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<div id="projectname">TheAlgorithms/C++<span id="projectnumber"> 1.0.0</span>
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</div>
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<div id="projectbrief">Set of algorithms implemented in C++.</div>
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<div id="projectbrief">All the algorithms implemented in C++</div>
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@@ -128,7 +145,9 @@ Include dependency graph for durand_kerner_roots.cpp:</div>
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<div class="dyncontent">
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<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../d4/d26/durand__kerner__roots_8cpp__incl.svg" width="100%" height="394"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div></div>
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<p><a href="../../da/df2/durand__kerner__roots_8cpp_source.html">Go to the source code of this file.</a></p>
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<table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="define-members" name="define-members"></a>
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Macros</h2></td></tr>
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<tr class="memitem:af270a96662132d0385cb6b4637c5a689" id="r_af270a96662132d0385cb6b4637c5a689"><td class="memItemLeft" align="right" valign="top">#define </td><td class="memItemRight" valign="bottom"><a class="el" href="#af270a96662132d0385cb6b4637c5a689">ACCURACY</a>   1e-10</td></tr>
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@@ -139,13 +158,13 @@ Macros</h2></td></tr>
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</table><table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
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Functions</h2></td></tr>
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<tr class="memitem:ae2ab49ba1969d7a5988f9bc2c8924569" id="r_ae2ab49ba1969d7a5988f9bc2c8924569"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a>< double > </td><td class="memItemRight" valign="bottom"><a class="el" href="#ae2ab49ba1969d7a5988f9bc2c8924569">poly_function</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< double > &coeffs, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a>< double > x)</td></tr>
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<tr class="memitem:ae2ab49ba1969d7a5988f9bc2c8924569" id="r_ae2ab49ba1969d7a5988f9bc2c8924569"><td class="memItemLeft" align="right" valign="top">std::complex< double > </td><td class="memItemRight" valign="bottom"><a class="el" href="#ae2ab49ba1969d7a5988f9bc2c8924569">poly_function</a> (const std::valarray< double > &coeffs, std::complex< double > x)</td></tr>
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<tr class="separator:ae2ab49ba1969d7a5988f9bc2c8924569"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a90219e35062007d1f1b68e9af071ab5c" id="r_a90219e35062007d1f1b68e9af071ab5c"><td class="memItemLeft" align="right" valign="top">const char * </td><td class="memItemRight" valign="bottom"><a class="el" href="#a90219e35062007d1f1b68e9af071ab5c">complex_str</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a>< double > &x)</td></tr>
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<tr class="memitem:a90219e35062007d1f1b68e9af071ab5c" id="r_a90219e35062007d1f1b68e9af071ab5c"><td class="memItemLeft" align="right" valign="top">const char * </td><td class="memItemRight" valign="bottom"><a class="el" href="#a90219e35062007d1f1b68e9af071ab5c">complex_str</a> (const std::complex< double > &x)</td></tr>
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<tr class="separator:a90219e35062007d1f1b68e9af071ab5c"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a024b8bc4755863315456d573a6732377" id="r_a024b8bc4755863315456d573a6732377"><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="#a024b8bc4755863315456d573a6732377">check_termination</a> (long double delta)</td></tr>
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<tr class="separator:a024b8bc4755863315456d573a6732377"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a2c35b320ace8677f9b331faf94f8b2fd" id="r_a2c35b320ace8677f9b331faf94f8b2fd"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a>< uint32_t, double > </td><td class="memItemRight" valign="bottom"><a class="el" href="#a2c35b320ace8677f9b331faf94f8b2fd">durand_kerner_algo</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< double > &coeffs, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a>< double > > *roots, bool write_log=false)</td></tr>
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<tr class="memitem:a2c35b320ace8677f9b331faf94f8b2fd" id="r_a2c35b320ace8677f9b331faf94f8b2fd"><td class="memItemLeft" align="right" valign="top">std::pair< uint32_t, double > </td><td class="memItemRight" valign="bottom"><a class="el" href="#a2c35b320ace8677f9b331faf94f8b2fd">durand_kerner_algo</a> (const std::valarray< double > &coeffs, std::valarray< std::complex< double > > *roots, bool write_log=false)</td></tr>
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<tr class="separator:a2c35b320ace8677f9b331faf94f8b2fd"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a1440a7779ac56f47a3f355ce4a8c7da0" id="r_a1440a7779ac56f47a3f355ce4a8c7da0"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a> ()</td></tr>
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<tr class="separator:a1440a7779ac56f47a3f355ce4a8c7da0"><td class="memSeparator" colspan="2"> </td></tr>
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@@ -170,6 +189,8 @@ Functions</h2></td></tr>
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iteration." style="pointer-events: none;" width="400" class="inline"/> <img src="https://raw.githubusercontent.com/TheAlgorithms/C-Plus-Plus/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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<p class="definition">Definition in file <a class="el" href="../../da/df2/durand__kerner__roots_8cpp_source.html">durand_kerner_roots.cpp</a>.</p>
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||||
</div><h2 class="groupheader">Macro Definition Documentation</h2>
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<a id="af270a96662132d0385cb6b4637c5a689" name="af270a96662132d0385cb6b4637c5a689"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#af270a96662132d0385cb6b4637c5a689">◆ </a></span>ACCURACY</h2>
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@@ -184,6 +205,8 @@ Functions</h2></td></tr>
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</div><div class="memdoc">
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<p>maximum accuracy limit </p>
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<p class="definition">Definition at line <a class="el" href="../../da/df2/durand__kerner__roots_8cpp_source.html#l00046">46</a> of file <a class="el" href="../../da/df2/durand__kerner__roots_8cpp_source.html">durand_kerner_roots.cpp</a>.</p>
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</div>
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<h2 class="groupheader">Function Documentation</h2>
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<dl class="section return"><dt>Returns</dt><dd><code>false</code> if termination not reached </dd>
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<dd>
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<code>true</code> if termination reached </dd></dl>
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<p class="definition">Definition at line <a class="el" href="../../da/df2/durand__kerner__roots_8cpp_source.html#l00092">92</a> of file <a class="el" href="../../da/df2/durand__kerner__roots_8cpp_source.html">durand_kerner_roots.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 92</span> {</div>
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<div class="line"><span class="lineno"> 93</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"><span class="lineno"> 94</span> <span class="keywordflow">if</span> (std::abs(past_delta - delta) <= <a class="code hl_define" href="#af270a96662132d0385cb6b4637c5a689">ACCURACY</a> || delta < <a class="code hl_define" href="#af270a96662132d0385cb6b4637c5a689">ACCURACY</a>)</div>
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@@ -217,7 +242,7 @@ Functions</h2></td></tr>
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||||
<div class="line"><span class="lineno"> 96</span> past_delta = delta;</div>
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<div class="line"><span class="lineno"> 97</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><span class="lineno"> 98</span>}</div>
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<div class="ttc" id="adurand__kerner__roots_8cpp_html_af270a96662132d0385cb6b4637c5a689"><div class="ttname"><a href="#af270a96662132d0385cb6b4637c5a689">ACCURACY</a></div><div class="ttdeci">#define ACCURACY</div><div class="ttdef"><b>Definition</b> durand_kerner_roots.cpp:46</div></div>
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<div class="ttc" id="adurand__kerner__roots_8cpp_html_af270a96662132d0385cb6b4637c5a689"><div class="ttname"><a href="#af270a96662132d0385cb6b4637c5a689">ACCURACY</a></div><div class="ttdeci">#define ACCURACY</div><div class="ttdef"><b>Definition</b> <a href="../../da/df2/durand__kerner__roots_8cpp_source.html#l00046">durand_kerner_roots.cpp:46</a></div></div>
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</div><!-- fragment -->
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@@ -230,7 +255,7 @@ Functions</h2></td></tr>
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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">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a>< double > &</td> <td class="paramname"><span class="paramname"><em>x</em></span></td><td>)</td>
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<td class="paramtype">const std::complex< double > &</td> <td class="paramname"><span class="paramname"><em>x</em></span></td><td>)</td>
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<td></td>
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@@ -242,23 +267,17 @@ Functions</h2></td></tr>
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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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<p class="definition">Definition at line <a class="el" href="../../da/df2/durand__kerner__roots_8cpp_source.html#l00077">77</a> of file <a class="el" href="../../da/df2/durand__kerner__roots_8cpp_source.html">durand_kerner_roots.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 77</span> {</div>
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<div class="line"><span class="lineno"> 78</span><span class="preprocessor">#define MAX_BUFF_SIZE 50</span></div>
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<div class="line"><span class="lineno"> 79</span> <span class="keyword">static</span> <span class="keywordtype">char</span> msg[MAX_BUFF_SIZE];</div>
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<div class="line"><span class="lineno"> 80</span> </div>
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<div class="line"><span class="lineno"> 81</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/fprintf.html">std::snprintf</a>(msg, MAX_BUFF_SIZE, <span class="stringliteral">"% 7.04g%+7.04gj"</span>, x.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/real.html">real</a>(), x.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/imag.html">imag</a>());</div>
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<div class="line"><span class="lineno"> 81</span> std::snprintf(msg, MAX_BUFF_SIZE, <span class="stringliteral">"% 7.04g%+7.04gj"</span>, x.real(), x.imag());</div>
