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<p>Test case: result should be: <br />
Circle with <br />
radius 1.821078397711709 <br />
centre at (2.142857142857143, 1.7857142857142856) </p><dl class="todo"><dt><b><a class="el" href="../../dd/da0/todo.html#_todo000007">Todo:</a></b></dt><dd>This test fails </dd></dl>
centre at (2.142857142857143, 1.7857142857142856) </p><dl class="todo"><dt><b><a class="el" href="../../dd/da0/todo.html#_todo000008">Todo:</a></b></dt><dd>This test fails </dd></dl>
<div class="fragment"><div class="line"><a name="l00188"></a><span class="lineno"> 188</span>&#160; {</div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;Point&gt;</a> Pv;</div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>&#160; Pv.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/push_back.html">push_back</a>(<a class="code" href="../../d8/dc8/struct_point.html">Point</a>(0.5, 1));</div>

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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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<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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<div class="memtemplate">
template&lt;typename T &gt; </div>
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<tr>
<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>
</tr>
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</div><div class="memdoc">
<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>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; <span class="keywordflow">if</span> (row == col) {</div>
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<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>
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<div class="ttc" id="amatrix__exponentiation_8cpp_html_a9977ad12548c4a49dee9dc3f0685aa54"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a></div><div class="ttdeci">ll mat_size</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:45</div></div>
<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div><div class="ttdoc">STL class.</div></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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<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>
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<div class="ttc" id="aode__midpoint__euler_8cpp_html_aa13517b8e5de1b75592052db7f7e237f"><div class="ttname"><a href="../../d6/dd3/ode__midpoint__euler_8cpp.html#aa13517b8e5de1b75592052db7f7e237f">save_exact_solution</a></div><div class="ttdeci">void save_exact_solution(const double &amp;X0, const double &amp;X_MAX, const double &amp;step_size, const std::valarray&lt; double &gt; &amp;Y0)</div><div class="ttdef"><b>Definition:</b> ode_midpoint_euler.cpp:156</div></div>
<div class="ttc" id="asqrt__double_8cpp_html_ae662282ad0740d2063ac404ca3bd74fc"><div class="ttname"><a href="../../da/d24/sqrt__double_8cpp.html#ae662282ad0740d2063ac404ca3bd74fc">Sqrt</a></div><div class="ttdeci">double Sqrt(double a)</div><div class="ttdef"><b>Definition:</b> sqrt_double.cpp:16</div></div>
<div class="ttc" id="asrand_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a></div><div class="ttdeci">T srand(T... args)</div></div>
<div class="ttc" id="aleast__common__multiple_8cpp_html_aa8d0e241db517813725e721a152e3a25"><div class="ttname"><a href="../../d4/d21/least__common__multiple_8cpp.html#aa8d0e241db517813725e721a152e3a25">lcm</a></div><div class="ttdeci">unsigned int lcm(unsigned int x, unsigned int y)</div><div class="ttdef"><b>Definition:</b> least_common_multiple.cpp:43</div></div>
<div class="ttc" id="aleast__common__multiple_8cpp_html_a88ec9ad42717780d6caaff9d3d6977f9"><div class="ttname"><a href="../../d4/d21/least__common__multiple_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">tests</a></div><div class="ttdeci">void tests()</div><div class="ttdef"><b>Definition:</b> least_common_multiple.cpp:48</div></div>
<div class="ttc" id="aprime__factorization_8cpp_html_af097796783684712b8326e5b82bfd4fe"><div class="ttname"><a href="../../db/d0d/prime__factorization_8cpp.html#af097796783684712b8326e5b82bfd4fe">prime_numbers</a></div><div class="ttdeci">std::vector&lt; int &gt; prime_numbers</div><div class="ttdef"><b>Definition:</b> prime_factorization.cpp:16</div></div>
<div class="ttc" id="aprimes__up__to__billion_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d4/d9c/primes__up__to__billion_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> primes_up_to_billion.cpp:26</div></div>
<div class="ttc" id="agroup__ode_html_ga3874d294ab00fe9ce8731c5b7991a089"><div class="ttname"><a href="../../d6/d60/group__ode.html#ga3874d294ab00fe9ce8731c5b7991a089">semi_implicit_euler</a></div><div class="ttdeci">double semi_implicit_euler(double dx, double x0, double x_max, std::valarray&lt; double &gt; *y, bool save_to_file=false)</div><div class="ttdoc">Compute approximation using the semi-implicit-Euler method in the given limits.</div><div class="ttdef"><b>Definition:</b> ode_semi_implicit_euler.cpp:103</div></div>
<div class="ttc" id="alu__decompose_8cpp_html_a98eb5807f21b783c341cab402ced6732"><div class="ttname"><a href="../../dd/d65/lu__decompose_8cpp.html#a98eb5807f21b783c341cab402ced6732">operator&lt;&lt;</a></div><div class="ttdeci">std::ostream &amp; operator&lt;&lt;(std::ostream &amp;out, std::vector&lt; std::vector&lt; T &gt;&gt; const &amp;v)</div><div class="ttdef"><b>Definition:</b> lu_decompose.cpp:75</div></div>
<div class="ttc" id="afalse__position_8cpp_html_a0a3abbca80bc98e7abcb3ae73abe0f14"><div class="ttname"><a href="../../dd/d29/false__position_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> false_position.cpp:24</div></div>
<div class="ttc" id="aclassstatistics_1_1stats__computer2_html_a7e7a1a2b0a03df0a70cac40d193421d2"><div class="ttname"><a href="../../d8/dab/classstatistics_1_1stats__computer2.html#a7e7a1a2b0a03df0a70cac40d193421d2">statistics::stats_computer2::operator&gt;&gt;</a></div><div class="ttdeci">friend std::istream &amp; operator&gt;&gt;(std::istream &amp;input, stats_computer2 &amp;stat)</div><div class="ttdef"><b>Definition:</b> realtime_stats.cpp:97</div></div>
<div class="ttc" id="anewton__raphson__method_8cpp_html_a0a3abbca80bc98e7abcb3ae73abe0f14"><div class="ttname"><a href="../../de/dd3/newton__raphson__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> newton_raphson_method.cpp:21</div></div>
<div class="ttc" id="amatrix__exponentiation_8cpp_html_a9977ad12548c4a49dee9dc3f0685aa54"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a></div><div class="ttdeci">ll mat_size</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:45</div></div>
<div class="ttc" id="agolden__search__extrema_8cpp_html_a002b2f4894492820fe708b1b7e7c5e70"><div class="ttname"><a href="../../d6/d7a/golden__search__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a></div><div class="ttdeci">#define EPSILON</div><div class="ttdoc">solution accuracy limit</div><div class="ttdef"><b>Definition:</b> golden_search_extrema.cpp:17</div></div>
<div class="ttc" id="abrent__method__extrema_8cpp_html_a6d0455dd5c30adda100e95f0423c786e"><div class="ttname"><a href="../../db/d01/brent__method__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> brent_method_extrema.cpp:188</div></div>
<div class="ttc" id="abasic_string_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a></div><div class="ttdoc">STL class.</div></div>
<div class="ttc" id="agroup__ode_html_ga827bf009831ddc477c5fa8891d5cb35f"><div class="ttname"><a href="../../d6/d60/group__ode.html#ga827bf009831ddc477c5fa8891d5cb35f">semi_implicit_euler_step</a></div><div class="ttdeci">void semi_implicit_euler_step(const double dx, const double &amp;x, std::valarray&lt; double &gt; *y, std::valarray&lt; double &gt; *dy)</div><div class="ttdoc">Compute next step approximation using the semi-implicit-Euler method.</div><div class="ttdef"><b>Definition:</b> ode_semi_implicit_euler.cpp:82</div></div>
<div class="ttc" id="auniform_int_distribution_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/uniform_int_distribution.html">std::uniform_int_distribution</a></div></div>
<div class="ttc" id="aprime__numbers_8cpp_html_a3b91f208e8365c95a295cfe3e67df5c3"><div class="ttname"><a href="../../de/d9b/prime__numbers_8cpp.html#a3b91f208e8365c95a295cfe3e67df5c3">primes</a></div><div class="ttdeci">std::vector&lt; int &gt; primes(int max)</div><div class="ttdef"><b>Definition:</b> prime_numbers.cpp:12</div></div>
