
| <p> |
| The functionality of test_data is split into the following parts: |
| </p> |
| <div class="itemizedlist"><ul type="disc"> |
| <li> |
| A functor that implements the function for which data is being generated: |
| this is the bit you have to write. |
| </li> |
| <li> |
| One of more parameters that are to be passed to the functor, these |
| are described in fairly abstract terms: give me N points distributed |
| like <span class="emphasis"><em>this</em></span> etc. |
| </li> |
| <li> |
| The class test_data, that takes the functor and descriptions of the |
| parameters and computes how ever many output points have been requested, |
| these are stored in a sorted container. |
| </li> |
| <li> |
| Routines to iterate over the test_data container and output the data |
| in either csv format, or as C++ source code (as a table using Boost.Array). |
| </li> |
| </ul></div> |
| <a name="math_toolkit.toolkit.internals2.test_data.example_1__output_data_for_graph_plotting"></a><h6> |
| <a name="id1223135"></a> |
| <a class="link" href="test_data.html#math_toolkit.toolkit.internals2.test_data.example_1__output_data_for_graph_plotting">Example |
| 1: Output Data for Graph Plotting</a> |
| </h6> |
| <p> |
| For example, lets say we want to graph the lgamma function between -3 and |
| 100, one could do this like so: |
| </p> |
| <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_data</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| <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">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| |
| <span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</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">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">;</span> |
| |
| <span class="comment">// create an object to hold the data: |
| </span> <span class="identifier">test_data</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="identifier">data</span><span class="special">;</span> |
| |
| <span class="comment">// insert 500 points at uniform intervals between just after -3 and 100: |
| </span> <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> |
| <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> |
| |
| <span class="comment">// print out in csv format: |
| </span> <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> |
| <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> |
| <span class="special">}</span> |
| </pre> |
| <p> |
| Which, when plotted, results in: |
| </p> |
| <p> |
| <span class="inlinemediaobject"><img src="../../../../graphs/lgamma.png" align="middle"></span> |
| </p> |
| <a name="math_toolkit.toolkit.internals2.test_data.example_2__creating_test_data"></a><h6> |
| <a name="id1223539"></a> |
| <a class="link" href="test_data.html#math_toolkit.toolkit.internals2.test_data.example_2__creating_test_data">Example |
| 2: Creating Test Data</a> |
| </h6> |
| <p> |
| As a second example, let's suppose we want to create highly accurate test |
| data for a special function. Since many special functions have two or more |
| independent parameters, it's very hard to effectively cover all of the |
| possible parameter space without generating gigabytes of data at great |
| computational expense. A second best approach is to provide the tools by |
| which a user (or the library maintainer) can quickly generate more data |
| on demand to probe the function over a particular domain of interest. |
| </p> |
| <p> |
| 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. |
| Rather than call our generic version of the beta function, we'll implement |
| a deliberately naive version of the beta function using lgamma, and rely |
| on the high precision of the data type used to get results accurate to |
| at least 128-bit precision. In this way our test data is independent of |
| whatever clever tricks we may wish to use inside the our beta function. |
| </p> |
| <p> |
| To start with then, here's the function object that creates the test data: |
| </p> |
| <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">ntl</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| <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">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| <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_data</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">fstream</span><span class="special">></span> |
| |
| <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_data</span><span class="special">.</span><span class="identifier">hpp</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">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">;</span> |
| |
| <span class="keyword">struct</span> <span class="identifier">beta_data_generator</span> |
| <span class="special">{</span> |
| <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> |
| <span class="special">{</span> |
| <span class="comment">// |
| </span> <span class="comment">// If we throw a domain error then test_data will |
| </span> <span class="comment">// ignore this input point. We'll use this to filter |
| </span> <span class="comment">// out all cases where a < b since the beta function |
| </span> <span class="comment">// is symmetrical in a and b: |
| </span> <span class="comment">// |
| </span> <span class="keyword">if</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="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> |
| |
| <span class="comment">// very naively calculate spots with lgamma: |
| </span> <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> |
| <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> |
| <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">&</span><span class="identifier">s1</span><span class="special">);</span> |
| <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">&</span><span class="identifier">s2</span><span class="special">);</span> |
| <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">&</span><span class="identifier">s3</span><span class="special">);</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> |
| <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> |
| <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> |
