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@@ -101,46 +101,52 @@ $(document).ready(function(){initNavTree('dd/d29/false__position_8cpp.html','../
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<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.
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<a href="#details">More...</a></p>
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<div class="textblock"><code>#include <cmath></code><br />
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<code>#include <cstdlib></code><br />
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<code>#include <iostream></code><br />
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<code>#include <limits></code><br />
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</div><div class="textblock"><div class="dynheader">
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Include dependency graph for false_position.cpp:</div>
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#define </td><td class="memItemRight" valign="bottom"><b>EPSILON</b>    1e-6</td></tr>
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<tr class="memitem:a0a3abbca80bc98e7abcb3ae73abe0f14"><td class="memItemLeft" align="right" valign="top"><a id="a0a3abbca80bc98e7abcb3ae73abe0f14"></a>
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#define </td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d29/false__position_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">MAX_ITERATIONS</a>   50000</td></tr>
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<tr class="memdesc:a0a3abbca80bc98e7abcb3ae73abe0f14"><td class="mdescLeft"> </td><td class="mdescRight">Maximum number of iterations to check. <br /></td></tr>
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<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>
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<tr class="memdesc:d1/de0/namespacenumerical__methods"><td class="mdescLeft"> </td><td class="mdescRight">for io operations <br /></td></tr>
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<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>
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<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>
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<tr class="memitem:a2003b5b2dcfff0769b957ab5c968b03d"><td class="memItemLeft" align="right" valign="top">static double </td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d29/false__position_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a> (double i)</td></tr>
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<tr class="memitem:a1ab31b90bc584c635ec159468ceed9b2"><td class="memTemplParams" colspan="2">template<typename T > </td></tr>
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<tr class="memitem:a1ab31b90bc584c635ec159468ceed9b2"><td class="memTemplItemLeft" align="right" valign="top">int </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d29/false__position_8cpp.html#a1ab31b90bc584c635ec159468ceed9b2">sgn</a> (T val)</td></tr>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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</table>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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<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>
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<p>Given two points \(a\) 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">
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<p>First, multiple intervals are selected with the interval gap provided. Separate recursive function called for every root. Roots are printed Separatelt.</p>
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<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">
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\[ x_{i+1} = \frac{a_i\cdot f(b_i) - b_i\cdot f(a_i)}{f(b_i) - f(a_i)} \]
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</p>
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<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>
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<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>
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<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>
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<dl class="section author"><dt>Author</dt><dd>Unknown author </dd>
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<dd>
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<a href="https://github.com/sampatil578">Samruddha Patil</a> </dd></dl>
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</div><h2 class="groupheader">Function Documentation</h2>
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<a id="a2003b5b2dcfff0769b957ab5c968b03d"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a2003b5b2dcfff0769b957ab5c968b03d">◆ </a></span>eq()</h2>
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<a id="a85a6ec58b5064d63d4f0df3854496713"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a85a6ec58b5064d63d4f0df3854496713">◆ </a></span>eq()</h2>
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<td class="memname">static double eq </td>
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<td class="memname">static float numerical_methods::false_position::eq </td>
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<td>(</td>
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<td class="paramtype">double </td>
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<td class="paramname"><em>i</em></td><td>)</td>
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<td class="paramtype">float </td>
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<td class="paramname"><em>x</em></td><td>)</td>
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<p>define \(f(x)\) to find root for </p>
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<div class="fragment"><div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  {</div>
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<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  <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>
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<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> }</div>
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<p>This function gives the value of f(x) for given x. </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">x</td><td>value for which we have to find value of f(x). </td></tr>
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</table>
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</dd>
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<dl class="section return"><dt>Returns</dt><dd>value of f(x) for given x. </dd></dl>
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<div class="fragment"><div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  {</div>
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<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>
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<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> }</div>
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</div><!-- fragment --><div class="dynheader">
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<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>
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<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>
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@@ -190,85 +204,188 @@ Here is the call graph for this function:</div>
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<p>main function </p>
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<div class="fragment"><div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  {</div>
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<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  <span class="keywordtype">double</span> a = -1, b = 1, x, z, m, n, c;</div>
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<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  <span class="keywordtype">int</span> i;</div>
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<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  </div>
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<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  <span class="comment">// loop to find initial intervals a, b</span></div>
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<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < <a class="code" href="../../dd/d29/false__position_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">MAX_ITERATIONS</a>; i++) {</div>
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<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  z = <a class="code" href="../../dd/d29/false__position_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(a);</div>
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<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  x = <a class="code" href="../../dd/d29/false__position_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(b);</div>
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<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  <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>
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<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  b++;</div>
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<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  a--;</div>
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<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  } <span class="keywordflow">else</span> { <span class="comment">// if opposite signs, we got our interval</span></div>
