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<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit</dd></dl>
<p>Driver Code </p>
<dl class="section examples"><dt>Examples</dt><dd><a class="el" href="../../dc/dc4/_2_users_2runner_2work_2_c-_plus-_plus_2_c-_plus-_plus_2numerical_methods_2rungekutta_8cpp-example.html#a5">/Users/runner/work/C-Plus-Plus/C-Plus-Plus/numerical_methods/rungekutta.cpp</a>, and <a class="el" href="../../dd/db0/_2_users_2runner_2work_2_c-_plus-_plus_2_c-_plus-_plus_2sorting_2wiggle_sort_8cpp-example.html#a10">/Users/runner/work/C-Plus-Plus/C-Plus-Plus/sorting/wiggle_sort.cpp</a>.</dd>
<dl class="section examples"><dt>Examples</dt><dd><a class="el" href="../../df/dcd/_2_users_2runner_2work_2_c-_plus-_plus_2_c-_plus-_plus_2math_2quadratic_equations_complex_numbers_8cpp-example.html#a9">/Users/runner/work/C-Plus-Plus/C-Plus-Plus/math/quadratic_equations_complex_numbers.cpp</a>, <a class="el" href="../../dc/dc4/_2_users_2runner_2work_2_c-_plus-_plus_2_c-_plus-_plus_2numerical_methods_2rungekutta_8cpp-example.html#a5">/Users/runner/work/C-Plus-Plus/C-Plus-Plus/numerical_methods/rungekutta.cpp</a>, and <a class="el" href="../../dd/db0/_2_users_2runner_2work_2_c-_plus-_plus_2_c-_plus-_plus_2sorting_2wiggle_sort_8cpp-example.html#a10">/Users/runner/work/C-Plus-Plus/C-Plus-Plus/sorting/wiggle_sort.cpp</a>.</dd>
</dl>
<div class="fragment"><div class="line"><span class="lineno"> 112</span> {</div>
<div class="line"><span class="lineno"> 113</span> <span class="comment">// Create following graph and test whether it is 3 colorable</span></div>

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<p>Calculate quadratic equation with complex roots, i.e. b^2 - 4ac &lt; 0.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;array&gt;</code><br />
<code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;cmath&gt;</code><br />
<code>#include &lt;complex&gt;</code><br />
<code>#include &lt;exception&gt;</code><br />
<code>#include &lt;iomanip&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
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<tr class="memdesc:dd/d47/namespacemath"><td class="mdescLeft">&#160;</td><td class="mdescRight">for IO operations <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:aacb1411ef2029e81f249c21e17c96fdb"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a>&lt; long double &gt;, 2 &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d47/namespacemath.html#aacb1411ef2029e81f249c21e17c96fdb">math::quadraticEquation</a> (long double a, long double b, long double c)</td></tr>
<tr class="memdesc:aacb1411ef2029e81f249c21e17c96fdb"><td class="mdescLeft">&#160;</td><td class="mdescRight">Quadratic equation calculator. <br /></td></tr>
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<tr class="memitem:af7a6d4e3dc85a6288c8f1f7094830c5a"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d18/quadratic__equations__complex__numbers_8cpp.html#af7a6d4e3dc85a6288c8f1f7094830c5a">assertArray</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a>&lt; long double &gt;, 2 &gt; input, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a>&lt; long double &gt;, 2 &gt; expected, size_t precision=10)</td></tr>
<tr class="memdesc:af7a6d4e3dc85a6288c8f1f7094830c5a"><td class="mdescLeft">&#160;</td><td class="mdescRight">Asserts an array of complex numbers. <br /></td></tr>
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<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d18/quadratic__equations__complex__numbers_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations to test quadraticEquation function. <br /></td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d18/quadratic__equations__complex__numbers_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Calculate quadratic equation with complex roots, i.e. b^2 - 4ac &lt; 0. </p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/Renjian-buchai" target="_blank">Renjian-buchai</a></dd></dl>
<p>@description Calculates any quadratic equation in form ax^2 + bx + c.</p>
<p>Quadratic equation: x = (-b +/- sqrt(b^2 - 4ac)) / 2a </p>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="af7a6d4e3dc85a6288c8f1f7094830c5a" name="af7a6d4e3dc85a6288c8f1f7094830c5a"></a>
<h2 class="memtitle"><span class="permalink"><a href="#af7a6d4e3dc85a6288c8f1f7094830c5a">&#9670;&#160;</a></span>assertArray()</h2>
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<td class="memname">void assertArray </td>
<td>(</td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a>&lt; long double &gt;, 2 &gt;&#160;</td>
<td class="paramname"><em>input</em>, </td>
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<td class="paramkey"></td>
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<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a>&lt; long double &gt;, 2 &gt;&#160;</td>
<td class="paramname"><em>expected</em>, </td>
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<td class="paramtype">size_t&#160;</td>
<td class="paramname"><em>precision</em> = <code>10</code>&#160;</td>
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<td>)</td>
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<p>Asserts an array of complex numbers. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">input</td><td>Input array of complex numbers. . </td></tr>
<tr><td class="paramname">expected</td><td>Expected array of complex numbers. </td></tr>
<tr><td class="paramname">precision</td><td>Precision to be asserted. Default=10 </td></tr>
</table>
</dd>
</dl>
<dl class="section examples"><dt>Examples</dt><dd><a class="el" href="../../df/dcd/_2_users_2runner_2work_2_c-_plus-_plus_2_c-_plus-_plus_2math_2quadratic_equations_complex_numbers_8cpp-example.html#a5">/Users/runner/work/C-Plus-Plus/C-Plus-Plus/math/quadratic_equations_complex_numbers.cpp</a>.</dd>
</dl>
<div class="fragment"><div class="line"><span class="lineno"> 102</span> {</div>
