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<p>Find approximate solution for \(f(x) = 0\) using Newton-Raphson interpolation algorithm.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;complex.h&gt;</code><br />
<code>#include &lt;limits.h&gt;</code><br />
<code>#include &lt;math.h&gt;</code><br />
<code>#include &lt;stdio.h&gt;</code><br />
<code>#include &lt;stdlib.h&gt;</code><br />
<code>#include &lt;time.h&gt;</code><br />
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Include dependency graph for newton_raphson_root.c:</div>
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Macros</h2></td></tr>
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#define&#160;</td><td class="memItemRight" valign="bottom"><b>ACCURACY</b>&#160;&#160;&#160;1e-10</td></tr>
<tr class="memdesc:af270a96662132d0385cb6b4637c5a689"><td class="mdescLeft">&#160;</td><td class="mdescRight">solution accuracy <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:a72f87d423a488946b319627a454d3925"><td class="memItemLeft" align="right" valign="top">double complex&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d08/newton__raphson__root_8c.html#a72f87d423a488946b319627a454d3925">func</a> (double complex x)</td></tr>
<tr class="memdesc:a72f87d423a488946b319627a454d3925"><td class="mdescLeft">&#160;</td><td class="mdescRight">Return value of the function to find the root for. <a href="../../dd/d08/newton__raphson__root_8c.html#a72f87d423a488946b319627a454d3925">More...</a><br /></td></tr>
<tr class="separator:a72f87d423a488946b319627a454d3925"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae713a1fd0c275fbec7edf263ac2c0337"><td class="memItemLeft" align="right" valign="top">double complex&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d08/newton__raphson__root_8c.html#ae713a1fd0c275fbec7edf263ac2c0337">d_func</a> (double complex x)</td></tr>
<tr class="memdesc:ae713a1fd0c275fbec7edf263ac2c0337"><td class="mdescLeft">&#160;</td><td class="mdescRight">Return first order derivative of the function. <a href="../../dd/d08/newton__raphson__root_8c.html#ae713a1fd0c275fbec7edf263ac2c0337">More...</a><br /></td></tr>
<tr class="separator:ae713a1fd0c275fbec7edf263ac2c0337"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a3c04138a5bfe5d72780bb7e82a18e627"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d08/newton__raphson__root_8c.html#a3c04138a5bfe5d72780bb7e82a18e627">main</a> (int argc, char **argv)</td></tr>
<tr class="memdesc:a3c04138a5bfe5d72780bb7e82a18e627"><td class="mdescLeft">&#160;</td><td class="mdescRight">main function <a href="../../dd/d08/newton__raphson__root_8c.html#a3c04138a5bfe5d72780bb7e82a18e627">More...</a><br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Find approximate solution for \(f(x) = 0\) using Newton-Raphson interpolation algorithm. </p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala" target="_blank">Krishna Vedala</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="ae713a1fd0c275fbec7edf263ac2c0337" name="ae713a1fd0c275fbec7edf263ac2c0337"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae713a1fd0c275fbec7edf263ac2c0337">&#9670;&nbsp;</a></span>d_func()</h2>
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<td class="memname">double complex d_func </td>
<td>(</td>
<td class="paramtype">double complex&#160;</td>
<td class="paramname"><em>x</em></td><td>)</td>
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<p>Return first order derivative of the function. </p>
<p >\(f&#39;(x)\) </p>
<div class="fragment"><div class="line"><span class="lineno"> 32</span>{ <span class="keywordflow">return</span> 2. * x; }</div>
</div><!-- fragment -->
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<a id="a72f87d423a488946b319627a454d3925" name="a72f87d423a488946b319627a454d3925"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a72f87d423a488946b319627a454d3925">&#9670;&nbsp;</a></span>func()</h2>
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<td class="memname">double complex func </td>
<td>(</td>
<td class="paramtype">double complex&#160;</td>
<td class="paramname"><em>x</em></td><td>)</td>
<td></td>
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<p>Return value of the function to find the root for. </p>
<p >\(f(x)\) </p>
<div class="fragment"><div class="line"><span class="lineno"> 23</span>{</div>
<div class="line"><span class="lineno"> 24</span> <span class="keywordflow">return</span> x * x - 3.; <span class="comment">/* x^2 = 3 - solution is sqrt(3) */</span></div>
<div class="line"><span class="lineno"> 25</span> <span class="comment">// return x * x - 2.; /* x^2 = 2 - solution is sqrt(2) */</span></div>
<div class="line"><span class="lineno"> 26</span>}</div>
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<a id="a3c04138a5bfe5d72780bb7e82a18e627" name="a3c04138a5bfe5d72780bb7e82a18e627"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a3c04138a5bfe5d72780bb7e82a18e627">&#9670;&nbsp;</a></span>main()</h2>
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<td class="memname">int main </td>
<td>(</td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>argc</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">char **&#160;</td>
<td class="paramname"><em>argv</em>&#160;</td>
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<td></td>
<td>)</td>
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<p>main function </p>
<div class="fragment"><div class="line"><span class="lineno"> 38</span>{</div>
