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<div class="title">durand_kerner_roots.c File Reference</div> </div>
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<div class="contents">
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<p>Compute all possible approximate roots of any given polynomial using <a href="https://en.wikipedia.org/wiki/Durand%E2%80%93Kerner_method">Durand Kerner algorithm</a>
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<a href="#details">More...</a></p>
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<div class="textblock"><code>#include <complex.h></code><br />
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<code>#include <limits.h></code><br />
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<code>#include <math.h></code><br />
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<code>#include <stdio.h></code><br />
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<code>#include <stdlib.h></code><br />
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<code>#include <string.h></code><br />
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<code>#include <time.h></code><br />
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</div><div class="textblock"><div class="dynheader">
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Include dependency graph for durand_kerner_roots.c:</div>
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<div class="dyncontent">
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../db/dff/durand__kerner__roots_8c__incl.svg" width="616" height="127"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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Macros</h2></td></tr>
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<tr class="memitem:af270a96662132d0385cb6b4637c5a689"><td class="memItemLeft" align="right" valign="top"><a id="af270a96662132d0385cb6b4637c5a689"></a>
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#define </td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d38/durand__kerner__roots_8c.html#af270a96662132d0385cb6b4637c5a689">ACCURACY</a>   1e-10</td></tr>
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<tr class="memdesc:af270a96662132d0385cb6b4637c5a689"><td class="mdescLeft"> </td><td class="mdescRight">maximum accuracy limit <br /></td></tr>
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<tr class="separator:af270a96662132d0385cb6b4637c5a689"><td class="memSeparator" colspan="2"> </td></tr>
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</table><table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
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Functions</h2></td></tr>
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<tr class="memitem:a321f9781a9744ccdaf0aba89f35ec29c"><td class="memItemLeft" align="right" valign="top">long double complex </td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d38/durand__kerner__roots_8c.html#a321f9781a9744ccdaf0aba89f35ec29c">poly_function</a> (long double *coeffs, unsigned int degree, long double complex x)</td></tr>
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<tr class="memdesc:a321f9781a9744ccdaf0aba89f35ec29c"><td class="mdescLeft"> </td><td class="mdescRight">Evaluate the value of a polynomial with given coefficients. <a href="../../da/d38/durand__kerner__roots_8c.html#a321f9781a9744ccdaf0aba89f35ec29c">More...</a><br /></td></tr>
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<tr class="separator:a321f9781a9744ccdaf0aba89f35ec29c"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:afa5b04ce11475d67049cba8273741fb7"><td class="memItemLeft" align="right" valign="top">const char * </td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d38/durand__kerner__roots_8c.html#afa5b04ce11475d67049cba8273741fb7">complex_str</a> (long double complex x)</td></tr>
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<tr class="memdesc:afa5b04ce11475d67049cba8273741fb7"><td class="mdescLeft"> </td><td class="mdescRight">create a textual form of complex number <a href="../../da/d38/durand__kerner__roots_8c.html#afa5b04ce11475d67049cba8273741fb7">More...</a><br /></td></tr>
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<tr class="separator:afa5b04ce11475d67049cba8273741fb7"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a26d5695ebed0818a3e7cf4b10aacab52"><td class="memItemLeft" align="right" valign="top">char </td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d38/durand__kerner__roots_8c.html#a26d5695ebed0818a3e7cf4b10aacab52">check_termination</a> (long double delta)</td></tr>
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<tr class="memdesc:a26d5695ebed0818a3e7cf4b10aacab52"><td class="mdescLeft"> </td><td class="mdescRight">check for termination condition <a href="../../da/d38/durand__kerner__roots_8c.html#a26d5695ebed0818a3e7cf4b10aacab52">More...</a><br /></td></tr>
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<tr class="separator:a26d5695ebed0818a3e7cf4b10aacab52"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a3c04138a5bfe5d72780bb7e82a18e627"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d38/durand__kerner__roots_8c.html#a3c04138a5bfe5d72780bb7e82a18e627">main</a> (int argc, char **argv)</td></tr>
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<tr class="separator:a3c04138a5bfe5d72780bb7e82a18e627"><td class="memSeparator" colspan="2"> </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>Compute all possible approximate roots of any given polynomial using <a href="https://en.wikipedia.org/wiki/Durand%E2%80%93Kerner_method">Durand Kerner algorithm</a> </p>
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<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a></dd></dl>
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<p>Test the algorithm online: <a href="https://gist.github.com/kvedala/27f1b0b6502af935f6917673ec43bcd7">https://gist.github.com/kvedala/27f1b0b6502af935f6917673ec43bcd7</a></p>
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<p>Try the highly unstable Wilkinson's polynomial: </p><div class="fragment"><div class="line">./numerical_methods/durand_kerner_roots.c 1 -210 20615 -1256850 53327946</div>
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<div class="line">-1672280820 40171771630 -756111184500 11310276995381 -135585182899530</div>
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<div class="line">1307535010540395 -10142299865511450 63030812099294896 -311333643161390640</div>
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<div class="line">1206647803780373360 -3599979517947607200 8037811822645051776</div>
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<div class="line">-12870931245150988800 13803759753640704000 -8752948036761600000</div>
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<div class="line">2432902008176640000</div>
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</div><!-- fragment --><p>Sample implementation results to compute approximate roots of the equation \(x^4-1=0\):<br />
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<img src="https://raw.githubusercontent.com/TheAlgorithms/C/docs/images/numerical_methods/durand_kerner_error.svg" alt="Error evolution during root approximations computed every
