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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">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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Include dependency graph for qr_eigen_values.cpp:</div>
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Namespaces</h2></td></tr>
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<tr class="memitem:d2/d3b/namespaceqr__algorithm"><td class="memItemLeft" align="right" valign="top">  </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">QR decomposition</a> of any rectangular matrix. <br /></td></tr>
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Macros</h2></td></tr>
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<tr class="memitem:aee57a411f07599034f5ceb8cc7d65b40"><td class="memItemLeft" align="right" valign="top">#define </td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d75/qr__eigen__values_8cpp.html#aee57a411f07599034f5ceb8cc7d65b40">LIMS</a>   9</td></tr>
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Functions</h2></td></tr>
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<tr class="memitem:a33cb0a68c36aa26fd599c7c66da86ed7"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d75/qr__eigen__values_8cpp.html#a33cb0a68c36aa26fd599c7c66da86ed7">create_matrix</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< double >> *A)</td></tr>
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<tr class="memitem:a7558fd7779bf207157ced66f275951a0"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d75/qr__eigen__values_8cpp.html#a7558fd7779bf207157ced66f275951a0">mat_mul</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< double >> &A, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< double >> &B, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< double >> *OUT)</td></tr>
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<tr class="separator:a7558fd7779bf207157ced66f275951a0"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a763896dbb4a7e95c4a1e614ac0819d66"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< double > </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d2/d3b/namespaceqr__algorithm.html#a763896dbb4a7e95c4a1e614ac0819d66">qr_algorithm::eigen_values</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< double >> *A, bool print_intermediates=false)</td></tr>
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<tr class="memitem:a1440a7779ac56f47a3f355ce4a8c7da0"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d75/qr__eigen__values_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a> ()</td></tr>
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<tr class="memitem:a0283886819c7c140a023582b7269e2d0"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d75/qr__eigen__values_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a> ()</td></tr>
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<tr class="memitem:a3c04138a5bfe5d72780bb7e82a18e627"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d75/qr__eigen__values_8cpp.html#a3c04138a5bfe5d72780bb7e82a18e627">main</a> (int argc, char **argv)</td></tr>
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</table>
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<a name="details" id="details"></a><h2 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">QR decomposition</a> method. </p>
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<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a> </dd></dl>
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</div><h2 class="groupheader">Macro Definition Documentation</h2>
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<a id="aee57a411f07599034f5ceb8cc7d65b40"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#aee57a411f07599034f5ceb8cc7d65b40">◆ </a></span>LIMS</h2>
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<td class="memname">#define LIMS   9</td>
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</div><div class="memdoc">
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<p>limit of range of matrix values </p>
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</div>
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</div>
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<h2 class="groupheader">Function Documentation</h2>
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<a id="a33cb0a68c36aa26fd599c7c66da86ed7"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a33cb0a68c36aa26fd599c7c66da86ed7">◆ </a></span>create_matrix()</h2>
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<td class="memname">void create_matrix </td>
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<td>(</td>
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<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< double >> * </td>
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<td class="paramname"><em>A</em></td><td>)</td>
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<td></td>
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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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<div class="fragment"><div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  {</div>
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<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  <span class="keywordtype">int</span> i, j, tmp, lim2 = <a class="code" href="../../de/d75/qr__eigen__values_8cpp.html#aee57a411f07599034f5ceb8cc7d65b40">LIMS</a> >> 1;</div>
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<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  <span class="keywordtype">int</span> <a class="code" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = A->size();</div>
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<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  </div>
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<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="preprocessor">#ifdef _OPENMP</span></div>
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<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="preprocessor">#pragma omp for</span></div>
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<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="preprocessor">#endif</span></div>
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<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  <span class="keywordflow">for</span> (i = 0; i < <a class="code" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
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<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  A[0][i][i] = (<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % <a class="code" href="../../de/d75/qr__eigen__values_8cpp.html#aee57a411f07599034f5ceb8cc7d65b40">LIMS</a>) - lim2;</div>
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<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  <span class="keywordflow">for</span> (j = i + 1; j < <a class="code" href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; j++) {</div>
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<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  tmp = (<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % <a class="code" href="../../de/d75/qr__eigen__values_8cpp.html#aee57a411f07599034f5ceb8cc7d65b40">LIMS</a>) - lim2;</div>
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<div class="line"><a name="l00039"></a><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"><a name="l00040"></a><span class="lineno"> 40</span>  A[0][j][i] = tmp;</div>
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<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  }</div>
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<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  }</div>
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<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> }</div>