| <span class="keyword">return</span> <span class="identifier">g1</span><span class="special">;</span> |
| <span class="special">}</span> |
| <span class="special">};</span> |
| </pre> |
| <p> |
| To create the data, we'll need to input the domains for a and b for which |
| the function will be tested: the function <code class="computeroutput"><span class="identifier">get_user_parameter_info</span></code> |
| is designed for just that purpose. The start of main will look something |
| like: |
| </p> |
| <pre class="programlisting"><span class="comment">// Set the precision on RR: |
| </span><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><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> |
| <span class="identifier">parameter_info</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">arg1</span><span class="special">,</span> <span class="identifier">arg2</span><span class="special">;</span> |
| <span class="identifier">test_data</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">data</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">"Welcome.\n"</span> |
| <span class="string">"This program will generate spot tests for the beta function:\n"</span> |
| <span class="string">" beta(a, b)\n\n"</span><span class="special">;</span> |
| |
| <span class="keyword">bool</span> <span class="identifier">cont</span><span class="special">;</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">line</span><span class="special">;</span> |
| |
| <span class="keyword">do</span><span class="special">{</span> |
| <span class="comment">// prompt the user for the domain of a and b to test: |
| </span> <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> |
| <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> |
| |
| <span class="comment">// create the data: |
| </span> <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> |
| |
| <span class="comment">// see if the user want's any more domains tested: |
| </span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Any more data [y/n]?"</span><span class="special">;</span> |
| <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> |
| <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> |
| <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> |
| <span class="special">}</span><span class="keyword">while</span><span class="special">(</span><span class="identifier">cont</span><span class="special">);</span> |
| </pre> |
| <div class="caution"><table border="0" summary="Caution"> |
| <tr> |
| <td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../../../../doc/src/images/caution.png"></td> |
| <th align="left">Caution</th> |
| </tr> |
| <tr><td align="left" valign="top"><p> |
| At this point one potential stumbling block should be mentioned: test_data<>::insert |
| will create a matrix of test data when there are two or more parameters, |
| so if we have two parameters and we're asked for a thousand points on |
| each, that's a <span class="emphasis"><em>million test points in total</em></span>. Don't |
| say you weren't warned! |
| </p></td></tr> |
| </table></div> |
| <p> |
| There's just one final step now, and that's to write the test data to file: |
| </p> |
| <pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Enter name of test data file [default=beta_data.ipp]"</span><span class="special">;</span> |
| <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> |
| <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> |
| <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> |
| <span class="identifier">line</span> <span class="special">=</span> <span class="string">"beta_data.ipp"</span><span class="special">;</span> |
| <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> |
| <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> |
| </pre> |
| <p> |
| The format of the test data looks something like: |
| </p> |
| <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"><</span><span class="identifier">T</span><span class="special">>(</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> |
| <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">T</span><span class="special">,</span> <span class="number">3</span><span class="special">>,</span> <span class="number">1830</span><span class="special">></span> |
| <span class="identifier">beta_med_data</span> <span class="special">=</span> <span class="special">{</span> |
| <span class="identifier">SC_</span><span class="special">(</span><span class="number">0.4883005917072296142578125</span><span class="special">),</span> |
| <span class="identifier">SC_</span><span class="special">(</span><span class="number">0.4883005917072296142578125</span><span class="special">),</span> |
| <span class="identifier">SC_</span><span class="special">(</span><span class="number">3.245912809500479157065104747353807392371</span><span class="special">),</span> |
| <span class="identifier">SC_</span><span class="special">(</span><span class="number">3.5808107852935791015625</span><span class="special">),</span> |
| <span class="identifier">SC_</span><span class="special">(</span><span class="number">0.4883005917072296142578125</span><span class="special">),</span> |
| <span class="identifier">SC_</span><span class="special">(</span><span class="number">1.007653173802923954909901438393379243537</span><span class="special">),</span> |
| <span class="comment">/* ... lots of rows skipped */</span> |
| <span class="special">};</span> |
| </pre> |
| <p> |
| The first two values in each row are the input parameters that were passed |
| to our functor and the last value is the return value from the functor. |
| Had our functor returned a <a class="link" href="../internals1/tuples.html" title="Tuples">boost::math::tuple</a> |
| rather than a value, then we would have had one entry for each element |
| in the tuple in addition to the input parameters. |
| </p> |
| <p> |
| The first #define serves two purposes: |
| </p> |
| <div class="itemizedlist"><ul type="disc"> |
| <li> |
| It reduces the file sizes considerably: all those <code class="computeroutput"><span class="keyword">static_cast</span></code>'s |
| add up to a lot of bytes otherwise (they are needed to suppress compiler |