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iteration." style="pointer-events: none;" width="400" class="inline"/> <img src="https://raw.githubusercontent.com/TheAlgorithms/C/docs/images/numerical_methods/durand_kerner_roots.svg" alt="Roots evolution - shows the initial approximation of the
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roots and their convergence to a final approximation along with the iterative
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approximations" style="pointer-events: none;" width="400" class="inline"/> </p>
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</div><h2 class="groupheader">Function Documentation</h2>
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<a id="a26d5695ebed0818a3e7cf4b10aacab52"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a26d5695ebed0818a3e7cf4b10aacab52">◆ </a></span>check_termination()</h2>
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<div class="memitem">
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<div class="memproto">
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<table class="memname">
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<tr>
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<td class="memname">char check_termination </td>
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<td>(</td>
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<td class="paramtype">long double </td>
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<td class="paramname"><em>delta</em></td><td>)</td>
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<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>check for termination condition </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="paramdir">[in]</td><td class="paramname">delta</td><td>point at which to evaluate the polynomial </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>0 if termination not reached </dd>
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<dd>
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1 if termination reached </dd></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="keyword">static</span> <span class="keywordtype">long</span> <span class="keywordtype">double</span> past_delta = INFINITY;</div>
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<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="keywordflow">if</span> (fabsl(past_delta - delta) <= <a class="code" href="../../da/d38/durand__kerner__roots_8c.html#af270a96662132d0385cb6b4637c5a689">ACCURACY</a> || delta < <a class="code" href="../../da/d38/durand__kerner__roots_8c.html#af270a96662132d0385cb6b4637c5a689">ACCURACY</a>)</div>
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<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <span class="keywordflow">return</span> 1;</div>
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<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  past_delta = delta;</div>
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<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a name="l00090"></a><span class="lineno"> 90</span> }</div>
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</div><!-- fragment -->
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</div>
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</div>
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<a id="afa5b04ce11475d67049cba8273741fb7"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#afa5b04ce11475d67049cba8273741fb7">◆ </a></span>complex_str()</h2>
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<div class="memitem">
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<div class="memproto">
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<table class="memname">
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<tr>
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<td class="memname">const char* complex_str </td>
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<td>(</td>
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<td class="paramtype">long double complex </td>
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<td class="paramname"><em>x</em></td><td>)</td>
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<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>create a textual form of complex number </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="paramdir">[in]</td><td class="paramname">x</td><td>point at which to evaluate the polynomial </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>pointer to converted string </dd></dl>
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<div class="fragment"><div class="line"><a name="l00067"></a><span class="lineno"> 67</span> {</div>
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<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="keyword">static</span> <span class="keywordtype">char</span> msg[50];</div>
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<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <span class="keywordtype">double</span> r = creal(x);</div>
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<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="keywordtype">double</span> c = cimag(x);</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>  sprintf(msg, <span class="stringliteral">"% 7.04g%+7.04gj"</span>, r, c);</div>
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<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  </div>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <span class="keywordflow">return</span> msg;</div>
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<div class="line"><a name="l00075"></a><span class="lineno"> 75</span> }</div>
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</div><!-- fragment -->
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</div>
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</div>
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<a id="a3c04138a5bfe5d72780bb7e82a18e627"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a3c04138a5bfe5d72780bb7e82a18e627">◆ </a></span>main()</h2>
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<div class="memitem">
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<div class="memproto">
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<tr>
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<td class="memname">int main </td>
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<td>(</td>
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<td class="paramtype">int </td>
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<td class="paramname"><em>argc</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">char ** </td>
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<td class="paramname"><em>argv</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>store intermediate values to a CSV file</p>
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<div class="fragment"><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>  <span class="keywordtype">long</span> <span class="keywordtype">double</span> *coeffs = NULL;</div>
