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<title>TheAlgorithms/C++: numerical_methods/qr_eigen_values.cpp File Reference</title>
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<div id="projectname">Algorithms_in_C++<span id="projectnumber"> 1.0.0</span>
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<div id="projectname">TheAlgorithms/C++<span id="projectnumber"> 1.0.0</span>
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</div>
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<div id="projectbrief">Set of algorithms implemented in C++.</div>
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<div id="projectbrief">All the algorithms implemented in C++</div>
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@@ -125,7 +142,9 @@ 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" 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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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="namespaces" name="namespaces"></a>
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Namespaces</h2></td></tr>
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<tr class="memitem:"><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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@@ -139,11 +158,11 @@ Macros</h2></td></tr>
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</table><table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 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> (<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: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="separator:a9bbf469d5525a816b0d6ca812119093d"><td class="memSeparator" colspan="2"> </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 <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="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="separator:abb8bf4c55e10685a5eb2ad3797fde1ae"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a28e2fa3e803abaea6c568dc45d69d8cc" id="r_a28e2fa3e803abaea6c568dc45d69d8cc"><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#a28e2fa3e803abaea6c568dc45d69d8cc">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: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="separator:a28e2fa3e803abaea6c568dc45d69d8cc"><td class="memSeparator" colspan="2"> </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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@@ -155,6 +174,8 @@ Functions</h2></td></tr>
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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" 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><h2 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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</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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<h2 class="groupheader">Function Documentation</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> <td class="paramname"><span class="paramname"><em>A</em></span></td><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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<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> <a class="code hl_variable" href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a> = A->size();</div>
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@@ -201,23 +226,17 @@ Functions</h2></td></tr>
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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 < <a class="code hl_variable" href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; i++) {</div>
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<div class="line"><span class="lineno"> 36</span> A[0][i][i] = (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % <a class="code hl_define" href="#aee57a411f07599034f5ceb8cc7d65b40">LIMS</a>) - lim2;</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 < <a class="code hl_variable" href="../../d8/dab/sparse__table_8cpp.html#a10f3ffb3f6f7e1b83d556b9c8de89a5d">N</a>; j++) {</div>
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<div class="line"><span class="lineno"> 38</span> tmp = (<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() % <a class="code hl_define" href="#aee57a411f07599034f5ceb8cc7d65b40">LIMS</a>) - lim2;</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> 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 class="ttc" id="asparse__table_8cpp_html_a10f3ffb3f6f7e1b83d556b9c8de89a5d"><div class="ttname"><a href="../../d8/dab/sparse__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:48</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_a9bbf469d5525a816b0d6ca812119093d_cgraph.svg" width="232" height="36"><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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</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 class="ttc" id="asparse__table_8cpp_html_a10f3ffb3f6f7e1b83d556b9c8de89a5d"><div class="ttname"><a href="../../d8/dab/sparse__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> <a href="../../d8/dab/sparse__table_8cpp_source.html#l00048">sparse_table.cpp:48</a></div></div>
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</div><!-- fragment -->
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<a id="a3c04138a5bfe5d72780bb7e82a18e627" name="a3c04138a5bfe5d72780bb7e82a18e627"></a>
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@@ -239,66 +258,56 @@ Here is the call graph for this function:</div>
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</table>
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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> = <a class="code hl_functionRef" 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"><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> <a class="code hl_classRef" 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"><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>
|
||||
<div class="line"><span class="lineno"> 255</span> <a class="code hl_functionRef" 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>
|
||||
<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>
|
||||