<div class="ttc" id="amiller__rabin_8cpp_html_a901288288ef5ebe8e97414cc30797cce"><div class="ttname"><a href="../../d6/d42/miller__rabin_8cpp.html#a901288288ef5ebe8e97414cc30797cce">miller_rabin_primality_test</a></div><div class="ttdeci">bool miller_rabin_primality_test(T num, T repeats)</div><div class="ttdef"><b>Definition:</b> miller_rabin.cpp:125</div></div>
<div class="ttc" id="aclock_t_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a></div></div>
<div class="ttc" id="aordinary__least__squares__regressor_8cpp_html_a67249e31221231cf3aaf3cfd870372d0"><div class="ttname"><a href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a67249e31221231cf3aaf3cfd870372d0">operator+</a></div><div class="ttdeci">std::vector&lt; T &gt; operator+(std::vector&lt; T &gt; const &amp;A, std::vector&lt; T &gt; const &amp;B)</div><div class="ttdef"><b>Definition:</b> ordinary_least_squares_regressor.cpp:196</div></div>
<div class="ttc" id="anewton__raphson__method_8cpp_html_a2003b5b2dcfff0769b957ab5c968b03d"><div class="ttname"><a href="../../de/dd3/newton__raphson__method_8cpp.html#a2003b5b2dcfff0769b957ab5c968b03d">eq</a></div><div class="ttdeci">static double eq(double i)</div><div class="ttdef"><b>Definition:</b> newton_raphson_method.cpp:29</div></div>
<div class="ttc" id="apair_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a></div></div>
<div class="ttc" id="abrent__method__extrema_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../db/d01/brent__method__extrema_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> brent_method_extrema.cpp:204</div></div>
<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>
<div class="ttc" id="abrent__method__extrema_8cpp_html_a002b2f4894492820fe708b1b7e7c5e70"><div class="ttname"><a href="../../db/d01/brent__method__extrema_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a></div><div class="ttdeci">#define EPSILON</div><div class="ttdoc">system accuracy limit</div><div class="ttdef"><b>Definition:</b> brent_method_extrema.cpp:23</div></div>
<div class="ttc" id="anewton__raphson__method_8cpp_html_a3d3f7f41977394680af6ebbed96f3386"><div class="ttname"><a href="../../de/dd3/newton__raphson__method_8cpp.html#a3d3f7f41977394680af6ebbed96f3386">eq_der</a></div><div class="ttdeci">static double eq_der(double i)</div><div class="ttdef"><b>Definition:</b> newton_raphson_method.cpp:39</div></div>
<div class="ttc" id="aode__forward__euler_8cpp_html_af3adf7b092a87868917ee5fb4255192b"><div class="ttname"><a href="../../db/dd3/ode__forward__euler_8cpp.html#af3adf7b092a87868917ee5fb4255192b">exact_solution</a></div><div class="ttdeci">void exact_solution(const double &amp;x, std::valarray&lt; double &gt; *y)</div><div class="ttdoc">Exact solution of the problem. Used for solution comparison.</div><div class="ttdef"><b>Definition:</b> ode_forward_euler.cpp:67</div></div>
<div class="ttc" id="aatof_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/byte/atof.html">std::atof</a></div><div class="ttdeci">T atof(T... args)</div></div>
<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div><div class="ttdoc">STL class.</div></div>
<div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/size.html">std::vector::size</a></div><div class="ttdeci">T size(T... args)</div></div>
<div class="ttc" id="apower__for__huge__numbers_8cpp_html_aa141a7904f0c4668bac112d652a3acf9"><div class="ttname"><a href="../../df/def/power__for__huge__numbers_8cpp.html#aa141a7904f0c4668bac112d652a3acf9">multiply</a></div><div class="ttdeci">int multiply(int x, int res[], int res_size)</div><div class="ttdef"><b>Definition:</b> power_for_huge_numbers.cpp:25</div></div>
<div class="ttc" id="aode__forward__euler_8cpp_html_a0ddf1224851353fc92bfbff6f499fa97"><div class="ttname"><a href="../../db/dd3/ode__forward__euler_8cpp.html#a0ddf1224851353fc92bfbff6f499fa97">main</a></div><div class="ttdeci">int main(int argc, char *argv[])</div><div class="ttdef"><b>Definition:</b> ode_forward_euler.cpp:188</div></div>
<div class="ttc" id="amatrix__exponentiation_8cpp_html_ad8389ed58fd0ec66df248014775ad1fa"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#ad8389ed58fd0ec66df248014775ad1fa">ans</a></div><div class="ttdeci">ll ans(ll n)</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:91</div></div>
<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="agroup__ode_html_ga8c319db420c3d97a83e9dcca803b6812"><div class="ttname"><a href="../../d6/d60/group__ode.html#ga8c319db420c3d97a83e9dcca803b6812">midpoint_euler_step</a></div><div class="ttdeci">void midpoint_euler_step(const double dx, const double &amp;x, std::valarray&lt; double &gt; *y, std::valarray&lt; double &gt; *dy)</div><div class="ttdoc">Compute next step approximation using the midpoint-Euler method.</div><div class="ttdef"><b>Definition:</b> ode_midpoint_euler.cpp:85</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="aordinary__least__squares__regressor_8cpp_html_a4921874435266592b222e3f2eda0e01f"><div class="ttname"><a href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a4921874435266592b222e3f2eda0e01f">is_square</a></div><div class="ttdeci">bool is_square(std::vector&lt; std::vector&lt; T &gt;&gt; const &amp;A)</div><div class="ttdef"><b>Definition:</b> ordinary_least_squares_regressor.cpp:55</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="anamespaceqr__algorithm_html"><div class="ttname"><a href="../../d2/d3b/namespaceqr__algorithm.html">qr_algorithm</a></div><div class="ttdoc">Functions to compute QR decomposition of any rectangular matrix.</div></div>
<div class="ttc" id="aordinary__least__squares__regressor_8cpp_html_ab6171f4db68a5e50ae0f3500a63acd26"><div class="ttname"><a href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#ab6171f4db68a5e50ae0f3500a63acd26">operator*</a></div><div class="ttdeci">std::vector&lt; std::vector&lt; T &gt; &gt; operator*(std::vector&lt; std::vector&lt; T &gt;&gt; const &amp;A, std::vector&lt; std::vector&lt; T &gt;&gt; const &amp;B)</div><div class="ttdef"><b>Definition:</b> ordinary_least_squares_regressor.cpp:72</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="agroup__ode_html_gaa197c6b7085ac9ea71abc4c063e6f52f"><div class="ttname"><a href="../../d6/d60/group__ode.html#gaa197c6b7085ac9ea71abc4c063e6f52f">forward_euler_step</a></div><div class="ttdeci">void forward_euler_step(const double dx, const double &amp;x, std::valarray&lt; double &gt; *y, std::valarray&lt; double &gt; *dy)</div><div class="ttdoc">Compute next step approximation using the forward-Euler method.</div><div class="ttdef"><b>Definition:</b> ode_forward_euler.cpp:86</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="aordinary__least__squares__regressor_8cpp_html_a98eb5807f21b783c341cab402ced6732"><div class="ttname"><a href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a98eb5807f21b783c341cab402ced6732">operator&lt;&lt;</a></div><div class="ttdeci">std::ostream &amp; operator&lt;&lt;(std::ostream &amp;out, std::vector&lt; std::vector&lt; T &gt;&gt; const &amp;v)</div><div class="ttdef"><b>Definition:</b> ordinary_least_squares_regressor.cpp:20</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="aode__forward__euler_8cpp_html_aa13517b8e5de1b75592052db7f7e237f"><div class="ttname"><a href="../../db/dd3/ode__forward__euler_8cpp.html#aa13517b8e5de1b75592052db7f7e237f">save_exact_solution</a></div><div class="ttdeci">void save_exact_solution(const double &amp;X0, const double &amp;X_MAX, const double &amp;step_size, const std::valarray&lt; double &gt; &amp;Y0)</div><div class="ttdef"><b>Definition:</b> ode_forward_euler.cpp:152</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="anamespaceqr__algorithm_html_a5422c76bfa322620de611083bd518d71"><div class="ttname"><a href="../../d2/d3b/namespaceqr__algorithm.html#a5422c76bfa322620de611083bd518d71">qr_algorithm::vector_proj</a></div><div class="ttdeci">std::valarray&lt; T &gt; vector_proj(const std::valarray&lt; T &gt; &amp;a, const std::valarray&lt; T &gt; &amp;b)</div><div class="ttdef"><b>Definition:</b> qr_decompose.h:104</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="anamespaceqr__algorithm_html_ad16da2183db22378435042f26af43d5f"><div class="ttname"><a href="../../d2/d3b/namespaceqr__algorithm.html#ad16da2183db22378435042f26af43d5f">qr_algorithm::vector_mag</a></div><div class="ttdeci">double vector_mag(const std::valarray&lt; T &gt; &amp;a)</div><div class="ttdef"><b>Definition:</b> qr_decompose.h:92</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="aclose_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ofstream/close.html">std::ofstream::close</a></div><div class="ttdeci">T close(T... args)</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="aperror_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/c/perror.html">std::perror</a></div><div class="ttdeci">T perror(T... args)</div></div>