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<div class="line"><span class="lineno"> 82</span> </div>
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<div class="line"><span class="lineno"> 83</span> <span class="keywordflow">return</span> msg;</div>
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<div class="line"><span class="lineno"> 84</span>}</div>
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<div class="ttc" id="afprintf_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/c/fprintf.html">std::snprintf</a></div><div class="ttdeci">T snprintf(T... args)</div></div>
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||||
<div class="ttc" id="aimag_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/complex/imag.html">std::complex::imag</a></div><div class="ttdeci">T imag(T... args)</div></div>
|
||||
<div class="ttc" id="areal_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/complex/real.html">std::complex::real</a></div><div class="ttdeci">T real(T... args)</div></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/df2/durand__kerner__roots_8cpp_a90219e35062007d1f1b68e9af071ab5c_cgraph.svg" width="284" height="135"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
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</div>
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</div><!-- fragment -->
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<a id="a2c35b320ace8677f9b331faf94f8b2fd" name="a2c35b320ace8677f9b331faf94f8b2fd"></a>
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@@ -268,14 +287,14 @@ Here is the call graph for this function:</div>
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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"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a>< uint32_t, double > durand_kerner_algo </td>
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<td class="memname">std::pair< uint32_t, double > durand_kerner_algo </td>
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<td>(</td>
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<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< double > &</td> <td class="paramname"><span class="paramname"><em>coeffs</em></span>, </td>
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<td class="paramtype">const std::valarray< double > &</td> <td class="paramname"><span class="paramname"><em>coeffs</em></span>, </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"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a>< double > > *</td> <td class="paramname"><span class="paramname"><em>roots</em></span>, </td>
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<td class="paramtype">std::valarray< std::complex< double > > *</td> <td class="paramname"><span class="paramname"><em>roots</em></span>, </td>
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<td class="paramkey"></td>
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@@ -294,20 +313,22 @@ Here is the call graph for this function:</div>
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</dd>
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</dl>
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<dl class="section return"><dt>Returns</dt><dd>pair of values - number of iterations taken and final accuracy achieved </dd></dl>
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<p class="definition">Definition at line <a class="el" href="../../da/df2/durand__kerner__roots_8cpp_source.html#l00110">110</a> of file <a class="el" href="../../da/df2/durand__kerner__roots_8cpp_source.html">durand_kerner_roots.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 112</span> {</div>
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<div class="line"><span class="lineno"> 113</span> <span class="keywordtype">long</span> <span class="keywordtype">double</span> tol_condition = 1;</div>
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<div class="line"><span class="lineno"> 114</span> uint32_t iter = 0;</div>
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<div class="line"><span class="lineno"> 115</span> <span class="keywordtype">int</span> n;</div>
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<div class="line"><span class="lineno"> 116</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a> log_file;</div>
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<div class="line"><span class="lineno"> 116</span> std::ofstream log_file;</div>
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<div class="line"><span class="lineno"> 117</span> </div>
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<div class="line"><span class="lineno"> 118</span> <span class="keywordflow">if</span> (write_log) {</div>
|
||||
<div class="line"><span class="lineno"> 119</span> <span class="comment">/*</span></div>
|
||||
<div class="line"><span class="lineno"> 120</span><span class="comment"> * store intermediate values to a CSV file</span></div>
|
||||
<div class="line"><span class="lineno"> 121</span><span class="comment"> */</span></div>
|
||||
<div class="line"><span class="lineno"> 122</span> log_file.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/open.html">open</a>(<span class="stringliteral">"durand_kerner.log.csv"</span>);</div>
|
||||
<div class="line"><span class="lineno"> 123</span> <span class="keywordflow">if</span> (!log_file.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>()) {</div>
|
||||
<div class="line"><span class="lineno"> 124</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/perror.html">perror</a>(<span class="stringliteral">"Unable to create a storage log file!"</span>);</div>
|
||||
<div class="line"><span class="lineno"> 125</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a>(EXIT_FAILURE);</div>
|
||||
<div class="line"><span class="lineno"> 122</span> log_file.open(<span class="stringliteral">"durand_kerner.log.csv"</span>);</div>
|
||||
<div class="line"><span class="lineno"> 123</span> <span class="keywordflow">if</span> (!log_file.is_open()) {</div>
|
||||
<div class="line"><span class="lineno"> 124</span> perror(<span class="stringliteral">"Unable to create a storage log file!"</span>);</div>
|
||||
<div class="line"><span class="lineno"> 125</span> std::exit(EXIT_FAILURE);</div>
|
||||
<div class="line"><span class="lineno"> 126</span> }</div>
|
||||
<div class="line"><span class="lineno"> 127</span> log_file << <span class="stringliteral">"iter#,"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 128</span> </div>
|
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@@ -326,7 +347,7 @@ Here is the call graph for this function:</div>
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||||
<div class="line"><span class="lineno"> 141</span> iter++;</div>
|
||||
<div class="line"><span class="lineno"> 142</span> break_loop = <span class="keyword">false</span>;</div>
|
||||
<div class="line"><span class="lineno"> 143</span> </div>
|
||||
<div class="line"><span class="lineno"> 144</span> <span class="keywordflow">if</span> (log_file.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>())</div>
|
||||
<div class="line"><span class="lineno"> 144</span> <span class="keywordflow">if</span> (log_file.is_open())</div>
|
||||
<div class="line"><span class="lineno"> 145</span> log_file << <span class="stringliteral">"\n"</span> << iter << <span class="stringliteral">","</span>;</div>
|
||||
<div class="line"><span class="lineno"> 146</span> </div>
|
||||
<div class="line"><span class="lineno"> 147</span><span class="preprocessor">#ifdef _OPENMP</span></div>
|
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@@ -336,17 +357,17 @@ Here is the call graph for this function:</div>
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<div class="line"><span class="lineno"> 151</span> <span class="keywordflow">if</span> (break_loop)</div>
|
||||
<div class="line"><span class="lineno"> 152</span> <span class="keywordflow">continue</span>;</div>
|
||||
<div class="line"><span class="lineno"> 153</span> </div>
|
||||
<div class="line"><span class="lineno"> 154</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex<double></a> numerator, denominator;</div>
|
||||
<div class="line"><span class="lineno"> 154</span> std::complex<double> numerator, denominator;</div>
|
||||
<div class="line"><span class="lineno"> 155</span> numerator = <a class="code hl_function" href="#ae2ab49ba1969d7a5988f9bc2c8924569">poly_function</a>(coeffs, (*roots)[n]);</div>
|
||||
<div class="line"><span class="lineno"> 156</span> denominator = 1.0;</div>
|
||||
<div class="line"><span class="lineno"> 157</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < roots->size(); i++)</div>
|
||||
<div class="line"><span class="lineno"> 158</span> <span class="keywordflow">if</span> (i != n)</div>
|
||||
<div class="line"><span class="lineno"> 159</span> denominator *= (*roots)[n] - (*roots)[i];</div>
|
||||
<div class="line"><span class="lineno"> 160</span> </div>
|
||||
<div class="line"><span class="lineno"> 161</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex<long double></a> delta = numerator / denominator;</div>
|
||||
<div class="line"><span class="lineno"> 161</span> std::complex<long double> delta = numerator / denominator;</div>
|
||||
<div class="line"><span class="lineno"> 162</span> </div>
|
||||
<div class="line"><span class="lineno"> 163</span> <span class="keywordflow">if</span> (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/isnan.html">std::isnan</a>(std::abs(delta)) || <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/isinf.html">std::isinf</a>(std::abs(delta))) {</div>
|
||||
<div class="line"><span class="lineno"> 164</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> << <span class="stringliteral">"\n\nOverflow/underrun error - got value = "</span></div>
|
||||
<div class="line"><span class="lineno"> 163</span> <span class="keywordflow">if</span> (std::isnan(std::abs(delta)) || std::isinf(std::abs(delta))) {</div>
|
||||
<div class="line"><span class="lineno"> 164</span> std::cerr << <span class="stringliteral">"\n\nOverflow/underrun error - got value = "</span></div>
|
||||
<div class="line"><span class="lineno"> 165</span> << std::abs(delta) << <span class="stringliteral">"\n"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 166</span> <span class="comment">// return std::pair<uint32_t, double>(iter, tol_condition);</span></div>
|
||||
<div class="line"><span class="lineno"> 167</span> break_loop = <span class="keyword">true</span>;</div>
|
||||
@@ -357,54 +378,38 @@ Here is the call graph for this function:</div>
|
||||
<div class="line"><span class="lineno"> 172</span><span class="preprocessor">#ifdef _OPENMP</span></div>
|
||||
<div class="line"><span class="lineno"> 173</span><span class="preprocessor">#pragma omp critical</span></div>
|
||||
<div class="line"><span class="lineno"> 174</span><span class="preprocessor">#endif</span></div>
|
||||
<div class="line"><span class="lineno"> 175</span> tol_condition = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a>(tol_condition, std::abs(std::abs(delta)));</div>
|
||||
<div class="line"><span class="lineno"> 175</span> tol_condition = std::max(tol_condition, std::abs(std::abs(delta)));</div>
|
||||
<div class="line"><span class="lineno"> 176</span> }</div>
|
||||
<div class="line"><span class="lineno"> 177</span> <span class="comment">// tol_condition /= (degree - 1);</span></div>
|
||||
<div class="line"><span class="lineno"> 178</span> </div>
|
||||
<div class="line"><span class="lineno"> 179</span> <span class="keywordflow">if</span> (break_loop)</div>
|
||||
<div class="line"><span class="lineno"> 180</span> <span class="keywordflow">break</span>;</div>
|
||||
<div class="line"><span class="lineno"> 181</span> </div>
|
||||
<div class="line"><span class="lineno"> 182</span> <span class="keywordflow">if</span> (log_file.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>()) {</div>
|
||||
