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<title>TheAlgorithms/C++: numerical_methods/midpoint_integral_method.cpp Source File</title>
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@@ -60,7 +60,7 @@ window.MathJax = {
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/* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&dn=expat.txt MIT */
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var searchBox = new SearchBox("searchBox", "../../search/",'.html');
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@@ -124,7 +124,7 @@ $(function(){initNavTree('df/d11/midpoint__integral__method_8cpp_source.html','.
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<div class="headertitle"><div class="title">midpoint_integral_method.cpp</div></div>
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</div><!--header-->
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<div class="contents">
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<a href="../../df/d11/midpoint__integral__method_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>
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<a href="../../df/d11/midpoint__integral__method_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>
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<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="preprocessor">#include <cassert></span> </div>
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<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="preprocessor">#include <cmath></span> </div>
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<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="preprocessor">#include <cstdint></span> </div>
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@@ -132,7 +132,7 @@ $(function(){initNavTree('df/d11/midpoint__integral__method_8cpp_source.html','.
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<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="preprocessor">#include <functional></span> </div>
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<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="preprocessor">#include <iostream></span> </div>
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<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="preprocessor">#include <map></span> </div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> </div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span></div>
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<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../d1/de0/namespacenumerical__methods.html">numerical_methods</a> {</div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../d9/daa/namespacemidpoint__rule.html">midpoint_rule</a> {</div>
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<div class="foldopen" id="foldopen00052" data-start="{" data-end="}">
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@@ -169,50 +169,50 @@ $(function(){initNavTree('df/d11/midpoint__integral__method_8cpp_source.html','.
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="keywordflow">return</span> evaluate_integral;</div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span>}</div>
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</div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> </div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"><a class="line" href="../../df/d11/midpoint__integral__method_8cpp.html#a7ee8e824ef3e138a9a21883b26d97226"> 90</a></span><span class="keywordtype">double</span> f(<span class="keywordtype">double</span> x) { <span class="keywordflow">return</span> std::sqrt(x) + std::log(x); }</div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"><a class="line" href="../../df/d11/midpoint__integral__method_8cpp.html#ae682ee71af44b1e9e884849cc6a6b040"> 97</a></span><span class="keywordtype">double</span> g(<span class="keywordtype">double</span> x) { <span class="keywordflow">return</span> std::exp(-x) * (4 - std::pow(x, 2)); }</div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"><a class="line" href="../../df/d11/midpoint__integral__method_8cpp.html#ae9f66040f8e0ba73c1c741261c22a52a"> 103</a></span><span class="keywordtype">double</span> k(<span class="keywordtype">double</span> x) { <span class="keywordflow">return</span> std::sqrt(2 * std::pow(x, 3) + 3); }</div>
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<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"><a class="line" href="../../df/d11/midpoint__integral__method_8cpp.html#ad53616fb4fa6880ae876bcba53365c51"> 109</a></span><span class="keywordtype">double</span> l(<span class="keywordtype">double</span> x) { <span class="keywordflow">return</span> x + std::log(2 * x + 1); }</div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span></div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"><a class="line" href="../../df/d11/midpoint__integral__method_8cpp.html#a7ee8e824ef3e138a9a21883b26d97226"> 90</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="../../df/d11/midpoint__integral__method_8cpp.html#a7ee8e824ef3e138a9a21883b26d97226">f</a>(<span class="keywordtype">double</span> x) { <span class="keywordflow">return</span> std::sqrt(x) + std::log(x); }</div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"><a class="line" href="../../df/d11/midpoint__integral__method_8cpp.html#ae682ee71af44b1e9e884849cc6a6b040"> 97</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="../../df/d11/midpoint__integral__method_8cpp.html#ae682ee71af44b1e9e884849cc6a6b040">g</a>(<span class="keywordtype">double</span> x) { <span class="keywordflow">return</span> std::exp(-x) * (4 - std::pow(x, 2)); }</div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"><a class="line" href="../../df/d11/midpoint__integral__method_8cpp.html#ae9f66040f8e0ba73c1c741261c22a52a"> 103</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="../../df/d11/midpoint__integral__method_8cpp.html#ae9f66040f8e0ba73c1c741261c22a52a">k</a>(<span class="keywordtype">double</span> x) { <span class="keywordflow">return</span> std::sqrt(2 * std::pow(x, 3) + 3); }</div>
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<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"><a class="line" href="../../df/d11/midpoint__integral__method_8cpp.html#ad53616fb4fa6880ae876bcba53365c51"> 109</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="../../df/d11/midpoint__integral__method_8cpp.html#ad53616fb4fa6880ae876bcba53365c51">l</a>(<span class="keywordtype">double</span> x) { <span class="keywordflow">return</span> x + std::log(2 * x + 1); }</div>
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<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> </div>
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<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span>} <span class="comment">// namespace midpoint_rule</span></div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span>} <span class="comment">// namespace numerical_methods</span></div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> </div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span></div>
