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@@ -122,11 +139,13 @@ Include dependency graph for lu_decompose.cpp:</div>
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Functions</h2></td></tr>
<tr class="memitem:a575c989afcc78e875031cd4273e62a3e" id="r_a575c989afcc78e875031cd4273e62a3e"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a575c989afcc78e875031cd4273e62a3e"><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="#a575c989afcc78e875031cd4273e62a3e">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#ac029b636b353cefbb18b2fcc71e427e4">matrix</a>&lt; T &gt; const &amp;v)</td></tr>
<tr class="memitem:a575c989afcc78e875031cd4273e62a3e"><td class="memTemplItemLeft" align="right" valign="top">std::ostream &amp;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="#a575c989afcc78e875031cd4273e62a3e">operator&lt;&lt;</a> (std::ostream &amp;out, <a class="el" href="../../d1/dbe/lu__decomposition_8h.html#ac029b636b353cefbb18b2fcc71e427e4">matrix</a>&lt; T &gt; const &amp;v)</td></tr>
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@@ -138,6 +157,8 @@ Functions</h2></td></tr>
<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" target="_blank">LU decomposition</a> of a square matrix </p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala" target="_blank">Krishna Vedala</a> </dd></dl>
<p class="definition">Definition in file <a class="el" href="../../dd/d65/lu__decompose_8cpp_source.html">lu_decompose.cpp</a>.</p>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a3c04138a5bfe5d72780bb7e82a18e627" name="a3c04138a5bfe5d72780bb7e82a18e627"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a3c04138a5bfe5d72780bb7e82a18e627">&#9670;&#160;</a></span>main()</h2>
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<p>Main function </p>
<p class="definition">Definition at line <a class="el" href="../../dd/d65/lu__decompose_8cpp_source.html#l00084">84</a> of file <a class="el" href="../../dd/d65/lu__decompose_8cpp_source.html">lu_decompose.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 84</span> {</div>
<div class="line"><span class="lineno"> 85</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="code hl_functionRef" 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"><span class="lineno"> 85</span> std::srand(std::time(NULL)); <span class="comment">// random number initializer</span></div>
<div class="line"><span class="lineno"> 86</span> </div>
<div class="line"><span class="lineno"> 87</span> <a class="code hl_function" href="#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>();</div>
<div class="line"><span class="lineno"> 88</span> <a class="code hl_function" href="#a0283886819c7c140a023582b7269e2d0">test2</a>();</div>
<div class="line"><span class="lineno"> 89</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 90</span>}</div>
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<div class="ttc" id="alu__decompose_8cpp_html_a1440a7779ac56f47a3f355ce4a8c7da0"><div class="ttname"><a href="#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="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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template&lt;typename T &gt; </div>
<table class="memname">
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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="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::ostream</a> &amp;</td> <td class="paramname"><span class="paramname"><em>out</em></span>, </td>
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<p>operator to print a matrix </p>
<p class="definition">Definition at line <a class="el" href="../../dd/d65/lu__decompose_8cpp_source.html#l00018">18</a> of file <a class="el" href="../../dd/d65/lu__decompose_8cpp_source.html">lu_decompose.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 18</span> {</div>
<div class="line"><span class="lineno"> 19</span> <span class="keyword">const</span> <span class="keywordtype">int</span> width = 10;</div>
<div class="line"><span class="lineno"> 20</span> <span class="keyword">const</span> <span class="keywordtype">char</span> separator = <span class="charliteral">&#39; &#39;</span>;</div>
<div class="line"><span class="lineno"> 21</span> </div>
<div class="line"><span class="lineno"> 22</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; v.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); row++) {</div>
<div class="line"><span class="lineno"> 23</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; v[row].<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>(); col++)</div>
<div class="line"><span class="lineno"> 24</span> out &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/left.html">std::left</a> &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setw.html">std::setw</a>(width) &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setfill.html">std::setfill</a>(separator)</div>
<div class="line"><span class="lineno"> 22</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; v.size(); row++) {</div>
<div class="line"><span class="lineno"> 23</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; v[row].size(); col++)</div>
<div class="line"><span class="lineno"> 24</span> out &lt;&lt; std::left &lt;&lt; std::setw(width) &lt;&lt; std::setfill(separator)</div>
<div class="line"><span class="lineno"> 25</span> &lt;&lt; v[row][col];</div>
<div class="line"><span class="lineno"> 26</span> out &lt;&lt; <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><span class="lineno"> 26</span> out &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 27</span> }</div>
<div class="line"><span class="lineno"> 28</span> </div>
<div class="line"><span class="lineno"> 29</span> <span class="keywordflow">return</span> out;</div>
<div class="line"><span class="lineno"> 30</span>}</div>
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<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>
