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Documentation for c6af943508
This commit is contained in:
realstealthninja
@@ -117,6 +117,7 @@ $(function(){initNavTree('da/df2/durand__kerner__roots_8cpp.html','../../'); ini
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<code>#include <cassert></code><br />
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<code>#include <cmath></code><br />
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<code>#include <complex></code><br />
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<code>#include <cstdint></code><br />
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<code>#include <cstdlib></code><br />
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<code>#include <ctime></code><br />
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<code>#include <fstream></code><br />
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@@ -209,14 +210,14 @@ Functions</h2></td></tr>
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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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<div class="fragment"><div class="line"><span class="lineno"> 91</span> {</div>
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<div class="line"><span class="lineno"> 92</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"> 93</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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<div class="line"><span class="lineno"> 94</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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<div class="line"><span class="lineno"> 95</span> past_delta = delta;</div>
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<div class="line"><span class="lineno"> 96</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
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<div class="line"><span class="lineno"> 97</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:45</div></div>
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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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<div class="line"><span class="lineno"> 95</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
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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><!-- fragment -->
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</div>
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</div>
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@@ -241,14 +242,14 @@ 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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<div class="fragment"><div class="line"><span class="lineno"> 76</span> {</div>
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<div class="line"><span class="lineno"> 77</span><span class="preprocessor">#define MAX_BUFF_SIZE 50</span></div>
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<div class="line"><span class="lineno"> 78</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"> 79</span> </div>
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<div class="line"><span class="lineno"> 80</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> </div>
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<div class="line"><span class="lineno"> 82</span> <span class="keywordflow">return</span> msg;</div>
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<div class="line"><span class="lineno"> 83</span>}</div>
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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"> 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>
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<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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@@ -293,103 +294,103 @@ 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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<div class="fragment"><div class="line"><span class="lineno"> 111</span> {</div>
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<div class="line"><span class="lineno"> 112</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"> 113</span> uint32_t iter = 0;</div>
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<div class="line"><span class="lineno"> 114</span> <span class="keywordtype">int</span> n;</div>
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<div class="line"><span class="lineno"> 115</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> </div>
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<div class="line"><span class="lineno"> 117</span> <span class="keywordflow">if</span> (write_log) {</div>
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<div class="line"><span class="lineno"> 118</span> <span class="comment">/*</span></div>
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<div class="line"><span class="lineno"> 119</span><span class="comment"> * store intermediate values to a CSV file</span></div>
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<div class="line"><span class="lineno"> 120</span><span class="comment"> */</span></div>
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<div class="line"><span class="lineno"> 121</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>
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<div class="line"><span class="lineno"> 122</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>
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<div class="line"><span class="lineno"> 123</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>
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<div class="line"><span class="lineno"> 124</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>
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<div class="line"><span class="lineno"> 125</span> }</div>
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<div class="line"><span class="lineno"> 126</span> log_file << <span class="stringliteral">"iter#,"</span>;</div>
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<div class="line"><span class="lineno"> 127</span> </div>