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<div class="foldopen" id="foldopen00123" data-start="{" data-end="}">
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<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"><a class="line" href="../../df/d11/midpoint__integral__method_8cpp.html#a2ae48a41e43dc6ab11b962742349646e"> 123</a></span><span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code hl_function" href="../../dd/d1e/generate__parentheses_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(std::int32_t N, <span class="keywordtype">double</span> <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, <span class="keywordtype">double</span> a, <span class="keywordtype">double</span> b,</div>
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<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> <span class="keywordtype">bool</span> used_argv_parameters) {</div>
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<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> <span class="comment">// Call midpoint() for each of the test functions f, g, k, l</span></div>
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<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> <span class="comment">// Assert with two decimal point precision</span></div>
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<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> <span class="keywordtype">double</span> result_f = numerical_methods::midpoint_rule::midpoint(</div>
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<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, numerical_methods::midpoint_rule::f);</div>
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||||
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> <span class="keywordtype">double</span> result_f = <a class="code hl_function" href="../../df/d11/midpoint__integral__method_8cpp.html#a7072493d1f0f8a91b2a71d4cc456c09c">numerical_methods::midpoint_rule::midpoint</a>(</div>
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||||
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, <a class="code hl_function" href="../../df/d11/midpoint__integral__method_8cpp.html#a7ee8e824ef3e138a9a21883b26d97226">numerical_methods::midpoint_rule::f</a>);</div>
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||||
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> assert((used_argv_parameters || (result_f >= 4.09 && result_f <= 4.10)) &&</div>
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<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> <span class="stringliteral">"The result of f(x) is wrong"</span>);</div>
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<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> std::cout << <span class="stringliteral">"The result of integral f(x) on interval ["</span> << a << <span class="stringliteral">", "</span> << b</div>
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<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> << <span class="stringliteral">"] is equal to: "</span> << result_f << std::endl;</div>
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<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> </div>
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||||
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> <span class="keywordtype">double</span> result_g = numerical_methods::midpoint_rule::midpoint(</div>
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||||
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, numerical_methods::midpoint_rule::g);</div>
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||||
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> <span class="keywordtype">double</span> result_g = <a class="code hl_function" href="../../df/d11/midpoint__integral__method_8cpp.html#a7072493d1f0f8a91b2a71d4cc456c09c">numerical_methods::midpoint_rule::midpoint</a>(</div>
|
||||
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, <a class="code hl_function" href="../../df/d11/midpoint__integral__method_8cpp.html#ae682ee71af44b1e9e884849cc6a6b040">numerical_methods::midpoint_rule::g</a>);</div>
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||||
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> assert((used_argv_parameters || (result_g >= 0.27 && result_g <= 0.28)) &&</div>
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<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> <span class="stringliteral">"The result of g(x) is wrong"</span>);</div>
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<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> std::cout << <span class="stringliteral">"The result of integral g(x) on interval ["</span> << a << <span class="stringliteral">", "</span> << b</div>
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<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> << <span class="stringliteral">"] is equal to: "</span> << result_g << std::endl;</div>
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<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> </div>
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<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> <span class="keywordtype">double</span> result_k = numerical_methods::midpoint_rule::midpoint(</div>
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<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, numerical_methods::midpoint_rule::k);</div>
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||||
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> <span class="keywordtype">double</span> result_k = <a class="code hl_function" href="../../df/d11/midpoint__integral__method_8cpp.html#a7072493d1f0f8a91b2a71d4cc456c09c">numerical_methods::midpoint_rule::midpoint</a>(</div>
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||||
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, <a class="code hl_function" href="../../df/d11/midpoint__integral__method_8cpp.html#ae9f66040f8e0ba73c1c741261c22a52a">numerical_methods::midpoint_rule::k</a>);</div>
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||||
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> assert((used_argv_parameters || (result_k >= 9.06 && result_k <= 9.07)) &&</div>
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||||
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> <span class="stringliteral">"The result of k(x) is wrong"</span>);</div>
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<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> std::cout << <span class="stringliteral">"The result of integral k(x) on interval ["</span> << a << <span class="stringliteral">", "</span> << b</div>