<div class="line"><span class="lineno"> 103</span> <span class="keywordtype">long</span> <span class="keywordtype">double</span> exponent = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(10, precision);</div>
<div class="line"><span class="lineno"> 104</span> input[0].real(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/round.html">std::round</a>(input[0].real() * exponent));</div>
<div class="line"><span class="lineno"> 105</span> input[1].real(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/round.html">std::round</a>(input[1].real() * exponent));</div>
<div class="line"><span class="lineno"> 106</span> input[0].imag(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/round.html">std::round</a>(input[0].imag() * exponent));</div>
<div class="line"><span class="lineno"> 107</span> input[1].imag(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/round.html">std::round</a>(input[1].imag() * exponent));</div>
<div class="line"><span class="lineno"> 108</span> </div>
<div class="line"><span class="lineno"> 109</span> expected[0].real(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/round.html">std::round</a>(expected[0].real() * exponent));</div>
<div class="line"><span class="lineno"> 110</span> expected[1].real(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/round.html">std::round</a>(expected[1].real() * exponent));</div>
<div class="line"><span class="lineno"> 111</span> expected[0].imag(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/round.html">std::round</a>(expected[0].imag() * exponent));</div>
<div class="line"><span class="lineno"> 112</span> expected[1].imag(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/round.html">std::round</a>(expected[1].imag() * exponent));</div>
<div class="line"><span class="lineno"> 113</span> </div>
<div class="line"><span class="lineno"> 114</span> assert(input == expected);</div>
<div class="line"><span class="lineno"> 115</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 class="ttc" id="around_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/round.html">std::round</a></div><div class="ttdeci">T round(T... args)</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&#160;</a></span>main()</h2>
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<td class="memname">int main </td>
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<td class="paramtype">void&#160;</td>
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<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 186</span> {</div>
<div class="line"><span class="lineno"> 187</span> <a class="code hl_function" href="../../da/d18/quadratic__equations__complex__numbers_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// Run self-test implementation.</span></div>
<div class="line"><span class="lineno"> 188</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 189</span>}</div>
<div class="ttc" id="aquadratic__equations__complex__numbers_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../da/d18/quadratic__equations__complex__numbers_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations to test quadraticEquation function.</div><div class="ttdef"><b>Definition:</b> quadratic_equations_complex_numbers.cpp:122</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&#160;</a></span>test()</h2>
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<td class="memname">static void test </td>
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<p>Self-test implementations to test quadraticEquation function. </p>
<dl class="section note"><dt>Note</dt><dd>There are 4 different types of solutions: Real and equal, real, complex, complex and equal. </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 122</span> {</div>
<div class="line"><span class="lineno"> 123</span> <span class="comment">// Values are equal and real.</span></div>
<div class="line"><span class="lineno"> 124</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input: \n&quot;</span></div>
<div class="line"><span class="lineno"> 125</span> <span class="stringliteral">&quot;a=1 \n&quot;</span></div>
<div class="line"><span class="lineno"> 126</span> <span class="stringliteral">&quot;b=-2 \n&quot;</span></div>
<div class="line"><span class="lineno"> 127</span> <span class="stringliteral">&quot;c=1 \n&quot;</span></div>
<div class="line"><span class="lineno"> 128</span> <span class="stringliteral">&quot;Expected output: \n&quot;</span></div>
<div class="line"><span class="lineno"> 129</span> <span class="stringliteral">&quot;(1, 0), (1, 0)\n\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 130</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::complex&lt;long double&gt;</a>, 2&gt; equalCase{</div>
<div class="line"><span class="lineno"> 131</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;long double&gt;</a>{1, 0}, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;long double&gt;</a>{1, 0}};</div>
<div class="line"><span class="lineno"> 132</span> assert(<a class="code hl_function" href="../../dd/d47/namespacemath.html#aacb1411ef2029e81f249c21e17c96fdb">math::quadraticEquation</a>(1, -2, 1) == equalCase);</div>
<div class="line"><span class="lineno"> 133</span> </div>
<div class="line"><span class="lineno"> 134</span> <span class="comment">// Values are equal and complex.</span></div>
<div class="line"><span class="lineno"> 135</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input: \n&quot;</span></div>
<div class="line"><span class="lineno"> 136</span> <span class="stringliteral">&quot;a=1 \n&quot;</span></div>
<div class="line"><span class="lineno"> 137</span> <span class="stringliteral">&quot;b=4 \n&quot;</span></div>
<div class="line"><span class="lineno"> 138</span> <span class="stringliteral">&quot;c=5 \n&quot;</span></div>
<div class="line"><span class="lineno"> 139</span> <span class="stringliteral">&quot;Expected output: \n&quot;</span></div>