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<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="keywordtype">long</span> <span class="keywordtype">double</span> complex *s0 = NULL;</div>
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<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> degree = 0;</div>
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<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> n, i;</div>
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<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  </div>
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<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  <span class="keywordflow">if</span> (argc < 2)</div>
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<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  {</div>
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<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  printf(</div>
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<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  <span class="stringliteral">"Please pass the coefficients of the polynomial as commandline "</span></div>
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<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <span class="stringliteral">"arguments.\n"</span>);</div>
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<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  }</div>
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<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  </div>
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<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  degree = argc - 1; <span class="comment">/* detected polynomial degree */</span></div>
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<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  coeffs = (<span class="keywordtype">long</span> <span class="keywordtype">double</span> *)malloc(</div>
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<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  degree * <span class="keyword">sizeof</span>(<span class="keywordtype">long</span> <span class="keywordtype">double</span>)); <span class="comment">/* store all input coefficients */</span></div>
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<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  s0 = (<span class="keywordtype">long</span> <span class="keywordtype">double</span> complex *)malloc(</div>
|
|
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  (degree - 1) *</div>
|
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<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  <span class="keyword">sizeof</span>(<span class="keywordtype">long</span> <span class="keywordtype">double</span> complex)); <span class="comment">/* number of roots = degree-1 */</span></div>
|
|
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  </div>
|
|
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <span class="comment">/* initialize random seed: */</span></div>
|
|
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  srand(time(NULL));</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> (!coeffs || !s0)</div>
|
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<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  {</div>
|
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<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  perror(<span class="stringliteral">"Unable to allocate memory!"</span>);</div>
|
|
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  <span class="keywordflow">if</span> (coeffs)</div>
|
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<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  free(coeffs);</div>
|
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<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  <span class="keywordflow">if</span> (s0)</div>
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<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  free(s0);</div>
|
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<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  <span class="keywordflow">return</span> EXIT_FAILURE;</div>
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<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  }</div>
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<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  </div>
|
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<div class="line"><a name="l00130"></a><span class="lineno"> 130</span> <span class="preprocessor">#if defined(DEBUG) || !defined(NDEBUG)</span></div>
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<div class="line"><a name="l00131"></a><span class="lineno"> 131</span> <span class="comment"> /**</span></div>
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<div class="line"><a name="l00132"></a><span class="lineno"> 132</span> <span class="comment"> * store intermediate values to a CSV file</span></div>
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<div class="line"><a name="l00133"></a><span class="lineno"> 133</span> <span class="comment"> */</span></div>
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<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  FILE *log_file = fopen(<span class="stringliteral">"durand_kerner.log.csv"</span>, <span class="stringliteral">"wt"</span>);</div>
|
|
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <span class="keywordflow">if</span> (!log_file)</div>
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<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  {</div>
|
|
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  perror(<span class="stringliteral">"Unable to create a storage log file!"</span>);</div>
|
|
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  free(coeffs);</div>
|
|
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  free(s0);</div>
|
|
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  <span class="keywordflow">return</span> EXIT_FAILURE;</div>
|
|
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  }</div>
|
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<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  fprintf(log_file, <span class="stringliteral">"iter#,"</span>);</div>
|
|
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span> <span class="preprocessor">#endif</span></div>
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<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  </div>
|
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<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  printf(<span class="stringliteral">"Computing the roots for:\n\t"</span>);</div>
|
|
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  <span class="keywordflow">for</span> (n = 0; n < degree; n++)</div>
|
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<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  {</div>
|
|
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  coeffs[n] = strtod(argv[n + 1], NULL);</div>
|
|
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  <span class="keywordflow">if</span> (n < degree - 1 && coeffs[n] != 0)</div>
|