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<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <span class="keywordflow">break</span>;</div>
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<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  }</div>
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<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  }</div>
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<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  </div>
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<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"\nFirst initial: "</span> << a;</div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"\nSecond initial: "</span> << b;</div>
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<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  </div>
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<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="keywordflow">for</span> (i = 0; i < <a class="code" href="../../dd/d29/false__position_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">MAX_ITERATIONS</a>; i++) {</div>
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<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  m = <a class="code" href="../../dd/d29/false__position_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(a);</div>
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<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  n = <a class="code" href="../../dd/d29/false__position_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(b);</div>
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<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  </div>
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<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  c = ((a * n) - (b * m)) / (n - m);</div>
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<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  </div>
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<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  a = c;</div>
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<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  z = <a class="code" href="../../dd/d29/false__position_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a>(c);</div>
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<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  </div>
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<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="keywordflow">if</span> (std::abs(z) < <a class="code" href="../../de/dd3/newton__raphson__method_8cpp.html#a75f355966e0a97665eaf5a4c79baa7af">EPSILON</a>) { <span class="comment">// stoping criteria</span></div>
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<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="keywordflow">break</span>;</div>
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<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  }</div>
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<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  }</div>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  </div>
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<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"\n\nRoot: "</span> << c << <span class="stringliteral">"\t\tSteps: "</span> << i << <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</span> }</div>
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</div><!-- fragment --><div class="dynheader">
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Here is the call graph for this function:</div>
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<div class="dyncontent">
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<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>
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</div>
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</div>
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<p>Main function. </p>
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<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
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<div class="fragment"><div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  {</div>
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<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  <span class="keywordtype">float</span> a=0, b=0,i=0,root=0;</div>
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<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  int16_t count=0;</div>
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<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <span class="keywordtype">float</span> range = 100000; <span class="comment">//Range in which we have to find the root. (-range,range)</span></div>
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<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <span class="keywordtype">float</span> gap = 0.5; <span class="comment">// interval gap. lesser the gap more the accuracy</span></div>
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<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  a = <a class="code" href="../../dd/d29/false__position_8cpp.html#a85a6ec58b5064d63d4f0df3854496713">numerical_methods::false_position::eq</a>((-1)*range);</div>
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<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  i=((-1)*range + gap);</div>
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<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <span class="comment">//while loop for selecting proper interval in provided range and with provided interval gap.</span></div>
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<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  <span class="keywordflow">while</span>(i<=range){</div>
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<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  b = <a class="code" href="../../dd/d29/false__position_8cpp.html#a85a6ec58b5064d63d4f0df3854496713">numerical_methods::false_position::eq</a>(i);</div>
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<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  <span class="keywordflow">if</span>(b==0){</div>
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<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  count++;</div>
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<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  <a class="code" href="../../dd/d29/false__position_8cpp.html#a85cb7bfb90abc898e042d624372c5345">numerical_methods::false_position::printRoot</a>(i,count);</div>
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<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  }</div>
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<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="keywordflow">if</span>(a*b<0){</div>
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<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  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>
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<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  count++;</div>
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<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  <a class="code" href="../../dd/d29/false__position_8cpp.html#a85cb7bfb90abc898e042d624372c5345">numerical_methods::false_position::printRoot</a>(root,count);</div>
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<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  }</div>
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<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  a=b;</div>
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<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  i+=gap;</div>
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<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  }</div>
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<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a name="l00129"></a><span class="lineno"> 129</span> }</div>
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</div><!-- fragment -->
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</div>
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</div>
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<a id="a1ab31b90bc584c635ec159468ceed9b2"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a1ab31b90bc584c635ec159468ceed9b2">◆ </a></span>sgn()</h2>
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<a id="a85cb7bfb90abc898e042d624372c5345"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a85cb7bfb90abc898e042d624372c5345">◆ </a></span>printRoot()</h2>
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<div class="memitem">
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<div class="memproto">
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<div class="memtemplate">
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template<typename T > </div>
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<table class="memname">
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<tr>
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<td class="memname">int sgn </td>
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<td class="memname">void numerical_methods::false_position::printRoot </td>
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<td>(</td>
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<td class="paramtype">T </td>