<div class="line"><span class="lineno"> 140</span> <span class="stringliteral">&quot;(-2, -1), (-2, 1)\n\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 141</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::complex&lt;long double&gt;</a>, 2&gt; complexCase{</div>
<div class="line"><span class="lineno"> 142</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;long double&gt;</a>{-2, -1}, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;long double&gt;</a>{-2, 1}};</div>
<div class="line"><span class="lineno"> 143</span> assert(<a class="code hl_function" href="../../dd/d47/namespacemath.html#aacb1411ef2029e81f249c21e17c96fdb">math::quadraticEquation</a>(1, 4, 5) == complexCase);</div>
<div class="line"><span class="lineno"> 144</span> </div>
<div class="line"><span class="lineno"> 145</span> <span class="comment">// Values are real.</span></div>
<div class="line"><span class="lineno"> 146</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input: \n&quot;</span></div>
<div class="line"><span class="lineno"> 147</span> <span class="stringliteral">&quot;a=1 \n&quot;</span></div>
<div class="line"><span class="lineno"> 148</span> <span class="stringliteral">&quot;b=5 \n&quot;</span></div>
<div class="line"><span class="lineno"> 149</span> <span class="stringliteral">&quot;c=1 \n&quot;</span></div>
<div class="line"><span class="lineno"> 150</span> <span class="stringliteral">&quot;Expected output: \n&quot;</span></div>
<div class="line"><span class="lineno"> 151</span> <span class="stringliteral">&quot;(-4.7912878475, 0), (-0.2087121525, 0)\n\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 152</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::complex&lt;long double&gt;</a>, 2&gt; floatCase{</div>
<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&lt;long double&gt;</a>{-4.7912878475, 0},</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&lt;long double&gt;</a>{-0.2087121525, 0}};</div>
<div class="line"><span class="lineno"> 155</span> <a class="code hl_function" href="../../da/d18/quadratic__equations__complex__numbers_8cpp.html#af7a6d4e3dc85a6288c8f1f7094830c5a">assertArray</a>(<a class="code hl_function" href="../../dd/d47/namespacemath.html#aacb1411ef2029e81f249c21e17c96fdb">math::quadraticEquation</a>(1, 5, 1), floatCase);</div>
<div class="line"><span class="lineno"> 156</span> </div>
<div class="line"><span class="lineno"> 157</span> <span class="comment">// Values are complex.</span></div>
<div class="line"><span class="lineno"> 158</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input: \n&quot;</span></div>
<div class="line"><span class="lineno"> 159</span> <span class="stringliteral">&quot;a=1 \n&quot;</span></div>
<div class="line"><span class="lineno"> 160</span> <span class="stringliteral">&quot;b=1 \n&quot;</span></div>
<div class="line"><span class="lineno"> 161</span> <span class="stringliteral">&quot;c=1 \n&quot;</span></div>
<div class="line"><span class="lineno"> 162</span> <span class="stringliteral">&quot;Expected output: \n&quot;</span></div>
<div class="line"><span class="lineno"> 163</span> <span class="stringliteral">&quot;(-0.5, -0.8660254038), (-0.5, 0.8660254038)\n\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 164</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::complex&lt;long double&gt;</a>, 2&gt; ifloatCase{</div>
<div class="line"><span class="lineno"> 165</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;long double&gt;</a>{-0.5, -0.8660254038},</div>
<div class="line"><span class="lineno"> 166</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;long double&gt;</a>{-0.5, 0.8660254038}};</div>
<div class="line"><span class="lineno"> 167</span> <a class="code hl_function" href="../../da/d18/quadratic__equations__complex__numbers_8cpp.html#af7a6d4e3dc85a6288c8f1f7094830c5a">assertArray</a>(<a class="code hl_function" href="../../dd/d47/namespacemath.html#aacb1411ef2029e81f249c21e17c96fdb">math::quadraticEquation</a>(1, 1, 1), ifloatCase);</div>
<div class="line"><span class="lineno"> 168</span> </div>
<div class="line"><span class="lineno"> 169</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Exception test: \n&quot;</span></div>
<div class="line"><span class="lineno"> 170</span> <span class="stringliteral">&quot;Input: \n&quot;</span></div>
<div class="line"><span class="lineno"> 171</span> <span class="stringliteral">&quot;a=0 \n&quot;</span></div>
<div class="line"><span class="lineno"> 172</span> <span class="stringliteral">&quot;b=0 \n&quot;</span></div>
<div class="line"><span class="lineno"> 173</span> <span class="stringliteral">&quot;c=0\n&quot;</span></div>
<div class="line"><span class="lineno"> 174</span> <span class="stringliteral">&quot;Expected output: Exception thrown \n&quot;</span>;</div>
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<div class="line"><span class="lineno"> 176</span> <a class="code hl_function" href="../../dd/d47/namespacemath.html#aacb1411ef2029e81f249c21e17c96fdb">math::quadraticEquation</a>(0, 0, 0);</div>
<div class="line"><span class="lineno"> 177</span> } <span class="keywordflow">catch</span> (<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/error/invalid_argument.html">std::invalid_argument</a>&amp; e) {</div>
<div class="line"><span class="lineno"> 178</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Exception thrown successfully \n&quot;</span>;</div>
<div class="line"><span class="lineno"> 179</span> }</div>
<div class="line"><span class="lineno"> 180</span>}</div>
<div class="ttc" id="aarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/array.html">std::array</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::cout</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="ainvalid_argument_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/error/invalid_argument.html">std::invalid_argument</a></div></div>
