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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 />
<code>#include &lt;iomanip&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;vector&gt;</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>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<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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<td>)</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> mat_size = 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> (mat_size != 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; mat_size; 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; mat_size; 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; mat_size; 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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<h2 class="memtitle"><span class="permalink"><a href="#a3c04138a5bfe5d72780bb7e82a18e627">&#9670;&nbsp;</a></span>main()</h2>
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<td class="memname">int main </td>
<td>(</td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>argc</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">char **&#160;</td>
<td class="paramname"><em>argv</em>&#160;</td>
</tr>
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<td></td>
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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> mat_size = 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; mat_size = <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(mat_size);</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(mat_size); <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(mat_size); <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; mat_size; 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>(mat_size);</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>(mat_size);</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>(mat_size);</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; mat_size; 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>
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<h2 class="memtitle"><span class="permalink"><a href="#a98eb5807f21b783c341cab402ced6732">&#9670;&nbsp;</a></span>operator&lt;&lt;()</h2>
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template&lt;typename T &gt; </div>
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a>&amp; operator&lt;&lt; </td>
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<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>
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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>
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