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<a href="../../dd/d29/false__position_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="preprocessor">#include &lt;cmath&gt;</span> </div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="preprocessor">#include &lt;iostream&gt;</span> </div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span></div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../d1/de0/namespacenumerical__methods.html">numerical_methods</a> {</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../df/dea/namespacefalse__position.html">false_position</a> {</div>
<div class="foldopen" id="foldopen00044" data-start="{" data-end="}">
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"><a class="line" href="../../dd/d29/false__position_8cpp.html#a85a6ec58b5064d63d4f0df3854496713"> 44</a></span><span class="keyword">static</span> <span class="keywordtype">float</span> <a class="code hl_function" href="../../dd/d29/false__position_8cpp.html#a85a6ec58b5064d63d4f0df3854496713">eq</a>(<span class="keywordtype">float</span> x) {</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="keywordflow">return</span> (x * x - x); <span class="comment">// original equation</span></div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span>}</div>
</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span></div>
<div class="foldopen" id="foldopen00055" data-start="{" data-end="}">
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"><a class="line" href="../../dd/d29/false__position_8cpp.html#a7d69b49dc37da1c02b3ab8c7fe783494"> 55</a></span><span class="keyword">static</span> <span class="keywordtype">float</span> <a class="code hl_function" href="../../dd/d29/false__position_8cpp.html#a7d69b49dc37da1c02b3ab8c7fe783494">regula_falsi</a>(<span class="keywordtype">float</span> x1, <span class="keywordtype">float</span> x2, <span class="keywordtype">float</span> y1, <span class="keywordtype">float</span> y2) {</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="keywordtype">float</span> diff = x1 - x2;</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <span class="keywordflow">if</span> (diff &lt; 0) {</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> diff = (-1) * diff;</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> }</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="keywordflow">if</span> (diff &lt; 0.00001) {</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="keywordflow">if</span> (y1 &lt; 0) {</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> y1 = -y1;</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> }</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <span class="keywordflow">if</span> (y2 &lt; 0) {</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> y2 = -y2;</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> }</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="keywordflow">if</span> (y1 &lt; y2) {</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <span class="keywordflow">return</span> x1;</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="keywordflow">return</span> x2;</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> }</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> }</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <span class="keywordtype">float</span> x3 = 0, y3 = 0;</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> x3 = x1 - (x1 - x2) * (y1) / (y1 - y2);</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> y3 = <a class="code hl_function" href="../../dd/d29/false__position_8cpp.html#a85a6ec58b5064d63d4f0df3854496713">eq</a>(x3);</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../dd/d29/false__position_8cpp.html#a7d69b49dc37da1c02b3ab8c7fe783494">regula_falsi</a>(x2, x3, y2, y3);</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span>}</div>
</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span></div>
<div class="foldopen" id="foldopen00084" data-start="{" data-end="}">
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"><a class="line" href="../../dd/d29/false__position_8cpp.html#a85cb7bfb90abc898e042d624372c5345"> 84</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="../../dd/d29/false__position_8cpp.html#a85cb7bfb90abc898e042d624372c5345">printRoot</a>(<span class="keywordtype">float</span> root, <span class="keyword">const</span> int16_t &amp;count) {</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> <span class="keywordflow">if</span> (count == 1) {</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Your 1st root is : &quot;</span> &lt;&lt; root &lt;&lt; std::endl;</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (count == 2) {</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Your 2nd root is : &quot;</span> &lt;&lt; root &lt;&lt; std::endl;</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (count == 3) {</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Your 3rd root is : &quot;</span> &lt;&lt; root &lt;&lt; std::endl;</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> } <span class="keywordflow">else</span> {</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> std::cout &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; std::endl;</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> }</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span>}</div>
</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span>} <span class="comment">// namespace false_position</span></div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span>} <span class="comment">// namespace numerical_methods</span></div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span></div>
<div class="foldopen" id="foldopen00102" data-start="{" data-end="}">
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"><a class="line" href="../../dd/d29/false__position_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4"> 102</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../dd/d29/false__position_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="keywordtype">float</span> a = 0, b = 0, i = 0, root = 0;</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> int16_t count = 0;</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> <span class="keywordtype">float</span> range =</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> 100000; <span class="comment">// Range in which we have to find the root. (-range,range)</span></div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> <span class="keywordtype">float</span> gap = 0.5; <span class="comment">// interval gap. lesser the gap more the accuracy</span></div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> a = <a class="code hl_function" href="../../dd/d29/false__position_8cpp.html#a85a6ec58b5064d63d4f0df3854496713">numerical_methods::false_position::eq</a>((-1) * range);</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> i = ((-1) * range + gap);</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> <span class="comment">// while loop for selecting proper interval in provided range and with</span></div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> <span class="comment">// provided interval gap.</span></div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> <span class="keywordflow">while</span> (i &lt;= range) {</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> b = <a class="code hl_function" href="../../dd/d29/false__position_8cpp.html#a85a6ec58b5064d63d4f0df3854496713">numerical_methods::false_position::eq</a>(i);</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> <span class="keywordflow">if</span> (b == 0) {</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> count++;</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <a class="code hl_function" href="../../dd/d29/false__position_8cpp.html#a85cb7bfb90abc898e042d624372c5345">numerical_methods::false_position::printRoot</a>(i, count);</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> }</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <span class="keywordflow">if</span> (a * b &lt; 0) {</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> root = <a class="code hl_function" href="../../dd/d29/false__position_8cpp.html#a7d69b49dc37da1c02b3ab8c7fe783494">numerical_methods::false_position::regula_falsi</a>(i - gap, i,</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> a, b);</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> count++;</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> <a class="code hl_function" href="../../dd/d29/false__position_8cpp.html#a85cb7bfb90abc898e042d624372c5345">numerical_methods::false_position::printRoot</a>(root, count);</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> }</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> a = b;</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> i += gap;</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> }</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span>}</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> <a href="#l00055">false_position.cpp:55</a></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> <a href="#l00044">false_position.cpp:44</a></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> <a href="#l00084">false_position.cpp:84</a></div></div>
<div class="ttc" id="afalse__position_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../dd/d29/false__position_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdoc">Main function.</div><div class="ttdef"><b>Definition</b> <a href="#l00102">false_position.cpp:102</a></div></div>
<div class="ttc" id="anamespacefalse__position_html"><div class="ttname"><a href="../../df/dea/namespacefalse__position.html">false_position</a></div><div class="ttdoc">Functions for [False Position] (https://en.wikipedia.org/wiki/Regula_falsi) method.</div></div>
<div class="ttc" id="anamespacenumerical__methods_html"><div class="ttname"><a href="../../d1/de0/namespacenumerical__methods.html">numerical_methods</a></div><div class="ttdoc">for assert</div></div>
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