<div class="ttc" id="anamespacemath_html_aacb1411ef2029e81f249c21e17c96fdb"><div class="ttname"><a href="../../dd/d47/namespacemath.html#aacb1411ef2029e81f249c21e17c96fdb">math::quadraticEquation</a></div><div class="ttdeci">std::array&lt; std::complex&lt; long double &gt;, 2 &gt; quadraticEquation(long double a, long double b, long double c)</div><div class="ttdoc">Quadratic equation calculator.</div><div class="ttdef"><b>Definition:</b> quadratic_equations_complex_numbers.cpp:53</div></div>
<div class="ttc" id="aquadratic__equations__complex__numbers_8cpp_html_af7a6d4e3dc85a6288c8f1f7094830c5a"><div class="ttname"><a href="../../da/d18/quadratic__equations__complex__numbers_8cpp.html#af7a6d4e3dc85a6288c8f1f7094830c5a">assertArray</a></div><div class="ttdeci">void assertArray(std::array&lt; std::complex&lt; long double &gt;, 2 &gt; input, std::array&lt; std::complex&lt; long double &gt;, 2 &gt; expected, size_t precision=10)</div><div class="ttdoc">Asserts an array of complex numbers.</div><div class="ttdef"><b>Definition:</b> quadratic_equations_complex_numbers.cpp:100</div></div>
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<div class="line"><span class="lineno"> 81</span> <span class="keywordflow">return</span> length * width * height / 3;</div>
<div class="line"><span class="lineno"> 82</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#aacb1411ef2029e81f249c21e17c96fdb">&#9670;&#160;</a></span>quadraticEquation()</h2>
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<tr>
<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a>&lt; long double &gt;, 2 &gt; math::quadraticEquation </td>
<td>(</td>
<td class="paramtype">long double&#160;</td>
<td class="paramname"><em>a</em>, </td>
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<tr>
<td class="paramkey"></td>
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<td class="paramtype">long double&#160;</td>
<td class="paramname"><em>b</em>, </td>
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<p>Quadratic equation calculator. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td>quadratic coefficient. </td></tr>
<tr><td class="paramname">b</td><td>linear coefficient. </td></tr>
<tr><td class="paramname">c</td><td>constant </td></tr>
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</dd>
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<dl class="section return"><dt>Returns</dt><dd>Array containing the roots of quadratic equation, incl. complex root. </dd></dl>
<dl class="section examples"><dt>Examples</dt><dd><a class="el" href="../../df/dcd/_2_users_2runner_2work_2_c-_plus-_plus_2_c-_plus-_plus_2math_2quadratic_equations_complex_numbers_8cpp-example.html#a1">/Users/runner/work/C-Plus-Plus/C-Plus-Plus/math/quadratic_equations_complex_numbers.cpp</a>.</dd>
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<div class="fragment"><div class="line"><span class="lineno"> 55</span> {</div>
<div class="line"><span class="lineno"> 56</span> <span class="keywordflow">if</span> (a == 0) {</div>
<div class="line"><span class="lineno"> 57</span> <span class="keywordflow">throw</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/error/invalid_argument.html">std::invalid_argument</a>(<span class="stringliteral">&quot;quadratic coefficient cannot be 0&quot;</span>);</div>
<div class="line"><span class="lineno"> 58</span> }</div>
<div class="line"><span class="lineno"> 59</span> </div>
<div class="line"><span class="lineno"> 60</span> <span class="keywordtype">long</span> <span class="keywordtype">double</span> discriminant = b * b - 4 * a * c;</div>
<div class="line"><span class="lineno"> 61</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::complex&lt;long double&gt;</a>, 2&gt; solutions{0, 0};</div>
<div class="line"><span class="lineno"> 62</span> </div>
<div class="line"><span class="lineno"> 63</span> <span class="keywordflow">if</span> (discriminant == 0) {</div>
<div class="line"><span class="lineno"> 64</span> solutions[0] = -b * 0.5 / a;</div>
<div class="line"><span class="lineno"> 65</span> solutions[1] = -b * 0.5 / a;</div>
<div class="line"><span class="lineno"> 66</span> <span class="keywordflow">return</span> solutions;</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="comment">// Complex root (discriminant &lt; 0)</span></div>
<div class="line"><span class="lineno"> 70</span> <span class="comment">// Note that the left term (-b / 2a) is always real. The imaginary part</span></div>
<div class="line"><span class="lineno"> 71</span> <span class="comment">// appears when b^2 - 4ac &lt; 0, so sqrt(b^2 - 4ac) has no real roots. So,</span></div>
<div class="line"><span class="lineno"> 72</span> <span class="comment">// the imaginary component is i * (+/-)sqrt(abs(b^2 - 4ac)) / 2a.</span></div>
<div class="line"><span class="lineno"> 73</span> <span class="keywordflow">if</span> (discriminant &gt; 0) {</div>
<div class="line"><span class="lineno"> 74</span> <span class="comment">// Since discriminant &gt; 0, there are only real roots. Therefore,</span></div>
<div class="line"><span class="lineno"> 75</span> <span class="comment">// imaginary component = 0.</span></div>
<div class="line"><span class="lineno"> 76</span> solutions[0] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;long double&gt;</a>{</div>
<div class="line"><span class="lineno"> 77</span> (-b - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(discriminant)) * 0.5 / a, 0};</div>
<div class="line"><span class="lineno"> 78</span> solutions[1] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;long double&gt;</a>{</div>
<div class="line"><span class="lineno"> 79</span> (-b + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(discriminant)) * 0.5 / a, 0};</div>
<div class="line"><span class="lineno"> 80</span> <span class="keywordflow">return</span> solutions;</div>
<div class="line"><span class="lineno"> 81</span> }</div>
<div class="line"><span class="lineno"> 82</span> <span class="comment">// Since b^2 - 4ac is &lt; 0, for faster computation, -discriminant is</span></div>
<div class="line"><span class="lineno"> 83</span> <span class="comment">// enough to make it positive.</span></div>
