backup/C-Plus-Plus
1
0
Fork 0
mirror of https://github.com/TheAlgorithms/C-Plus-Plus.git synced 2026-07-27 08:51:41 +08:00
Code Issues Projects Releases Wiki Activity

Documentation for 8b1eab204b

Browse Source
This commit is contained in:
realstealthninja
2024-11-04 12:43:05 +00:00
parent 4fb6e622e9
commit a7bccf7d01
6732 changed files with 153919 additions and 365711 deletions
Download Patch File Download Diff File Expand all files Collapse all files

198
db/d40/integral__approximation2_8cpp.html
View File

@@ -1,3 +1,4 @@
<!-- HTML header for doxygen 1.12.0-->
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en-US">
<head>
@@ -5,10 +6,15 @@
<meta http-equiv="X-UA-Compatible" content="IE=11"/>
<meta name="generator" content="Doxygen 1.12.0"/>
<meta name="viewport" content="width=device-width, initial-scale=1"/>
<title>Algorithms_in_C++: math/integral_approximation2.cpp File Reference</title>
<title>TheAlgorithms/C++: math/integral_approximation2.cpp File Reference</title>
<link rel="icon" href="../../favicon.svg" type="image/x-icon" />
<link href="../../tabs.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="../../jquery.js"></script>
<script type="text/javascript" src="../../dynsections.js"></script>
<script type="text/javascript" src="https://cdn.jsdelivr.net/npm/@xpack-3rd-party/doxygen-awesome-css@2.2.0-1/doxygen-awesome-darkmode-toggle.js"></script>
<script type="text/javascript">
DoxygenAwesomeDarkModeToggle.init()
</script>
<script type="text/javascript" src="../../clipboard.js"></script>
<link href="../../navtree.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="../../navtreedata.js"></script>
@@ -18,14 +24,24 @@
<link href="../../search/search.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="../../search/searchdata.js"></script>
<script type="text/javascript" src="../../search/search.js"></script>
<script type="text/x-mathjax-config">
MathJax.Hub.Config({
extensions: ["tex2jax.js", "TeX/AMSmath.js", "TeX/AMSsymbols.js"],
jax: ["input/TeX","output/HTML-CSS"],
});
<script type="text/javascript">
window.MathJax = {
options: {
ignoreHtmlClass: 'tex2jax_ignore',
processHtmlClass: 'tex2jax_process'
},
loader: {
load: ['[tex]/ams']
},
tex: {
macros: {},
packages: ['base','configmacros','ams']
}
};
</script>
<script type="text/javascript" async="async" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.7/MathJax.js?config=TeX-MML-AM_CHTML/MathJax.js"></script>
<script type="text/javascript" id="MathJax-script" async="async" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-chtml.js"></script>
<link href="../../doxygen.css" rel="stylesheet" type="text/css" />
<link href="../../doxygen-awesome.css" rel="stylesheet" type="text/css"/>
</head>
<body>
<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
@@ -33,10 +49,11 @@ MathJax.Hub.Config({
<table cellspacing="0" cellpadding="0">
<tbody>
<tr id="projectrow">
<td id="projectlogo"><img alt="Logo" src="../../project_logo.png"/></td>
<td id="projectalign">
<div id="projectname">Algorithms_in_C++<span id="projectnumber">&#160;1.0.0</span>
<div id="projectname">TheAlgorithms/C++<span id="projectnumber">&#160;1.0.0</span>
</div>
<div id="projectbrief">Set of algorithms implemented in C++.</div>
<div id="projectbrief">All the algorithms implemented in C++</div>
</td>
</tr>
</tbody>
@@ -127,7 +144,9 @@ Include dependency graph for integral_approximation2.cpp:</div>
<div class="dyncontent">
<div class="center"><iframe scrolling="no" frameborder="0" src="../../d5/d5c/integral__approximation2_8cpp__incl.svg" width="598" height="111"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
</div>
</div><table class="memberdecls">
</div>
<p><a href="../../db/d40/integral__approximation2_8cpp_source.html">Go to the source code of this file.</a></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="namespaces" name="namespaces"></a>
Namespaces</h2></td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html">math</a></td></tr>
@@ -144,10 +163,10 @@ Typedefs</h2></td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:a71249ee535f16f8ed2e9cc8f0199a2cf" id="r_a71249ee535f16f8ed2e9cc8f0199a2cf"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; double &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a71249ee535f16f8ed2e9cc8f0199a2cf">math::monte_carlo::generate_samples</a> (const double &amp;start_point, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">Function</a> &amp;pdf, const uint32_t &amp;num_samples, const uint32_t &amp;discard=100000)</td></tr>
<tr class="memitem:a71249ee535f16f8ed2e9cc8f0199a2cf" id="r_a71249ee535f16f8ed2e9cc8f0199a2cf"><td class="memItemLeft" align="right" valign="top">std::vector&lt; double &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a71249ee535f16f8ed2e9cc8f0199a2cf">math::monte_carlo::generate_samples</a> (const double &amp;start_point, const Function &amp;pdf, const uint32_t &amp;num_samples, const uint32_t &amp;discard=100000)</td></tr>
<tr class="memdesc:a71249ee535f16f8ed2e9cc8f0199a2cf"><td class="mdescLeft">&#160;</td><td class="mdescRight">short-hand for std::functions used in this implementation <br /></td></tr>
<tr class="separator:a71249ee535f16f8ed2e9cc8f0199a2cf"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:af7da9ba8932f1f48b9bbc2d80471af51" id="r_af7da9ba8932f1f48b9bbc2d80471af51"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#af7da9ba8932f1f48b9bbc2d80471af51">math::monte_carlo::integral_monte_carlo</a> (const double &amp;start_point, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">Function</a> &amp;function, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">Function</a> &amp;pdf, const uint32_t &amp;num_samples=1000000)</td></tr>
<tr class="memitem:af7da9ba8932f1f48b9bbc2d80471af51" id="r_af7da9ba8932f1f48b9bbc2d80471af51"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#af7da9ba8932f1f48b9bbc2d80471af51">math::monte_carlo::integral_monte_carlo</a> (const double &amp;start_point, const Function &amp;function, const Function &amp;pdf, const uint32_t &amp;num_samples=1000000)</td></tr>
<tr class="memdesc:af7da9ba8932f1f48b9bbc2d80471af51"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute an approximation of an integral using Monte Carlo integration. <br /></td></tr>
<tr class="separator:af7da9ba8932f1f48b9bbc2d80471af51"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d" id="r_aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
@@ -162,7 +181,26 @@ Functions</h2></td></tr>
<p>In mathematics, Monte Carlo integration is a technique for numerical integration using random numbers. It is a particular Monte Carlo method that numerically computes a definite integral. While other algorithms usually evaluate the integrand at a regular grid, Monte Carlo randomly chooses points at which the integrand is evaluated. This method is particularly useful for higher-dimensional integrals.</p>
<p>This implementation supports arbitrary pdfs. These pdfs are sampled using the <a href="https://en.wikipedia.org/wiki/Metropolis–Hastings_algorithm" target="_blank">Metropolis-Hastings algorithm</a>. This can be swapped out by every other sampling techniques for example the inverse method. Metropolis-Hastings was chosen because it is the most general and can also be extended for a higher dimensional sampling space.</p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/DerAndereDomenic" target="_blank">Domenic Zingsheim</a> </dd></dl>
</div><h2 class="groupheader">Typedef Documentation</h2>
<p class="definition">Definition in file <a class="el" href="../../db/d40/integral__approximation2_8cpp_source.html">integral_approximation2.cpp</a>.</p>
</div><h2 class="groupheader">Macro Definition Documentation</h2>
<a id="a525335710b53cb064ca56b936120431e" name="a525335710b53cb064ca56b936120431e"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a525335710b53cb064ca56b936120431e">&#9670;&#160;</a></span>_USE_MATH_DEFINES</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">#define _USE_MATH_DEFINES</td>
</tr>
</table>
</div><div class="memdoc">
<p class="definition">Definition at line <a class="el" href="../../db/d40/integral__approximation2_8cpp_source.html#l00024">24</a> of file <a class="el" href="../../db/d40/integral__approximation2_8cpp_source.html">integral_approximation2.cpp</a>.</p>
</div>
</div>
<h2 class="groupheader">Typedef Documentation</h2>
<a id="aa546b0e9315b7d9e9a8f6b71dd643de7" name="aa546b0e9315b7d9e9a8f6b71dd643de7"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aa546b0e9315b7d9e9a8f6b71dd643de7">&#9670;&#160;</a></span>Function</h2>
@@ -170,14 +208,15 @@ Functions</h2></td></tr>
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">using <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">math::monte_carlo::Function</a></td>
<td class="memname">using math::monte_carlo::Function</td>
</tr>
</table>
</div><div class="memdoc">
<b>Initial value:</b><div class="fragment"><div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a>&lt;double(</div>
<b>Initial value:</b><div class="fragment"><div class="line"> std::function&lt;double(</div>
<div class="line"> <span class="keywordtype">double</span>&amp;)&gt;</div>
<div class="ttc" id="afunction_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a></div></div>
</div><!-- fragment -->
<p class="definition">Definition at line <a class="el" href="../../db/d40/integral__approximation2_8cpp_source.html#l00046">46</a> of file <a class="el" href="../../db/d40/integral__approximation2_8cpp_source.html">integral_approximation2.cpp</a>.</p>
</div>
</div>
<h2 class="groupheader">Function Documentation</h2>
@@ -188,14 +227,14 @@ Functions</h2></td></tr>
<div class="memproto">
<table class="memname">
<tr>
<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; double &gt; math::monte_carlo::generate_samples </td>
<td class="memname">std::vector&lt; double &gt; math::monte_carlo::generate_samples </td>
<td>(</td>
<td class="paramtype">const double &amp;</td> <td class="paramname"><span class="paramname"><em>start_point</em></span>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">Function</a> &amp;</td> <td class="paramname"><span class="paramname"><em>pdf</em></span>, </td>
<td class="paramtype">const Function &amp;</td> <td class="paramname"><span class="paramname"><em>pdf</em></span>, </td>
</tr>
<tr>
<td class="paramkey"></td>
@@ -222,22 +261,24 @@ Functions</h2></td></tr>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>A vector of size num_samples with samples distributed according to the pdf </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../db/d40/integral__approximation2_8cpp_source.html#l00064">64</a> of file <a class="el" href="../../db/d40/integral__approximation2_8cpp_source.html">integral_approximation2.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 67</span> {</div>
<div class="line"><span class="lineno"> 68</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a> samples;</div>
<div class="line"><span class="lineno"> 69</span> samples.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/reserve.html">reserve</a>(num_samples);</div>
<div class="line"><span class="lineno"> 68</span> std::vector&lt;double&gt; samples;</div>
<div class="line"><span class="lineno"> 69</span> samples.reserve(num_samples);</div>
<div class="line"><span class="lineno"> 70</span> </div>
<div class="line"><span class="lineno"> 71</span> <span class="keywordtype">double</span> x_t = start_point;</div>
<div class="line"><span class="lineno"> 72</span> </div>
<div class="line"><span class="lineno"> 73</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random.html">std::default_random_engine</a> generator;</div>
<div class="line"><span class="lineno"> 74</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/uniform_real_distribution.html">std::uniform_real_distribution&lt;double&gt;</a> uniform(0.0, 1.0);</div>
<div class="line"><span class="lineno"> 75</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/normal_distribution.html">std::normal_distribution&lt;double&gt;</a> normal(0.0, 1.0);</div>
<div class="line"><span class="lineno"> 76</span> generator.seed(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">time</a>(<span class="keyword">nullptr</span>));</div>
<div class="line"><span class="lineno"> 73</span> std::default_random_engine generator;</div>
<div class="line"><span class="lineno"> 74</span> std::uniform_real_distribution&lt;double&gt; uniform(0.0, 1.0);</div>
<div class="line"><span class="lineno"> 75</span> std::normal_distribution&lt;double&gt; normal(0.0, 1.0);</div>
<div class="line"><span class="lineno"> 76</span> generator.seed(time(<span class="keyword">nullptr</span>));</div>
<div class="line"><span class="lineno"> 77</span> </div>
<div class="line"><span class="lineno"> 78</span> <span class="keywordflow">for</span> (uint32_t t = 0; t &lt; num_samples + discard; ++t) {</div>
<div class="line"><span class="lineno"> 79</span> <span class="comment">// Generate a new proposal according to some mutation strategy.</span></div>
<div class="line"><span class="lineno"> 80</span> <span class="comment">// This is arbitrary and can be swapped.</span></div>
<div class="line"><span class="lineno"> 81</span> <span class="keywordtype">double</span> x_dash = normal(generator) + x_t;</div>
<div class="line"><span class="lineno"> 82</span> <span class="keywordtype">double</span> acceptance_probability = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a>(pdf(x_dash) / pdf(x_t), 1.0);</div>
<div class="line"><span class="lineno"> 82</span> <span class="keywordtype">double</span> acceptance_probability = std::min(pdf(x_dash) / pdf(x_t), 1.0);</div>
<div class="line"><span class="lineno"> 83</span> <span class="keywordtype">double</span> u = uniform(generator);</div>
<div class="line"><span class="lineno"> 84</span> </div>
<div class="line"><span class="lineno"> 85</span> <span class="comment">// Accept &quot;new state&quot; according to the acceptance_probability</span></div>
@@ -246,26 +287,13 @@ Functions</h2></td></tr>
<div class="line"><span class="lineno"> 88</span> }</div>
<div class="line"><span class="lineno"> 89</span> </div>
<div class="line"><span class="lineno"> 90</span> <span class="keywordflow">if</span> (t &gt;= discard) {</div>
<div class="line"><span class="lineno"> 91</span> samples.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(x_t);</div>
<div class="line"><span class="lineno"> 91</span> samples.push_back(x_t);</div>
<div class="line"><span class="lineno"> 92</span> }</div>
<div class="line"><span class="lineno"> 93</span> }</div>
<div class="line"><span class="lineno"> 94</span> </div>
<div class="line"><span class="lineno"> 95</span> <span class="keywordflow">return</span> samples;</div>
<div class="line"><span class="lineno"> 96</span>}</div>
<div class="ttc" id="amin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/min.html">std::min</a></div><div class="ttdeci">T min(T... args)</div></div>
<div class="ttc" id="anormal_distribution_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/normal_distribution.html">std::normal_distribution</a></div></div>
<div class="ttc" id="apush_back_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">std::vector::push_back</a></div><div class="ttdeci">T push_back(T... args)</div></div>
<div class="ttc" id="arandom_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random.html">std::default_random_engine</a></div></div>
<div class="ttc" id="areserve_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/reserve.html">std::vector::reserve</a></div><div class="ttdeci">T reserve(T... args)</div></div>
<div class="ttc" id="atime_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a></div><div class="ttdeci">T time(T... args)</div></div>
<div class="ttc" id="auniform_real_distribution_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/uniform_real_distribution.html">std::uniform_real_distribution</a></div></div>
<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div></div>
</div><!-- fragment --><div class="dynheader">
Here is the call graph for this function:</div>
<div class="dyncontent">
<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/d40/integral__approximation2_8cpp_a71249ee535f16f8ed2e9cc8f0199a2cf_cgraph.svg" width="351" height="135"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
</div>
</div><!-- fragment -->
</div>
</div>
<a id="af7da9ba8932f1f48b9bbc2d80471af51" name="af7da9ba8932f1f48b9bbc2d80471af51"></a>
@@ -282,12 +310,12 @@ Here is the call graph for this function:</div>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">Function</a> &amp;</td> <td class="paramname"><span class="paramname"><em>function</em></span>, </td>
<td class="paramtype">const Function &amp;</td> <td class="paramname"><span class="paramname"><em>function</em></span>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">Function</a> &amp;</td> <td class="paramname"><span class="paramname"><em>pdf</em></span>, </td>
<td class="paramtype">const Function &amp;</td> <td class="paramname"><span class="paramname"><em>pdf</em></span>, </td>
</tr>
<tr>
<td class="paramkey"></td>
@@ -308,9 +336,11 @@ Here is the call graph for this function:</div>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>The approximation of the integral according to 1/N \sum_{i}^N f(x_i) / p(x_i) </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../db/d40/integral__approximation2_8cpp_source.html#l00112">112</a> of file <a class="el" href="../../db/d40/integral__approximation2_8cpp_source.html">integral_approximation2.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 114</span> {</div>
<div class="line"><span class="lineno"> 115</span> <span class="keywordtype">double</span> integral = 0.0;</div>