<div class="line"><span class="lineno"> 182</span> <span class="keywordflow">if</span> (log_file.is_open()) {</div>
|
||||
<div class="line"><span class="lineno"> 183</span> <span class="keywordflow">for</span> (n = 0; n < roots->size(); n++)</div>
|
||||
<div class="line"><span class="lineno"> 184</span> log_file << <a class="code hl_function" href="#a90219e35062007d1f1b68e9af071ab5c">complex_str</a>((*roots)[n]) << <span class="stringliteral">","</span>;</div>
|
||||
<div class="line"><span class="lineno"> 185</span> }</div>
|
||||
<div class="line"><span class="lineno"> 186</span> </div>
|
||||
<div class="line"><span class="lineno"> 187</span><span class="preprocessor">#if defined(DEBUG) || !defined(NDEBUG)</span></div>
|
||||
<div class="line"><span class="lineno"> 188</span> <span class="keywordflow">if</span> (iter % 500 == 0) {</div>
|
||||
<div class="line"><span class="lineno"> 189</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Iter: "</span> << iter << <span class="stringliteral">"\t"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 189</span> std::cout << <span class="stringliteral">"Iter: "</span> << iter << <span class="stringliteral">"\t"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 190</span> <span class="keywordflow">for</span> (n = 0; n < roots->size(); n++)</div>
|
||||
<div class="line"><span class="lineno"> 191</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"\t"</span> << <a class="code hl_function" href="#a90219e35062007d1f1b68e9af071ab5c">complex_str</a>((*roots)[n]);</div>
|
||||
<div class="line"><span class="lineno"> 192</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"\t\tabsolute average change: "</span> << tol_condition</div>
|
||||
<div class="line"><span class="lineno"> 191</span> std::cout << <span class="stringliteral">"\t"</span> << <a class="code hl_function" href="#a90219e35062007d1f1b68e9af071ab5c">complex_str</a>((*roots)[n]);</div>
|
||||
<div class="line"><span class="lineno"> 192</span> std::cout << <span class="stringliteral">"\t\tabsolute average change: "</span> << tol_condition</div>
|
||||
<div class="line"><span class="lineno"> 193</span> << <span class="stringliteral">"\n"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 194</span> }</div>
|
||||
<div class="line"><span class="lineno"> 195</span><span class="preprocessor">#endif</span></div>
|
||||
<div class="line"><span class="lineno"> 196</span> </div>
|
||||
<div class="line"><span class="lineno"> 197</span> <span class="keywordflow">if</span> (log_file.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">is_open</a>())</div>
|
||||
<div class="line"><span class="lineno"> 197</span> <span class="keywordflow">if</span> (log_file.is_open())</div>
|
||||
<div class="line"><span class="lineno"> 198</span> log_file << tol_condition;</div>
|
||||
<div class="line"><span class="lineno"> 199</span> }</div>
|
||||
<div class="line"><span class="lineno"> 200</span> </div>
|
||||
<div class="line"><span class="lineno"> 201</span> <span class="keywordflow">return</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair<uint32_t, long double></a>(iter, tol_condition);</div>
|
||||
<div class="line"><span class="lineno"> 201</span> <span class="keywordflow">return</span> std::pair<uint32_t, long double>(iter, tol_condition);</div>
|
||||
<div class="line"><span class="lineno"> 202</span>}</div>
|
||||
<div class="ttc" id="abasic_ofstream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a></div></div>
|
||||
<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a></div></div>
|
||||
<div class="ttc" id="acomplex_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a></div></div>
|
||||
<div class="ttc" id="adurand__kerner__roots_8cpp_html_a024b8bc4755863315456d573a6732377"><div class="ttname"><a href="#a024b8bc4755863315456d573a6732377">check_termination</a></div><div class="ttdeci">bool check_termination(long double delta)</div><div class="ttdef"><b>Definition</b> durand_kerner_roots.cpp:92</div></div>
|
||||
<div class="ttc" id="adurand__kerner__roots_8cpp_html_a90219e35062007d1f1b68e9af071ab5c"><div class="ttname"><a href="#a90219e35062007d1f1b68e9af071ab5c">complex_str</a></div><div class="ttdeci">const char * complex_str(const std::complex< double > &x)</div><div class="ttdef"><b>Definition</b> durand_kerner_roots.cpp:77</div></div>
|
||||
<div class="ttc" id="adurand__kerner__roots_8cpp_html_ae2ab49ba1969d7a5988f9bc2c8924569"><div class="ttname"><a href="#ae2ab49ba1969d7a5988f9bc2c8924569">poly_function</a></div><div class="ttdeci">std::complex< double > poly_function(const std::valarray< double > &coeffs, std::complex< double > x)</div><div class="ttdef"><b>Definition</b> durand_kerner_roots.cpp:54</div></div>
|
||||
<div class="ttc" id="aexit_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/program/exit.html">std::exit</a></div><div class="ttdeci">T exit(T... args)</div></div>
|
||||
<div class="ttc" id="ais_open_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">std::ofstream::is_open</a></div><div class="ttdeci">T is_open(T... args)</div></div>
|
||||
<div class="ttc" id="aisinf_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/isinf.html">std::isinf</a></div><div class="ttdeci">T isinf(T... args)</div></div>
|
||||
<div class="ttc" id="aisnan_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/isnan.html">std::isnan</a></div><div class="ttdeci">T isnan(T... args)</div></div>
|
||||
<div class="ttc" id="amax_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a></div><div class="ttdeci">T max(T... args)</div></div>
|
||||
<div class="ttc" id="aopen_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ofstream/open.html">std::ofstream::open</a></div><div class="ttdeci">T open(T... args)</div></div>
|
||||
<div class="ttc" id="apair_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a></div></div>
|
||||
<div class="ttc" id="aperror_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/c/perror.html">std::perror</a></div><div class="ttdeci">T perror(T... args)</div></div>
|
||||
</div><!-- fragment --><div class="dynheader">
|
||||
Here is the call graph for this function:</div>
|
||||
<div class="dyncontent">
|
||||
<div class="center"><iframe scrolling="no" frameborder="0" src="../../da/df2/durand__kerner__roots_8cpp_a2c35b320ace8677f9b331faf94f8b2fd_cgraph.svg" width="526" height="431"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
|
||||
</div>
|
||||
|
||||
<div class="ttc" id="adurand__kerner__roots_8cpp_html_a024b8bc4755863315456d573a6732377"><div class="ttname"><a href="#a024b8bc4755863315456d573a6732377">check_termination</a></div><div class="ttdeci">bool check_termination(long double delta)</div><div class="ttdef"><b>Definition</b> <a href="../../da/df2/durand__kerner__roots_8cpp_source.html#l00092">durand_kerner_roots.cpp:92</a></div></div>
|
||||
<div class="ttc" id="adurand__kerner__roots_8cpp_html_a90219e35062007d1f1b68e9af071ab5c"><div class="ttname"><a href="#a90219e35062007d1f1b68e9af071ab5c">complex_str</a></div><div class="ttdeci">const char * complex_str(const std::complex< double > &x)</div><div class="ttdef"><b>Definition</b> <a href="../../da/df2/durand__kerner__roots_8cpp_source.html#l00077">durand_kerner_roots.cpp:77</a></div></div>
|
||||
<div class="ttc" id="adurand__kerner__roots_8cpp_html_ae2ab49ba1969d7a5988f9bc2c8924569"><div class="ttname"><a href="#ae2ab49ba1969d7a5988f9bc2c8924569">poly_function</a></div><div class="ttdeci">std::complex< double > poly_function(const std::valarray< double > &coeffs, std::complex< double > x)</div><div class="ttdef"><b>Definition</b> <a href="../../da/df2/durand__kerner__roots_8cpp_source.html#l00054">durand_kerner_roots.cpp:54</a></div></div>
|
||||
</div><!-- fragment -->
|
||||
</div>
|
||||
</div>
|
||||
<a id="a3c04138a5bfe5d72780bb7e82a18e627" name="a3c04138a5bfe5d72780bb7e82a18e627"></a>
|
||||
@@ -425,37 +430,39 @@ Here is the call graph for this function:</div>
|
||||
</tr>
|
||||
</table>
|
||||
</div><div class="memdoc">
|
||||
|
||||
<p class="definition">Definition at line <a class="el" href="../../da/df2/durand__kerner__roots_8cpp_source.html#l00284">284</a> of file <a class="el" href="../../da/df2/durand__kerner__roots_8cpp_source.html">durand_kerner_roots.cpp</a>.</p>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 284</span> {</div>
|
||||
<div class="line"><span class="lineno"> 285</span> <span class="comment">/* initialize random seed: */</span></div>
|
||||
<div class="line"><span class="lineno"> 286</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>));</div>
|
||||
<div class="line"><span class="lineno"> 286</span> std::srand(std::time(<span class="keyword">nullptr</span>));</div>
|
||||
<div class="line"><span class="lineno"> 287</span> </div>
|
||||
<div class="line"><span class="lineno"> 288</span> <span class="keywordflow">if</span> (argc < 2) {</div>
|
||||
<div class="line"><span class="lineno"> 289</span> <a class="code hl_function" href="#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>(); <span class="comment">// run tests when no input is provided</span></div>
|
||||
<div class="line"><span class="lineno"> 290</span> <a class="code hl_function" href="#a0283886819c7c140a023582b7269e2d0">test2</a>(); <span class="comment">// and skip tests when input polynomial is provided</span></div>
|
||||
<div class="line"><span class="lineno"> 291</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Please pass the coefficients of the polynomial as "</span></div>
|
||||
<div class="line"><span class="lineno"> 291</span> std::cout << <span class="stringliteral">"Please pass the coefficients of the polynomial as "</span></div>
|
||||
<div class="line"><span class="lineno"> 292</span> <span class="stringliteral">"commandline "</span></div>
|
||||
<div class="line"><span class="lineno"> 293</span> <span class="stringliteral">"arguments.\n"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 294</span> <span class="keywordflow">return</span> 0;</div>
|
||||
<div class="line"><span class="lineno"> 295</span> }</div>
|
||||
<div class="line"><span class="lineno"> 296</span> </div>
|
||||
<div class="line"><span class="lineno"> 297</span> <span class="keywordtype">int</span> n, degree = argc - 1; <span class="comment">// detected polynomial degree</span></div>
|
||||
<div class="line"><span class="lineno"> 298</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray<double></a> coeffs(degree); <span class="comment">// create coefficiencts array</span></div>
|
||||
<div class="line"><span class="lineno"> 298</span> std::valarray<double> coeffs(degree); <span class="comment">// create coefficiencts array</span></div>
|
||||
<div class="line"><span class="lineno"> 299</span> </div>
|
||||
<div class="line"><span class="lineno"> 300</span> <span class="comment">// number of roots = degree - 1</span></div>
|
||||
<div class="line"><span class="lineno"> 301</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray<std::complex<double></a>> s0(degree - 1);</div>
|
||||
<div class="line"><span class="lineno"> 301</span> std::valarray<std::complex<double>> s0(degree - 1);</div>
|
||||
<div class="line"><span class="lineno"> 302</span> </div>
|
||||
<div class="line"><span class="lineno"> 303</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Computing the roots for:\n\t"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 303</span> std::cout << <span class="stringliteral">"Computing the roots for:\n\t"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 304</span> <span class="keywordflow">for</span> (n = 0; n < degree; n++) {</div>
|
||||
<div class="line"><span class="lineno"> 305</span> coeffs[n] = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/strtof.html">strtod</a>(argv[n + 1], <span class="keyword">nullptr</span>);</div>
|
||||
<div class="line"><span class="lineno"> 305</span> coeffs[n] = strtod(argv[n + 1], <span class="keyword">nullptr</span>);</div>
|
||||
