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<p>Functions associated with <a href="https://en.wikipedia.org/wiki/LU_decomposition">LU Decomposition</a> of a square matrix.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;valarray&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
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Include dependency graph for lu_decomposition.h:</div>
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<p><a href="../../d1/dbe/lu__decomposition_8h_source.html">Go to the source code of this file.</a></p>
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<tr class="memitem:aed8766713ee9b561a4acdcdff5f90ea5"><td class="memTemplItemLeft" align="right" valign="top">using&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d1/dbe/lu__decomposition_8h.html#aed8766713ee9b561a4acdcdff5f90ea5">matrix</a> = <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; T &gt; &gt;</td></tr>
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Functions</h2></td></tr>
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<tr class="memitem:a75b8a228c6419ecda6077255d6d60509"><td class="memTemplItemLeft" align="right" valign="top">int&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d1/dbe/lu__decomposition_8h.html#a75b8a228c6419ecda6077255d6d60509">lu_decomposition</a> (const <a class="el" href="../../d1/dbe/lu__decomposition_8h.html#aed8766713ee9b561a4acdcdff5f90ea5">matrix</a>&lt; T &gt; &amp;A, <a class="el" href="../../d1/dbe/lu__decomposition_8h.html#aed8766713ee9b561a4acdcdff5f90ea5">matrix</a>&lt; double &gt; *L, <a class="el" href="../../d1/dbe/lu__decomposition_8h.html#aed8766713ee9b561a4acdcdff5f90ea5">matrix</a>&lt; double &gt; *U)</td></tr>
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<tr class="memitem:a3108d43bd32c6fb3b3c158476c51ba7f"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a3108d43bd32c6fb3b3c158476c51ba7f"><td class="memTemplItemLeft" align="right" valign="top">double&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f">determinant_lu</a> (const <a class="el" href="../../d1/dbe/lu__decomposition_8h.html#aed8766713ee9b561a4acdcdff5f90ea5">matrix</a>&lt; T &gt; &amp;A)</td></tr>
<tr class="memdesc:a3108d43bd32c6fb3b3c158476c51ba7f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute determinant of an NxN square matrix using LU decomposition. Using LU decomposition, the determinant is given by the product of diagonal elements of matrices L and U. <a href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f">More...</a><br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Functions associated with <a href="https://en.wikipedia.org/wiki/LU_decomposition">LU Decomposition</a> of a square matrix. </p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a> </dd></dl>
</div><h2 class="groupheader">Typedef Documentation</h2>
<a id="aed8766713ee9b561a4acdcdff5f90ea5"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aed8766713ee9b561a4acdcdff5f90ea5">&#9670;&nbsp;</a></span>matrix</h2>
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template&lt;typename T &gt; </div>
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<td class="memname">using <a class="el" href="../../d1/dbe/lu__decomposition_8h.html#aed8766713ee9b561a4acdcdff5f90ea5">matrix</a> = <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt;<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt;T&gt; &gt;</td>
</tr>
</table>
</div><div class="memdoc">
<p>Define matrix type as a <code><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html" title="STL class.">std::vector</a></code> of <code><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html" title="STL class.">std::valarray</a></code> </p>
</div>
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<h2 class="groupheader">Function Documentation</h2>
<a id="a3108d43bd32c6fb3b3c158476c51ba7f"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a3108d43bd32c6fb3b3c158476c51ba7f">&#9670;&nbsp;</a></span>determinant_lu()</h2>
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template&lt;typename T &gt; </div>
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<td class="memname">double determinant_lu </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="../../d1/dbe/lu__decomposition_8h.html#aed8766713ee9b561a4acdcdff5f90ea5">matrix</a>&lt; T &gt; &amp;&#160;</td>
<td class="paramname"><em>A</em></td><td>)</td>
<td></td>
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<p>Compute determinant of an NxN square matrix using LU decomposition. Using LU decomposition, the determinant is given by the product of diagonal elements of matrices L and U. </p>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">T</td><td>datatype of input matrix - int, unsigned int, double, etc </td></tr>
</table>
</dd>
</dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">A</td><td>input square matrix </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>determinant of matrix A </dd></dl>
<div class="fragment"><div class="line"><a name="l00090"></a><span class="lineno"> 90</span>&#160; {</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;double&gt;</a> L(A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(), <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()));</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;double&gt;</a> U(A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(), <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()));</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160; </div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160; <span class="keywordflow">if</span> (<a class="code" href="../../d1/dbe/lu__decomposition_8h.html#a75b8a228c6419ecda6077255d6d60509">lu_decomposition</a>(A, &amp;L, &amp;U) &lt; 0)</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160; </div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160; <span class="keywordtype">double</span> result = 1.f;</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>&#160; result *= L[i][i] * U[i][i];</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>&#160; }</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>&#160; <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a75b8a228c6419ecda6077255d6d60509">&#9670;&nbsp;</a></span>lu_decomposition()</h2>
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template&lt;typename T &gt; </div>
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<td class="memname">int lu_decomposition </td>
<td>(</td>
<td class="paramtype">const <a class="el" href="../../d1/dbe/lu__decomposition_8h.html#aed8766713ee9b561a4acdcdff5f90ea5">matrix</a>&lt; T &gt; &amp;&#160;</td>
<td class="paramname"><em>A</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="../../d1/dbe/lu__decomposition_8h.html#aed8766713ee9b561a4acdcdff5f90ea5">matrix</a>&lt; double &gt; *&#160;</td>