<div class="line"><span class="lineno"> 116</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a> samples =</div>
<div class="line"><span class="lineno"> 116</span> std::vector&lt;double&gt; samples =</div>
<div class="line"><span class="lineno"> 117</span> <a class="code hl_function" href="#a71249ee535f16f8ed2e9cc8f0199a2cf">generate_samples</a>(start_point, pdf, num_samples);</div>
<div class="line"><span class="lineno"> 118</span> </div>
<div class="line"><span class="lineno"> 119</span> <span class="keywordflow">for</span> (<span class="keywordtype">double</span> sample : samples) {</div>
@@ -319,13 +349,8 @@ Here is the call graph for this function:</div>
<div class="line"><span class="lineno"> 122</span> </div>
<div class="line"><span class="lineno"> 123</span> <span class="keywordflow">return</span> integral / <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(samples.size());</div>
<div class="line"><span class="lineno"> 124</span>}</div>
<div class="ttc" id="aintegral__approximation2_8cpp_html_a71249ee535f16f8ed2e9cc8f0199a2cf"><div class="ttname"><a href="#a71249ee535f16f8ed2e9cc8f0199a2cf">math::monte_carlo::generate_samples</a></div><div class="ttdeci">std::vector&lt; double &gt; generate_samples(const double &amp;start_point, const Function &amp;pdf, const uint32_t &amp;num_samples, const uint32_t &amp;discard=100000)</div><div class="ttdoc">short-hand for std::functions used in this implementation</div><div class="ttdef"><b>Definition</b> integral_approximation2.cpp:64</div></div>
</div><!-- fragment --><div class="dynheader">
Here is the call graph for this function:</div>
<div class="dyncontent">
<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/d40/integral__approximation2_8cpp_af7da9ba8932f1f48b9bbc2d80471af51_cgraph.svg" width="540" height="143"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
</div>
<div class="ttc" id="aintegral__approximation2_8cpp_html_a71249ee535f16f8ed2e9cc8f0199a2cf"><div class="ttname"><a href="#a71249ee535f16f8ed2e9cc8f0199a2cf">math::monte_carlo::generate_samples</a></div><div class="ttdeci">std::vector&lt; double &gt; generate_samples(const double &amp;start_point, const Function &amp;pdf, const uint32_t &amp;num_samples, const uint32_t &amp;discard=100000)</div><div class="ttdoc">short-hand for std::functions used in this implementation</div><div class="ttdef"><b>Definition</b> <a href="../../db/d40/integral__approximation2_8cpp_source.html#l00064">integral_approximation2.cpp:64</a></div></div>
</div><!-- fragment -->
</div>
</div>
<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
@@ -345,17 +370,14 @@ Here is the call graph for this function:</div>
<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../db/d40/integral__approximation2_8cpp_source.html#l00215">215</a> of file <a class="el" href="../../db/d40/integral__approximation2_8cpp_source.html">integral_approximation2.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 215</span> {</div>
<div class="line"><span class="lineno"> 216</span> <a class="code hl_function" href="#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><span class="lineno"> 217</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 218</span>}</div>
<div class="ttc" id="aintegral__approximation2_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> integral_approximation2.cpp:133</div></div>
</div><!-- fragment --><div class="dynheader">
Here is the call graph for this function:</div>
<div class="dyncontent">
<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/d40/integral__approximation2_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg" width="271" height="184"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
</div>
<div class="ttc" id="aintegral__approximation2_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> <a href="../../db/d40/integral__approximation2_8cpp_source.html#l00133">integral_approximation2.cpp:133</a></div></div>
</div><!-- fragment -->
</div>
</div>
<a id="aa8dca7b867074164d5f45b0f3851269d" name="aa8dca7b867074164d5f45b0f3851269d"></a>
@@ -383,25 +405,27 @@ Here is the call graph for this function:</div>
<p>Self-test implementations. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../db/d40/integral__approximation2_8cpp_source.html#l00133">133</a> of file <a class="el" href="../../db/d40/integral__approximation2_8cpp_source.html">integral_approximation2.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 133</span> {</div>
<div class="line"><span class="lineno"> 134</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Disclaimer: Because this is a randomized algorithm,&quot;</span></div>
<div class="line"><span class="lineno"> 135</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 136</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div>
<div class="line"><span class="lineno"> 134</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Disclaimer: Because this is a randomized algorithm,&quot;</span></div>
<div class="line"><span class="lineno"> 135</span> &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 136</span> std::cout</div>
<div class="line"><span class="lineno"> 137</span> &lt;&lt; <span class="stringliteral">&quot;it may happen that singular samples deviate from the true result.&quot;</span></div>
<div class="line"><span class="lineno"> 138</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div>
<div class="line"><span class="lineno"> 139</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 138</span> &lt;&lt; std::endl</div>
<div class="line"><span class="lineno"> 139</span> &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 140</span> ;</div>
<div class="line"><span class="lineno"> 141</span> </div>
<div class="line"><span class="lineno"> 142</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">math::monte_carlo::Function</a> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a4251b4df4748a0b9c43a48f61bdd2397">f</a>;</div>
<div class="line"><span class="lineno"> 143</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/functional/function.html">math::monte_carlo::Function</a> pdf;</div>
<div class="line"><span class="lineno"> 142</span> math::monte_carlo::Function <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a4251b4df4748a0b9c43a48f61bdd2397">f</a>;</div>
<div class="line"><span class="lineno"> 143</span> math::monte_carlo::Function pdf;</div>
<div class="line"><span class="lineno"> 144</span> <span class="keywordtype">double</span> integral = 0;</div>
<div class="line"><span class="lineno"> 145</span> <span class="keywordtype">double</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/lower_bound.html">lower_bound</a> = 0, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/upper_bound.html">upper_bound</a> = 0;</div>
<div class="line"><span class="lineno"> 145</span> <span class="keywordtype">double</span> lower_bound = 0, upper_bound = 0;</div>
<div class="line"><span class="lineno"> 146</span> </div>
<div class="line"><span class="lineno"> 147</span> <span class="comment">/* \int_{-2}^{2} -x^2 + 4 dx */</span></div>
<div class="line"><span class="lineno"> 148</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a4251b4df4748a0b9c43a48f61bdd2397">f</a> = [&amp;](<span class="keywordtype">double</span>&amp; x) { <span class="keywordflow">return</span> -x * x + 4.0; };</div>
<div class="line"><span class="lineno"> 149</span> </div>
<div class="line"><span class="lineno"> 150</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/lower_bound.html">lower_bound</a> = -2.0;</div>
<div class="line"><span class="lineno"> 151</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/upper_bound.html">upper_bound</a> = 2.0;</div>
<div class="line"><span class="lineno"> 150</span> lower_bound = -2.0;</div>
<div class="line"><span class="lineno"> 151</span> upper_bound = 2.0;</div>
<div class="line"><span class="lineno"> 152</span> pdf = [&amp;](<span class="keywordtype">double</span>&amp; x) {</div>
<div class="line"><span class="lineno"> 153</span> <span class="keywordflow">if</span> (x &gt;= lower_bound &amp;&amp; x &lt;= -1.0) {</div>
<div class="line"><span class="lineno"> 154</span> <span class="keywordflow">return</span> 0.1;</div>
@@ -418,14 +442,14 @@ Here is the call graph for this function:</div>
<div class="line"><span class="lineno"> 165</span> integral = <a class="code hl_function" href="#af7da9ba8932f1f48b9bbc2d80471af51">math::monte_carlo::integral_monte_carlo</a>(</div>
<div class="line"><span class="lineno"> 166</span> (upper_bound - lower_bound) / 2.0, f, pdf);</div>
<div class="line"><span class="lineno"> 167</span> </div>
<div class="line"><span class="lineno"> 168</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;This number should be close to 10.666666: &quot;</span> &lt;&lt; integral</div>
<div class="line"><span class="lineno"> 169</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 168</span> std::cout &lt;&lt; <span class="stringliteral">&quot;This number should be close to 10.666666: &quot;</span> &lt;&lt; integral</div>
<div class="line"><span class="lineno"> 169</span> &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 170</span> </div>
<div class="line"><span class="lineno"> 171</span> <span class="comment">/* \int_{0}^{1} e^x dx */</span></div>
<div class="line"><span class="lineno"> 172</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a4251b4df4748a0b9c43a48f61bdd2397">f</a> = [&amp;](<span class="keywordtype">double</span>&amp; x) { <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/exp.html">std::exp</a>(x); };</div>
<div class="line"><span class="lineno"> 172</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a4251b4df4748a0b9c43a48f61bdd2397">f</a> = [&amp;](<span class="keywordtype">double</span>&amp; x) { <span class="keywordflow">return</span> std::exp(x); };</div>
<div class="line"><span class="lineno"> 173</span> </div>
<div class="line"><span class="lineno"> 174</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/lower_bound.html">lower_bound</a> = 0.0;</div>
<div class="line"><span class="lineno"> 175</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/upper_bound.html">upper_bound</a> = 1.0;</div>
<div class="line"><span class="lineno"> 174</span> lower_bound = 0.0;</div>
<div class="line"><span class="lineno"> 175</span> upper_bound = 1.0;</div>
<div class="line"><span class="lineno"> 176</span> pdf = [&amp;](<span class="keywordtype">double</span>&amp; x) {</div>
<div class="line"><span class="lineno"> 177</span> <span class="keywordflow">if</span> (x &gt;= lower_bound &amp;&amp; x &lt;= 0.2) {</div>
<div class="line"><span class="lineno"> 178</span> <span class="keywordflow">return</span> 0.1;</div>
@@ -442,39 +466,27 @@ Here is the call graph for this function:</div>
<div class="line"><span class="lineno"> 189</span> integral = <a class="code hl_function" href="#af7da9ba8932f1f48b9bbc2d80471af51">math::monte_carlo::integral_monte_carlo</a>(</div>
<div class="line"><span class="lineno"> 190</span> (upper_bound - lower_bound) / 2.0, f, pdf);</div>
<div class="line"><span class="lineno"> 191</span> </div>
<div class="line"><span class="lineno"> 192</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;This number should be close to 1.7182818: &quot;</span> &lt;&lt; integral</div>
<div class="line"><span class="lineno"> 193</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 192</span> std::cout &lt;&lt; <span class="stringliteral">&quot;This number should be close to 1.7182818: &quot;</span> &lt;&lt; integral</div>
<div class="line"><span class="lineno"> 193</span> &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 194</span> </div>
<div class="line"><span class="lineno"> 195</span> <span class="comment">/* \int_{-\infty}^{\infty} sinc(x) dx, sinc(x) = sin(pi * x) / (pi * x)</span></div>
<div class="line"><span class="lineno"> 196</span><span class="comment"> This is a difficult integral because of its infinite domain.</span></div>
<div class="line"><span class="lineno"> 197</span><span class="comment"> Therefore, it may deviate largely from the expected result.</span></div>
<div class="line"><span class="lineno"> 198</span><span class="comment"> */</span></div>
<div class="line"><span class="lineno"> 199</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a4251b4df4748a0b9c43a48f61bdd2397">f</a> = [&amp;](<span class="keywordtype">double</span>&amp; x) { <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sin.html">std::sin</a>(M_PI * x) / (M_PI * x); };</div>
<div class="line"><span class="lineno"> 199</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a4251b4df4748a0b9c43a48f61bdd2397">f</a> = [&amp;](<span class="keywordtype">double</span>&amp; x) { <span class="keywordflow">return</span> std::sin(M_PI * x) / (M_PI * x); };</div>
<div class="line"><span class="lineno"> 200</span> </div>
<div class="line"><span class="lineno"> 201</span> pdf = [&amp;](<span class="keywordtype">double</span>&amp; x) {</div>
<div class="line"><span class="lineno"> 202</span> <span class="keywordflow">return</span> 1.0 / <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(2.0 * M_PI) * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/exp.html">std::exp</a>(-x * x / 2.0);</div>
<div class="line"><span class="lineno"> 202</span> <span class="keywordflow">return</span> 1.0 / std::sqrt(2.0 * M_PI) * std::exp(-x * x / 2.0);</div>
<div class="line"><span class="lineno"> 203</span> };</div>
<div class="line"><span class="lineno"> 204</span> </div>
<div class="line"><span class="lineno"> 205</span> integral = <a class="code hl_function" href="#af7da9ba8932f1f48b9bbc2d80471af51">math::monte_carlo::integral_monte_carlo</a>(0.0, f, pdf, 10000000);</div>
<div class="line"><span class="lineno"> 206</span> </div>
<div class="line"><span class="lineno"> 207</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;This number should be close to 1.0: &quot;</span> &lt;&lt; integral</div>
<div class="line"><span class="lineno"> 208</span> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 207</span> std::cout &lt;&lt; <span class="stringliteral">&quot;This number should be close to 1.0: &quot;</span> &lt;&lt; integral</div>
<div class="line"><span class="lineno"> 208</span> &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 209</span>}</div>
<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a4251b4df4748a0b9c43a48f61bdd2397"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a4251b4df4748a0b9c43a48f61bdd2397">numerical_methods::simpson_method::f</a></div><div class="ttdeci">double f(double x)</div><div class="ttdoc">A function f(x) that will be used to test the method.</div><div class="ttdef"><b>Definition</b> composite_simpson_rule.cpp:113</div></div>
<div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
<div class="ttc" id="aexp_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/exp.html">std::exp</a></div><div class="ttdeci">T exp(T... args)</div></div>
<div class="ttc" id="aintegral__approximation2_8cpp_html_af7da9ba8932f1f48b9bbc2d80471af51"><div class="ttname"><a href="#af7da9ba8932f1f48b9bbc2d80471af51">math::monte_carlo::integral_monte_carlo</a></div><div class="ttdeci">double integral_monte_carlo(const double &amp;start_point, const Function &amp;function, const Function &amp;pdf, const uint32_t &amp;num_samples=1000000)</div><div class="ttdoc">Compute an approximation of an integral using Monte Carlo integration.</div><div class="ttdef"><b>Definition</b> integral_approximation2.cpp:112</div></div>
<div class="ttc" id="alower_bound_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/lower_bound.html">std::lower_bound</a></div><div class="ttdeci">T lower_bound(T... args)</div></div>
<div class="ttc" id="asin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/sin.html">std::sin</a></div><div class="ttdeci">T sin(T... args)</div></div>
<div class="ttc" id="asqrt_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a></div><div class="ttdeci">T sqrt(T... args)</div></div>
<div class="ttc" id="aupper_bound_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/upper_bound.html">std::upper_bound</a></div><div class="ttdeci">T upper_bound(T... args)</div></div>
</div><!-- fragment --><div class="dynheader">
Here is the call graph for this function:</div>
<div class="dyncontent">
<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/d40/integral__approximation2_8cpp_aa8dca7b867074164d5f45b0f3851269d_cgraph.svg" width="174" height="184"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
</div>
<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a4251b4df4748a0b9c43a48f61bdd2397"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a4251b4df4748a0b9c43a48f61bdd2397">numerical_methods::simpson_method::f</a></div><div class="ttdeci">double f(double x)</div><div class="ttdoc">A function f(x) that will be used to test the method.</div><div class="ttdef"><b>Definition</b> <a href="../../d4/d18/composite__simpson__rule_8cpp_source.html#l00113">composite_simpson_rule.cpp:113</a></div></div>
<div class="ttc" id="aintegral__approximation2_8cpp_html_af7da9ba8932f1f48b9bbc2d80471af51"><div class="ttname"><a href="#af7da9ba8932f1f48b9bbc2d80471af51">math::monte_carlo::integral_monte_carlo</a></div><div class="ttdeci">double integral_monte_carlo(const double &amp;start_point, const Function &amp;function, const Function &amp;pdf, const uint32_t &amp;num_samples=1000000)</div><div class="ttdoc">Compute an approximation of an integral using Monte Carlo integration.</div><div class="ttdef"><b>Definition</b> <a href="../../db/d40/integral__approximation2_8cpp_source.html#l00112">integral_approximation2.cpp:112</a></div></div>
</div><!-- fragment -->
</div>
</div>
</div><!-- contents -->