<div class="line"><span class="lineno"> 306</span> <span class="keywordflow">if</span> (n < degree - 1 && coeffs[n] != 0)</div>
|
||||
<div class="line"><span class="lineno"> 307</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"("</span> << coeffs[n] << <span class="stringliteral">") x^"</span> << degree - n - 1 << <span class="stringliteral">" + "</span>;</div>
|
||||
<div class="line"><span class="lineno"> 307</span> std::cout << <span class="stringliteral">"("</span> << coeffs[n] << <span class="stringliteral">") x^"</span> << degree - n - 1 << <span class="stringliteral">" + "</span>;</div>
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||||
<div class="line"><span class="lineno"> 308</span> <span class="keywordflow">else</span> <span class="keywordflow">if</span> (coeffs[n] != 0)</div>
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<div class="line"><span class="lineno"> 309</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"("</span> << coeffs[n] << <span class="stringliteral">") x^"</span> << degree - n - 1</div>
|
||||
<div class="line"><span class="lineno"> 309</span> std::cout << <span class="stringliteral">"("</span> << coeffs[n] << <span class="stringliteral">") x^"</span> << degree - n - 1</div>
|
||||
<div class="line"><span class="lineno"> 310</span> << <span class="stringliteral">" = 0\n"</span>;</div>
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||||
<div class="line"><span class="lineno"> 311</span> </div>
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<div class="line"><span class="lineno"> 312</span> <span class="comment">/* initialize root approximations with random values */</span></div>
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<div class="line"><span class="lineno"> 313</span> <span class="keywordflow">if</span> (n < degree - 1) {</div>
|
||||
<div class="line"><span class="lineno"> 314</span> s0[n] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex<double></a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % 100, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % 100);</div>
|
||||
<div class="line"><span class="lineno"> 314</span> s0[n] = std::complex<double>(std::rand() % 100, std::rand() % 100);</div>
|
||||
<div class="line"><span class="lineno"> 315</span> s0[n] -= 50.f;</div>
|
||||
<div class="line"><span class="lineno"> 316</span> s0[n] /= 50.f;</div>
|
||||
<div class="line"><span class="lineno"> 317</span> }</div>
|
||||
@@ -468,30 +475,24 @@ Here is the call graph for this function:</div>
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<div class="line"><span class="lineno"> 324</span> coeffs /= tmp;</div>
|
||||
<div class="line"><span class="lineno"> 325</span> }</div>
|
||||
<div class="line"><span class="lineno"> 326</span> </div>
|
||||
<div class="line"><span class="lineno"> 327</span> clock_t end_time, start_time = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">clock</a>();</div>
|
||||
<div class="line"><span class="lineno"> 327</span> clock_t end_time, start_time = clock();</div>
|
||||
<div class="line"><span class="lineno"> 328</span> <span class="keyword">auto</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <a class="code hl_function" href="#a2c35b320ace8677f9b331faf94f8b2fd">durand_kerner_algo</a>(coeffs, &s0, <span class="keyword">true</span>);</div>
|
||||
<div class="line"><span class="lineno"> 329</span> end_time = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">clock</a>();</div>
|
||||
<div class="line"><span class="lineno"> 329</span> end_time = clock();</div>
|
||||
<div class="line"><span class="lineno"> 330</span> </div>
|
||||
<div class="line"><span class="lineno"> 331</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"\nIterations: "</span> << <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.first << <span class="stringliteral">"\n"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 331</span> std::cout << <span class="stringliteral">"\nIterations: "</span> << <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.first << <span class="stringliteral">"\n"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 332</span> <span class="keywordflow">for</span> (n = 0; n < degree - 1; n++)</div>
|
||||
<div class="line"><span class="lineno"> 333</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"\t"</span> << <a class="code hl_function" href="#a90219e35062007d1f1b68e9af071ab5c">complex_str</a>(s0[n]) << <span class="stringliteral">"\n"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 334</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"absolute average change: "</span> << <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.second << <span class="stringliteral">"\n"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 335</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Time taken: "</span></div>
|
||||
<div class="line"><span class="lineno"> 333</span> std::cout << <span class="stringliteral">"\t"</span> << <a class="code hl_function" href="#a90219e35062007d1f1b68e9af071ab5c">complex_str</a>(s0[n]) << <span class="stringliteral">"\n"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 334</span> std::cout << <span class="stringliteral">"absolute average change: "</span> << <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.second << <span class="stringliteral">"\n"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 335</span> std::cout << <span class="stringliteral">"Time taken: "</span></div>
|
||||
<div class="line"><span class="lineno"> 336</span> << <span class="keyword">static_cast<</span><span class="keywordtype">double</span><span class="keyword">></span>(end_time - start_time) / CLOCKS_PER_SEC</div>
|
||||
<div class="line"><span class="lineno"> 337</span> << <span class="stringliteral">" sec\n"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 338</span> </div>
|
||||
<div class="line"><span class="lineno"> 339</span> <span class="keywordflow">return</span> 0;</div>
|
||||
<div class="line"><span class="lineno"> 340</span>}</div>
|
||||
<div class="ttc" id="aclock_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a></div><div class="ttdeci">T clock(T... args)</div></div>
|
||||
<div class="ttc" id="adurand__kerner__roots_8cpp_html_a0283886819c7c140a023582b7269e2d0"><div class="ttname"><a href="#a0283886819c7c140a023582b7269e2d0">test2</a></div><div class="ttdeci">void test2()</div><div class="ttdef"><b>Definition</b> durand_kerner_roots.cpp:243</div></div>
|
||||
<div class="ttc" id="adurand__kerner__roots_8cpp_html_a1440a7779ac56f47a3f355ce4a8c7da0"><div class="ttname"><a href="#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a></div><div class="ttdeci">void test1()</div><div class="ttdef"><b>Definition</b> durand_kerner_roots.cpp:208</div></div>
|
||||
<div class="ttc" id="adurand__kerner__roots_8cpp_html_a2c35b320ace8677f9b331faf94f8b2fd"><div class="ttname"><a href="#a2c35b320ace8677f9b331faf94f8b2fd">durand_kerner_algo</a></div><div class="ttdeci">std::pair< uint32_t, double > durand_kerner_algo(const std::valarray< double > &coeffs, std::valarray< std::complex< double > > *roots, bool write_log=false)</div><div class="ttdef"><b>Definition</b> durand_kerner_roots.cpp:110</div></div>
|
||||
<div class="ttc" id="afibonacci__sum_8cpp_html_aadb40ac4c74a7efc0680b83eeee138aa"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">math::fibonacci_sum::result</a></div><div class="ttdeci">uint64_t result(uint64_t n)</div><div class="ttdef"><b>Definition</b> fibonacci_sum.cpp:77</div></div>
|
||||
<div class="ttc" id="arand_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a></div><div class="ttdeci">T rand(T... args)</div></div>
|
||||
<div class="ttc" id="asrand_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a></div><div class="ttdeci">T srand(T... args)</div></div>
|
||||
<div class="ttc" id="astrtof_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/byte/strtof.html">std::strtod</a></div><div class="ttdeci">T strtod(T... args)</div></div>
|
||||
<div class="ttc" id="atime_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a></div><div class="ttdeci">T time(T... args)</div></div>
|
||||
<div class="ttc" id="avalarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a></div></div>
|
||||
<div class="ttc" id="adurand__kerner__roots_8cpp_html_a0283886819c7c140a023582b7269e2d0"><div class="ttname"><a href="#a0283886819c7c140a023582b7269e2d0">test2</a></div><div class="ttdeci">void test2()</div><div class="ttdef"><b>Definition</b> <a href="../../da/df2/durand__kerner__roots_8cpp_source.html#l00243">durand_kerner_roots.cpp:243</a></div></div>
|
||||
<div class="ttc" id="adurand__kerner__roots_8cpp_html_a1440a7779ac56f47a3f355ce4a8c7da0"><div class="ttname"><a href="#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a></div><div class="ttdeci">void test1()</div><div class="ttdef"><b>Definition</b> <a href="../../da/df2/durand__kerner__roots_8cpp_source.html#l00208">durand_kerner_roots.cpp:208</a></div></div>
|
||||
<div class="ttc" id="adurand__kerner__roots_8cpp_html_a2c35b320ace8677f9b331faf94f8b2fd"><div class="ttname"><a href="#a2c35b320ace8677f9b331faf94f8b2fd">durand_kerner_algo</a></div><div class="ttdeci">std::pair< uint32_t, double > durand_kerner_algo(const std::valarray< double > &coeffs, std::valarray< std::complex< double > > *roots, bool write_log=false)</div><div class="ttdef"><b>Definition</b> <a href="../../da/df2/durand__kerner__roots_8cpp_source.html#l00110">durand_kerner_roots.cpp:110</a></div></div>
|
||||
<div class="ttc" id="afibonacci__sum_8cpp_html_aadb40ac4c74a7efc0680b83eeee138aa"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">math::fibonacci_sum::result</a></div><div class="ttdeci">uint64_t result(uint64_t n)</div><div class="ttdef"><b>Definition</b> <a href="../../de/dc3/fibonacci__sum_8cpp_source.html#l00077">fibonacci_sum.cpp:77</a></div></div>
|
||||
</div><!-- fragment -->
|
||||
</div>
|
||||
</div>
|
||||
@@ -502,14 +503,14 @@ Here is the call graph for this function:</div>
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||||
<div class="memproto">
|
||||
<table class="memname">
|
||||
<tr>
|
||||
<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a>< double > poly_function </td>
|
||||
<td class="memname">std::complex< double > poly_function </td>
|
||||
<td>(</td>
|
||||
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< double > &</td> <td class="paramname"><span class="paramname"><em>coeffs</em></span>, </td>
|
||||
<td class="paramtype">const std::valarray< double > &</td> <td class="paramname"><span class="paramname"><em>coeffs</em></span>, </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td class="paramkey"></td>
|
||||
<td></td>
|
||||
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a>< double ></td> <td class="paramname"><span class="paramname"><em>x</em></span> )</td>
|
||||
<td class="paramtype">std::complex< double ></td> <td class="paramname"><span class="paramname"><em>x</em></span> )</td>
|
||||
</tr>
|
||||
</table>
|
||||
</div><div class="memdoc">
|
||||
@@ -521,6 +522,8 @@ Here is the call graph for this function:</div>
|
||||
</dd>
|
||||
</dl>
|
||||
<dl class="section return"><dt>Returns</dt><dd>\(f(x)\) </dd></dl>
|
||||
|
||||
<p class="definition">Definition at line <a class="el" href="../../da/df2/durand__kerner__roots_8cpp_source.html#l00054">54</a> of file <a class="el" href="../../da/df2/durand__kerner__roots_8cpp_source.html">durand_kerner_roots.cpp</a>.</p>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 55</span> {</div>
|
||||
<div class="line"><span class="lineno"> 56</span> <span class="keywordtype">double</span> real = 0.f, imag = 0.f;</div>
|
||||
<div class="line"><span class="lineno"> 57</span> <span class="keywordtype">int</span> n;</div>
|
||||
@@ -529,21 +532,15 @@ Here is the call graph for this function:</div>
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||||
<div class="line"><span class="lineno"> 60</span> <span class="comment">// #pragma omp target teams distribute reduction(+ : real, imag)</span></div>
