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<div class="headertitle"><div class="title">qr_eigen_values.cpp File Reference</div></div>
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<div class="contents">
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<p>Compute real eigen values and eigen vectors of a symmetric matrix using <a href="https://en.wikipedia.org/wiki/QR_decomposition" target="_blank">QR decomposition</a> method.
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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 <cmath></code><br />
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<code>#include <cstdlib></code><br />
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<code>#include <ctime></code><br />
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<code>#include <iostream></code><br />
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<code>#include "<a class="el" href="../../d4/d68/qr__decompose_8h_source.html">./qr_decompose.h</a>"</code><br />
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</div><div class="textblock"><div class="dynheader">
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Include dependency graph for qr_eigen_values.cpp:</div>
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<div class="dyncontent">
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<div class="center"><iframe scrolling="no" loading="lazy" frameborder="0" src="../../d4/d72/qr__eigen__values_8cpp__incl.svg" width="626" height="199"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
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<p><a href="../../de/d75/qr__eigen__values_8cpp_source.html">Go to the source code of this file.</a></p>
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<table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 id="header-namespaces" class="groupheader"><a id="namespaces" name="namespaces"></a>
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Namespaces</h2></td></tr>
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<tr class="memitem:qr_5Falgorithm" id="r_qr_5Falgorithm"><td class="memItemLeft" align="right" valign="top">namespace  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d2/d3b/namespaceqr__algorithm.html">qr_algorithm</a></td></tr>
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<tr class="memdesc:d2/d3b/namespaceqr__algorithm"><td class="mdescLeft"> </td><td class="mdescRight">Functions to compute <a href="https://en.wikipedia.org/wiki/QR_decomposition" target="_blank">QR decomposition</a> of any rectangular matrix. <br /></td></tr>
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</table><table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 id="header-define-members" class="groupheader"><a id="define-members" name="define-members"></a>
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Macros</h2></td></tr>
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<tr class="memitem:aee57a411f07599034f5ceb8cc7d65b40" id="r_aee57a411f07599034f5ceb8cc7d65b40"><td class="memItemLeft" align="right" valign="top">#define </td><td class="memItemRight" valign="bottom"><a class="el" href="#aee57a411f07599034f5ceb8cc7d65b40">LIMS</a>   9</td></tr>
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</table><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:a9bbf469d5525a816b0d6ca812119093d" id="r_a9bbf469d5525a816b0d6ca812119093d"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="#a9bbf469d5525a816b0d6ca812119093d">create_matrix</a> (std::valarray< std::valarray< double > > *A)</td></tr>
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<tr class="memitem:abb8bf4c55e10685a5eb2ad3797fde1ae" id="r_abb8bf4c55e10685a5eb2ad3797fde1ae"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="#abb8bf4c55e10685a5eb2ad3797fde1ae">mat_mul</a> (const std::valarray< std::valarray< double > > &A, const std::valarray< std::valarray< double > > &B, std::valarray< std::valarray< double > > *OUT)</td></tr>
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<tr class="memitem:a28e2fa3e803abaea6c568dc45d69d8cc" id="r_a28e2fa3e803abaea6c568dc45d69d8cc"><td class="memItemLeft" align="right" valign="top">std::valarray< double > </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d2/d3b/namespaceqr__algorithm.html#a28e2fa3e803abaea6c568dc45d69d8cc">qr_algorithm::eigen_values</a> (std::valarray< std::valarray< double > > *A, bool print_intermediates=false)</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:a3c04138a5bfe5d72780bb7e82a18e627" id="r_a3c04138a5bfe5d72780bb7e82a18e627"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="#a3c04138a5bfe5d72780bb7e82a18e627">main</a> (int argc, char **argv)</td></tr>
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<tr class="memitem:adfbdf47277c8cfee229b05b72f1f7834" id="r_adfbdf47277c8cfee229b05b72f1f7834"><td class="memTemplParams" colspan="2">template<typename T> </td></tr>
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<tr class="memitem:adfbdf47277c8cfee229b05b72f1f7834 template"><td class="memItemLeft" align="right" valign="top">std::ostream & </td><td class="memItemRight" valign="bottom"><a class="el" href="#adfbdf47277c8cfee229b05b72f1f7834">operator<<</a> (std::ostream &out, std::valarray< std::valarray< T > > const &v)</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>Compute real eigen values and eigen vectors of a symmetric matrix using <a href="https://en.wikipedia.org/wiki/QR_decomposition" target="_blank">QR decomposition</a> method. </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="../../de/d75/qr__eigen__values_8cpp_source.html">qr_eigen_values.cpp</a>.</p>
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</div><a name="doc-define-members" id="doc-define-members"></a><h2 id="header-doc-define-members" class="groupheader">Macro Definition Documentation</h2>