<td class="paramname"><em>L</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="../../d1/dbe/lu__decomposition_8h.html#aed8766713ee9b561a4acdcdff5f90ea5">matrix</a>&lt; double &gt; *&#160;</td>
<td class="paramname"><em>U</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Perform LU decomposition on matrix </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">A</td><td>matrix to decompose </td></tr>
<tr><td class="paramdir">[out]</td><td class="paramname">L</td><td>output L matrix </td></tr>
<tr><td class="paramdir">[out]</td><td class="paramname">U</td><td>output U matrix </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>0 if no errors </dd>
<dd>
negative if error occurred </dd></dl>
<div class="fragment"><div class="line"><a name="l00029"></a><span class="lineno"> 29</span>&#160; {</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160; <span class="keywordtype">int</span> row, col, j;</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>&#160; <span class="keywordtype">int</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> = A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160; </div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160; <span class="keywordflow">if</span> (<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> != A[0].size()) {</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160; <span class="comment">// check matrix is a square matrix</span></div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Not a square matrix!\n&quot;</span>;</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160; <span class="keywordflow">return</span> -1;</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; }</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160; </div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; <span class="comment">// regularize each row</span></div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; <span class="keywordflow">for</span> (row = 0; row &lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; row++) {</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; <span class="comment">// Upper triangular matrix</span></div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; <span class="keywordflow">for</span> (col = row; col &lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; col++) {</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; <span class="comment">// Summation of L[i,j] * U[j,k]</span></div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160; <span class="keywordtype">double</span> lu_sum = 0.;</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; <span class="keywordflow">for</span> (j = 0; j &lt; row; j++) {</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; lu_sum += L[0][row][j] * U[0][j][col];</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; }</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; </div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160; <span class="comment">// Evaluate U[i,k]</span></div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; U[0][row][col] = A[row][col] - lu_sum;</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; }</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; </div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; <span class="comment">// Lower triangular matrix</span></div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; <span class="keywordflow">for</span> (col = row; col &lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; col++) {</div>
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<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; </div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; <span class="comment">// Summation of L[i,j] * U[j,k]</span></div>
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<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; <span class="keywordflow">for</span> (j = 0; j &lt; row; j++) {</div>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; </div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; <span class="comment">// Evaluate U[i,k]</span></div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; L[0][col][row] = (A[col][row] - lu_sum) / U[0][row][row];</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; }</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; }</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; </div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160;}</div>
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<div class="title">lu_decomposition.h</div> </div>
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<div class="contents">
<a href="../../d1/dbe/lu__decomposition_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span>&#160;<span class="comment"> * @file lu_decomposition.h</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span>&#160;<span class="comment"> * @author [Krishna Vedala](https://github.com/kvedala)</span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span>&#160;<span class="comment"> * @brief Functions associated with [LU</span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span>&#160;<span class="comment"> * Decomposition](https://en.wikipedia.org/wiki/LU_decomposition)</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span>&#160;<span class="comment"> * of a square matrix.</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span>&#160;<span class="preprocessor">#pragma once</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span>&#160; </div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span>&#160;<span class="preprocessor">#include &lt;iostream&gt;</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span>&#160;<span class="preprocessor">#include &lt;valarray&gt;</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span>&#160;<span class="preprocessor">#include &lt;vector&gt;</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span>&#160;<span class="preprocessor">#include &lt;omp.h&gt;</span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span>&#160;<span class="comment">/** Define matrix type as a `std::vector` of `std::valarray` */</span></div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00019"></a><span class="lineno"><a class="line" href="../../d1/dbe/lu__decomposition_8h.html#aed8766713ee9b561a4acdcdff5f90ea5"> 19</a></span>&#160;<span class="keyword">using</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix</a> = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::valarray&lt;T&gt;</a>&gt;;</div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span>&#160;<span class="comment">/** Perform LU decomposition on matrix</span></div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span>&#160;<span