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diff --git a/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/fp_eg/gi.html b/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/fp_eg/gi.html new file mode 100644 index 0000000000..73a46081dd --- /dev/null +++ b/libs/multiprecision/doc/html/boost_multiprecision/tut/floats/fp_eg/gi.html @@ -0,0 +1,158 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Calculating an Integral</title> +<link rel="stylesheet" href="../../../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../../../index.html" title="Chapter 1. Boost.Multiprecision"> +<link rel="up" href="../fp_eg.html" title="Examples"> +<link rel="prev" href="nd.html" title="Calculating a Derivative"> +<link rel="next" href="poly_eg.html" title="Polynomial Evaluation"> +</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="nd.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../fp_eg.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="poly_eg.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +<div class="section"> +<div class="titlepage"><div><div><h5 class="title"> +<a name="boost_multiprecision.tut.floats.fp_eg.gi"></a><a class="link" href="gi.html" title="Calculating an Integral">Calculating + an Integral</a> +</h5></div></div></div> +<p> + Similar to the generic derivative example, we can calculate integrals + in a similar manner: + </p> +<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">value_type</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">function_type</span><span class="special">></span> +<span class="keyword">inline</span> <span class="identifier">value_type</span> <span class="identifier">integral</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">value_type</span> <span class="identifier">a</span><span class="special">,</span> + <span class="keyword">const</span> <span class="identifier">value_type</span> <span class="identifier">b</span><span class="special">,</span> + <span class="keyword">const</span> <span class="identifier">value_type</span> <span class="identifier">tol</span><span class="special">,</span> + <span class="identifier">function_type</span> <span class="identifier">func</span><span class="special">)</span> +<span class="special">{</span> + <span class="keyword">unsigned</span> <span class="identifier">n</span> <span class="special">=</span> <span class="number">1U</span><span class="special">;</span> + + <span class="identifier">value_type</span> <span class="identifier">h</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">b</span> <span class="special">-</span> <span class="identifier">a</span><span class="special">);</span> + <span class="identifier">value_type</span> <span class="identifier">I</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">func</span><span class="special">(</span><span class="identifier">a</span><span class="special">)</span> <span class="special">+</span> <span class="identifier">func</span><span class="special">(</span><span class="identifier">b</span><span class="special">))</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">h</span> <span class="special">/</span> <span class="number">2</span><span class="special">);</span> + + <span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">k</span> <span class="special">=</span> <span class="number">0U</span><span class="special">;</span> <span class="identifier">k</span> <span class="special"><</span> <span class="number">8U</span><span class="special">;</span> <span class="identifier">k</span><span class="special">++)</span> + <span class="special">{</span> + <span class="identifier">h</span> <span class="special">/=</span> <span class="number">2</span><span class="special">;</span> + + <span class="identifier">value_type</span> <span class="identifier">sum</span><span class="special">(</span><span class="number">0</span><span class="special">);</span> + <span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">j</span> <span class="special">=</span> <span class="number">1U</span><span class="special">;</span> <span class="identifier">j</span> <span class="special"><=</span> <span class="identifier">n</span><span class="special">;</span> <span class="identifier">j</span><span class="special">++)</span> + <span class="special">{</span> + <span class="identifier">sum</span> <span class="special">+=</span> <span class="identifier">func</span><span class="special">(</span><span class="identifier">a</span> <span class="special">+</span> <span class="special">(</span><span class="identifier">value_type</span><span class="special">((</span><span class="identifier">j</span> <span class="special">*</span> <span class="number">2</span><span class="special">)</span> <span class="special">-</span> <span class="number">1</span><span class="special">)</span> <span class="special">*</span> <span class="identifier">h</span><span class="special">));</span> + <span class="special">}</span> + + <span class="keyword">const</span> <span class="identifier">value_type</span> <span class="identifier">I0</span> <span class="special">=</span> <span class="identifier">I</span><span class="special">;</span> + <span