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<a id="aee57a411f07599034f5ceb8cc7d65b40" name="aee57a411f07599034f5ceb8cc7d65b40"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#aee57a411f07599034f5ceb8cc7d65b40">◆ </a></span>LIMS</h2>
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<table class="memname">
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<td class="memname">#define LIMS   9</td>
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</tr>
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</table>
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</div><div class="memdoc">
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<p>limit of range of matrix values </p>
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<p class="definition">Definition at line <a class="el" href="../../de/d75/qr__eigen__values_8cpp_source.html#l00020">20</a> of file <a class="el" href="../../de/d75/qr__eigen__values_8cpp_source.html">qr_eigen_values.cpp</a>.</p>
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</div>
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</div>
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<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="a9bbf469d5525a816b0d6ca812119093d" name="a9bbf469d5525a816b0d6ca812119093d"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a9bbf469d5525a816b0d6ca812119093d">◆ </a></span>create_matrix()</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">void create_matrix </td>
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<td>(</td>
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<td class="paramtype">std::valarray< std::valarray< double > > *</td> <td class="paramname"><span class="paramname"><em>A</em></span></td><td>)</td>
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<td></td>
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</tr>
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</div><div class="memdoc">
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<p>create a symmetric square matrix of given size with random elements. A symmetric square matrix will <em>always</em> have real eigen values.</p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramdir">[out]</td><td class="paramname">A</td><td>matrix to create (must be pre-allocated in memory) </td></tr>
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</table>
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</dd>
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</dl>
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<p class="definition">Definition at line <a class="el" href="../../de/d75/qr__eigen__values_8cpp_source.html#l00028">28</a> of file <a class="el" href="../../de/d75/qr__eigen__values_8cpp_source.html">qr_eigen_values.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 28</span> {</div>
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<div class="line"><span class="lineno"> 29</span> <span class="keywordtype">int</span> i, j, tmp, lim2 = <a class="code hl_define" href="#aee57a411f07599034f5ceb8cc7d65b40">LIMS</a> >> 1;</div>
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<div class="line"><span class="lineno"> 30</span> <span class="keywordtype">int</span> N = A->size();</div>
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<div class="line"><span class="lineno"> 31</span> </div>
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<div class="line"><span class="lineno"> 32</span><span class="preprocessor">#ifdef _OPENMP</span></div>
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<div class="line"><span class="lineno"> 33</span><span class="preprocessor">#pragma omp for</span></div>
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<div class="line"><span class="lineno"> 34</span><span class="preprocessor">#endif</span></div>
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<div class="line"><span class="lineno"> 35</span> <span class="keywordflow">for</span> (i = 0; i < N; i++) {</div>
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<div class="line"><span class="lineno"> 36</span> A[0][i][i] = (std::rand() % <a class="code hl_define" href="#aee57a411f07599034f5ceb8cc7d65b40">LIMS</a>) - lim2;</div>
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<div class="line"><span class="lineno"> 37</span> <span class="keywordflow">for</span> (j = i + 1; j < N; j++) {</div>
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<div class="line"><span class="lineno"> 38</span> tmp = (std::rand() % <a class="code hl_define" href="#aee57a411f07599034f5ceb8cc7d65b40">LIMS</a>) - lim2;</div>
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<div class="line"><span class="lineno"> 39</span> A[0][i][j] = tmp; <span class="comment">// summetrically distribute random values</span></div>
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<div class="line"><span class="lineno"> 40</span> A[0][j][i] = tmp;</div>
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<div class="line"><span class="lineno"> 41</span> }</div>
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<div class="line"><span class="lineno"> 42</span> }</div>
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<div class="line"><span class="lineno"> 43</span>}</div>
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<div class="ttc" id="aqr__eigen__values_8cpp_html_aee57a411f07599034f5ceb8cc7d65b40"><div class="ttname"><a href="#aee57a411f07599034f5ceb8cc7d65b40">LIMS</a></div><div class="ttdeci">#define LIMS</div><div class="ttdef"><b>Definition</b> <a href="../../de/d75/qr__eigen__values_8cpp_source.html#l00020">qr_eigen_values.cpp:20</a></div></div>
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</div><!-- fragment -->