<div 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:91</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="aordinary__least__squares__regressor_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> ordinary_least_squares_regressor.cpp:358</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="aordinary__least__squares__regressor_8cpp_html_a4bcaaf41c66da4d3a471dacef133def7"><div class="ttname"><a href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a4bcaaf41c66da4d3a471dacef133def7">predict_OLS_regressor</a></div><div class="ttdeci">std::vector&lt; float &gt; predict_OLS_regressor(std::vector&lt; std::vector&lt; T &gt;&gt; const &amp;X, std::vector&lt; float &gt; const &amp;beta)</div><div class="ttdef"><b>Definition:</b> ordinary_least_squares_regressor.cpp:340</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="anamespaceqr__algorithm_html_a7c63c78d6839b8ad73b77c161210b514"><div class="ttname"><a href="../../d2/d3b/namespaceqr__algorithm.html#a7c63c78d6839b8ad73b77c161210b514">qr_algorithm::operator&lt;&lt;</a></div><div class="ttdeci">std::ostream &amp; operator&lt;&lt;(std::ostream &amp;out, std::valarray&lt; std::valarray&lt; T &gt;&gt; const &amp;v)</div><div class="ttdef"><b>Definition:</b> qr_decompose.h:33</div></div>
<div class="ttc" id="agroup__ode_html_gae0509f8843e2bc42de2abbd00a14b7b9"><div class="ttname"><a href="../../d6/d60/group__ode.html#gae0509f8843e2bc42de2abbd00a14b7b9">forward_euler</a></div><div class="ttdeci">double forward_euler(double dx, double x0, double x_max, std::valarray&lt; double &gt; *y, bool save_to_file=false)</div><div class="ttdoc">Compute approximation using the forward-Euler method in the given limits.</div><div class="ttdef"><b>Definition:</b> ode_forward_euler.cpp:102</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="aode__semi__implicit__euler_8cpp_html_abaeae8f62a018d197f0187a1c80a90fe"><div class="ttname"><a href="../../d3/d06/ode__semi__implicit__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe">problem</a></div><div class="ttdeci">void problem(const double &amp;x, std::valarray&lt; double &gt; *y, std::valarray&lt; double &gt; *dy)</div><div class="ttdoc">Problem statement for a system with first-order differential equations. Updates the system differenti...</div><div class="ttdef"><b>Definition:</b> ode_semi_implicit_euler.cpp:53</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="asin_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/sin.html">std::sin</a></div><div class="ttdeci">T sin(T... args)</div></div>
<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="anewton__raphson__method_8cpp_html_a002b2f4894492820fe708b1b7e7c5e70"><div class="ttname"><a href="../../de/dd3/newton__raphson__method_8cpp.html#a002b2f4894492820fe708b1b7e7c5e70">EPSILON</a></div><div class="ttdeci">#define EPSILON</div><div class="ttdoc">system accuracy limit</div><div class="ttdef"><b>Definition:</b> newton_raphson_method.cpp:20</div></div>
<div class="ttc" id="aode__forward__euler_8cpp_html_abaeae8f62a018d197f0187a1c80a90fe"><div class="ttname"><a href="../../db/dd3/ode__forward__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe">problem</a></div><div class="ttdeci">void problem(const double &amp;x, std::valarray&lt; double &gt; *y, std::valarray&lt; double &gt; *dy)</div><div class="ttdoc">Problem statement for a system with first-order differential equations. Updates the system differenti...</div><div class="ttdef"><b>Definition:</b> ode_forward_euler.cpp:54</div></div>
<div class="ttc" id="ahash__search_8cpp_html_a6e1a77282bc65ad359d753d25df23243"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a6e1a77282bc65ad359d753d25df23243">data</a></div><div class="ttdeci">int data[MAX]</div><div class="ttdoc">test data</div><div class="ttdef"><b>Definition:</b> hash_search.cpp:24</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="aordinary__least__squares__regressor_8cpp_html_a38ff1d954e9b7de93eb20e2dd101a045"><div class="ttname"><a href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a38ff1d954e9b7de93eb20e2dd101a045">fit_OLS_regressor</a></div><div class="ttdeci">std::vector&lt; float &gt; fit_OLS_regressor(std::vector&lt; std::vector&lt; T &gt;&gt; const &amp;X, std::vector&lt; T &gt; const &amp;Y)</div><div class="ttdef"><b>Definition:</b> ordinary_least_squares_regressor.cpp:310</div></div>
<div class="ttc" id="aordinary__least__squares__regressor_8cpp_html_a31be3fe36e76b87d5616ff8e7918cd24"><div class="ttname"><a href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a31be3fe36e76b87d5616ff8e7918cd24">operator-</a></div><div class="ttdeci">std::vector&lt; T &gt; operator-(std::vector&lt; T &gt; const &amp;A, std::vector&lt; T &gt; const &amp;B)</div><div class="ttdef"><b>Definition:</b> ordinary_least_squares_regressor.cpp:175</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="aordinary__least__squares__regressor_8cpp_html_a98ab8f75d981088369b89b8be2182483"><div class="ttname"><a href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a98ab8f75d981088369b89b8be2182483">get_inverse</a></div><div class="ttdeci">std::vector&lt; std::vector&lt; float &gt; &gt; get_inverse(std::vector&lt; std::vector&lt; T &gt;&gt; const &amp;A)</div><div class="ttdef"><b>Definition:</b> ordinary_least_squares_regressor.cpp:218</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="anamespaceqr__algorithm_html_a8ea313a1a1b5f9d0e3e332c29c6446ec"><div class="ttname"><a href="../../d2/d3b/namespaceqr__algorithm.html#a8ea313a1a1b5f9d0e3e332c29c6446ec">qr_algorithm::vector_dot</a></div><div class="ttdeci">double vector_dot(const std::valarray&lt; T &gt; &amp;a, const std::valarray&lt; T &gt; &amp;b)</div><div class="ttdef"><b>Definition:</b> qr_decompose.h:76</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="aode__midpoint__euler_8cpp_html_abaeae8f62a018d197f0187a1c80a90fe"><div class="ttname"><a href="../../d6/dd3/ode__midpoint__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe">problem</a></div><div class="ttdeci">void problem(const double &amp;x, std::valarray&lt; double &gt; *y, std::valarray&lt; double &gt; *dy)</div><div class="ttdoc">Problem statement for a system with first-order differential equations. Updates the system differenti...</div><div class="ttdef"><b>Definition:</b> ode_midpoint_euler.cpp:53</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="anewton__raphson__method_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../de/dd3/newton__raphson__method_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdef"><b>Definition:</b> newton_raphson_method.cpp:44</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="agroup__ode_html_ga36ff0710861ca39d957046c0b09b2985"><div class="ttname"><a href="../../d6/d60/group__ode.html#ga36ff0710861ca39d957046c0b09b2985">midpoint_euler</a></div><div class="ttdeci">double midpoint_euler(double dx, double x0, double x_max, std::valarray&lt; double &gt; *y, bool save_to_file=false)</div><div class="ttdoc">Compute approximation using the midpoint-Euler method in the given limits.</div><div class="ttdef"><b>Definition:</b> ode_midpoint_euler.cpp:107</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="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="anamespaceqr__algorithm_html_ab1ac74497ffb2101040cc1efe3546de8"><div class="ttname"><a href="../../d2/d3b/namespaceqr__algorithm.html#ab1ac74497ffb2101040cc1efe3546de8">qr_algorithm::qr_decompose</a></div><div class="ttdeci">void qr_decompose(const std::valarray&lt; std::valarray&lt; T &gt;&gt; &amp;A, std::valarray&lt; std::valarray&lt; T &gt;&gt; *Q, std::valarray&lt; std::valarray&lt; T &gt;&gt; *R)</div><div class="ttdef"><b>Definition:</b> qr_decompose.h:146</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="aode__semi__implicit__euler_8cpp_html_a0ddf1224851353fc92bfbff6f499fa97"><div class="ttname"><a href="../../d3/d06/ode__semi__implicit__euler_8cpp.html#a0ddf1224851353fc92bfbff6f499fa97">main</a></div><div class="ttdeci">int main(int argc, char *argv[])</div><div class="ttdef"><b>Definition:</b> ode_semi_implicit_euler.cpp:189</div></div>
