mirror of
https://github.com/TheAlgorithms/C-Plus-Plus.git
synced 2026-03-21 12:23:13 +08:00
397 lines
28 KiB
HTML
397 lines
28 KiB
HTML
<!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">
|
|
<head>
|
|
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
|
|
<meta http-equiv="X-UA-Compatible" content="IE=9"/>
|
|
<meta name="generator" content="Doxygen 1.9.1"/>
|
|
<meta name="viewport" content="width=device-width, initial-scale=1"/>
|
|
<title>Algorithms_in_C++: numerical_methods/false_position.cpp File Reference</title>
|
|
<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>
|
|
<link href="../../navtree.css" rel="stylesheet" type="text/css"/>
|
|
<script type="text/javascript" src="../../resize.js"></script>
|
|
<script type="text/javascript" src="../../navtreedata.js"></script>
|
|
<script type="text/javascript" src="../../navtree.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/x-mathjax-config">
|
|
MathJax.Hub.Config({
|
|
extensions: ["tex2jax.js", "TeX/AMSmath.js", "TeX/AMSsymbols.js"],
|
|
jax: ["input/TeX","output/HTML-CSS"],
|
|
});
|
|
</script>
|
|
<script type="text/javascript" async="async" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.7/MathJax.js?config=TeX-MML-AM_CHTML/MathJax.js"></script>
|
|
<link href="../../doxygen.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 style="height: 56px;">
|
|
<td id="projectalign" style="padding-left: 0.5em;">
|
|
<div id="projectname">Algorithms_in_C++
|
|
 <span id="projectnumber">1.0.0</span>
|
|
</div>
|
|
<div id="projectbrief">Set of algorithms implemented in C++.</div>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</div>
|
|
<!-- end header part -->
|
|
<!-- Generated by Doxygen 1.9.1 -->
|
|
<script type="text/javascript">
|
|
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&dn=gpl-2.0.txt GPL-v2 */
|
|
var searchBox = new SearchBox("searchBox", "../../search",false,'Search','.html');
|
|
/* @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:cf05388f2679ee054f2beb29a391d25f4e673ac3&dn=gpl-2.0.txt GPL-v2 */
|
|
$(function() {
|
|
initMenu('../../',true,false,'search.php','Search');
|
|
$(document).ready(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:cf05388f2679ee054f2beb29a391d25f4e673ac3&dn=gpl-2.0.txt GPL-v2 */
|
|
$(document).ready(function(){initNavTree('dd/d29/false__position_8cpp.html','../../'); initResizable(); });
|
|
/* @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">
|
|
<iframe src="javascript:void(0)" frameborder="0"
|
|
name="MSearchResults" id="MSearchResults">
|
|
</iframe>
|
|
</div>
|
|
|
|
<div class="header">
|
|
<div class="summary">
|
|
<a href="#namespaces">Namespaces</a> |
|
|
<a href="#func-members">Functions</a> </div>
|
|
<div class="headertitle">
|
|
<div class="title">false_position.cpp File Reference</div> </div>
|
|
</div><!--header-->
|
|
<div class="contents">
|
|
|
|
<p>Solve the equation \(f(x)=0\) using <a href="https://en.wikipedia.org/wiki/Regula_falsi">false position method</a>, also known as the Secant method.