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</div>
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</div>
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<a id="a3c04138a5bfe5d72780bb7e82a18e627" name="a3c04138a5bfe5d72780bb7e82a18e627"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a3c04138a5bfe5d72780bb7e82a18e627">◆ </a></span>main()</h2>
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<div class="memitem">
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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">int</td> <td class="paramname"><span class="paramname"><em>argc</em></span>, </td>
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</tr>
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<tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">char **</td> <td class="paramname"><span class="paramname"><em>argv</em></span> )</td>
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</tr>
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</table>
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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="../../de/d75/qr__eigen__values_8cpp_source.html#l00243">243</a> of file <a class="el" href="../../de/d75/qr__eigen__values_8cpp_source.html">qr_eigen_values.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 243</span> {</div>
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<div class="line"><span class="lineno"> 244</span> <span class="keywordtype">int</span> <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> = 5;</div>
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<div class="line"><span class="lineno"> 245</span> <span class="keywordflow">if</span> (argc == 2) {</div>
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<div class="line"><span class="lineno"> 246</span> <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> = atoi(argv[1]);</div>
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<div class="line"><span class="lineno"> 247</span> } <span class="keywordflow">else</span> { <span class="comment">// if invalid input argument is given run tests</span></div>
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<div class="line"><span class="lineno"> 248</span> <a class="code hl_function" href="#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>();</div>
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<div class="line"><span class="lineno"> 249</span> <a class="code hl_function" href="#a0283886819c7c140a023582b7269e2d0">test2</a>();</div>
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<div class="line"><span class="lineno"> 250</span> std::cout << <span class="stringliteral">"Usage: ./qr_eigen_values [mat_size]\n"</span>;</div>
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<div class="line"><span class="lineno"> 251</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><span class="lineno"> 252</span> }</div>
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<div class="line"><span class="lineno"> 253</span> </div>
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<div class="line"><span class="lineno"> 254</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> < 2) {</div>
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<div class="line"><span class="lineno"> 255</span> fprintf(stderr, <span class="stringliteral">"Matrix size should be > 2\n"</span>);</div>
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<div class="line"><span class="lineno"> 256</span> <span class="keywordflow">return</span> -1;</div>
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<div class="line"><span class="lineno"> 257</span> }</div>
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<div class="line"><span class="lineno"> 258</span> </div>
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<div class="line"><span class="lineno"> 259</span> <span class="comment">// initialize random number generator</span></div>
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<div class="line"><span class="lineno"> 260</span> std::srand(std::time(<span class="keyword">nullptr</span>));</div>
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<div class="line"><span class="lineno"> 261</span> </div>
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<div class="line"><span class="lineno"> 262</span> <span class="keywordtype">int</span> i, rows = <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>, columns = <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"> 263</span> </div>
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<div class="line"><span class="lineno"> 264</span> std::valarray<std::valarray<double>> A(rows);</div>
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<div class="line"><span class="lineno"> 265</span> </div>
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<div class="line"><span class="lineno"> 266</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < rows; i++) {</div>
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<div class="line"><span class="lineno"> 267</span> A[i] = std::valarray<double>(columns);</div>
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<div class="line"><span class="lineno"> 268</span> }</div>
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<div class="line"><span class="lineno"> 269</span> </div>
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<div class="line"><span class="lineno"> 270</span> <span class="comment">/* create a random matrix */</span></div>
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<div class="line"><span class="lineno"> 271</span> <a class="code hl_function" href="#a9bbf469d5525a816b0d6ca812119093d">create_matrix</a>(&A);</div>
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<div class="line"><span class="lineno"> 272</span> </div>