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<div class="line"><span class="lineno"> 128</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>
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<div class="line"><span class="lineno"> 129</span> </div>
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<div class="line"><span class="lineno"> 130</span> log_file << <span class="stringliteral">"avg. correction"</span>;</div>
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<div class="line"><span class="lineno"> 131</span> log_file << <span class="stringliteral">"\n0,"</span>;</div>
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<div class="line"><span class="lineno"> 132</span> <span class="keywordflow">for</span> (n = 0; n < roots->size(); n++)</div>
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<div class="line"><span class="lineno"> 133</span> log_file << <a class="code hl_function" href="#a90219e35062007d1f1b68e9af071ab5c">complex_str</a>((*roots)[n]) << <span class="stringliteral">","</span>;</div>
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<div class="line"><span class="lineno"> 134</span> }</div>
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<div class="line"><span class="lineno"> 135</span> </div>
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<div class="line"><span class="lineno"> 136</span> <span class="keywordtype">bool</span> break_loop = <span class="keyword">false</span>;</div>
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<div class="line"><span class="lineno"> 137</span> <span class="keywordflow">while</span> (!<a class="code hl_function" href="#a024b8bc4755863315456d573a6732377">check_termination</a>(tol_condition) && iter < INT16_MAX &&</div>
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<div class="line"><span class="lineno"> 138</span> !break_loop) {</div>
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<div class="line"><span class="lineno"> 139</span> tol_condition = 0;</div>
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<div class="line"><span class="lineno"> 140</span> iter++;</div>
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<div class="line"><span class="lineno"> 141</span> break_loop = <span class="keyword">false</span>;</div>
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<div class="line"><span class="lineno"> 142</span> </div>
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<div class="line"><span class="lineno"> 143</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>
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<div class="line"><span class="lineno"> 144</span> log_file << <span class="stringliteral">"\n"</span> << iter << <span class="stringliteral">","</span>;</div>
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<div class="line"><span class="lineno"> 145</span> </div>
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<div class="line"><span class="lineno"> 146</span><span class="preprocessor">#ifdef _OPENMP</span></div>
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<div class="line"><span class="lineno"> 147</span><span class="preprocessor">#pragma omp parallel for shared(break_loop, tol_condition)</span></div>
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<div class="line"><span class="lineno"> 148</span><span class="preprocessor">#endif</span></div>
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<div class="line"><span class="lineno"> 149</span> <span class="keywordflow">for</span> (n = 0; n < roots->size(); n++) {</div>
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<div class="line"><span class="lineno"> 150</span> <span class="keywordflow">if</span> (break_loop)</div>
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<div class="line"><span class="lineno"> 151</span> <span class="keywordflow">continue</span>;</div>
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<div class="line"><span class="lineno"> 152</span> </div>
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<div class="line"><span class="lineno"> 153</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>
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<div class="line"><span class="lineno"> 154</span> numerator = <a class="code hl_function" href="#ae2ab49ba1969d7a5988f9bc2c8924569">poly_function</a>(coeffs, (*roots)[n]);</div>
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<div class="line"><span class="lineno"> 155</span> denominator = 1.0;</div>
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<div class="line"><span class="lineno"> 156</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < roots->size(); i++)</div>
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<div class="line"><span class="lineno"> 157</span> <span class="keywordflow">if</span> (i != n)</div>
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<div class="line"><span class="lineno"> 158</span> denominator *= (*roots)[n] - (*roots)[i];</div>
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<div class="line"><span class="lineno"> 159</span> </div>
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<div class="line"><span class="lineno"> 160</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>
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<div class="line"><span class="lineno"> 161</span> </div>
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<div class="line"><span class="lineno"> 162</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>
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<div class="line"><span class="lineno"> 163</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>
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<div class="line"><span class="lineno"> 164</span> << std::abs(delta) << <span class="stringliteral">"\n"</span>;</div>
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<div class="line"><span class="lineno"> 165</span> <span class="comment">// return std::pair<uint32_t, double>(iter, tol_condition);</span></div>
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<div class="line"><span class="lineno"> 166</span> break_loop = <span class="keyword">true</span>;</div>
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<div class="line"><span class="lineno"> 167</span> }</div>