10
db/d40/integral__approximation2_8cpp_a71249ee535f16f8ed2e9cc8f0199a2cf_cgraph.map
View File

@@ -1,10 +0,0 @@
<map id="math::monte_carlo::generate_samples" name="math::monte_carlo::generate_samples">
<area shape="rect" id="Node000001" title="short&#45;hand for std::functions used in this implementation" alt="" coords="5,47,143,88"/>
<area shape="poly" id="edge1_Node000001_Node000001" title=" " alt="" coords="37,47,35,37,41,28,54,23,74,21,95,23,108,29,105,34,94,28,74,26,56,28,45,32,40,38,42,46"/>
<area shape="rect" id="Node000002" href="/Users/runner/work/C-Plus-Plus/C-Plus-Plus/doc/cppreference-doxygen-web.tag.xml$cpp/algorithm/min.html#" title=" " alt="" coords="234,5,302,31"/>
<area shape="poly" id="edge2_Node000001_Node000002" title=" " alt="" coords="143,47,218,28,220,33,144,53"/>
<area shape="rect" id="Node000003" href="/Users/runner/work/C-Plus-Plus/C-Plus-Plus/doc/cppreference-doxygen-web.tag.xml$cpp/container/vector/push_back.html#" title=" " alt="" coords="191,55,345,80"/>
<area shape="poly" id="edge3_Node000001_Node000003" title=" " alt="" coords="143,65,175,65,175,70,143,70"/>
<area shape="rect" id="Node000004" href="/Users/runner/work/C-Plus-Plus/C-Plus-Plus/doc/cppreference-doxygen-web.tag.xml$cpp/container/vector/reserve.html#" title=" " alt="" coords="201,104,335,130"/>
<area shape="poly" id="edge4_Node000001_Node000004" title=" " alt="" coords="144,82,201,97,199,102,143,88"/>
</map>

1
db/d40/integral__approximation2_8cpp_a71249ee535f16f8ed2e9cc8f0199a2cf_cgraph.md5
View File

@@ -1 +0,0 @@
6e59671e4799cabb0ddcc6bb203b23ff

111
db/d40/integral__approximation2_8cpp_a71249ee535f16f8ed2e9cc8f0199a2cf_cgraph.svg
View File

@@ -1,111 +0,0 @@
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<!-- Generated by graphviz version 12.1.2 (20240928.0832)
-->
<!-- Title: math::monte_carlo::generate_samples Pages: 1 -->
<svg width="263pt" height="101pt"
viewBox="0.00 0.00 262.75 101.25" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<svg id="main" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" xml:space="preserve">
<style type="text/css"><![CDATA[
.node, .edge {opacity: 0.7;}
.node.selected, .edge.selected {opacity: 1;}
.edge:hover path { stroke: red; }
.edge:hover polygon { stroke: red; fill: red; }
]]></style>
<script type="application/ecmascript" xlink:href="../../svg.min.js"/>
<svg id="graph" class="graph">
<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 97.25)">
<title>math::monte_carlo::generate_samples</title>
<!-- Node1 -->
<g id="Node000001" class="node">
<title>Node1</title>
<g id="a_Node000001"><a xlink:title="short&#45;hand for std::functions used in this implementation">
<polygon fill="#999999" stroke="#666666" points="103,-61.88 0,-61.88 0,-31.38 103,-31.38 103,-61.88"/>
<text text-anchor="start" x="8" y="-48.38" font-family="Helvetica,sans-Serif" font-size="10.00">math::monte_carlo::</text>
<text text-anchor="middle" x="51.5" y="-37.12" font-family="Helvetica,sans-Serif" font-size="10.00">generate_samples</text>
</a>
</g>
</g>
<!-- Node1&#45;&gt;Node1 -->
<g id="edge1_Node000001_Node000001" class="edge">
<title>Node1&#45;&gt;Node1</title>
<g id="a_edge1_Node000001_Node000001"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M25.74,-62.36C20.48,-71.43 29.07,-79.88 51.5,-79.88 63.77,-79.88 71.89,-77.35 75.88,-73.58"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="79.33,-74.22 77.08,-63.86 72.38,-73.36 79.33,-74.22"/>
</a>
</g>
</g>
<!-- Node2 -->
<g id="Node000002" class="node">
<title>Node2</title>
<g id="a_Node000002"><a target="_blank" xlink:href="http://en.cppreference.com/w/cpp/algorithm/min.html#" xlink:title=" ">
<polygon fill="white" stroke="#666666" points="222.5,-93.25 171.25,-93.25 171.25,-74 222.5,-74 222.5,-93.25"/>
<text text-anchor="middle" x="196.88" y="-79.75" font-family="Helvetica,sans-Serif" font-size="10.00">std::min</text>
</a>
</g>
</g>
<!-- Node1&#45;&gt;Node2 -->
<g id="edge2_Node000001_Node000002" class="edge">
<title>Node1&#45;&gt;Node2</title>
<g id="a_edge2_Node000001_Node000002"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M103.45,-59.77C122.2,-64.61 143.03,-69.99 160.15,-74.41"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="158.79,-77.67 169.35,-76.78 160.54,-70.89 158.79,-77.67"/>
</a>
</g>
</g>
<!-- Node3 -->
<g id="Node000003" class="node">
<title>Node3</title>
<g id="a_Node000003"><a target="_blank" xlink:href="http://en.cppreference.com/w/cpp/container/vector/push_back.html#" xlink:title=" ">
<polygon fill="white" stroke="#666666" points="254.75,-56.25 139,-56.25 139,-37 254.75,-37 254.75,-56.25"/>
<text text-anchor="middle" x="196.88" y="-42.75" font-family="Helvetica,sans-Serif" font-size="10.00">std::vector::push_back</text>
</a>
</g>
</g>
<!-- Node1&#45;&gt;Node3 -->
<g id="edge3_Node000001_Node000003" class="edge">
<title>Node1&#45;&gt;Node3</title>
<g id="a_edge3_Node000001_Node000003"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M103.45,-46.62C111.22,-46.62 119.34,-46.62 127.41,-46.62"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="127.23,-50.13 137.23,-46.63 127.23,-43.13 127.23,-50.13"/>
</a>
</g>
</g>
<!-- Node4 -->
<g id="Node000004" class="node">
<title>Node4</title>
<g id="a_Node000004"><a target="_blank" xlink:href="http://en.cppreference.com/w/cpp/container/vector/reserve.html#" xlink:title=" ">
<polygon fill="white" stroke="#666666" points="247.25,-19.25 146.5,-19.25 146.5,0 247.25,0 247.25,-19.25"/>
<text text-anchor="middle" x="196.88" y="-5.75" font-family="Helvetica,sans-Serif" font-size="10.00">std::vector::reserve</text>
</a>
</g>
</g>
<!-- Node1&#45;&gt;Node4 -->
<g id="edge4_Node000001_Node000004" class="edge">
<title>Node1&#45;&gt;Node4</title>
<g id="a_edge4_Node000001_Node000004"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M103.45,-33.48C117.3,-29.9 132.27,-26.04 146.05,-22.48"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="146.53,-25.97 155.34,-20.09 144.78,-19.2 146.53,-25.97"/>
</a>
</g>
</g>
</g>
</svg>
</svg>
<style type='text/css'>
<![CDATA[
[data-mouse-over-selected='false'] { opacity: 0.7; }
[data-mouse-over-selected='true'] { opacity: 1.0; }
]]>
</style>
<script type="application/ecmascript"><![CDATA[
document.addEventListener('DOMContentLoaded', (event) => {
highlightEdges();
highlightAdjacentNodes();
});
]]></script>
</svg>
Side by Side

Before

Width:  |  Height:  |  Size: 4.7 KiB

85
db/d40/integral__approximation2_8cpp_a71249ee535f16f8ed2e9cc8f0199a2cf_cgraph_org.svg
View File