class="comment"> * \param[in] A matrix to decompose</span></div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>&#160;<span class="comment"> * \param[out] L output L matrix</span></div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>&#160;<span class="comment"> * \param[out] U output U matrix</span></div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>&#160;<span class="comment"> * \returns 0 if no errors</span></div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>&#160;<span class="comment"> * \returns negative if error occurred</span></div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00029"></a><span class="lineno"><a class="line" href="../../d1/dbe/lu__decomposition_8h.html#a75b8a228c6419ecda6077255d6d60509"> 29</a></span>&#160;<span class="keywordtype">int</span> <a class="code" href="../../d1/dbe/lu__decomposition_8h.html#a75b8a228c6419ecda6077255d6d60509">lu_decomposition</a>(<span class="keyword">const</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;T&gt;</a> &amp;A, <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;double&gt;</a> *L, <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;double&gt;</a> *U) {</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160; <span class="keywordtype">int</span> row, col, j;</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>&#160; <span class="keywordtype">int</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> = A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160; </div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160; <span class="keywordflow">if</span> (<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> != A[0].size()) {</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160; <span class="comment">// check matrix is a square matrix</span></div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a> &lt;&lt; <span class="stringliteral">&quot;Not a square matrix!\n&quot;</span>;</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160; <span class="keywordflow">return</span> -1;</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; }</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160; </div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; <span class="comment">// regularize each row</span></div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; <span class="keywordflow">for</span> (row = 0; row &lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; row++) {</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; <span class="comment">// Upper triangular matrix</span></div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; <span class="keywordflow">for</span> (col = row; col &lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; col++) {</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; <span class="comment">// Summation of L[i,j] * U[j,k]</span></div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160; <span class="keywordtype">double</span> lu_sum = 0.;</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; <span class="keywordflow">for</span> (j = 0; j &lt; row; j++) {</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; lu_sum += L[0][row][j] * U[0][j][col];</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; }</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; </div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160; <span class="comment">// Evaluate U[i,k]</span></div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; U[0][row][col] = A[row][col] - lu_sum;</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; }</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; </div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; <span class="comment">// Lower triangular matrix</span></div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; <span class="keywordflow">for</span> (col = row; col &lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; col++) {</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; <span class="keywordflow">if</span> (row == col) {</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; L[0][row][col] = 1.;</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; <span class="keywordflow">continue</span>;</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; }</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; </div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; <span class="comment">// Summation of L[i,j] * U[j,k]</span></div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; <span class="keywordtype">double</span> lu_sum = 0.;</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; <span class="keywordflow">for</span> (j = 0; j &lt; row; j++) {</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; lu_sum += L[0][col][j] * U[0][j][row];</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; }</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; </div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; <span class="comment">// Evaluate U[i,k]</span></div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; L[0][col][row] = (A[col][row] - lu_sum) / U[0][row][row];</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; }</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; }</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; </div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160;}</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160;<span class="comment">/**</span></div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160;<span class="comment"> * @brief Compute determinant of an NxN square matrix using LU decomposition.</span></div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160;<span class="comment"> * Using LU decomposition, the determinant is given by the product of diagonal</span></div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160;<span class="comment"> * elements of matrices L and U.</span></div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160;<span class="comment"> * @tparam T datatype of input matrix - int, unsigned int, double, etc</span></div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160;<span class="comment"> * @param A input square matrix</span></div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160;<span class="comment"> * @return determinant of matrix A</span></div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00090"></a><span class="lineno"><a class="line" href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f"> 90</a></span>&#160;<span class="keywordtype">double</span> <a class="code" href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f">determinant_lu</a>(<span class="keyword">const</span> <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;T&gt;</a> &amp;A) {</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;double&gt;</a> L(A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(), <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()));</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;double&gt;</a> U(A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(), <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>()));</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160; </div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160; <span class="keywordflow">if</span> (<a class="code" href="../../d1/dbe/lu__decomposition_8h.html#a75b8a228c6419ecda6077255d6d60509">lu_decomposition</a>(A, &amp;L, &amp;U) &lt; 0)</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160; </div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160; <span class="keywordtype">double</span> result = 1.f;</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; A.