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<div class="line"><span class="lineno"> 273</span> std::cout << A << <span class="stringliteral">"\n"</span>;</div>
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<div class="line"><span class="lineno"> 274</span> </div>
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<div class="line"><span class="lineno"> 275</span> clock_t t1 = clock();</div>
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<div class="line"><span class="lineno"> 276</span> std::valarray<double> eigen_vals = <a class="code hl_function" href="../../d2/d3b/namespaceqr__algorithm.html#a28e2fa3e803abaea6c568dc45d69d8cc">qr_algorithm::eigen_values</a>(&A);</div>
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<div class="line"><span class="lineno"> 277</span> <span class="keywordtype">double</span> dtime = <span class="keyword">static_cast<</span><span class="keywordtype">double</span><span class="keyword">></span>(clock() - t1) / CLOCKS_PER_SEC;</div>
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<div class="line"><span class="lineno"> 278</span> </div>
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<div class="line"><span class="lineno"> 279</span> std::cout << <span class="stringliteral">"Eigen vals: "</span>;</div>
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<div class="line"><span class="lineno"> 280</span> <span class="keywordflow">for</span> (i = 0; i < <a class="code hl_variable" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) std::cout << eigen_vals[i] << <span class="stringliteral">"\t"</span>;</div>
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<div class="line"><span class="lineno"> 281</span> std::cout << <span class="stringliteral">"\nTime taken to compute: "</span> << dtime << <span class="stringliteral">" sec\n"</span>;</div>
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<div class="line"><span class="lineno"> 282</span> </div>
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<div class="line"><span class="lineno"> 283</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><span class="lineno"> 284</span>}</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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<div class="ttc" id="anamespaceqr__algorithm_html_a28e2fa3e803abaea6c568dc45d69d8cc"><div class="ttname"><a href="../../d2/d3b/namespaceqr__algorithm.html#a28e2fa3e803abaea6c568dc45d69d8cc">qr_algorithm::eigen_values</a></div><div class="ttdeci">std::valarray< double > eigen_values(std::valarray< std::valarray< double > > *A, bool print_intermediates=false)</div><div class="ttdef"><b>Definition</b> <a href="../../de/d75/qr__eigen__values_8cpp_source.html#l00098">qr_eigen_values.cpp:98</a></div></div>
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<div class="ttc" id="aqr__eigen__values_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="../../de/d75/qr__eigen__values_8cpp_source.html#l00210">qr_eigen_values.cpp:210</a></div></div>
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<div class="ttc" id="aqr__eigen__values_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="../../de/d75/qr__eigen__values_8cpp_source.html#l00177">qr_eigen_values.cpp:177</a></div></div>
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<div class="ttc" id="aqr__eigen__values_8cpp_html_a9bbf469d5525a816b0d6ca812119093d"><div class="ttname"><a href="#a9bbf469d5525a816b0d6ca812119093d">create_matrix</a></div><div class="ttdeci">void create_matrix(std::valarray< std::valarray< double > > *A)</div><div class="ttdef"><b>Definition</b> <a href="../../de/d75/qr__eigen__values_8cpp_source.html#l00028">qr_eigen_values.cpp:28</a></div></div>
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<a id="abb8bf4c55e10685a5eb2ad3797fde1ae" name="abb8bf4c55e10685a5eb2ad3797fde1ae"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#abb8bf4c55e10685a5eb2ad3797fde1ae">◆ </a></span>mat_mul()</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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<td class="memname">void mat_mul </td>
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<td>(</td>
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<td class="paramtype">const std::valarray< std::valarray< double > > &</td> <td class="paramname"><span class="paramname"><em>A</em></span>, </td>
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</tr>
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<tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">const std::valarray< std::valarray< double > > &</td> <td class="paramname"><span class="paramname"><em>B</em></span>, </td>
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</tr>
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<tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">std::valarray< std::valarray< double > > *</td> <td class="paramname"><span class="paramname"><em>OUT</em></span> )</td>
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<p>Perform multiplication of two matrices.</p><ul>
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<li>R2 must be equal to C1</li>
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<li>Resultant matrix size should be R1xC2 <dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramdir">[in]</td><td class="paramname">A</td><td>first matrix to multiply </td></tr>
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<tr><td class="paramdir">[in]</td><td class="paramname">B</td><td>second matrix to multiply </td></tr>
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<tr><td class="paramdir">[out]</td><td class="paramname">OUT</td><td>output matrix (must be pre-allocated) </td></tr>
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</table>
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</dd>