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Here is the call graph for this function:</div>
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</table>
</div><div class="memdoc">
<p>Test LU decomposition </p><dl class="todo"><dt><b><a class="el" href="../../dd/da0/todo.html#_todo000006">Todo</a></b></dt><dd>better ways to self-check a matrix output? </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../dd/d65/lu__decompose_8cpp_source.html#l00036">36</a> of file <a class="el" href="../../dd/d65/lu__decompose_8cpp_source.html">lu_decompose.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 36</span> {</div>
<div class="line"><span class="lineno"> 37</span> <span class="keywordtype">int</span> <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> = 3; <span class="comment">// default matrix size</span></div>
<div class="line"><span class="lineno"> 38</span> <span class="keyword">const</span> <span class="keywordtype">int</span> range = 50;</div>
<div class="line"><span class="lineno"> 39</span> <span class="keyword">const</span> <span class="keywordtype">int</span> range2 = range &gt;&gt; 1;</div>
<div class="line"><span class="lineno"> 40</span> </div>
<div class="line"><span class="lineno"> 41</span> <span class="comment">/* Create a square matrix with random values */</span></div>
<div class="line"><span class="lineno"> 42</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;double&gt;</a> A(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>));</div>
<div class="line"><span class="lineno"> 43</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;double&gt;</a> L(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>)); <span class="comment">// output</span></div>
<div class="line"><span class="lineno"> 44</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;double&gt;</a> U(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>)); <span class="comment">// output</span></div>
<div class="line"><span class="lineno"> 42</span> <a class="code hl_typedef" href="../../d1/dbe/lu__decomposition_8h.html#ac029b636b353cefbb18b2fcc71e427e4">matrix&lt;double&gt;</a> A(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>, std::valarray&lt;double&gt;(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>));</div>
<div class="line"><span class="lineno"> 43</span> <a class="code hl_typedef" href="../../d1/dbe/lu__decomposition_8h.html#ac029b636b353cefbb18b2fcc71e427e4">matrix&lt;double&gt;</a> L(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>, std::valarray&lt;double&gt;(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>)); <span class="comment">// output</span></div>
<div class="line"><span class="lineno"> 44</span> <a class="code hl_typedef" href="../../d1/dbe/lu__decomposition_8h.html#ac029b636b353cefbb18b2fcc71e427e4">matrix&lt;double&gt;</a> U(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>, std::valarray&lt;double&gt;(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>)); <span class="comment">// output</span></div>
<div class="line"><span class="lineno"> 45</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
<div class="line"><span class="lineno"> 46</span> <span class="comment">// calloc so that all valeus are &#39;0&#39; by default</span></div>
<div class="line"><span class="lineno"> 47</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; j++)</div>
<div class="line"><span class="lineno"> 48</span> <span class="comment">/* create random values in the limits [-range2, range-1] */</span></div>
<div class="line"><span class="lineno"> 49</span> A[i][j] = <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % range - range2);</div>
<div class="line"><span class="lineno"> 49</span> A[i][j] = <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(std::rand() % range - range2);</div>
<div class="line"><span class="lineno"> 50</span> }</div>
<div class="line"><span class="lineno"> 51</span> </div>
<div class="line"><span class="lineno"> 52</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> start_t = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
<div class="line"><span class="lineno"> 52</span> std::clock_t start_t = std::clock();</div>
<div class="line"><span class="lineno"> 53</span> <a class="code hl_function" href="../../d1/dbe/lu__decomposition_8h.html#a75b8a228c6419ecda6077255d6d60509">lu_decomposition</a>(A, &amp;L, &amp;U);</div>
<div class="line"><span class="lineno"> 54</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a> end_t = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a>();</div>
<div class="line"><span class="lineno"> 55</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Time taken: &quot;</span></div>
<div class="line"><span class="lineno"> 54</span> std::clock_t end_t = std::clock();</div>
<div class="line"><span class="lineno"> 55</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Time taken: &quot;</span></div>
<div class="line"><span class="lineno"> 56</span> &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"><span class="lineno"> 57</span> </div>
<div class="line"><span class="lineno"> 58</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;A = \n&quot;</span> &lt;&lt; A &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 59</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;L = \n&quot;</span> &lt;&lt; L &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 60</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;U = \n&quot;</span> &lt;&lt; U &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 58</span> std::cout &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"><span class="lineno"> 59</span> std::cout &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"><span class="lineno"> 60</span> std::cout &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"><span class="lineno"> 61</span>}</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="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="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="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="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="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="avalarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</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>
