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24 | </div> | |
25 | <div class="section"> | |
26 | <div class="titlepage"><div><div><h2 class="title" style="clear: both"> | |
27 | <a name="math_toolkit.examples"></a><a class="link" href="examples.html" title="Examples">Examples</a> | |
28 | </h2></div></div></div> | |
29 | <h4> | |
30 | <a name="math_toolkit.examples.h0"></a> | |
31 | <span class="phrase"><a name="math_toolkit.examples.je_lambda"></a></span><a class="link" href="examples.html#math_toolkit.examples.je_lambda">Jahnke-Emden-Lambda | |
32 | function</a> | |
33 | </h4> | |
34 | <p> | |
35 | The following code uses <code class="computeroutput"><span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">cstdfloat</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></code> | |
36 | in combination with <code class="computeroutput"><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">hpp</span><span class="special">></span></code> to | |
37 | compute a simplified version of the <a href="http://mathworld.wolfram.com/LambdaFunction.html" target="_top">Jahnke-Emden-Lambda | |
38 | function</a>. Here, we specify a floating-point type with <span class="bold"><strong>exactly | |
39 | 64 bits</strong></span> (i.e., <code class="computeroutput"><span class="identifier">float64_t</span></code>). | |
40 | If we were to use, for instance, built-in <code class="computeroutput"><span class="keyword">double</span></code>, | |
41 | then there would be no guarantee that the code would behave identically on | |
42 | all platforms. With <code class="computeroutput"><span class="identifier">float64_t</span></code> | |
43 | from <code class="computeroutput"><span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">cstdfloat</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></code>, | |
44 | however, it is very likely to be identical. | |
45 | </p> | |
46 | <p> | |
47 | Using <code class="computeroutput"><span class="identifier">float64_t</span></code>, we know that | |
48 | this code is as portable as possible and uses a floating-point type with approximately | |
49 | 15 decimal digits of precision, regardless of the compiler or version or operating | |
50 | system. | |
51 | </p> | |
52 | <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">cstdfloat</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> <span class="comment">// For float_64_t, float128_t. Must be first include!</span> | |
53 | <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">cmath</span><span class="special">></span> <span class="comment">// for pow function.</span> | |
54 | <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">hpp</span><span class="special">></span> <span class="comment">// For gamma function.</span> | |
55 | </pre> | |
56 | <pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">float64_t</span> <span class="identifier">jahnke_emden_lambda</span><span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">float64_t</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">float64_t</span> <span class="identifier">x</span><span class="special">)</span> | |
57 | <span class="special">{</span> | |
58 | <span class="keyword">const</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">float64_t</span> <span class="identifier">gamma_v_plus_one</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">v</span> <span class="special">+</span> <span class="number">1</span><span class="special">);</span> | |
59 | <span class="keyword">const</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">float64_t</span> <span class="identifier">x_half_pow_v</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">pow</span><span class="special">(</span><span class="identifier">x</span> <span class="special">/</span><span class="number">2</span><span class="special">,</span> <span class="identifier">v</span><span class="special">);</span> | |
60 | ||
61 | <span class="keyword">return</span> <span class="identifier">gamma_v_plus_one</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">cyl_bessel_j</span><span class="special">(</span><span class="identifier">x</span><span class="special">,</span> <span class="identifier">v</span><span class="special">)</span> <span class="special">/</span> <span class="identifier">x_half_pow_v</span><span class="special">;</span> | |
62 | <span class="special">}</span> | |
63 | </pre> | |
64 | <p> | |
65 | Ensure that all possibly significant digits (17) including trailing zeros are | |
66 | shown. | |
67 | </p> | |
68 | <pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</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">float64_t</span><span class="special">>::</span><span class="identifier">max_digits10</span><span class="special">);</span> | |
69 | <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">.</span><span class="identifier">setf</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">ios</span><span class="special">::</span><span class="identifier">showpoint</span><span class="special">);</span> <span class="comment">// Show trailing zeros.</span> | |
70 | ||
71 | <span class="keyword">try</span> | |