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<div class="line"><span class="lineno"> 168</span> </div>
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<div class="line"><span class="lineno"> 169</span> (*roots)[n] -= delta;</div>
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<div class="line"><span class="lineno"> 170</span> </div>
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<div class="line"><span class="lineno"> 171</span><span class="preprocessor">#ifdef _OPENMP</span></div>
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<div class="line"><span class="lineno"> 172</span><span class="preprocessor">#pragma omp critical</span></div>
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<div class="line"><span class="lineno"> 173</span><span class="preprocessor">#endif</span></div>
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<div class="line"><span class="lineno"> 174</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>
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<div class="line"><span class="lineno"> 175</span> }</div>
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<div class="line"><span class="lineno"> 176</span> <span class="comment">// tol_condition /= (degree - 1);</span></div>
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<div class="line"><span class="lineno"> 177</span> </div>
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<div class="line"><span class="lineno"> 178</span> <span class="keywordflow">if</span> (break_loop)</div>
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<div class="line"><span class="lineno"> 179</span> <span class="keywordflow">break</span>;</div>
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<div class="line"><span class="lineno"> 180</span> </div>
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<div class="line"><span class="lineno"> 181</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>
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<div class="line"><span class="lineno"> 182</span> <span class="keywordflow">for</span> (n = 0; n < roots->size(); n++)</div>
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<div class="line"><span class="lineno"> 183</span> log_file << <a class="code hl_function" href="#a90219e35062007d1f1b68e9af071ab5c">complex_str</a>((*roots)[n]) << <span class="stringliteral">","</span>;</div>
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<div class="line"><span class="lineno"> 184</span> }</div>
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<div class="line"><span class="lineno"> 185</span> </div>
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<div class="line"><span class="lineno"> 186</span><span class="preprocessor">#if defined(DEBUG) || !defined(NDEBUG)</span></div>
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<div class="line"><span class="lineno"> 187</span> <span class="keywordflow">if</span> (iter % 500 == 0) {</div>
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<div class="line"><span class="lineno"> 188</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>
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<div class="line"><span class="lineno"> 189</span> <span class="keywordflow">for</span> (n = 0; n < roots->size(); n++)</div>
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<div class="line"><span class="lineno"> 190</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>
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<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\tabsolute average change: "</span> << tol_condition</div>
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<div class="line"><span class="lineno"> 192</span> << <span class="stringliteral">"\n"</span>;</div>
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<div class="line"><span class="lineno"> 193</span> }</div>
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<div class="line"><span class="lineno"> 194</span><span class="preprocessor">#endif</span></div>
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<div class="line"><span class="lineno"> 195</span> </div>
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<div class="line"><span class="lineno"> 196</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>
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<div class="line"><span class="lineno"> 197</span> log_file << tol_condition;</div>
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<div class="line"><span class="lineno"> 198</span> }</div>
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<div class="line"><span class="lineno"> 199</span> </div>
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<div class="line"><span class="lineno"> 200</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>
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<div class="line"><span class="lineno"> 201</span>}</div>
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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"> 117</span> </div>
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<div class="line"><span class="lineno"> 118</span> <span class="keywordflow">if</span> (write_log) {</div>
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<div class="line"><span class="lineno"> 119</span> <span class="comment">/*</span></div>
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<div class="line"><span class="lineno"> 120</span><span class="comment"> * store intermediate values to a CSV file</span></div>
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<div class="line"><span class="lineno"> 121</span><span class="comment"> */</span></div>
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<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>
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<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>
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<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"> 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>
|
||||
<div class="line"><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"><span class="lineno"> 130</span> </div>
|
||||