<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> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>));</div>
|
||||
<div class="line"><span class="lineno"> 260</span> std::srand(std::time(<span class="keyword">nullptr</span>));</div>
|
||||
<div class="line"><span class="lineno"> 261</span> </div>
|
||||
<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> <a class="code hl_classRef" 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"><span class="lineno"> 264</span> std::valarray<std::valarray<double>> A(rows);</div>
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<div class="line"><span class="lineno"> 267</span> A[i] = <a class="code hl_classRef" 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"><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> <a class="code hl_classRef" 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"><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 = <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">clock</a>();</div>
|
||||
<div class="line"><span class="lineno"> 276</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray<double></a> eigen_vals = <a class="code hl_function" href="../../d2/d3b/namespaceqr__algorithm.html#a28e2fa3e803abaea6c568dc45d69d8cc">qr_algorithm::eigen_values</a>(&A);</div>
|
||||
<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>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">clock</a>() - t1) / CLOCKS_PER_SEC;</div>
|
||||
<div class="line"><span class="lineno"> 275</span> clock_t t1 = clock();</div>
|
||||
<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>
|
||||
<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>
|
||||
<div class="line"><span class="lineno"> 278</span> </div>
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||||
<div class="line"><span class="lineno"> 279</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Eigen vals: "</span>;</div>
|
||||
<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++) <a class="code hl_classRef" 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>
|
||||
<div class="line"><span class="lineno"> 281</span> <a class="code hl_classRef" 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>
|
||||
<div class="line"><span class="lineno"> 279</span> std::cout << <span class="stringliteral">"Eigen vals: "</span>;</div>
|
||||
<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>
|
||||
<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>
|
||||
<div class="line"><span class="lineno"> 282</span> </div>
|
||||
<div class="line"><span class="lineno"> 283</span> <span class="keywordflow">return</span> 0;</div>
|
||||
<div class="line"><span class="lineno"> 284</span>}</div>
|
||||
<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>
|
||||
<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
|
||||
<div class="ttc" id="aclock_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a></div><div class="ttdeci">T clock(T... args)</div></div>
|
||||
<div class="ttc" id="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>
|
||||
<div class="ttc" id="amatrix__exponentiation_8cpp_html_a9977ad12548c4a49dee9dc3f0685aa54"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#a9977ad12548c4a49dee9dc3f0685aa54">mat_size</a></div><div class="ttdeci">ll mat_size</div><div class="ttdef"><b>Definition</b> matrix_exponentiation.cpp:45</div></div>
|
||||
<div class="ttc" id="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> qr_eigen_values.cpp:98</div></div>
|
||||
<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> qr_eigen_values.cpp:210</div></div>
|
||||
<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> qr_eigen_values.cpp:177</div></div>
|
||||
<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> qr_eigen_values.cpp:28</div></div>
|
||||
<div class="ttc" id="asrand_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a></div><div class="ttdeci">T srand(T... args)</div></div>
|
||||
<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>
|
||||
<div class="ttc" id="avalarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a></div></div>
|
||||
</div><!-- fragment --><div class="dynheader">
|
||||
Here is the call graph for this function:</div>
|
||||
<div class="dyncontent">
|
||||
<div class="center"><div class="zoom"><iframe scrolling="no" frameborder="0" src="../../de/d75/qr__eigen__values_8cpp_a3c04138a5bfe5d72780bb7e82a18e627_cgraph.svg" width="100%" height="514"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div></div>
|
||||
</div>
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||||
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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>
|
||||
<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>
|
||||
<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>
|
||||
<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>
|
||||
<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>
|
||||
</div><!-- fragment -->
|
||||
</div>
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||||
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||||
<a id="abb8bf4c55e10685a5eb2ad3797fde1ae" name="abb8bf4c55e10685a5eb2ad3797fde1ae"></a>
|
||||
@@ -310,17 +319,17 @@ Here is the call graph for this function:</div>
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||||
<tr>
|
||||
<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>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>< double > > &</td> <td class="paramname"><span class="paramname"><em>A</em></span>, </td>
|
||||
<td class="paramtype">const std::valarray< std::valarray< double > > &</td> <td class="paramname"><span class="paramname"><em>A</em></span>, </td>
|
||||
</tr>
|
||||
<tr>
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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> <td class="paramname"><span class="paramname"><em>B</em></span>, </td>
|
||||
<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></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> <td class="paramname"><span class="paramname"><em>OUT</em></span> )</td>
|
||||
<td class="paramtype">std::valarray< std::valarray< double > > *</td> <td class="paramname"><span class="paramname"><em>OUT</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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@@ -337,13 +346,15 @@ Here is the call graph for this function:</div>