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); i++) {</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>&#160; result *= L[i][i] * U[i][i];</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>&#160; }</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>&#160; <span class="keywordflow">return</span> result;</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160;}</div>
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<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>
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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="asieve__of__eratosthenes_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> sieve_of_eratosthenes.cpp:59</div></div>
<div class="ttc" id="asieve__of__eratosthenes_8cpp_html_af50a5c87d27cfd3462745b37fb9b0f46"><div class="ttname"><a href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#af50a5c87d27cfd3462745b37fb9b0f46">print</a></div><div class="ttdeci">void print(uint32_t N)</div><div class="ttdef"><b>Definition:</b> sieve_of_eratosthenes.cpp:40</div></div>
<div class="ttc" id="adurand__kerner__roots_8cpp_html_a3bada3e58ad8d1b00918db2ffe83a740"><div class="ttname"><a href="../../da/df2/durand__kerner__roots_8cpp.html#a3bada3e58ad8d1b00918db2ffe83a740">complex_str</a></div><div class="ttdeci">const char * complex_str(const std::complex&lt; double &gt; &amp;x)</div><div class="ttdef"><b>Definition:</b> durand_kerner_roots.cpp:76</div></div>
<div class="ttc" id="agolden__search__extrema_8cpp_html_a6d0455dd5c30adda100e95f0423c786e"><div class="ttname"><a href="../../d6/d7a/golden__search__extrema_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">test3</a></div><div class="ttdeci">void test3()</div><div class="ttdoc">Test function to find maxima for the function in the interval Expected result: .</div><div class="ttdef"><b>Definition:</b> golden_search_extrema.cpp:123</div></div>
<div class="ttc" id="abrent__method__extrema_8cpp_html_a1aa76a6d5fd4d333f9072beff1dc486b"><div class="ttname"><a href="../../db/d01/brent__method__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a></div><div class="ttdeci">double get_minima(const std::function&lt; double(double)&gt; &amp;f, double lim_a, double lim_b)</div><div class="ttdoc">Get the real root of a function in the given interval.</div><div class="ttdef"><b>Definition:</b> brent_method_extrema.cpp:35</div></div>
<div class="ttc" id="asetfill_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/setfill.html">std::setfill</a></div><div class="ttdeci">T setfill(T... args)</div></div>
<div class="ttc" id="afunction_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/functional/function.html">std::function</a></div></div>
<div class="ttc" id="abisection__method_8cpp_html_a1ab31b90bc584c635ec159468ceed9b2"><div class="ttname"><a href="../../d7/d6a/bisection__method_8cpp.html#a1ab31b90bc584c635ec159468ceed9b2">sgn</a></div><div class="ttdeci">int sgn(T val)</div><div class="ttdef"><b>Definition:</b> bisection_method.cpp:32</div></div>
<div class="ttc" id="aclassstatistics_1_1stats__computer1_html_af57e942d49f4fd70f059f224b4ac07e1"><div class="ttname"><a href="../../d7/d7c/classstatistics_1_1stats__computer1.html#af57e942d49f4fd70f059f224b4ac07e1">statistics::stats_computer1::std</a></div><div class="ttdeci">double std() const</div><div class="ttdef"><b>Definition:</b> realtime_stats.cpp:48</div></div>
<div class="ttc" id="aprime__factorization_8cpp_html_acfb0df439a4beae5a34ef131ce737c1b"><div class="ttname"><a href="../../db/d0d/prime__factorization_8cpp.html#acfb0df439a4beae5a34ef131ce737c1b">factors</a></div><div class="ttdeci">std::vector&lt; std::pair&lt; int, int &gt; &gt; factors</div><div class="ttdef"><b>Definition:</b> prime_factorization.cpp:19</div></div>
<div class="ttc" id="aprime__factorization_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../db/d0d/prime__factorization_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> prime_factorization.cpp:62</div></div>
<div class="ttc" id="amiller__rabin_8cpp_html_a798398d5bfd375a3c0ce68100842f6f5"><div class="ttname"><a href="../../d6/d42/miller__rabin_8cpp.html#a798398d5bfd375a3c0ce68100842f6f5">reverse_binary</a></div><div class="ttdeci">std::vector&lt; T &gt; reverse_binary(T num)</div><div class="ttdef"><b>Definition:</b> miller_rabin.cpp:19</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>
<div class="ttc" id="apower__for__huge__numbers_8cpp_html_ae249a2af508aa94266023ce8aa81426f"><div class="ttname"><a href="../../df/def/power__for__huge__numbers_8cpp.html#ae249a2af508aa94266023ce8aa81426f">power</a></div><div class="ttdeci">void power(int x, int n)</div><div class="ttdef"><b>Definition:</b> power_for_huge_numbers.cpp:56</div></div>
<div class="ttc" id="agolden__search__extrema_8cpp_html_a1440a7779ac56f47a3f355ce4a8c7da0"><div class="ttname"><a href="../../d6/d7a/golden__search__extrema_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a></div><div class="ttdeci">void test1()</div><div class="ttdoc">Test function to find minima for the function in the interval Expected result = 2.</div><div class="ttdef"><b>Definition:</b> golden_search_extrema.cpp:78</div></div>
<div class="ttc" id="aprime__numbers_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../de/d9b/prime__numbers_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> prime_numbers.cpp:26</div></div>
<div class="ttc" id="amersenne_twister_engine_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/mersenne_twister_engine.html">std::mt19937</a></div></div>
<div class="ttc" id="apush_back_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">std::vector::push_back</a></div><div class="ttdeci">T push_back(T... args)</div></div>