<div class="line"><span class="lineno"> 131</span> log_file << <span class="stringliteral">"avg. correction"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 132</span> log_file << <span class="stringliteral">"\n0,"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 133</span> <span class="keywordflow">for</span> (n = 0; n < roots->size(); n++)</div>
|
||||
<div class="line"><span class="lineno"> 134</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"> 135</span> }</div>
|
||||
<div class="line"><span class="lineno"> 136</span> </div>
|
||||
<div class="line"><span class="lineno"> 137</span> <span class="keywordtype">bool</span> break_loop = <span class="keyword">false</span>;</div>
|
||||
<div class="line"><span class="lineno"> 138</span> <span class="keywordflow">while</span> (!<a class="code hl_function" href="#a024b8bc4755863315456d573a6732377">check_termination</a>(tol_condition) && iter < INT16_MAX &&</div>
|
||||
<div class="line"><span class="lineno"> 139</span> !break_loop) {</div>
|
||||
<div class="line"><span class="lineno"> 140</span> tol_condition = 0;</div>
|
||||
<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"> 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>
|
||||
<div class="line"><span class="lineno"> 148</span><span class="preprocessor">#pragma omp parallel for shared(break_loop, tol_condition)</span></div>
|
||||
<div class="line"><span class="lineno"> 149</span><span class="preprocessor">#endif</span></div>
|
||||
<div class="line"><span class="lineno"> 150</span> <span class="keywordflow">for</span> (n = 0; n < roots->size(); n++) {</div>
|
||||
<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"> 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"> 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"> 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>
|
||||
<div class="line"><span class="lineno"> 168</span> }</div>
|
||||
<div class="line"><span class="lineno"> 169</span> </div>
|
||||
<div class="line"><span class="lineno"> 170</span> (*roots)[n] -= delta;</div>
|
||||
<div class="line"><span class="lineno"> 171</span> </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"> 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"> 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"> 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"> 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"> 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"> 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:91</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:76</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:53</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>
|
||||
@@ -424,68 +425,68 @@ Here is the call graph for this function:</div>
|
||||
</tr>
|
||||
</table>
|
||||
</div><div class="memdoc">
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 283</span> {</div>
|
||||
<div class="line"><span class="lineno"> 284</span> <span class="comment">/* initialize random seed: */</span></div>
|
||||
<div class="line"><span class="lineno"> 285</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> </div>
|
||||
<div class="line"><span class="lineno"> 287</span> <span class="keywordflow">if</span> (argc < 2) {</div>
|
||||
<div class="line"><span class="lineno"> 288</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"> 289</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"> 290</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> <span class="stringliteral">"commandline "</span></div>
|
||||
<div class="line"><span class="lineno"> 292</span> <span class="stringliteral">"arguments.\n"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 293</span> <span class="keywordflow">return</span> 0;</div>
|
||||
<div class="line"><span class="lineno"> 294</span> }</div>
|
||||
<div class="line"><span class="lineno"> 295</span> </div>
|
||||
<div class="line"><span class="lineno"> 296</span> <span class="keywordtype">int</span> n, degree = argc - 1; <span class="comment">// detected polynomial degree</span></div>
|
||||
<div class="line"><span class="lineno"> 297</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> </div>
|
||||
<div class="line"><span class="lineno"> 299</span> <span class="comment">// number of roots = degree - 1</span></div>
|
||||
<div class="line"><span class="lineno"> 300</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> </div>
|
||||
<div class="line"><span class="lineno"> 302</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> <span class="keywordflow">for</span> (n = 0; n < degree; n++) {</div>
|
||||
<div class="line"><span class="lineno"> 304</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> <span class="keywordflow">if</span> (n < degree - 1 && coeffs[n] != 0)</div>
|
||||
<div class="line"><span class="lineno"> 306</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> <span class="keywordflow">else</span> <span class="keywordflow">if</span> (coeffs[n] != 0)</div>
|
||||
<div class="line"><span class="lineno"> 308</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> << <span class="stringliteral">" = 0\n"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 310</span> </div>
|
||||
<div class="line"><span class="lineno"> 311</span> <span class="comment">/* initialize root approximations with random values */</span></div>
|
||||
<div class="line"><span class="lineno"> 312</span> <span class="keywordflow">if</span> (n < degree - 1) {</div>
|
||||
<div class="line"><span class="lineno"> 313</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] -= 50.f;</div>
|
||||
<div class="line"><span class="lineno"> 315</span> s0[n] /= 50.f;</div>
|
||||
<div class="line"><span class="lineno"> 316</span> }</div>
|
||||
<div class="line"><span class="lineno"> 317</span> }</div>
|
||||
<div class="line"><span class="lineno"> 318</span> </div>
|
||||
<div class="line"><span class="lineno"> 319</span> <span class="comment">// numerical errors less when the first coefficient is "1"</span></div>
|
||||
<div class="line"><span class="lineno"> 320</span> <span class="comment">// hence, we normalize the first coefficient</span></div>
|
||||
<div class="line"><span class="lineno"> 321</span> {</div>
|
||||
<div class="line"><span class="lineno"> 322</span> <span class="keywordtype">double</span> tmp = coeffs[0];</div>
|
||||
