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Math: Regenerate docs with patches applied.

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2017-11-09 13:32:24 +00:00
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@@ -122,7 +122,7 @@ This manual is also available in <a href="http://sourceforge.net/projects/boost/
</div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"><p><small>Last revised: November 09, 2017 at 13:23:44 GMT</small></p></td>
<td align="left"><p><small>Last revised: November 09, 2017 at 13:29:30 GMT</small></p></td>
<td align="right"><div class="copyright-footer"></div></td>
</tr></table>
<hr>

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<div class="section">
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<a name="id1746802"></a>Function Index</h2></div></div></div>
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<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="id1775740"></a>Class Index</h2></div></div></div>
<a name="id1766964"></a>Class Index</h2></div></div></div>
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<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="id1777039"></a>Typedef Index</h2></div></div></div>
<a name="id1772551"></a>Typedef Index</h2></div></div></div>
<p><a class="link" href="s03.html#idx_id_58">A</a> <a class="link" href="s03.html#idx_id_59">B</a> <a class="link" href="s03.html#idx_id_60">C</a> <a class="link" href="s03.html#idx_id_61">D</a> <a class="link" href="s03.html#idx_id_62">E</a> <a class="link" href="s03.html#idx_id_63">F</a> <a class="link" href="s03.html#idx_id_64">G</a> <a class="link" href="s03.html#idx_id_65">H</a> <a class="link" href="s03.html#idx_id_66">I</a> <a class="link" href="s03.html#idx_id_69">L</a> <a class="link" href="s03.html#idx_id_71">N</a> <a class="link" href="s03.html#idx_id_72">O</a> <a class="link" href="s03.html#idx_id_73">P</a> <a class="link" href="s03.html#idx_id_75">R</a> <a class="link" href="s03.html#idx_id_76">S</a> <a class="link" href="s03.html#idx_id_77">T</a> <a class="link" href="s03.html#idx_id_78">U</a> <a class="link" href="s03.html#idx_id_79">V</a> <a class="link" href="s03.html#idx_id_80">W</a></p>
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</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="id1781607"></a>Macro Index</h2></div></div></div>
<a name="id1776222"></a>Macro Index</h2></div></div></div>
<p><a class="link" href="s04.html#idx_id_87">B</a> <a class="link" href="s04.html#idx_id_91">F</a></p>
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</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="id1785816"></a>Index</h2></div></div></div>
<a name="id1775387"></a>Index</h2></div></div></div>
<p><a class="link" href="s05.html#idx_id_112">2</a> <a class="link" href="s05.html#idx_id_113">4</a> <a class="link" href="s05.html#idx_id_114">A</a> <a class="link" href="s05.html#idx_id_115">B</a> <a class="link" href="s05.html#idx_id_116">C</a> <a class="link" href="s05.html#idx_id_117">D</a> <a class="link" href="s05.html#idx_id_118">E</a> <a class="link" href="s05.html#idx_id_119">F</a> <a class="link" href="s05.html#idx_id_120">G</a> <a class="link" href="s05.html#idx_id_121">H</a> <a class="link" href="s05.html#idx_id_122">I</a> <a class="link" href="s05.html#idx_id_123">J</a> <a class="link" href="s05.html#idx_id_124">K</a> <a class="link" href="s05.html#idx_id_125">L</a> <a class="link" href="s05.html#idx_id_126">M</a> <a class="link" href="s05.html#idx_id_127">N</a> <a class="link" href="s05.html#idx_id_128">O</a> <a class="link" href="s05.html#idx_id_129">P</a> <a class="link" href="s05.html#idx_id_130">Q</a> <a class="link" href="s05.html#idx_id_131">R</a> <a class="link" href="s05.html#idx_id_132">S</a> <a class="link" href="s05.html#idx_id_133">T</a> <a class="link" href="s05.html#idx_id_134">U</a> <a class="link" href="s05.html#idx_id_135">V</a> <a class="link" href="s05.html#idx_id_136">W</a> <a class="link" href="s05.html#idx_id_137">X</a> <a class="link" href="s05.html#idx_id_138">Y</a> <a class="link" href="s05.html#idx_id_139">Z</a></p>
