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@@ -99,24 +99,29 @@ $(document).ready(function(){initNavTree('dd/d65/lu__decompose_8cpp.html','../..
<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 />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for lu_decompose.cpp:</div>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
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>
<tr class="separator:af703fd0afe349e567d7a82350e03cace"><td class="memSeparator" colspan="2">&#160;</td></tr>
<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>
<tr class="separator:a98eb5807f21b783c341cab402ced6732"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a9459fcd1f020373d73eae2bad43786d0"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a9459fcd1f020373d73eae2bad43786d0"><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#a9459fcd1f020373d73eae2bad43786d0">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="el" href="../../d1/dbe/lu__decomposition_8h.html#aed8766713ee9b561a4acdcdff5f90ea5">matrix</a>&lt; T &gt; const &amp;v)</td></tr>
<tr class="separator:a9459fcd1f020373d73eae2bad43786d0"><td class="memSeparator" colspan="2">&#160;</td></tr>
<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>
<tr class="separator:a1440a7779ac56f47a3f355ce4a8c7da0"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a0283886819c7c140a023582b7269e2d0"><td class="memItemLeft" align="right" valign="top"><a id="a0283886819c7c140a023582b7269e2d0"></a>
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>
<tr class="separator:a0283886819c7c140a023582b7269e2d0"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a3c04138a5bfe5d72780bb7e82a18e627"><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#a3c04138a5bfe5d72780bb7e82a18e627">main</a> (int argc, char **argv)</td></tr>
<tr class="separator:a3c04138a5bfe5d72780bb7e82a18e627"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table>
@@ -124,97 +129,6 @@ Functions</h2></td></tr>
<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>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<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>
</tr>
<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>
</tr>
<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>
</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="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>
</div><!-- fragment -->
</div>
</div>
<a id="a3c04138a5bfe5d72780bb7e82a18e627"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a3c04138a5bfe5d72780bb7e82a18e627">&#9670;&nbsp;</a></span>main()</h2>
@@ -241,53 +155,24 @@ negative if error occurred </dd></dl>
</table>
</div><div class="memdoc">
<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>
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<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>
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<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>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; <a class="code" href="../../d1/dbe/lu__decomposition_8h.html#a75b8a228c6419ecda6077255d6d60509">lu_decomposition</a>(A, &amp;L, &amp;U);</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</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="l00055"></a><span class="lineno"> 55</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="l00056"></a><span class="lineno"> 56</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="l00057"></a><span class="lineno"> 57</span>&#160; </div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</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="l00059"></a><span class="lineno"> 59</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="l00060"></a><span class="lineno"> 60</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="l00061"></a><span class="lineno"> 61</span>&#160;}</div>
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@@ -342,17 +277,18 @@ Here is the call graph for this function:</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="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="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="alu__decompose_8cpp_html_a0283886819c7c140a023582b7269e2d0"><div class="ttname"><a href="../../dd/d65/lu__decompose_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a></div><div class="ttdeci">void test2()</div><div class="ttdoc">Test determinant computation using LU decomposition.</div><div class="ttdef"><b>Definition:</b> lu_decompose.cpp:66</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="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="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cerr</a></div></div>
<div class="ttc" id="aatoi_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/byte/atoi.html">std::atoi</a></div><div class="ttdeci">T atoi(T... args)</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="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="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="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="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="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="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="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="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="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>
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