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<dl class="section return"><dt>Returns</dt><dd>pointer to resultant matrix </dd></dl>
|
||||
</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>
|
||||
<div class="line"><span class="lineno"> 57</span> <span class="keywordtype">int</span> R1 = A.size();</div>
|
||||
<div class="line"><span class="lineno"> 58</span> <span class="keywordtype">int</span> C1 = A[0].size();</div>
|
||||
<div class="line"><span class="lineno"> 59</span> <span class="keywordtype">int</span> R2 = B.size();</div>
|
||||
<div class="line"><span class="lineno"> 60</span> <span class="keywordtype">int</span> C2 = B[0].size();</div>
|
||||
<div class="line"><span class="lineno"> 61</span> <span class="keywordflow">if</span> (C1 != R2) {</div>
|
||||
<div class="line"><span class="lineno"> 62</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/perror.html">perror</a>(<span class="stringliteral">"Matrix dimensions mismatch!"</span>);</div>
|
||||
<div class="line"><span class="lineno"> 62</span> perror(<span class="stringliteral">"Matrix dimensions mismatch!"</span>);</div>
|
||||
<div class="line"><span class="lineno"> 63</span> <span class="keywordflow">return</span>;</div>
|
||||
<div class="line"><span class="lineno"> 64</span> }</div>
|
||||
<div class="line"><span class="lineno"> 65</span> </div>
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@@ -356,8 +367,7 @@ Here is the call graph for this function:</div>
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<div class="line"><span class="lineno"> 72</span> }</div>
|
||||
<div class="line"><span class="lineno"> 73</span> }</div>
|
||||
<div class="line"><span class="lineno"> 74</span>}</div>
|
||||
<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> composite_simpson_rule.cpp:117</div></div>
|
||||
<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>
|
||||
<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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|
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@@ -382,35 +392,31 @@ Here is the call graph for this function:</div>
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||||
\end{bmatrix}\]
|
||||
</p>
|
||||
<p> which are approximately, {15.56158, 0.384227} </p>
|
||||
|
||||
<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>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 177</span> {</div>
|
||||
<div class="line"><span class="lineno"> 178</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray<std::valarray<double></a>> X = {{5, 7}, {7, 11}};</div>
|
||||
<div class="line"><span class="lineno"> 178</span> std::valarray<std::valarray<double>> X = {{5, 7}, {7, 11}};</div>
|
||||
<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>
|
||||
<div class="line"><span class="lineno"> 180</span> </div>
|
||||
<div class="line"><span class="lineno"> 181</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"------- Test 1 -------"</span> << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
|
||||
<div class="line"><span class="lineno"> 182</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray<double></a> eig_vals = <a class="code hl_function" href="../../d2/d3b/namespaceqr__algorithm.html#a28e2fa3e803abaea6c568dc45d69d8cc">qr_algorithm::eigen_values</a>(&X);</div>
|
||||
<div class="line"><span class="lineno"> 181</span> std::cout << <span class="stringliteral">"------- Test 1 -------"</span> << std::endl;</div>
|
||||
<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> <a class="code hl_classRef" 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>
|
||||
<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>
|
||||
<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>
|
||||
<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> <a class="code hl_classRef" 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"><span class="lineno"> 190</span> std::cout << <span class="stringliteral">"("</span> << eig_vals[j] << <span class="stringliteral">") "</span>;</div>
|
||||
<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>
|
||||
<div class="line"><span class="lineno"> 194</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"found\n"</span>;</div>
|
||||
<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> <a class="code hl_classRef" 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>
|
||||
<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="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:77</div></div>
|
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Here is the call graph for this function:</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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\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>
|
||||
|
||||
<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> <a class="code hl_classRef" 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>
|
||||
<div class="line"><span class="lineno"> 211</span> std::valarray<std::valarray<double>> X = {{-4, 4, 2, 0, -3},</div>
|
||||
<div class="line"><span class="lineno"> 212</span> {4, -4, 4, -3, -1},</div>
|
||||
<div class="line"><span class="lineno"> 213</span> {2, 4, 4, 3, -3},</div>
|
||||
<div class="line"><span class="lineno"> 214</span> {0, -3, 3, -1, -3},</div>
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@@ -446,32 +454,27 @@ Here is the call graph for this function:</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>
|
||||
<div class="line"><span class="lineno"> 217</span> -5.98994}; <span class="comment">// corresponding y-values</span></div>
|
||||
<div class="line"><span class="lineno"> 218</span> </div>
|
||||