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<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> << <span class="stringliteral">"] is equal to: "</span> << result_k << std::endl;</div>
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<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> </div>
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<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> <span class="keywordtype">double</span> result_l = numerical_methods::midpoint_rule::midpoint(</div>
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<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, numerical_methods::midpoint_rule::l);</div>
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<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> <span class="keywordtype">double</span> result_l = <a class="code hl_function" href="../../df/d11/midpoint__integral__method_8cpp.html#a7072493d1f0f8a91b2a71d4cc456c09c">numerical_methods::midpoint_rule::midpoint</a>(</div>
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||||
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, <a class="code hl_function" href="../../df/d11/midpoint__integral__method_8cpp.html#ad53616fb4fa6880ae876bcba53365c51">numerical_methods::midpoint_rule::l</a>);</div>
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||||
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> assert((used_argv_parameters || (result_l >= 7.16 && result_l <= 7.17)) &&</div>
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<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> <span class="stringliteral">"The result of l(x) is wrong"</span>);</div>
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<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> std::cout << <span class="stringliteral">"The result of integral l(x) on interval ["</span> << a << <span class="stringliteral">", "</span> << b</div>
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<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> << <span class="stringliteral">"] is equal to: "</span> << result_l << std::endl;</div>
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<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span>}</div>
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</div>
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<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> </div>
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<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span></div>
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<div class="foldopen" id="foldopen00162" data-start="{" data-end="}">
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<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"><a class="line" href="../../df/d11/midpoint__integral__method_8cpp.html#a3c04138a5bfe5d72780bb7e82a18e627"> 162</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../dd/d1e/generate__parentheses_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4">main</a>(<span class="keywordtype">int</span> argc, <span class="keywordtype">char</span>** argv) {</div>
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<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> std::int32_t N =</div>
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@@ -255,6 +255,10 @@ $(function(){initNavTree('df/d11/midpoint__integral__method_8cpp_source.html','.
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<div class="ttc" id="agenerate__parentheses_8cpp_html_gae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../dd/d1e/generate__parentheses_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdoc">Main function.</div><div class="ttdef"><b>Definition</b> <a href="../../dd/d1e/generate__parentheses_8cpp_source.html#l00110">generate_parentheses.cpp:110</a></div></div>
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<div class="ttc" id="ahash__search_8cpp_html_a566eaf0ffafd50bc61e644561fd27001"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a></div><div class="ttdeci">int h(int key)</div><div class="ttdef"><b>Definition</b> <a href="../../d1/df3/hash__search_8cpp_source.html#l00045">hash_search.cpp:45</a></div></div>
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<div class="ttc" id="amidpoint__integral__method_8cpp_html_a7072493d1f0f8a91b2a71d4cc456c09c"><div class="ttname"><a href="../../df/d11/midpoint__integral__method_8cpp.html#a7072493d1f0f8a91b2a71d4cc456c09c">numerical_methods::midpoint_rule::midpoint</a></div><div class="ttdeci">double midpoint(const std::int32_t N, const double h, const double a, const std::function< double(double)> &func)</div><div class="ttdoc">Main function for implementing the Midpoint Integral Method implementation.</div><div class="ttdef"><b>Definition</b> <a href="#l00052">midpoint_integral_method.cpp:52</a></div></div>
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<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> <a href="#l00090">midpoint_integral_method.cpp:90</a></div></div>
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<div class="ttc" id="amidpoint__integral__method_8cpp_html_ad53616fb4fa6880ae876bcba53365c51"><div class="ttname"><a href="../../df/d11/midpoint__integral__method_8cpp.html#ad53616fb4fa6880ae876bcba53365c51">numerical_methods::midpoint_rule::l</a></div><div class="ttdeci">double l(double x)</div><div class="ttdoc">A function l(x) that will be used to test the method.</div><div class="ttdef"><b>Definition</b> <a href="#l00109">midpoint_integral_method.cpp:109</a></div></div>
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<div class="ttc" id="amidpoint__integral__method_8cpp_html_ae682ee71af44b1e9e884849cc6a6b040"><div class="ttname"><a href="../../df/d11/midpoint__integral__method_8cpp.html#ae682ee71af44b1e9e884849cc6a6b040">numerical_methods::midpoint_rule::g</a></div><div class="ttdeci">double g(double x)</div><div class="ttdoc">A function g(x) that will be used to test the method.</div><div class="ttdef"><b>Definition</b> <a href="#l00097">midpoint_integral_method.cpp:97</a></div></div>
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<div class="ttc" id="amidpoint__integral__method_8cpp_html_ae9f66040f8e0ba73c1c741261c22a52a"><div class="ttname"><a href="../../df/d11/midpoint__integral__method_8cpp.html#ae9f66040f8e0ba73c1c741261c22a52a">numerical_methods::midpoint_rule::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">A function k(x) that will be used to test the method.</div><div class="ttdef"><b>Definition</b> <a href="#l00103">midpoint_integral_method.cpp:103</a></div></div>
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<div class="ttc" id="anamespacemidpoint__rule_html"><div class="ttname"><a href="../../d9/daa/namespacemidpoint__rule.html">midpoint_rule</a></div><div class="ttdoc">Functions for the Midpoint Integral method implementation.</div></div>
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