<div class="ttc" id="asize_t_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/types/size_t.html">std::size_t</a></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="aode__semi__implicit__euler_8cpp_html_aa13517b8e5de1b75592052db7f7e237f"><div class="ttname"><a href="../../d3/d06/ode__semi__implicit__euler_8cpp.html#aa13517b8e5de1b75592052db7f7e237f">save_exact_solution</a></div><div class="ttdeci">void save_exact_solution(const double &amp;X0, const double &amp;X_MAX, const double &amp;step_size, const std::valarray&lt; double &gt; &amp;Y0)</div><div class="ttdef"><b>Definition:</b> ode_semi_implicit_euler.cpp:153</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="aode__semi__implicit__euler_8cpp_html_af3adf7b092a87868917ee5fb4255192b"><div class="ttname"><a href="../../d3/d06/ode__semi__implicit__euler_8cpp.html#af3adf7b092a87868917ee5fb4255192b">exact_solution</a></div><div class="ttdeci">void exact_solution(const double &amp;x, std::valarray&lt; double &gt; *y)</div><div class="ttdoc">Exact solution of the problem. Used for solution comparison.</div><div class="ttdef"><b>Definition:</b> ode_semi_implicit_euler.cpp:66</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="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="anumeric_limits_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/types/numeric_limits.html">std::numeric_limits</a></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="aode__midpoint__euler_8cpp_html_af3adf7b092a87868917ee5fb4255192b"><div class="ttname"><a href="../../d6/dd3/ode__midpoint__euler_8cpp.html#af3adf7b092a87868917ee5fb4255192b">exact_solution</a></div><div class="ttdeci">void exact_solution(const double &amp;x, std::valarray&lt; double &gt; *y)</div><div class="ttdoc">Exact solution of the problem. Used for solution comparison.</div><div class="ttdef"><b>Definition:</b> ode_midpoint_euler.cpp:66</div></div>
<div class="ttc" id="alu__decompose_8cpp_html_af703fd0afe349e567d7a82350e03cace"><div class="ttname"><a href="../../dd/d65/lu__decompose_8cpp.html#af703fd0afe349e567d7a82350e03cace">lu_decomposition</a></div><div class="ttdeci">int lu_decomposition(const std::vector&lt; std::vector&lt; double &gt;&gt; &amp;A, std::vector&lt; std::vector&lt; double &gt;&gt; *L, std::vector&lt; std::vector&lt; double &gt;&gt; *U)</div><div class="ttdef"><b>Definition:</b> lu_decompose.cpp:22</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="aordinary__least__squares__regressor_8cpp_html_a30acf52af3184bc22274234ef5a73536"><div class="ttname"><a href="../../dc/d38/ordinary__least__squares__regressor_8cpp.html#a30acf52af3184bc22274234ef5a73536">operator/</a></div><div class="ttdeci">std::vector&lt; float &gt; operator/(std::vector&lt; T &gt; const &amp;A, float const scalar)</div><div class="ttdef"><b>Definition:</b> ordinary_least_squares_regressor.cpp:166</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>
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@@ -256,6 +256,7 @@ Numerical Methods</h1>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/gaussian_elimination.cpp">Gaussian Elimination</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/golden_search_extrema.cpp">Golden Search Extrema</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/lu_decompose.cpp">Lu Decompose</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/lu_decomposition.h">Lu Decomposition</a></li>
<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/newton_raphson_method.cpp">Newton Raphson Method</a></li>
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<li><a href="https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/numerical_methods/ode_midpoint_euler.cpp">Ode Midpoint Euler</a></li>

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<dl class="section note"><dt>Note</dt><dd>Do not know the application of this, however. </dd>
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<dl class="todo"><dt><b><a class="el" href="../../dd/da0/todo.html#_todo000006">Todo:</a></b></dt><dd>implement as a C++ class </dd></dl>
<dl class="todo"><dt><b><a class="el" href="../../dd/da0/todo.html#_todo000007">Todo:</a></b></dt><dd>implement as a C++ class </dd></dl>
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<h2 class="memtitle"><span class="permalink"><a href="#a392fb874e547e582e9c66a08a1f23326">&#9670;&nbsp;</a></span>MAX</h2>

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<p>get_input function is to receive input from standard IO </p><dl class="todo"><dt><b><a class="el" href="../../dd/da0/todo.html#_todo000011">Todo:</a></b></dt><dd>@christianbender Get input from STDIO or write input to memory as done above. </dd></dl>
<p>get_input function is to receive input from standard IO </p><dl class="todo"><dt><b><a class="el" href="../../dd/da0/todo.html#_todo000012">Todo:</a></b></dt><dd>@christianbender Get input from STDIO or write input to memory as done above. </dd></dl>
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<p><a href="https://en.wikipedia.org/wiki/LU_decompositon">LU decomposition</a> of a square matrix
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;ctime&gt;</code><br />
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;ctime&gt;</code><br />
<code>#include &lt;iomanip&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
<code>#include &quot;<a class="el" href="../../d1/dbe/lu__decomposition_8h_source.html">./lu_decomposition.h</a>&quot;</code><br />
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Include dependency graph for lu_decompose.cpp:</div>
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Functions</h2></td></tr>
<tr class="memitem:af703fd0afe349e567d7a82350e03cace"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d65/lu__decompose_8cpp.html#af703fd0afe349e567d7a82350e03cace">lu_decomposition</a> (const <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/container/vector.html">std::vector</a>&lt; double &gt;&gt; &amp;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/container/vector.html">std::vector</a>&lt; double &gt;&gt; *L, <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/container/vector.html">std::vector</a>&lt; double &gt;&gt; *U)</td></tr>
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<tr class="memitem:a98eb5807f21b783c341cab402ced6732"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a98eb5807f21b783c341cab402ced6732"><td class="memTemplItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../dd/d65/lu__decompose_8cpp.html#a98eb5807f21b783c341cab402ced6732">operator&lt;&lt;</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> &amp;out, <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/container/vector.html">std::vector</a>&lt; T &gt;&gt; const &amp;v)</td></tr>
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<tr class="memitem:a1440a7779ac56f47a3f355ce4a8c7da0"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d65/lu__decompose_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a> ()</td></tr>
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void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d65/lu__decompose_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a> ()</td></tr>
<tr class="memdesc:a0283886819c7c140a023582b7269e2d0"><td class="mdescLeft">&#160;</td><td class="mdescRight">Test determinant computation using LU decomposition. <br /></td></tr>
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<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/LU_decompositon">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">Function Documentation</h2>
<a id="af703fd0afe349e567d7a82350e03cace"></a>
<h2 class="memtitle"><span class="permalink"><a href="#af703fd0afe349e567d7a82350e03cace">&#9670;&nbsp;</a></span>lu_decomposition()</h2>
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<td class="memname">int lu_decomposition </td>
<td>(</td>
<td class="paramtype">const <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/container/vector.html">std::vector</a>&lt; double &gt;&gt; &amp;&#160;</td>
<td class="paramname"><em>A</em>, </td>
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<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><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/container/vector.html">std::vector</a>&lt; double &gt;&gt; *&#160;</td>