<div class="line"><span class="lineno"> 323</span> coeffs /= tmp;</div>
|
||||
<div class="line"><span class="lineno"> 324</span> }</div>
|
||||
<div class="line"><span class="lineno"> 325</span> </div>
|
||||
<div class="line"><span class="lineno"> 326</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> <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"> 328</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> </div>
|
||||
<div class="line"><span class="lineno"> 330</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> <span class="keywordflow">for</span> (n = 0; n < degree - 1; n++)</div>
|
||||
<div class="line"><span class="lineno"> 332</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"> 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">"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"> 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">"Time taken: "</span></div>
|
||||
<div class="line"><span class="lineno"> 335</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"> 336</span> << <span class="stringliteral">" sec\n"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 337</span> </div>
|
||||
<div class="line"><span class="lineno"> 338</span> <span class="keywordflow">return</span> 0;</div>
|
||||
<div class="line"><span class="lineno"> 339</span>}</div>
|
||||
<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"> 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"> 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"> 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"> 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"> 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"> 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"> 308</span> <span class="keywordflow">else</span> <span class="keywordflow">if</span> (coeffs[n] != 0)</div>
|
||||
<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"> 310</span> << <span class="stringliteral">" = 0\n"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 311</span> </div>
|
||||
<div class="line"><span class="lineno"> 312</span> <span class="comment">/* initialize root approximations with random values */</span></div>
|
||||
<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"> 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>
|
||||
<div class="line"><span class="lineno"> 318</span> }</div>
|
||||
<div class="line"><span class="lineno"> 319</span> </div>
|
||||
<div class="line"><span class="lineno"> 320</span> <span class="comment">// numerical errors less when the first coefficient is "1"</span></div>
|
||||
<div class="line"><span class="lineno"> 321</span> <span class="comment">// hence, we normalize the first coefficient</span></div>
|
||||
<div class="line"><span class="lineno"> 322</span> {</div>
|
||||
<div class="line"><span class="lineno"> 323</span> <span class="keywordtype">double</span> tmp = coeffs[0];</div>
|
||||
<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"> 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"> 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"> 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"> 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:242</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:207</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:109</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:76</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>
|
||||
@@ -520,22 +521,22 @@ Here is the call graph for this function:</div>
|
||||
</dd>
|
||||
</dl>
|
||||
<dl class="section return"><dt>Returns</dt><dd>\(f(x)\) </dd></dl>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 54</span> {</div>
|
||||
<div class="line"><span class="lineno"> 55</span> <span class="keywordtype">double</span> real = 0.f, imag = 0.f;</div>
|
||||
<div class="line"><span class="lineno"> 56</span> <span class="keywordtype">int</span> n;</div>
|
||||
<div class="line"><span class="lineno"> 57</span> </div>
|
||||
<div class="line"><span class="lineno"> 58</span> <span class="comment">// #ifdef _OPENMP</span></div>
|
||||
<div class="line"><span class="lineno"> 59</span> <span class="comment">// #pragma omp target teams distribute reduction(+ : real, imag)</span></div>
|
||||
<div class="line"><span class="lineno"> 60</span> <span class="comment">// #endif</span></div>
|
||||
<div class="line"><span class="lineno"> 61</span> <span class="keywordflow">for</span> (n = 0; n < coeffs.size(); n++) {</div>
|
||||
<div class="line"><span class="lineno"> 62</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"> 63</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"> 64</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"> 65</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"> 66</span> }</div>
|
||||
<div class="line"><span class="lineno"> 67</span> </div>
|
||||
<div class="line"><span class="lineno"> 68</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>}</div>
|
||||
<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>
|
||||
<div class="line"><span class="lineno"> 58</span> </div>
|
||||
<div class="line"><span class="lineno"> 59</span> <span class="comment">// #ifdef _OPENMP</span></div>
|
||||
<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"> 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"> 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>
|
||||
@@ -560,36 +561,36 @@ Here is the call graph for this function:</div>
|
||||
</table>
|
||||
</div><div class="memdoc">
|
||||
<p>Self test the algorithm by checking the roots for \(x^2+4=0\) to which the roots are \(0 \pm 2i\) </p>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 207</span> {</div>
|
||||
<div class="line"><span class="lineno"> 208</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"> 209</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"> 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>> expected = {</div>
|
||||
<div class="line"><span class="lineno"> 211</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"> 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.) <span class="comment">// known expected roots</span></div>
|
||||
<div class="line"><span class="lineno"> 213</span> };</div>
|
||||
<div class="line"><span class="lineno"> 214</span> </div>