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<div class="ttc" id="adata__structures_2sparse__table_8cpp_html_a10f3ffb3f6f7e1b83d556b9c8de89a5d"><div class="ttname"><a href="../../d6/d42/data__structures_2sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">data_structures::sparse_table::N</a></div><div class="ttdeci">constexpr uint32_t N</div><div class="ttdoc">A struct to represent sparse table for min() as their invariant function, for the given array A....</div><div class="ttdef"><b>Definition:</b> sparse_table.cpp:47</div></div>
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<div class="ttc" id="aqr__eigen__values_8cpp_html_aee57a411f07599034f5ceb8cc7d65b40"><div class="ttname"><a href="../../de/d75/qr__eigen__values_8cpp.html#aee57a411f07599034f5ceb8cc7d65b40">LIMS</a></div><div class="ttdeci">#define LIMS</div><div class="ttdef"><b>Definition:</b> qr_eigen_values.cpp:20</div></div>
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<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>
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</div><!-- fragment --><div class="dynheader">
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Here is the call graph for this function:</div>
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<div class="dyncontent">
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../de/d75/qr__eigen__values_8cpp_a33cb0a68c36aa26fd599c7c66da86ed7_cgraph.svg" width="235" height="38"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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<a id="a3c04138a5bfe5d72780bb7e82a18e627"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a3c04138a5bfe5d72780bb7e82a18e627">◆ </a></span>main()</h2>
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<td class="memname">int main </td>
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<td>(</td>
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<td class="paramname"><em>argc</em>, </td>
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<td>)</td>
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<p>main function </p>
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<div class="fragment"><div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  {</div>
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<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  <span class="keywordtype">int</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> = 5;</div>
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<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  <span class="keywordflow">if</span> (argc == 2) {</div>
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<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atoi.html">atoi</a>(argv[1]);</div>
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<div class="line"><a name="l00247"></a><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"><a name="l00248"></a><span class="lineno"> 248</span>  <a class="code" href="../../de/d75/qr__eigen__values_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>();</div>
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<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  <a class="code" href="../../de/d75/qr__eigen__values_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>();</div>
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<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Usage: ./qr_eigen_values [mat_size]\n"</span>;</div>
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<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  }</div>
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<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  </div>
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<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  <span class="keywordflow">if</span> (<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a> < 2) {</div>
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<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/fprintf.html">fprintf</a>(stderr, <span class="stringliteral">"Matrix size should be > 2\n"</span>);</div>
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<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  <span class="keywordflow">return</span> -1;</div>
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<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  }</div>
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<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  </div>
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<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  <span class="comment">// initialize random number generator</span></div>
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<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>));</div>
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<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  </div>
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<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  <span class="keywordtype">int</span> i, rows = <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>, columns = <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>;</div>
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<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  </div>
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<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray<std::valarray<double></a>> A(rows);</div>
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<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  </div>
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<div class="line"><a name="l00266"></a><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"><a name="l00267"></a><span class="lineno"> 267</span>  A[i] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray<double></a>(columns);</div>
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<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  }</div>
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<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  </div>
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<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  <span class="comment">/* create a random matrix */</span></div>
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<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  <a class="code" href="../../de/d75/qr__eigen__values_8cpp.html#a33cb0a68c36aa26fd599c7c66da86ed7">create_matrix</a>(&A);</div>
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<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  </div>
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<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << A << <span class="stringliteral">"\n"</span>;</div>
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<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  </div>
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<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  clock_t t1 = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">clock</a>();</div>
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<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray<double></a> eigen_vals = <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#a763896dbb4a7e95c4a1e614ac0819d66">qr_algorithm::eigen_values</a>(&A);</div>
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<div class="line"><a name="l00277"></a><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>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">clock</a>() - t1) / CLOCKS_PER_SEC;</div>
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<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  </div>
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<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Eigen vals: "</span>;</div>
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<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  <span class="keywordflow">for</span> (i = 0; i < <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a>; i++) <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << eigen_vals[i] << <span class="stringliteral">"\t"</span>;</div>