<td class="paramname"><em>L</em>, </td>
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<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><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/container/vector.html">std::vector</a>&lt; double &gt;&gt; *&#160;</td>
<td class="paramname"><em>U</em>&#160;</td>
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<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="l00024"></a><span class="lineno"> 24</span>&#160; {</div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>&#160; <span class="keywordtype">int</span> row, col, j;</div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</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="l00027"></a><span class="lineno"> 27</span>&#160; </div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</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="l00029"></a><span class="lineno"> 29</span>&#160; <span class="comment">// check matrix is a square matrix</span></div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</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="l00031"></a><span class="lineno"> 31</span>&#160; <span class="keywordflow">return</span> -1;</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; </div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160; <span class="comment">// regularize each row</span></div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</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="l00036"></a><span class="lineno"> 36</span>&#160; <span class="comment">// Upper triangular matrix</span></div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</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="l00041"></a><span class="lineno"> 41</span>&#160; <span class="comment">// Summation of L[i,j] * U[j,k]</span></div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; <span class="keywordtype">double</span> lu_sum = 0.;</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; <span class="keywordflow">for</span> (j = 0; j &lt; row; j++) lu_sum += L[0][row][j] * U[0][j][col];</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; </div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; <span class="comment">// Evaluate U[i,k]</span></div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; U[0][row][col] = A[row][col] - lu_sum;</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160; }</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; </div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; <span class="comment">// Lower triangular matrix</span></div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</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="l00054"></a><span class="lineno"> 54</span>&#160; <span class="keywordflow">if</span> (row == col) {</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; L[0][row][col] = 1.;</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; <span class="keywordflow">continue</span>;</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; }</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; </div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; <span class="comment">// Summation of L[i,j] * U[j,k]</span></div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; <span class="keywordtype">double</span> lu_sum = 0.;</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; <span class="keywordflow">for</span> (j = 0; j &lt; row; j++) lu_sum += L[0][col][j] * U[0][j][row];</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; </div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; <span class="comment">// Evaluate U[i,k]</span></div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; L[0][col][row] = (A[col][row] - lu_sum) / U[0][row][row];</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; }</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; </div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160;}</div>
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<p>Main function </p>
<div class="fragment"><div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160; {</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160; <span class="keywordtype">int</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> = 3; <span class="comment">// default matrix size</span></div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> range = 50;</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> range2 = range &gt;&gt; 1;</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>&#160; </div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160; <span class="keywordflow">if</span> (argc == 2)</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atoi.html">atoi</a>(argv[1]);</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160; </div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(NULL)); <span class="comment">// random number initializer</span></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="comment">/* Create a square matrix with random values */</span></div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;double&gt;</a>&gt; A(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>);</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;double&gt;</a>&gt; L(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>); <span class="comment">// output</span></div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;std::vector&lt;double&gt;</a>&gt; U(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>); <span class="comment">// output</span></div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>&#160; <span class="comment">// calloc so that all valeus are &#39;0&#39; by default</span></div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>&#160; A[i] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>);</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>&#160; L[i] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>);</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>&#160; U[i] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector&lt;double&gt;</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>);</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; j++)</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>&#160; <span class="comment">/* create random values in the limits [-range2, range-1] */</span></div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>&#160; A[i][j] = <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range - range2);</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>&#160; }</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>&#160; </div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> start_t = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>&#160; <a class="code" href="../../dd/d65/lu__decompose_8cpp.html#af703fd0afe349e567d7a82350e03cace">lu_decomposition</a>(A, &amp;L, &amp;U);</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> end_t = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Time taken: &quot;</span></div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>&#160; &lt;&lt; <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(end_t - start_t) / CLOCKS_PER_SEC &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>&#160; </div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;A = \n&quot;</span> &lt;&lt; A &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;L = \n&quot;</span> &lt;&lt; L &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;U = \n&quot;</span> &lt;&lt; U &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>&#160; </div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>&#160;}</div>
<div class="fragment"><div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160; {</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(NULL)); <span class="comment">// random number initializer</span></div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160; </div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160; <a class="code" href="../../dd/d65/lu__decompose_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>();</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160; <a class="code" href="../../dd/d65/lu__decompose_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>();</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a98eb5807f21b783c341cab402ced6732">&#9670;&nbsp;</a></span>operator&lt;&lt;()</h2>