|
|
<a href="#details">More...</a></p>
|
|
<div class="textblock"><code>#include <cmath></code><br />
|
|
<code>#include <iostream></code><br />
|
|
</div><div class="textblock"><div class="dynheader">
|
|
Include dependency graph for false_position.cpp:</div>
|
|
<div class="dyncontent">
|
|
<div class="center"><iframe scrolling="no" frameborder="0" src="../../dc/de2/false__position_8cpp__incl.svg" width="178" height="127"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
|
|
</div>
|
|
</div>
|
|
</div><table class="memberdecls">
|
|
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="namespaces"></a>
|
|
Namespaces</h2></td></tr>
|
|
<tr class="memitem:d1/de0/namespacenumerical__methods"><td class="memItemLeft" align="right" valign="top">  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/de0/namespacenumerical__methods.html">numerical_methods</a></td></tr>
|
|
<tr class="memdesc:d1/de0/namespacenumerical__methods"><td class="mdescLeft"> </td><td class="mdescRight">for io operations <br /></td></tr>
|
|
<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
|
|
<tr class="memitem:df/dea/namespacefalse__position"><td class="memItemLeft" align="right" valign="top">  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dea/namespacefalse__position.html">false_position</a></td></tr>
|
|
<tr class="memdesc:df/dea/namespacefalse__position"><td class="mdescLeft"> </td><td class="mdescRight">Functions for <a href="https://en.wikipedia.org/wiki/Regula_falsi">False Position</a> method. <br /></td></tr>
|
|
<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
|
|
</table><table class="memberdecls">
|
|
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
|
|
Functions</h2></td></tr>
|
|
<tr class="memitem:a85a6ec58b5064d63d4f0df3854496713"><td class="memItemLeft" align="right" valign="top">static float </td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d29/false__position_8cpp.html#a85a6ec58b5064d63d4f0df3854496713">numerical_methods::false_position::eq</a> (float x)</td></tr>
|
|
<tr class="memdesc:a85a6ec58b5064d63d4f0df3854496713"><td class="mdescLeft"> </td><td class="mdescRight">This function gives the value of f(x) for given x. <a href="../../dd/d29/false__position_8cpp.html#a85a6ec58b5064d63d4f0df3854496713">More...</a><br /></td></tr>
|
|
<tr class="separator:a85a6ec58b5064d63d4f0df3854496713"><td class="memSeparator" colspan="2"> </td></tr>
|
|
<tr class="memitem:a7d69b49dc37da1c02b3ab8c7fe783494"><td class="memItemLeft" align="right" valign="top">static float </td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d29/false__position_8cpp.html#a7d69b49dc37da1c02b3ab8c7fe783494">numerical_methods::false_position::regula_falsi</a> (float x1, float x2, float y1, float y2)</td></tr>
|
|
<tr class="memdesc:a7d69b49dc37da1c02b3ab8c7fe783494"><td class="mdescLeft"> </td><td class="mdescRight">This function finds root of the equation in given interval i.e. (x1,x2). <a href="../../dd/d29/false__position_8cpp.html#a7d69b49dc37da1c02b3ab8c7fe783494">More...</a><br /></td></tr>
|
|
<tr class="separator:a7d69b49dc37da1c02b3ab8c7fe783494"><td class="memSeparator" colspan="2"> </td></tr>
|
|
<tr class="memitem:a85cb7bfb90abc898e042d624372c5345"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d29/false__position_8cpp.html#a85cb7bfb90abc898e042d624372c5345">numerical_methods::false_position::printRoot</a> (float root, const int16_t &count)</td></tr>
|
|
<tr class="memdesc:a85cb7bfb90abc898e042d624372c5345"><td class="mdescLeft"> </td><td class="mdescRight">This function prints roots of the equation. <a href="../../dd/d29/false__position_8cpp.html#a85cb7bfb90abc898e042d624372c5345">More...</a><br /></td></tr>
|
|
<tr class="separator:a85cb7bfb90abc898e042d624372c5345"><td class="memSeparator" colspan="2"> </td></tr>
|
|
<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d29/false__position_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
|
|
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft"> </td><td class="mdescRight">Main function. <a href="../../dd/d29/false__position_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">More...</a><br /></td></tr>
|
|
<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2"> </td></tr>
|
|
</table>
|
|
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
|
|
<div class="textblock"><p>Solve the equation \(f(x)=0\) using <a href="https://en.wikipedia.org/wiki/Regula_falsi">false position method</a>, also known as the Secant method. </p>
|
|
<p>First, multiple intervals are selected with the interval gap provided. Separate recursive function called for every root. Roots are printed Separatelt.</p>
|
|
<p>For an interval [a,b] \(a\) and \(b\) such that \(f(a)<0\) and \(f(b)>0\), then the \((i+1)^\text{th}\) approximation is given by: </p><p class="formulaDsp">
|
|
\[ x_{i+1} = \frac{a_i\cdot f(b_i) - b_i\cdot f(a_i)}{f(b_i) - f(a_i)} \]
|
|
</p>
|
|
<p> For the next iteration, the interval is selected as: \([a,x]\) if \(x>0\) or \([x,b]\) if \(x<0\). The Process is continued till a close enough approximation is achieved.</p>
|
|
