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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.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;cmath&gt;</code><br />
<code>#include &lt;cstdlib&gt;</code><br />
<code>#include &lt;ctime&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &quot;<a class="el" href="../../d4/d68/qr__decompose_8h_source.html">./qr_decompose.h</a>&quot;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for qr_eigen_values.cpp:</div>
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<tr class="memitem:d2/d3b/namespaceqr__algorithm"><td class="memItemLeft" align="right" valign="top"> &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d2/d3b/namespaceqr__algorithm.html">qr_algorithm</a></td></tr>
<tr class="memdesc:d2/d3b/namespaceqr__algorithm"><td class="mdescLeft">&#160;</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>
<tr class="memitem:aee57a411f07599034f5ceb8cc7d65b40"><td class="memItemLeft" align="right" valign="top">#define&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d75/qr__eigen__values_8cpp.html#aee57a411f07599034f5ceb8cc7d65b40">LIMS</a>&#160;&#160;&#160;9</td></tr>
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Functions</h2></td></tr>
<tr class="memitem:a33cb0a68c36aa26fd599c7c66da86ed7"><td class="memItemLeft" align="right" valign="top">void&#160;</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>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; *A)</td></tr>
<tr class="separator:a33cb0a68c36aa26fd599c7c66da86ed7"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a7558fd7779bf207157ced66f275951a0"><td class="memItemLeft" align="right" valign="top">void&#160;</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>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; &amp;A, const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; &amp;B, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; *OUT)</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>&lt; double &gt;&#160;</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>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; *A, bool print_intermediates=false)</td></tr>
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<tr class="memitem:a1440a7779ac56f47a3f355ce4a8c7da0"><td class="memItemLeft" align="right" valign="top">void&#160;</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&#160;</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&#160;</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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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<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>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a> </dd></dl>
</div><h2 class="groupheader">Macro Definition Documentation</h2>
<a id="aee57a411f07599034f5ceb8cc7d65b40"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aee57a411f07599034f5ceb8cc7d65b40">&#9670;&nbsp;</a></span>LIMS</h2>
<div class="memitem">
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<td class="memname">#define LIMS&#160;&#160;&#160;9</td>
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</table>
</div><div class="memdoc">
<p>limit of range of matrix values </p>
</div>
</div>
<h2 class="groupheader">Function Documentation</h2>
<a id="a33cb0a68c36aa26fd599c7c66da86ed7"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a33cb0a68c36aa26fd599c7c66da86ed7">&#9670;&nbsp;</a></span>create_matrix()</h2>
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<td class="memname">void create_matrix </td>
<td>(</td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; *&#160;</td>
<td class="paramname"><em>A</em></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<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>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[out]</td><td class="paramname">A</td><td>matrix to create (must be pre-allocated in memory) </td></tr>
</table>
</dd>
</dl>
<div class="fragment"><div class="line"><a name="l00028"></a><span class="lineno"> 28</span>&#160; {</div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>&#160; <span class="keywordtype">int</span> i, j, tmp, lim2 = <a class="code" href="../../de/d75/qr__eigen__values_8cpp.html#aee57a411f07599034f5ceb8cc7d65b40">LIMS</a> &gt;&gt; 1;</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160; <span class="keywordtype">int</span> N = A-&gt;size();</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>&#160; </div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160; <span class="keywordflow">for</span> (i = 0; i &lt; N; i++) {</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160; 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>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; <span class="keywordflow">for</span> (j = i + 1; j &lt; N; j++) {</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160; 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>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; A[0][i][j] = tmp; <span class="comment">// summetrically distribute random values</span></div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; A[0][j][i] = tmp;</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; }</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; }</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160;}</div>
</div><!-- fragment --><div class="dynheader">
Here is the call graph for this function:</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a3c04138a5bfe5d72780bb7e82a18e627">&#9670;&nbsp;</a></span>main()</h2>
<div class="memitem">
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<td class="memname">int main </td>
<td>(</td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>argc</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">char **&#160;</td>
<td class="paramname"><em>argv</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>main function </p>
