backup/C-Plus-Plus
1
0
Fork 0
mirror of https://github.com/TheAlgorithms/C-Plus-Plus.git synced 2026-03-23 13:22:47 +08:00
Code Issues Projects Releases Wiki Activity

Documentation for 0c22356706

Browse Source
This commit is contained in:
github-actions
2020-10-30 11:37:21 +00:00
parent 1033b1c367
commit 008ae67aed
208 changed files with 4970 additions and 4621 deletions
Download Patch File Download Diff File Expand all files Collapse all files

297
dd/d29/false__position_8cpp.html
View File

@@ -91,7 +91,7 @@ $(document).ready(function(){initNavTree('dd/d29/false__position_8cpp.html','../
<div class="header">
<div class="summary">
<a href="#define-members">Macros</a> &#124;
<a href="#namespaces">Namespaces</a> &#124;
<a href="#func-members">Functions</a> </div>
<div class="headertitle">
<div class="title">false_position.cpp File Reference</div> </div>
@@ -101,46 +101,52 @@ $(document).ready(function(){initNavTree('dd/d29/false__position_8cpp.html','../
<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 &lt;cmath&gt;</code><br />
<code>#include &lt;cstdlib&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;limits&gt;</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="328" height="127"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
<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="define-members"></a>
Macros</h2></td></tr>
<tr class="memitem:a002b2f4894492820fe708b1b7e7c5e70"><td class="memItemLeft" align="right" valign="top"><a id="a002b2f4894492820fe708b1b7e7c5e70"></a>
#define&#160;</td><td class="memItemRight" valign="bottom"><b>EPSILON</b>&#160;&#160;&#160; 1e-6</td></tr>
<tr class="separator:a002b2f4894492820fe708b1b7e7c5e70"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a0a3abbca80bc98e7abcb3ae73abe0f14"><td class="memItemLeft" align="right" valign="top"><a id="a0a3abbca80bc98e7abcb3ae73abe0f14"></a>
#define&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d29/false__position_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">MAX_ITERATIONS</a>&#160;&#160;&#160;50000</td></tr>
<tr class="memdesc:a0a3abbca80bc98e7abcb3ae73abe0f14"><td class="mdescLeft">&#160;</td><td class="mdescRight">Maximum number of iterations to check. <br /></td></tr>
<tr class="separator:a0a3abbca80bc98e7abcb3ae73abe0f14"><td class="memSeparator" colspan="2">&#160;</td></tr>
<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"> &#160;</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">&#160;</td><td class="mdescRight">for io operations <br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:df/dea/namespacefalse__position"><td class="memItemLeft" align="right" valign="top"> &#160;</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">&#160;</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">&#160;</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:a2003b5b2dcfff0769b957ab5c968b03d"><td class="memItemLeft" align="right" valign="top">static double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d29/false__position_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a> (double i)</td></tr>
<tr class="separator:a2003b5b2dcfff0769b957ab5c968b03d"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a1ab31b90bc584c635ec159468ceed9b2"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a1ab31b90bc584c635ec159468ceed9b2"><td class="memTemplItemLeft" align="right" valign="top">int&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d29/false__position_8cpp.html#a1ab31b90bc584c635ec159468ceed9b2">sgn</a> (T val)</td></tr>
<tr class="separator:a1ab31b90bc584c635ec159468ceed9b2"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a85a6ec58b5064d63d4f0df3854496713"><td class="memItemLeft" align="right" valign="top">static float&#160;</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">&#160;</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">&#160;</td></tr>
<tr class="memitem:a7d69b49dc37da1c02b3ab8c7fe783494"><td class="memItemLeft" align="right" valign="top">static float&#160;</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">&#160;</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">&#160;</td></tr>
<tr class="memitem:a85cb7bfb90abc898e042d624372c5345"><td class="memItemLeft" align="right" valign="top">void&#160;</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 &amp;count)</td></tr>
<tr class="memdesc:a85cb7bfb90abc898e042d624372c5345"><td class="mdescLeft">&#160;</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">&#160;</td></tr>
<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</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">&#160;</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">&#160;</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>Given two points \(a\) and \(b\) such that \(f(a)&lt;0\) and \(f(b)&gt;0\), then the \((i+1)^\text{th}\) approximation is given by: </p><p class="formulaDsp">
<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 \(f(a)&lt;0\) and \(f(b)&gt;0\), 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 \(x&gt;0\) or \([x,b]\) if \(x&lt;0\). 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 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="a2003b5b2dcfff0769b957ab5c968b03d"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a2003b5b2dcfff0769b957ab5c968b03d">&#9670;&nbsp;</a></span>eq()</h2>
<a id="a85a6ec58b5064d63d4f0df3854496713"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a85a6ec58b5064d63d4f0df3854496713">&#9670;&nbsp;</a></span>eq()</h2>
<div class="memitem">
<div class="memproto">
@@ -149,10 +155,10 @@ Functions</h2></td></tr>
<td class="mlabels-left">
<table class="memname">
<tr>
<td class="memname">static double eq </td>
<td class="memname">static float numerical_methods::false_position::eq </td>
<td>(</td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>i</em></td><td>)</td>
<td class="paramtype">float&#160;</td>
<td class="paramname"><em>x</em></td><td>)</td>
<td></td>
</tr>
</table>
@@ -162,14 +168,22 @@ Functions</h2></td></tr>
</tr>
</table>
</div><div class="memdoc">
<p>define \(f(x)\) to find root for </p>
<div class="fragment"><div class="line"><a name="l00028"></a><span class="lineno"> 28</span>&#160; {</div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>&#160; <span class="keywordflow">return</span> (<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(i, 3) - (4 * i) - 9); <span class="comment">// origial equation</span></div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160;}</div>
<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>&#160; {</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; <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>&#160;}</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_a2003b5b2dcfff0769b957ab5c968b03d_cgraph.svg" width="170" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
