Documentation for f4403718ef
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@@ -169,17 +169,17 @@ Some known values are:</p><ul>
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<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> -= <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> / n;</div>
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<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <span class="keywordflow">return</span> <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
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@@ -143,6 +143,10 @@ Functions</h2></td></tr>
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<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a>.precision(12);</div>
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<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/fixed.html">std::fixed</a> << <a class="code" href="../../da/d24/sqrt__double_8cpp.html#ae662282ad0740d2063ac404ca3bd74fc">Sqrt</a>(n);</div>
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<div class="line"><a name="l00049"></a><span class="lineno"> 49</span> }</div>
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<div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
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<div class="ttc" id="afixed_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/fixed.html">std::fixed</a></div><div class="ttdeci">T fixed(T... args)</div></div>
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<div class="ttc" id="asqrt__double_8cpp_html_ae662282ad0740d2063ac404ca3bd74fc"><div class="ttname"><a href="../../da/d24/sqrt__double_8cpp.html#ae662282ad0740d2063ac404ca3bd74fc">Sqrt</a></div><div class="ttdeci">double Sqrt(double a)</div><div class="ttdef"><b>Definition:</b> sqrt_double.cpp:16</div></div>
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<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
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<div class="ttc" id="afixed_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/fixed.html">std::fixed</a></div><div class="ttdeci">T fixed(T... args)</div></div>
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<div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
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<title>Algorithms_in_C++: Complex Class Reference</title>
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@@ -215,6 +215,8 @@ double </td><td class="memItemRight" valign="bottom"><b>im</b></td></tr>
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<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  re = x * <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">std::cos</a>(y);</div>
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||||
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  im = x * <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sin.html">std::sin</a>(y);</div>
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<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  }</div>
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<div class="ttc" id="acos_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">std::cos</a></div><div class="ttdeci">T cos(T... args)</div></div>
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<div class="ttc" id="asin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/sin.html">std::sin</a></div><div class="ttdeci">T sin(T... args)</div></div>
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</dd>
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<div class="fragment"><div class="line"><a name="l00058"></a><span class="lineno"> 58</span> : re(other.<a class="code" href="../../da/d5a/class_complex.html#a312e4b19146128408fb06e0150b0faf6">real</a>()), im(other.<a class="code" href="../../da/d5a/class_complex.html#af8aacf982e2e6c142921bc850f6dc974">imag</a>()) {}</div>
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<div class="ttc" id="aclass_complex_html_a312e4b19146128408fb06e0150b0faf6"><div class="ttname"><a href="../../da/d5a/class_complex.html#a312e4b19146128408fb06e0150b0faf6">Complex::real</a></div><div class="ttdeci">double real() const</div><div class="ttdoc">Member function to get real value of our complex number. Member function (getter) to access the class...</div><div class="ttdef"><b>Definition:</b> complex_numbers.cpp:64</div></div>
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<div class="ttc" id="aclass_complex_html_af8aacf982e2e6c142921bc850f6dc974"><div class="ttname"><a href="../../da/d5a/class_complex.html#af8aacf982e2e6c142921bc850f6dc974">Complex::imag</a></div><div class="ttdeci">double imag() const</div><div class="ttdoc">Member function to get imaginary value of our complex number. Member function (getter) to access the ...</div><div class="ttdef"><b>Definition:</b> complex_numbers.cpp:70</div></div>
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<div class="fragment"><div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  {</div>
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<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  <span class="keywordflow">return</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(this->re * this->re + this->im * this->im);</div>
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<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  }</div>
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<div class="ttc" id="asqrt_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a></div><div class="ttdeci">T sqrt(T... args)</div></div>
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<p>Member function to give the argument of our complex number. </p>
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<dl class="section return"><dt>Returns</dt><dd>Argument of our <a class="el" href="../../da/d5a/class_complex.html" title="Class Complex to represent complex numbers as a field.">Complex</a> number in radians. </dd></dl>
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<div class="fragment"><div class="line"><a name="l00087"></a><span class="lineno"> 87</span> { <span class="keywordflow">return</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/atan2.html">std::atan2</a>(this->im, this->re); }</div>
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<div class="ttc" id="aatan2_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/atan2.html">std::atan2</a></div><div class="ttdeci">T atan2(T... args)</div></div>
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<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  this->re * other.im + this->im * other.re);</div>
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||||
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="keywordflow">return</span> <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>;</div>
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<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  }</div>
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<div class="ttc" id="aclass_complex_html"><div class="ttname"><a href="../../da/d5a/class_complex.html">Complex</a></div><div class="ttdoc">Class Complex to represent complex numbers as a field.</div><div class="ttdef"><b>Definition:</b> complex_numbers.cpp:20</div></div>
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<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>
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<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  <span class="keywordflow">throw</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/error/invalid_argument.html">std::invalid_argument</a>(<span class="stringliteral">"Undefined Value"</span>);</div>
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<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  }</div>
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<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  }</div>
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<div class="ttc" id="aclass_complex_html_a3cfc522c782726f49ee20af17b77f867"><div class="ttname"><a href="../../da/d5a/class_complex.html#a3cfc522c782726f49ee20af17b77f867">Complex::Complex</a></div><div class="ttdeci">Complex(double x=0.f, double y=0.f, bool is_polar=false)</div><div class="ttdoc">Complex Constructor which initialises our complex number.</div><div class="ttdef"><b>Definition:</b> complex_numbers.cpp:43</div></div>
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<div class="ttc" id="ainvalid_argument_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/error/invalid_argument.html">std::invalid_argument</a></div></div>
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<div class="ttc" id="aclass_complex_html"><div class="ttname"><a href="../../da/d5a/class_complex.html">Complex</a></div><div class="ttdoc">Class Complex to represent complex numbers as a field.</div><div class="ttdef"><b>Definition:</b> complex_numbers.cpp:20</div></div>
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<div class="ttc" id="aatan2_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/atan2.html">std::atan2</a></div><div class="ttdeci">T atan2(T... args)</div></div>
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</div><!-- fragment --><p>Sample implementation results to compute approximate roots of the equation \(x^4-1=0\):<br />
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</div><!-- fragment --><p> Sample implementation results to compute approximate roots of the equation \(x^4-1=0\):<br />
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<img src="https://raw.githubusercontent.com/TheAlgorithms/C-Plus-Plus/docs/images/numerical_methods/durand_kerner_error.svg" alt="Error evolution during root approximations computed every
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iteration." style="pointer-events: none;" width="400" class="inline"/> <img src="https://raw.githubusercontent.com/TheAlgorithms/C-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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<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>
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<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  << <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>.second << <span class="stringliteral">" accuracy"</span></div>
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