@@ -1,85 +0,0 @@
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<!-- Generated by graphviz version 12.1.2 (20240928.0832)
-->
<!-- Title: math::monte_carlo::generate_samples Pages: 1 -->
<svg width="263pt" height="101pt"
viewBox="0.00 0.00 262.75 101.25" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 97.25)">
<title>math::monte_carlo::generate_samples</title>
<!-- Node1 -->
<g id="Node000001" class="node">
<title>Node1</title>
<g id="a_Node000001"><a xlink:title="short&#45;hand for std::functions used in this implementation">
<polygon fill="#999999" stroke="#666666" points="103,-61.88 0,-61.88 0,-31.38 103,-31.38 103,-61.88"/>
<text text-anchor="start" x="8" y="-48.38" font-family="Helvetica,sans-Serif" font-size="10.00">math::monte_carlo::</text>
<text text-anchor="middle" x="51.5" y="-37.12" font-family="Helvetica,sans-Serif" font-size="10.00">generate_samples</text>
</a>
</g>
</g>
<!-- Node1&#45;&gt;Node1 -->
<g id="edge1_Node000001_Node000001" class="edge">
<title>Node1&#45;&gt;Node1</title>
<g id="a_edge1_Node000001_Node000001"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M25.74,-62.36C20.48,-71.43 29.07,-79.88 51.5,-79.88 63.77,-79.88 71.89,-77.35 75.88,-73.58"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="79.33,-74.22 77.08,-63.86 72.38,-73.36 79.33,-74.22"/>
</a>
</g>
</g>
<!-- Node2 -->
<g id="Node000002" class="node">
<title>Node2</title>
<g id="a_Node000002"><a target="_blank" xlink:href="http://en.cppreference.com/w/cpp/algorithm/min.html#" xlink:title=" ">
<polygon fill="white" stroke="#666666" points="222.5,-93.25 171.25,-93.25 171.25,-74 222.5,-74 222.5,-93.25"/>
<text text-anchor="middle" x="196.88" y="-79.75" font-family="Helvetica,sans-Serif" font-size="10.00">std::min</text>
</a>
</g>
</g>
<!-- Node1&#45;&gt;Node2 -->
<g id="edge2_Node000001_Node000002" class="edge">
<title>Node1&#45;&gt;Node2</title>
<g id="a_edge2_Node000001_Node000002"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M103.45,-59.77C122.2,-64.61 143.03,-69.99 160.15,-74.41"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="158.79,-77.67 169.35,-76.78 160.54,-70.89 158.79,-77.67"/>
</a>
</g>
</g>
<!-- Node3 -->
<g id="Node000003" class="node">
<title>Node3</title>
<g id="a_Node000003"><a target="_blank" xlink:href="http://en.cppreference.com/w/cpp/container/vector/push_back.html#" xlink:title=" ">
<polygon fill="white" stroke="#666666" points="254.75,-56.25 139,-56.25 139,-37 254.75,-37 254.75,-56.25"/>
<text text-anchor="middle" x="196.88" y="-42.75" font-family="Helvetica,sans-Serif" font-size="10.00">std::vector::push_back</text>
</a>
</g>
</g>
<!-- Node1&#45;&gt;Node3 -->
<g id="edge3_Node000001_Node000003" class="edge">
<title>Node1&#45;&gt;Node3</title>
<g id="a_edge3_Node000001_Node000003"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M103.45,-46.62C111.22,-46.62 119.34,-46.62 127.41,-46.62"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="127.23,-50.13 137.23,-46.63 127.23,-43.13 127.23,-50.13"/>
</a>
</g>
</g>
<!-- Node4 -->
<g id="Node000004" class="node">
<title>Node4</title>
<g id="a_Node000004"><a target="_blank" xlink:href="http://en.cppreference.com/w/cpp/container/vector/reserve.html#" xlink:title=" ">
<polygon fill="white" stroke="#666666" points="247.25,-19.25 146.5,-19.25 146.5,0 247.25,0 247.25,-19.25"/>
<text text-anchor="middle" x="196.88" y="-5.75" font-family="Helvetica,sans-Serif" font-size="10.00">std::vector::reserve</text>
</a>
</g>
</g>
<!-- Node1&#45;&gt;Node4 -->
<g id="edge4_Node000001_Node000004" class="edge">
<title>Node1&#45;&gt;Node4</title>
<g id="a_edge4_Node000001_Node000004"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M103.45,-33.48C117.3,-29.9 132.27,-26.04 146.05,-22.48"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="146.53,-25.97 155.34,-20.09 144.78,-19.2 146.53,-25.97"/>
</a>
</g>
</g>
</g>
</svg>
Side by Side

Before

Width:  |  Height:  |  Size: 4.0 KiB

11
db/d40/integral__approximation2_8cpp_aa8dca7b867074164d5f45b0f3851269d_cgraph.map
View File

@@ -1,11 +0,0 @@
<map id="test" name="test">
<area shape="rect" id="Node000001" title="Self&#45;test implementations." alt="" coords="5,80,49,106"/>
<area shape="rect" id="Node000002" href="/Users/runner/work/C-Plus-Plus/C-Plus-Plus/doc/cppreference-doxygen-web.tag.xml$cpp/io/manip/endl.html#" title=" " alt="" coords="97,5,168,31"/>
<area shape="poly" id="edge1_Node000001_Node000002" title=" " alt="" coords="45,77,95,40,98,38,101,42,98,44,48,82"/>
<area shape="rect" id="Node000003" href="/Users/runner/work/C-Plus-Plus/C-Plus-Plus/doc/cppreference-doxygen-web.tag.xml$cpp/numeric/math/exp.html#" title=" " alt="" coords="98,55,166,80"/>
<area shape="poly" id="edge2_Node000001_Node000003" title=" " alt="" coords="48,85,82,77,84,82,50,90"/>
<area shape="rect" id="Node000004" href="/Users/runner/work/C-Plus-Plus/C-Plus-Plus/doc/cppreference-doxygen-web.tag.xml$cpp/numeric/math/sin.html#" title=" " alt="" coords="100,104,164,130"/>
<area shape="poly" id="edge3_Node000001_Node000004" title=" " alt="" coords="50,95,85,103,84,109,49,100"/>
<area shape="rect" id="Node000005" href="/Users/runner/work/C-Plus-Plus/C-Plus-Plus/doc/cppreference-doxygen-web.tag.xml$cpp/numeric/math/sqrt.html#" title=" " alt="" coords="98,153,167,179"/>
<area shape="poly" id="edge4_Node000001_Node000005" title=" " alt="" coords="48,104,98,140,101,142,98,146,95,144,45,108"/>
</map>

1
db/d40/integral__approximation2_8cpp_aa8dca7b867074164d5f45b0f3851269d_cgraph.md5
View File

@@ -1 +0,0 @@
f7c52ce989430da0ad39e012eb8f3633

119
db/d40/integral__approximation2_8cpp_aa8dca7b867074164d5f45b0f3851269d_cgraph.svg
View File

@@ -1,119 +0,0 @@
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<!-- Generated by graphviz version 12.1.2 (20240928.0832)
-->
<!-- Title: test Pages: 1 -->
<svg width="130pt" height="138pt"
viewBox="0.00 0.00 130.00 138.25" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<svg id="main" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" xml:space="preserve">
<style type="text/css"><![CDATA[
.node, .edge {opacity: 0.7;}
.node.selected, .edge.selected {opacity: 1;}
.edge:hover path { stroke: red; }
.edge:hover polygon { stroke: red; fill: red; }
]]></style>
<script type="application/ecmascript" xlink:href="../../svg.min.js"/>
<svg id="graph" class="graph">
<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 134.25)">
<title>test</title>
<!-- Node1 -->
<g id="Node000001" class="node">
<title>Node1</title>
<g id="a_Node000001"><a xlink:title="Self&#45;test implementations.">
<polygon fill="#999999" stroke="#666666" points="32.5,-74.25 0,-74.25 0,-55 32.5,-55 32.5,-74.25"/>
<text text-anchor="middle" x="16.25" y="-60.75" font-family="Helvetica,sans-Serif" font-size="10.00">test</text>
</a>
</g>
</g>
<!-- Node2 -->
<g id="Node000002" class="node">
<title>Node2</title>
<g id="a_Node000002"><a target="_blank" xlink:href="http://en.cppreference.com/w/cpp/io/manip/endl.html#" xlink:title=" ">
<polygon fill="white" stroke="#666666" points="122,-130.25 68.5,-130.25 68.5,-111 122,-111 122,-130.25"/>
<text text-anchor="middle" x="95.25" y="-116.75" font-family="Helvetica,sans-Serif" font-size="10.00">std::endl</text>
</a>
</g>
</g>
<!-- Node1&#45;&gt;Node2 -->
<g id="edge1_Node000001_Node000002" class="edge">
<title>Node1&#45;&gt;Node2</title>
<g id="a_edge1_Node000001_Node000002"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M30.66,-74.73C40.96,-82.45 55.56,-93.3 68.5,-102.62 69.18,-103.12 69.87,-103.61 70.57,-104.11"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="68.34,-106.82 78.53,-109.73 72.38,-101.1 68.34,-106.82"/>
</a>
</g>
</g>
<!-- Node3 -->
<g id="Node000003" class="node">
<title>Node3</title>
<g id="a_Node000003"><a target="_blank" xlink:href="http://en.cppreference.com/w/cpp/numeric/math/exp.html#" xlink:title=" ">
<polygon fill="white" stroke="#666666" points="120.88,-93.25 69.62,-93.25 69.62,-74 120.88,-74 120.88,-93.25"/>
<text text-anchor="middle" x="95.25" y="-79.75" font-family="Helvetica,sans-Serif" font-size="10.00">std::exp</text>
</a>
</g>
</g>
<!-- Node1&#45;&gt;Node3 -->
<g id="edge2_Node000001_Node000003" class="edge">
<title>Node1&#45;&gt;Node3</title>
<g id="a_edge2_Node000001_Node000003"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M32.83,-68.47C40.19,-70.28 49.29,-72.53 58.22,-74.74"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="57.28,-78.11 67.82,-77.1 58.95,-71.31 57.28,-78.11"/>
</a>
</g>
</g>
<!-- Node4 -->
<g id="Node000004" class="node">
<title>Node4</title>
<g id="a_Node000004"><a target="_blank" xlink:href="http://en.cppreference.com/w/cpp/numeric/math/sin.html#" xlink:title=" ">
<polygon fill="white" stroke="#666666" points="119.38,-56.25 71.12,-56.25 71.12,-37 119.38,-37 119.38,-56.25"/>
<text text-anchor="middle" x="95.25" y="-42.75" font-family="Helvetica,sans-Serif" font-size="10.00">std::sin</text>
</a>
</g>
</g>
<!-- Node1&#45;&gt;Node4 -->
<g id="edge3_Node000001_Node000004" class="edge">
<title>Node1&#45;&gt;Node4</title>
<g id="a_edge3_Node000001_Node000004"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M32.83,-60.98C40.58,-59.17 50.28,-56.9 59.66,-54.71"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="60.38,-58.14 69.32,-52.45 58.79,-51.32 60.38,-58.14"/>
</a>
</g>
</g>
<!-- Node5 -->
<g id="Node000005" class="node">
<title>Node5</title>
<g id="a_Node000005"><a target="_blank" xlink:href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html#" xlink:title=" ">
<polygon fill="white" stroke="#666666" points="121.25,-19.25 69.25,-19.25 69.25,0 121.25,0 121.25,-19.25"/>
<text text-anchor="middle" x="95.25" y="-5.75" font-family="Helvetica,sans-Serif" font-size="10.00">std::sqrt</text>
</a>
</g>
</g>
<!-- Node1&#45;&gt;Node5 -->
<g id="edge4_Node000001_Node000005" class="edge">
<title>Node1&#45;&gt;Node5</title>
<g id="a_edge4_Node000001_Node000005"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M31.13,-54.52C41.42,-47.05 55.8,-36.65 68.5,-27.62 69.18,-27.14 69.88,-26.65 70.58,-26.15"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="72.38,-29.16 78.55,-20.55 68.35,-23.44 72.38,-29.16"/>
</a>
</g>
</g>
</g>
</svg>
</svg>
<style type='text/css'>
<![CDATA[
[data-mouse-over-selected='false'] { opacity: 0.7; }
[data-mouse-over-selected='true'] { opacity: 1.0; }
]]>
</style>
<script type="application/ecmascript"><![CDATA[
document.addEventListener('DOMContentLoaded', (event) => {
highlightEdges();
highlightAdjacentNodes();
});
]]></script>
</svg>
Side by Side

Before

Width:  |  Height:  |  Size: 4.9 KiB

93
db/d40/integral__approximation2_8cpp_aa8dca7b867074164d5f45b0f3851269d_cgraph_org.svg
View File