<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>
@@ -190,85 +204,188 @@ Here is the call graph for this function:</div>
</tr>
</table>
</div><div class="memdoc">
<p>main function </p>
<div class="fragment"><div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; {</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; <span class="keywordtype">double</span> a = -1, b = 1, x, z, m, n, c;</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; <span class="keywordtype">int</span> i;</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; </div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; <span class="comment">// loop to find initial intervals a, b</span></div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code" href="../../dd/d29/false__position_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">MAX_ITERATIONS</a>; i++) {</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; z = <a class="code" href="../../dd/d29/false__position_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(a);</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; x = <a class="code" href="../../dd/d29/false__position_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(b);</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160; <span class="keywordflow">if</span> (<a class="code" href="../../dd/d29/false__position_8cpp.html#a1ab31b90bc584c635ec159468ceed9b2">sgn</a>(z) == <a class="code" href="../../dd/d29/false__position_8cpp.html#a1ab31b90bc584c635ec159468ceed9b2">sgn</a>(x)) { <span class="comment">// same signs, increase interval</span></div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; b++;</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; a--;</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; } <span class="keywordflow">else</span> { <span class="comment">// if opposite signs, we got our interval</span></div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160; }</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; }</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; </div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nFirst initial: &quot;</span> &lt;&lt; a;</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nSecond initial: &quot;</span> &lt;&lt; b;</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; </div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; <span class="keywordflow">for</span> (i = 0; i &lt; <a class="code" href="../../dd/d29/false__position_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">MAX_ITERATIONS</a>; i++) {</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; m = <a class="code" href="../../dd/d29/false__position_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(a);</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; n = <a class="code" href="../../dd/d29/false__position_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(b);</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; </div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; c = ((a * n) - (b * m)) / (n - m);</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; </div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; a = c;</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; z = <a class="code" href="../../dd/d29/false__position_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(c);</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; </div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; <span class="keywordflow">if</span> (std::abs(z) &lt; <a class="code" href="../../de/dd3/newton__raphson__method_8cpp.html#a75f355966e0a97665eaf5a4c79baa7af">EPSILON</a>) { <span class="comment">// stoping criteria</span></div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; }</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; }</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; </div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\n\nRoot: &quot;</span> &lt;&lt; c &lt;&lt; <span class="stringliteral">&quot;\t\tSteps: &quot;</span> &lt;&lt; i &lt;&lt; <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="l00073"></a><span class="lineno"> 73</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160;}</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_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg" width="302" height="139"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
</div>
</div>
<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="l00106"></a><span class="lineno"> 106</span>&#160; {</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>&#160; <span class="keywordtype">float</span> a=0, b=0,i=0,root=0;</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>&#160; int16_t count=0;</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>&#160; <span class="keywordtype">float</span> range = 100000; <span class="comment">//Range in which we have to find the root. (-range,range)</span></div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>&#160; <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="l00111"></a><span class="lineno"> 111</span>&#160; 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="l00112"></a><span class="lineno"> 112</span>&#160; i=((-1)*range + gap);</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>&#160; <span class="comment">//while loop for selecting proper interval in provided range and with provided interval gap.</span></div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>&#160; <span class="keywordflow">while</span>(i&lt;=range){</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>&#160; 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="l00116"></a><span class="lineno"> 116</span>&#160; <span class="keywordflow">if</span>(b==0){</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>&#160; count++;</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>&#160; <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="l00119"></a><span class="lineno"> 119</span>&#160; }</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>&#160; <span class="keywordflow">if</span>(a*b&lt;0){</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>&#160; root = <a class="code" href="../../dd/d29/false__position_8cpp.html#a7d69b49dc37da1c02b3ab8c7fe783494">numerical_methods::false_position::regula_falsi</a>(i-gap,i,a,b);</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>&#160; count++;</div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>&#160; <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="l00124"></a><span class="lineno"> 124</span>&#160; }</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>&#160; a=b;</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>&#160; i+=gap;</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>&#160; }</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>&#160;}</div>
</div><!-- fragment -->
</div>
</div>