<dl class="section see"><dt>See also</dt><dd><a class="el" href="../../de/dd3/newton__raphson__method_8cpp.html" title="Solve the equation using Newton-Raphson method for both real and complex solutions.">newton_raphson_method.cpp</a>, <a class="el" href="../../d7/d6a/bisection__method_8cpp.html" title="Solve the equation using bisection method">bisection_method.cpp</a></dd></dl>
|
|
<dl class="section author"><dt>Author</dt><dd>Unknown author </dd>
|
|
<dd>
|
|
<a href="https://github.com/sampatil578">Samruddha Patil</a> </dd></dl>
|
|
</div><h2 class="groupheader">Function Documentation</h2>
|
|
<a id="a85a6ec58b5064d63d4f0df3854496713"></a>
|
|
<h2 class="memtitle"><span class="permalink"><a href="#a85a6ec58b5064d63d4f0df3854496713">◆ </a></span>eq()</h2>
|
|
|
|
<div class="memitem">
|
|
<div class="memproto">
|
|
<table class="mlabels">
|
|
<tr>
|
|
<td class="mlabels-left">
|
|
<table class="memname">
|
|
<tr>
|
|
<td class="memname">static float numerical_methods::false_position::eq </td>
|
|
<td>(</td>
|
|
<td class="paramtype">float </td>
|
|
<td class="paramname"><em>x</em></td><td>)</td>
|
|
<td></td>
|
|
</tr>
|
|
</table>
|
|
</td>
|
|
<td class="mlabels-right">
|
|
<span class="mlabels"><span class="mlabel">static</span></span> </td>
|
|
</tr>
|
|
</table>
|
|
</div><div class="memdoc">
|
|
|
|
<p>This function gives the value of f(x) for given x. </p>
|
|
<dl class="params"><dt>Parameters</dt><dd>
|
|
<table class="params">
|
|
<tr><td class="paramname">x</td><td>value for which we have to find value of f(x). </td></tr>
|
|
</table>
|
|
</dd>
|
|
</dl>
|
|
<dl class="section return"><dt>Returns</dt><dd>value of f(x) for given x. </dd></dl>
|
|
<div class="fragment"><div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  {</div>
|
|
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  <span class="keywordflow">return</span> (x * x - x); <span class="comment">// original equation</span></div>
|
|
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> }</div>
|
|
</div><!-- fragment --><div class="dynheader">
|
|
Here is the call graph for this function:</div>
|
|
<div class="dyncontent">
|
|
<div class="center"><iframe scrolling="no" frameborder="0" src="../../dd/d29/false__position_8cpp_a85a6ec58b5064d63d4f0df3854496713_cgraph.svg" width="154" height="76"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
|
|
</div>
|
|
</div>
|
|
|
|
</div>
|
|
</div>
|
|
<a id="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
|
|
<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">◆ </a></span>main()</h2>
|
|
|
|
<div class="memitem">
|
|
<div class="memproto">
|
|
<table class="memname">
|
|
<tr>
|
|
<td class="memname">int main </td>
|
|
<td>(</td>
|
|
<td class="paramtype">void </td>
|
|
<td class="paramname"></td><td>)</td>
|
|
<td></td>
|
|
</tr>
|
|
</table>
|
|
</div><div class="memdoc">
|
|
|
|
<p>Main function. </p>
|
|
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
|
|
<div class="fragment"><div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  {</div>
|
|
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="keywordtype">float</span> a = 0, b = 0, i = 0, root = 0;</div>
|
|
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  int16_t count = 0;</div>
|
|
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  <span class="keywordtype">float</span> range =</div>
|
|
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  100000; <span class="comment">// Range in which we have to find the root. (-range,range)</span></div>
|
|
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  <span class="keywordtype">float</span> gap = 0.5; <span class="comment">// interval gap. lesser the gap more the accuracy</span></div>
|
|
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  a = <a class="code" href="../../dd/d29/false__position_8cpp.html#a85a6ec58b5064d63d4f0df3854496713">numerical_methods::false_position::eq</a>((-1) * range);</div>
|
|
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  i = ((-1) * range + gap);</div>
|
|
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <span class="comment">// while loop for selecting proper interval in provided range and with</span></div>
|
|
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  <span class="comment">// provided interval gap.</span></div>
|
|
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="keywordflow">while</span> (i <= range) {</div>
|
|
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  b = <a class="code" href="../../dd/d29/false__position_8cpp.html#a85a6ec58b5064d63d4f0df3854496713">numerical_methods::false_position::eq</a>(i);</div>
|
|
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  <span class="keywordflow">if</span> (b == 0) {</div>
|
|
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  count++;</div>
|
|
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  <a class="code" href="../../dd/d29/false__position_8cpp.html#a85cb7bfb90abc898e042d624372c5345">numerical_methods::false_position::printRoot</a>(i, count);</div>
|
|
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  }</div>