@@ -1,93 +0,0 @@
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<!-- Generated by graphviz version 12.1.2 (20240928.0832)
-->
<!-- Title: test Pages: 1 -->
<svg width="130pt" height="138pt"
viewBox="0.00 0.00 130.00 138.25" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 134.25)">
<title>test</title>
<!-- Node1 -->
<g id="Node000001" class="node">
<title>Node1</title>
<g id="a_Node000001"><a xlink:title="Self&#45;test implementations.">
<polygon fill="#999999" stroke="#666666" points="32.5,-74.25 0,-74.25 0,-55 32.5,-55 32.5,-74.25"/>
<text text-anchor="middle" x="16.25" y="-60.75" font-family="Helvetica,sans-Serif" font-size="10.00">test</text>
</a>
</g>
</g>
<!-- Node2 -->
<g id="Node000002" class="node">
<title>Node2</title>
<g id="a_Node000002"><a target="_blank" xlink:href="http://en.cppreference.com/w/cpp/io/manip/endl.html#" xlink:title=" ">
<polygon fill="white" stroke="#666666" points="122,-130.25 68.5,-130.25 68.5,-111 122,-111 122,-130.25"/>
<text text-anchor="middle" x="95.25" y="-116.75" font-family="Helvetica,sans-Serif" font-size="10.00">std::endl</text>
</a>
</g>
</g>
<!-- Node1&#45;&gt;Node2 -->
<g id="edge1_Node000001_Node000002" class="edge">
<title>Node1&#45;&gt;Node2</title>
<g id="a_edge1_Node000001_Node000002"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M30.66,-74.73C40.96,-82.45 55.56,-93.3 68.5,-102.62 69.18,-103.12 69.87,-103.61 70.57,-104.11"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="68.34,-106.82 78.53,-109.73 72.38,-101.1 68.34,-106.82"/>
</a>
</g>
</g>
<!-- Node3 -->
<g id="Node000003" class="node">
<title>Node3</title>
<g id="a_Node000003"><a target="_blank" xlink:href="http://en.cppreference.com/w/cpp/numeric/math/exp.html#" xlink:title=" ">
<polygon fill="white" stroke="#666666" points="120.88,-93.25 69.62,-93.25 69.62,-74 120.88,-74 120.88,-93.25"/>
<text text-anchor="middle" x="95.25" y="-79.75" font-family="Helvetica,sans-Serif" font-size="10.00">std::exp</text>
</a>
</g>
</g>
<!-- Node1&#45;&gt;Node3 -->
<g id="edge2_Node000001_Node000003" class="edge">
<title>Node1&#45;&gt;Node3</title>
<g id="a_edge2_Node000001_Node000003"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M32.83,-68.47C40.19,-70.28 49.29,-72.53 58.22,-74.74"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="57.28,-78.11 67.82,-77.1 58.95,-71.31 57.28,-78.11"/>
</a>
</g>
</g>
<!-- Node4 -->
<g id="Node000004" class="node">
<title>Node4</title>
<g id="a_Node000004"><a target="_blank" xlink:href="http://en.cppreference.com/w/cpp/numeric/math/sin.html#" xlink:title=" ">
<polygon fill="white" stroke="#666666" points="119.38,-56.25 71.12,-56.25 71.12,-37 119.38,-37 119.38,-56.25"/>
<text text-anchor="middle" x="95.25" y="-42.75" font-family="Helvetica,sans-Serif" font-size="10.00">std::sin</text>
</a>
</g>
</g>
<!-- Node1&#45;&gt;Node4 -->
<g id="edge3_Node000001_Node000004" class="edge">
<title>Node1&#45;&gt;Node4</title>
<g id="a_edge3_Node000001_Node000004"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M32.83,-60.98C40.58,-59.17 50.28,-56.9 59.66,-54.71"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="60.38,-58.14 69.32,-52.45 58.79,-51.32 60.38,-58.14"/>
</a>
</g>
</g>
<!-- Node5 -->
<g id="Node000005" class="node">
<title>Node5</title>
<g id="a_Node000005"><a target="_blank" xlink:href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html#" xlink:title=" ">
<polygon fill="white" stroke="#666666" points="121.25,-19.25 69.25,-19.25 69.25,0 121.25,0 121.25,-19.25"/>
<text text-anchor="middle" x="95.25" y="-5.75" font-family="Helvetica,sans-Serif" font-size="10.00">std::sqrt</text>
</a>
</g>
</g>
<!-- Node1&#45;&gt;Node5 -->
<g id="edge4_Node000001_Node000005" class="edge">
<title>Node1&#45;&gt;Node5</title>
<g id="a_edge4_Node000001_Node000005"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M31.13,-54.52C41.42,-47.05 55.8,-36.65 68.5,-27.62 69.18,-27.14 69.88,-26.65 70.58,-26.15"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="72.38,-29.16 78.55,-20.55 68.35,-23.44 72.38,-29.16"/>
</a>
</g>
</g>
</g>
</svg>
Side by Side

Before

Width:  |  Height:  |  Size: 4.1 KiB

13
db/d40/integral__approximation2_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.map
View File

@@ -1,13 +0,0 @@
<map id="main" name="main">
<area shape="rect" id="Node000001" title="Main function." alt="" coords="5,80,55,106"/>
<area shape="rect" id="Node000002" href="$db/d40/integral__approximation2_8cpp.html#aa8dca7b867074164d5f45b0f3851269d" title="Self&#45;test implementations." alt="" coords="103,80,146,106"/>
<area shape="poly" id="edge1_Node000001_Node000002" title=" " alt="" coords="55,90,87,90,87,96,55,96"/>
<area shape="rect" id="Node000003" href="/Users/runner/work/C-Plus-Plus/C-Plus-Plus/doc/cppreference-doxygen-web.tag.xml$cpp/io/manip/endl.html#" title=" " alt="" coords="194,5,265,31"/>
<area shape="poly" id="edge2_Node000002_Node000003" title=" " alt="" coords="142,77,192,40,195,38,198,42,196,44,145,82"/>
<area shape="rect" id="Node000004" href="/Users/runner/work/C-Plus-Plus/C-Plus-Plus/doc/cppreference-doxygen-web.tag.xml$cpp/numeric/math/exp.html#" title=" " alt="" coords="196,55,264,80"/>
<area shape="poly" id="edge3_Node000002_Node000004" title=" " alt="" coords="146,85,180,77,181,82,147,90"/>
<area shape="rect" id="Node000005" href="/Users/runner/work/C-Plus-Plus/C-Plus-Plus/doc/cppreference-doxygen-web.tag.xml$cpp/numeric/math/sin.html#" title=" " alt="" coords="198,104,262,130"/>
<area shape="poly" id="edge4_Node000002_Node000005" title=" " alt="" coords="147,95,183,103,182,109,146,100"/>
<area shape="rect" id="Node000006" href="/Users/runner/work/C-Plus-Plus/C-Plus-Plus/doc/cppreference-doxygen-web.tag.xml$cpp/numeric/math/sqrt.html#" title=" " alt="" coords="195,153,264,179"/>
<area shape="poly" id="edge5_Node000002_Node000006" title=" " alt="" coords="146,104,196,140,198,142,195,146,192,144,143,108"/>
</map>

1
db/d40/integral__approximation2_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.md5
View File

@@ -1 +0,0 @@
99eced2e92c4878ee05448ada282565d

137
db/d40/integral__approximation2_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg
View File

@@ -1,137 +0,0 @@
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<!-- Generated by graphviz version 12.1.2 (20240928.0832)
-->
<!-- Title: main Pages: 1 -->
<svg width="203pt" height="138pt"
viewBox="0.00 0.00 203.00 138.25" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<svg id="main" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" xml:space="preserve">
<style type="text/css"><![CDATA[
.node, .edge {opacity: 0.7;}
.node.selected, .edge.selected {opacity: 1;}
.edge:hover path { stroke: red; }
.edge:hover polygon { stroke: red; fill: red; }
]]></style>
<script type="application/ecmascript" xlink:href="../../svg.min.js"/>
<svg id="graph" class="graph">
<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 134.25)">
<title>main</title>
<!-- Node1 -->
<g id="Node000001" class="node">
<title>Node1</title>
<g id="a_Node000001"><a xlink:title="Main function.">
<polygon fill="#999999" stroke="#666666" points="37,-74.25 0,-74.25 0,-55 37,-55 37,-74.25"/>
<text text-anchor="middle" x="18.5" y="-60.75" font-family="Helvetica,sans-Serif" font-size="10.00">main</text>
</a>
</g>
</g>
<!-- Node2 -->
<g id="Node000002" class="node">
<title>Node2</title>
<g id="a_Node000002"><a xlink:href="../../db/d40/integral__approximation2_8cpp.html#aa8dca7b867074164d5f45b0f3851269d" target="_top" xlink:title="Self&#45;test implementations.">
<polygon fill="white" stroke="#666666" points="105.5,-74.25 73,-74.25 73,-55 105.5,-55 105.5,-74.25"/>
<text text-anchor="middle" x="89.25" y="-60.75" font-family="Helvetica,sans-Serif" font-size="10.00">test</text>
</a>
</g>
</g>
<!-- Node1&#45;&gt;Node2 -->
<g id="edge1_Node000001_Node000002" class="edge">
<title>Node1&#45;&gt;Node2</title>
<g id="a_edge1_Node000001_Node000002"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M37.2,-64.62C44.58,-64.62 53.31,-64.62 61.45,-64.62"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="61.2,-68.13 71.2,-64.63 61.2,-61.13 61.2,-68.13"/>
</a>
</g>
</g>
<!-- Node3 -->
<g id="Node000003" class="node">
<title>Node3</title>
<g id="a_Node000003"><a target="_blank" xlink:href="http://en.cppreference.com/w/cpp/io/manip/endl.html#" xlink:title=" ">
<polygon fill="white" stroke="#666666" points="195,-130.25 141.5,-130.25 141.5,-111 195,-111 195,-130.25"/>
<text text-anchor="middle" x="168.25" y="-116.75" font-family="Helvetica,sans-Serif" font-size="10.00">std::endl</text>
</a>
</g>
</g>
<!-- Node2&#45;&gt;Node3 -->
<g id="edge2_Node000002_Node000003" class="edge">
<title>Node2&#45;&gt;Node3</title>
<g id="a_edge2_Node000002_Node000003"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M103.66,-74.73C113.96,-82.45 128.56,-93.3 141.5,-102.62 142.18,-103.12 142.87,-103.61 143.57,-104.11"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="141.34,-106.82 151.53,-109.73 145.38,-101.1 141.34,-106.82"/>
</a>
</g>
</g>
<!-- Node4 -->
<g id="Node000004" class="node">
<title>Node4</title>
<g id="a_Node000004"><a target="_blank" xlink:href="http://en.cppreference.com/w/cpp/numeric/math/exp.html#" xlink:title=" ">
<polygon fill="white" stroke="#666666" points="193.88,-93.25 142.62,-93.25 142.62,-74 193.88,-74 193.88,-93.25"/>
<text text-anchor="middle" x="168.25" y="-79.75" font-family="Helvetica,sans-Serif" font-size="10.00">std::exp</text>
</a>
</g>
</g>
<!-- Node2&#45;&gt;Node4 -->
<g id="edge3_Node000002_Node000004" class="edge">
<title>Node2&#45;&gt;Node4</title>
<g id="a_edge3_Node000002_Node000004"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M105.83,-68.47C113.19,-70.28 122.29,-72.53 131.22,-74.74"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="130.28,-78.11 140.82,-77.1 131.95,-71.31 130.28,-78.11"/>
</a>
</g>
</g>
<!-- Node5 -->
<g id="Node000005" class="node">
<title>Node5</title>
<g id="a_Node000005"><a target="_blank" xlink:href="http://en.cppreference.com/w/cpp/numeric/math/sin.html#" xlink:title=" ">
<polygon fill="white" stroke="#666666" points="192.38,-56.25 144.12,-56.25 144.12,-37 192.38,-37 192.38,-56.25"/>
<text text-anchor="middle" x="168.25" y="-42.75" font-family="Helvetica,sans-Serif" font-size="10.00">std::sin</text>
</a>
</g>
</g>
<!-- Node2&#45;&gt;Node5 -->
<g id="edge4_Node000002_Node000005" class="edge">
<title>Node2&#45;&gt;Node5</title>
<g id="a_edge4_Node000002_Node000005"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M105.83,-60.98C113.58,-59.17 123.28,-56.9 132.66,-54.71"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="133.38,-58.14 142.32,-52.45 131.79,-51.32 133.38,-58.14"/>
</a>
</g>
</g>
<!-- Node6 -->
<g id="Node000006" class="node">
<title>Node6</title>
<g id="a_Node000006"><a target="_blank" xlink:href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html#" xlink:title=" ">
<polygon fill="white" stroke="#666666" points="194.25,-19.25 142.25,-19.25 142.25,0 194.25,0 194.25,-19.25"/>
<text text-anchor="middle" x="168.25" y="-5.75" font-family="Helvetica,sans-Serif" font-size="10.00">std::sqrt</text>
</a>
</g>
</g>
<!-- Node2&#45;&gt;Node6 -->
<g id="edge5_Node000002_Node000006" class="edge">
<title>Node2&#45;&gt;Node6</title>
<g id="a_edge5_Node000002_Node000006"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M104.13,-54.52C114.42,-47.05 128.8,-36.65 141.5,-27.62 142.18,-27.14 142.88,-26.65 143.58,-26.15"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="145.38,-29.16 151.55,-20.55 141.35,-23.44 145.38,-29.16"/>
</a>
</g>
</g>
</g>
</svg>
</svg>
<style type='text/css'>
<![CDATA[
[data-mouse-over-selected='false'] { opacity: 0.7; }
[data-mouse-over-selected='true'] { opacity: 1.0; }
]]>
</style>
<script type="application/ecmascript"><![CDATA[
document.addEventListener('DOMContentLoaded', (event) => {
highlightEdges();
highlightAdjacentNodes();
});
]]></script>
</svg>
Side by Side

Before

Width:  |  Height:  |  Size: 5.8 KiB

111
db/d40/integral__approximation2_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph_org.svg
View File