<div class="fragment"><div class="line"><a name="l00243"></a><span class="lineno"> 243</span>&#160; {</div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>&#160; <span class="keywordtype">int</span> mat_size = 5;</div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>&#160; <span class="keywordflow">if</span> (argc == 2) {</div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>&#160; mat_size = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/byte/atoi.html">atoi</a>(argv[1]);</div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>&#160; } <span class="keywordflow">else</span> { <span class="comment">// if invalid input argument is given run tests</span></div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>&#160; <a class="code" href="../../de/d75/qr__eigen__values_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>();</div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>&#160; <a class="code" href="../../de/d75/qr__eigen__values_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>();</div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Usage: ./qr_eigen_values [mat_size]\n&quot;</span>;</div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>&#160; }</div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>&#160; </div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>&#160; <span class="keywordflow">if</span> (mat_size &lt; 2) {</div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/fprintf.html">fprintf</a>(stderr, <span class="stringliteral">&quot;Matrix size should be &gt; 2\n&quot;</span>);</div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>&#160; <span class="keywordflow">return</span> -1;</div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>&#160; }</div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>&#160; </div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>&#160; <span class="comment">// initialize random number generator</span></div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>));</div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>&#160; </div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>&#160; <span class="keywordtype">int</span> i, rows = mat_size, columns = mat_size;</div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>&#160; </div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::valarray&lt;double&gt;</a>&gt; A(rows);</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>&#160; </div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; rows; i++) {</div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>&#160; A[i] = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a>(columns);</div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>&#160; }</div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>&#160; </div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>&#160; <span class="comment">/* create a random matrix */</span></div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>&#160; <a class="code" href="../../de/d75/qr__eigen__values_8cpp.html#a33cb0a68c36aa26fd599c7c66da86ed7">create_matrix</a>(&amp;A);</div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>&#160; </div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; A &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>&#160; </div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>&#160; clock_t t1 = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">clock</a>();</div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> eigen_vals = <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#a763896dbb4a7e95c4a1e614ac0819d66">qr_algorithm::eigen_values</a>(&amp;A);</div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>&#160; <span class="keywordtype">double</span> dtime = <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">clock</a>() - t1) / CLOCKS_PER_SEC;</div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>&#160; </div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Eigen vals: &quot;</span>;</div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>&#160; <span class="keywordflow">for</span> (i = 0; i &lt; mat_size; i++) <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; eigen_vals[i] &lt;&lt; <span class="stringliteral">&quot;\t&quot;</span>;</div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;\nTime taken to compute: &quot;</span> &lt;&lt; dtime &lt;&lt; <span class="stringliteral">&quot; sec\n&quot;</span>;</div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>&#160; </div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a7558fd7779bf207157ced66f275951a0">&#9670;&nbsp;</a></span>mat_mul()</h2>
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<td class="memname">void mat_mul </td>
<td>(</td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; &amp;&#160;</td>
<td class="paramname"><em>A</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; &amp;&#160;</td>
<td class="paramname"><em>B</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt;&gt; *&#160;</td>
<td class="paramname"><em>OUT</em>&#160;</td>
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<td></td>
<td>)</td>
<td></td><td></td>
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<p>Perform multiplication of two matrices.</p><ul>
<li>R2 must be equal to C1</li>
<li>Resultant matrix size should be R1xC2 <dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">A</td><td>first matrix to multiply </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">B</td><td>second matrix to multiply </td></tr>
<tr><td class="paramdir">[out]</td><td class="paramname">OUT</td><td>output matrix (must be pre-allocated) </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>pointer to resultant matrix </dd></dl>
</li>
</ul>
<div class="fragment"><div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; {</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; <span class="keywordtype">int</span> R1 = A.size();</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; <span class="keywordtype">int</span> C1 = A[0].size();</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; <span class="keywordtype">int</span> R2 = B.size();</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; <span class="keywordtype">int</span> C2 = B[0].size();</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; <span class="keywordflow">if</span> (C1 != R2) {</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/perror.html">perror</a>(<span class="stringliteral">&quot;Matrix dimensions mismatch!&quot;</span>);</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; }</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; </div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; R1; i++) {</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; C2; j++) {</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; OUT[0][i][j] = 0.f;</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> = 0; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a> &lt; C1; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>++) {</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; OUT[0][i][j] += A[i][<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>] * B[<a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#afcf0d19607cd0edd8ae333d2b9c220c0">k</a>][j];</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; }</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; }</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; }</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a1440a7779ac56f47a3f355ce4a8c7da0">&#9670;&nbsp;</a></span>test1()</h2>