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<a name="math_toolkit.barycentric.h0"></a>
<span class="phrase"><a name="math_toolkit.barycentric.synopsis"></a></span><a class="link" href="barycentric.html#math_toolkit.barycentric.synopsis">Synopsis</a>
</h4>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">barycentric_rational_interpolation</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">interpolators</span><span class="special">/</span><span class="identifier">barycentric_rational</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<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">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Real</span><span class="special">&gt;</span>
@@ -62,7 +62,7 @@
x[n-1] where x[i+1] &gt; x[i], and a vector of dependent variables y[0], y[1],
... , y[n-1]. The call is trivial:
</p>
<pre class="programlisting"><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">barycentric_rational</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">interpolant</span><span class="special">(</span><span class="identifier">x</span><span class="special">.</span><span class="identifier">data</span><span class="special">(),</span> <span class="identifier">y</span><span class="special">.</span><span class="identifier">data</span><span class="special">(),</span> <span class="identifier">y</span><span class="special">.</span><span class="identifier">size</span><span class="special">());</span>
<pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">barycentric_rational</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">interpolant</span><span class="special">(</span><span class="identifier">x</span><span class="special">.</span><span class="identifier">data</span><span class="special">(),</span> <span class="identifier">y</span><span class="special">.</span><span class="identifier">data</span><span class="special">(),</span> <span class="identifier">y</span><span class="special">.</span><span class="identifier">size</span><span class="special">());</span>
</pre>
<p>
This implicitly calls the constructor with approximation order 3, and hence
@@ -70,7 +70,7 @@
then the error is &#119926;(h<sup>d+1</sup>). A call to the constructor with an explicit approximation
order could be
</p>
<pre class="programlisting"><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">barycentric_rational</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">interpolant</span><span class="special">(</span><span class="identifier">x</span><span class="special">.</span><span class="identifier">data</span><span class="special">(),</span> <span class="identifier">y</span><span class="special">.</span><span class="identifier">data</span><span class="special">(),</span> <span class="identifier">y</span><span class="special">.</span><span class="identifier">size</span><span class="special">(),</span> <span class="number">5</span><span class="special">);</span>
<pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">barycentric_rational</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">interpolant</span><span class="special">(</span><span class="identifier">x</span><span class="special">.</span><span class="identifier">data</span><span class="special">(),</span> <span class="identifier">y</span><span class="special">.</span><span class="identifier">data</span><span class="special">(),</span> <span class="identifier">y</span><span class="special">.</span><span class="identifier">size</span><span class="special">(),</span> <span class="number">5</span><span class="special">);</span>
</pre>
<p>
To evaluate the interpolant, simply use