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<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  printf(<span class="stringliteral">"(%Lg) x^%d + "</span>, coeffs[n], degree - n - 1);</div>
|
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<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (coeffs[n] != 0)</div>
|
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<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  printf(<span class="stringliteral">"(%Lg) x^%d = 0\n"</span>, coeffs[n], degree - n - 1);</div>
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<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  </div>
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<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  <span class="keywordtype">double</span> tmp;</div>
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<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  <span class="keywordflow">if</span> (n > 0)</div>
|
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<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  coeffs[n] /= tmp; <span class="comment">/* numerical errors less when the first</span></div>
|
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<div class="line"><a name="l00157"></a><span class="lineno"> 157</span> <span class="comment"> coefficient is "1" */</span></div>
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<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  <span class="keywordflow">else</span></div>
|
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<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  {</div>
|
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<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  tmp = coeffs[0];</div>
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<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  coeffs[0] = 1;</div>
|
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<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  }</div>
|
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<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  </div>
|
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<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  <span class="comment">/* initialize root approximations with random values */</span></div>
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<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  <span class="keywordflow">if</span> (n < degree - 1)</div>
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<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  {</div>
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<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  s0[n] = (<span class="keywordtype">long</span> double)rand() + (<span class="keywordtype">long</span> double)rand() * I;</div>
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<div class="line"><a name="l00168"></a><span class="lineno"> 168</span> <span class="preprocessor">#if defined(DEBUG) || !defined(NDEBUG)</span></div>
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<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  fprintf(log_file, <span class="stringliteral">"root_%d,"</span>, n);</div>
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<div class="line"><a name="l00170"></a><span class="lineno"> 170</span> <span class="preprocessor">#endif</span></div>
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<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  }</div>
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<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  }</div>
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<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  </div>
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<div class="line"><a name="l00174"></a><span class="lineno"> 174</span> <span class="preprocessor">#if defined(DEBUG) || !defined(NDEBUG)</span></div>
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<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  fprintf(log_file, <span class="stringliteral">"avg. correction"</span>);</div>
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<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  fprintf(log_file, <span class="stringliteral">"\n0,"</span>);</div>
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<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  <span class="keywordflow">for</span> (n = 0; n < degree - 1; n++)</div>
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<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  fprintf(log_file, <span class="stringliteral">"%s,"</span>, <a class="code" href="../../da/d38/durand__kerner__roots_8c.html#afa5b04ce11475d67049cba8273741fb7">complex_str</a>(s0[n]));</div>
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<div class="line"><a name="l00179"></a><span class="lineno"> 179</span> <span class="preprocessor">#endif</span></div>
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<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  </div>
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<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  <span class="keywordtype">double</span> tol_condition = 1;</div>
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<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">long</span> iter = 0;</div>
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<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  </div>
|
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<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  clock_t end_time, start_time = clock();</div>
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<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  <span class="keywordflow">while</span> (!<a class="code" href="../../da/d38/durand__kerner__roots_8c.html#a26d5695ebed0818a3e7cf4b10aacab52">check_termination</a>(tol_condition) && iter < INT_MAX)</div>
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<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  {</div>
|
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<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  <span class="keywordtype">long</span> <span class="keywordtype">double</span> complex delta = 0;</div>
|
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<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  tol_condition = 0;</div>
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<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  iter++;</div>
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<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  </div>
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<div class="line"><a name="l00191"></a><span class="lineno"> 191</span> <span class="preprocessor">#if defined(DEBUG) || !defined(NDEBUG)</span></div>
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<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  fprintf(log_file, <span class="stringliteral">"\n%ld,"</span>, iter);</div>
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<div class="line"><a name="l00193"></a><span class="lineno"> 193</span> <span class="preprocessor">#endif</span></div>