<div class="ttc" id="amodular__inverse__fermat__little__theorem_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d8/d53/modular__inverse__fermat__little__theorem_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> modular_inverse_fermat_little_theorem.cpp:84</div></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_ac38b9cfd2a39d856e0feba3b5d241ded"><div class="ttname"><a href="../../da/df2/durand__kerner__roots_8cpp.html#ac38b9cfd2a39d856e0feba3b5d241ded">durand_kerner_algo</a></div><div class="ttdeci">std::pair&lt; uint32_t, double &gt; durand_kerner_algo(const std::valarray&lt; double &gt; &amp;coeffs, std::valarray&lt; std::complex&lt; double &gt;&gt; *roots, bool write_log=false)</div><div class="ttdef"><b>Definition:</b> durand_kerner_roots.cpp:109</div></div>
<div class="ttc" id="alu__decompose_8cpp_html_a1440a7779ac56f47a3f355ce4a8c7da0"><div class="ttname"><a href="../../dd/d65/lu__decompose_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a></div><div class="ttdeci">void test1()</div><div class="ttdef"><b>Definition:</b> lu_decompose.cpp:36</div></div>
<div class="ttc" id="asum__of__digits_8cpp_html_ae1a3968e7947464bee7714f6d43b7002"><div class="ttname"><a href="../../d4/d83/sum__of__digits_8cpp.html#ae1a3968e7947464bee7714f6d43b7002">test</a></div><div class="ttdeci">void test()</div><div class="ttdef"><b>Definition:</b> sum_of_digits.cpp:58</div></div>
<div class="ttc" id="aisnan_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/isnan.html">std::isnan</a></div><div class="ttdeci">T isnan(T... args)</div></div>
<div class="ttc" id="anamespacestatistics_html"><div class="ttname"><a href="../../d2/dcf/namespacestatistics.html">statistics</a></div><div class="ttdoc">Statistical algorithms.</div></div>
<div class="ttc" id="asum__of__digits_8cpp_html_a0283886819c7c140a023582b7269e2d0"><div class="ttname"><a href="../../d4/d83/sum__of__digits_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a></div><div class="ttdeci">void test2()</div><div class="ttdef"><b>Definition:</b> sum_of_digits.cpp:49</div></div>
<div class="ttc" id="asieve__of__eratosthenes_8cpp_html_a02fd73d861ef2e4aabb38c0c9ff82947"><div class="ttname"><a href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#a02fd73d861ef2e4aabb38c0c9ff82947">init</a></div><div class="ttdeci">void init()</div><div class="ttdef"><b>Definition:</b> sieve_of_eratosthenes.cpp:52</div></div>
<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>
<div class="ttc" id="arandom_device_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/random_device.html">std::random_device</a></div></div>
<div class="ttc" id="ainfinity_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/types/numeric_limits/infinity.html">std::numeric_limits::infinity</a></div><div class="ttdeci">T infinity(T... args)</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="abasic_ofstream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a></div><div class="ttdoc">STL class.</div></div>
<div class="ttc" id="afalse__position_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../dd/d29/false__position_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> false_position.cpp:39</div></div>
<div class="ttc" id="aisinf_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/isinf.html">std::isinf</a></div><div class="ttdeci">T isinf(T... args)</div></div>
<div class="ttc" id="aclassstatistics_1_1stats__computer2_html_af6198817084276113b3c064e87ce0555"><div class="ttname"><a href="../../d8/dab/classstatistics_1_1stats__computer2.html#af6198817084276113b3c064e87ce0555">statistics::stats_computer2::variance</a></div><div class="ttdeci">double variance() const</div><div class="ttdef"><b>Definition:</b> realtime_stats.cpp:89</div></div>
<div class="ttc" id="aleast__common__multiple_8cpp_html_a8ba1fc66e4134ab25b2602b323150563"><div class="ttname"><a href="../../d4/d21/least__common__multiple_8cpp.html#a8ba1fc66e4134ab25b2602b323150563">gcd</a></div><div class="ttdeci">unsigned int gcd(unsigned int x, unsigned int y)</div><div class="ttdef"><b>Definition:</b> least_common_multiple.cpp:16</div></div>
<div class="ttc" id="asqrt__double_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../da/d24/sqrt__double_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> sqrt_double.cpp:42</div></div>
<div class="ttc" id="asieve__of__eratosthenes_8cpp_html_abce89d8999986f085c368969590376b8"><div class="ttname"><a href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#abce89d8999986f085c368969590376b8">sieve</a></div><div class="ttdeci">void sieve(uint32_t N)</div><div class="ttdef"><b>Definition:</b> sieve_of_eratosthenes.cpp:25</div></div>
<div class="ttc" id="amiller__rabin_8cpp_html_ad6c2c67ea416d0e80003a88623f98b29"><div class="ttname"><a href="../../d6/d42/miller__rabin_8cpp.html#ad6c2c67ea416d0e80003a88623f98b29">modular_exponentiation</a></div><div class="ttdeci">T modular_exponentiation(T base, const std::vector&lt; T &gt; &amp;rev_binary_exponent, T mod)</div><div class="ttdef"><b>Definition:</b> miller_rabin.cpp:43</div></div>
<div class="ttc" id="adurand__kerner__roots_8cpp_html_a51637ff89e55ca749993d3e84b95d153"><div class="ttname"><a href="../../da/df2/durand__kerner__roots_8cpp.html#a51637ff89e55ca749993d3e84b95d153">poly_function</a></div><div class="ttdeci">std::complex&lt; double &gt; poly_function(const std::valarray&lt; double &gt; &amp;coeffs, std::complex&lt; double &gt; x)</div><div class="ttdef"><b>Definition:</b> durand_kerner_roots.cpp:53</div></div>
<div class="ttc" id="alu__decompose_8cpp_html_a3c04138a5bfe5d72780bb7e82a18e627"><div class="ttname"><a href="../../dd/d65/lu__decompose_8cpp.html#a3c04138a5bfe5d72780bb7e82a18e627">main</a></div><div class="ttdeci">int main(int argc, char **argv)</div><div class="ttdef"><b>Definition:</b> lu_decompose.cpp:84</div></div>
<div class="ttc" id="avalarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a></div><div class="ttdoc">STL class.</div></div>
<div class="ttc" id="areal_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/complex/real.html">std::complex::real</a></div><div class="ttdeci">T real(T... args)</div></div>
<div class="ttc" id="adurand__kerner__roots_8cpp_html_a1440a7779ac56f47a3f355ce4a8c7da0"><div class="ttname"><a href="../../da/df2/durand__kerner__roots_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a></div><div class="ttdeci">void test1()</div><div class="ttdef"><b>Definition:</b> durand_kerner_roots.cpp:207</div></div>
<div class="ttc" id="agaussian__elimination_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d0/de2/gaussian__elimination_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> gaussian_elimination.cpp:9</div></div>
<div class="ttc" id="aopen_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ofstream/open.html">std::ofstream::open</a></div><div class="ttdeci">T open(T... args)</div></div>
