mirror of
https://github.com/TheAlgorithms/C-Plus-Plus.git
synced 2026-04-01 09:43:06 +08:00
Documentation for c26eea874d
This commit is contained in:
realstealthninja
@@ -4,7 +4,7 @@
|
||||
<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="generator" content="Doxygen 1.13.2"/>
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1"/>
|
||||
<title>TheAlgorithms/C++: numerical_methods/composite_simpson_rule.cpp File Reference</title>
|
||||
<link rel="icon" href="../../favicon.svg" type="image/x-icon" />
|
||||
@@ -60,7 +60,7 @@ window.MathJax = {
|
||||
</table>
|
||||
</div>
|
||||
<!-- end header part -->
|
||||
<!-- Generated by Doxygen 1.12.0 -->
|
||||
<!-- Generated by Doxygen 1.13.2 -->
|
||||
<script type="text/javascript">
|
||||
/* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&dn=expat.txt MIT */
|
||||
var searchBox = new SearchBox("searchBox", "../../search/",'.html');
|
||||
@@ -229,7 +229,7 @@ Functions</h2></td></tr>
|
||||
<div class="line"><span class="lineno"> 72</span> </div>
|
||||
<div class="line"><span class="lineno"> 73</span> <span class="comment">// Create the data table</span></div>
|
||||
<div class="line"><span class="lineno"> 74</span> <span class="keywordtype">double</span> temp = NAN;</div>
|
||||
<div class="line"><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>
|
||||
<div class="line"><span class="lineno"> 75</span> <span class="keywordflow">for</span> (std::int32_t i = 0; i <= N; i++) {</div>
|
||||
<div class="line"><span class="lineno"> 76</span> temp = func(xi);</div>
|
||||
<div class="line"><span class="lineno"> 77</span> data_table.insert(</div>
|
||||
<div class="line"><span class="lineno"> 78</span> std::pair<std::int32_t, double>(i, temp)); <span class="comment">// add i and f(xi)</span></div>
|
||||
@@ -239,7 +239,7 @@ Functions</h2></td></tr>
|
||||
<div class="line"><span class="lineno"> 82</span> <span class="comment">// Evaluate the integral.</span></div>
|
||||
<div class="line"><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>
|
||||
<div class="line"><span class="lineno"> 84</span> <span class="keywordtype">double</span> evaluate_integral = 0;</div>
|
||||
<div class="line"><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>
|
||||
<div class="line"><span class="lineno"> 85</span> <span class="keywordflow">for</span> (std::int32_t i = 0; i <= N; i++) {</div>
|
||||
<div class="line"><span class="lineno"> 86</span> <span class="keywordflow">if</span> (i == 0 || i == N) {</div>
|
||||
<div class="line"><span class="lineno"> 87</span> evaluate_integral += data_table.at(i);</div>
|
||||
<div class="line"><span class="lineno"> 88</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (i % 2 == 1) {</div>
|
||||
@@ -261,7 +261,6 @@ Functions</h2></td></tr>
|
||||
<div class="line"><span class="lineno"> 104</span> <span class="keywordflow">return</span> evaluate_integral;</div>
|
||||
<div class="line"><span class="lineno"> 105</span>}</div>
|
||||
<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>
|
||||
<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>
|
||||
</div><!-- fragment -->
|
||||
</div>
|
||||
</div>
|
||||
@@ -394,7 +393,7 @@ Functions</h2></td></tr>
|
||||
|
||||
<p class="definition">Definition at line <a class="el" href="../../d4/d18/composite__simpson__rule_8cpp_source.html#l00170">170</a> of file <a class="el" href="../../d4/d18/composite__simpson__rule_8cpp_source.html">composite_simpson_rule.cpp</a>.</p>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 170</span> {</div>
|
||||
<div class="line"><span class="lineno"> 171</span> std::int32_t <a class="code hl_variable" href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = 16; </div>
|
||||
<div class="line"><span class="lineno"> 171</span> std::int32_t N = 16; </div>
|
||||
<div class="line"><span class="lineno"> 173</span> <span class="keywordtype">double</span> a = 1, b = 3; </div>
|
||||
<div class="line"><span class="lineno"> 175</span> <span class="keywordtype">double</span> <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a> = NAN; </div>
|
||||
<div class="line"><span class="lineno"> 176</span> </div>
|
||||
@@ -405,7 +404,7 @@ Functions</h2></td></tr>
|
||||
<div class="line"><span class="lineno"> 181</span> <span class="comment">// Get user input (by the command line parameters or the console after</span></div>
|
||||
<div class="line"><span class="lineno"> 182</span> <span class="comment">// displaying messages)</span></div>
|
||||