<div class="line"><span class="lineno"> 84</span> solutions[0] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;long double&gt;</a>{</div>
<div class="line"><span class="lineno"> 85</span> -b * 0.5 / a, -<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(-discriminant) * 0.5 / a};</div>
<div class="line"><span class="lineno"> 86</span> solutions[1] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;long double&gt;</a>{</div>
<div class="line"><span class="lineno"> 87</span> -b * 0.5 / a, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(-discriminant) * 0.5 / a};</div>
<div class="line"><span class="lineno"> 88</span> </div>
<div class="line"><span class="lineno"> 89</span> <span class="keywordflow">return</span> solutions;</div>
<div class="line"><span class="lineno"> 90</span>}</div>
<div class="ttc" id="aarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/array.html">std::array</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>
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<div class="headertitle"><div class="title">/Users/runner/work/C-Plus-Plus/C-Plus-Plus/math/quadratic_equations_complex_numbers.cpp</div></div>
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<p>int <a class="el" href="../../da/d18/quadratic__equations__complex__numbers_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4" title="Main function.">main()</a> { using <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>; using <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex</a>; using <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a>;</p>
<p>array&lt;complex&lt;long double, 2&gt; solutions = quadraticEquation(1, 2, 1); cout &lt;&lt; solutions[0] &lt;&lt; " " &lt;&lt; solutions[1] &lt;&lt; "\n";</p>
<p>solutions = quadraticEquation(1, 1, 1); // Reusing solutions. cout &lt;&lt; solutions[0] &lt;&lt; " " &lt;&lt; solutions[1] &lt;&lt; "\n"; return 0; }</p>
<p>Output: (-1, 0) (-1, 0) (-0.5,0.866025) (-0.5,0.866025)</p>
<div class="fragment"><div class="line"><span class="comment">/**</span></div>
<div class="line"><span class="comment"> * @file</span></div>
<div class="line"><span class="comment"> * @brief Calculate quadratic equation with complex roots, i.e. b^2 - 4ac &lt; 0.</span></div>
<div class="line"><span class="comment"> *</span></div>
<div class="line"><span class="comment"> * @author [Renjian-buchai](https://github.com/Renjian-buchai)</span></div>
<div class="line"><span class="comment"> *</span></div>
<div class="line"><span class="comment"> * @description Calculates any quadratic equation in form ax^2 + bx + c.</span></div>
<div class="line"><span class="comment"> *</span></div>
<div class="line"><span class="comment"> * Quadratic equation:</span></div>
<div class="line"><span class="comment"> * x = (-b +/- sqrt(b^2 - 4ac)) / 2a</span></div>
<div class="line"><span class="comment"> *</span></div>
<div class="line"><span class="comment"> * @example</span></div>
<div class="line"><span class="comment"> * int main() {</span></div>
<div class="line"><span class="comment"> * using std::array;</span></div>
<div class="line"><span class="comment"> * using std::complex;</span></div>
<div class="line"><span class="comment"> * using std::cout;</span></div>
<div class="line"><span class="comment"> *</span></div>
<div class="line"><span class="comment"> * array&lt;complex&lt;long double, 2&gt; solutions = quadraticEquation(1, 2, 1);</span></div>
<div class="line"><span class="comment"> * cout &lt;&lt; solutions[0] &lt;&lt; &quot; &quot; &lt;&lt; solutions[1] &lt;&lt; &quot;\n&quot;;</span></div>
<div class="line"><span class="comment"> *</span></div>
<div class="line"><span class="comment"> * solutions = quadraticEquation(1, 1, 1); // Reusing solutions.</span></div>
<div class="line"><span class="comment"> * cout &lt;&lt; solutions[0] &lt;&lt; &quot; &quot; &lt;&lt; solutions[1] &lt;&lt; &quot;\n&quot;;</span></div>
<div class="line"><span class="comment"> * return 0;</span></div>
<div class="line"><span class="comment"> * }</span></div>
<div class="line"><span class="comment"> *</span></div>
<div class="line"><span class="comment"> * Output:</span></div>
<div class="line"><span class="comment"> * (-1, 0) (-1, 0)</span></div>
<div class="line"><span class="comment"> * (-0.5,0.866025) (-0.5,0.866025)</span></div>
<div class="line"><span class="comment"> */</span></div>
<div class="line"> </div>
<div class="line"><span class="preprocessor">#include &lt;array&gt;</span> <span class="comment">/// std::array</span></div>
<div class="line"><span class="preprocessor">#include &lt;cassert&gt;</span> <span class="comment">/// assert</span></div>
<div class="line"><span class="preprocessor">#include &lt;cmath&gt;</span> <span class="comment">/// std::sqrt, std::trunc, std::pow</span></div>
<div class="line"><span class="preprocessor">#include &lt;complex&gt;</span> <span class="comment">/// std::complex</span></div>
<div class="line"><span class="preprocessor">#include &lt;exception&gt;</span> <span class="comment">/// std::invalid_argument</span></div>
<div class="line"><span class="preprocessor">#include &lt;iomanip&gt;</span> <span class="comment">/// std::setprecision</span></div>
<div class="line"><span class="preprocessor">#include &lt;iostream&gt;</span> <span class="comment">/// std::cout</span></div>
<div class="line"><span class="comment"></span> </div>
<div class="line"><span class="comment">/**</span></div>
<div class="line"><span class="comment"> * @namespace</span></div>
<div class="line"><span class="comment"> * @brief Mathematical algorithms</span></div>
<div class="line"><span class="comment"> */</span></div>
<div class="line"><span class="keyword">namespace </span><a class="code hl_namespace" href="../../dd/d47/namespacemath.html">math</a> {</div>
<div class="line"><span class="comment"></span> </div>
<div class="line"><span class="comment">/**</span></div>