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<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> <a href="../../d1/dbe/lu__decomposition_8h_source.html#l00029">lu_decomposition.h:29</a></div></div>
<div class="ttc" id="alu__decomposition_8h_html_ac029b636b353cefbb18b2fcc71e427e4"><div class="ttname"><a href="../../d1/dbe/lu__decomposition_8h.html#ac029b636b353cefbb18b2fcc71e427e4">matrix</a></div><div class="ttdeci">std::vector&lt; std::valarray&lt; T &gt; &gt; matrix</div><div class="ttdef"><b>Definition</b> <a href="../../d1/dbe/lu__decomposition_8h_source.html#l00019">lu_decomposition.h:19</a></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> <a href="../../d7/d35/matrix__exponentiation_8cpp_source.html#l00045">matrix_exponentiation.cpp:45</a></div></div>
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<p>Test determinant computation using LU decomposition </p>
<div class="fragment"><div class="line"><span class="lineno"> 66</span> {</div>
<div class="line"><span class="lineno"> 67</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Determinant test 1...&quot;</span>;</div>
<div class="line"><span class="lineno"> 68</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;int&gt;</a> A1({{1, 2, 3}, {4, 9, 6}, {7, 8, 9}});</div>
<div class="line"><span class="lineno"> 69</span> assert(<a class="code hl_function" href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f">determinant_lu</a>(A1) == -48);</div>
<div class="line"><span class="lineno"> 70</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 71</span> </div>
<div class="line"><span class="lineno"> 72</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Determinant test 2...&quot;</span>;</div>
<div class="line"><span class="lineno"> 73</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;int&gt;</a> A2({{1, 2, 3}, {4, 5, 6}, {7, 8, 9}});</div>
<div class="line"><span class="lineno"> 74</span> assert(<a class="code hl_function" href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f">determinant_lu</a>(A2) == 0);</div>
<div class="line"><span class="lineno"> 75</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 76</span> </div>
<div class="line"><span class="lineno"> 77</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Determinant test 3...&quot;</span>;</div>
<div class="line"><span class="lineno"> 78</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">matrix&lt;float&gt;</a> A3({{1.2, 2.3, 3.4}, {4.5, 5.6, 6.7}, {7.8, 8.9, 9.0}});</div>
<div class="line"><span class="lineno"> 79</span> assert(<a class="code hl_function" href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f">determinant_lu</a>(A3) == 3.63);</div>
<div class="line"><span class="lineno"> 80</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 81</span>}</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="ttdef"><b>Definition</b> lu_decomposition.h:90</div></div>
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<p class="definition">Definition at line <a class="el" href="../../dd/d65/lu__decompose_8cpp_source.html#l00066">66</a> of file <a class="el" href="../../dd/d65/lu__decompose_8cpp_source.html">lu_decompose.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 66</span> {</div>
<div class="line"><span class="lineno"> 67</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Determinant test 1...&quot;</span>;</div>
<div class="line"><span class="lineno"> 68</span> <a class="code hl_typedef" href="../../d1/dbe/lu__decomposition_8h.html#ac029b636b353cefbb18b2fcc71e427e4">matrix&lt;int&gt;</a> A1({{1, 2, 3}, {4, 9, 6}, {7, 8, 9}});</div>
<div class="line"><span class="lineno"> 69</span> assert(<a class="code hl_function" href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f">determinant_lu</a>(A1) == -48);</div>
<div class="line"><span class="lineno"> 70</span> std::cout &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 71</span> </div>
<div class="line"><span class="lineno"> 72</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Determinant test 2...&quot;</span>;</div>
<div class="line"><span class="lineno"> 73</span> <a class="code hl_typedef" href="../../d1/dbe/lu__decomposition_8h.html#ac029b636b353cefbb18b2fcc71e427e4">matrix&lt;int&gt;</a> A2({{1, 2, 3}, {4, 5, 6}, {7, 8, 9}});</div>
<div class="line"><span class="lineno"> 74</span> assert(<a class="code hl_function" href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f">determinant_lu</a>(A2) == 0);</div>
<div class="line"><span class="lineno"> 75</span> std::cout &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 76</span> </div>
<div class="line"><span class="lineno"> 77</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Determinant test 3...&quot;</span>;</div>
<div class="line"><span class="lineno"> 78</span> <a class="code hl_typedef" href="../../d1/dbe/lu__decomposition_8h.html#ac029b636b353cefbb18b2fcc71e427e4">matrix&lt;float&gt;</a> A3({{1.2, 2.3, 3.4}, {4.5, 5.6, 6.7}, {7.8, 8.9, 9.0}});</div>
<div class="line"><span class="lineno"> 79</span> assert(<a class="code hl_function" href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f">determinant_lu</a>(A3) == 3.63);</div>
<div class="line"><span class="lineno"> 80</span> std::cout &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 81</span>}</div>
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<div class="headertitle"><div class="title">lu_decompose.cpp</div></div>
