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<div class="contents">
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<p><a href="https://en.wikipedia.org/wiki/LU_decompositon" target="_blank">LU decomposition</a> of a square matrix
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<a href="#details">More...</a></p>
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<div class="textblock"><code>#include <cassert></code><br />
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<code>#include <ctime></code><br />
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<code>#include <iomanip></code><br />
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<code>#include <iostream></code><br />
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<code>#include "<a class="el" href="../../d1/dbe/lu__decomposition_8h_source.html">./lu_decomposition.h</a>"</code><br />
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<table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 id="header-func-members" class="groupheader"><a id="func-members" name="func-members"></a>
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Functions</h2></td></tr>
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<tr class="memitem:a575c989afcc78e875031cd4273e62a3e" id="r_a575c989afcc78e875031cd4273e62a3e"><td class="memTemplParams" colspan="2">template<typename T> </td></tr>
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<tr class="memitem:a575c989afcc78e875031cd4273e62a3e template"><td class="memItemLeft" align="right" valign="top">std::ostream & </td><td class="memItemRight" valign="bottom"><a class="el" href="#a575c989afcc78e875031cd4273e62a3e">operator<<</a> (std::ostream &out, <a class="el" href="../../d1/dbe/lu__decomposition_8h.html#ac029b636b353cefbb18b2fcc71e427e4">matrix</a>< T > const &v)</td></tr>
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<tr class="memitem:a1440a7779ac56f47a3f355ce4a8c7da0" id="r_a1440a7779ac56f47a3f355ce4a8c7da0"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a> ()</td></tr>
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<tr class="memitem:a0283886819c7c140a023582b7269e2d0" id="r_a0283886819c7c140a023582b7269e2d0"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="#a0283886819c7c140a023582b7269e2d0">test2</a> ()</td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4" id="r_ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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</table>
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<a name="details" id="details"></a><h2 id="header-details" class="groupheader">Detailed Description</h2>
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<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/LU_decompositon" target="_blank">LU decomposition</a> of a square matrix </p>
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<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala" target="_blank">Krishna Vedala</a> </dd></dl>
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<p class="definition">Definition in file <a class="el" href="../../dd/d65/lu__decompose_8cpp_source.html">lu_decompose.cpp</a>.</p>
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</div><a name="doc-func-members" id="doc-func-members"></a><h2 id="header-doc-func-members" class="groupheader">Function Documentation</h2>
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<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">◆ </a></span>main()</h2>
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<div class="memitem">
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<div class="memproto">
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<table class="memname">
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<tr>
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<td class="memname">int main </td>
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<td>(</td>
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<td class="paramtype">void</td> <td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
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<td></td>
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</div><div class="memdoc">
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<p>Main function </p>
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<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>
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<div class="fragment"><div class="line"><span class="lineno"> 84</span> {</div>
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<div class="line"><span class="lineno"> 85</span> std::srand(std::time(NULL)); <span class="comment">// random number initializer</span></div>
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<div class="line"><span class="lineno"> 86</span> </div>
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<div class="line"><span class="lineno"> 87</span> <a class="code hl_function" href="#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>();</div>
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<div class="line"><span class="lineno"> 88</span> <a class="code hl_function" href="#a0283886819c7c140a023582b7269e2d0">test2</a>();</div>
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<div class="line"><span class="lineno"> 89</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><span class="lineno"> 90</span>}</div>
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<div class="ttc" id="alu__decompose_8cpp_html_a0283886819c7c140a023582b7269e2d0"><div class="ttname"><a href="#a0283886819c7c140a023582b7269e2d0">test2</a></div><div class="ttdeci">void test2()</div><div class="ttdef"><b>Definition</b> <a href="../../dd/d65/lu__decompose_8cpp_source.html#l00066">lu_decompose.cpp:66</a></div></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> <a href="../../dd/d65/lu__decompose_8cpp_source.html#l00036">lu_decompose.cpp:36</a></div></div>
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</div><!-- fragment -->
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<a id="a575c989afcc78e875031cd4273e62a3e" name="a575c989afcc78e875031cd4273e62a3e"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a575c989afcc78e875031cd4273e62a3e">◆ </a></span>operator<<()</h2>
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<div class="memproto">
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<div class="memtemplate">
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template<typename T> </div>
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<table class="memname">
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<tr>
