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Documentation for c26eea874d
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realstealthninja
@@ -4,7 +4,7 @@
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<title>TheAlgorithms/C++: numerical_methods/composite_simpson_rule.cpp Source File</title>
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<link rel="icon" href="../../favicon.svg" type="image/x-icon" />
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@@ -60,7 +60,7 @@ window.MathJax = {
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</table>
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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 +124,8 @@ $(function(){initNavTree('d4/d18/composite__simpson__rule_8cpp_source.html','../
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<div class="headertitle"><div class="title">composite_simpson_rule.cpp</div></div>
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</div><!--header-->
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<div class="contents">
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<a href="../../d4/d18/composite__simpson__rule_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="../../d4/d18/composite__simpson__rule_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="l00037" name="l00037"></a><span class="lineno"> 37</span> </div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span><span class="preprocessor">#include <cassert></span> </div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="preprocessor">#include <cmath></span> </div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="preprocessor">#include <cmath></span></div>
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@@ -133,7 +134,7 @@ $(function(){initNavTree('d4/d18/composite__simpson__rule_8cpp_source.html','../
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span><span class="preprocessor">#include <functional></span> </div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span><span class="preprocessor">#include <iostream></span> </div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span><span class="preprocessor">#include <map></span> </div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> </div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span></div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</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="l00056" name="l00056"></a><span class="lineno"> 56</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../d3/d6d/namespacesimpson__method.html">simpson_method</a> {</div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span><span class="keywordtype">double</span> evaluate_by_simpson(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,</div>
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@@ -144,7 +145,7 @@ $(function(){initNavTree('d4/d18/composite__simpson__rule_8cpp_source.html','../
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> </div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <span class="comment">// Create the data table</span></div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="keywordtype">double</span> temp = NAN;</div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="keywordflow">for</span> (std::int32_t i = 0; i <= <a class="code hl_variable" href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="keywordflow">for</span> (std::int32_t i = 0; i <= N; i++) {</div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> temp = func(xi);</div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> data_table.insert(</div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> std::pair<std::int32_t, double>(i, temp)); <span class="comment">// add i and f(xi)</span></div>
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@@ -154,7 +155,7 @@ $(function(){initNavTree('d4/d18/composite__simpson__rule_8cpp_source.html','../
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="comment">// Evaluate the integral.</span></div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="comment">// Remember: f(x0) + 4*f(x1) + 2*f(x2) + ... + 2*f(xN-2) + 4*f(xN-1) + f(xN)</span></div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <span class="keywordtype">double</span> evaluate_integral = 0;</div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> <span class="keywordflow">for</span> (std::int32_t i = 0; i <= <a class="code hl_variable" href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> <span class="keywordflow">for</span> (std::int32_t i = 0; i <= N; i++) {</div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="keywordflow">if</span> (i == 0 || i == N) {</div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> evaluate_integral += data_table.at(i);</div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (i % 2 == 1) {</div>
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@@ -175,48 +176,48 @@ $(function(){initNavTree('d4/d18/composite__simpson__rule_8cpp_source.html','../
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="comment">// Else return</span></div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <span class="keywordflow">return</span> evaluate_integral;</div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span>}</div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> </div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span></div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"><a class="line" href="../../d4/d18/composite__simpson__rule_8cpp.html#a4251b4df4748a0b9c43a48f61bdd2397"> 113</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a4251b4df4748a0b9c43a48f61bdd2397">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="l00115" name="l00115"></a><span class="lineno"><a class="line" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad"> 115</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">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="l00117" name="l00117"></a><span class="lineno"><a class="line" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442"> 117</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">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="l00119" name="l00119"></a><span class="lineno"><a class="line" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a"> 119</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">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="l00120" name="l00120"></a><span class="lineno"> 120</span>} <span class="comment">// namespace simpson_method</span></div>
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<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span>} <span class="comment">// namespace numerical_methods</span></div>
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<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> </div>
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<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span></div>
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<div class="foldopen" id="foldopen00132" data-start="{" data-end="}">
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<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"><a class="line" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2ae48a41e43dc6ab11b962742349646e"> 132</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="l00133" name="l00133"></a><span class="lineno"> 133</span> <span class="keywordtype">bool</span> used_argv_parameters) {</div>
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<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> <span class="comment">// Call the functions and find the integral of each function</span></div>