|
||||
<div class="line"><span class="lineno"> 61</span> <span class="comment">// #endif</span></div>
|
||||
<div class="line"><span class="lineno"> 62</span> <span class="keywordflow">for</span> (n = 0; n < coeffs.size(); n++) {</div>
|
||||
<div class="line"><span class="lineno"> 63</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex<double></a> tmp =</div>
|
||||
<div class="line"><span class="lineno"> 64</span> coeffs[n] * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(x, coeffs.size() - n - 1);</div>
|
||||
<div class="line"><span class="lineno"> 65</span> real += tmp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/real.html">real</a>();</div>
|
||||
<div class="line"><span class="lineno"> 66</span> imag += tmp.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex/imag.html">imag</a>();</div>
|
||||
<div class="line"><span class="lineno"> 63</span> std::complex<double> tmp =</div>
|
||||
<div class="line"><span class="lineno"> 64</span> coeffs[n] * std::pow(x, coeffs.size() - n - 1);</div>
|
||||
<div class="line"><span class="lineno"> 65</span> real += tmp.real();</div>
|
||||
<div class="line"><span class="lineno"> 66</span> imag += tmp.imag();</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="keywordflow">return</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex<double></a>(real, imag);</div>
|
||||
<div class="line"><span class="lineno"> 69</span> <span class="keywordflow">return</span> std::complex<double>(real, imag);</div>
|
||||
<div class="line"><span class="lineno"> 70</span>}</div>
|
||||
<div class="ttc" id="apow_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a></div><div class="ttdeci">T pow(T... args)</div></div>
|
||||
</div><!-- fragment --><div class="dynheader">
|
||||
Here is the call graph for this function:</div>
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||||
<div class="dyncontent">
|
||||
<div class="center"><iframe scrolling="no" frameborder="0" src="../../da/df2/durand__kerner__roots_8cpp_ae2ab49ba1969d7a5988f9bc2c8924569_cgraph.svg" width="290" height="135"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
|
||||
</div>
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||||
|
||||
</div><!-- fragment -->
|
||||
</div>
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</div>
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<a id="a1440a7779ac56f47a3f355ce4a8c7da0" name="a1440a7779ac56f47a3f355ce4a8c7da0"></a>
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@@ -561,17 +558,19 @@ Here is the call graph for this function:</div>
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||||
</table>
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||||
</div><div class="memdoc">
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||||
<p>Self test the algorithm by checking the roots for \(x^2+4=0\) to which the roots are \(0 \pm 2i\) </p>
|
||||
|
||||
<p class="definition">Definition at line <a class="el" href="../../da/df2/durand__kerner__roots_8cpp_source.html#l00208">208</a> of file <a class="el" href="../../da/df2/durand__kerner__roots_8cpp_source.html">durand_kerner_roots.cpp</a>.</p>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 208</span> {</div>
|
||||
<div class="line"><span class="lineno"> 209</span> <span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray<double></a> coeffs = {1, 0, 4}; <span class="comment">// x^2 - 2 = 0</span></div>
|
||||
<div class="line"><span class="lineno"> 210</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray<std::complex<double></a>> roots(2);</div>
|
||||
<div class="line"><span class="lineno"> 211</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray<std::complex<double></a>> expected = {</div>
|
||||
<div class="line"><span class="lineno"> 212</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex<double></a>(0., 2.),</div>
|
||||
<div class="line"><span class="lineno"> 213</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex<double></a>(0., -2.) <span class="comment">// known expected roots</span></div>
|
||||
<div class="line"><span class="lineno"> 209</span> <span class="keyword">const</span> std::valarray<double> coeffs = {1, 0, 4}; <span class="comment">// x^2 - 2 = 0</span></div>
|
||||
<div class="line"><span class="lineno"> 210</span> std::valarray<std::complex<double>> roots(2);</div>
|
||||
<div class="line"><span class="lineno"> 211</span> std::valarray<std::complex<double>> expected = {</div>
|
||||
<div class="line"><span class="lineno"> 212</span> std::complex<double>(0., 2.),</div>
|
||||
<div class="line"><span class="lineno"> 213</span> std::complex<double>(0., -2.) <span class="comment">// known expected roots</span></div>
|
||||
<div class="line"><span class="lineno"> 214</span> };</div>
|
||||
<div class="line"><span class="lineno"> 215</span> </div>
|
||||
<div class="line"><span class="lineno"> 216</span> <span class="comment">/* initialize root approximations with random values */</span></div>
|
||||
<div class="line"><span class="lineno"> 217</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> n = 0; n < roots.size(); n++) {</div>
|
||||
<div class="line"><span class="lineno"> 218</span> roots[n] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex<double></a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % 100, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % 100);</div>
|
||||
<div class="line"><span class="lineno"> 218</span> roots[n] = std::complex<double>(std::rand() % 100, std::rand() % 100);</div>
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@@ -587,16 +586,11 @@ Here is the call graph for this function:</div>
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<div class="line"><span class="lineno"> 231</span> assert(err1);</div>
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<div class="line"><span class="lineno"> 232</span> }</div>
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<div class="line"><span class="lineno"> 235</span> << <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.second << <span class="stringliteral">" accuracy"</span></div>
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<p>Self test the algorithm by checking the roots for \(0.015625x^3-1=0\) to which the roots are \((4+0i),\,(-2\pm3.464i)\) </p>
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<p class="definition">Definition at line <a class="el" href="../../da/df2/durand__kerner__roots_8cpp_source.html#l00243">243</a> of file <a class="el" href="../../da/df2/durand__kerner__roots_8cpp_source.html">durand_kerner_roots.cpp</a>.</p>
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<div class="line"><span class="lineno"> 245</span> 1. / 64., 0., 0., -1.};</div>
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<div class="line"><span class="lineno"> 247</span> <span class="keyword">const</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray<std::complex<double></a>> expected = {</div>
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<div class="line"><span class="lineno"> 246</span> std::valarray<std::complex<double>> roots(3);</div>
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<div class="line"><span class="lineno"> 249</span> std::complex<double>(-2., -3.46410162) <span class="comment">// known expected roots</span></div>
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<div class="headertitle"><div class="title">durand_kerner_roots.cpp</div></div>
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<a href="../../da/df2/durand__kerner__roots_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="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="preprocessor">#include <algorithm></span></div>
|
||||
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="preprocessor">#include <cassert></span></div>
|
||||
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span><span class="preprocessor">#include <cmath></span></div>
|
||||
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span><span class="preprocessor">#include <complex></span></div>
|
||||
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span><span class="preprocessor">#include <cstdint></span></div>
|
||||
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span><span class="preprocessor">#include <cstdlib></span></div>
|
||||
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span><span class="preprocessor">#include <ctime></span></div>
|
||||
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="preprocessor">#include <fstream></span></div>
|
||||
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="preprocessor">#include <iostream></span></div>
|
||||
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span><span class="preprocessor">#include <valarray></span></div>
|
||||
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="preprocessor">#ifdef _OPENMP</span></div>
|
||||
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span><span class="preprocessor">#include <omp.h></span></div>
|
||||
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span><span class="preprocessor">#endif</span></div>
|
||||
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> </div>
|
||||
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"><a class="line" href="../../da/df2/durand__kerner__roots_8cpp.html#af270a96662132d0385cb6b4637c5a689"> 46</a></span><span class="preprocessor">#define ACCURACY 1e-10 </span></div>
|
||||
<div class="foldopen" id="foldopen00054" data-start="{" data-end="}">
|
||||
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"><a class="line" href="../../da/df2/durand__kerner__roots_8cpp.html#ae2ab49ba1969d7a5988f9bc2c8924569"> 54</a></span>std::complex<double> <a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#ae2ab49ba1969d7a5988f9bc2c8924569">poly_function</a>(<span class="keyword">const</span> std::valarray<double> &coeffs,</div>
|
||||
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> std::complex<double> x) {</div>
|
||||
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="keywordtype">double</span> real = 0.f, imag = 0.f;</div>
|
||||
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <span class="keywordtype">int</span> n;</div>
|
||||
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> </div>
|
||||
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <span class="comment">// #ifdef _OPENMP</span></div>
|
||||
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="comment">// #pragma omp target teams distribute reduction(+ : real, imag)</span></div>
|
||||
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="comment">// #endif</span></div>
|
||||
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="keywordflow">for</span> (n = 0; n < coeffs.size(); n++) {</div>
|
||||
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> std::complex<double> tmp =</div>
|
||||
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> coeffs[n] * std::pow(x, coeffs.size() - n - 1);</div>
|
||||
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> real += tmp.real();</div>
|
||||
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> imag += tmp.imag();</div>
|
||||
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> }</div>
|
||||
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> </div>
|
||||
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="keywordflow">return</span> std::complex<double>(real, imag);</div>
|
||||
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span>}</div>
|
||||
</div>
|
||||
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> </div>
|
||||
<div class="foldopen" id="foldopen00077" data-start="{" data-end="}">
|
||||
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"><a class="line" href="../../da/df2/durand__kerner__roots_8cpp.html#a90219e35062007d1f1b68e9af071ab5c"> 77</a></span><span class="keyword">const</span> <span class="keywordtype">char</span> *<a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#a90219e35062007d1f1b68e9af071ab5c">complex_str</a>(<span class="keyword">const</span> std::complex<double> &x) {</div>