<div class="line"><span class="comment"> * @brief Quadratic equation calculator.</span></div>
<div class="line"><span class="comment"> * @param a quadratic coefficient.</span></div>
<div class="line"><span class="comment"> * @param b linear coefficient.</span></div>
<div class="line"><span class="comment"> * @param c constant</span></div>
<div class="line"><span class="comment"> * @return Array containing the roots of quadratic equation, incl. complex</span></div>
<div class="line"><span class="comment"> * root.</span></div>
<div class="line"><span class="comment"> */</span></div>
<div class="line"><a id="_a0" name="_a0"></a><a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::complex&lt;long double&gt;</a>, 2&gt; <a id="a1" name="a1"></a><a class="code hl_function" href="../../dd/d47/namespacemath.html#aacb1411ef2029e81f249c21e17c96fdb">quadraticEquation</a>(<span class="keywordtype">long</span> <span class="keywordtype">double</span> a,</div>
<div class="line"> <span class="keywordtype">long</span> <span class="keywordtype">double</span> b,</div>
<div class="line"> <span class="keywordtype">long</span> <span class="keywordtype">double</span> c) {</div>
<div class="line"> <span class="keywordflow">if</span> (a == 0) {</div>
<div class="line"> <span class="keywordflow">throw</span> <a id="_a2" name="_a2"></a><a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/error/invalid_argument.html">std::invalid_argument</a>(<span class="stringliteral">&quot;quadratic coefficient cannot be 0&quot;</span>);</div>
<div class="line"> }</div>
<div class="line"> </div>
<div class="line"> <span class="keywordtype">long</span> <span class="keywordtype">double</span> discriminant = b * b - 4 * a * c;</div>
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::complex&lt;long double&gt;</a>, 2&gt; solutions{0, 0};</div>
<div class="line"> </div>
<div class="line"> <span class="keywordflow">if</span> (discriminant == 0) {</div>
<div class="line"> solutions[0] = -b * 0.5 / a;</div>
<div class="line"> solutions[1] = -b * 0.5 / a;</div>
<div class="line"> <span class="keywordflow">return</span> solutions;</div>
<div class="line"> }</div>
<div class="line"> </div>
<div class="line"> <span class="comment">// Complex root (discriminant &lt; 0)</span></div>
<div class="line"> <span class="comment">// Note that the left term (-b / 2a) is always real. The imaginary part</span></div>
<div class="line"> <span class="comment">// appears when b^2 - 4ac &lt; 0, so sqrt(b^2 - 4ac) has no real roots. So,</span></div>
<div class="line"> <span class="comment">// the imaginary component is i * (+/-)sqrt(abs(b^2 - 4ac)) / 2a.</span></div>
<div class="line"> <span class="keywordflow">if</span> (discriminant &gt; 0) {</div>
<div class="line"> <span class="comment">// Since discriminant &gt; 0, there are only real roots. Therefore,</span></div>
<div class="line"> <span class="comment">// imaginary component = 0.</span></div>
<div class="line"> solutions[0] = <a id="_a3" name="_a3"></a><a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;long double&gt;</a>{</div>
<div class="line"> (-b - <a id="a4" name="a4"></a><a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(discriminant)) * 0.5 / a, 0};</div>
<div class="line"> solutions[1] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;long double&gt;</a>{</div>
<div class="line"> (-b + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(discriminant)) * 0.5 / a, 0};</div>
<div class="line"> <span class="keywordflow">return</span> solutions;</div>
<div class="line"> }</div>
<div class="line"> <span class="comment">// Since b^2 - 4ac is &lt; 0, for faster computation, -discriminant is</span></div>
<div class="line"> <span class="comment">// enough to make it positive.</span></div>
<div class="line"> solutions[0] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;long double&gt;</a>{</div>
<div class="line"> -b * 0.5 / a, -<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(-discriminant) * 0.5 / a};</div>
<div class="line"> solutions[1] = <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;long double&gt;</a>{</div>
<div class="line"> -b * 0.5 / a, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(-discriminant) * 0.5 / a};</div>
<div class="line"> </div>
<div class="line"> <span class="keywordflow">return</span> solutions;</div>
<div class="line">}</div>
<div class="line"> </div>
<div class="line">} <span class="comment">// namespace math</span></div>
<div class="line"><span class="comment"></span> </div>
<div class="line"><span class="comment">/**</span></div>
<div class="line"><span class="comment"> * @brief Asserts an array of complex numbers.</span></div>
<div class="line"><span class="comment"> * @param input Input array of complex numbers. .</span></div>
<div class="line"><span class="comment"> * @param expected Expected array of complex numbers.</span></div>
<div class="line"><span class="comment"> * @param precision Precision to be asserted. Default=10</span></div>
<div class="line"><span class="comment"> */</span></div>
<div class="line"><span class="keywordtype">void</span> <a id="a5" name="a5"></a><a class="code hl_function" href="../../da/d18/quadratic__equations__complex__numbers_8cpp.html#af7a6d4e3dc85a6288c8f1f7094830c5a">assertArray</a>(<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt;<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;long double&gt;</a>, 2&gt; input,</div>
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>&lt;<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;long double&gt;</a>, 2&gt; expected,</div>
<div class="line"> <span class="keywordtype">size_t</span> precision = 10) {</div>
<div class="line"> <span class="keywordtype">long</span> <span class="keywordtype">double</span> exponent = <a id="a6" name="a6"></a><a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(10, precision);</div>
<div class="line"> input[0].real(<a id="a7" name="a7"></a><a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/round.html">std::round</a>(input[0].real() * exponent));</div>