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<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"\nTime taken to compute: "</span> << dtime << <span class="stringliteral">" sec\n"</span>;</div>
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<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  </div>
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<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a name="l00284"></a><span class="lineno"> 284</span> }</div>
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<div class="ttc" id="aatoi_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/byte/atoi.html">std::atoi</a></div><div class="ttdeci">T atoi(T... args)</div></div>
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<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>
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<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>
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<div class="ttc" id="afprintf_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/c/fprintf.html">std::fprintf</a></div><div class="ttdeci">T fprintf(T... args)</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> matrix_exponentiation.cpp:45</div></div>
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<div class="ttc" id="anamespaceqr__algorithm_html_a763896dbb4a7e95c4a1e614ac0819d66"><div class="ttname"><a href="../../d2/d3b/namespaceqr__algorithm.html#a763896dbb4a7e95c4a1e614ac0819d66">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> qr_eigen_values.cpp:98</div></div>
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<div class="ttc" id="aqr__eigen__values_8cpp_html_a0283886819c7c140a023582b7269e2d0"><div class="ttname"><a href="../../de/d75/qr__eigen__values_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a></div><div class="ttdeci">void test2()</div><div class="ttdef"><b>Definition:</b> qr_eigen_values.cpp:210</div></div>
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<div class="ttc" id="aqr__eigen__values_8cpp_html_a1440a7779ac56f47a3f355ce4a8c7da0"><div class="ttname"><a href="../../de/d75/qr__eigen__values_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a></div><div class="ttdeci">void test1()</div><div class="ttdef"><b>Definition:</b> qr_eigen_values.cpp:177</div></div>
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<div class="ttc" id="aqr__eigen__values_8cpp_html_a33cb0a68c36aa26fd599c7c66da86ed7"><div class="ttname"><a href="../../de/d75/qr__eigen__values_8cpp.html#a33cb0a68c36aa26fd599c7c66da86ed7">create_matrix</a></div><div class="ttdeci">void create_matrix(std::valarray< std::valarray< double >> *A)</div><div class="ttdef"><b>Definition:</b> qr_eigen_values.cpp:28</div></div>
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<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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<div class="ttc" id="atime_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a></div><div class="ttdeci">T time(T... args)</div></div>
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<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>
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Here is the call graph for this function:</div>
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<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../de/d75/qr__eigen__values_8cpp_a3c04138a5bfe5d72780bb7e82a18e627_cgraph.svg" width="100%" height="518"><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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<a id="a7558fd7779bf207157ced66f275951a0"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a7558fd7779bf207157ced66f275951a0">◆ </a></span>mat_mul()</h2>
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<div class="memitem">
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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 <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< double >> & </td>
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<td class="paramname"><em>A</em>, </td>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< double >> & </td>
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<td class="paramname"><em>B</em>, </td>
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<td></td>
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<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< double >> * </td>
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<td class="paramname"><em>OUT</em> </td>
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<td>)</td>
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</div><div class="memdoc">
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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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<div class="fragment"><div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  {</div>
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<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  <span class="keywordtype">int</span> R1 = A.size();</div>
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<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="keywordtype">int</span> C1 = A[0].size();</div>
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<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  <span class="keywordtype">int</span> R2 = B.size();</div>
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<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <span class="keywordtype">int</span> C2 = B[0].size();</div>
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<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  <span class="keywordflow">if</span> (C1 != R2) {</div>
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<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/perror.html">perror</a>(<span class="stringliteral">"Matrix dimensions mismatch!"</span>);</div>
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<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="keywordflow">return</span>;</div>
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<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  }</div>
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<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  </div>
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<div class="line"><a name="l00066"></a><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"><a name="l00067"></a><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"><a name="l00068"></a><span class="lineno"> 68</span>  OUT[0][i][j] = 0.f;</div>
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<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k < C1; k++) {</div>
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<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  OUT[0][i][j] += A[i][k] * B[k][j];</div>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  }</div>
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<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  }</div>
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<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  }</div>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</span> }</div>
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<div class="ttc" id="aperror_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/c/perror.html">std::perror</a></div><div class="ttdeci">T perror(T... args)</div></div>
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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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<p>test function to compute eigen values of a 2x2 matrix </p><p class="formulaDsp">
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\[\begin{bmatrix} 5 & 7\\ 7 & 11 \end{bmatrix}\]
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</p>
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<p> which are approximately, {15.56158, 0.384227} </p>