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<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  </div>
|
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<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  <span class="keywordflow">for</span> (n = 0; n < degree - 1; n++)</div>
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<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  {</div>
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<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  <span class="keywordtype">long</span> <span class="keywordtype">double</span> complex numerator =</div>
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<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  <a class="code" href="../../da/d38/durand__kerner__roots_8c.html#a321f9781a9744ccdaf0aba89f35ec29c">poly_function</a>(coeffs, degree, s0[n]);</div>
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<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  <span class="keywordtype">long</span> <span class="keywordtype">double</span> complex denominator = 1.0;</div>
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<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  <span class="keywordflow">for</span> (i = 0; i < degree - 1; i++)</div>
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<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  <span class="keywordflow">if</span> (i != n)</div>
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<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  denominator *= s0[n] - s0[i];</div>
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<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  </div>
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<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  delta = numerator / denominator;</div>
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<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  </div>
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<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  <span class="keywordflow">if</span> (isnan(cabsl(delta)) || isinf(cabsl(delta)))</div>
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<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  {</div>
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<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  printf(<span class="stringliteral">"\n\nOverflow/underrun error - got value = %Lg"</span>,</div>
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<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  cabsl(delta));</div>
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<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  <span class="keywordflow">goto</span> end;</div>
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<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  }</div>
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<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  </div>
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<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  s0[n] -= delta;</div>
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<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  </div>
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<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  tol_condition = fmaxl(tol_condition, fabsl(cabsl(delta)));</div>
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<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  </div>
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<div class="line"><a name="l00217"></a><span class="lineno"> 217</span> <span class="preprocessor">#if defined(DEBUG) || !defined(NDEBUG)</span></div>
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<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  fprintf(log_file, <span class="stringliteral">"%s,"</span>, <a class="code" href="../../da/d38/durand__kerner__roots_8c.html#afa5b04ce11475d67049cba8273741fb7">complex_str</a>(s0[n]));</div>
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<div class="line"><a name="l00219"></a><span class="lineno"> 219</span> <span class="preprocessor">#endif</span></div>
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<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  }</div>
|
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<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  <span class="comment">// tol_condition /= (degree - 1);</span></div>
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<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  </div>
|
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<div class="line"><a name="l00223"></a><span class="lineno"> 223</span> <span class="preprocessor">#if defined(DEBUG) || !defined(NDEBUG)</span></div>
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<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  <span class="keywordflow">if</span> (iter % 500 == 0)</div>
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<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  {</div>
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<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  printf(<span class="stringliteral">"Iter: %lu\t"</span>, iter);</div>
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|
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  <span class="keywordflow">for</span> (n = 0; n < degree - 1; n++) printf(<span class="stringliteral">"\t%s"</span>, <a class="code" href="../../da/d38/durand__kerner__roots_8c.html#afa5b04ce11475d67049cba8273741fb7">complex_str</a>(s0[n]));</div>
|
|
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  printf(<span class="stringliteral">"\t\tabsolute average change: %.4g\n"</span>, tol_condition);</div>
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<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  }</div>
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<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  </div>
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<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  fprintf(log_file, <span class="stringliteral">"%.4g"</span>, tol_condition);</div>
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<div class="line"><a name="l00232"></a><span class="lineno"> 232</span> <span class="preprocessor">#endif</span></div>
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<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  }</div>
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<div class="line"><a name="l00234"></a><span class="lineno"> 234</span> end:</div>
|
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<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  </div>
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<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  end_time = clock();</div>
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<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  </div>
|
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<div class="line"><a name="l00238"></a><span class="lineno"> 238</span> <span class="preprocessor">#if defined(DEBUG) || !defined(NDEBUG)</span></div>