| warnings when <code class="computeroutput"><span class="identifier">T</span></code> is |
| narrower than a <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>). |
| </li> |
| <li> |
| It provides a useful customisation point: for example if we were testing |
| a user-defined type that has more precision than a <code class="computeroutput"><span class="keyword">long</span> |
| <span class="keyword">double</span></code> we could change it to: |
| </li> |
| </ul></div> |
| <p> |
| <code class="literal">#define SC_(x) lexical_cast<T>(BOOST_STRINGIZE(x))</code> |
| </p> |
| <p> |
| in order to ensure that no truncation of the values occurs prior to conversion |
| to <code class="computeroutput"><span class="identifier">T</span></code>. Note that this isn't |
| used by default as it's rather hard on the compiler when the table is large. |
| </p> |
| <a name="math_toolkit.toolkit.internals2.test_data.example_3__profiling_a_continued_fraction_for_convergence_and_accuracy"></a><h6> |
| <a name="id1227084"></a> |
| <a class="link" href="test_data.html#math_toolkit.toolkit.internals2.test_data.example_3__profiling_a_continued_fraction_for_convergence_and_accuracy">Example |
| 3: Profiling a Continued Fraction for Convergence and Accuracy</a> |
| </h6> |
| <p> |
| Alternatively, lets say we want to profile a continued fraction for convergence |
| and error. As an example, we'll use the continued fraction for the upper |
| incomplete gamma function, the following function object returns the next |
| a<sub>N </sub> and b<sub>N </sub> of the continued fraction each time it's invoked: |
| </p> |
| <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="keyword">struct</span> <span class="identifier">upper_incomplete_gamma_fract</span> |
| <span class="special">{</span> |
| <span class="keyword">private</span><span class="special">:</span> |
| <span class="identifier">T</span> <span class="identifier">z</span><span class="special">,</span> <span class="identifier">a</span><span class="special">;</span> |
| <span class="keyword">int</span> <span class="identifier">k</span><span class="special">;</span> |
| <span class="keyword">public</span><span class="special">:</span> |
| <span class="keyword">typedef</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span><span class="identifier">T</span><span class="special">></span> <span class="identifier">result_type</span><span class="special">;</span> |
| |
| <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> |
| <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> |
| <span class="special">{</span> |
| <span class="special">}</span> |
| |
| <span class="identifier">result_type</span> <span class="keyword">operator</span><span class="special">()()</span> |
| <span class="special">{</span> |
| <span class="special">++</span><span class="identifier">k</span><span class="special">;</span> |
| <span class="identifier">z</span> <span class="special">+=</span> <span class="number">2</span><span class="special">;</span> |
| <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> |
| <span class="special">}</span> |
| <span class="special">};</span> |
| </pre> |
| <p> |
| We want to measure both the relative error, and the rate of convergence |
| of this fraction, so we'll write a functor that returns both as a <a class="link" href="../internals1/tuples.html" title="Tuples">boost::math::tuple</a>: |
| class test_data will unpack the tuple for us, and create one column of |
| data for each element in the tuple (in addition to the input parameters): |
| </p> |
| <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_data</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| <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> |
| <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">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| <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">ntl</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| <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">tuple</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| |
| <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="keyword">struct</span> <span class="identifier">profile_gamma_fraction</span> |
| <span class="special">{</span> |
| <span class="keyword">typedef</span> <a class="link" href="../internals1/tuples.html" title="Tuples">boost::math::tuple</a><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">T</span><span class="special">></span> <span class="identifier">result_type</span><span class="special">;</span> |
| |
| <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> |
| <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">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">;</span> |
| <span class="comment">// estimate the true value, using arbitary precision |
| </span> <span class="comment">// arithmetic and NTL::RR: |
| </span> <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> |
| <span class="identifier">upper_incomplete_gamma_fract</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">f1</span><span class="special">(</span><span class="identifier">rval</span><span class="special">,</span> <span class="identifier">rval</span><span class="special">);</span> |
| <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> |
| <span class="comment">// |
| </span> <span class="comment">// Now get the aproximation at double precision, along with the number of |
| </span> <span class="comment">// iterations required: |
| </span> <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"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">>::</span><span class="identifier">max</span><span class="special">();</span> |
| <span class="identifier">upper_incomplete_gamma_fract</span><span class="special"><</span><span class="identifier">T</span><span class="special">></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> |
| <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"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">digits</span><span class="special">,</span> <span class="identifier">iters</span><span class="special">);</span> |
| <span class="comment">// |