|
||||
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span><span class="preprocessor">#define MAX_BUFF_SIZE 50</span></div>
|
||||
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="keyword">static</span> <span class="keywordtype">char</span> msg[MAX_BUFF_SIZE];</div>
|
||||
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> </div>
|
||||
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> std::snprintf(msg, MAX_BUFF_SIZE, <span class="stringliteral">"% 7.04g%+7.04gj"</span>, x.real(), x.imag());</div>
|
||||
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> </div>
|
||||
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="keywordflow">return</span> msg;</div>
|
||||
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span>}</div>
|
||||
</div>
|
||||
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> </div>
|
||||
<div class="foldopen" id="foldopen00092" data-start="{" data-end="}">
|
||||
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"><a class="line" href="../../da/df2/durand__kerner__roots_8cpp.html#a024b8bc4755863315456d573a6732377"> 92</a></span><span class="keywordtype">bool</span> <a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#a024b8bc4755863315456d573a6732377">check_termination</a>(<span class="keywordtype">long</span> <span class="keywordtype">double</span> delta) {</div>
|
||||
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="keyword">static</span> <span class="keywordtype">long</span> <span class="keywordtype">double</span> past_delta = INFINITY;</div>
|
||||
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="keywordflow">if</span> (std::abs(past_delta - delta) <= <a class="code hl_define" href="../../da/df2/durand__kerner__roots_8cpp.html#af270a96662132d0385cb6b4637c5a689">ACCURACY</a> || delta < <a class="code hl_define" href="../../da/df2/durand__kerner__roots_8cpp.html#af270a96662132d0385cb6b4637c5a689">ACCURACY</a>)</div>
|
||||
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
|
||||
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> past_delta = delta;</div>
|
||||
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
|
||||
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span>}</div>
|
||||
</div>
|
||||
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> </div>
|
||||
<div class="foldopen" id="foldopen00110" data-start="{" data-end="}">
|
||||
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"><a class="line" href="../../da/df2/durand__kerner__roots_8cpp.html#a2c35b320ace8677f9b331faf94f8b2fd"> 110</a></span>std::pair<uint32_t, double> <a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#a2c35b320ace8677f9b331faf94f8b2fd">durand_kerner_algo</a>(</div>
|
||||
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> <span class="keyword">const</span> std::valarray<double> &coeffs,</div>
|
||||
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> std::valarray<std::complex<double>> *roots, <span class="keywordtype">bool</span> write_log = <span class="keyword">false</span>) {</div>
|
||||
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> <span class="keywordtype">long</span> <span class="keywordtype">double</span> tol_condition = 1;</div>
|
||||
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> uint32_t iter = 0;</div>
|
||||
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <span class="keywordtype">int</span> n;</div>
|
||||
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> std::ofstream log_file;</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> (write_log) {</div>
|
||||
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> <span class="comment">/*</span></div>
|
||||
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span><span class="comment"> * store intermediate values to a CSV file</span></div>
|
||||
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span><span class="comment"> */</span></div>
|
||||
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> log_file.open(<span class="stringliteral">"durand_kerner.log.csv"</span>);</div>
|
||||
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> <span class="keywordflow">if</span> (!log_file.is_open()) {</div>
|
||||
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> perror(<span class="stringliteral">"Unable to create a storage log file!"</span>);</div>
|
||||
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> std::exit(EXIT_FAILURE);</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> log_file << <span class="stringliteral">"iter#,"</span>;</div>
|
||||
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> </div>
|
||||
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> <span class="keywordflow">for</span> (n = 0; n < roots->size(); n++) log_file << <span class="stringliteral">"root_"</span> << n << <span class="stringliteral">","</span>;</div>
|
||||
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> </div>
|
||||
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> log_file << <span class="stringliteral">"avg. correction"</span>;</div>
|
||||
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> log_file << <span class="stringliteral">"\n0,"</span>;</div>
|
||||
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> <span class="keywordflow">for</span> (n = 0; n < roots->size(); n++)</div>
|
||||
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> log_file << <a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#a90219e35062007d1f1b68e9af071ab5c">complex_str</a>((*roots)[n]) << <span class="stringliteral">","</span>;</div>
|
||||
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> }</div>
|
||||
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> </div>
|
||||
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> <span class="keywordtype">bool</span> break_loop = <span class="keyword">false</span>;</div>
|
||||
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> <span class="keywordflow">while</span> (!<a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#a024b8bc4755863315456d573a6732377">check_termination</a>(tol_condition) && iter < INT16_MAX &&</div>
|
||||
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> !break_loop) {</div>
|
||||
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> tol_condition = 0;</div>
|
||||
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> iter++;</div>
|
||||
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> break_loop = <span class="keyword">false</span>;</div>
|
||||
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> </div>
|
||||
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> <span class="keywordflow">if</span> (log_file.is_open())</div>
|
||||
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> log_file << <span class="stringliteral">"\n"</span> << iter << <span class="stringliteral">","</span>;</div>
|
||||
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> </div>
|
||||
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span><span class="preprocessor">#ifdef _OPENMP</span></div>
|
||||
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span><span class="preprocessor">#pragma omp parallel for shared(break_loop, tol_condition)</span></div>
|
||||
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span><span class="preprocessor">#endif</span></div>
|
||||
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> <span class="keywordflow">for</span> (n = 0; n < roots->size(); n++) {</div>
|
||||
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> <span class="keywordflow">if</span> (break_loop)</div>
|
||||
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> <span class="keywordflow">continue</span>;</div>
|
||||
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> </div>
|
||||
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> std::complex<double> numerator, denominator;</div>
|
||||
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> numerator = <a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#ae2ab49ba1969d7a5988f9bc2c8924569">poly_function</a>(coeffs, (*roots)[n]);</div>
|
||||
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> denominator = 1.0;</div>
|
||||
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < roots->size(); i++)</div>
|
||||
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> <span class="keywordflow">if</span> (i != n)</div>
|
||||
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> denominator *= (*roots)[n] - (*roots)[i];</div>
|
||||
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> </div>
|
||||
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> std::complex<long double> delta = numerator / denominator;</div>
|
||||
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> </div>
|
||||
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> <span class="keywordflow">if</span> (std::isnan(std::abs(delta)) || std::isinf(std::abs(delta))) {</div>
|
||||
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> std::cerr << <span class="stringliteral">"\n\nOverflow/underrun error - got value = "</span></div>
|
||||
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> << std::abs(delta) << <span class="stringliteral">"\n"</span>;</div>
|
||||
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> <span class="comment">// return std::pair<uint32_t, double>(iter, tol_condition);</span></div>
|
||||
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> break_loop = <span class="keyword">true</span>;</div>
|
||||
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> }</div>
|
||||
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> </div>
|
||||
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> (*roots)[n] -= delta;</div>
|
||||
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> </div>
|
||||
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span><span class="preprocessor">#ifdef _OPENMP</span></div>
|
||||
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span><span class="preprocessor">#pragma omp critical</span></div>
|
||||
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span><span class="preprocessor">#endif</span></div>
|
||||
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> tol_condition = std::max(tol_condition, std::abs(std::abs(delta)));</div>
|
||||
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> }</div>
|
||||
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> <span class="comment">// tol_condition /= (degree - 1);</span></div>
|
||||
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> </div>
|
||||
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> <span class="keywordflow">if</span> (break_loop)</div>
|
||||
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> <span class="keywordflow">break</span>;</div>
|
||||
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> </div>
|
||||
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> <span class="keywordflow">if</span> (log_file.is_open()) {</div>
|
||||
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> <span class="keywordflow">for</span> (n = 0; n < roots->size(); n++)</div>
|
||||
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> log_file << <a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#a90219e35062007d1f1b68e9af071ab5c">complex_str</a>((*roots)[n]) << <span class="stringliteral">","</span>;</div>
|
||||
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> }</div>
|
||||
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> </div>
|
||||
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span><span class="preprocessor">#if defined(DEBUG) || !defined(NDEBUG)</span></div>
|
||||
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> <span class="keywordflow">if</span> (iter % 500 == 0) {</div>
|
||||
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> std::cout << <span class="stringliteral">"Iter: "</span> << iter << <span class="stringliteral">"\t"</span>;</div>