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</dl>
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<dl class="section return"><dt>Returns</dt><dd>pointer to resultant matrix </dd></dl>
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</li>
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</ul>
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<p class="definition">Definition at line <a class="el" href="../../de/d75/qr__eigen__values_8cpp_source.html#l00054">54</a> of file <a class="el" href="../../de/d75/qr__eigen__values_8cpp_source.html">qr_eigen_values.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 56</span> {</div>
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<div class="line"><span class="lineno"> 57</span> <span class="keywordtype">int</span> R1 = A.size();</div>
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<div class="line"><span class="lineno"> 58</span> <span class="keywordtype">int</span> C1 = A[0].size();</div>
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<div class="line"><span class="lineno"> 59</span> <span class="keywordtype">int</span> R2 = B.size();</div>
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<div class="line"><span class="lineno"> 60</span> <span class="keywordtype">int</span> C2 = B[0].size();</div>
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<div class="line"><span class="lineno"> 61</span> <span class="keywordflow">if</span> (C1 != R2) {</div>
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<div class="line"><span class="lineno"> 62</span> perror(<span class="stringliteral">"Matrix dimensions mismatch!"</span>);</div>
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<div class="line"><span class="lineno"> 63</span> <span class="keywordflow">return</span>;</div>
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<div class="line"><span class="lineno"> 64</span> }</div>
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<div class="line"><span class="lineno"> 65</span> </div>
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<div class="line"><span class="lineno"> 66</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < R1; i++) {</div>
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<div class="line"><span class="lineno"> 67</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < C2; j++) {</div>
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<div class="line"><span class="lineno"> 68</span> OUT[0][i][j] = 0.f;</div>
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<div class="line"><span class="lineno"> 69</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> < C1; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++) {</div>
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<div class="line"><span class="lineno"> 70</span> OUT[0][i][j] += A[i][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>] * B[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>][j];</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> }</div>
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<div class="line"><span class="lineno"> 73</span> }</div>
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<div class="line"><span class="lineno"> 74</span>}</div>
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<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a1b74d828b33760094906797042b89442"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition</b> <a href="../../d4/d18/composite__simpson__rule_8cpp_source.html#l00117">composite_simpson_rule.cpp:117</a></div></div>
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<a id="adfbdf47277c8cfee229b05b72f1f7834" name="adfbdf47277c8cfee229b05b72f1f7834"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#adfbdf47277c8cfee229b05b72f1f7834">◆ </a></span>operator<<()</h2>
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<div class="memitem">
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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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<td class="memname">std::ostream & qr_algorithm::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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</tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">std::valarray< std::valarray< 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="../../d4/d68/qr__decompose_8h_source.html#l00033">33</a> of file <a class="el" href="../../d4/d68/qr__decompose_8h_source.html">qr_decompose.h</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 34</span> {</div>
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<div class="line"><span class="lineno"> 35</span> <span class="keyword">const</span> <span class="keywordtype">int</span> width = 12;</div>
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<div class="line"><span class="lineno"> 36</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"> 37</span> </div>
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<div class="line"><span class="lineno"> 38</span> out.precision(4);</div>
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<div class="line"><span class="lineno"> 39</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"> 40</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"> 41</span> out << std::right << std::setw(width) << std::setfill(separator)</div>
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<div class="line"><span class="lineno"> 42</span> << v[row][col];</div>
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<div class="line"><span class="lineno"> 43</span> out << std::endl;</div>
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<div class="line"><span class="lineno"> 44</span> }</div>
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<div class="line"><span class="lineno"> 45</span> </div>