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<td class="paramname"><em>val</em></td><td>)</td>
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<td class="paramtype">float </td>
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<td class="paramname"><em>root</em>, </td>
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</tr>
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<tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">const int16_t & </td>
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<td class="paramname"><em>count</em> </td>
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</tr>
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<tr>
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<td></td>
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<td>)</td>
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<td></td><td></td>
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</tr>
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</table>
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</div><div class="memdoc">
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<p>get the sign of any given number </p>
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<div class="fragment"><div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  {</div>
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<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  <span class="keywordflow">return</span> (T(0) < val) - (val < T(0));</div>
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<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> }</div>
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</div><!-- fragment -->
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<p>This function prints roots of the equation. </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">root</td><td>which we have to print. </td></tr>
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<tr><td class="paramname">count</td><td>which is count of the root in an interval [-range,range]. </td></tr>
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</table>
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</dd>
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</dl>
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<div class="fragment"><div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  {</div>
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<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="keywordflow">if</span>(count==1){</div>
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<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>
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<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  }</div>
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<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span>(count==2){</div>
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<div class="line"><a name="l00089"></a><span class="lineno"> 89</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>
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<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  }</div>
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<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span>(count==3){</div>
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<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 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>
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<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  }</div>
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<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  <span class="keywordflow">else</span>{</div>
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<div class="line"><a name="l00095"></a><span class="lineno"> 95</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>
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<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  }</div>
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<div class="line"><a name="l00097"></a><span class="lineno"> 97</span> }</div>
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</div><!-- fragment --><div class="dynheader">
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Here is the call graph for this function:</div>
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<div class="dyncontent">
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<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>
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</div>
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<a id="a7d69b49dc37da1c02b3ab8c7fe783494"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a7d69b49dc37da1c02b3ab8c7fe783494">◆ </a></span>regula_falsi()</h2>
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<div class="memproto">
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<td class="memname">static float numerical_methods::false_position::regula_falsi </td>
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<td>(</td>
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<td class="paramtype">float </td>
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<td class="paramname"><em>y1</em>, </td>
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<td class="paramkey"></td>
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<td class="paramname"><em>y2</em> </td>
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</tr>
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<td>)</td>
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</table>
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</td>
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<span class="mlabels"><span class="mlabel">static</span></span> </td>
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<p>This function finds root of the equation in given interval i.e. (x1,x2). </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">x1,x2</td><td>values for an interval in which root is present. </td></tr>
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<tr><td class="paramname">y1,y2</td><td>values of function at x1, x2 espectively. </td></tr>
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</table>
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</dd>
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</dl>
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<dl class="section return"><dt>Returns</dt><dd>root of the equation in the given interval. </dd></dl>
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<div class="fragment"><div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  {</div>
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<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  <span class="keywordtype">float</span> diff = x1-x2;</div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="keywordflow">if</span>(diff<0){</div>
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<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  diff= (-1)*diff;</div>
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<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  }</div>
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<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  <span class="keywordflow">if</span>(diff<0.00001){ </div>
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<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <span class="keywordflow">if</span> (y1<0) {</div>
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<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  y1=-y1;</div>
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<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  }</div>
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<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="keywordflow">if</span> (y2<0) {</div>
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<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  y2=-y2;</div>
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<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  }</div>
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<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="keywordflow">if</span> (y1<y2) {</div>
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<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="keywordflow">return</span> x1;</div>
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<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  }</div>
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<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <span class="keywordflow">else</span> {</div>
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<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="keywordflow">return</span> x2;</div>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  }</div>
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<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  }</div>
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<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  <span class="keywordtype">float</span> x3=0,y3=0;</div>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  x3 = x1 - (x1-x2)*(y1)/(y1-y2);</div>
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<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>
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<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>
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<div class="line"><a name="l00077"></a><span class="lineno"> 77</span> }</div>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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