|
||||
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> <span class="keywordflow">for</span> (n = 0; n < roots->size(); n++)</div>
|
||||
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> std::cout << <span class="stringliteral">"\t"</span> << <a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#a90219e35062007d1f1b68e9af071ab5c">complex_str</a>((*roots)[n]);</div>
|
||||
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> std::cout << <span class="stringliteral">"\t\tabsolute average change: "</span> << tol_condition</div>
|
||||
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> << <span class="stringliteral">"\n"</span>;</div>
|
||||
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> }</div>
|
||||
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span><span class="preprocessor">#endif</span></div>
|
||||
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> </div>
|
||||
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> <span class="keywordflow">if</span> (log_file.is_open())</div>
|
||||
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> log_file << tol_condition;</div>
|
||||
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> }</div>
|
||||
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> </div>
|
||||
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> <span class="keywordflow">return</span> std::pair<uint32_t, long double>(iter, tol_condition);</div>
|
||||
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span>}</div>
|
||||
</div>
|
||||
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> </div>
|
||||
<div class="foldopen" id="foldopen00208" data-start="{" data-end="}">
|
||||
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"><a class="line" href="../../da/df2/durand__kerner__roots_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0"> 208</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>() {</div>
|
||||
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> <span class="keyword">const</span> std::valarray<double> coeffs = {1, 0, 4}; <span class="comment">// x^2 - 2 = 0</span></div>
|
||||
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> std::valarray<std::complex<double>> roots(2);</div>
|
||||
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> std::valarray<std::complex<double>> expected = {</div>
|
||||
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> std::complex<double>(0., 2.),</div>
|
||||
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> std::complex<double>(0., -2.) <span class="comment">// known expected roots</span></div>
|
||||
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> };</div>
|
||||
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> </div>
|
||||
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> <span class="comment">/* initialize root approximations with random values */</span></div>
|
||||
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> n = 0; n < roots.size(); n++) {</div>
|
||||
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span> roots[n] = std::complex<double>(std::rand() % 100, std::rand() % 100);</div>
|
||||
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span> roots[n] -= 50.f;</div>
|
||||
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span> roots[n] /= 25.f;</div>
|
||||
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> }</div>
|
||||
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> </div>
|
||||
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span> <span class="keyword">auto</span> result = <a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#a2c35b320ace8677f9b331faf94f8b2fd">durand_kerner_algo</a>(coeffs, &roots, <span class="keyword">false</span>);</div>
|
||||
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span> </div>
|
||||
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < roots.size(); i++) {</div>
|
||||
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span> <span class="comment">// check if approximations are have < 0.1% error with one of the</span></div>
|
||||
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</span> <span class="comment">// expected roots</span></div>
|
||||
<div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span> <span class="keywordtype">bool</span> err1 = <span class="keyword">false</span>;</div>
|
||||
<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < roots.size(); j++)</div>
|
||||
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span> err1 |= std::abs(std::abs(roots[i] - expected[j])) < 1e-3;</div>
|
||||
<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> assert(err1);</div>
|
||||
<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span> }</div>
|
||||
<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span> </div>
|
||||
<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span> std::cout << <span class="stringliteral">"Test 1 passed! - "</span> << result.first << <span class="stringliteral">" iterations, "</span></div>
|
||||
<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span> << result.second << <span class="stringliteral">" accuracy"</span></div>
|
||||
<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span> << <span class="stringliteral">"\n"</span>;</div>
|
||||
<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span>}</div>
|
||||
</div>
|
||||
<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span> </div>
|
||||
<div class="foldopen" id="foldopen00243" data-start="{" data-end="}">
|
||||
<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"><a class="line" href="../../da/df2/durand__kerner__roots_8cpp.html#a0283886819c7c140a023582b7269e2d0"> 243</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>() {</div>
|
||||
<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"> 244</span> <span class="keyword">const</span> std::valarray<double> coeffs = {<span class="comment">// 0.015625 x^3 - 1 = 0</span></div>
|
||||
<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span> 1. / 64., 0., 0., -1.};</div>
|
||||
<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span> std::valarray<std::complex<double>> roots(3);</div>
|
||||
<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span> <span class="keyword">const</span> std::valarray<std::complex<double>> expected = {</div>
|
||||
<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span> std::complex<double>(4., 0.), std::complex<double>(-2., 3.46410162),</div>
|
||||
<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> std::complex<double>(-2., -3.46410162) <span class="comment">// known expected roots</span></div>
|
||||
<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> };</div>
|
||||
<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> </div>
|
||||
<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> <span class="comment">/* initialize root approximations with random values */</span></div>
|
||||
<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> n = 0; n < roots.size(); n++) {</div>
|
||||
<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span> roots[n] = std::complex<double>(std::rand() % 100, std::rand() % 100);</div>
|
||||
<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span> roots[n] -= 50.f;</div>
|
||||
<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span> roots[n] /= 25.f;</div>
|
||||
<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> }</div>
|
||||
<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span> </div>
|
||||
<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span> <span class="keyword">auto</span> result = <a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#a2c35b320ace8677f9b331faf94f8b2fd">durand_kerner_algo</a>(coeffs, &roots, <span class="keyword">false</span>);</div>
|
||||
<div class="line"><a id="l00260" name="l00260"></a><span class="lineno"> 260</span> </div>
|
||||
<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < roots.size(); i++) {</div>
|
||||
<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span> <span class="comment">// check if approximations are have < 0.1% error with one of the</span></div>
|
||||
<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span> <span class="comment">// expected roots</span></div>
|
||||
<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span> <span class="keywordtype">bool</span> err1 = <span class="keyword">false</span>;</div>
|
||||
<div class="line"><a id="l00265" name="l00265"></a><span class="lineno"> 265</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < roots.size(); j++)</div>
|
||||
<div class="line"><a id="l00266" name="l00266"></a><span class="lineno"> 266</span> err1 |= std::abs(std::abs(roots[i] - expected[j])) < 1e-3;</div>
|
||||
<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span> assert(err1);</div>
|
||||
<div class="line"><a id="l00268" name="l00268"></a><span class="lineno"> 268</span> }</div>
|
||||
<div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span> </div>
|
||||
<div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span> std::cout << <span class="stringliteral">"Test 2 passed! - "</span> << result.first << <span class="stringliteral">" iterations, "</span></div>
|
||||
<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span> << result.second << <span class="stringliteral">" accuracy"</span></div>
|
||||
<div class="line"><a id="l00272" name="l00272"></a><span class="lineno"> 272</span> << <span class="stringliteral">"\n"</span>;</div>
|
||||
<div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</span>}</div>
|
||||
</div>
|
||||
<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span> </div>
|
||||
<div class="line"><a id="l00275" name="l00275"></a><span class="lineno"> 275</span><span class="comment">/***</span></div>
|
||||
<div class="line"><a id="l00276" name="l00276"></a><span class="lineno"> 276</span><span class="comment"> * Main function.</span></div>
|
||||
<div class="line"><a id="l00277" name="l00277"></a><span class="lineno"> 277</span><span class="comment"> * The comandline input arguments are taken as coeffiecients of a</span></div>
|
||||
<div class="line"><a id="l00278" name="l00278"></a><span class="lineno"> 278</span><span class="comment"> *polynomial. For example, this command</span></div>
|
||||
<div class="line"><a id="l00279" name="l00279"></a><span class="lineno"> 279</span><span class="comment"> * ```sh</span></div>
|
||||
<div class="line"><a id="l00280" name="l00280"></a><span class="lineno"> 280</span><span class="comment"> * ./durand_kerner_roots 1 0 -4</span></div>
|
||||
<div class="line"><a id="l00281" name="l00281"></a><span class="lineno"> 281</span><span class="comment"> * ```</span></div>
|
||||
<div class="line"><a id="l00282" name="l00282"></a><span class="lineno"> 282</span><span class="comment"> * will find roots of the polynomial \f$1\cdot x^2 + 0\cdot x^1 + (-4)=0\f$</span></div>
|
||||
<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span><span class="comment"> **/</span></div>
|
||||
<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span><span class="keywordtype">int</span> <a class="code hl_function" href="../../dd/d1e/generate__parentheses_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4">main</a>(<span class="keywordtype">int</span> argc, <span class="keywordtype">char</span> **argv) {</div>
|
||||
<div class="line"><a id="l00285" name="l00285"></a><span class="lineno"> 285</span> <span class="comment">/* initialize random seed: */</span></div>
|
||||
<div class="line"><a id="l00286" name="l00286"></a><span class="lineno"> 286</span> std::srand(std::time(<span class="keyword">nullptr</span>));</div>
|
||||
<div class="line"><a id="l00287" name="l00287"></a><span class="lineno"> 287</span> </div>
|
||||
<div class="line"><a id="l00288" name="l00288"></a><span class="lineno"> 288</span> <span class="keywordflow">if</span> (argc < 2) {</div>
|
||||