<a id="a1ab31b90bc584c635ec159468ceed9b2"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a1ab31b90bc584c635ec159468ceed9b2">&#9670;&nbsp;</a></span>sgn()</h2>
<a id="a85cb7bfb90abc898e042d624372c5345"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a85cb7bfb90abc898e042d624372c5345">&#9670;&nbsp;</a></span>printRoot()</h2>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;typename T &gt; </div>
<table class="memname">
<tr>
<td class="memname">int sgn </td>
<td class="memname">void numerical_methods::false_position::printRoot </td>
<td>(</td>
<td class="paramtype">T&#160;</td>
<td class="paramname"><em>val</em></td><td>)</td>
<td class="paramtype">float&#160;</td>
<td class="paramname"><em>root</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const int16_t &amp;&#160;</td>
<td class="paramname"><em>count</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>get the sign of any given number </p>
<div class="fragment"><div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160; {</div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160; <span class="keywordflow">return</span> (T(0) &lt; val) - (val &lt; T(0));</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160;}</div>
</div><!-- fragment -->
<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>&#160; {</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; <span class="keywordflow">if</span>(count==1){</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Your 1st root is : &quot;</span> &lt;&lt; root &lt;&lt; <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>&#160; }</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160; <span class="keywordflow">else</span> <span class="keywordflow">if</span>(count==2){</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Your 2nd root is : &quot;</span> &lt;&lt; root &lt;&lt; <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="l00090"></a><span class="lineno"> 90</span>&#160; }</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160; <span class="keywordflow">else</span> <span class="keywordflow">if</span>(count==3){</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Your 3rd root is : &quot;</span> &lt;&lt; root &lt;&lt; <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>&#160; }</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160; <span class="keywordflow">else</span>{</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Your &quot;</span>&lt;&lt;count&lt;&lt;<span class="stringliteral">&quot;th root is : &quot;</span> &lt;&lt; root &lt;&lt; <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="l00096"></a><span class="lineno"> 96</span>&#160; }</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160;}</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">&#9670;&nbsp;</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&#160;</td>
<td class="paramname"><em>x1</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">float&#160;</td>
<td class="paramname"><em>x2</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">float&#160;</td>
<td class="paramname"><em>y1</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">float&#160;</td>
<td class="paramname"><em>y2</em>&#160;</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="l00054"></a><span class="lineno"> 54</span>&#160; {</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; <span class="keywordtype">float</span> diff = x1-x2;</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; <span class="keywordflow">if</span>(diff&lt;0){</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; diff= (-1)*diff;</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; }</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; <span class="keywordflow">if</span>(diff&lt;0.00001){ </div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; <span class="keywordflow">if</span> (y1&lt;0) {</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; y1=-y1;</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; }</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; <span class="keywordflow">if</span> (y2&lt;0) {</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; y2=-y2;</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; }</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; <span class="keywordflow">if</span> (y1&lt;y2) {</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; <span class="keywordflow">return</span> x1;</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; }</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; <span class="keywordflow">return</span> x2;</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; }</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; }</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; <span class="keywordtype">float</span> x3=0,y3=0;</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; x3 = x1 - (x1-x2)*(y1)/(y1-y2);</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; 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>&#160; <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>&#160;}</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 -->
<div class="ttc" id="afalse__position_8cpp_html_a0a3abbca80bc98e7abcb3ae73abe0f14"><div class="ttname"><a href="../../dd/d29/false__position_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> false_position.cpp:24</div></div>
<div class="ttc" id="anewton__raphson__method_8cpp_html_a75f355966e0a97665eaf5a4c79baa7af"><div class="ttname"><a href="../../de/dd3/newton__raphson__method_8cpp.html#a75f355966e0a97665eaf5a4c79baa7af">EPSILON</a></div><div class="ttdeci">constexpr double EPSILON</div><div class="ttdoc">system accuracy limit</div><div class="ttdef"><b>Definition:</b> newton_raphson_method.cpp:20</div></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:54</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="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="afalse__position_8cpp_html_a1ab31b90bc584c635ec159468ceed9b2"><div class="ttname"><a href="../../dd/d29/false__position_8cpp.html#a1ab31b90bc584c635ec159468ceed9b2">sgn</a></div><div class="ttdeci">int sgn(T val)</div><div class="ttdef"><b>Definition:</b> false_position.cpp:34</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 class="ttc" id="afalse__position_8cpp_html_a2003b5b2dcfff0769b957ab5c968b03d"><div class="ttname"><a href="../../dd/d29/false__position_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a></div><div class="ttdeci">static double eq(double i)</div><div class="ttdef"><b>Definition:</b> false_position.cpp:28</div></div>
<div class="ttc" id="apow_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a></div><div class="ttdeci">T pow(T... args)</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 &amp;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>
<!-- start footer part -->
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
<ul>