<div class="ttc" id="adurand__kerner__roots_8cpp_html_af270a96662132d0385cb6b4637c5a689"><div class="ttname"><a href="../../da/df2/durand__kerner__roots_8cpp.html#af270a96662132d0385cb6b4637c5a689">ACCURACY</a></div><div class="ttdeci">#define ACCURACY</div><div class="ttdef"><b>Definition:</b> durand_kerner_roots.cpp:45</div></div>
<div class="ttc" id="aclassstatistics_1_1stats__computer1_html_a390697dcee210b91823ceff04b25081b"><div class="ttname"><a href="../../d7/d7c/classstatistics_1_1stats__computer1.html#a390697dcee210b91823ceff04b25081b">statistics::stats_computer1::mean</a></div><div class="ttdeci">double mean() const</div><div class="ttdef"><b>Definition:</b> realtime_stats.cpp:42</div></div>
<div class="ttc" id="aclassstatistics_1_1stats__computer2_html"><div class="ttname"><a href="../../d8/dab/classstatistics_1_1stats__computer2.html">statistics::stats_computer2</a></div><div class="ttdef"><b>Definition:</b> realtime_stats.cpp:72</div></div>
<div class="ttc" id="arealtime__stats_8cpp_html_a3c04138a5bfe5d72780bb7e82a18e627"><div class="ttname"><a href="../../d0/d08/realtime__stats_8cpp.html#a3c04138a5bfe5d72780bb7e82a18e627">main</a></div><div class="ttdeci">int main(int argc, char **argv)</div><div class="ttdef"><b>Definition:</b> realtime_stats.cpp:158</div></div>
<div class="ttc" id="afalse__position_8cpp_html_a1ab31b90bc584c635ec159468ceed9b2"><div class="ttname"><a href="../../dd/d29/false__position_8cpp.html#a1ab31b90bc584c635ec159468ceed9b2">sgn</a></div><div class="ttdeci">int sgn(T val)</div><div class="ttdef"><b>Definition:</b> false_position.cpp:34</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="aswap_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a></div><div class="ttdeci">T swap(T... args)</div></div>
<div class="ttc" id="alu__decomposition_8h_html"><div class="ttname"><a href="../../d1/dbe/lu__decomposition_8h.html">lu_decomposition.h</a></div><div class="ttdoc">Functions associated with LU Decomposition of a square matrix.</div></div>
<div class="ttc" id="arealtime__stats_8cpp_html_aa54c915581fcc495489175a4386d59fd"><div class="ttname"><a href="../../d0/d08/realtime__stats_8cpp.html#aa54c915581fcc495489175a4386d59fd">test_function</a></div><div class="ttdeci">void test_function(const float *test_data, const int number_of_samples)</div><div class="ttdef"><b>Definition:</b> realtime_stats.cpp:118</div></div>
<div class="ttc" id="aprime__factorization_8cpp_html_affe577b9bce8f604f5e2f861c63c7099"><div class="ttname"><a href="../../db/d0d/prime__factorization_8cpp.html#affe577b9bce8f604f5e2f861c63c7099">SieveOfEratosthenes</a></div><div class="ttdeci">void SieveOfEratosthenes(int N)</div><div class="ttdef"><b>Definition:</b> prime_factorization.cpp:23</div></div>
<div class="ttc" id="asubstr_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string/substr.html">std::string::substr</a></div><div class="ttdeci">T substr(T... args)</div></div>
<div class="ttc" id="amiller__rabin_8cpp_html_a6f9c31c1047aa3191676d64571d4c506"><div class="ttname"><a href="../../d6/d42/miller__rabin_8cpp.html#a6f9c31c1047aa3191676d64571d4c506">miller_test</a></div><div class="ttdeci">bool miller_test(T d, T num)</div><div class="ttdef"><b>Definition:</b> miller_rabin.cpp:73</div></div>
<div class="ttc" id="aleast__common__multiple_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d4/d21/least__common__multiple_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> least_common_multiple.cpp:67</div></div>
<div class="ttc" id="alu__decomposition_8h_html_a75b8a228c6419ecda6077255d6d60509"><div class="ttname"><a href="../../d1/dbe/lu__decomposition_8h.html#a75b8a228c6419ecda6077255d6d60509">lu_decomposition</a></div><div class="ttdeci">int lu_decomposition(const matrix&lt; T &gt; &amp;A, matrix&lt; double &gt; *L, matrix&lt; double &gt; *U)</div><div class="ttdef"><b>Definition:</b> lu_decomposition.h:29</div></div>
<div class="ttc" id="asieve__of__eratosthenes_8cpp_html_a392fb874e547e582e9c66a08a1f23326"><div class="ttname"><a href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#a392fb874e547e582e9c66a08a1f23326">MAX</a></div><div class="ttdeci">#define MAX</div><div class="ttdef"><b>Definition:</b> sieve_of_eratosthenes.cpp:16</div></div>
<div class="ttc" id="amodular__inverse__fermat__little__theorem_8cpp_html_a4c6eefd1254eab3e8d34bf02c205e0f4"><div class="ttname"><a href="../../d8/d53/modular__inverse__fermat__little__theorem_8cpp.html#a4c6eefd1254eab3e8d34bf02c205e0f4">binExpo</a></div><div class="ttdeci">int64_t binExpo(int64_t a, int64_t b, int64_t m)</div><div class="ttdef"><b>Definition:</b> modular_inverse_fermat_little_theorem.cpp:52</div></div>
<div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
<div class="ttc" id="aclassstatistics_1_1stats__computer1_html_aa13bf7c38de112f71921a5525d71a2f2"><div class="ttname"><a href="../../d7/d7c/classstatistics_1_1stats__computer1.html#aa13bf7c38de112f71921a5525d71a2f2">statistics::stats_computer1::new_val</a></div><div class="ttdeci">void new_val(T x)</div><div class="ttdef"><b>Definition:</b> realtime_stats.cpp:32</div></div>
<div class="ttc" id="abrent__method__extrema_8cpp_html_a0283886819c7c140a023582b7269e2d0"><div class="ttname"><a href="../../db/d01/brent__method__extrema_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a></div><div class="ttdeci">void test2()</div><div class="ttdoc">Test function to find root for the function in the interval Expected result: .</div><div class="ttdef"><b>Definition:</b> brent_method_extrema.cpp:165</div></div>
<div class="ttc" id="aleft_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/left.html">std::left</a></div><div class="ttdeci">T left(T... args)</div></div>
<div class="ttc" id="aclassstatistics_1_1stats__computer2_html_ade6de704deea24fdc88077b3d9a0d534"><div class="ttname"><a href="../../d8/dab/classstatistics_1_1stats__computer2.html#ade6de704deea24fdc88077b3d9a0d534">statistics::stats_computer2::new_val</a></div><div class="ttdeci">void new_val(T x)</div><div class="ttdef"><b>Definition:</b> realtime_stats.cpp:77</div></div>
<div class="ttc" id="aclassstatistics_1_1stats__computer1_html_a27f0a03e2fd2254f1c81fe668226bd92"><div class="ttname"><a href="../../d7/d7c/classstatistics_1_1stats__computer1.html#a27f0a03e2fd2254f1c81fe668226bd92">statistics::stats_computer1::variance</a></div><div class="ttdeci">double variance() const</div><div class="ttdef"><b>Definition:</b> realtime_stats.cpp:45</div></div>
<div class="ttc" id="asum__of__digits_8cpp_html_a4619c78b6ad985713024f930f31c4395"><div class="ttname"><a href="../../d4/d83/sum__of__digits_8cpp.html#a4619c78b6ad985713024f930f31c4395">sum_of_digits</a></div><div class="ttdeci">int sum_of_digits(int num)</div><div class="ttdef"><b>Definition:</b> sum_of_digits.cpp:23</div></div>