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<div class="line"><span class="lineno"> 46</span> <span class="keywordflow">return</span> out;</div>
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<div class="line"><span class="lineno"> 47</span>}</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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<div class="memitem">
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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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<p>test function to compute eigen values of a 2x2 matrix </p><p class="formulaDsp">
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\[\begin{bmatrix}
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5 & 7\\
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7 & 11
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\end{bmatrix}\]
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</p>
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<p> which are approximately, {15.56158, 0.384227} </p>
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<p class="definition">Definition at line <a class="el" href="../../de/d75/qr__eigen__values_8cpp_source.html#l00177">177</a> of file <a class="el" href="../../de/d75/qr__eigen__values_8cpp_source.html">qr_eigen_values.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 177</span> {</div>
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<div class="line"><span class="lineno"> 178</span> std::valarray<std::valarray<double>> X = {{5, 7}, {7, 11}};</div>
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<div class="line"><span class="lineno"> 179</span> <span class="keywordtype">double</span> y[] = {15.56158, 0.384227}; <span class="comment">// corresponding y-values</span></div>
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<div class="line"><span class="lineno"> 180</span> </div>
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<div class="line"><span class="lineno"> 181</span> std::cout << <span class="stringliteral">"------- Test 1 -------"</span> << std::endl;</div>
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<div class="line"><span class="lineno"> 182</span> std::valarray<double> eig_vals = <a class="code hl_function" href="../../d2/d3b/namespaceqr__algorithm.html#a28e2fa3e803abaea6c568dc45d69d8cc">qr_algorithm::eigen_values</a>(&X);</div>
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<div class="line"><span class="lineno"> 183</span> </div>
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<div class="line"><span class="lineno"> 184</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < 2; i++) {</div>
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<div class="line"><span class="lineno"> 185</span> std::cout << i + 1 << <span class="stringliteral">"/2 Checking for "</span> << y[i] << <span class="stringliteral">" --> "</span>;</div>
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<div class="line"><span class="lineno"> 186</span> <span class="keywordtype">bool</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <span class="keyword">false</span>;</div>
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<div class="line"><span class="lineno"> 187</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < 2 && !<a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>; j++) {</div>
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<div class="line"><span class="lineno"> 188</span> <span class="keywordflow">if</span> (std::abs(y[i] - eig_vals[j]) < 0.1) {</div>
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<div class="line"><span class="lineno"> 189</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <span class="keyword">true</span>;</div>
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<div class="line"><span class="lineno"> 190</span> std::cout << <span class="stringliteral">"("</span> << eig_vals[j] << <span class="stringliteral">") "</span>;</div>
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<div class="line"><span class="lineno"> 191</span> }</div>
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<div class="line"><span class="lineno"> 192</span> }</div>
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<div class="line"><span class="lineno"> 193</span> assert(result); <span class="comment">// ensure that i^th expected eigen value was computed</span></div>
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<div class="line"><span class="lineno"> 194</span> std::cout << <span class="stringliteral">"found\n"</span>;</div>
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<div class="line"><span class="lineno"> 195</span> }</div>
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<div class="line"><span class="lineno"> 196</span> std::cout << <span class="stringliteral">"Test 1 Passed\n\n"</span>;</div>
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<div class="line"><span class="lineno"> 197</span>}</div>
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<div class="ttc" id="afibonacci__sum_8cpp_html_aadb40ac4c74a7efc0680b83eeee138aa"><div class="ttname"><a href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">math::fibonacci_sum::result</a></div><div class="ttdeci">uint64_t result(uint64_t n)</div><div class="ttdef"><b>Definition</b> <a href="../../de/dc3/fibonacci__sum_8cpp_source.html#l00077">fibonacci_sum.cpp:77</a></div></div>
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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 function to compute eigen values of a 2x2 matrix </p><p class="formulaDsp">
|
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\[\begin{bmatrix}
|
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-4& 4& 2& 0& -3\\