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<a href="../../dd/d65/lu__decompose_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span> </div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="preprocessor">#include &lt;cassert&gt;</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="preprocessor">#include &lt;ctime&gt;</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="preprocessor">#include &lt;iomanip&gt;</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="preprocessor">#include &lt;iostream&gt;</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span> </div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="preprocessor">#include &quot;<a class="code" href="../../d1/dbe/lu__decomposition_8h.html">./lu_decomposition.h</a>&quot;</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span> </div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="foldopen" id="foldopen00018" data-start="{" data-end="}">
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"><a class="line" href="../../dd/d65/lu__decompose_8cpp.html#a575c989afcc78e875031cd4273e62a3e"> 18</a></span>std::ostream &amp;<a class="code hl_function" href="../../dd/d65/lu__decompose_8cpp.html#a575c989afcc78e875031cd4273e62a3e">operator&lt;&lt;</a>(std::ostream &amp;out, <a class="code hl_typedef" href="../../d1/dbe/lu__decomposition_8h.html#ac029b636b353cefbb18b2fcc71e427e4">matrix&lt;T&gt;</a> <span class="keyword">const</span> &amp;v) {</div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> <span class="keyword">const</span> <span class="keywordtype">int</span> width = 10;</div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span> <span class="keyword">const</span> <span class="keywordtype">char</span> separator = <span class="charliteral">&#39; &#39;</span>;</div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span> </div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row &lt; v.size(); row++) {</div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col &lt; v[row].size(); col++)</div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> out &lt;&lt; std::left &lt;&lt; std::setw(width) &lt;&lt; std::setfill(separator)</div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> &lt;&lt; v[row][col];</div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> out &lt;&lt; std::endl;</div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> }</div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> </div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> <span class="keywordflow">return</span> out;</div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span>}</div>
</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> </div>
<div class="foldopen" id="foldopen00036" data-start="{" data-end="}">
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"><a class="line" href="../../dd/d65/lu__decompose_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0"> 36</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="../../dd/d65/lu__decompose_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>() {</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> <span class="keywordtype">int</span> <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> = 3; <span class="comment">// default matrix size</span></div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> <span class="keyword">const</span> <span class="keywordtype">int</span> range = 50;</div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> <span class="keyword">const</span> <span class="keywordtype">int</span> range2 = range &gt;&gt; 1;</div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> </div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <span class="comment">/* Create a square matrix with random values */</span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <a class="code hl_typedef" href="../../d1/dbe/lu__decomposition_8h.html#ac029b636b353cefbb18b2fcc71e427e4">matrix&lt;double&gt;</a> A(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>, std::valarray&lt;double&gt;(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>));</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <a class="code hl_typedef" href="../../d1/dbe/lu__decomposition_8h.html#ac029b636b353cefbb18b2fcc71e427e4">matrix&lt;double&gt;</a> L(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>, std::valarray&lt;double&gt;(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>)); <span class="comment">// output</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <a class="code hl_typedef" href="../../d1/dbe/lu__decomposition_8h.html#ac029b636b353cefbb18b2fcc71e427e4">matrix&lt;double&gt;</a> U(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>, std::valarray&lt;double&gt;(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>)); <span class="comment">// output</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> <span class="comment">// calloc so that all valeus are &#39;0&#39; by default</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; j++)</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> <span class="comment">/* create random values in the limits [-range2, range-1] */</span></div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> A[i][j] = <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(std::rand() % range - range2);</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> }</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> </div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> std::clock_t start_t = std::clock();</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <a class="code hl_function" href="../../d1/dbe/lu__decomposition_8h.html#a75b8a228c6419ecda6077255d6d60509">lu_decomposition</a>(A, &amp;L, &amp;U);</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> std::clock_t end_t = std::clock();</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Time taken: &quot;</span></div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> &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 id="l00057" name="l00057"></a><span class="lineno"> 57</span> </div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> std::cout &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 id="l00059" name="l00059"></a><span class="lineno"> 59</span> std::cout &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 id="l00060" name="l00060"></a><span class="lineno"> 60</span> std::cout &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 id="l00061" name="l00061"></a><span class="lineno"> 61</span>}</div>
