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realstealthninja
2025-05-19 11:38:33 +00:00
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@@ -4,7 +4,7 @@
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<title>TheAlgorithms/C++: math/integral_approximation2.cpp Source File</title>
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@@ -60,7 +60,7 @@ window.MathJax = {
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@@ -124,7 +124,8 @@ $(function(){initNavTree('db/d40/integral__approximation2_8cpp_source.html','../
<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>
<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="l00023" name="l00023"></a><span class="lineno"> 23</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>
@@ -133,13 +134,13 @@ $(function(){initNavTree('db/d40/integral__approximation2_8cpp_source.html','../
<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="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="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>
@@ -175,7 +176,7 @@ $(function(){initNavTree('db/d40/integral__approximation2_8cpp_source.html','../
<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="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>
@@ -194,7 +195,7 @@ $(function(){initNavTree('db/d40/integral__approximation2_8cpp_source.html','../
<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="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>
@@ -228,7 +229,7 @@ $(function(){initNavTree('db/d40/integral__approximation2_8cpp_source.html','../
<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="l00165" name="l00165"></a><span class="lineno"> 165</span> integral = <a class="code hl_function" href="../../db/d40/integral__approximation2_8cpp.html#af7da9ba8932f1f48b9bbc2d80471af51">math::monte_carlo::integral_monte_carlo</a>(</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>
@@ -252,7 +253,7 @@ $(function(){initNavTree('db/d40/integral__approximation2_8cpp_source.html','../
<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="l00189" name="l00189"></a><span class="lineno"> 189</span> integral = <a class="code hl_function" href="../../db/d40/integral__approximation2_8cpp.html#af7da9ba8932f1f48b9bbc2d80471af51">math::monte_carlo::integral_monte_carlo</a>(</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>
@@ -268,13 +269,13 @@ $(function(){initNavTree('db/d40/integral__approximation2_8cpp_source.html','../
<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="l00205" name="l00205"></a><span class="lineno"> 205</span> integral = <a class="code hl_function" href="../../db/d40/integral__approximation2_8cpp.html#af7da9ba8932f1f48b9bbc2d80471af51">math::monte_carlo::integral_monte_carlo</a>(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="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>
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