<div class="line"><span class="lineno"> 219</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"------- Test 2 -------"</span> << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><span class="lineno"> 220</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray<double></a> 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"> 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> <a class="code hl_classRef" 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"><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> <a class="code hl_classRef" 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"><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> <a class="code hl_classRef" 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"><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> <a class="code hl_classRef" 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"><span class="lineno"> 235</span> std::cout << <span class="stringliteral">"found\n"</span>;</div>
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<div class="line"><span class="lineno"> 237</span> <a class="code hl_classRef" 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"><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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<div class="headertitle"><div class="title">qr_eigen_values.cpp</div></div>
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<a href="../../de/d75/qr__eigen__values_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span> </div>
|
||||
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="preprocessor">#include <cassert></span></div>
|
||||
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="preprocessor">#include <cmath></span></div>
|
||||
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="preprocessor">#include <cstdlib></span></div>
|
||||
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="preprocessor">#include <ctime></span></div>
|
||||
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="preprocessor">#include <iostream></span></div>
|
||||
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span><span class="preprocessor">#ifdef _OPENMP</span></div>
|
||||
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="preprocessor">#include <omp.h></span></div>
|
||||
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="preprocessor">#endif</span></div>
|
||||
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span> </div>
|
||||
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include "<a class="code" href="../../d4/d68/qr__decompose_8h.html">./qr_decompose.h</a>"</span></div>
|
||||
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="keyword">using </span>qr_algorithm::operator<<;</div>
|
||||
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> </div>
|
||||
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"><a class="line" href="../../de/d75/qr__eigen__values_8cpp.html#aee57a411f07599034f5ceb8cc7d65b40"> 20</a></span><span class="preprocessor">#define LIMS 9 </span></div>
|
||||
<div class="foldopen" id="foldopen00028" data-start="{" data-end="}">
|
||||
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"><a class="line" href="../../de/d75/qr__eigen__values_8cpp.html#a9bbf469d5525a816b0d6ca812119093d"> 28</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="../../de/d75/qr__eigen__values_8cpp.html#a9bbf469d5525a816b0d6ca812119093d">create_matrix</a>(std::valarray<std::valarray<double>> *A) {</div>
|
||||
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> <span class="keywordtype">int</span> i, j, tmp, lim2 = <a class="code hl_define" href="../../de/d75/qr__eigen__values_8cpp.html#aee57a411f07599034f5ceb8cc7d65b40">LIMS</a> >> 1;</div>
|
||||
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> <span class="keywordtype">int</span> N = A->size();</div>
|
||||
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> </div>
|
||||
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="preprocessor">#ifdef _OPENMP</span></div>
|
||||
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="preprocessor">#pragma omp for</span></div>
|
||||
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span><span class="preprocessor">#endif</span></div>
|
||||
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> <span class="keywordflow">for</span> (i = 0; i < N; i++) {</div>
|
||||
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> A[0][i][i] = (std::rand() % <a class="code hl_define" href="../../de/d75/qr__eigen__values_8cpp.html#aee57a411f07599034f5ceb8cc7d65b40">LIMS</a>) - lim2;</div>
|
||||
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> <span class="keywordflow">for</span> (j = i + 1; j < N; j++) {</div>
|
||||
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> tmp = (std::rand() % <a class="code hl_define" href="../../de/d75/qr__eigen__values_8cpp.html#aee57a411f07599034f5ceb8cc7d65b40">LIMS</a>) - lim2;</div>
|
||||
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> A[0][i][j] = tmp; <span class="comment">// summetrically distribute random values</span></div>
|
||||
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> A[0][j][i] = tmp;</div>
|
||||
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> }</div>
|
||||
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> }</div>
|
||||
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span>}</div>
|
||||
</div>
|
||||
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> </div>
|
||||
<div class="foldopen" id="foldopen00054" data-start="{" data-end="}">
|
||||
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"><a class="line" href="../../de/d75/qr__eigen__values_8cpp.html#abb8bf4c55e10685a5eb2ad3797fde1ae"> 54</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="../../de/d75/qr__eigen__values_8cpp.html#abb8bf4c55e10685a5eb2ad3797fde1ae">mat_mul</a>(<span class="keyword">const</span> std::valarray<std::valarray<double>> &A,</div>
|
||||
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="keyword">const</span> std::valarray<std::valarray<double>> &B,</div>
|
||||
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> std::valarray<std::valarray<double>> *OUT) {</div>
|
||||
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <span class="keywordtype">int</span> R1 = A.size();</div>
|
||||
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="keywordtype">int</span> C1 = A[0].size();</div>
|
||||
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <span class="keywordtype">int</span> R2 = B.size();</div>
|
||||
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="keywordtype">int</span> C2 = B[0].size();</div>
|
||||
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="keywordflow">if</span> (C1 != R2) {</div>