|
|
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  <span class="keywordflow">if</span> (a * b < 0) {</div>
|
|
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  root = <a class="code" href="../../dd/d29/false__position_8cpp.html#a7d69b49dc37da1c02b3ab8c7fe783494">numerical_methods::false_position::regula_falsi</a>(i - gap, i,</div>
|
|
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  a, b);</div>
|
|
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  count++;</div>
|
|
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  <a class="code" href="../../dd/d29/false__position_8cpp.html#a85cb7bfb90abc898e042d624372c5345">numerical_methods::false_position::printRoot</a>(root, count);</div>
|
|
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  }</div>
|
|
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  a = b;</div>
|
|
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  i += gap;</div>
|
|
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  }</div>
|
|
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  <span class="keywordflow">return</span> 0;</div>
|
|
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span> }</div>
|
|
<div class="ttc" id="afalse__position_8cpp_html_a7d69b49dc37da1c02b3ab8c7fe783494"><div class="ttname"><a href="../../dd/d29/false__position_8cpp.html#a7d69b49dc37da1c02b3ab8c7fe783494">numerical_methods::false_position::regula_falsi</a></div><div class="ttdeci">static float regula_falsi(float x1, float x2, float y1, float y2)</div><div class="ttdoc">This function finds root of the equation in given interval i.e. (x1,x2).</div><div class="ttdef"><b>Definition:</b> false_position.cpp:55</div></div>
|
|
<div class="ttc" id="afalse__position_8cpp_html_a85a6ec58b5064d63d4f0df3854496713"><div class="ttname"><a href="../../dd/d29/false__position_8cpp.html#a85a6ec58b5064d63d4f0df3854496713">numerical_methods::false_position::eq</a></div><div class="ttdeci">static float eq(float x)</div><div class="ttdoc">This function gives the value of f(x) for given x.</div><div class="ttdef"><b>Definition:</b> false_position.cpp:44</div></div>
|
|
<div class="ttc" id="afalse__position_8cpp_html_a85cb7bfb90abc898e042d624372c5345"><div class="ttname"><a href="../../dd/d29/false__position_8cpp.html#a85cb7bfb90abc898e042d624372c5345">numerical_methods::false_position::printRoot</a></div><div class="ttdeci">void printRoot(float root, const int16_t &count)</div><div class="ttdoc">This function prints roots of the equation.</div><div class="ttdef"><b>Definition:</b> false_position.cpp:84</div></div>
|
|
</div><!-- fragment -->
|
|
</div>
|
|
</div>
|
|
<a id="a85cb7bfb90abc898e042d624372c5345"></a>
|
|
<h2 class="memtitle"><span class="permalink"><a href="#a85cb7bfb90abc898e042d624372c5345">◆ </a></span>printRoot()</h2>
|
|
|
|
<div class="memitem">
|
|
<div class="memproto">
|
|
<table class="memname">
|
|
<tr>
|
|
<td class="memname">void numerical_methods::false_position::printRoot </td>
|
|
<td>(</td>
|
|
<td class="paramtype">float </td>
|
|
<td class="paramname"><em>root</em>, </td>
|
|
</tr>
|
|
<tr>
|
|
<td class="paramkey"></td>
|
|
<td></td>
|
|
<td class="paramtype">const int16_t & </td>
|
|
<td class="paramname"><em>count</em> </td>
|
|
</tr>
|
|
<tr>
|
|
<td></td>
|
|
<td>)</td>
|
|
<td></td><td></td>
|
|
</tr>
|
|
</table>
|
|
</div><div class="memdoc">
|
|
|
|
<p>This function prints roots of the equation. </p>
|
|
<dl class="params"><dt>Parameters</dt><dd>
|
|
<table class="params">
|
|
<tr><td class="paramname">root</td><td>which we have to print. </td></tr>
|
|
<tr><td class="paramname">count</td><td>which is count of the root in an interval [-range,range]. </td></tr>
|
|
</table>
|
|
</dd>
|
|
</dl>
|
|
<div class="fragment"><div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  {</div>
|
|
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="keywordflow">if</span> (count == 1) {</div>
|
|
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Your 1st root is : "</span> << root << <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
|
|
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (count == 2) {</div>
|
|
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Your 2nd root is : "</span> << root << <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
|
|
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (count == 3) {</div>
|
|
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Your 3rd root is : "</span> << root << <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
|
|
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  } <span class="keywordflow">else</span> {</div>
|
|
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Your "</span> << count << <span class="stringliteral">"th root is : "</span> << root << <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
|
|
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  }</div>
|
|
<div class="line"><a name="l00094"></a><span class="lineno"> 94</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="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><!-- fragment --><div class="dynheader">