@@ -1,111 +0,0 @@
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<!-- Generated by graphviz version 12.1.2 (20240928.0832)
-->
<!-- Title: main Pages: 1 -->
<svg width="203pt" height="138pt"
viewBox="0.00 0.00 203.00 138.25" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 134.25)">
<title>main</title>
<!-- Node1 -->
<g id="Node000001" class="node">
<title>Node1</title>
<g id="a_Node000001"><a xlink:title="Main function.">
<polygon fill="#999999" stroke="#666666" points="37,-74.25 0,-74.25 0,-55 37,-55 37,-74.25"/>
<text text-anchor="middle" x="18.5" y="-60.75" font-family="Helvetica,sans-Serif" font-size="10.00">main</text>
</a>
</g>
</g>
<!-- Node2 -->
<g id="Node000002" class="node">
<title>Node2</title>
<g id="a_Node000002"><a xlink:href="../../db/d40/integral__approximation2_8cpp.html#aa8dca7b867074164d5f45b0f3851269d" target="_top" xlink:title="Self&#45;test implementations.">
<polygon fill="white" stroke="#666666" points="105.5,-74.25 73,-74.25 73,-55 105.5,-55 105.5,-74.25"/>
<text text-anchor="middle" x="89.25" y="-60.75" font-family="Helvetica,sans-Serif" font-size="10.00">test</text>
</a>
</g>
</g>
<!-- Node1&#45;&gt;Node2 -->
<g id="edge1_Node000001_Node000002" class="edge">
<title>Node1&#45;&gt;Node2</title>
<g id="a_edge1_Node000001_Node000002"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M37.2,-64.62C44.58,-64.62 53.31,-64.62 61.45,-64.62"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="61.2,-68.13 71.2,-64.63 61.2,-61.13 61.2,-68.13"/>
</a>
</g>
</g>
<!-- Node3 -->
<g id="Node000003" class="node">
<title>Node3</title>
<g id="a_Node000003"><a target="_blank" xlink:href="http://en.cppreference.com/w/cpp/io/manip/endl.html#" xlink:title=" ">
<polygon fill="white" stroke="#666666" points="195,-130.25 141.5,-130.25 141.5,-111 195,-111 195,-130.25"/>
<text text-anchor="middle" x="168.25" y="-116.75" font-family="Helvetica,sans-Serif" font-size="10.00">std::endl</text>
</a>
</g>
</g>
<!-- Node2&#45;&gt;Node3 -->
<g id="edge2_Node000002_Node000003" class="edge">
<title>Node2&#45;&gt;Node3</title>
<g id="a_edge2_Node000002_Node000003"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M103.66,-74.73C113.96,-82.45 128.56,-93.3 141.5,-102.62 142.18,-103.12 142.87,-103.61 143.57,-104.11"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="141.34,-106.82 151.53,-109.73 145.38,-101.1 141.34,-106.82"/>
</a>
</g>
</g>
<!-- Node4 -->
<g id="Node000004" class="node">
<title>Node4</title>
<g id="a_Node000004"><a target="_blank" xlink:href="http://en.cppreference.com/w/cpp/numeric/math/exp.html#" xlink:title=" ">
<polygon fill="white" stroke="#666666" points="193.88,-93.25 142.62,-93.25 142.62,-74 193.88,-74 193.88,-93.25"/>
<text text-anchor="middle" x="168.25" y="-79.75" font-family="Helvetica,sans-Serif" font-size="10.00">std::exp</text>
</a>
</g>
</g>
<!-- Node2&#45;&gt;Node4 -->
<g id="edge3_Node000002_Node000004" class="edge">
<title>Node2&#45;&gt;Node4</title>
<g id="a_edge3_Node000002_Node000004"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M105.83,-68.47C113.19,-70.28 122.29,-72.53 131.22,-74.74"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="130.28,-78.11 140.82,-77.1 131.95,-71.31 130.28,-78.11"/>
</a>
</g>
</g>
<!-- Node5 -->
<g id="Node000005" class="node">
<title>Node5</title>
<g id="a_Node000005"><a target="_blank" xlink:href="http://en.cppreference.com/w/cpp/numeric/math/sin.html#" xlink:title=" ">
<polygon fill="white" stroke="#666666" points="192.38,-56.25 144.12,-56.25 144.12,-37 192.38,-37 192.38,-56.25"/>
<text text-anchor="middle" x="168.25" y="-42.75" font-family="Helvetica,sans-Serif" font-size="10.00">std::sin</text>
</a>
</g>
</g>
<!-- Node2&#45;&gt;Node5 -->
<g id="edge4_Node000002_Node000005" class="edge">
<title>Node2&#45;&gt;Node5</title>
<g id="a_edge4_Node000002_Node000005"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M105.83,-60.98C113.58,-59.17 123.28,-56.9 132.66,-54.71"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="133.38,-58.14 142.32,-52.45 131.79,-51.32 133.38,-58.14"/>
</a>
</g>
</g>
<!-- Node6 -->
<g id="Node000006" class="node">
<title>Node6</title>
<g id="a_Node000006"><a target="_blank" xlink:href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html#" xlink:title=" ">
<polygon fill="white" stroke="#666666" points="194.25,-19.25 142.25,-19.25 142.25,0 194.25,0 194.25,-19.25"/>
<text text-anchor="middle" x="168.25" y="-5.75" font-family="Helvetica,sans-Serif" font-size="10.00">std::sqrt</text>
</a>
</g>
</g>
<!-- Node2&#45;&gt;Node6 -->
<g id="edge5_Node000002_Node000006" class="edge">
<title>Node2&#45;&gt;Node6</title>
<g id="a_edge5_Node000002_Node000006"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M104.13,-54.52C114.42,-47.05 128.8,-36.65 141.5,-27.62 142.18,-27.14 142.88,-26.65 143.58,-26.15"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="145.38,-29.16 151.55,-20.55 141.35,-23.44 145.38,-29.16"/>
</a>
</g>
</g>
</g>
</svg>
Side by Side

Before

Width:  |  Height:  |  Size: 5.0 KiB

15
db/d40/integral__approximation2_8cpp_af7da9ba8932f1f48b9bbc2d80471af51_cgraph.map
View File

@@ -1,15 +0,0 @@
<map id="math::monte_carlo::integral_monte_carlo" name="math::monte_carlo::integral_monte_carlo">
<area shape="rect" id="Node000001" title="Compute an approximation of an integral using Monte Carlo integration." alt="" coords="5,76,147,117"/>
<area shape="poly" id="edge6_Node000001_Node000001" title=" " alt="" coords="40,76,38,67,44,58,57,52,76,50,96,52,109,59,106,63,95,57,76,55,58,57,48,62,44,68,45,75"/>
<area shape="rect" id="Node000002" href="$db/d40/integral__approximation2_8cpp.html#a71249ee535f16f8ed2e9cc8f0199a2cf" title="short&#45;hand for std::functions used in this implementation" alt="" coords="195,47,332,88"/>
<area shape="poly" id="edge1_Node000001_Node000002" title=" " alt="" coords="147,83,179,78,180,83,148,88"/>
<area shape="rect" id="Node000006" href="/Users/runner/work/C-Plus-Plus/C-Plus-Plus/doc/cppreference-doxygen-web.tag.xml$cpp/container/vector/size.html#" title=" " alt="" coords="206,112,321,138"/>
<area shape="poly" id="edge7_Node000001_Node000006" title=" " alt="" coords="148,105,191,111,190,117,147,110"/>
<area shape="poly" id="edge2_Node000002_Node000002" title=" " alt="" coords="228,47,226,37,232,28,244,23,263,21,284,23,296,29,294,34,282,28,263,26,246,28,235,32,231,38,233,46"/>
<area shape="rect" id="Node000003" href="/Users/runner/work/C-Plus-Plus/C-Plus-Plus/doc/cppreference-doxygen-web.tag.xml$cpp/algorithm/min.html#" title=" " alt="" coords="423,5,491,31"/>
<area shape="poly" id="edge3_Node000002_Node000003" title=" " alt="" coords="332,47,408,28,409,33,333,53"/>
<area shape="rect" id="Node000004" href="/Users/runner/work/C-Plus-Plus/C-Plus-Plus/doc/cppreference-doxygen-web.tag.xml$cpp/container/vector/push_back.html#" title=" " alt="" coords="380,55,534,80"/>
<area shape="poly" id="edge4_Node000002_Node000004" title=" " alt="" coords="333,65,365,65,365,70,333,70"/>
<area shape="rect" id="Node000005" href="/Users/runner/work/C-Plus-Plus/C-Plus-Plus/doc/cppreference-doxygen-web.tag.xml$cpp/container/vector/reserve.html#" title=" " alt="" coords="390,104,524,130"/>
<area shape="poly" id="edge5_Node000002_Node000005" title=" " alt="" coords="333,82,390,97,389,102,332,88"/>
</map>

1
db/d40/integral__approximation2_8cpp_af7da9ba8932f1f48b9bbc2d80471af51_cgraph.md5
View File

@@ -1 +0,0 @@
0483166e6298ee719c0e4bfa270c14d8

157
db/d40/integral__approximation2_8cpp_af7da9ba8932f1f48b9bbc2d80471af51_cgraph.svg
View File

@@ -1,157 +0,0 @@
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<!-- Generated by graphviz version 12.1.2 (20240928.0832)
-->
<!-- Title: math::monte_carlo::integral_monte_carlo Pages: 1 -->
<svg width="405pt" height="107pt"
viewBox="0.00 0.00 404.75 107.25" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<svg id="main" version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" xml:space="preserve">
<style type="text/css"><![CDATA[
.node, .edge {opacity: 0.7;}
.node.selected, .edge.selected {opacity: 1;}
.edge:hover path { stroke: red; }
.edge:hover polygon { stroke: red; fill: red; }
]]></style>
<script type="application/ecmascript" xlink:href="../../svg.min.js"/>
<svg id="graph" class="graph">
<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 103.25)">
<title>math::monte_carlo::integral_monte_carlo</title>
<!-- Node1 -->
<g id="Node000001" class="node">
<title>Node1</title>
<g id="a_Node000001"><a xlink:title="Compute an approximation of an integral using Monte Carlo integration.">
<polygon fill="#999999" stroke="#666666" points="106,-45.88 0,-45.88 0,-15.37 106,-15.37 106,-45.88"/>
<text text-anchor="start" x="8" y="-32.38" font-family="Helvetica,sans-Serif" font-size="10.00">math::monte_carlo::</text>
<text text-anchor="middle" x="53" y="-21.12" font-family="Helvetica,sans-Serif" font-size="10.00">integral_monte_carlo</text>
</a>
</g>
</g>
<!-- Node1&#45;&gt;Node1 -->
<g id="edge6_Node000001_Node000001" class="edge">
<title>Node1&#45;&gt;Node1</title>
<g id="a_edge6_Node000001_Node000001"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M28.1,-46.36C23.02,-55.43 31.32,-63.88 53,-63.88 64.86,-63.88 72.71,-61.35 76.56,-57.58"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="80.01,-58.21 77.72,-47.86 73.06,-57.38 80.01,-58.21"/>
</a>
</g>
</g>
<!-- Node2 -->
<g id="Node000002" class="node">
<title>Node2</title>
<g id="a_Node000002"><a xlink:href="../../db/d40/integral__approximation2_8cpp.html#a71249ee535f16f8ed2e9cc8f0199a2cf" target="_top" xlink:title="short&#45;hand for std::functions used in this implementation">
<polygon fill="white" stroke="#666666" points="245,-67.88 142,-67.88 142,-37.38 245,-37.38 245,-67.88"/>
<text text-anchor="start" x="150" y="-54.38" font-family="Helvetica,sans-Serif" font-size="10.00">math::monte_carlo::</text>
<text text-anchor="middle" x="193.5" y="-43.12" font-family="Helvetica,sans-Serif" font-size="10.00">generate_samples</text>
</a>
</g>
</g>
<!-- Node1&#45;&gt;Node2 -->
<g id="edge1_Node000001_Node000002" class="edge">
<title>Node1&#45;&gt;Node2</title>
<g id="a_edge1_Node000001_Node000002"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M106.36,-38.94C114.27,-40.2 122.5,-41.51 130.59,-42.79"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="129.98,-46.24 140.4,-44.35 131.08,-39.32 129.98,-46.24"/>
</a>
</g>
</g>
<!-- Node6 -->
<g id="Node000006" class="node">
<title>Node6</title>
<g id="a_Node000006"><a target="_blank" xlink:href="http://en.cppreference.com/w/cpp/container/vector/size.html#" xlink:title=" ">
<polygon fill="white" stroke="#666666" points="236.75,-19.25 150.25,-19.25 150.25,0 236.75,0 236.75,-19.25"/>
<text text-anchor="middle" x="193.5" y="-5.75" font-family="Helvetica,sans-Serif" font-size="10.00">std::vector::size</text>
</a>
</g>
</g>
<!-- Node1&#45;&gt;Node6 -->
<g id="edge7_Node000001_Node000006" class="edge">
<title>Node1&#45;&gt;Node6</title>
<g id="a_edge7_Node000001_Node000006"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M106.36,-22.69C116.94,-21.08 128.07,-19.39 138.7,-17.78"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="139.12,-21.26 148.48,-16.3 138.07,-14.34 139.12,-21.26"/>
</a>
</g>
</g>
<!-- Node2&#45;&gt;Node2 -->
<g id="edge2_Node000002_Node000002" class="edge">
<title>Node2&#45;&gt;Node2</title>
<g id="a_edge2_Node000002_Node000002"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M168.6,-68.36C163.52,-77.43 171.82,-85.88 193.5,-85.88 205.36,-85.88 213.21,-83.35 217.06,-79.58"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="220.51,-80.21 218.22,-69.86 213.56,-79.38 220.51,-80.21"/>
</a>
</g>
</g>
<!-- Node3 -->
<g id="Node000003" class="node">
<title>Node3</title>
<g id="a_Node000003"><a target="_blank" xlink:href="http://en.cppreference.com/w/cpp/algorithm/min.html#" xlink:title=" ">
<polygon fill="white" stroke="#666666" points="364.5,-99.25 313.25,-99.25 313.25,-80 364.5,-80 364.5,-99.25"/>
<text text-anchor="middle" x="338.88" y="-85.75" font-family="Helvetica,sans-Serif" font-size="10.00">std::min</text>
</a>
</g>
</g>
<!-- Node2&#45;&gt;Node3 -->
<g id="edge3_Node000002_Node000003" class="edge">
<title>Node2&#45;&gt;Node3</title>
<g id="a_edge3_Node000002_Node000003"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M245.45,-65.77C264.2,-70.61 285.03,-75.99 302.15,-80.41"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="300.79,-83.67 311.35,-82.78 302.54,-76.89 300.79,-83.67"/>
</a>
</g>
</g>
<!-- Node4 -->
<g id="Node000004" class="node">
<title>Node4</title>
<g id="a_Node000004"><a target="_blank" xlink:href="http://en.cppreference.com/w/cpp/container/vector/push_back.html#" xlink:title=" ">
<polygon fill="white" stroke="#666666" points="396.75,-62.25 281,-62.25 281,-43 396.75,-43 396.75,-62.25"/>
<text text-anchor="middle" x="338.88" y="-48.75" font-family="Helvetica,sans-Serif" font-size="10.00">std::vector::push_back</text>
</a>
</g>
</g>
<!-- Node2&#45;&gt;Node4 -->
<g id="edge4_Node000002_Node000004" class="edge">
<title>Node2&#45;&gt;Node4</title>
<g id="a_edge4_Node000002_Node000004"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M245.45,-52.62C253.22,-52.62 261.34,-52.62 269.41,-52.62"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="269.23,-56.13 279.23,-52.63 269.23,-49.13 269.23,-56.13"/>
</a>
</g>
</g>
<!-- Node5 -->
<g id="Node000005" class="node">
<title>Node5</title>
<g id="a_Node000005"><a target="_blank" xlink:href="http://en.cppreference.com/w/cpp/container/vector/reserve.html#" xlink:title=" ">
<polygon fill="white" stroke="#666666" points="389.25,-25.25 288.5,-25.25 288.5,-6 389.25,-6 389.25,-25.25"/>
<text text-anchor="middle" x="338.88" y="-11.75" font-family="Helvetica,sans-Serif" font-size="10.00">std::vector::reserve</text>
</a>
</g>
</g>
<!-- Node2&#45;&gt;Node5 -->
<g id="edge5_Node000002_Node000005" class="edge">
<title>Node2&#45;&gt;Node5</title>
<g id="a_edge5_Node000002_Node000005"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M245.45,-39.48C259.3,-35.9 274.27,-32.04 288.05,-28.48"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="288.53,-31.97 297.34,-26.09 286.78,-25.2 288.53,-31.97"/>
</a>
</g>
</g>
</g>
</svg>
</svg>
<style type='text/css'>
<![CDATA[
[data-mouse-over-selected='false'] { opacity: 0.7; }
[data-mouse-over-selected='true'] { opacity: 1.0; }
]]>
</style>
<script type="application/ecmascript"><![CDATA[
document.addEventListener('DOMContentLoaded', (event) => {
highlightEdges();
highlightAdjacentNodes();
});
]]></script>
</svg>
Side by Side