<div class="line"><a id="l00289" name="l00289"></a><span class="lineno"> 289</span> <a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>(); <span class="comment">// run tests when no input is provided</span></div>
|
||||
<div class="line"><a id="l00290" name="l00290"></a><span class="lineno"> 290</span> <a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>(); <span class="comment">// and skip tests when input polynomial is provided</span></div>
|
||||
<div class="line"><a id="l00291" name="l00291"></a><span class="lineno"> 291</span> std::cout << <span class="stringliteral">"Please pass the coefficients of the polynomial as "</span></div>
|
||||
<div class="line"><a id="l00292" name="l00292"></a><span class="lineno"> 292</span> <span class="stringliteral">"commandline "</span></div>
|
||||
<div class="line"><a id="l00293" name="l00293"></a><span class="lineno"> 293</span> <span class="stringliteral">"arguments.\n"</span>;</div>
|
||||
<div class="line"><a id="l00294" name="l00294"></a><span class="lineno"> 294</span> <span class="keywordflow">return</span> 0;</div>
|
||||
<div class="line"><a id="l00295" name="l00295"></a><span class="lineno"> 295</span> }</div>
|
||||
<div class="line"><a id="l00296" name="l00296"></a><span class="lineno"> 296</span> </div>
|
||||
<div class="line"><a id="l00297" name="l00297"></a><span class="lineno"> 297</span> <span class="keywordtype">int</span> n, degree = argc - 1; <span class="comment">// detected polynomial degree</span></div>
|
||||
<div class="line"><a id="l00298" name="l00298"></a><span class="lineno"> 298</span> std::valarray<double> coeffs(degree); <span class="comment">// create coefficiencts array</span></div>
|
||||
<div class="line"><a id="l00299" name="l00299"></a><span class="lineno"> 299</span> </div>
|
||||
<div class="line"><a id="l00300" name="l00300"></a><span class="lineno"> 300</span> <span class="comment">// number of roots = degree - 1</span></div>
|
||||
<div class="line"><a id="l00301" name="l00301"></a><span class="lineno"> 301</span> std::valarray<std::complex<double>> s0(degree - 1);</div>
|
||||
<div class="line"><a id="l00302" name="l00302"></a><span class="lineno"> 302</span> </div>
|
||||
<div class="line"><a id="l00303" name="l00303"></a><span class="lineno"> 303</span> std::cout << <span class="stringliteral">"Computing the roots for:\n\t"</span>;</div>
|
||||
<div class="line"><a id="l00304" name="l00304"></a><span class="lineno"> 304</span> <span class="keywordflow">for</span> (n = 0; n < degree; n++) {</div>
|
||||
<div class="line"><a id="l00305" name="l00305"></a><span class="lineno"> 305</span> coeffs[n] = strtod(argv[n + 1], <span class="keyword">nullptr</span>);</div>
|
||||
<div class="line"><a id="l00306" name="l00306"></a><span class="lineno"> 306</span> <span class="keywordflow">if</span> (n < degree - 1 && coeffs[n] != 0)</div>
|
||||
<div class="line"><a id="l00307" name="l00307"></a><span class="lineno"> 307</span> std::cout << <span class="stringliteral">"("</span> << coeffs[n] << <span class="stringliteral">") x^"</span> << degree - n - 1 << <span class="stringliteral">" + "</span>;</div>
|
||||
<div class="line"><a id="l00308" name="l00308"></a><span class="lineno"> 308</span> <span class="keywordflow">else</span> <span class="keywordflow">if</span> (coeffs[n] != 0)</div>
|
||||
<div class="line"><a id="l00309" name="l00309"></a><span class="lineno"> 309</span> std::cout << <span class="stringliteral">"("</span> << coeffs[n] << <span class="stringliteral">") x^"</span> << degree - n - 1</div>
|
||||
<div class="line"><a id="l00310" name="l00310"></a><span class="lineno"> 310</span> << <span class="stringliteral">" = 0\n"</span>;</div>
|
||||
<div class="line"><a id="l00311" name="l00311"></a><span class="lineno"> 311</span> </div>
|
||||
<div class="line"><a id="l00312" name="l00312"></a><span class="lineno"> 312</span> <span class="comment">/* initialize root approximations with random values */</span></div>
|
||||
<div class="line"><a id="l00313" name="l00313"></a><span class="lineno"> 313</span> <span class="keywordflow">if</span> (n < degree - 1) {</div>
|
||||
<div class="line"><a id="l00314" name="l00314"></a><span class="lineno"> 314</span> s0[n] = std::complex<double>(std::rand() % 100, std::rand() % 100);</div>
|
||||
<div class="line"><a id="l00315" name="l00315"></a><span class="lineno"> 315</span> s0[n] -= 50.f;</div>
|
||||
<div class="line"><a id="l00316" name="l00316"></a><span class="lineno"> 316</span> s0[n] /= 50.f;</div>
|
||||
<div class="line"><a id="l00317" name="l00317"></a><span class="lineno"> 317</span> }</div>
|
||||
<div class="line"><a id="l00318" name="l00318"></a><span class="lineno"> 318</span> }</div>
|
||||
<div class="line"><a id="l00319" name="l00319"></a><span class="lineno"> 319</span> </div>
|
||||
<div class="line"><a id="l00320" name="l00320"></a><span class="lineno"> 320</span> <span class="comment">// numerical errors less when the first coefficient is "1"</span></div>
|
||||
<div class="line"><a id="l00321" name="l00321"></a><span class="lineno"> 321</span> <span class="comment">// hence, we normalize the first coefficient</span></div>
|
||||
<div class="line"><a id="l00322" name="l00322"></a><span class="lineno"> 322</span> {</div>
|
||||
<div class="line"><a id="l00323" name="l00323"></a><span class="lineno"> 323</span> <span class="keywordtype">double</span> tmp = coeffs[0];</div>
|
||||
<div class="line"><a id="l00324" name="l00324"></a><span class="lineno"> 324</span> coeffs /= tmp;</div>
|
||||
<div class="line"><a id="l00325" name="l00325"></a><span class="lineno"> 325</span> }</div>
|
||||
<div class="line"><a id="l00326" name="l00326"></a><span class="lineno"> 326</span> </div>
|
||||
<div class="line"><a id="l00327" name="l00327"></a><span class="lineno"> 327</span> clock_t end_time, start_time = clock();</div>
|
||||
<div class="line"><a id="l00328" name="l00328"></a><span class="lineno"> 328</span> <span class="keyword">auto</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#a2c35b320ace8677f9b331faf94f8b2fd">durand_kerner_algo</a>(coeffs, &s0, <span class="keyword">true</span>);</div>
|
||||
<div class="line"><a id="l00329" name="l00329"></a><span class="lineno"> 329</span> end_time = clock();</div>
|
||||
<div class="line"><a id="l00330" name="l00330"></a><span class="lineno"> 330</span> </div>
|
||||
<div class="line"><a id="l00331" name="l00331"></a><span class="lineno"> 331</span> std::cout << <span class="stringliteral">"\nIterations: "</span> << <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.first << <span class="stringliteral">"\n"</span>;</div>
|
||||
<div class="line"><a id="l00332" name="l00332"></a><span class="lineno"> 332</span> <span class="keywordflow">for</span> (n = 0; n < degree - 1; n++)</div>
|
||||
<div class="line"><a id="l00333" name="l00333"></a><span class="lineno"> 333</span> std::cout << <span class="stringliteral">"\t"</span> << <a class="code hl_function" href="../../da/df2/durand__kerner__roots_8cpp.html#a90219e35062007d1f1b68e9af071ab5c">complex_str</a>(s0[n]) << <span class="stringliteral">"\n"</span>;</div>
|
||||
<div class="line"><a id="l00334" name="l00334"></a><span class="lineno"> 334</span> std::cout << <span class="stringliteral">"absolute average change: "</span> << <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.second << <span class="stringliteral">"\n"</span>;</div>
|
||||
<div class="line"><a id="l00335" name="l00335"></a><span class="lineno"> 335</span> std::cout << <span class="stringliteral">"Time taken: "</span></div>
|
||||
<div class="line"><a id="l00336" name="l00336"></a><span class="lineno"> 336</span> << <span class="keyword">static_cast<</span><span class="keywordtype">double</span><span class="keyword">></span>(end_time - start_time) / CLOCKS_PER_SEC</div>
|
||||
<div class="line"><a id="l00337" name="l00337"></a><span class="lineno"> 337</span> << <span class="stringliteral">" sec\n"</span>;</div>
|
||||
<div class="line"><a id="l00338" name="l00338"></a><span class="lineno"> 338</span> </div>
|
||||
<div class="line"><a id="l00339" name="l00339"></a><span class="lineno"> 339</span> <span class="keywordflow">return</span> 0;</div>
|
||||
<div class="line"><a id="l00340" name="l00340"></a><span class="lineno"> 340</span>}</div>
|
||||
<div class="ttc" id="adurand__kerner__roots_8cpp_html_a024b8bc4755863315456d573a6732377"><div class="ttname"><a href="../../da/df2/durand__kerner__roots_8cpp.html#a024b8bc4755863315456d573a6732377">check_termination</a></div><div class="ttdeci">bool check_termination(long double delta)</div><div class="ttdef"><b>Definition</b> <a href="#l00092">durand_kerner_roots.cpp:92</a></div></div>
|
||||
<div class="ttc" id="adurand__kerner__roots_8cpp_html_a0283886819c7c140a023582b7269e2d0"><div class="ttname"><a href="../../da/df2/durand__kerner__roots_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a></div><div class="ttdeci">void test2()</div><div class="ttdef"><b>Definition</b> <a href="#l00243">durand_kerner_roots.cpp:243</a></div></div>
|
||||
<div class="ttc" id="adurand__kerner__roots_8cpp_html_a1440a7779ac56f47a3f355ce4a8c7da0"><div class="ttname"><a href="../../da/df2/durand__kerner__roots_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a></div><div class="ttdeci">void test1()</div><div class="ttdef"><b>Definition</b> <a href="#l00208">durand_kerner_roots.cpp:208</a></div></div>
|
||||
<div class="ttc" id="adurand__kerner__roots_8cpp_html_a2c35b320ace8677f9b331faf94f8b2fd"><div class="ttname"><a href="../../da/df2/durand__kerner__roots_8cpp.html#a2c35b320ace8677f9b331faf94f8b2fd">durand_kerner_algo</a></div><div class="ttdeci">std::pair< uint32_t, double > durand_kerner_algo(const std::valarray< double > &coeffs, std::valarray< std::complex< double > > *roots, bool write_log=false)</div><div class="ttdef"><b>Definition</b> <a href="#l00110">durand_kerner_roots.cpp:110</a></div></div>
|
||||
<div class="ttc" id="adurand__kerner__roots_8cpp_html_a90219e35062007d1f1b68e9af071ab5c"><div class="ttname"><a href="../../da/df2/durand__kerner__roots_8cpp.html#a90219e35062007d1f1b68e9af071ab5c">complex_str</a></div><div class="ttdeci">const char * complex_str(const std::complex< double > &x)</div><div class="ttdef"><b>Definition</b> <a href="#l00077">durand_kerner_roots.cpp:77</a></div></div>
|
||||
<div class="ttc" id="adurand__kerner__roots_8cpp_html_ae2ab49ba1969d7a5988f9bc2c8924569"><div class="ttname"><a href="../../da/df2/durand__kerner__roots_8cpp.html#ae2ab49ba1969d7a5988f9bc2c8924569">poly_function</a></div><div class="ttdeci">std::complex< double > poly_function(const std::valarray< double > &coeffs, std::complex< double > x)</div><div class="ttdef"><b>Definition</b> <a href="#l00054">durand_kerner_roots.cpp:54</a></div></div>
|
||||
<div class="ttc" id="adurand__kerner__roots_8cpp_html_af270a96662132d0385cb6b4637c5a689"><div class="ttname"><a href="../../da/df2/durand__kerner__roots_8cpp.html#af270a96662132d0385cb6b4637c5a689">ACCURACY</a></div><div class="ttdeci">#define ACCURACY</div><div class="ttdef"><b>Definition</b> <a href="#l00046">durand_kerner_roots.cpp:46</a></div></div>
|
||||
<div class="ttc" id="afibonacci__sum_8cpp_html_aadb40ac4c74a7efc0680b83eeee138aa"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">math::fibonacci_sum::result</a></div><div class="ttdeci">uint64_t result(uint64_t n)</div><div class="ttdef"><b>Definition</b> <a href="../../de/dc3/fibonacci__sum_8cpp_source.html#l00077">fibonacci_sum.cpp:77</a></div></div>
|
||||
<div class="ttc" id="agenerate__parentheses_8cpp_html_gae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../dd/d1e/generate__parentheses_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdoc">Main function.</div><div class="ttdef"><b>Definition</b> <a href="../../dd/d1e/generate__parentheses_8cpp_source.html#l00110">generate_parentheses.cpp:110</a></div></div>
|
||||
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