class="identifier">I</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">I</span> <span class="special">/</span> <span class="number">2</span><span class="special">)</span> <span class="special">+</span> <span class="special">(</span><span class="identifier">h</span> <span class="special">*</span> <span class="identifier">sum</span><span class="special">);</span> + + <span class="keyword">const</span> <span class="identifier">value_type</span> <span class="identifier">ratio</span> <span class="special">=</span> <span class="identifier">I0</span> <span class="special">/</span> <span class="identifier">I</span><span class="special">;</span> + <span class="keyword">const</span> <span class="identifier">value_type</span> <span class="identifier">delta</span> <span class="special">=</span> <span class="identifier">ratio</span> <span class="special">-</span> <span class="number">1</span><span class="special">;</span> + <span class="keyword">const</span> <span class="identifier">value_type</span> <span class="identifier">delta_abs</span> <span class="special">=</span> <span class="special">((</span><span class="identifier">delta</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">delta</span> <span class="special">:</span> <span class="identifier">delta</span><span class="special">);</span> + + <span class="keyword">if</span><span class="special">((</span><span class="identifier">k</span> <span class="special">></span> <span class="number">1U</span><span class="special">)</span> <span class="special">&&</span> <span class="special">(</span><span class="identifier">delta_abs</span> <span class="special"><</span> <span class="identifier">tol</span><span class="special">))</span> + <span class="special">{</span> + <span class="keyword">break</span><span class="special">;</span> + <span class="special">}</span> + + <span class="identifier">n</span> <span class="special">*=</span> <span class="number">2U</span><span class="special">;</span> + <span class="special">}</span> + + <span class="keyword">return</span> <span class="identifier">I</span><span class="special">;</span> +<span class="special">}</span> +</pre> +<p> + The following sample program shows how the function can be called, we + begin by defining a function object, which when integrated should yield + the Bessel J function: + </p> +<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">value_type</span><span class="special">></span> +<span class="keyword">class</span> <span class="identifier">cyl_bessel_j_integral_rep</span> +<span class="special">{</span> +<span class="keyword">public</span><span class="special">:</span> + <span class="identifier">cyl_bessel_j_integral_rep</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">unsigned</span> <span class="identifier">N</span><span class="special">,</span> + <span class="keyword">const</span> <span class="identifier">value_type</span><span class="special">&</span> <span class="identifier">X</span><span class="special">)</span> <span class="special">:</span> <span class="identifier">n</span><span class="special">(</span><span class="identifier">N</span><span class="special">),</span> <span class="identifier">x</span><span class="special">(</span><span class="identifier">X</span><span class="special">)</span> <span class="special">{</span> <span class="special">}</span> + + <span class="identifier">value_type</span> <span class="keyword">operator</span><span class="special">()(</span><span class="keyword">const</span> <span class="identifier">value_type</span><span class="special">&</span> <span class="identifier">t</span><span class="special">)</span> <span class="keyword">const</span> + <span class="special">{</span> + <span class="comment">// pi * Jn(x) = Int_0^pi [cos(x * sin(t) - n*t) dt]</span> + <span class="keyword">return</span> <span class="identifier">cos</span><span class="special">(</span><span class="identifier">x</span> <span class="special">*</span> <span class="identifier">sin</span><span class="special">(</span><span class="identifier">t</span><span class="special">)</span> <span class="special">-</span> <span class="special">(</span><span class="identifier">n</span> <span class="special">*</span> <span class="identifier">t</span><span class="special">));</span> + <span class="special">}</span> + +<span class="keyword">private</span><span class="special">:</span> + <span class="keyword">const</span> <span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">;</span> + <span class="keyword">const</span> <span class="identifier">value_type</span> <span class="identifier">x</span><span class="special">;</span> +<span class="special">};</span> +</pre> +<pre class="programlisting"> <span class="comment">/* The function can now be called as follows: */</span> +<span class="keyword">int</span> <span class="identifier">main</span><span class="special">(</span><span class="keyword">int</span><span class="special">,</span> <span class="keyword">char</span><span class="special">**)</span> +<span class="special">{</span> + <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special">;</span> + <span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">cpp_dec_float_50</span> <span class="identifier">mp_type</span><span