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<div class="fragment"><div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  {</div>
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<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray<std::valarray<double></a>> X = {{5, 7}, {7, 11}};</div>
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<div class="line"><a name="l00179"></a><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"><a name="l00180"></a><span class="lineno"> 180</span>  </div>
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<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"------- Test 1 -------"</span> << <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray<double></a> eig_vals = <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#a763896dbb4a7e95c4a1e614ac0819d66">qr_algorithm::eigen_values</a>(&X);</div>
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<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  </div>
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<div class="line"><a name="l00184"></a><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"><a name="l00185"></a><span class="lineno"> 185</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << i + 1 << <span class="stringliteral">"/2 Checking for "</span> << y[i] << <span class="stringliteral">" --> "</span>;</div>
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<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  <span class="keywordtype">bool</span> <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < 2 && !<a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>; j++) {</div>
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<div class="line"><a name="l00188"></a><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"><a name="l00189"></a><span class="lineno"> 189</span>  <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <span class="keyword">true</span>;</div>
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<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"("</span> << eig_vals[j] << <span class="stringliteral">") "</span>;</div>
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<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  }</div>
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<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  }</div>
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<div class="line"><a name="l00193"></a><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"><a name="l00194"></a><span class="lineno"> 194</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"found\n"</span>;</div>
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<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  }</div>
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<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Test 1 Passed\n\n"</span>;</div>
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<div class="line"><a name="l00197"></a><span class="lineno"> 197</span> }</div>
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<div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</div></div>
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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> fibonacci_sum.cpp:76</div></div>
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<a id="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"></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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\[\begin{bmatrix} -4& 4& 2& 0& -3\\ 4& -4& 4& -3& -1\\ 2& 4& 4& 3& -3\\ 0& -3& 3& -1&-1\\ -3& -1& -3& -3& 0 \end{bmatrix}\]
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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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<div class="fragment"><div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  {</div>
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<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray<std::valarray<double></a>> X = {{-4, 4, 2, 0, -3},</div>
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<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  {4, -4, 4, -3, -1},</div>
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<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  {2, 4, 4, 3, -3},</div>
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<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  {0, -3, 3, -1, -3},</div>
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<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  {-3, -1, -3, -3, 0}};</div>
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<div class="line"><a name="l00216"></a><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"><a name="l00217"></a><span class="lineno"> 217</span>  -5.98994}; <span class="comment">// corresponding y-values</span></div>
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<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  </div>
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<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"------- Test 2 -------"</span> << <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray<double></a> eig_vals = <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#a763896dbb4a7e95c4a1e614ac0819d66">qr_algorithm::eigen_values</a>(&X);</div>
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<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  </div>
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<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << X << <span class="stringliteral">"\n"</span></div>
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<div class="line"><a name="l00223"></a><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"><a name="l00224"></a><span class="lineno"> 224</span>  </div>
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<div class="line"><a name="l00225"></a><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"><a name="l00226"></a><span class="lineno"> 226</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << i + 1 << <span class="stringliteral">"/5 Checking for "</span> << y[i] << <span class="stringliteral">" --> "</span>;</div>
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<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  <span class="keywordtype">bool</span> <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <span class="keyword">false</span>;</div>
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<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < 5 && !<a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a>; j++) {</div>
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<div class="line"><a name="l00229"></a><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"><a name="l00230"></a><span class="lineno"> 230</span>  <a class="code" href="../../de/dc3/fibonacci__sum_8cpp.html#aadb40ac4c74a7efc0680b83eeee138aa">result</a> = <span class="keyword">true</span>;</div>
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<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"("</span> << eig_vals[j] << <span class="stringliteral">") "</span>;</div>
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<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  }</div>
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<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  }</div>
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<div class="line"><a name="l00234"></a><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"><a name="l00235"></a><span class="lineno"> 235</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"found\n"</span>;</div>
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<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  }</div>
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<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Test 2 Passed\n\n"</span>;</div>
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<div class="line"><a name="l00238"></a><span class="lineno"> 238</span> }</div>
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