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<div class="line"><span class="lineno"> 215</span> <span class="comment">/* initialize root approximations with random values */</span></div>
|
||||
<div class="line"><span class="lineno"> 216</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> n = 0; n < roots.size(); n++) {</div>
|
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<div class="line"><span class="lineno"> 217</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] -= 50.f;</div>
|
||||
<div class="line"><span class="lineno"> 219</span> roots[n] /= 25.f;</div>
|
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<div class="line"><span class="lineno"> 220</span> }</div>
|
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<div class="line"><span class="lineno"> 221</span> </div>
|
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<div class="line"><span class="lineno"> 222</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, &roots, <span class="keyword">false</span>);</div>
|
||||
<div class="line"><span class="lineno"> 223</span> </div>
|
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<div class="line"><span class="lineno"> 224</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < roots.size(); i++) {</div>
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<div class="line"><span class="lineno"> 225</span> <span class="comment">// check if approximations are have < 0.1% error with one of the</span></div>
|
||||
<div class="line"><span class="lineno"> 226</span> <span class="comment">// expected roots</span></div>
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||||
<div class="line"><span class="lineno"> 227</span> <span class="keywordtype">bool</span> err1 = <span class="keyword">false</span>;</div>
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||||
<div class="line"><span class="lineno"> 228</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < roots.size(); j++)</div>
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<div class="line"><span class="lineno"> 229</span> err1 |= std::abs(std::abs(roots[i] - expected[j])) < 1e-3;</div>
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<div class="line"><span class="lineno"> 230</span> assert(err1);</div>
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<div class="line"><span class="lineno"> 231</span> }</div>
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<div class="line"><span class="lineno"> 232</span> </div>
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<div class="line"><span class="lineno"> 233</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">"Test 1 passed! - "</span> << <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.first << <span class="stringliteral">" iterations, "</span></div>
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<div class="line"><span class="lineno"> 234</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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<div class="line"><span class="lineno"> 235</span> << <span class="stringliteral">"\n"</span>;</div>
|
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<div class="line"><span class="lineno"> 236</span>}</div>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 208</span> {</div>
|
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<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"> 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"> 219</span> roots[n] -= 50.f;</div>
|
||||
<div class="line"><span class="lineno"> 220</span> roots[n] /= 25.f;</div>
|
||||
<div class="line"><span class="lineno"> 221</span> }</div>
|
||||
<div class="line"><span class="lineno"> 222</span> </div>
|
||||
<div class="line"><span class="lineno"> 223</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, &roots, <span class="keyword">false</span>);</div>
|
||||
<div class="line"><span class="lineno"> 224</span> </div>
|
||||
<div class="line"><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"><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"><span class="lineno"> 227</span> <span class="comment">// expected roots</span></div>
|
||||
<div class="line"><span class="lineno"> 228</span> <span class="keywordtype">bool</span> err1 = <span class="keyword">false</span>;</div>
|
||||
<div class="line"><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"><span class="lineno"> 230</span> err1 |= std::abs(std::abs(roots[i] - expected[j])) < 1e-3;</div>
|
||||
<div class="line"><span class="lineno"> 231</span> assert(err1);</div>
|
||||
<div class="line"><span class="lineno"> 232</span> }</div>
|
||||
<div class="line"><span class="lineno"> 233</span> </div>
|
||||
<div class="line"><span class="lineno"> 234</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">"Test 1 passed! - "</span> << <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.first << <span class="stringliteral">" iterations, "</span></div>
|
||||
<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>
|
||||
<div class="line"><span class="lineno"> 236</span> << <span class="stringliteral">"\n"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 237</span>}</div>
|
||||
</div><!-- fragment --><div class="dynheader">
|
||||
Here is the call graph for this function:</div>
|
||||
<div class="dyncontent">
|
||||
@@ -613,37 +614,37 @@ Here is the call graph for this function:</div>
|
||||
</table>
|
||||
</div><div class="memdoc">
|
||||
<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>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 242</span> {</div>
|
||||
<div class="line"><span class="lineno"> 243</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 = {<span class="comment">// 0.015625 x^3 - 1 = 0</span></div>
|
||||
<div class="line"><span class="lineno"> 244</span> 1. / 64., 0., 0., -1.};</div>
|
||||
<div class="line"><span class="lineno"> 245</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(3);</div>
|
||||
<div class="line"><span class="lineno"> 246</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>
|
||||
<div class="line"><span class="lineno"> 247</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex<double></a>(4., 0.), <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex<double></a>(-2., 3.46410162),</div>