Before

Width:  |  Height:  |  Size: 7.0 KiB

131
db/d40/integral__approximation2_8cpp_af7da9ba8932f1f48b9bbc2d80471af51_cgraph_org.svg
View File

@@ -1,131 +0,0 @@
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<!-- Generated by graphviz version 12.1.2 (20240928.0832)
-->
<!-- Title: math::monte_carlo::integral_monte_carlo Pages: 1 -->
<svg width="405pt" height="107pt"
viewBox="0.00 0.00 404.75 107.25" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 103.25)">
<title>math::monte_carlo::integral_monte_carlo</title>
<!-- Node1 -->
<g id="Node000001" class="node">
<title>Node1</title>
<g id="a_Node000001"><a xlink:title="Compute an approximation of an integral using Monte Carlo integration.">
<polygon fill="#999999" stroke="#666666" points="106,-45.88 0,-45.88 0,-15.37 106,-15.37 106,-45.88"/>
<text text-anchor="start" x="8" y="-32.38" font-family="Helvetica,sans-Serif" font-size="10.00">math::monte_carlo::</text>
<text text-anchor="middle" x="53" y="-21.12" font-family="Helvetica,sans-Serif" font-size="10.00">integral_monte_carlo</text>
</a>
</g>
</g>
<!-- Node1&#45;&gt;Node1 -->
<g id="edge6_Node000001_Node000001" class="edge">
<title>Node1&#45;&gt;Node1</title>
<g id="a_edge6_Node000001_Node000001"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M28.1,-46.36C23.02,-55.43 31.32,-63.88 53,-63.88 64.86,-63.88 72.71,-61.35 76.56,-57.58"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="80.01,-58.21 77.72,-47.86 73.06,-57.38 80.01,-58.21"/>
</a>
</g>
</g>
<!-- Node2 -->
<g id="Node000002" class="node">
<title>Node2</title>
<g id="a_Node000002"><a xlink:href="../../db/d40/integral__approximation2_8cpp.html#a71249ee535f16f8ed2e9cc8f0199a2cf" target="_top" xlink:title="short&#45;hand for std::functions used in this implementation">
<polygon fill="white" stroke="#666666" points="245,-67.88 142,-67.88 142,-37.38 245,-37.38 245,-67.88"/>
<text text-anchor="start" x="150" y="-54.38" font-family="Helvetica,sans-Serif" font-size="10.00">math::monte_carlo::</text>
<text text-anchor="middle" x="193.5" y="-43.12" font-family="Helvetica,sans-Serif" font-size="10.00">generate_samples</text>
</a>
</g>
</g>
<!-- Node1&#45;&gt;Node2 -->
<g id="edge1_Node000001_Node000002" class="edge">
<title>Node1&#45;&gt;Node2</title>
<g id="a_edge1_Node000001_Node000002"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M106.36,-38.94C114.27,-40.2 122.5,-41.51 130.59,-42.79"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="129.98,-46.24 140.4,-44.35 131.08,-39.32 129.98,-46.24"/>
</a>
</g>
</g>
<!-- Node6 -->
<g id="Node000006" class="node">
<title>Node6</title>
<g id="a_Node000006"><a target="_blank" xlink:href="http://en.cppreference.com/w/cpp/container/vector/size.html#" xlink:title=" ">
<polygon fill="white" stroke="#666666" points="236.75,-19.25 150.25,-19.25 150.25,0 236.75,0 236.75,-19.25"/>
<text text-anchor="middle" x="193.5" y="-5.75" font-family="Helvetica,sans-Serif" font-size="10.00">std::vector::size</text>
</a>
</g>
</g>
<!-- Node1&#45;&gt;Node6 -->
<g id="edge7_Node000001_Node000006" class="edge">
<title>Node1&#45;&gt;Node6</title>
<g id="a_edge7_Node000001_Node000006"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M106.36,-22.69C116.94,-21.08 128.07,-19.39 138.7,-17.78"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="139.12,-21.26 148.48,-16.3 138.07,-14.34 139.12,-21.26"/>
</a>
</g>
</g>
<!-- Node2&#45;&gt;Node2 -->
<g id="edge2_Node000002_Node000002" class="edge">
<title>Node2&#45;&gt;Node2</title>
<g id="a_edge2_Node000002_Node000002"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M168.6,-68.36C163.52,-77.43 171.82,-85.88 193.5,-85.88 205.36,-85.88 213.21,-83.35 217.06,-79.58"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="220.51,-80.21 218.22,-69.86 213.56,-79.38 220.51,-80.21"/>
</a>
</g>
</g>
<!-- Node3 -->
<g id="Node000003" class="node">
<title>Node3</title>
<g id="a_Node000003"><a target="_blank" xlink:href="http://en.cppreference.com/w/cpp/algorithm/min.html#" xlink:title=" ">
<polygon fill="white" stroke="#666666" points="364.5,-99.25 313.25,-99.25 313.25,-80 364.5,-80 364.5,-99.25"/>
<text text-anchor="middle" x="338.88" y="-85.75" font-family="Helvetica,sans-Serif" font-size="10.00">std::min</text>
</a>
</g>
</g>
<!-- Node2&#45;&gt;Node3 -->
<g id="edge3_Node000002_Node000003" class="edge">
<title>Node2&#45;&gt;Node3</title>
<g id="a_edge3_Node000002_Node000003"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M245.45,-65.77C264.2,-70.61 285.03,-75.99 302.15,-80.41"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="300.79,-83.67 311.35,-82.78 302.54,-76.89 300.79,-83.67"/>
</a>
</g>
</g>
<!-- Node4 -->
<g id="Node000004" class="node">
<title>Node4</title>
<g id="a_Node000004"><a target="_blank" xlink:href="http://en.cppreference.com/w/cpp/container/vector/push_back.html#" xlink:title=" ">
<polygon fill="white" stroke="#666666" points="396.75,-62.25 281,-62.25 281,-43 396.75,-43 396.75,-62.25"/>
<text text-anchor="middle" x="338.88" y="-48.75" font-family="Helvetica,sans-Serif" font-size="10.00">std::vector::push_back</text>
</a>
</g>
</g>
<!-- Node2&#45;&gt;Node4 -->
<g id="edge4_Node000002_Node000004" class="edge">
<title>Node2&#45;&gt;Node4</title>
<g id="a_edge4_Node000002_Node000004"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M245.45,-52.62C253.22,-52.62 261.34,-52.62 269.41,-52.62"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="269.23,-56.13 279.23,-52.63 269.23,-49.13 269.23,-56.13"/>
</a>
</g>
</g>
<!-- Node5 -->
<g id="Node000005" class="node">
<title>Node5</title>
<g id="a_Node000005"><a target="_blank" xlink:href="http://en.cppreference.com/w/cpp/container/vector/reserve.html#" xlink:title=" ">
<polygon fill="white" stroke="#666666" points="389.25,-25.25 288.5,-25.25 288.5,-6 389.25,-6 389.25,-25.25"/>
<text text-anchor="middle" x="338.88" y="-11.75" font-family="Helvetica,sans-Serif" font-size="10.00">std::vector::reserve</text>
</a>
</g>
</g>
<!-- Node2&#45;&gt;Node5 -->
<g id="edge5_Node000002_Node000005" class="edge">
<title>Node2&#45;&gt;Node5</title>
<g id="a_edge5_Node000002_Node000005"><a xlink:title=" ">
<path fill="none" stroke="#63b8ff" d="M245.45,-39.48C259.3,-35.9 274.27,-32.04 288.05,-28.48"/>
<polygon fill="#63b8ff" stroke="#63b8ff" points="288.53,-31.97 297.34,-26.09 286.78,-25.2 288.53,-31.97"/>
</a>
</g>
</g>
</g>
</svg>
Side by Side