<a id="a9459fcd1f020373d73eae2bad43786d0"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a9459fcd1f020373d73eae2bad43786d0">&#9670;&nbsp;</a></span>operator&lt;&lt;()</h2>
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@@ -303,7 +188,7 @@ template&lt;typename T &gt; </div>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><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/container/vector.html">std::vector</a>&lt; T &gt;&gt; const &amp;&#160;</td>
<td class="paramtype"><a class="el" href="../../d1/dbe/lu__decomposition_8h.html#aed8766713ee9b561a4acdcdff5f90ea5">matrix</a>&lt; T &gt; const &amp;&#160;</td>
<td class="paramname"><em>v</em>&#160;</td>
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@@ -314,23 +199,73 @@ template&lt;typename T &gt; </div>
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<p>operator to print a matrix </p>
<div class="fragment"><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="keyword">const</span> <span class="keywordtype">int</span> width = 10;</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; <span class="keyword">const</span> <span class="keywordtype">char</span> separator = <span class="charliteral">&#39; &#39;</span>;</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160; </div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; v.size(); row++) {</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; v[row].size(); col++)</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160; out &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">std::left</a> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setw.html">std::setw</a>(width) &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setfill.html">std::setfill</a>(separator)</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160; &lt;&lt; v[row][col];</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160; out &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; }</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160; </div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160; <span class="keywordflow">return</span> out;</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160;}</div>
<div class="fragment"><div class="line"><a name="l00018"></a><span class="lineno"> 18</span>&#160; {</div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> width = 10;</div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span>&#160; <span class="keyword">const</span> <span class="keywordtype">char</span> separator = <span class="charliteral">&#39; &#39;</span>;</div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span>&#160; </div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; v.size(); row++) {</div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; v[row].size(); col++)</div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>&#160; out &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">std::left</a> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setw.html">std::setw</a>(width) &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setfill.html">std::setfill</a>(separator)</div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>&#160; &lt;&lt; v[row][col];</div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>&#160; out &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>&#160; }</div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>&#160; </div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>&#160; <span class="keywordflow">return</span> out;</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a1440a7779ac56f47a3f355ce4a8c7da0">&#9670;&nbsp;</a></span>test1()</h2>
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<tr>
<td class="memname">void test1 </td>
<td>(</td>
<td class="paramname"></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Test LU decomposition </p><dl class="todo"><dt><b><a class="el" href="../../dd/da0/todo.html#_todo000004">Todo:</a></b></dt><dd>better ways to self-check a matrix output? </dd></dl>
<div class="fragment"><div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160; {</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; <span class="keywordtype">int</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> = 3; <span class="comment">// default matrix size</span></div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> range = 50;</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> range2 = range &gt;&gt; 1;</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; </div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; <span class="comment">/* Create a square matrix with random values */</span></div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;double&gt;</a> A(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>, <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>));</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;double&gt;</a> L(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>, <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>)); <span class="comment">// output</span></div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;double&gt;</a> U(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>, <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>)); <span class="comment">// output</span></div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; <span class="comment">// calloc so that all valeus are &#39;0&#39; by default</span></div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; j++)</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; <span class="comment">/* create random values in the limits [-range2, range-1] */</span></div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; A[i][j] = <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range - range2);</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; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> start_t = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
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</li>
<li>isPrime()
: <a class="el" href="d8/d53/modular__inverse__fermat__little__theorem_8cpp.html#a09660096b134753128952246f4f4e4bd">modular_inverse_fermat_little_theorem.cpp</a>
</li>
<li>IsPrime()
: <a class="el" href="da/d7b/primality__test_8cpp.html#a2bfa6adead2bdcbf1dac94cbe08d7eaf">primality_test.cpp</a>
</li>
<li>isPrime()
: <a class="el" href="d8/d53/modular__inverse__fermat__little__theorem_8cpp.html#a09660096b134753128952246f4f4e4bd">modular_inverse_fermat_little_theorem.cpp</a>
</li>
<li>it_ternary_search()
: <a class="el" href="dc/dfe/ternary__search_8cpp.html#ae30dfe2894191bfeffe5b3b1854b95b0">ternary_search.cpp</a>
</li>

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@@ -109,7 +109,7 @@ $(document).ready(function(){initNavTree('globals_func_l.html',''); initResizabl
: <a class="el" href="d9/d02/linear__search_8cpp.html#a84ac3988a534eb60ca351ed6caf56d84">linear_search.cpp</a>
</li>
<li>lu_decomposition()
: <a class="el" href="dd/d65/lu__decompose_8cpp.html#af703fd0afe349e567d7a82350e03cace">lu_decompose.cpp</a>
: <a class="el" href="d1/dbe/lu__decomposition_8h.html#a75b8a228c6419ecda6077255d6d60509">lu_decomposition.h</a>
</li>
</ul>
</div><!-- contents -->

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@@ -111,7 +111,7 @@ $(document).ready(function(){initNavTree('globals_func_o.html',''); initResizabl
<li>operator&lt;&lt;()
: <a class="el" href="d5/d67/complex__numbers_8cpp.html#af738b2a6921f0a6868bb7c5b4c0d18e0">complex_numbers.cpp</a>
, <a class="el" href="dc/d38/ordinary__least__squares__regressor_8cpp.html#aa799b4cec1681219887d89d037cfab50">ordinary_least_squares_regressor.cpp</a>
, <a class="el" href="dd/d65/lu__decompose_8cpp.html#a98eb5807f21b783c341cab402ced6732">lu_decompose.cpp</a>
, <a class="el" href="dd/d65/lu__decompose_8cpp.html#a9459fcd1f020373d73eae2bad43786d0">lu_decompose.cpp</a>
</li>
<li>operator==()
: <a class="el" href="d5/d67/complex__numbers_8cpp.html#a5a73e9d4e68af8cedb95bd0864054b89">complex_numbers.cpp</a>

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@@ -106,6 +106,7 @@ $(document).ready(function(){initNavTree('globals_func_t.html',''); initResizabl
</li>
<li>test1()
: <a class="el" href="d5/db0/adaline__learning_8cpp.html#a52053d88ea1bcbbed9aca67ab4eeb499">adaline_learning.cpp</a>
, <a class="el" href="dd/d65/lu__decompose_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">lu_decompose.cpp</a>