|
||||
<div class="line"><span class="lineno"> 248</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex<double></a>(-2., -3.46410162) <span class="comment">// known expected roots</span></div>
|
||||
<div class="line"><span class="lineno"> 249</span> };</div>
|
||||
<div class="line"><span class="lineno"> 250</span> </div>
|
||||
<div class="line"><span class="lineno"> 251</span> <span class="comment">/* initialize root approximations with random values */</span></div>
|
||||
<div class="line"><span class="lineno"> 252</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> n = 0; n < roots.size(); n++) {</div>
|
||||
<div class="line"><span class="lineno"> 253</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"> 254</span> roots[n] -= 50.f;</div>
|
||||
<div class="line"><span class="lineno"> 255</span> roots[n] /= 25.f;</div>
|
||||
<div class="line"><span class="lineno"> 256</span> }</div>
|
||||
<div class="line"><span class="lineno"> 257</span> </div>
|
||||
<div class="line"><span class="lineno"> 258</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, &roots, <span class="keyword">false</span>);</div>
|
||||
<div class="line"><span class="lineno"> 259</span> </div>
|
||||
<div class="line"><span class="lineno"> 260</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < roots.size(); i++) {</div>
|
||||
<div class="line"><span class="lineno"> 261</span> <span class="comment">// check if approximations are have < 0.1% error with one of the</span></div>
|
||||
<div class="line"><span class="lineno"> 262</span> <span class="comment">// expected roots</span></div>
|
||||
<div class="line"><span class="lineno"> 263</span> <span class="keywordtype">bool</span> err1 = <span class="keyword">false</span>;</div>
|
||||
<div class="line"><span class="lineno"> 264</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < roots.size(); j++)</div>
|
||||
<div class="line"><span class="lineno"> 265</span> err1 |= std::abs(std::abs(roots[i] - expected[j])) < 1e-3;</div>
|
||||
<div class="line"><span class="lineno"> 266</span> assert(err1);</div>
|
||||
<div class="line"><span class="lineno"> 267</span> }</div>
|
||||
<div class="line"><span class="lineno"> 268</span> </div>
|
||||
<div class="line"><span class="lineno"> 269</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">"Test 2 passed! - "</span> << <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.first << <span class="stringliteral">" iterations, "</span></div>
|
||||
<div class="line"><span class="lineno"> 270</span> << <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.second << <span class="stringliteral">" accuracy"</span></div>
|
||||
<div class="line"><span class="lineno"> 271</span> << <span class="stringliteral">"\n"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 272</span>}</div>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 243</span> {</div>
|
||||
<div class="line"><span class="lineno"> 244</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 = {<span class="comment">// 0.015625 x^3 - 1 = 0</span></div>
|
||||
<div class="line"><span class="lineno"> 245</span> 1. / 64., 0., 0., -1.};</div>
|
||||
<div class="line"><span class="lineno"> 246</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(3);</div>
|
||||
<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>
|
||||
<div class="line"><span class="lineno"> 248</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex<double></a>(4., 0.), <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex<double></a>(-2., 3.46410162),</div>
|
||||
<div class="line"><span class="lineno"> 249</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex<double></a>(-2., -3.46410162) <span class="comment">// known expected roots</span></div>
|
||||
<div class="line"><span class="lineno"> 250</span> };</div>
|
||||
<div class="line"><span class="lineno"> 251</span> </div>
|
||||
<div class="line"><span class="lineno"> 252</span> <span class="comment">/* initialize root approximations with random values */</span></div>
|
||||
<div class="line"><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"><span class="lineno"> 254</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"> 255</span> roots[n] -= 50.f;</div>
|
||||
<div class="line"><span class="lineno"> 256</span> roots[n] /= 25.f;</div>
|
||||
<div class="line"><span class="lineno"> 257</span> }</div>
|
||||
<div class="line"><span class="lineno"> 258</span> </div>
|
||||
<div class="line"><span class="lineno"> 259</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, &roots, <span class="keyword">false</span>);</div>
|
||||
<div class="line"><span class="lineno"> 260</span> </div>
|
||||
<div class="line"><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"><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"><span class="lineno"> 263</span> <span class="comment">// expected roots</span></div>
|
||||
<div class="line"><span class="lineno"> 264</span> <span class="keywordtype">bool</span> err1 = <span class="keyword">false</span>;</div>
|
||||
<div class="line"><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"><span class="lineno"> 266</span> err1 |= std::abs(std::abs(roots[i] - expected[j])) < 1e-3;</div>
|
||||
<div class="line"><span class="lineno"> 267</span> assert(err1);</div>
|
||||
<div class="line"><span class="lineno"> 268</span> }</div>
|
||||
<div class="line"><span class="lineno"> 269</span> </div>
|
||||
<div class="line"><span class="lineno"> 270</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">"Test 2 passed! - "</span> << <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.first << <span class="stringliteral">" iterations, "</span></div>
|
||||
<div class="line"><span class="lineno"> 271</span> << <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.second << <span class="stringliteral">" accuracy"</span></div>
|
||||
<div class="line"><span class="lineno"> 272</span> << <span class="stringliteral">"\n"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 273</span>}</div>
|
||||
</div><!-- fragment --><div class="dynheader">
|
||||
Here is the call graph for this function:</div>
|
||||
<div class="dyncontent">
|
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|
||||
Reference in New Issue
Block a user