|
||||
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> perror(<span class="stringliteral">"Matrix dimensions mismatch!"</span>);</div>
|
||||
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="keywordflow">return</span>;</div>
|
||||
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> }</div>
|
||||
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> </div>
|
||||
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < R1; i++) {</div>
|
||||
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < C2; j++) {</div>
|
||||
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> OUT[0][i][j] = 0.f;</div>
|
||||
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k < C1; k++) {</div>
|
||||
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> OUT[0][i][j] += A[i][k] * B[k][j];</div>
|
||||
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> }</div>
|
||||
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> }</div>
|
||||
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> }</div>
|
||||
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span>}</div>
|
||||
</div>
|
||||
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> </div>
|
||||
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../d2/d3b/namespaceqr__algorithm.html">qr_algorithm</a> {</div>
|
||||
<div class="foldopen" id="foldopen00098" data-start="{" data-end="}">
|
||||
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"><a class="line" href="../../d2/d3b/namespaceqr__algorithm.html#a28e2fa3e803abaea6c568dc45d69d8cc"> 98</a></span>std::valarray<double> <a class="code hl_function" href="../../d2/d3b/namespaceqr__algorithm.html#a28e2fa3e803abaea6c568dc45d69d8cc">eigen_values</a>(std::valarray<std::valarray<double>> *A,</div>
|
||||
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> <span class="keywordtype">bool</span> print_intermediates = <span class="keyword">false</span>) {</div>
|
||||
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <span class="keywordtype">int</span> rows = A->size();</div>
|
||||
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <span class="keywordtype">int</span> columns = rows;</div>
|
||||
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="keywordtype">int</span> counter = 0, num_eigs = rows - 1;</div>
|
||||
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="keywordtype">double</span> last_eig = 0;</div>
|
||||
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> </div>
|
||||
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> std::valarray<std::valarray<double>> Q(rows);</div>
|
||||
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> std::valarray<std::valarray<double>> R(columns);</div>
|
||||
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> </div>
|
||||
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> <span class="comment">/* number of eigen values = matrix size */</span></div>
|
||||
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> std::valarray<double> eigen_vals(rows);</div>
|
||||
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < rows; i++) {</div>
|
||||
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> Q[i] = std::valarray<double>(columns);</div>
|
||||
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> R[i] = std::valarray<double>(columns);</div>
|
||||
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> }</div>
|
||||
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> </div>
|
||||
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <span class="comment">/* continue till all eigen values are found */</span></div>
|
||||
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <span class="keywordflow">while</span> (num_eigs > 0) {</div>
|
||||
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="comment">/* iterate with QR decomposition */</span></div>
|
||||
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <span class="keywordflow">while</span> (std::abs(A[0][num_eigs][num_eigs - 1]) ></div>
|
||||
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> std::numeric_limits<double>::epsilon()) {</div>
|
||||
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> <span class="comment">// initial approximation = last diagonal element</span></div>
|
||||
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> last_eig = A[0][num_eigs][num_eigs];</div>
|
||||
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < rows; i++) {</div>
|
||||
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> A[0][i][i] -= last_eig; <span class="comment">/* A - cI */</span></div>
|
||||
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> }</div>
|
||||
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> </div>
|
||||
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> <a class="code hl_function" href="../../d2/d3b/namespaceqr__algorithm.html#a73ce637634fc49e1d10d190eb388ebf1">qr_decompose</a>(*A, &Q, &R);</div>
|
||||
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> </div>
|
||||
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> <span class="keywordflow">if</span> (print_intermediates) {</div>
|
||||
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> std::cout << *A << <span class="stringliteral">"\n"</span>;</div>
|
||||
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> std::cout << Q << <span class="stringliteral">"\n"</span>;</div>
|
||||
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> std::cout << R << <span class="stringliteral">"\n"</span>;</div>
|
||||
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> printf(<span class="stringliteral">"-------------------- %d ---------------------\n"</span>,</div>
|
||||
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> ++counter);</div>
|
||||
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> }</div>
|
||||
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> </div>
|
||||
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> <span class="comment">// new approximation A' = R * Q</span></div>
|
||||
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> <a class="code hl_function" href="../../de/d75/qr__eigen__values_8cpp.html#abb8bf4c55e10685a5eb2ad3797fde1ae">mat_mul</a>(R, Q, A);</div>
|
||||