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<td class="memname">std::ostream & operator<< </td>
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<td>(</td>
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<td class="paramtype">std::ostream &</td> <td class="paramname"><span class="paramname"><em>out</em></span>, </td>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype"><a class="el" href="../../d1/dbe/lu__decomposition_8h.html#ac029b636b353cefbb18b2fcc71e427e4">matrix</a>< T > const &</td> <td class="paramname"><span class="paramname"><em>v</em></span> )</td>
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</div><div class="memdoc">
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<p>operator to print a matrix </p>
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<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>
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<div class="fragment"><div class="line"><span class="lineno"> 18</span> {</div>
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<div class="line"><span class="lineno"> 19</span> <span class="keyword">const</span> <span class="keywordtype">int</span> width = 10;</div>
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<div class="line"><span class="lineno"> 20</span> <span class="keyword">const</span> <span class="keywordtype">char</span> separator = <span class="charliteral">' '</span>;</div>
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<div class="line"><span class="lineno"> 21</span> </div>
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<div class="line"><span class="lineno"> 22</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> row = 0; row < v.size(); row++) {</div>
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<div class="line"><span class="lineno"> 23</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> col = 0; col < v[row].size(); col++)</div>
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<div class="line"><span class="lineno"> 24</span> out << std::left << std::setw(width) << std::setfill(separator)</div>
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<div class="line"><span class="lineno"> 25</span> << v[row][col];</div>
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<div class="line"><span class="lineno"> 26</span> out << std::endl;</div>
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<div class="line"><span class="lineno"> 27</span> }</div>
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<div class="line"><span class="lineno"> 28</span> </div>
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<div class="line"><span class="lineno"> 29</span> <span class="keywordflow">return</span> out;</div>
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<div class="line"><span class="lineno"> 30</span>}</div>
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</div><!-- fragment -->
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</div>
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</div>
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<a id="a1440a7779ac56f47a3f355ce4a8c7da0" name="a1440a7779ac56f47a3f355ce4a8c7da0"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a1440a7779ac56f47a3f355ce4a8c7da0">◆ </a></span>test1()</h2>
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<td class="memname">void test1 </td>
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<td>(</td>
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<td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
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<td></td>
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</div><div class="memdoc">
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<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>
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<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>
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<div class="fragment"><div class="line"><span class="lineno"> 36</span> {</div>
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<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>
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<div class="line"><span class="lineno"> 38</span> <span class="keyword">const</span> <span class="keywordtype">int</span> range = 50;</div>
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<div class="line"><span class="lineno"> 39</span> <span class="keyword">const</span> <span class="keywordtype">int</span> range2 = range >> 1;</div>
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<div class="line"><span class="lineno"> 40</span> </div>
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<div class="line"><span class="lineno"> 41</span> <span class="comment">/* Create a square matrix with random values */</span></div>
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<div class="line"><span class="lineno"> 42</span> <a class="code hl_typedef" href="../../d1/dbe/lu__decomposition_8h.html#ac029b636b353cefbb18b2fcc71e427e4">matrix<double></a> A(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>, std::valarray<double>(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>));</div>
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<div class="line"><span class="lineno"> 43</span> <a class="code hl_typedef" href="../../d1/dbe/lu__decomposition_8h.html#ac029b636b353cefbb18b2fcc71e427e4">matrix<double></a> L(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>, std::valarray<double>(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>)); <span class="comment">// output</span></div>
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<div class="line"><span class="lineno"> 44</span> <a class="code hl_typedef" href="../../d1/dbe/lu__decomposition_8h.html#ac029b636b353cefbb18b2fcc71e427e4">matrix<double></a> U(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>, std::valarray<double>(<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>)); <span class="comment">// output</span></div>
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<div class="line"><span class="lineno"> 45</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) {</div>
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<div class="line"><span class="lineno"> 46</span> <span class="comment">// calloc so that all valeus are '0' by default</span></div>
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<div class="line"><span class="lineno"> 47</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; j++)</div>
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<div class="line"><span class="lineno"> 48</span> <span class="comment">/* create random values in the limits [-range2, range-1] */</span></div>
