backup/C-Plus-Plus
1
0
Fork 0
mirror of https://github.com/TheAlgorithms/C-Plus-Plus.git synced 2026-03-21 20:31:43 +08:00
Code Issues Projects Releases Wiki Activity
Files
a7bccf7d0117d07aaf0d7b4a758996cc4d89d0f7
C-Plus-Plus/d7/d6a/bisection__method_8cpp_source.html
realstealthninja a7bccf7d01 Documentation for 8b1eab204b
2024-11-04 12:43:05 +00:00

205 lines
17 KiB
HTML
Raw Blame History

<!-- HTML header for doxygen 1.12.0-->
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en-US">
<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="viewport" content="width=device-width, initial-scale=1"/>
<title>TheAlgorithms/C++: numerical_methods/bisection_method.cpp Source File</title>
<link rel="icon" href="../../favicon.svg" type="image/x-icon" />
<link href="../../tabs.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="../../jquery.js"></script>
<script type="text/javascript" src="../../dynsections.js"></script>
<script type="text/javascript" src="https://cdn.jsdelivr.net/npm/@xpack-3rd-party/doxygen-awesome-css@2.2.0-1/doxygen-awesome-darkmode-toggle.js"></script>
<script type="text/javascript">
DoxygenAwesomeDarkModeToggle.init()
</script>
<script type="text/javascript" src="../../clipboard.js"></script>
<link href="../../navtree.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="../../navtreedata.js"></script>
<script type="text/javascript" src="../../navtree.js"></script>
<script type="text/javascript" src="../../resize.js"></script>
<script type="text/javascript" src="../../cookie.js"></script>
<link href="../../search/search.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="../../search/searchdata.js"></script>
<script type="text/javascript" src="../../search/search.js"></script>
<script type="text/javascript">
window.MathJax = {
options: {
ignoreHtmlClass: 'tex2jax_ignore',
processHtmlClass: 'tex2jax_process'
},
loader: {
load: ['[tex]/ams']
},
tex: {
macros: {},
packages: ['base','configmacros','ams']
}
};
</script>
<script type="text/javascript" id="MathJax-script" async="async" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-chtml.js"></script>
<link href="../../doxygen.css" rel="stylesheet" type="text/css" />
<link href="../../doxygen-awesome.css" rel="stylesheet" type="text/css"/>
</head>
<body>
<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
<div id="titlearea">
<table cellspacing="0" cellpadding="0">
<tbody>
<tr id="projectrow">
<td id="projectlogo"><img alt="Logo" src="../../project_logo.png"/></td>
<td id="projectalign">
<div id="projectname">TheAlgorithms/C++<span id="projectnumber">&#160;1.0.0</span>
</div>
<div id="projectbrief">All the algorithms implemented in C++</div>
</td>
</tr>
</tbody>
</table>
</div>
<!-- end header part -->
<!-- Generated by Doxygen 1.12.0 -->
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&amp;dn=expat.txt MIT */
var searchBox = new SearchBox("searchBox", "../../search/",'.html');
/* @license-end */
</script>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&amp;dn=expat.txt MIT */
$(function() { codefold.init(1); });
/* @license-end */
</script>
<script type="text/javascript" src="../../menudata.js"></script>
<script type="text/javascript" src="../../menu.js"></script>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&amp;dn=expat.txt MIT */
$(function() {
initMenu('../../',true,false,'search.php','Search',true);
$(function() { init_search(); });
});
/* @license-end */
</script>
<div id="main-nav"></div>
</div><!-- top -->
<div id="side-nav" class="ui-resizable side-nav-resizable">
<div id="nav-tree">
<div id="nav-tree-contents">
<div id="nav-sync" class="sync"></div>
</div>
</div>
<div id="splitbar" style="-moz-user-select:none;"
class="ui-resizable-handle">
</div>
</div>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&amp;dn=expat.txt MIT */
$(function(){initNavTree('d7/d6a/bisection__method_8cpp_source.html','../../'); initResizable(true); });
/* @license-end */
</script>
<div id="doc-content">
<!-- window showing the filter options -->
<div id="MSearchSelectWindow"
onmouseover="return searchBox.OnSearchSelectShow()"
onmouseout="return searchBox.OnSearchSelectHide()"
onkeydown="return searchBox.OnSearchSelectKey(event)">
</div>
<!-- iframe showing the search results (closed by default) -->
<div id="MSearchResultsWindow">
<div id="MSearchResults">
<div class="SRPage">
<div id="SRIndex">
<div id="SRResults"></div>
<div class="SRStatus" id="Loading">Loading...</div>
<div class="SRStatus" id="Searching">Searching...</div>
<div class="SRStatus" id="NoMatches">No Matches</div>
</div>
</div>
</div>
</div>
<div class="header">
<div class="headertitle"><div class="title">bisection_method.cpp</div></div>
</div><!--header-->
<div class="contents">
<a href="../../d7/d6a/bisection__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>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="preprocessor">#include &lt;cmath&gt;</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include &lt;iostream&gt;</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="preprocessor">#include &lt;limits&gt;</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> </div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="preprocessor">#define EPSILON \</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="preprocessor"> 1e-6 </span><span class="comment">// std::numeric_limits&lt;double&gt;::epsilon() ///&lt; system accuracy limit</span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"><a class="line" href="../../d7/d6a/bisection__method_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14"> 22</a></span><span class="preprocessor">#define MAX_ITERATIONS 50000 </span></div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> </div>
<div class="foldopen" id="foldopen00026" data-start="{" data-end="}">
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"><a class="line" href="../../d7/d6a/bisection__method_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d"> 26</a></span><span class="keyword">static</span> <span class="keywordtype">double</span> <a class="code hl_function" href="../../d7/d6a/bisection__method_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(<span class="keywordtype">double</span> i) {</div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> <span class="keywordflow">return</span> (std::pow(i, 3) - (4 * i) - 9); <span class="comment">// original equation</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span>}</div>
</div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> </div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="foldopen" id="foldopen00032" data-start="{" data-end="}">