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<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> <span class="keywordtype">double</span> result_f = numerical_methods::simpson_method::evaluate_by_simpson(</div>
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||||
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, numerical_methods::simpson_method::f);</div>
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||||
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a4251b4df4748a0b9c43a48f61bdd2397">numerical_methods::simpson_method::f</a>);</div>
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<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> assert((used_argv_parameters || (result_f >= 4.09 && result_f <= 4.10)) &&</div>
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<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> <span class="stringliteral">"The result of f(x) is wrong"</span>);</div>
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<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</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="l00140" name="l00140"></a><span class="lineno"> 140</span> << <span class="stringliteral">"] is equal to: "</span> << result_f << std::endl;</div>
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<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> </div>
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<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> <span class="keywordtype">double</span> result_g = numerical_methods::simpson_method::evaluate_by_simpson(</div>
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<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, numerical_methods::simpson_method::g);</div>
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||||
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a2f67508d5f392b0321772169342c98ad">numerical_methods::simpson_method::g</a>);</div>
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||||
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> assert((used_argv_parameters || (result_g >= 0.27 && result_g <= 0.28)) &&</div>
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<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> <span class="stringliteral">"The result of g(x) is wrong"</span>);</div>
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<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</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="l00147" name="l00147"></a><span class="lineno"> 147</span> << <span class="stringliteral">"] is equal to: "</span> << result_g << std::endl;</div>
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<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> </div>
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<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> <span class="keywordtype">double</span> result_k = numerical_methods::simpson_method::evaluate_by_simpson(</div>
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<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, numerical_methods::simpson_method::k);</div>
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||||
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a>);</div>
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<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> assert((used_argv_parameters || (result_k >= 9.06 && result_k <= 9.07)) &&</div>
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<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> <span class="stringliteral">"The result of k(x) is wrong"</span>);</div>
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<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</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="l00154" name="l00154"></a><span class="lineno"> 154</span> << <span class="stringliteral">"] is equal to: "</span> << result_k << std::endl;</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="l00156" name="l00156"></a><span class="lineno"> 156</span> <span class="keywordtype">double</span> result_l = numerical_methods::simpson_method::evaluate_by_simpson(</div>
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<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, numerical_methods::simpson_method::l);</div>
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||||
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> N, <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, a, <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a6d8df83a6f26ce24a75d3b358b7f5b8a">numerical_methods::simpson_method::l</a>);</div>
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<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> assert((used_argv_parameters || (result_l >= 7.16 && result_l <= 7.17)) &&</div>
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<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> <span class="stringliteral">"The result of l(x) is wrong"</span>);</div>
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<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</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="l00161" name="l00161"></a><span class="lineno"> 161</span> << <span class="stringliteral">"] is equal to: "</span> << result_l << std::endl;</div>
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<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span>}</div>
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</div>
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<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> </div>
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<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span></div>
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<div class="foldopen" id="foldopen00170" data-start="{" data-end="}">
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<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"><a class="line" href="../../d4/d18/composite__simpson__rule_8cpp.html#a3c04138a5bfe5d72780bb7e82a18e627"> 170</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="l00171" name="l00171"></a><span class="lineno"> 171</span> std::int32_t N = 16; </div>
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@@ -262,15 +263,14 @@ $(function(){initNavTree('d4/d18/composite__simpson__rule_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="anamespacenumerical__methods_html"><div class="ttname"><a href="../../d1/de0/namespacenumerical__methods.html">numerical_methods</a></div><div class="ttdoc">for assert</div></div>
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||||
<div class="ttc" id="anamespacesimpson__method_html"><div class="ttname"><a href="../../d3/d6d/namespacesimpson__method.html">simpson_method</a></div><div class="ttdoc">Contains the Simpson's method implementation.</div></div>
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<div class="ttc" id="asparse__table_8cpp_html_a10f3ffb3f6f7e1b83d556b9c8de89a5d"><div class="ttname"><a href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">data_structures::sparse_table::N</a></div><div class="ttdeci">constexpr uint32_t N</div><div class="ttdoc">A struct to represent sparse table for min() as their invariant function, for the given array A....</div><div class="ttdef"><b>Definition</b> <a href="../../d8/dab/sparse__table_8cpp_source.html#l00048">sparse_table.cpp:48</a></div></div>
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<div class="ttc" id="anamespacesimpson__method_html"><div class="ttname"><a href="../../d3/d6d/namespacesimpson__method.html">simpson_method</a></div><div class="ttdoc">Contains the Simpson's method implementation.</div></div>
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