class="special">;</span> + + <span class="keyword">const</span> <span class="keyword">float</span> <span class="identifier">j2_f</span> <span class="special">=</span> + <span class="identifier">integral</span><span class="special">(</span><span class="number">0.0F</span><span class="special">,</span> + <span class="identifier">pi</span><span class="special"><</span><span class="keyword">float</span><span class="special">>(),</span> + <span class="number">0.01F</span><span class="special">,</span> + <span class="identifier">cyl_bessel_j_integral_rep</span><span class="special"><</span><span class="keyword">float</span><span class="special">>(</span><span class="number">2U</span><span class="special">,</span> <span class="number">1.23F</span><span class="special">))</span> <span class="special">/</span> <span class="identifier">pi</span><span class="special"><</span><span class="keyword">float</span><span class="special">>();</span> + + <span class="keyword">const</span> <span class="keyword">double</span> <span class="identifier">j2_d</span> <span class="special">=</span> + <span class="identifier">integral</span><span class="special">(</span><span class="number">0.0</span><span class="special">,</span> + <span class="identifier">pi</span><span class="special"><</span><span class="keyword">double</span><span class="special">>(),</span> + <span class="number">0.0001</span><span class="special">,</span> + <span class="identifier">cyl_bessel_j_integral_rep</span><span class="special"><</span><span class="keyword">double</span><span class="special">>(</span><span class="number">2U</span><span class="special">,</span> <span class="number">1.23</span><span class="special">))</span> <span class="special">/</span> <span class="identifier">pi</span><span class="special"><</span><span class="keyword">double</span><span class="special">>();</span> + + <span class="keyword">const</span> <span class="identifier">mp_type</span> <span class="identifier">j2_mp</span> <span class="special">=</span> + <span class="identifier">integral</span><span class="special">(</span><span class="identifier">mp_type</span><span class="special">(</span><span class="number">0</span><span class="special">),</span> + <span class="identifier">pi</span><span class="special"><</span><span class="identifier">mp_type</span><span class="special">>(),</span> + <span class="identifier">mp_type</span><span class="special">(</span><span class="number">1.0E-20</span><span class="special">),</span> + <span class="identifier">cyl_bessel_j_integral_rep</span><span class="special"><</span><span class="identifier">mp_type</span><span class="special">>(</span><span class="number">2U</span><span class="special">,</span> <span class="identifier">mp_type</span><span class="special">(</span><span class="number">123</span><span class="special">)</span> <span class="special">/</span> <span class="number">100</span><span class="special">))</span> <span class="special">/</span> <span class="identifier">pi</span><span class="special"><</span><span class="identifier">mp_type</span><span class="special">>();</span> + + <span class="comment">// 0.166369</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</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="keyword">float</span><span class="special">>::</span><span class="identifier">digits10</span><span class="special">)</span> + <span class="special"><<</span> <span class="identifier">j2_f</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">// 0.166369383786814</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</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="keyword">double</span><span class="special">>::</span><span class="identifier">digits10</span><span class="special">)</span> + <span class="special"><<</span> <span class="identifier">j2_d</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">// 0.16636938378681407351267852431513159437103348245333</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</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">mp_type</span><span class="special">>::</span><span class="identifier">digits10</span><span class="special">)</span> + <span class="special"><<</span> <span class="identifier">j2_mp</span> + <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> + + <span class="comment">//</span> + <span class="comment">// Print true value for comparison:</span> + <span class="comment">// 0.166369383786814073512678524315131594371033482453329</span> + <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</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="number">2</span><span class="special">,</span> <span class="identifier">mp_type</span><span class="special">(</span><span class="number">123</span><span class="special">)</span> <span class="special">/</span> <span class="number">100</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="special">}</span> +</pre> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<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="nd.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../fp_eg.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="poly_eg.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> |