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<div class="line"><span class="lineno"> 49</span> A[i][j] = <span class="keyword">static_cast<</span><span class="keywordtype">double</span><span class="keyword">></span>(std::rand() % range - range2);</div>
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<div class="line"><span class="lineno"> 50</span> }</div>
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<div class="line"><span class="lineno"> 51</span> </div>
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<div class="line"><span class="lineno"> 52</span> std::clock_t start_t = std::clock();</div>
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<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, &L, &U);</div>
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<div class="line"><span class="lineno"> 54</span> std::clock_t end_t = std::clock();</div>
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<div class="line"><span class="lineno"> 55</span> std::cout << <span class="stringliteral">"Time taken: "</span></div>
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<div class="line"><span class="lineno"> 56</span> << <span class="keyword">static_cast<</span><span class="keywordtype">double</span><span class="keyword">></span>(end_t - start_t) / CLOCKS_PER_SEC << <span class="stringliteral">"\n"</span>;</div>
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<div class="line"><span class="lineno"> 57</span> </div>
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<div class="line"><span class="lineno"> 58</span> std::cout << <span class="stringliteral">"A = \n"</span> << A << <span class="stringliteral">"\n"</span>;</div>
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<div class="line"><span class="lineno"> 59</span> std::cout << <span class="stringliteral">"L = \n"</span> << L << <span class="stringliteral">"\n"</span>;</div>
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<div class="line"><span class="lineno"> 60</span> std::cout << <span class="stringliteral">"U = \n"</span> << U << <span class="stringliteral">"\n"</span>;</div>
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<div class="line"><span class="lineno"> 61</span>}</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< T > &A, matrix< double > *L, matrix< double > *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>
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<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< std::valarray< T > > 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>
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<div class="ttc" id="amatrix__exponentiation_8cpp_html_a9977ad12548c4a49dee9dc3f0685aa54"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a></div><div class="ttdeci">ll mat_size</div><div class="ttdef"><b>Definition</b> <a href="../../d7/d35/matrix__exponentiation_8cpp_source.html#l00045">matrix_exponentiation.cpp:45</a></div></div>
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<a id="a0283886819c7c140a023582b7269e2d0" name="a0283886819c7c140a023582b7269e2d0"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a0283886819c7c140a023582b7269e2d0">◆ </a></span>test2()</h2>
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<td class="memname">void test2 </td>
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<td>(</td>
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<td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
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<p>Test determinant computation using LU decomposition </p>
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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>
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<div class="fragment"><div class="line"><span class="lineno"> 66</span> {</div>
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<div class="line"><span class="lineno"> 67</span> std::cout << <span class="stringliteral">"Determinant test 1..."</span>;</div>
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<div class="line"><span class="lineno"> 68</span> <a class="code hl_typedef" href="../../d1/dbe/lu__decomposition_8h.html#ac029b636b353cefbb18b2fcc71e427e4">matrix<int></a> A1({{1, 2, 3}, {4, 9, 6}, {7, 8, 9}});</div>
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<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>
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<div class="line"><span class="lineno"> 70</span> std::cout << <span class="stringliteral">"passed\n"</span>;</div>
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<div class="line"><span class="lineno"> 71</span> </div>
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<div class="line"><span class="lineno"> 72</span> std::cout << <span class="stringliteral">"Determinant test 2..."</span>;</div>
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<div class="line"><span class="lineno"> 73</span> <a class="code hl_typedef" href="../../d1/dbe/lu__decomposition_8h.html#ac029b636b353cefbb18b2fcc71e427e4">matrix<int></a> A2({{1, 2, 3}, {4, 5, 6}, {7, 8, 9}});</div>
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<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>
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<div class="line"><span class="lineno"> 75</span> std::cout << <span class="stringliteral">"passed\n"</span>;</div>
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<div class="line"><span class="lineno"> 76</span> </div>
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<div class="line"><span class="lineno"> 77</span> std::cout << <span class="stringliteral">"Determinant test 3..."</span>;</div>
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<div class="line"><span class="lineno"> 78</span> <a class="code hl_typedef" href="../../d1/dbe/lu__decomposition_8h.html#ac029b636b353cefbb18b2fcc71e427e4">matrix<float></a> A3({{1.2, 2.3, 3.4}, {4.5, 5.6, 6.7}, {7.8, 8.9, 9.0}});</div>
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<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>
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<div class="line"><span class="lineno"> 80</span> std::cout << <span class="stringliteral">"passed\n"</span>;</div>
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<div class="line"><span class="lineno"> 81</span>}</div>
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<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< T > &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>
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