<div class="line"> input[1].real(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/round.html">std::round</a>(input[1].real() * exponent));</div>
<div class="line"> input[0].imag(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/round.html">std::round</a>(input[0].imag() * exponent));</div>
<div class="line"> input[1].imag(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/round.html">std::round</a>(input[1].imag() * exponent));</div>
<div class="line"> </div>
<div class="line"> expected[0].real(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/round.html">std::round</a>(expected[0].real() * exponent));</div>
<div class="line"> expected[1].real(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/round.html">std::round</a>(expected[1].real() * exponent));</div>
<div class="line"> expected[0].imag(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/round.html">std::round</a>(expected[0].imag() * exponent));</div>
<div class="line"> expected[1].imag(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/round.html">std::round</a>(expected[1].imag() * exponent));</div>
<div class="line"> </div>
<div class="line"> assert(input == expected);</div>
<div class="line">}</div>
<div class="line"><span class="comment"></span> </div>
<div class="line"><span class="comment">/**</span></div>
<div class="line"><span class="comment"> * @brief Self-test implementations to test quadraticEquation function.</span></div>
<div class="line"><span class="comment"> * @note There are 4 different types of solutions: Real and equal, real,</span></div>
<div class="line"><span class="comment"> * complex, complex and equal.</span></div>
<div class="line"><span class="comment"> */</span></div>
<div class="line"><span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code hl_function" href="../../d6/d2c/caesar__cipher_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a>() {</div>
<div class="line"> <span class="comment">// Values are equal and real.</span></div>
<div class="line"> <a id="_a8" name="_a8"></a><a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input: \n&quot;</span></div>
<div class="line"> <span class="stringliteral">&quot;a=1 \n&quot;</span></div>
<div class="line"> <span class="stringliteral">&quot;b=-2 \n&quot;</span></div>
<div class="line"> <span class="stringliteral">&quot;c=1 \n&quot;</span></div>
<div class="line"> <span class="stringliteral">&quot;Expected output: \n&quot;</span></div>
<div class="line"> <span class="stringliteral">&quot;(1, 0), (1, 0)\n\n&quot;</span>;</div>
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::complex&lt;long double&gt;</a>, 2&gt; equalCase{</div>
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;long double&gt;</a>{1, 0}, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;long double&gt;</a>{1, 0}};</div>
<div class="line"> assert(<a class="code hl_function" href="../../dd/d47/namespacemath.html#aacb1411ef2029e81f249c21e17c96fdb">math::quadraticEquation</a>(1, -2, 1) == equalCase);</div>
<div class="line"> </div>
<div class="line"> <span class="comment">// Values are equal and complex.</span></div>
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input: \n&quot;</span></div>
<div class="line"> <span class="stringliteral">&quot;a=1 \n&quot;</span></div>
<div class="line"> <span class="stringliteral">&quot;b=4 \n&quot;</span></div>
<div class="line"> <span class="stringliteral">&quot;c=5 \n&quot;</span></div>
<div class="line"> <span class="stringliteral">&quot;Expected output: \n&quot;</span></div>
<div class="line"> <span class="stringliteral">&quot;(-2, -1), (-2, 1)\n\n&quot;</span>;</div>
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::complex&lt;long double&gt;</a>, 2&gt; complexCase{</div>
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;long double&gt;</a>{-2, -1}, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;long double&gt;</a>{-2, 1}};</div>
<div class="line"> assert(<a class="code hl_function" href="../../dd/d47/namespacemath.html#aacb1411ef2029e81f249c21e17c96fdb">math::quadraticEquation</a>(1, 4, 5) == complexCase);</div>
<div class="line"> </div>
<div class="line"> <span class="comment">// Values are real.</span></div>
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input: \n&quot;</span></div>
<div class="line"> <span class="stringliteral">&quot;a=1 \n&quot;</span></div>
<div class="line"> <span class="stringliteral">&quot;b=5 \n&quot;</span></div>
<div class="line"> <span class="stringliteral">&quot;c=1 \n&quot;</span></div>
<div class="line"> <span class="stringliteral">&quot;Expected output: \n&quot;</span></div>
<div class="line"> <span class="stringliteral">&quot;(-4.7912878475, 0), (-0.2087121525, 0)\n\n&quot;</span>;</div>
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::complex&lt;long double&gt;</a>, 2&gt; floatCase{</div>
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;long double&gt;</a>{-4.7912878475, 0},</div>
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;long double&gt;</a>{-0.2087121525, 0}};</div>
<div class="line"> <a class="code hl_function" href="../../da/d18/quadratic__equations__complex__numbers_8cpp.html#af7a6d4e3dc85a6288c8f1f7094830c5a">assertArray</a>(<a class="code hl_function" href="../../dd/d47/namespacemath.html#aacb1411ef2029e81f249c21e17c96fdb">math::quadraticEquation</a>(1, 5, 1), floatCase);</div>
<div class="line"> </div>
<div class="line"> <span class="comment">// Values are complex.</span></div>
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Input: \n&quot;</span></div>
<div class="line"> <span class="stringliteral">&quot;a=1 \n&quot;</span></div>
<div class="line"> <span class="stringliteral">&quot;b=1 \n&quot;</span></div>
<div class="line"> <span class="stringliteral">&quot;c=1 \n&quot;</span></div>
<div class="line"> <span class="stringliteral">&quot;Expected output: \n&quot;</span></div>