<div class="line"><span class="lineno"> 39</span> <span class="keywordtype">double</span> delta = 1;</div>
<div class="line"><span class="lineno"> 40</span> <span class="keywordtype">double</span> complex cdelta = 1;</div>
<div class="line"><span class="lineno"> 41</span> </div>
<div class="line"><span class="lineno"> 42</span> <span class="comment">/* initialize random seed: */</span></div>
<div class="line"><span class="lineno"> 43</span> srand(time(NULL));</div>
<div class="line"><span class="lineno"> 44</span> </div>
<div class="line"><span class="lineno"> 45</span> <span class="comment">/* random initial approximation */</span></div>
<div class="line"><span class="lineno"> 46</span> <span class="keywordtype">double</span> complex root = (rand() % 100 - 50) + (rand() % 100 - 50) * I;</div>
<div class="line"><span class="lineno"> 47</span> </div>
<div class="line"><span class="lineno"> 48</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> counter = 0;</div>
<div class="line"><span class="lineno"> 49</span> <span class="comment">/* iterate till a convergence is reached */</span></div>
<div class="line"><span class="lineno"> 50</span> <span class="keywordflow">while</span> (delta &gt; <a class="code hl_define" href="../../dd/d08/newton__raphson__root_8c.html#af270a96662132d0385cb6b4637c5a689">ACCURACY</a> &amp;&amp; counter &lt; ULONG_MAX)</div>
<div class="line"><span class="lineno"> 51</span> {</div>
<div class="line"><span class="lineno"> 52</span> cdelta = <a class="code hl_function" href="../../dd/d08/newton__raphson__root_8c.html#a72f87d423a488946b319627a454d3925">func</a>(root) / <a class="code hl_function" href="../../dd/d08/newton__raphson__root_8c.html#ae713a1fd0c275fbec7edf263ac2c0337">d_func</a>(root);</div>
<div class="line"><span class="lineno"> 53</span> root += -cdelta;</div>
<div class="line"><span class="lineno"> 54</span> counter++;</div>
<div class="line"><span class="lineno"> 55</span> delta = fabs(cabs(cdelta));</div>
<div class="line"><span class="lineno"> 56</span> </div>
<div class="line"><span class="lineno"> 57</span><span class="preprocessor">#if defined(DEBUG) || !defined(NDEBUG)</span></div>
<div class="line"><span class="lineno"> 58</span> <span class="keywordflow">if</span> (counter % 50 == 0)</div>
<div class="line"><span class="lineno"> 59</span> {</div>
<div class="line"><span class="lineno"> 60</span> <span class="keywordtype">double</span> r = creal(root);</div>
<div class="line"><span class="lineno"> 61</span> <span class="keywordtype">double</span> c = cimag(root);</div>
<div class="line"><span class="lineno"> 62</span> </div>
<div class="line"><span class="lineno"> 63</span> printf(<span class="stringliteral">&quot;Iter %5lu: Root: %4.4g%c%4.4gi\t\tdelta: %.4g\n&quot;</span>, counter,</div>
<div class="line"><span class="lineno"> 64</span> r, c &gt;= 0 ? <span class="charliteral">&#39;+&#39;</span> : <span class="charliteral">&#39;-&#39;</span>, c &gt;= 0 ? c : -c, delta);</div>
<div class="line"><span class="lineno"> 65</span> }</div>
<div class="line"><span class="lineno"> 66</span><span class="preprocessor">#endif</span></div>
<div class="line"><span class="lineno"> 67</span> }</div>
<div class="line"><span class="lineno"> 68</span> </div>
<div class="line"><span class="lineno"> 69</span> <span class="keywordtype">double</span> r = creal(root);</div>
<div class="line"><span class="lineno"> 70</span> <span class="keywordtype">double</span> c = fabs(cimag(root)) &lt; <a class="code hl_define" href="../../dd/d08/newton__raphson__root_8c.html#af270a96662132d0385cb6b4637c5a689">ACCURACY</a> ? 0 : cimag(root);</div>
<div class="line"><span class="lineno"> 71</span> </div>
<div class="line"><span class="lineno"> 72</span> printf(<span class="stringliteral">&quot;Iter %5lu: Root: %4.4g%c%4.4gi\t\tdelta: %.4g\n&quot;</span>, counter, r,</div>
<div class="line"><span class="lineno"> 73</span> c &gt;= 0 ? <span class="charliteral">&#39;+&#39;</span> : <span class="charliteral">&#39;-&#39;</span>, c &gt;= 0 ? c : -c, delta);</div>
<div class="line"><span class="lineno"> 74</span> </div>
<div class="line"><span class="lineno"> 75</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 76</span>}</div>
<div class="ttc" id="anewton__raphson__root_8c_html_a72f87d423a488946b319627a454d3925"><div class="ttname"><a href="../../dd/d08/newton__raphson__root_8c.html#a72f87d423a488946b319627a454d3925">func</a></div><div class="ttdeci">double complex func(double complex x)</div><div class="ttdoc">Return value of the function to find the root for.</div><div class="ttdef"><b>Definition:</b> newton_raphson_root.c:22</div></div>
<div class="ttc" id="anewton__raphson__root_8c_html_ae713a1fd0c275fbec7edf263ac2c0337"><div class="ttname"><a href="../../dd/d08/newton__raphson__root_8c.html#ae713a1fd0c275fbec7edf263ac2c0337">d_func</a></div><div class="ttdeci">double complex d_func(double complex x)</div><div class="ttdoc">Return first order derivative of the function.</div><div class="ttdef"><b>Definition:</b> newton_raphson_root.c:32</div></div>
<div class="ttc" id="anewton__raphson__root_8c_html_af270a96662132d0385cb6b4637c5a689"><div class="ttname"><a href="../../dd/d08/newton__raphson__root_8c.html#af270a96662132d0385cb6b4637c5a689">ACCURACY</a></div><div class="ttdeci">#define ACCURACY</div><div class="ttdoc">solution accuracy</div><div class="ttdef"><b>Definition:</b> newton_raphson_root.c:16</div></div>
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