|
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<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  fclose(log_file);</div>
|
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<div class="line"><a name="l00240"></a><span class="lineno"> 240</span> <span class="preprocessor">#endif</span></div>
|
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<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  </div>
|
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<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  printf(<span class="stringliteral">"\nIterations: %lu\n"</span>, iter);</div>
|
|
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  <span class="keywordflow">for</span> (n = 0; n < degree - 1; n++) printf(<span class="stringliteral">"\t%s\n"</span>, <a class="code" href="../../da/d38/durand__kerner__roots_8c.html#afa5b04ce11475d67049cba8273741fb7">complex_str</a>(s0[n]));</div>
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|
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  printf(<span class="stringliteral">"absolute average change: %.4g\n"</span>, tol_condition);</div>
|
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<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  printf(<span class="stringliteral">"Time taken: %.4g sec\n"</span>,</div>
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<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  (end_time - start_time) / (<span class="keywordtype">double</span>)CLOCKS_PER_SEC);</div>
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<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  </div>
|
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<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  free(coeffs);</div>
|
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<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  free(s0);</div>
|
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<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  </div>
|
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<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a name="l00252"></a><span class="lineno"> 252</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="../../da/d38/durand__kerner__roots_8c_a3c04138a5bfe5d72780bb7e82a18e627_cgraph.svg" width="238" 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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</div>
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</div>
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<a id="a321f9781a9744ccdaf0aba89f35ec29c"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a321f9781a9744ccdaf0aba89f35ec29c">◆ </a></span>poly_function()</h2>
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<div class="memitem">
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<div class="memproto">
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<table class="memname">
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<tr>
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<td class="memname">long double complex poly_function </td>
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<td>(</td>
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<td class="paramtype">long double * </td>
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<td class="paramname"><em>coeffs</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">unsigned int </td>
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<td class="paramname"><em>degree</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">long double complex </td>
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<td class="paramname"><em>x</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>Evaluate the value of a polynomial with given coefficients. </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="paramdir">[in]</td><td class="paramname">coeffs</td><td>coefficients of the polynomial </td></tr>
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<tr><td class="paramdir">[in]</td><td class="paramname">degree</td><td>degree of polynomial </td></tr>
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<tr><td class="paramdir">[in]</td><td class="paramname">x</td><td>point at which to evaluate the polynomial </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>\(f(x)\) </dd></dl>
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<div class="fragment"><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>  <span class="keywordtype">long</span> <span class="keywordtype">double</span> complex out = 0.;</div>
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<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> n;</div>
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<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  </div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="keywordflow">for</span> (n = 0; n < degree; n++) out += coeffs[n] * cpow(x, degree - n - 1);</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">return</span> out;</div>
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<div class="line"><a name="l00059"></a><span class="lineno"> 59</span> }</div>
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</div><!-- fragment -->
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<div class="ttc" id="adurand__kerner__roots_8c_html_afa5b04ce11475d67049cba8273741fb7"><div class="ttname"><a href="../../da/d38/durand__kerner__roots_8c.html#afa5b04ce11475d67049cba8273741fb7">complex_str</a></div><div class="ttdeci">const char * complex_str(long double complex x)</div><div class="ttdoc">create a textual form of complex number</div><div class="ttdef"><b>Definition:</b> durand_kerner_roots.c:66</div></div>
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<div class="ttc" id="adurand__kerner__roots_8c_html_a26d5695ebed0818a3e7cf4b10aacab52"><div class="ttname"><a href="../../da/d38/durand__kerner__roots_8c.html#a26d5695ebed0818a3e7cf4b10aacab52">check_termination</a></div><div class="ttdeci">char check_termination(long double delta)</div><div class="ttdoc">check for termination condition</div><div class="ttdef"><b>Definition:</b> durand_kerner_roots.c:83</div></div>
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<div class="ttc" id="adurand__kerner__roots_8c_html_a321f9781a9744ccdaf0aba89f35ec29c"><div class="ttname"><a href="../../da/d38/durand__kerner__roots_8c.html#a321f9781a9744ccdaf0aba89f35ec29c">poly_function</a></div><div class="ttdeci">long double complex poly_function(long double *coeffs, unsigned int degree, long double complex x)</div><div class="ttdoc">Evaluate the value of a polynomial with given coefficients.</div><div class="ttdef"><b>Definition:</b> durand_kerner_roots.c:50</div></div>
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<div class="ttc" id="adurand__kerner__roots_8c_html_af270a96662132d0385cb6b4637c5a689"><div class="ttname"><a href="../../da/d38/durand__kerner__roots_8c.html#af270a96662132d0385cb6b4637c5a689">ACCURACY</a></div><div class="ttdeci">#define ACCURACY</div><div class="ttdoc">maximum accuracy limit</div><div class="ttdef"><b>Definition:</b> durand_kerner_roots.c:41</div></div>
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