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@@ -27,7 +27,7 @@
<a name="math_toolkit.conventions"></a><a class="link" href="conventions.html" title="Document Conventions">Document Conventions</a>
</h2></div></div></div>
<p>
<a class="indexterm" name="id895182"></a>
<a class="indexterm" name="id888279"></a>
</p>
<p>
This documentation aims to use of the following naming and formatting conventions.

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<p>
All three of the double-exponential integrators are thread safe as long as
BOOST_MATH_NO_ATOMIC_INT is not set. Since the integrators store a large
amount of fairly hard to compute data, it is recomended that these objects
amount of fairly hard to compute data, it is recommended that these objects
are stored and reused as much as possible.
</p>
<p>

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@@ -27,7 +27,7 @@
<a name="math_toolkit.navigation"></a><a class="link" href="navigation.html" title="Navigation">Navigation</a>
</h2></div></div></div>
<p>
<a class="indexterm" name="id895068"></a>
<a class="indexterm" name="id888172"></a>
</p>
<p>
Boost.Math documentation is provided in both HTML and PDF formats.

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</p>
<pre class="programlisting"><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">quadrature</span><span class="special">::</span><span class="identifier">trapezoidal</span><span class="special">;</span>
<span class="keyword">auto</span> <span class="identifier">f</span> <span class="special">=</span> <span class="special">[](</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">)</span> <span class="special">{</span> <span class="keyword">return</span> <span class="number">1</span><span class="special">/(</span><span class="number">5</span> <span class="special">-</span> <span class="number">4</span><span class="special">*</span><span class="identifier">cos</span><span class="special">(</span><span class="identifier">x</span><span class="special">));</span> <span class="special">};</span>
<span class="keyword">double</span> <span class="identifier">I</span> <span class="special">=</span> <span class="identifier">trapezoidal</span><span class="special">(</span><span class="identifier">f</span><span class="special">,</span> <span class="number">0</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">constants</span><span class="special">::</span><span class="identifier">two_pi</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;());</span>
<span class="keyword">double</span> <span class="identifier">I</span> <span class="special">=</span> <span class="identifier">trapezoidal</span><span class="special">(</span><span class="identifier">f</span><span class="special">,</span> <span class="number">0.0</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">constants</span><span class="special">::</span><span class="identifier">two_pi</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;());</span>
</pre>
<p>
Since the routine is adaptive, step sizes are halved continuously until a tolerance
@@ -113,7 +113,7 @@
types, it may be of interest to allow the algorithm to compute more refinements:
</p>
<pre class="programlisting"><span class="identifier">size_t</span> <span class="identifier">max_refinements</span> <span class="special">=</span> <span class="number">15</span><span class="special">;</span>
<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">I</span> <span class="special">=</span> <span class="identifier">trapezoidal</span><span class="special">(</span><span class="identifier">f</span><span class="special">,</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">two_pi</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;(),</span> <span class="number">1e-9L</span><span class="special">,</span> <span class="identifier">max_refinements</span><span class="special">);</span>
<span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">I</span> <span class="special">=</span> <span class="identifier">trapezoidal</span><span class="special">(</span><span class="identifier">f</span><span class="special">,</span> <span class="number">0.0L</span><span class="special">,</span> <span class="identifier">two_pi</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;(),</span> <span class="number">1e-9L</span><span class="special">,</span> <span class="identifier">max_refinements</span><span class="special">);</span>
</pre>
<p>
Note that the maximum allowed compute time grows exponentially with <code class="computeroutput"><span class="identifier">max_refinements</span></code>. The routine will not throw
@@ -125,7 +125,7 @@
</p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">error_estimate</span><span class="special">;</span>
<span class="keyword">double</span> <span class="identifier">L1</span><span class="special">;</span>
<span class="keyword">double</span> <span class="identifier">I</span> <span class="special">=</span> <span class="identifier">trapezoidal</span><span class="special">(</span><span class="identifier">f</span><span class="special">,</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">two_pi</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;(),</span> <span class="identifier">tolerance</span><span class="special">,</span> <span class="identifier">max_refinements</span><span class="special">,</span> <span class="special">&amp;</span><span class="identifier">error_estimate</span><span class="special">,</span> <span class="special">&amp;</span><span class="identifier">L1</span><span class="special">);</span>
<span class="keyword">double</span> <span class="identifier">I</span> <span class="special">=</span> <span class="identifier">trapezoidal</span><span class="special">(</span><span class="identifier">f</span><span class="special">,</span> <span class="number">0.0</span><span class="special">,</span> <span class="identifier">two_pi</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;(),</span> <span class="identifier">tolerance</span><span class="special">,</span> <span class="identifier">max_refinements</span><span class="special">,</span> <span class="special">&amp;</span><span class="identifier">error_estimate</span><span class="special">,</span> <span class="special">&amp;</span><span class="identifier">L1</span><span class="special">);</span>
<span class="keyword">if</span> <span class="special">(</span><span class="identifier">error_estimate</span> <span class="special">&gt;</span> <span class="identifier">tolerance</span><span class="special">*</span><span class="identifier">L1</span><span class="special">)</span>
<span class="special">{</span>
<span class="keyword">double</span> <span class="identifier">I</span> <span class="special">=</span> <span class="identifier">some_other_quadrature_method</span><span class="special">(</span><span class="identifier">f</span><span class="special">,</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">two_pi</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;());</span>