mirror of
https://github.com/TheAlgorithms/C-Plus-Plus.git
synced 2026-03-22 04:42:10 +08:00
392 lines
26 KiB
HTML
392 lines
26 KiB
HTML
<!-- 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 1.14.0"/>
|
|
<meta name="viewport" content="width=device-width, initial-scale=1"/>
|
|
<title>TheAlgorithms/C++: numerical_methods/false_position.cpp File Reference</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="../../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"> 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 1.14.0 -->
|
|
<script type="text/javascript">
|
|
var searchBox = new SearchBox("searchBox", "../../search/",'.html');
|
|
</script>
|
|
<script type="text/javascript">
|
|
$(function() { codefold.init(); });
|
|
</script>
|
|
<script type="text/javascript" src="../../menudata.js"></script>
|
|
<script type="text/javascript" src="../../menu.js"></script>
|
|
<script type="text/javascript">
|
|
$(function() {
|
|
initMenu('../../',true,false,'search.php','Search',true);
|
|
$(function() { init_search(); });
|
|
});
|
|
</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">
|
|
$(function(){initNavTree('dd/d29/false__position_8cpp.html','../../',''); });
|
|
</script>
|
|
<div id="container">
|
|
<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">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" target="_blank">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" loading="lazy" frameborder="0" src="../../dc/de2/false__position_8cpp__incl.svg" width="178" height="126"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
|
|
</div>
|
|
</div>
|
|
<p><a href="../../dd/d29/false__position_8cpp_source.html">Go to the source code of this file.</a></p>
|
|
<table class="memberdecls">
|
|
<tr class="heading"><td colspan="2"><h2 id="header-namespaces" class="groupheader"><a id="namespaces" name="namespaces"></a>
|
|
Namespaces</h2></td></tr>
|
|
<tr class="memitem:numerical_5Fmethods" id="r_numerical_5Fmethods"><td class="memItemLeft" align="right" valign="top">namespace  </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 assert <br /></td></tr>
|
|
<tr class="memitem:false_5Fposition" id="r_false_5Fposition"><td class="memItemLeft" align="right" valign="top">namespace  </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 [False Position] (<a href="https://en.wikipedia.org/wiki/Regula_falsi">https://en.wikipedia.org/wiki/Regula_falsi</a>) method. <br /></td></tr>
|
|
</table><table class="memberdecls">
|
|
<tr class="heading"><td colspan="2"><h2 id="header-func-members" class="groupheader"><a id="func-members" name="func-members"></a>
|
|
Functions</h2></td></tr>
|
|
<tr class="memitem:a85a6ec58b5064d63d4f0df3854496713" id="r_a85a6ec58b5064d63d4f0df3854496713"><td class="memItemLeft" align="right" valign="top">static float </td><td class="memItemRight" valign="bottom"><a class="el" href="#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. <br /></td></tr>
|
|
<tr class="memitem:a7d69b49dc37da1c02b3ab8c7fe783494" id="r_a7d69b49dc37da1c02b3ab8c7fe783494"><td class="memItemLeft" align="right" valign="top">static float </td><td class="memItemRight" valign="bottom"><a class="el" href="#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). <br /></td></tr>
|
|
<tr class="memitem:a85cb7bfb90abc898e042d624372c5345" id="r_a85cb7bfb90abc898e042d624372c5345"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="#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. <br /></td></tr>
|
|
<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4" id="r_ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
|
|
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft"> </td><td class="mdescRight">Main function. <br /></td></tr>
|
|
</table>
|
|
<a name="details" id="details"></a><h2 id="header-details" 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" target="_blank">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" target="_blank">Samruddha Patil</a> </dd></dl>