</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> </div>
<div class="foldopen" id="foldopen00066" data-start="{" data-end="}">
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"><a class="line" href="../../dd/d65/lu__decompose_8cpp.html#a0283886819c7c140a023582b7269e2d0"> 66</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="../../dd/d65/lu__decompose_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>() {</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Determinant test 1...&quot;</span>;</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <a class="code hl_typedef" href="../../d1/dbe/lu__decomposition_8h.html#ac029b636b353cefbb18b2fcc71e427e4">matrix&lt;int&gt;</a> A1({{1, 2, 3}, {4, 9, 6}, {7, 8, 9}});</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> assert(<a class="code hl_function" href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f">determinant_lu</a>(A1) == -48);</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> std::cout &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> </div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Determinant test 2...&quot;</span>;</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <a class="code hl_typedef" href="../../d1/dbe/lu__decomposition_8h.html#ac029b636b353cefbb18b2fcc71e427e4">matrix&lt;int&gt;</a> A2({{1, 2, 3}, {4, 5, 6}, {7, 8, 9}});</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> assert(<a class="code hl_function" href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f">determinant_lu</a>(A2) == 0);</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> std::cout &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> </div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Determinant test 3...&quot;</span>;</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <a class="code hl_typedef" href="../../d1/dbe/lu__decomposition_8h.html#ac029b636b353cefbb18b2fcc71e427e4">matrix&lt;float&gt;</a> A3({{1.2, 2.3, 3.4}, {4.5, 5.6, 6.7}, {7.8, 8.9, 9.0}});</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> assert(<a class="code hl_function" href="../../d1/dbe/lu__decomposition_8h.html#a3108d43bd32c6fb3b3c158476c51ba7f">determinant_lu</a>(A3) == 3.63);</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> std::cout &lt;&lt; <span class="stringliteral">&quot;passed\n&quot;</span>;</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span>}</div>
</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> </div>
<div class="foldopen" id="foldopen00084" data-start="{" data-end="}">
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"><a class="line" href="../../dd/d65/lu__decompose_8cpp.html#a3c04138a5bfe5d72780bb7e82a18e627"> 84</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../dd/d1e/generate__parentheses_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4">main</a>(<span class="keywordtype">int</span> argc, <span class="keywordtype">char</span> **argv) {</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> std::srand(std::time(NULL)); <span class="comment">// random number initializer</span></div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> </div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <a class="code hl_function" href="../../dd/d65/lu__decompose_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>();</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <a class="code hl_function" href="../../dd/d65/lu__decompose_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>();</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span>}</div>
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<div class="ttc" id="agenerate__parentheses_8cpp_html_gae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../dd/d1e/generate__parentheses_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdoc">Main function.</div><div class="ttdef"><b>Definition</b> <a href="../../dd/d1e/generate__parentheses_8cpp_source.html#l00110">generate_parentheses.cpp:110</a></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="ttdef"><b>Definition</b> <a href="#l00066">lu_decompose.cpp:66</a></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> <a href="#l00036">lu_decompose.cpp:36</a></div></div>
<div class="ttc" id="alu__decompose_8cpp_html_a575c989afcc78e875031cd4273e62a3e"><div class="ttname"><a href="../../dd/d65/lu__decompose_8cpp.html#a575c989afcc78e875031cd4273e62a3e">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> <a href="#l00018">lu_decompose.cpp:18</a></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="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="ttdef"><b>Definition</b> <a href="../../d1/dbe/lu__decomposition_8h_source.html#l00090">lu_decomposition.h:90</a></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> <a href="../../d1/dbe/lu__decomposition_8h_source.html#l00029">lu_decomposition.h:29</a></div></div>
<div class="ttc" id="alu__decomposition_8h_html_ac029b636b353cefbb18b2fcc71e427e4"><div class="ttname"><a href="../../d1/dbe/lu__decomposition_8h.html#ac029b636b353cefbb18b2fcc71e427e4">matrix</a></div><div class="ttdeci">std::vector&lt; std::valarray&lt; T &gt; &gt; matrix</div><div class="ttdef"><b>Definition</b> <a href="../../d1/dbe/lu__decomposition_8h_source.html#l00019">lu_decomposition.h:19</a></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> <a href="../../d7/d35/matrix__exponentiation_8cpp_source.html#l00045">matrix_exponentiation.cpp:45</a></div></div>
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