<div class="ttc" id="anumber__of__positive__divisors_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d0/da2/number__of__positive__divisors_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> number_of_positive_divisors.cpp:62</div></div>
<div class="ttc" id="abegin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/begin.html">std::vector::cbegin</a></div><div class="ttdeci">T cbegin(T... args)</div></div>
<div class="ttc" id="amiller__rabin_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d6/d42/miller__rabin_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> miller_rabin.cpp:183</div></div>
<div class="ttc" id="astrtof_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/byte/strtof.html">std::strtod</a></div><div class="ttdeci">T strtod(T... args)</div></div>
<div class="ttc" id="apower__for__huge__numbers_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../df/def/power__for__huge__numbers_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> power_for_huge_numbers.cpp:82</div></div>
<div class="ttc" id="aprime__factorization_8cpp_html_a0ece0145fb29a5cf48378c23dde2da46"><div class="ttname"><a href="../../db/d0d/prime__factorization_8cpp.html#a0ece0145fb29a5cf48378c23dde2da46">prime_factorization</a></div><div class="ttdeci">void prime_factorization(int num)</div><div class="ttdef"><b>Definition:</b> prime_factorization.cpp:40</div></div>
<div class="ttc" id="asum__of__digits_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d4/d83/sum__of__digits_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> sum_of_digits.cpp:68</div></div>
<div class="ttc" id="alu__decomposition_8h_html_a3108d43bd32c6fb3b3c158476c51ba7f"><div class="ttname"><a href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f">determinant_lu</a></div><div class="ttdeci">double determinant_lu(const matrix&lt; T &gt; &amp;A)</div><div class="ttdoc">Compute determinant of an NxN square matrix using LU decomposition. Using LU decomposition,...</div><div class="ttdef"><b>Definition:</b> lu_decomposition.h:90</div></div>
<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>
<div class="ttc" id="aclassstatistics_1_1stats__computer1_html"><div class="ttname"><a href="../../d7/d7c/classstatistics_1_1stats__computer1.html">statistics::stats_computer1</a></div><div class="ttdef"><b>Definition:</b> realtime_stats.cpp:27</div></div>
<div class="ttc" id="agolden__search__extrema_8cpp_html_a0283886819c7c140a023582b7269e2d0"><div class="ttname"><a href="../../d6/d7a/golden__search__extrema_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a></div><div class="ttdeci">void test2()</div><div class="ttdoc">Test function to find maxima for the function in the interval Expected result: .</div><div class="ttdef"><b>Definition:</b> golden_search_extrema.cpp:100</div></div>
<div class="ttc" id="aclassstatistics_1_1stats__computer2_html_acf2e84df4fc386bb3295016ef8fd156e"><div class="ttname"><a href="../../d8/dab/classstatistics_1_1stats__computer2.html#acf2e84df4fc386bb3295016ef8fd156e">statistics::stats_computer2::std</a></div><div class="ttdeci">double std() const</div><div class="ttdef"><b>Definition:</b> realtime_stats.cpp:92</div></div>
<div class="ttc" id="agolden__search__extrema_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d6/d7a/golden__search__extrema_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> golden_search_extrema.cpp:139</div></div>
<div class="ttc" id="asieve__of__eratosthenes_8cpp_html_a0560e21edb54d5ad8d80b2d80348ce22"><div class="ttname"><a href="../../d8/ddf/sieve__of__eratosthenes_8cpp.html#a0560e21edb54d5ad8d80b2d80348ce22">isprime</a></div><div class="ttdeci">bool isprime[MAX]</div><div class="ttdef"><b>Definition:</b> sieve_of_eratosthenes.cpp:19</div></div>
<div class="ttc" id="asum__of__digits_8cpp_html_a1440a7779ac56f47a3f355ce4a8c7da0"><div class="ttname"><a href="../../d4/d83/sum__of__digits_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a></div><div class="ttdeci">void test1()</div><div class="ttdef"><b>Definition:</b> sum_of_digits.cpp:40</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 class="ttdoc">STL class.</div></div>
<div class="ttc" id="aimag_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/complex/imag.html">std::complex::imag</a></div><div class="ttdeci">T imag(T... args)</div></div>
<div class="ttc" id="afalse__position_8cpp_html_a2003b5b2dcfff0769b957ab5c968b03d"><div class="ttname"><a href="../../dd/d29/false__position_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a></div><div class="ttdeci">static double eq(double i)</div><div class="ttdef"><b>Definition:</b> false_position.cpp:28</div></div>
<div class="ttc" id="abrent__method__extrema_8cpp_html_a1440a7779ac56f47a3f355ce4a8c7da0"><div class="ttname"><a href="../../db/d01/brent__method__extrema_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a></div><div class="ttdeci">void test1()</div><div class="ttdoc">Test function to find root for the function in the interval Expected result = 2.</div><div class="ttdef"><b>Definition:</b> brent_method_extrema.cpp:143</div></div>
<div class="ttc" id="astring__fibonacci_8cpp_html_a28052eee05d43c2ebc5147c52bd50c35"><div class="ttname"><a href="../../de/d47/string__fibonacci_8cpp.html#a28052eee05d43c2ebc5147c52bd50c35">add</a></div><div class="ttdeci">std::string add(std::string a, std::string b)</div><div class="ttdef"><b>Definition:</b> string_fibonacci.cpp:24</div></div>
<div class="ttc" id="amake_pair_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a></div><div class="ttdeci">T make_pair(T... args)</div></div>
<div class="ttc" id="atime_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a></div><div class="ttdeci">T time(T... args)</div></div>
<div class="ttc" id="abisection__method_8cpp_html_a0a3abbca80bc98e7abcb3ae73abe0f14"><div class="ttname"><a href="../../d7/d6a/bisection__method_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">MAX_ITERATIONS</a></div><div class="ttdeci">#define MAX_ITERATIONS</div><div class="ttdoc">Maximum number of iterations to check.</div><div class="ttdef"><b>Definition:</b> bisection_method.cpp:22</div></div>
<div class="ttc" id="aend_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/end.html">std::vector::cend</a></div><div class="ttdeci">T cend(T... args)</div></div>
<div class="ttc" id="asetw_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/setw.html">std::setw</a></div><div class="ttdeci">T setw(T... args)</div></div>
<div class="ttc" id="amax_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/algorithm/max.html">std::max</a></div><div class="ttdeci">T max(T... args)</div></div>
<div class="ttc" id="astring__fibonacci_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../de/d47/string__fibonacci_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> string_fibonacci.cpp:81</div></div>