<div class="line"><span class="lineno"> 183</span> <span class="keywordflow">if</span> (argc == 4) {</div>
|
||||
<div class="line"><span class="lineno"> 184</span> <a class="code hl_variable" href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = std::atoi(argv[1]);</div>
|
||||
<div class="line"><span class="lineno"> 184</span> N = std::atoi(argv[1]);</div>
|
||||
<div class="line"><span class="lineno"> 185</span> a = std::atof(argv[2]);</div>
|
||||
<div class="line"><span class="lineno"> 186</span> b = std::atof(argv[3]);</div>
|
||||
<div class="line"><span class="lineno"> 187</span> <span class="comment">// Check if a<b else abort</span></div>
|
||||
@@ -414,10 +413,10 @@ Functions</h2></td></tr>
|
||||
<div class="line"><span class="lineno"> 190</span> <span class="keywordflow">if</span> (N < 16 || a != 1 || b != 3) {</div>
|
||||
<div class="line"><span class="lineno"> 191</span> used_argv_parameters = <span class="keyword">true</span>;</div>
|
||||
<div class="line"><span class="lineno"> 192</span> }</div>
|
||||
<div class="line"><span class="lineno"> 193</span> std::cout << <span class="stringliteral">"You selected N="</span> << <a class="code hl_variable" href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> << <span class="stringliteral">", a="</span> << a << <span class="stringliteral">", b="</span> << b</div>
|
||||
<div class="line"><span class="lineno"> 193</span> std::cout << <span class="stringliteral">"You selected N="</span> << N << <span class="stringliteral">", a="</span> << a << <span class="stringliteral">", b="</span> << b</div>
|
||||
<div class="line"><span class="lineno"> 194</span> << std::endl;</div>
|
||||
<div class="line"><span class="lineno"> 195</span> } <span class="keywordflow">else</span> {</div>
|
||||
<div class="line"><span class="lineno"> 196</span> std::cout << <span class="stringliteral">"Default N="</span> << <a class="code hl_variable" href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> << <span class="stringliteral">", a="</span> << a << <span class="stringliteral">", b="</span> << b</div>
|
||||
<div class="line"><span class="lineno"> 196</span> std::cout << <span class="stringliteral">"Default N="</span> << N << <span class="stringliteral">", a="</span> << a << <span class="stringliteral">", b="</span> << b</div>
|
||||
<div class="line"><span class="lineno"> 197</span> << std::endl;</div>
|
||||
<div class="line"><span class="lineno"> 198</span> }</div>
|
||||
<div class="line"><span class="lineno"> 199</span> </div>
|
||||
@@ -469,7 +468,7 @@ Functions</h2></td></tr>
|
||||
</table>
|
||||
</td>
|
||||
<td class="mlabels-right">
|
||||
<span class="mlabels"><span class="mlabel">static</span></span> </td>
|
||||
<span class="mlabels"><span class="mlabel static">static</span></span> </td>
|
||||
</tr>
|
||||
</table>
|
||||
</div><div class="memdoc">
|
||||
@@ -490,33 +489,37 @@ Functions</h2></td></tr>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 133</span> {</div>
|
||||
<div class="line"><span class="lineno"> 134</span> <span class="comment">// Call the functions and find the integral of each function</span></div>
|
||||
<div class="line"><span class="lineno"> 135</span> <span class="keywordtype">double</span> result_f = numerical_methods::simpson_method::evaluate_by_simpson(</div>
|
||||
<div class="line"><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>
|
||||
<div class="line"><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="#a4251b4df4748a0b9c43a48f61bdd2397">numerical_methods::simpson_method::f</a>);</div>
|
||||
<div class="line"><span class="lineno"> 137</span> assert((used_argv_parameters || (result_f >= 4.09 && result_f <= 4.10)) &&</div>
|
||||
<div class="line"><span class="lineno"> 138</span> <span class="stringliteral">"The result of f(x) is wrong"</span>);</div>
|
||||
<div class="line"><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>
|
||||
<div class="line"><span class="lineno"> 140</span> << <span class="stringliteral">"] is equal to: "</span> << result_f << std::endl;</div>
|
||||
<div class="line"><span class="lineno"> 141</span> </div>
|
||||
<div class="line"><span class="lineno"> 142</span> <span class="keywordtype">double</span> result_g = numerical_methods::simpson_method::evaluate_by_simpson(</div>
|
||||
<div class="line"><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>
|
||||
<div class="line"><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="#a2f67508d5f392b0321772169342c98ad">numerical_methods::simpson_method::g</a>);</div>