, <a class="el" href="de/d75/qr__eigen__values_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">qr_eigen_values.cpp</a>
, <a class="el" href="d4/def/kohonen__som__topology_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">kohonen_som_topology.cpp</a>
, <a class="el" href="d9/d49/kohonen__som__trace_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">kohonen_som_trace.cpp</a>
@@ -124,16 +125,17 @@ $(document).ready(function(){initNavTree('globals_func_t.html',''); initResizabl
, <a class="el" href="db/d01/brent__method__extrema_8cpp.html#a0283886819c7c140a023582b7269e2d0">brent_method_extrema.cpp</a>
, <a class="el" href="da/df2/durand__kerner__roots_8cpp.html#a0283886819c7c140a023582b7269e2d0">durand_kerner_roots.cpp</a>
, <a class="el" href="d6/d7a/golden__search__extrema_8cpp.html#a0283886819c7c140a023582b7269e2d0">golden_search_extrema.cpp</a>
, <a class="el" href="dd/d65/lu__decompose_8cpp.html#a0283886819c7c140a023582b7269e2d0">lu_decompose.cpp</a>
, <a class="el" href="de/d75/qr__eigen__values_8cpp.html#a0283886819c7c140a023582b7269e2d0">qr_eigen_values.cpp</a>
, <a class="el" href="d0/d01/smallest__circle_8cpp.html#a0283886819c7c140a023582b7269e2d0">smallest_circle.cpp</a>
</li>
<li>test3()
: <a class="el" href="d0/d01/smallest__circle_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">smallest_circle.cpp</a>
: <a class="el" href="d9/d49/kohonen__som__trace_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">kohonen_som_trace.cpp</a>
, <a class="el" href="db/d01/brent__method__extrema_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">brent_method_extrema.cpp</a>
, <a class="el" href="d6/d7a/golden__search__extrema_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">golden_search_extrema.cpp</a>
, <a class="el" href="d0/d01/smallest__circle_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">smallest_circle.cpp</a>
, <a class="el" href="d5/db0/adaline__learning_8cpp.html#a992bdf1fdb0b9d414bcf7981d2d87aa9">adaline_learning.cpp</a>
, <a class="el" href="d4/def/kohonen__som__topology_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">kohonen_som_topology.cpp</a>
, <a class="el" href="d9/d49/kohonen__som__trace_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">kohonen_som_trace.cpp</a>
, <a class="el" href="db/d01/brent__method__extrema_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">brent_method_extrema.cpp</a>
</li>
<li>test_2d_classes()
: <a class="el" href="d4/def/kohonen__som__topology_8cpp.html#a6b5e744876fd980a3451cbb385d4e755">kohonen_som_topology.cpp</a>
@@ -163,9 +165,9 @@ $(document).ready(function(){initNavTree('globals_func_t.html',''); initResizabl
: <a class="el" href="d9/d49/kohonen__som__trace_8cpp.html#a412b7afa156306b1f8788643c91a1c60">kohonen_som_trace.cpp</a>
</li>
<li>tests()
: <a class="el" href="d7/d89/double__factorial_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">double_factorial.cpp</a>
: <a class="el" href="d9/dfd/comb__sort_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">comb_sort.cpp</a>
, <a class="el" href="d7/d89/double__factorial_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">double_factorial.cpp</a>
, <a class="el" href="d5/d67/complex__numbers_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">complex_numbers.cpp</a>
, <a class="el" href="d9/dfd/comb__sort_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">comb_sort.cpp</a>
, <a class="el" href="d4/d21/least__common__multiple_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">least_common_multiple.cpp</a>
, <a class="el" href="d6/d42/miller__rabin_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">miller_rabin.cpp</a>
</li>

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@@ -123,16 +123,18 @@ $(document).ready(function(){initNavTree('globals_i.html',''); initResizable();
<li>is_square()
: <a class="el" href="dc/d38/ordinary__least__squares__regressor_8cpp.html#a4921874435266592b222e3f2eda0e01f">ordinary_least_squares_regressor.cpp</a>
</li>
<li>isprime
: <a class="el" href="d8/ddf/sieve__of__eratosthenes_8cpp.html#a0560e21edb54d5ad8d80b2d80348ce22">sieve_of_eratosthenes.cpp</a>
</li>
<li>IsPrime()
: <a class="el" href="da/d7b/primality__test_8cpp.html#a2bfa6adead2bdcbf1dac94cbe08d7eaf">primality_test.cpp</a>
</li>
<li>isprime
: <a class="el" href="db/d0d/prime__factorization_8cpp.html#a7fe38b570a51e448430d6a0f072c2f23">prime_factorization.cpp</a>
, <a class="el" href="d8/ddf/sieve__of__eratosthenes_8cpp.html#a0560e21edb54d5ad8d80b2d80348ce22">sieve_of_eratosthenes.cpp</a>
</li>
<li>isPrime()
: <a class="el" href="d8/d53/modular__inverse__fermat__little__theorem_8cpp.html#a09660096b134753128952246f4f4e4bd">modular_inverse_fermat_little_theorem.cpp</a>
</li>
<li>isprime
: <a class="el" href="db/d0d/prime__factorization_8cpp.html#a7fe38b570a51e448430d6a0f072c2f23">prime_factorization.cpp</a>
</li>
<li>it_ternary_search()
: <a class="el" href="dc/dfe/ternary__search_8cpp.html#ae30dfe2894191bfeffe5b3b1854b95b0">ternary_search.cpp</a>
</li>

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@@ -118,7 +118,7 @@ $(document).ready(function(){initNavTree('globals_l.html',''); initResizable();
: <a class="el" href="d7/d35/matrix__exponentiation_8cpp.html#ae1d1ec9482079231e898236e2b23c9ba">matrix_exponentiation.cpp</a>
</li>
<li>lu_decomposition()
: <a class="el" href="dd/d65/lu__decompose_8cpp.html#af703fd0afe349e567d7a82350e03cace">lu_decompose.cpp</a>
: <a class="el" href="d1/dbe/lu__decomposition_8h.html#a75b8a228c6419ecda6077255d6d60509">lu_decomposition.h</a>
</li>
</ul>
</div><!-- contents -->

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@@ -121,6 +121,7 @@ $(document).ready(function(){initNavTree('globals_m.html',''); initResizable();
, <a class="el" href="d8/d8a/exponential__search_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">exponential_search.cpp</a>
, <a class="el" href="d1/df3/hash__search_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">hash_search.cpp</a>
, <a class="el" href="d2/d0b/fast__power_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">fast_power.cpp</a>
, <a class="el" href="d4/d83/sum__of__digits_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">sum_of_digits.cpp</a>
, <a class="el" href="d6/dce/rabin__karp_8cpp.html#a840291bc02cba5474a4cb46a9b9566fe">rabin_karp.cpp</a>
, <a class="el" href="de/d6a/knuth__morris__pratt_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">knuth_morris_pratt.cpp</a>
, <a class="el" href="d3/d7d/brute__force__string__searching_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">brute_force_string_searching.cpp</a>
@@ -131,12 +132,11 @@ $(document).ready(function(){initNavTree('globals_m.html',''); initResizable();
, <a class="el" href="d9/dfd/comb__sort_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">comb_sort.cpp</a>
, <a class="el" href="dc/db5/text__search_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">text_search.cpp</a>
, <a class="el" href="dc/dfe/ternary__search_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">ternary_search.cpp</a>
, <a class="el" href="d9/d69/median__search_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">median_search.cpp</a>
, <a class="el" href="d4/d83/sum__of__digits_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">sum_of_digits.cpp</a>
, <a class="el" href="d9/dd7/interpolation__search_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">interpolation_search.cpp</a>
, <a class="el" href="df/d39/interpolation__search2_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">interpolation_search2.cpp</a>
, <a class="el" href="d7/d6a/bisection__method_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">bisection_method.cpp</a>
, <a class="el" href="d9/d02/linear__search_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">linear_search.cpp</a>
, <a class="el" href="d9/d69/median__search_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">median_search.cpp</a>
, <a class="el" href="d8/d6c/line__segment__intersection_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">line_segment_intersection.cpp</a>
, <a class="el" href="d4/d5d/math_2armstrong__number_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">armstrong_number.cpp</a>
, <a class="el" href="d9/d89/fibonacci_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">fibonacci.cpp</a>
@@ -147,6 +147,7 @@ $(document).ready(function(){initNavTree('globals_m.html',''); initResizable();