72 | <span class="special">{</span> <span class="comment">// Always use try'n'catch blocks to ensure any error messages are displayed.</span> | |
73 | ||
74 | <span class="comment">// Evaluate and display an evaluation of the Jahnke-Emden lambda function:</span> | |
75 | <span class="identifier">boost</span><span class="special">::</span><span class="identifier">float64_t</span> <span class="identifier">v</span> <span class="special">=</span> <span class="number">1.</span><span class="special">;</span> | |
76 | <span class="identifier">boost</span><span class="special">::</span><span class="identifier">float64_t</span> <span class="identifier">x</span> <span class="special">=</span> <span class="number">1.</span><span class="special">;</span> | |
77 | <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">jahnke_emden_lambda</span><span class="special">(</span><span class="identifier">v</span><span class="special">,</span> <span class="identifier">x</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 0.88010117148986700</span> | |
78 | </pre> | |
79 | <p> | |
80 | For details, see <a href="../../../example/cstdfloat_example.cpp" target="_top">cstdfloat_example.cpp</a> | |
81 | - a extensive example program. | |
82 | </p> | |
83 | <h4> | |
84 | <a name="math_toolkit.examples.h1"></a> | |
85 | <span class="phrase"><a name="math_toolkit.examples.normal_table"></a></span><a class="link" href="examples.html#math_toolkit.examples.normal_table">Normal | |
86 | distribution table</a> | |
87 | </h4> | |
88 | <p> | |
89 | This example shows printing tables of a normal distribution's PDF and CDF, | |
90 | using <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span></code> implementation of normal distribution. | |
91 | </p> | |
92 | <p> | |
93 | A function templated on floating-point type prints a table for a range of standard | |
94 | variate z values. | |
95 | </p> | |
96 | <p> | |
97 | The example shows use of the specified-width typedefs to either use a specific | |
98 | width, or to use the maximum available on the platform, perhaps a high as 128-bit. | |
99 | </p> | |
100 | <p> | |
101 | The number of digits displayed is controlled by the precision of the type, | |
102 | so there are no spurious insignificant decimal digits: | |
103 | </p> | |
104 | <pre class="programlisting"><span class="identifier">float_32_t</span> <span class="number">0</span> <span class="number">0.39894228</span> | |
105 | <span class="identifier">float_128_t</span> <span class="number">0</span> <span class="number">0.398942280401432702863218082711682655</span> | |
106 | </pre> | |
107 | <p> | |
108 | Some sample output for two different platforms is appended to the code at | |
109 | <a href="../../../example/normal_tables.cpp" target="_top">normal_tables.cpp</a>. | |
110 | </p> | |
111 | <pre class="programlisting"><span class="preprocessor">#ifdef</span> <span class="identifier">BOOST_FLOAT32_C</span> | |
112 | <span class="identifier">normal_table</span><span class="special"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">float32_t</span><span class="special">>();</span> <span class="comment">// Usually type float</span> | |
113 | <span class="preprocessor">#endif</span> | |
114 | <span class="identifier">normal_table</span><span class="special"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">float64_t</span><span class="special">>();</span> <span class="comment">// Uusually type double. Assume that float64_t is always available.</span> | |
115 | <span class="preprocessor">#ifdef</span> <span class="identifier">BOOST_FLOAT80_C</span> | |
116 | <span class="identifier">normal_table</span><span class="special"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">float80_t</span><span class="special">>();</span> <span class="comment">// Type long double on some X86 platforms.</span> | |
117 | <span class="preprocessor">#endif</span> | |
118 | <span class="preprocessor">#ifdef</span> <span class="identifier">BOOST_FLOAT128_C</span> | |
119 | <span class="identifier">normal_table</span><span class="special"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">float128_t</span><span class="special">>();</span> <span class="comment">// Type _Quad on some Intel and __float128 on some GCC platforms.</span> | |
120 | <span class="preprocessor">#endif</span> | |
121 | <span class="identifier">normal_table</span><span class="special"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">floatmax_t</span><span class="special">>();</span> | |
122 | </pre> | |
123 | </div> | |
124 | <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> | |
125 | <td align="left"></td> | |
126 | <td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal, | |
127 | Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert | |
128 | Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani, | |
129 | Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p> | |
130 | Distributed under the Boost Software License, Version 1.0. (See accompanying | |
131 | file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) | |
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