|
|
|
|
<p class="definition">Definition in file <a class="el" href="../../dd/d29/false__position_8cpp_source.html">false_position.cpp</a>.</p>
|
|
</div><a name="doc-func-members" id="doc-func-members"></a><h2 id="header-doc-func-members" class="groupheader">Function Documentation</h2>
|
|
<a id="a85a6ec58b5064d63d4f0df3854496713" name="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">float numerical_methods::false_position::eq </td>
|
|
<td>(</td>
|
|
<td class="paramtype">float</td> <td class="paramname"><span class="paramname"><em>x</em></span></td><td>)</td>
|
|
<td></td>
|
|
</tr>
|
|
</table>
|
|
</td>
|
|
<td class="mlabels-right">
|
|
<span class="mlabels"><span class="mlabel static">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>
|
|
|
|
<p class="definition">Definition at line <a class="el" href="../../dd/d29/false__position_8cpp_source.html#l00044">44</a> of file <a class="el" href="../../dd/d29/false__position_8cpp_source.html">false_position.cpp</a>.</p>
|
|
<div class="fragment"><div class="line"><span class="lineno"> 44</span> {</div>
|
|
<div class="line"><span class="lineno"> 45</span> <span class="keywordflow">return</span> (x * x - x); <span class="comment">// original equation</span></div>
|
|
<div class="line"><span class="lineno"> 46</span>}</div>
|
|
</div><!-- fragment -->
|
|
</div>
|
|
</div>
|
|
<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="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"><span class="paramname"><em></em></span></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>
|
|
|
|
<p class="definition">Definition at line <a class="el" href="../../dd/d29/false__position_8cpp_source.html#l00102">102</a> of file <a class="el" href="../../dd/d29/false__position_8cpp_source.html">false_position.cpp</a>.</p>
|
|
<div class="fragment"><div class="line"><span class="lineno"> 102</span> {</div>
|
|
<div class="line"><span class="lineno"> 103</span> <span class="keywordtype">float</span> a = 0, b = 0, i = 0, root = 0;</div>
|
|
<div class="line"><span class="lineno"> 104</span> int16_t count = 0;</div>
|
|
<div class="line"><span class="lineno"> 105</span> <span class="keywordtype">float</span> range =</div>
|
|
<div class="line"><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"><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"><span class="lineno"> 108</span> a = <a class="code hl_function" href="#a85a6ec58b5064d63d4f0df3854496713">numerical_methods::false_position::eq</a>((-1) * range);</div>
|
|
<div class="line"><span class="lineno"> 109</span> i = ((-1) * range + gap);</div>
|
|
<div class="line"><span class="lineno"> 110</span> <span class="comment">// while loop for selecting proper interval in provided range and with</span></div>
|
|
<div class="line"><span class="lineno"> 111</span> <span class="comment">// provided interval gap.</span></div>
|
|
<div class="line"><span class="lineno"> 112</span> <span class="keywordflow">while</span> (i <= range) {</div>
|
|
<div class="line"><span class="lineno"> 113</span> b = <a class="code hl_function" href="#a85a6ec58b5064d63d4f0df3854496713">numerical_methods::false_position::eq</a>(i);</div>
|
|
<div class="line"><span class="lineno"> 114</span> <span class="keywordflow">if</span> (b == 0) {</div>
|
|
<div class="line"><span class="lineno"> 115</span> count++;</div>
|
|
<div class="line"><span class="lineno"> 116</span> <a class="code hl_function" href="#a85cb7bfb90abc898e042d624372c5345">numerical_methods::false_position::printRoot</a>(i, count);</div>
|
|
<div class="line"><span class="lineno"> 117</span> }</div>
|
|
<div class="line"><span class="lineno"> 118</span> <span class="keywordflow">if</span> (a * b < 0) {</div>
|
|
<div class="line"><span class="lineno"> 119</span> root = <a class="code hl_function" href="#a7d69b49dc37da1c02b3ab8c7fe783494">numerical_methods::false_position::regula_falsi</a>(i - gap, i,</div>