|
|
Here is the call graph for this function:</div>
|
|
<div class="dyncontent">
|
|
<div class="center"><iframe scrolling="no" frameborder="0" src="../../dd/d29/false__position_8cpp_a85cb7bfb90abc898e042d624372c5345_cgraph.svg" width="174" height="76"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
|
|
</div>
|
|
</div>
|
|
|
|
</div>
|
|
</div>
|
|
<a id="a7d69b49dc37da1c02b3ab8c7fe783494"></a>
|
|
<h2 class="memtitle"><span class="permalink"><a href="#a7d69b49dc37da1c02b3ab8c7fe783494">◆ </a></span>regula_falsi()</h2>
|
|
|
|
<div class="memitem">
|
|
<div class="memproto">
|
|
<table class="mlabels">
|
|
<tr>
|
|
<td class="mlabels-left">
|
|
<table class="memname">
|
|
<tr>
|
|
<td class="memname">static float numerical_methods::false_position::regula_falsi </td>
|
|
<td>(</td>
|
|
<td class="paramtype">float </td>
|
|
<td class="paramname"><em>x1</em>, </td>
|
|
</tr>
|
|
<tr>
|
|
<td class="paramkey"></td>
|
|
<td></td>
|
|
<td class="paramtype">float </td>
|
|
<td class="paramname"><em>x2</em>, </td>
|
|
</tr>
|
|
<tr>
|
|
<td class="paramkey"></td>
|
|
<td></td>
|
|
<td class="paramtype">float </td>
|
|
<td class="paramname"><em>y1</em>, </td>
|
|
</tr>
|
|
<tr>
|
|
<td class="paramkey"></td>
|
|
<td></td>
|
|
<td class="paramtype">float </td>
|
|
<td class="paramname"><em>y2</em> </td>
|
|
</tr>
|
|
<tr>
|
|
<td></td>
|
|
<td>)</td>
|
|
<td></td><td></td>
|
|
</tr>
|
|
</table>
|
|
</td>
|
|
<td class="mlabels-right">
|
|
<span class="mlabels"><span class="mlabel">static</span></span> </td>
|
|
</tr>
|
|
</table>
|
|
</div><div class="memdoc">
|
|
|
|
<p>This function finds root of the equation in given interval i.e. (x1,x2). </p>
|
|
<dl class="params"><dt>Parameters</dt><dd>
|
|
<table class="params">
|
|
<tr><td class="paramname">x1,x2</td><td>values for an interval in which root is present. </td></tr>
|
|
<tr><td class="paramname">y1,y2</td><td>values of function at x1, x2 espectively. </td></tr>
|
|
</table>
|
|
</dd>
|
|
</dl>
|
|
<dl class="section return"><dt>Returns</dt><dd>root of the equation in the given interval. </dd></dl>
|
|
<div class="fragment"><div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  {</div>
|
|
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="keywordtype">float</span> diff = x1 - x2;</div>
|
|
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  <span class="keywordflow">if</span> (diff < 0) {</div>
|
|
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  diff = (-1) * diff;</div>
|
|
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  }</div>
|
|
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <span class="keywordflow">if</span> (diff < 0.00001) {</div>
|
|
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  <span class="keywordflow">if</span> (y1 < 0) {</div>
|
|
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  y1 = -y1;</div>
|
|
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  }</div>
|
|
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <span class="keywordflow">if</span> (y2 < 0) {</div>
|
|
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  y2 = -y2;</div>
|
|
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  }</div>
|
|
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="keywordflow">if</span> (y1 < y2) {</div>
|
|
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="keywordflow">return</span> x1;</div>
|
|
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  } <span class="keywordflow">else</span> {</div>
|
|
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="keywordflow">return</span> x2;</div>
|
|
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  }</div>
|
|
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  }</div>
|
|
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  <span class="keywordtype">float</span> x3 = 0, y3 = 0;</div>
|
|
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  x3 = x1 - (x1 - x2) * (y1) / (y1 - y2);</div>
|
|
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  y3 = <a class="code" href="../../dd/d29/false__position_8cpp.html#a85a6ec58b5064d63d4f0df3854496713">eq</a>(x3);</div>
|
|
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="keywordflow">return</span> <a class="code" href="../../dd/d29/false__position_8cpp.html#a7d69b49dc37da1c02b3ab8c7fe783494">regula_falsi</a>(x2, x3, y2, y3);</div>
|
|
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span> }</div>
|
|
</div><!-- fragment --><div class="dynheader">
|
|
Here is the call graph for this function:</div>
|
|
<div class="dyncontent">
|
|
<div class="center"><iframe scrolling="no" frameborder="0" src="../../dd/d29/false__position_8cpp_a7d69b49dc37da1c02b3ab8c7fe783494_cgraph.svg" width="378" height="76"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
|
|
</div>
|
|
</div>
|
|
|
|
</div>
|
|
</div>
|
|
</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="../../dd/d29/false__position_8cpp.html">false_position.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> 1.9.1 </li>
|
|
</ul>
|
|
</div>
|
|
</body>
|
|
</html>
|