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4& -4& 4& -3& -1\\
|
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2& 4& 4& 3& -3\\
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0& -3& 3& -1&-1\\
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-3& -1& -3& -3& 0
|
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\end{bmatrix}\]
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</p>
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<p> which are approximately, {9.27648, -9.26948, 2.0181, -1.03516, -5.98994} </p>
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<p class="definition">Definition at line <a class="el" href="../../de/d75/qr__eigen__values_8cpp_source.html#l00210">210</a> of file <a class="el" href="../../de/d75/qr__eigen__values_8cpp_source.html">qr_eigen_values.cpp</a>.</p>
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<div class="fragment"><div class="line"><span class="lineno"> 210</span> {</div>
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<div class="line"><span class="lineno"> 211</span> std::valarray<std::valarray<double>> X = {{-4, 4, 2, 0, -3},</div>
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<div class="line"><span class="lineno"> 212</span> {4, -4, 4, -3, -1},</div>
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<div class="line"><span class="lineno"> 213</span> {2, 4, 4, 3, -3},</div>
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<div class="line"><span class="lineno"> 214</span> {0, -3, 3, -1, -3},</div>
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<div class="line"><span class="lineno"> 215</span> {-3, -1, -3, -3, 0}};</div>
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<div class="line"><span class="lineno"> 216</span> <span class="keywordtype">double</span> y[] = {9.27648, -9.26948, 2.0181, -1.03516,</div>
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<div class="line"><span class="lineno"> 217</span> -5.98994}; <span class="comment">// corresponding y-values</span></div>
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<div class="line"><span class="lineno"> 218</span> </div>
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<div class="line"><span class="lineno"> 219</span> std::cout << <span class="stringliteral">"------- Test 2 -------"</span> << std::endl;</div>
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<div class="line"><span class="lineno"> 220</span> std::valarray<double> eig_vals = <a class="code hl_function" href="../../d2/d3b/namespaceqr__algorithm.html#a28e2fa3e803abaea6c568dc45d69d8cc">qr_algorithm::eigen_values</a>(&X);</div>
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<div class="line"><span class="lineno"> 221</span> </div>
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<div class="line"><span class="lineno"> 222</span> std::cout << X << <span class="stringliteral">"\n"</span></div>
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<div class="line"><span class="lineno"> 223</span> << <span class="stringliteral">"Eigen values: "</span> << eig_vals << <span class="stringliteral">"\n"</span>;</div>
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<div class="line"><span class="lineno"> 224</span> </div>
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<div class="line"><span class="lineno"> 225</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < 5; i++) {</div>
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<div class="line"><span class="lineno"> 226</span> std::cout << i + 1 << <span class="stringliteral">"/5 Checking for "</span> << y[i] << <span class="stringliteral">" --> "</span>;</div>
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<div class="line"><span class="lineno"> 227</span> <span class="keywordtype">bool</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <span class="keyword">false</span>;</div>
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<div class="line"><span class="lineno"> 228</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < 5 && !<a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>; j++) {</div>
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<div class="line"><span class="lineno"> 229</span> <span class="keywordflow">if</span> (std::abs(y[i] - eig_vals[j]) < 0.1) {</div>
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<div class="line"><span class="lineno"> 230</span> <a class="code hl_function" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <span class="keyword">true</span>;</div>
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<div class="line"><span class="lineno"> 231</span> std::cout << <span class="stringliteral">"("</span> << eig_vals[j] << <span class="stringliteral">") "</span>;</div>
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<div class="line"><span class="lineno"> 232</span> }</div>
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<div class="line"><span class="lineno"> 233</span> }</div>
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<div class="line"><span class="lineno"> 234</span> assert(result); <span class="comment">// ensure that i^th expected eigen value was computed</span></div>
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<div class="line"><span class="lineno"> 235</span> std::cout << <span class="stringliteral">"found\n"</span>;</div>
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<div class="line"><span class="lineno"> 236</span> }</div>
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<div class="line"><span class="lineno"> 237</span> std::cout << <span class="stringliteral">"Test 2 Passed\n\n"</span>;</div>
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<div class="line"><span class="lineno"> 238</span>}</div>
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