<div class="ttc" id="anumber__of__positive__divisors_8cpp_html_ad89ccced8504b5116046cfa03066ffeb"><div class="ttname"><a href="../../d0/da2/number__of__positive__divisors_8cpp.html#ad89ccced8504b5116046cfa03066ffeb">number_of_positive_divisors</a></div><div class="ttdeci">int number_of_positive_divisors(int n)</div><div class="ttdef"><b>Definition:</b> number_of_positive_divisors.cpp:34</div></div>
<div class="ttc" id="abisection__method_8cpp_html_a2003b5b2dcfff0769b957ab5c968b03d"><div class="ttname"><a href="../../d7/d6a/bisection__method_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a></div><div class="ttdeci">static double eq(double i)</div><div class="ttdef"><b>Definition:</b> bisection_method.cpp:26</div></div>
<div class="ttc" id="agolden__search__extrema_8cpp_html_a1aa76a6d5fd4d333f9072beff1dc486b"><div class="ttname"><a href="../../d6/d7a/golden__search__extrema_8cpp.html#a1aa76a6d5fd4d333f9072beff1dc486b">get_minima</a></div><div class="ttdeci">double get_minima(const std::function&lt; double(double)&gt; &amp;f, double lim_a, double lim_b)</div><div class="ttdoc">Get the minima of a function in the given interval. To get the maxima, simply negate the function....</div><div class="ttdef"><b>Definition:</b> golden_search_extrema.cpp:29</div></div>
<div class="ttc" id="astring__fibonacci_8cpp_html_ad8055ee368a5d5b24de01bdde6bf8fca"><div class="ttname"><a href="../../de/d47/string__fibonacci_8cpp.html#ad8055ee368a5d5b24de01bdde6bf8fca">fib_Accurate</a></div><div class="ttdeci">void fib_Accurate(uint64_t n)</div><div class="ttdef"><b>Definition:</b> string_fibonacci.cpp:68</div></div>
<div class="ttc" id="aprimes__up__to__billion_8cpp_html_a031cada84819ed6426f58e4f7e81261c"><div class="ttname"><a href="../../d4/d9c/primes__up__to__billion_8cpp.html#a031cada84819ed6426f58e4f7e81261c">Sieve</a></div><div class="ttdeci">void Sieve(int64_t n)</div><div class="ttdef"><b>Definition:</b> primes_up_to_billion.cpp:13</div></div>
<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>
<div class="ttc" id="alu__decompose_8cpp_html_a9459fcd1f020373d73eae2bad43786d0"><div class="ttname"><a href="../../dd/d65/lu__decompose_8cpp.html#a9459fcd1f020373d73eae2bad43786d0">operator&lt;&lt;</a></div><div class="ttdeci">std::ostream &amp; operator&lt;&lt;(std::ostream &amp;out, matrix&lt; T &gt; const &amp;v)</div><div class="ttdef"><b>Definition:</b> lu_decompose.cpp:18</div></div>
<div class="ttc" id="aclassstatistics_1_1stats__computer2_html_a8290966ad468f2a8c266d008bc60720e"><div class="ttname"><a href="../../d8/dab/classstatistics_1_1stats__computer2.html#a8290966ad468f2a8c266d008bc60720e">statistics::stats_computer2::mean</a></div><div class="ttdeci">double mean() const</div><div class="ttdef"><b>Definition:</b> realtime_stats.cpp:86</div></div>
<div class="ttc" id="amodular__inverse__fermat__little__theorem_8cpp_html_a09660096b134753128952246f4f4e4bd"><div class="ttname"><a href="../../d8/d53/modular__inverse__fermat__little__theorem_8cpp.html#a09660096b134753128952246f4f4e4bd">isPrime</a></div><div class="ttdeci">bool isPrime(int64_t m)</div><div class="ttdef"><b>Definition:</b> modular_inverse_fermat_little_theorem.cpp:68</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="adurand__kerner__roots_8cpp_html_a0283886819c7c140a023582b7269e2d0"><div class="ttname"><a href="../../da/df2/durand__kerner__roots_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a></div><div class="ttdeci">void test2()</div><div class="ttdef"><b>Definition:</b> durand_kerner_roots.cpp:242</div></div>
<div class="ttc" id="abisection__method_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d7/d6a/bisection__method_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> bisection_method.cpp:37</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="apower__for__huge__numbers_8cpp_html_a392fb874e547e582e9c66a08a1f23326"><div class="ttname"><a href="../../df/def/power__for__huge__numbers_8cpp.html#a392fb874e547e582e9c66a08a1f23326">MAX</a></div><div class="ttdeci">#define MAX</div><div class="ttdef"><b>Definition:</b> power_for_huge_numbers.cpp:10</div></div>
<div class="ttc" id="aclassstatistics_1_1stats__computer1_html_ab5b4bfecdf391cae7edb1fe98548b846"><div class="ttname"><a href="../../d7/d7c/classstatistics_1_1stats__computer1.html#ab5b4bfecdf391cae7edb1fe98548b846">statistics::stats_computer1::operator&gt;&gt;</a></div><div class="ttdeci">friend std::istream &amp; operator&gt;&gt;(std::istream &amp;input, stats_computer1 &amp;stat)</div><div class="ttdef"><b>Definition:</b> realtime_stats.cpp:53</div></div>
<div class="ttc" id="amiller__rabin_8cpp_html_a88ec9ad42717780d6caaff9d3d6977f9"><div class="ttname"><a href="../../d6/d42/miller__rabin_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a></div><div class="ttdeci">void tests()</div><div class="ttdef"><b>Definition:</b> miller_rabin.cpp:157</div></div>
<div class="ttc" id="aprimes__up__to__billion_8cpp_html_ac0f4b77b901ddb15dab4c4dee1ac6e95"><div class="ttname"><a href="../../d4/d9c/primes__up__to__billion_8cpp.html#ac0f4b77b901ddb15dab4c4dee1ac6e95">prime</a></div><div class="ttdeci">char prime[100000000]</div><div class="ttdef"><b>Definition:</b> primes_up_to_billion.cpp:10</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="aprime__factorization_8cpp_html_a7fe38b570a51e448430d6a0f072c2f23"><div class="ttname"><a href="../../db/d0d/prime__factorization_8cpp.html#a7fe38b570a51e448430d6a0f072c2f23">isprime</a></div><div class="ttdeci">bool isprime[1000006]</div><div class="ttdef"><b>Definition:</b> prime_factorization.cpp:13</div></div>
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@@ -164,7 +164,7 @@ int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../..
<dl class="section copyright"><dt>Copyright</dt><dd>2020 Arctic2333</dd></dl>
<p>In this algorithm, we use the method of division and reservation remainder to construct the hash function, and use the method of chain address to solve the conflict, that is, we link a chain list after the data, and store all the records whose keywords are synonyms in the same linear chain list.</p>
<dl class="section warning"><dt>Warning</dt><dd>This program is only for educational purposes. It has serious flaws in implementation with regards to memory management resulting in large amounts of memory leaks. </dd></dl>
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<dl class="section warning"><dt>Warning</dt><dd>dynamic memory allocated to <code>n</code> never gets freed. </dd></dl>
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<div class="fragment"><div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; { <span class="comment">// Construct hash table</span></div>
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