, <a class="el" href="d6/d7a/golden__search__extrema_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">golden_search_extrema.cpp</a>
, <a class="el" href="de/dcf/binary__exponent_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">binary_exponent.cpp</a>
, <a class="el" href="d4/da0/gcd__iterative__euclidean_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">gcd_iterative_euclidean.cpp</a>
, <a class="el" href="dd/d65/lu__decompose_8cpp.html#a3c04138a5bfe5d72780bb7e82a18e627">lu_decompose.cpp</a>
, <a class="el" href="d3/d19/sparse__matrix_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">sparse_matrix.cpp</a>
, <a class="el" href="d0/d01/smallest__circle_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">smallest_circle.cpp</a>
, <a class="el" href="da/d7b/primality__test_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">primality_test.cpp</a>
@@ -163,11 +164,10 @@ $(document).ready(function(){initNavTree('globals_m.html',''); initResizable();
, <a class="el" href="d3/d24/qr__decomposition_8cpp.html#a840291bc02cba5474a4cb46a9b9566fe">qr_decomposition.cpp</a>
, <a class="el" href="dc/d38/ordinary__least__squares__regressor_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">ordinary_least_squares_regressor.cpp</a>
, <a class="el" href="d3/d06/ode__semi__implicit__euler_8cpp.html#a0ddf1224851353fc92bfbff6f499fa97">ode_semi_implicit_euler.cpp</a>
, <a class="el" href="d6/dd3/ode__midpoint__euler_8cpp.html#a0ddf1224851353fc92bfbff6f499fa97">ode_midpoint_euler.cpp</a>
, <a class="el" href="dd/d65/lu__decompose_8cpp.html#a3c04138a5bfe5d72780bb7e82a18e627">lu_decompose.cpp</a>
, <a class="el" href="de/dd3/newton__raphson__method_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">newton_raphson_method.cpp</a>
, <a class="el" href="d1/d11/gcd__of__n__numbers_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">gcd_of_n_numbers.cpp</a>
, <a class="el" href="db/dd3/ode__forward__euler_8cpp.html#a0ddf1224851353fc92bfbff6f499fa97">ode_forward_euler.cpp</a>
, <a class="el" href="d6/dd3/ode__midpoint__euler_8cpp.html#a0ddf1224851353fc92bfbff6f499fa97">ode_midpoint_euler.cpp</a>
, <a class="el" href="d3/dce/linkedlist__implentation__usingarray_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">linkedlist_implentation_usingarray.cpp</a>
, <a class="el" href="df/ddd/connected__components_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">connected_components.cpp</a>
, <a class="el" href="d5/df6/check__amicable__pair_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">check_amicable_pair.cpp</a>
@@ -179,10 +179,10 @@ $(document).ready(function(){initNavTree('globals_m.html',''); initResizable();
, <a class="el" href="d5/db0/adaline__learning_8cpp.html#a3c04138a5bfe5d72780bb7e82a18e627">adaline_learning.cpp</a>
, <a class="el" href="d5/d67/complex__numbers_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">complex_numbers.cpp</a>
, <a class="el" href="d8/d53/modular__inverse__fermat__little__theorem_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">modular_inverse_fermat_little_theorem.cpp</a>
, <a class="el" href="db/d0d/prime__factorization_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">prime_factorization.cpp</a>
, <a class="el" href="d0/da2/number__of__positive__divisors_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">number_of_positive_divisors.cpp</a>
, <a class="el" href="d7/d89/double__factorial_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">double_factorial.cpp</a>
, <a class="el" href="df/def/power__for__huge__numbers_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">power_for_huge_numbers.cpp</a>
, <a class="el" href="db/d0d/prime__factorization_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">prime_factorization.cpp</a>
</li>
<li>mat_mul()
: <a class="el" href="de/d75/qr__eigen__values_8cpp.html#a7558fd7779bf207157ced66f275951a0">qr_eigen_values.cpp</a>
@@ -190,17 +190,20 @@ $(document).ready(function(){initNavTree('globals_m.html',''); initResizable();
<li>mat_size
: <a class="el" href="d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">matrix_exponentiation.cpp</a>
</li>
<li>matrix
: <a class="el" href="d1/dbe/lu__decomposition_8h.html#aed8766713ee9b561a4acdcdff5f90ea5">lu_decomposition.h</a>
</li>
<li>MAX
: <a class="el" href="d8/ddf/sieve__of__eratosthenes_8cpp.html#a392fb874e547e582e9c66a08a1f23326">sieve_of_eratosthenes.cpp</a>
, <a class="el" href="dc/dc5/paranthesis__matching_8cpp.html#a392fb874e547e582e9c66a08a1f23326">paranthesis_matching.cpp</a>
, <a class="el" href="df/def/power__for__huge__numbers_8cpp.html#a392fb874e547e582e9c66a08a1f23326">power_for_huge_numbers.cpp</a>
, <a class="el" href="d1/df3/hash__search_8cpp.html#a392fb874e547e582e9c66a08a1f23326">hash_search.cpp</a>
, <a class="el" href="dc/dfe/ternary__search_8cpp.html#a392fb874e547e582e9c66a08a1f23326">ternary_search.cpp</a>
, <a class="el" href="dc/dc5/paranthesis__matching_8cpp.html#a392fb874e547e582e9c66a08a1f23326">paranthesis_matching.cpp</a>
, <a class="el" href="d4/d32/fibonacci__fast_8cpp.html#a392fb874e547e582e9c66a08a1f23326">fibonacci_fast.cpp</a>
, <a class="el" href="df/def/power__for__huge__numbers_8cpp.html#a392fb874e547e582e9c66a08a1f23326">power_for_huge_numbers.cpp</a>
</li>
<li>MAX_ITERATIONS
: <a class="el" href="de/dd3/newton__raphson__method_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">newton_raphson_method.cpp</a>
, <a class="el" href="dd/d29/false__position_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">false_position.cpp</a>
: <a class="el" href="dd/d29/false__position_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">false_position.cpp</a>
, <a class="el" href="de/dd3/newton__raphson__method_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">newton_raphson_method.cpp</a>
, <a class="el" href="d7/d6a/bisection__method_8cpp.html#a0a3abbca80bc98e7abcb3ae73abe0f14">bisection_method.cpp</a>
</li>
<li>MAX_NUM
@@ -243,8 +246,8 @@ $(document).ready(function(){initNavTree('globals_m.html',''); initResizable();
: <a class="el" href="db/d3c/tower__of__hanoi_8cpp.html#af4cfc41e546f1f8d25f01e0804e8b61d">tower_of_hanoi.cpp</a>
</li>
<li>multiply()
: <a class="el" href="df/def/power__for__huge__numbers_8cpp.html#aa141a7904f0c4668bac112d652a3acf9">power_for_huge_numbers.cpp</a>
, <a class="el" href="d7/d35/matrix__exponentiation_8cpp.html#ac62a499b83c7895dd0aa69da1b64c904">matrix_exponentiation.cpp</a>
: <a class="el" href="d7/d35/matrix__exponentiation_8cpp.html#ac62a499b83c7895dd0aa69da1b64c904">matrix_exponentiation.cpp</a>
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, <a class="el" href="dc/d38/ordinary__least__squares__regressor_8cpp.html#aa799b4cec1681219887d89d037cfab50">ordinary_least_squares_regressor.cpp</a>
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</li>
<li>operator==()
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: <a class="el" href="dc/d38/ordinary__least__squares__regressor_8cpp.html#a4bcaaf41c66da4d3a471dacef133def7">ordinary_least_squares_regressor.cpp</a>
</li>
<li>PRIME
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</li>
<li>prime
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</li>
<li>PRIME
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</li>
<li>prime_factorization()
: <a class="el" href="db/d0d/prime__factorization_8cpp.html#a0ece0145fb29a5cf48378c23dde2da46">prime_factorization.cpp</a>
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, <a class="el" href="da/df2/durand__kerner__roots_8cpp.html#a0283886819c7c140a023582b7269e2d0">durand_kerner_roots.cpp</a>
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: <a class="el" href="db/d01/brent__method__extrema_8cpp.html#a6d0455dd5c30adda100e95f0423c786e">brent_method_extrema.cpp</a>
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: <a class="el" href="d4/def/kohonen__som__topology_8cpp.html#a6b5e744876fd980a3451cbb385d4e755">kohonen_som_topology.cpp</a>
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: <a class="el" href="d5/d67/complex__numbers_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">complex_numbers.cpp</a>
, <a class="el" href="d4/d21/least__common__multiple_8cpp.html#a88ec9ad42717780d6caaff9d3d6977f9">least_common_multiple.cpp</a>
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<li>TH()
: <a class="el" href="db/d3c/tower__of__hanoi_8cpp.html#ab037f72a5eac476535a6cfbbcb965417">tower_of_hanoi.cpp</a>

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