| </span> <span class="comment">// Work out the relative error, as measured in units of epsilon: |
| </span> <span class="identifier">T</span> <span class="identifier">err</span> <span class="special">=</span> <span class="identifier">real_cast</span><span class="special"><</span><span class="identifier">T</span><span class="special">>(</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"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">epsilon</span><span class="special">());</span> |
| <span class="comment">// |
| </span> <span class="comment">// now just return the results as a tuple: |
| </span> <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> |
| <span class="special">}</span> |
| <span class="special">};</span> |
| </pre> |
| <p> |
| Feeding that functor into test_data allows rapid output of csv data, for |
| whatever type <code class="computeroutput"><span class="identifier">T</span></code> we may |
| be interested in: |
| </p> |
| <pre class="programlisting"><span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</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">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">;</span> |
| <span class="comment">// create an object to hold the data: |
| </span> <span class="identifier">test_data</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="identifier">data</span><span class="special">;</span> |
| <span class="comment">// insert 500 points at uniform intervals between just after 0 and 100: |
| </span> <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"><</span><span class="keyword">double</span><span class="special">>(),</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> |
| <span class="comment">// print out in csv format: |
| </span> <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> |
| <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> |
| <span class="special">}</span> |
| </pre> |
| <p> |
| This time there's no need to plot a graph, the first few rows are: |
| </p> |
| <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> |
| |
| <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> |
| <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> |
| <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> |
| <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> |
| <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> |
| <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> |
| </pre> |
| <p> |
| So it's pretty clear that this fraction shouldn't be used for small values |
| of a and z. |
| </p> |
| <a name="math_toolkit.toolkit.internals2.test_data.reference"></a><h5> |
| <a name="id1228743"></a> |
| <a class="link" href="test_data.html#math_toolkit.toolkit.internals2.test_data.reference">reference</a> |
| </h5> |
| <a name="test_data_reference"></a><p> |
| </p> |
| <p> |
| Most of this tool has been described already in the examples above, we'll |
| just add the following notes on the non-member functions: |
| </p> |
| <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">parameter_info</span><span class="special"><</span><span class="identifier">T</span><span class="special">></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> |
| </pre> |
| <p> |
| Tells class test_data to test <span class="emphasis"><em>n_points</em></span> random values |
| in the range [start_range,end_range]. |
| </p> |
| <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">parameter_info</span><span class="special"><</span><span class="identifier">T</span><span class="special">></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> |
| </pre> |
| <p> |
| Tells class test_data to test <span class="emphasis"><em>n_points</em></span> evenly spaced |
| values in the range [start_range,end_range]. |
| </p> |
| <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">parameter_info</span><span class="special"><</span><span class="identifier">T</span><span class="special">></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> |
| </pre> |
| <p> |
| Tells class test_data to test points of the form <span class="emphasis"><em>basis + R * |
| 2<sup>expon</sup></em></span> for each <span class="emphasis"><em>expon</em></span> in the range [start_exponent, |
| end_exponent], and <span class="emphasis"><em>R</em></span> a random number in [0.5, 1]. |
| </p> |
| <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="keyword">bool</span> <span class="identifier">get_user_parameter_info</span><span class="special">(</span><span class="identifier">parameter_info</span><span class="special"><</span><span class="identifier">T</span><span class="special">>&</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> |
| </pre> |
| <p> |
| Prompts the user for the parameter range and form to use. |
| </p> |
| <p> |
| Finally, if we don't want the parameter to be included in the output, we |
| can tell test_data by setting it a "dummy parameter": |
| </p> |
| <pre class="programlisting"><span class="identifier">parameter_info</span><span class="special"><</span><span class="keyword">double</span><span class="special">></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> |
| <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> |
| </pre> |
| <p> |
| This is useful when the functor used transforms the parameter in some way |
| before passing it to the function under test, usually the functor will |
| then return both the transformed input and the result in a tuple, so there's |
| no need for the original pseudo-parameter to be included in program output. |
| </p> |
| </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 , 2007, 2008, 2009, 2010 John Maddock, Paul A. Bristow, |
| Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and |
| Thijs van den Berg<p> |
| Distributed under the Boost Software License, Version 1.0. (See accompanying |
| file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) |
| </p> |
| </div></td> |
| </tr></table> |
| <hr> |
| <div class="spirit-nav"> |
| <a accesskey="p" href="error_test.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../internals2.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="../../using_udt.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> |
| </div> |
| </body> |
| </html> |