|
|
<div class="line"><span class="lineno"> 120</span> a, b);</div>
|
|
<div class="line"><span class="lineno"> 121</span> count++;</div>
|
|
<div class="line"><span class="lineno"> 122</span> <a class="code hl_function" href="#a85cb7bfb90abc898e042d624372c5345">numerical_methods::false_position::printRoot</a>(root, count);</div>
|
|
<div class="line"><span class="lineno"> 123</span> }</div>
|
|
<div class="line"><span class="lineno"> 124</span> a = b;</div>
|
|
<div class="line"><span class="lineno"> 125</span> i += gap;</div>
|
|
<div class="line"><span class="lineno"> 126</span> }</div>
|
|
<div class="line"><span class="lineno"> 127</span> <span class="keywordflow">return</span> 0;</div>
|
|
<div class="line"><span class="lineno"> 128</span>}</div>
|
|
<div class="ttc" id="afalse__position_8cpp_html_a7d69b49dc37da1c02b3ab8c7fe783494"><div class="ttname"><a href="#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> <a href="../../dd/d29/false__position_8cpp_source.html#l00055">false_position.cpp:55</a></div></div>
|
|
<div class="ttc" id="afalse__position_8cpp_html_a85a6ec58b5064d63d4f0df3854496713"><div class="ttname"><a href="#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> <a href="../../dd/d29/false__position_8cpp_source.html#l00044">false_position.cpp:44</a></div></div>
|
|
<div class="ttc" id="afalse__position_8cpp_html_a85cb7bfb90abc898e042d624372c5345"><div class="ttname"><a href="#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> <a href="../../dd/d29/false__position_8cpp_source.html#l00084">false_position.cpp:84</a></div></div>
|
|
</div><!-- fragment -->
|
|
</div>
|
|
</div>
|
|
<a id="a85cb7bfb90abc898e042d624372c5345" name="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"><span class="paramname"><em>root</em></span>, </td>
|
|
</tr>
|
|
<tr>
|
|
<td class="paramkey"></td>
|
|
<td></td>
|
|
<td class="paramtype">const int16_t &</td> <td class="paramname"><span class="paramname"><em>count</em></span> )</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>
|
|
|
|
<p class="definition">Definition at line <a class="el" href="../../dd/d29/false__position_8cpp_source.html#l00084">84</a> of file <a class="el" href="../../dd/d29/false__position_8cpp_source.html">false_position.cpp</a>.</p>
|
|
<div class="fragment"><div class="line"><span class="lineno"> 84</span> {</div>
|
|
<div class="line"><span class="lineno"> 85</span> <span class="keywordflow">if</span> (count == 1) {</div>
|
|
<div class="line"><span class="lineno"> 86</span> std::cout << <span class="stringliteral">"Your 1st root is : "</span> << root << std::endl;</div>
|
|
<div class="line"><span class="lineno"> 87</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (count == 2) {</div>
|
|
<div class="line"><span class="lineno"> 88</span> std::cout << <span class="stringliteral">"Your 2nd root is : "</span> << root << std::endl;</div>
|
|
<div class="line"><span class="lineno"> 89</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (count == 3) {</div>
|
|
<div class="line"><span class="lineno"> 90</span> std::cout << <span class="stringliteral">"Your 3rd root is : "</span> << root << std::endl;</div>
|
|
<div class="line"><span class="lineno"> 91</span> } <span class="keywordflow">else</span> {</div>
|
|
<div class="line"><span class="lineno"> 92</span> std::cout << <span class="stringliteral">"Your "</span> << count << <span class="stringliteral">"th root is : "</span> << root << std::endl;</div>
|
|
<div class="line"><span class="lineno"> 93</span> }</div>
|
|
<div class="line"><span class="lineno"> 94</span>}</div>
|
|
</div><!-- fragment -->
|
|
</div>
|
|
</div>
|
|
<a id="a7d69b49dc37da1c02b3ab8c7fe783494" name="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">float numerical_methods::false_position::regula_falsi </td>
|
|
<td>(</td>
|
|
<td class="paramtype">float</td> <td class="paramname"><span class="paramname"><em>x1</em></span>, </td>
