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@@ -384,13 +384,13 @@ Here is the call graph for this function:</div>
<div class="line"><a id="l00139" name="l00139"></a><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"><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> <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="../../df/d11/midpoint__integral__method_8cpp.html#a7ee8e824ef3e138a9a21883b26d97226">f</a>;</div>
<div class="line"><a id="l00142" name="l00142"></a><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"><a id="l00143" name="l00143"></a><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"><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> <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"><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> <a class="code hl_function" href="../../df/d11/midpoint__integral__method_8cpp.html#a7ee8e824ef3e138a9a21883b26d97226">f</a> = [&amp;](<span class="keywordtype">double</span>&amp; x) { <span class="keywordflow">return</span> -x * x + 4.0; };</div>
<div class="line"><a id="l00148" name="l00148"></a><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"><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> <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"><a id="l00151" name="l00151"></a><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>
@@ -414,7 +414,7 @@ Here is the call graph for this function:</div>
<div class="line"><a id="l00169" name="l00169"></a><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"><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> <a class="code hl_function" href="../../df/d11/midpoint__integral__method_8cpp.html#a7ee8e824ef3e138a9a21883b26d97226">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"><a id="l00172" name="l00172"></a><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"><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> <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"><a id="l00175" name="l00175"></a><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>
@@ -441,7 +441,7 @@ Here is the call graph for this function:</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> <a class="code hl_function" href="../../df/d11/midpoint__integral__method_8cpp.html#a7ee8e824ef3e138a9a21883b26d97226">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"><a id="l00199" name="l00199"></a><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"><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 / <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>
@@ -453,12 +453,12 @@ Here is the call graph for this function:</div>
<div class="line"><a id="l00208" name="l00208"></a><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"><a id="l00209" name="l00209"></a><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:111</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="afunction_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</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> 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="amidpoint__integral__method_8cpp_html_a7ee8e824ef3e138a9a21883b26d97226"><div class="ttname"><a href="../../df/d11/midpoint__integral__method_8cpp.html#a7ee8e824ef3e138a9a21883b26d97226">numerical_methods::midpoint_rule::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> midpoint_integral_method.cpp:90</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>