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"><a class="line" href="../../d7/d6a/bisection__method_8cpp.html#a1ab31b90bc584c635ec159468ceed9b2"> 32</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../d7/d6a/bisection__method_8cpp.html#a1ab31b90bc584c635ec159468ceed9b2">sgn</a>(T val) {</div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> <span class="keywordflow">return</span> (T(0) &lt; val) - (val &lt; T(0));</div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span>}</div>
</div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> </div>
<div class="foldopen" id="foldopen00037" data-start="{" data-end="}">
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"><a class="line" href="../../d7/d6a/bisection__method_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4"> 37</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../d7/d6a/bisection__method_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <span class="keywordtype">double</span> a = -1, b = 1, x, z;</div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> <span class="keywordtype">int</span> i;</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> </div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <span class="comment">// loop to find initial intervals a, b</span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_define" href="../../d7/d6a/bisection__method_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">MAX_ITERATIONS</a>; i++) {</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> z = <a class="code hl_function" href="../../d7/d6a/bisection__method_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(a);</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> x = <a class="code hl_function" href="../../d7/d6a/bisection__method_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(b);</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="keywordflow">if</span> (<a class="code hl_function" href="../../d7/d6a/bisection__method_8cpp.html#a1ab31b90bc584c635ec159468ceed9b2">sgn</a>(z) == <a class="code hl_function" href="../../d7/d6a/bisection__method_8cpp.html#a1ab31b90bc584c635ec159468ceed9b2">sgn</a>(x)) { <span class="comment">// same signs, increase interval</span></div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> b++;</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> a--;</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> } <span class="keywordflow">else</span> { <span class="comment">// if opposite signs, we got our interval</span></div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> }</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> }</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> </div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> std::cout &lt;&lt; <span class="stringliteral">&quot;\nFirst initial: &quot;</span> &lt;&lt; a;</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> std::cout &lt;&lt; <span class="stringliteral">&quot;\nSecond initial: &quot;</span> &lt;&lt; b;</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> </div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="comment">// start iterations</span></div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code hl_define" href="../../d7/d6a/bisection__method_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">MAX_ITERATIONS</a>; i++) {</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> x = (a + b) / 2;</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> z = <a class="code hl_function" href="../../d7/d6a/bisection__method_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(x);</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> std::cout &lt;&lt; <span class="stringliteral">&quot;\n\nz: &quot;</span> &lt;&lt; z &lt;&lt; <span class="stringliteral">&quot;\t[&quot;</span> &lt;&lt; a &lt;&lt; <span class="stringliteral">&quot; , &quot;</span> &lt;&lt; b</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> &lt;&lt; <span class="stringliteral">&quot; | Bisect: &quot;</span> &lt;&lt; x &lt;&lt; <span class="stringliteral">&quot;]&quot;</span>;</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> </div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="keywordflow">if</span> (z &lt; 0) {</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> a = x;</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> b = x;</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> }</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> </div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="keywordflow">if</span> (std::abs(z) &lt; EPSILON) <span class="comment">// stoping criteria</span></div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> }</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> </div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> std::cout &lt;&lt; <span class="stringliteral">&quot;\n\nRoot: &quot;</span> &lt;&lt; x &lt;&lt; <span class="stringliteral">&quot;\t\tSteps: &quot;</span> &lt;&lt; i &lt;&lt; std::endl;</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span>}</div>
</div>
<div class="ttc" id="abisection__method_8cpp_html_a0a3abbca80bc98e7abcb3ae73abe0f14"><div class="ttname"><a href="../../d7/d6a/bisection__method_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">MAX_ITERATIONS</a></div><div class="ttdeci">#define MAX_ITERATIONS</div><div class="ttdoc">Maximum number of iterations to check.</div><div class="ttdef"><b>Definition</b> <a href="#l00022">bisection_method.cpp:22</a></div></div>
<div class="ttc" id="abisection__method_8cpp_html_a1ab31b90bc584c635ec159468ceed9b2"><div class="ttname"><a href="../../d7/d6a/bisection__method_8cpp.html#a1ab31b90bc584c635ec159468ceed9b2">sgn</a></div><div class="ttdeci">int sgn(T val)</div><div class="ttdef"><b>Definition</b> <a href="#l00032">bisection_method.cpp:32</a></div></div>
<div class="ttc" id="abisection__method_8cpp_html_a2003b5b2dcfff0769b957ab5c968b03d"><div class="ttname"><a href="../../d7/d6a/bisection__method_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a></div><div class="ttdeci">static double eq(double i)</div><div class="ttdef"><b>Definition</b> <a href="#l00026">bisection_method.cpp:26</a></div></div>
<div class="ttc" id="abisection__method_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d7/d6a/bisection__method_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition</b> <a href="#l00037">bisection_method.cpp:37</a></div></div>
</div><!-- fragment --></div><!-- contents -->
</div><!-- doc-content -->
<!-- start footer part -->
<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="../../d7/d6a/bisection__method_8cpp.html">bisection_method.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>
</ul>
</div>
</body>
</html>
Reference in New Issue View Git Blame Copy Permalink