|
|
</tr>
|
|
<tr>
|
|
<td class="paramkey"></td>
|
|
<td></td>
|
|
<td class="paramtype">float</td> <td class="paramname"><span class="paramname"><em>x2</em></span>, </td>
|
|
</tr>
|
|
<tr>
|
|
<td class="paramkey"></td>
|
|
<td></td>
|
|
<td class="paramtype">float</td> <td class="paramname"><span class="paramname"><em>y1</em></span>, </td>
|
|
</tr>
|
|
<tr>
|
|
<td class="paramkey"></td>
|
|
<td></td>
|
|
<td class="paramtype">float</td> <td class="paramname"><span class="paramname"><em>y2</em></span> )</td>
|
|
</tr>
|
|
</table>
|
|
</td>
|
|
<td class="mlabels-right">
|
|
<span class="mlabels"><span class="mlabel static">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>
|
|
|
|
<p class="definition">Definition at line <a class="el" href="../../dd/d29/false__position_8cpp_source.html#l00055">55</a> of file <a class="el" href="../../dd/d29/false__position_8cpp_source.html">false_position.cpp</a>.</p>
|
|
<div class="fragment"><div class="line"><span class="lineno"> 55</span> {</div>
|
|
<div class="line"><span class="lineno"> 56</span> <span class="keywordtype">float</span> diff = x1 - x2;</div>
|
|
<div class="line"><span class="lineno"> 57</span> <span class="keywordflow">if</span> (diff < 0) {</div>
|
|
<div class="line"><span class="lineno"> 58</span> diff = (-1) * diff;</div>
|
|
<div class="line"><span class="lineno"> 59</span> }</div>
|
|
<div class="line"><span class="lineno"> 60</span> <span class="keywordflow">if</span> (diff < 0.00001) {</div>
|
|
<div class="line"><span class="lineno"> 61</span> <span class="keywordflow">if</span> (y1 < 0) {</div>
|
|
<div class="line"><span class="lineno"> 62</span> y1 = -y1;</div>
|
|
<div class="line"><span class="lineno"> 63</span> }</div>
|
|
<div class="line"><span class="lineno"> 64</span> <span class="keywordflow">if</span> (y2 < 0) {</div>
|
|
<div class="line"><span class="lineno"> 65</span> y2 = -y2;</div>
|
|
<div class="line"><span class="lineno"> 66</span> }</div>
|
|
<div class="line"><span class="lineno"> 67</span> <span class="keywordflow">if</span> (y1 < y2) {</div>
|
|
<div class="line"><span class="lineno"> 68</span> <span class="keywordflow">return</span> x1;</div>
|
|
<div class="line"><span class="lineno"> 69</span> } <span class="keywordflow">else</span> {</div>
|
|
<div class="line"><span class="lineno"> 70</span> <span class="keywordflow">return</span> x2;</div>
|
|
<div class="line"><span class="lineno"> 71</span> }</div>
|
|
<div class="line"><span class="lineno"> 72</span> }</div>
|
|
<div class="line"><span class="lineno"> 73</span> <span class="keywordtype">float</span> x3 = 0, y3 = 0;</div>
|
|
<div class="line"><span class="lineno"> 74</span> x3 = x1 - (x1 - x2) * (y1) / (y1 - y2);</div>
|
|
<div class="line"><span class="lineno"> 75</span> y3 = <a class="code hl_function" href="#a85a6ec58b5064d63d4f0df3854496713">eq</a>(x3);</div>
|
|
<div class="line"><span class="lineno"> 76</span> <span class="keywordflow">return</span> <a class="code hl_function" href="#a7d69b49dc37da1c02b3ab8c7fe783494">regula_falsi</a>(x2, x3, y2, y3);</div>
|
|
<div class="line"><span class="lineno"> 77</span>}</div>
|
|
</div><!-- fragment -->
|
|
</div>
|
|
</div>
|
|
</div><!-- contents -->
|
|
</div><!-- doc-content -->
|
|
<div id="page-nav" class="page-nav-panel">
|
|
<div id="page-nav-resize-handle"></div>
|
|
<div id="page-nav-tree">
|
|
<div id="page-nav-contents">
|
|
</div><!-- page-nav-contents -->
|
|
</div><!-- page-nav-tree -->
|
|
</div><!-- page-nav -->
|
|
</div><!-- container -->
|
|
<!-- start footer part -->
|
|
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
|
|
<ul>
|
|
<li class="navelem"><a href="../../dir_9c6faab82c22511b50177aa2e38e2780.html">numerical_methods</a></li><li class="navelem"><a 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> 1.14.0 </li>
|
|
</ul>
|
|
</div>
|
|
</body>
|
|
</html>
|