<div class="line"> <span class="stringliteral">&quot;(-0.5, -0.8660254038), (-0.5, 0.8660254038)\n\n&quot;</span>;</div>
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::complex&lt;long double&gt;</a>, 2&gt; ifloatCase{</div>
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;long double&gt;</a>{-0.5, -0.8660254038},</div>
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/complex.html">std::complex&lt;long double&gt;</a>{-0.5, 0.8660254038}};</div>
<div class="line"> <a class="code hl_function" href="../../da/d18/quadratic__equations__complex__numbers_8cpp.html#af7a6d4e3dc85a6288c8f1f7094830c5a">assertArray</a>(<a class="code hl_function" href="../../dd/d47/namespacemath.html#aacb1411ef2029e81f249c21e17c96fdb">math::quadraticEquation</a>(1, 1, 1), ifloatCase);</div>
<div class="line"> </div>
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Exception test: \n&quot;</span></div>
<div class="line"> <span class="stringliteral">&quot;Input: \n&quot;</span></div>
<div class="line"> <span class="stringliteral">&quot;a=0 \n&quot;</span></div>
<div class="line"> <span class="stringliteral">&quot;b=0 \n&quot;</span></div>
<div class="line"> <span class="stringliteral">&quot;c=0\n&quot;</span></div>
<div class="line"> <span class="stringliteral">&quot;Expected output: Exception thrown \n&quot;</span>;</div>
<div class="line"> <span class="keywordflow">try</span> {</div>
<div class="line"> <a class="code hl_function" href="../../dd/d47/namespacemath.html#aacb1411ef2029e81f249c21e17c96fdb">math::quadraticEquation</a>(0, 0, 0);</div>
<div class="line"> } <span class="keywordflow">catch</span> (<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/error/invalid_argument.html">std::invalid_argument</a>&amp; e) {</div>
<div class="line"> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Exception thrown successfully \n&quot;</span>;</div>
<div class="line"> }</div>
<div class="line">}</div>
<div class="line"><span class="comment"></span> </div>
<div class="line"><span class="comment">/**</span></div>
<div class="line"><span class="comment"> * @brief Main function</span></div>
<div class="line"><span class="comment"> * @returns 0 on exit</span></div>
<div class="line"><span class="comment"> */</span></div>
<div class="line"><span class="keywordtype">int</span> <a id="a9" name="a9"></a><a class="code hl_function" href="../../d3/d40/graph__coloring_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
<div class="line"> <a class="code hl_function" href="../../d6/d2c/caesar__cipher_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a>(); <span class="comment">// Run self-test implementation.</span></div>
<div class="line"> <span class="keywordflow">return</span> 0;</div>
<div class="line">}</div>
<div class="ttc" id="aarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/array.html">std::array</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::cout</a></div></div>
<div class="ttc" id="acaesar__cipher_8cpp_html_ae1a3968e7947464bee7714f6d43b7002"><div class="ttname"><a href="../../d6/d2c/caesar__cipher_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a></div><div class="ttdeci">void test()</div><div class="ttdef"><b>Definition:</b> caesar_cipher.cpp:100</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="agraph__coloring_8cpp_html_gae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d3/d40/graph__coloring_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdoc">Main function.</div><div class="ttdef"><b>Definition:</b> graph_coloring.cpp:112</div></div>
<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>
<div class="ttc" id="anamespacemath_html"><div class="ttname"><a href="../../dd/d47/namespacemath.html">math</a></div><div class="ttdoc">for IO operations</div></div>
<div class="ttc" id="anamespacemath_html_aacb1411ef2029e81f249c21e17c96fdb"><div class="ttname"><a href="../../dd/d47/namespacemath.html#aacb1411ef2029e81f249c21e17c96fdb">math::quadraticEquation</a></div><div class="ttdeci">std::array&lt; std::complex&lt; long double &gt;, 2 &gt; quadraticEquation(long double a, long double b, long double c)</div><div class="ttdoc">Quadratic equation calculator.</div><div class="ttdef"><b>Definition:</b> quadratic_equations_complex_numbers.cpp:53</div></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 class="ttc" id="aquadratic__equations__complex__numbers_8cpp_html_af7a6d4e3dc85a6288c8f1f7094830c5a"><div class="ttname"><a href="../../da/d18/quadratic__equations__complex__numbers_8cpp.html#af7a6d4e3dc85a6288c8f1f7094830c5a">assertArray</a></div><div class="ttdeci">void assertArray(std::array&lt; std::complex&lt; long double &gt;, 2 &gt; input, std::array&lt; std::complex&lt; long double &gt;, 2 &gt; expected, size_t precision=10)</div><div class="ttdoc">Asserts an array of complex numbers.</div><div class="ttdef"><b>Definition:</b> quadratic_equations_complex_numbers.cpp:100</div></div>
<div class="ttc" id="around_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/round.html">std::round</a></div><div class="ttdeci">T round(T... args)</div></div>
<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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<tr class="memdesc:d4/d9c/primes__up__to__billion_8cpp"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute prime numbers upto 1 billion. <br /></td></tr>
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<tr class="memdesc:da/d18/quadratic__equations__complex__numbers_8cpp"><td class="mdescLeft">&#160;</td><td class="mdescRight">Calculate quadratic equation with complex roots, i.e. b^2 - 4ac &lt; 0. <br /></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">file &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="d0/d08/realtime__stats_8cpp.html">realtime_stats.cpp</a></td></tr>
<tr class="memdesc:d0/d08/realtime__stats_8cpp"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute statistics for data entered in rreal-time. <br /></td></tr>
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