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<td class="memname">void test1 </td>
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<p>test function to compute eigen values of a 2x2 matrix </p><p class="formulaDsp">
\[\begin{bmatrix} 5 &amp; 7\\ 7 &amp; 11 \end{bmatrix}\]
</p>
<p> which are approximately, {15.56158, 0.384227} </p>
<div class="fragment"><div class="line"><a name="l00177"></a><span class="lineno"> 177</span>&#160; {</div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::valarray&lt;double&gt;</a>&gt; X = {{5, 7}, {7, 11}};</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>&#160; <span class="keywordtype">double</span> y[] = {15.56158, 0.384227}; <span class="comment">// corresponding y-values</span></div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>&#160; </div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;------- Test 1 -------&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> eig_vals = <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#a763896dbb4a7e95c4a1e614ac0819d66">qr_algorithm::eigen_values</a>(&amp;X);</div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>&#160; </div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 2; i++) {</div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i + 1 &lt;&lt; <span class="stringliteral">&quot;/2 Checking for &quot;</span> &lt;&lt; y[i] &lt;&lt; <span class="stringliteral">&quot; --&gt; &quot;</span>;</div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>&#160; <span class="keywordtype">bool</span> result = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; 2 &amp;&amp; !result; j++) {</div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>&#160; <span class="keywordflow">if</span> (std::abs(y[i] - eig_vals[j]) &lt; 0.1) {</div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>&#160; result = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;(&quot;</span> &lt;&lt; eig_vals[j] &lt;&lt; <span class="stringliteral">&quot;) &quot;</span>;</div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>&#160; }</div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>&#160; }</div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>&#160; assert(result); <span class="comment">// ensure that i^th expected eigen value was computed</span></div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;found\n&quot;</span>;</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>&#160; }</div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 1 Passed\n\n&quot;</span>;</div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a0283886819c7c140a023582b7269e2d0">&#9670;&nbsp;</a></span>test2()</h2>
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<td class="memname">void test2 </td>
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<p>test function to compute eigen values of a 2x2 matrix </p><p class="formulaDsp">
\[\begin{bmatrix} -4&amp; 4&amp; 2&amp; 0&amp; -3\\ 4&amp; -4&amp; 4&amp; -3&amp; -1\\ 2&amp; 4&amp; 4&amp; 3&amp; -3\\ 0&amp; -3&amp; 3&amp; -1&amp;-1\\ -3&amp; -1&amp; -3&amp; -3&amp; 0 \end{bmatrix}\]
</p>
<p> which are approximately, {9.27648, -9.26948, 2.0181, -1.03516, -5.98994} </p>
<div class="fragment"><div class="line"><a name="l00210"></a><span class="lineno"> 210</span>&#160; {</div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;std::valarray&lt;double&gt;</a>&gt; X = {{-4, 4, 2, 0, -3},</div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>&#160; {4, -4, 4, -3, -1},</div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>&#160; {2, 4, 4, 3, -3},</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>&#160; {0, -3, 3, -1, -3},</div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>&#160; {-3, -1, -3, -3, 0}};</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>&#160; <span class="keywordtype">double</span> y[] = {9.27648, -9.26948, 2.0181, -1.03516,</div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>&#160; -5.98994}; <span class="comment">// corresponding y-values</span></div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>&#160; </div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;------- Test 2 -------&quot;</span> &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt;double&gt;</a> eig_vals = <a class="code" href="../../d2/d3b/namespaceqr__algorithm.html#a763896dbb4a7e95c4a1e614ac0819d66">qr_algorithm::eigen_values</a>(&amp;X);</div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>&#160; </div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; X &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span></div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>&#160; &lt;&lt; <span class="stringliteral">&quot;Eigen values: &quot;</span> &lt;&lt; eig_vals &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>&#160; </div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 5; i++) {</div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; i + 1 &lt;&lt; <span class="stringliteral">&quot;/5 Checking for &quot;</span> &lt;&lt; y[i] &lt;&lt; <span class="stringliteral">&quot; --&gt; &quot;</span>;</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>&#160; <span class="keywordtype">bool</span> result = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; 5 &amp;&amp; !result; j++) {</div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>&#160; <span class="keywordflow">if</span> (std::abs(y[i] - eig_vals[j]) &lt; 0.1) {</div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>&#160; result = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;(&quot;</span> &lt;&lt; eig_vals[j] &lt;&lt; <span class="stringliteral">&quot;) &quot;</span>;</div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>&#160; }</div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>&#160; }</div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>&#160; assert(result); <span class="comment">// ensure that i^th expected eigen value was computed</span></div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;found\n&quot;</span>;</div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>&#160; }</div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test 2 Passed\n\n&quot;</span>;</div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>&#160;}</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>
<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&lt; std::valarray&lt; double &gt;&gt; *A)</div><div class="ttdef"><b>Definition:</b> qr_eigen_values.cpp:28</div></div>
<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&lt; double &gt; eigen_values(std::valarray&lt; std::valarray&lt; double &gt;&gt; *A, bool print_intermediates=false)</div><div class="ttdef"><b>Definition:</b> qr_eigen_values.cpp:98</div></div>
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