|
||||
<div class="line"><span class="lineno"> 144</span> assert((used_argv_parameters || (result_g >= 0.27 && result_g <= 0.28)) &&</div>
|
||||
<div class="line"><span class="lineno"> 145</span> <span class="stringliteral">"The result of g(x) is wrong"</span>);</div>
|
||||
<div class="line"><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>
|
||||
<div class="line"><span class="lineno"> 147</span> << <span class="stringliteral">"] is equal to: "</span> << result_g << std::endl;</div>
|
||||
<div class="line"><span class="lineno"> 148</span> </div>
|
||||
<div class="line"><span class="lineno"> 149</span> <span class="keywordtype">double</span> result_k = numerical_methods::simpson_method::evaluate_by_simpson(</div>
|
||||
<div class="line"><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>
|
||||
<div class="line"><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="#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a>);</div>
|
||||
<div class="line"><span class="lineno"> 151</span> assert((used_argv_parameters || (result_k >= 9.06 && result_k <= 9.07)) &&</div>
|
||||
<div class="line"><span class="lineno"> 152</span> <span class="stringliteral">"The result of k(x) is wrong"</span>);</div>
|
||||
<div class="line"><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>
|
||||
<div class="line"><span class="lineno"> 154</span> << <span class="stringliteral">"] is equal to: "</span> << result_k << std::endl;</div>
|
||||
<div class="line"><span class="lineno"> 155</span> </div>
|
||||
<div class="line"><span class="lineno"> 156</span> <span class="keywordtype">double</span> result_l = numerical_methods::simpson_method::evaluate_by_simpson(</div>
|
||||
<div class="line"><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>
|
||||
<div class="line"><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="#a6d8df83a6f26ce24a75d3b358b7f5b8a">numerical_methods::simpson_method::l</a>);</div>
|
||||
<div class="line"><span class="lineno"> 158</span> assert((used_argv_parameters || (result_l >= 7.16 && result_l <= 7.17)) &&</div>
|
||||
<div class="line"><span class="lineno"> 159</span> <span class="stringliteral">"The result of l(x) is wrong"</span>);</div>
|
||||
<div class="line"><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>
|
||||
<div class="line"><span class="lineno"> 161</span> << <span class="stringliteral">"] is equal to: "</span> << result_l << std::endl;</div>
|
||||
<div class="line"><span class="lineno"> 162</span>}</div>
|
||||
<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a1b74d828b33760094906797042b89442"><div class="ttname"><a href="#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition</b> <a href="../../d4/d18/composite__simpson__rule_8cpp_source.html#l00117">composite_simpson_rule.cpp:117</a></div></div>
|
||||
<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a2f67508d5f392b0321772169342c98ad"><div class="ttname"><a href="#a2f67508d5f392b0321772169342c98ad">numerical_methods::simpson_method::g</a></div><div class="ttdeci">double g(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition</b> <a href="../../d4/d18/composite__simpson__rule_8cpp_source.html#l00115">composite_simpson_rule.cpp:115</a></div></div>
|
||||
<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a4251b4df4748a0b9c43a48f61bdd2397"><div class="ttname"><a href="#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="acomposite__simpson__rule_8cpp_html_a6d8df83a6f26ce24a75d3b358b7f5b8a"><div class="ttname"><a href="#a6d8df83a6f26ce24a75d3b358b7f5b8a">numerical_methods::simpson_method::l</a></div><div class="ttdeci">double l(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition</b> <a href="../../d4/d18/composite__simpson__rule_8cpp_source.html#l00119">composite_simpson_rule.cpp:119</a></div></div>
|
||||
</div><!-- fragment -->
|
||||
</div>
|
||||
</div>
|
||||
@@ -526,7 +529,7 @@ Functions</h2></td></tr>
|
||||
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
|
||||
<ul>
|
||||
<li class="navelem"><a class="el" href="../../dir_9c6faab82c22511b50177aa2e38e2780.html">numerical_methods</a></li><li class="navelem"><a class="el" href="../../d4/d18/composite__simpson__rule_8cpp.html">composite_simpson_rule.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>
|
||||
<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> 1.13.2 </li>
|
||||
</ul>
|
||||
</div>
|
||||
</body>
|
||||
|
||||
Reference in New Issue
Block a user