Before

Width:  |  Height:  |  Size: 6.2 KiB

300
db/d40/integral__approximation2_8cpp_source.html Normal file
View File

@@ -0,0 +1,300 @@
<!-- HTML header for doxygen 1.12.0-->
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en-US">
<head>
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
<meta http-equiv="X-UA-Compatible" content="IE=11"/>
<meta name="generator" content="Doxygen 1.12.0"/>
<meta name="viewport" content="width=device-width, initial-scale=1"/>
<title>TheAlgorithms/C++: math/integral_approximation2.cpp Source File</title>
<link rel="icon" href="../../favicon.svg" type="image/x-icon" />
<link href="../../tabs.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="../../jquery.js"></script>
<script type="text/javascript" src="../../dynsections.js"></script>
<script type="text/javascript" src="https://cdn.jsdelivr.net/npm/@xpack-3rd-party/doxygen-awesome-css@2.2.0-1/doxygen-awesome-darkmode-toggle.js"></script>
<script type="text/javascript">
DoxygenAwesomeDarkModeToggle.init()
</script>
<script type="text/javascript" src="../../clipboard.js"></script>
<link href="../../navtree.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="../../navtreedata.js"></script>
<script type="text/javascript" src="../../navtree.js"></script>
<script type="text/javascript" src="../../resize.js"></script>
<script type="text/javascript" src="../../cookie.js"></script>
<link href="../../search/search.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="../../search/searchdata.js"></script>
<script type="text/javascript" src="../../search/search.js"></script>
<script type="text/javascript">
window.MathJax = {
options: {
ignoreHtmlClass: 'tex2jax_ignore',
processHtmlClass: 'tex2jax_process'
},
loader: {
load: ['[tex]/ams']
},
tex: {
macros: {},
packages: ['base','configmacros','ams']
}
};
</script>
<script type="text/javascript" id="MathJax-script" async="async" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-chtml.js"></script>
<link href="../../doxygen.css" rel="stylesheet" type="text/css" />
<link href="../../doxygen-awesome.css" rel="stylesheet" type="text/css"/>
</head>
<body>
<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
<div id="titlearea">
<table cellspacing="0" cellpadding="0">
<tbody>
<tr id="projectrow">
<td id="projectlogo"><img alt="Logo" src="../../project_logo.png"/></td>
<td id="projectalign">
<div id="projectname">TheAlgorithms/C++<span id="projectnumber">&#160;1.0.0</span>
</div>
<div id="projectbrief">All the algorithms implemented in C++</div>
</td>
</tr>
</tbody>
</table>
</div>
<!-- end header part -->
<!-- Generated by Doxygen 1.12.0 -->
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&amp;dn=expat.txt MIT */
var searchBox = new SearchBox("searchBox", "../../search/",'.html');
/* @license-end */
</script>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&amp;dn=expat.txt MIT */
$(function() { codefold.init(1); });
/* @license-end */
</script>
<script type="text/javascript" src="../../menudata.js"></script>
<script type="text/javascript" src="../../menu.js"></script>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&amp;dn=expat.txt MIT */
$(function() {
initMenu('../../',true,false,'search.php','Search',true);
$(function() { init_search(); });
});
/* @license-end */
</script>
<div id="main-nav"></div>
</div><!-- top -->
<div id="side-nav" class="ui-resizable side-nav-resizable">
<div id="nav-tree">
<div id="nav-tree-contents">
<div id="nav-sync" class="sync"></div>
</div>
</div>
<div id="splitbar" style="-moz-user-select:none;"
class="ui-resizable-handle">
</div>
</div>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&amp;dn=expat.txt MIT */
$(function(){initNavTree('db/d40/integral__approximation2_8cpp_source.html','../../'); initResizable(true); });
/* @license-end */
</script>
<div id="doc-content">
<!-- window showing the filter options -->
<div id="MSearchSelectWindow"
onmouseover="return searchBox.OnSearchSelectShow()"
onmouseout="return searchBox.OnSearchSelectHide()"
onkeydown="return searchBox.OnSearchSelectKey(event)">
</div>
<!-- iframe showing the search results (closed by default) -->
<div id="MSearchResultsWindow">
<div id="MSearchResults">
<div class="SRPage">
<div id="SRIndex">
<div id="SRResults"></div>
<div class="SRStatus" id="Loading">Loading...</div>
<div class="SRStatus" id="Searching">Searching...</div>
<div class="SRStatus" id="NoMatches">No Matches</div>
</div>
</div>
</div>
</div>
<div class="header">
<div class="headertitle"><div class="title">integral_approximation2.cpp</div></div>
</div><!--header-->
<div class="contents">
<a href="../../db/d40/integral__approximation2_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span> </div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="preprocessor">#define _USE_MATH_DEFINES </span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="preprocessor">#include &lt;cmath&gt;</span> </div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="preprocessor">#include &lt;cstdint&gt;</span> </div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="preprocessor">#include &lt;ctime&gt;</span> </div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="preprocessor">#include &lt;functional&gt;</span> </div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="preprocessor">#include &lt;iostream&gt;</span> </div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="preprocessor">#include &lt;random&gt;</span> </div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span><span class="preprocessor">#include &lt;vector&gt;</span> </div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> </div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../dd/d47/namespacemath.html">math</a> {</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../d0/da4/namespacemonte__carlo.html">monte_carlo</a> {</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> </div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span><span class="keyword">using </span>Function = std::function&lt;double(</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <span class="keywordtype">double</span>&amp;)&gt;; </div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> </div>
<div class="foldopen" id="foldopen00064" data-start="{" data-end="}">
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"><a class="line" href="../../db/d40/integral__approximation2_8cpp.html#a71249ee535f16f8ed2e9cc8f0199a2cf"> 64</a></span>std::vector&lt;double&gt; <a class="code hl_function" href="../../db/d40/integral__approximation2_8cpp.html#a71249ee535f16f8ed2e9cc8f0199a2cf">generate_samples</a>(<span class="keyword">const</span> <span class="keywordtype">double</span>&amp; start_point,</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="keyword">const</span> Function&amp; pdf,</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="keyword">const</span> uint32_t&amp; num_samples,</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="keyword">const</span> uint32_t&amp; discard = 100000) {</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> std::vector&lt;double&gt; samples;</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> samples.reserve(num_samples);</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> </div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="keywordtype">double</span> x_t = start_point;</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> </div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> std::default_random_engine generator;</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> std::uniform_real_distribution&lt;double&gt; uniform(0.0, 1.0);</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> std::normal_distribution&lt;double&gt; normal(0.0, 1.0);</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> generator.seed(time(<span class="keyword">nullptr</span>));</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> </div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="keywordflow">for</span> (uint32_t t = 0; t &lt; num_samples + discard; ++t) {</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="comment">// Generate a new proposal according to some mutation strategy.</span></div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="comment">// This is arbitrary and can be swapped.</span></div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="keywordtype">double</span> x_dash = normal(generator) + x_t;</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="keywordtype">double</span> acceptance_probability = std::min(pdf(x_dash) / pdf(x_t), 1.0);</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="keywordtype">double</span> u = uniform(generator);</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> </div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> <span class="comment">// Accept &quot;new state&quot; according to the acceptance_probability</span></div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="keywordflow">if</span> (u &lt;= acceptance_probability) {</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> x_t = x_dash;</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> }</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> </div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <span class="keywordflow">if</span> (t &gt;= discard) {</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> samples.push_back(x_t);</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> }</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> }</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> </div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <span class="keywordflow">return</span> samples;</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span>}</div>
</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> </div>
<div class="foldopen" id="foldopen00112" data-start="{" data-end="}">
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"><a class="line" href="../../db/d40/integral__approximation2_8cpp.html#af7da9ba8932f1f48b9bbc2d80471af51"> 112</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="../../db/d40/integral__approximation2_8cpp.html#af7da9ba8932f1f48b9bbc2d80471af51">integral_monte_carlo</a>(<span class="keyword">const</span> <span class="keywordtype">double</span>&amp; start_point, <span class="keyword">const</span> Function&amp; function,</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> <span class="keyword">const</span> Function&amp; pdf,</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> <span class="keyword">const</span> uint32_t&amp; num_samples = 1000000) {</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <span class="keywordtype">double</span> integral = 0.0;</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> std::vector&lt;double&gt; samples =</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <a class="code hl_function" href="../../db/d40/integral__approximation2_8cpp.html#a71249ee535f16f8ed2e9cc8f0199a2cf">generate_samples</a>(start_point, pdf, num_samples);</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> </div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> <span class="keywordflow">for</span> (<span class="keywordtype">double</span> sample : samples) {</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> integral += function(sample) / pdf(sample);</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> }</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> </div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> <span class="keywordflow">return</span> integral / <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(samples.size());</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span>}</div>
</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> </div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span>} <span class="comment">// namespace monte_carlo</span></div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span>} <span class="comment">// namespace math</span></div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> </div>
<div class="foldopen" id="foldopen00133" data-start="{" data-end="}">
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"><a class="line" href="../../db/d40/integral__approximation2_8cpp.html#aa8dca7b867074164d5f45b0f3851269d"> 133</a></span><span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code hl_function" href="../../db/d40/integral__approximation2_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>() {</div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Disclaimer: Because this is a randomized algorithm,&quot;</span></div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> &lt;&lt; std::endl;</div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> std::cout</div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> &lt;&lt; <span class="stringliteral">&quot;it may happen that singular samples deviate from the true result.&quot;</span></div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> &lt;&lt; std::endl</div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> &lt;&lt; std::endl;</div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> ;</div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> </div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> math::monte_carlo::Function f;</div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> math::monte_carlo::Function pdf;</div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> <span class="keywordtype">double</span> integral = 0;</div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> <span class="keywordtype">double</span> lower_bound = 0, upper_bound = 0;</div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> </div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> <span class="comment">/* \int_{-2}^{2} -x^2 + 4 dx */</span></div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> f = [&amp;](<span class="keywordtype">double</span>&amp; x) { <span class="keywordflow">return</span> -x * x + 4.0; };</div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> </div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> lower_bound = -2.0;</div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> upper_bound = 2.0;</div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> pdf = [&amp;](<span class="keywordtype">double</span>&amp; x) {</div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> <span class="keywordflow">if</span> (x &gt;= lower_bound &amp;&amp; x &lt;= -1.0) {</div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> <span class="keywordflow">return</span> 0.1;</div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> }</div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> <span class="keywordflow">if</span> (x &lt;= upper_bound &amp;&amp; x &gt;= 1.0) {</div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> <span class="keywordflow">return</span> 0.1;</div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> }</div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> <span class="keywordflow">if</span> (x &gt; -1.0 &amp;&amp; x &lt; 1.0) {</div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> <span class="keywordflow">return</span> 0.4;</div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> }</div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> <span class="keywordflow">return</span> 0.0;</div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> };</div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> </div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> integral = math::monte_carlo::integral_monte_carlo(</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> (upper_bound - lower_bound) / 2.0, f, pdf);</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> </div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> std::cout &lt;&lt; <span class="stringliteral">&quot;This number should be close to 10.666666: &quot;</span> &lt;&lt; integral</div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> &lt;&lt; std::endl;</div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> </div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> <span class="comment">/* \int_{0}^{1} e^x dx */</span></div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> f = [&amp;](<span class="keywordtype">double</span>&amp; x) { <span class="keywordflow">return</span> std::exp(x); };</div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> </div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> lower_bound = 0.0;</div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> upper_bound = 1.0;</div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> pdf = [&amp;](<span class="keywordtype">double</span>&amp; x) {</div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> <span class="keywordflow">if</span> (x &gt;= lower_bound &amp;&amp; x &lt;= 0.2) {</div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> <span class="keywordflow">return</span> 0.1;</div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> }</div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> <span class="keywordflow">if</span> (x &gt; 0.2 &amp;&amp; x &lt;= 0.4) {</div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> <span class="keywordflow">return</span> 0.4;</div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> }</div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> <span class="keywordflow">if</span> (x &gt; 0.4 &amp;&amp; x &lt; upper_bound) {</div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> <span class="keywordflow">return</span> 1.5;</div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> }</div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> <span class="keywordflow">return</span> 0.0;</div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> };</div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> </div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> integral = math::monte_carlo::integral_monte_carlo(</div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> (upper_bound - lower_bound) / 2.0, f, pdf);</div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> </div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> std::cout &lt;&lt; <span class="stringliteral">&quot;This number should be close to 1.7182818: &quot;</span> &lt;&lt; integral</div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> &lt;&lt; std::endl;</div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> </div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> <span class="comment">/* \int_{-\infty}^{\infty} sinc(x) dx, sinc(x) = sin(pi * x) / (pi * x)</span></div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span><span class="comment"> This is a difficult integral because of its infinite domain.</span></div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span><span class="comment"> Therefore, it may deviate largely from the expected result.</span></div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span><span class="comment"> */</span></div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> f = [&amp;](<span class="keywordtype">double</span>&amp; x) { <span class="keywordflow">return</span> std::sin(M_PI * x) / (M_PI * x); };</div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> </div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> pdf = [&amp;](<span class="keywordtype">double</span>&amp; x) {</div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span> <span class="keywordflow">return</span> 1.0 / std::sqrt(2.0 * M_PI) * std::exp(-x * x / 2.0);</div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> };</div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> </div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> integral = math::monte_carlo::integral_monte_carlo(0.0, f, pdf, 10000000);</div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> </div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> std::cout &lt;&lt; <span class="stringliteral">&quot;This number should be close to 1.0: &quot;</span> &lt;&lt; integral</div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> &lt;&lt; std::endl;</div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span>}</div>
</div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> </div>
<div class="foldopen" id="foldopen00215" data-start="{" data-end="}">
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"><a class="line" href="../../db/d40/integral__approximation2_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4"> 215</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../db/d40/integral__approximation2_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> <a class="code hl_function" href="../../db/d40/integral__approximation2_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// run self-test implementations</span></div>
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span>}</div>
</div>
<div class="ttc" id="aintegral__approximation2_8cpp_html_a71249ee535f16f8ed2e9cc8f0199a2cf"><div class="ttname"><a href="../../db/d40/integral__approximation2_8cpp.html#a71249ee535f16f8ed2e9cc8f0199a2cf">math::monte_carlo::generate_samples</a></div><div class="ttdeci">std::vector&lt; double &gt; generate_samples(const double &amp;start_point, const Function &amp;pdf, const uint32_t &amp;num_samples, const uint32_t &amp;discard=100000)</div><div class="ttdoc">short-hand for std::functions used in this implementation</div><div class="ttdef"><b>Definition</b> <a href="#l00064">integral_approximation2.cpp:64</a></div></div>
<div class="ttc" id="aintegral__approximation2_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../db/d40/integral__approximation2_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> <a href="#l00133">integral_approximation2.cpp:133</a></div></div>
<div class="ttc" id="aintegral__approximation2_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../db/d40/integral__approximation2_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdoc">Main function.</div><div class="ttdef"><b>Definition</b> <a href="#l00215">integral_approximation2.cpp:215</a></div></div>
<div class="ttc" id="aintegral__approximation2_8cpp_html_af7da9ba8932f1f48b9bbc2d80471af51"><div class="ttname"><a href="../../db/d40/integral__approximation2_8cpp.html#af7da9ba8932f1f48b9bbc2d80471af51">math::monte_carlo::integral_monte_carlo</a></div><div class="ttdeci">double integral_monte_carlo(const double &amp;start_point, const Function &amp;function, const Function &amp;pdf, const uint32_t &amp;num_samples=1000000)</div><div class="ttdoc">Compute an approximation of an integral using Monte Carlo integration.</div><div class="ttdef"><b>Definition</b> <a href="#l00112">integral_approximation2.cpp:112</a></div></div>
<div class="ttc" id="anamespacemath_html"><div class="ttname"><a href="../../dd/d47/namespacemath.html">math</a></div><div class="ttdoc">for assert</div></div>
<div class="ttc" id="anamespacemonte__carlo_html"><div class="ttname"><a href="../../d0/da4/namespacemonte__carlo.html">monte_carlo</a></div><div class="ttdoc">Functions for the Monte Carlo Integration implementation.</div></div>
</div><!-- fragment --></div><!-- contents -->
</div><!-- doc-content -->
<!-- start footer part -->
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>
<li class="navelem"><a class="el" href="../../dir_296d53ceaeaa7e099814a6def439fe8a.html">math</a></li><li class="navelem"><a class="el" href="../../db/d40/integral__approximation2_8cpp.html">integral_approximation2.cpp</a></li>
<li class="footer">Generated by <a href="https://www.doxygen.org/index.html"><img class="footer" src="../../doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.12.0 </li>
</ul>
</div>
</body>
</html>