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> </div>
|
||||
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < rows; i++) {</div>
|
||||
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> A[0][i][i] += last_eig; <span class="comment">/* A + cI */</span></div>
|
||||
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> }</div>
|
||||
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> }</div>
|
||||
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> </div>
|
||||
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> <span class="comment">/* store the converged eigen value */</span></div>
|
||||
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> eigen_vals[num_eigs] = last_eig;</div>
|
||||
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> <span class="comment">// A[0][num_eigs][num_eigs];</span></div>
|
||||
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> <span class="keywordflow">if</span> (print_intermediates) {</div>
|
||||
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> std::cout << <span class="stringliteral">"========================\n"</span>;</div>
|
||||
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> std::cout << <span class="stringliteral">"Eigen value: "</span> << last_eig << <span class="stringliteral">",\n"</span>;</div>
|
||||
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> std::cout << <span class="stringliteral">"========================\n"</span>;</div>
|
||||
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> }</div>
|
||||
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> </div>
|
||||
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> num_eigs--;</div>
|
||||
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> rows--;</div>
|
||||
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> columns--;</div>
|
||||
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> }</div>
|
||||
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> eigen_vals[0] = A[0][0][0];</div>
|
||||
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> </div>
|
||||
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> <span class="keywordflow">if</span> (print_intermediates) {</div>
|
||||
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> std::cout << Q << <span class="stringliteral">"\n"</span>;</div>
|
||||
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> std::cout << R << <span class="stringliteral">"\n"</span>;</div>
|
||||
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> }</div>
|
||||
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> </div>
|
||||
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> <span class="keywordflow">return</span> eigen_vals;</div>
|
||||
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span>}</div>
|
||||
</div>
|
||||
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> </div>
|
||||
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span>} <span class="comment">// namespace qr_algorithm</span></div>
|
||||
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> </div>
|
||||
<div class="foldopen" id="foldopen00177" data-start="{" data-end="}">
|
||||
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"><a class="line" href="../../de/d75/qr__eigen__values_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0"> 177</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="../../de/d75/qr__eigen__values_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>() {</div>
|
||||
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> std::valarray<std::valarray<double>> X = {{5, 7}, {7, 11}};</div>
|
||||
<div class="line"><a id="l00179" 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>
|
||||
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> </div>
|
||||
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> std::cout << <span class="stringliteral">"------- Test 1 -------"</span> << std::endl;</div>
|
||||
<div class="line"><a id="l00182" name="l00182"></a><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>
|
||||
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> </div>
|
||||
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < 2; i++) {</div>
|
||||
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> std::cout << i + 1 << <span class="stringliteral">"/2 Checking for "</span> << y[i] << <span class="stringliteral">" --> "</span>;</div>
|
||||
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> <span class="keywordtype">bool</span> result = <span class="keyword">false</span>;</div>
|
||||
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < 2 && !result; j++) {</div>
|
||||
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> <span class="keywordflow">if</span> (std::abs(y[i] - eig_vals[j]) < 0.1) {</div>
|
||||
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> result = <span class="keyword">true</span>;</div>
|
||||
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> std::cout << <span class="stringliteral">"("</span> << eig_vals[j] << <span class="stringliteral">") "</span>;</div>
|
||||
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> }</div>
|
||||
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> }</div>
|
||||
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> assert(result); <span class="comment">// ensure that i^th expected eigen value was computed</span></div>
|
||||
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> std::cout << <span class="stringliteral">"found\n"</span>;</div>
|
||||
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> }</div>
|
||||
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> std::cout << <span class="stringliteral">"Test 1 Passed\n\n"</span>;</div>
|
||||
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span>}</div>
|
||||
</div>
|
||||
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> </div>
|
||||
<div class="foldopen" id="foldopen00210" data-start="{" data-end="}">
|
||||
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"><a class="line" href="../../de/d75/qr__eigen__values_8cpp.html#a0283886819c7c140a023582b7269e2d0"> 210</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="../../de/d75/qr__eigen__values_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>() {</div>
|
||||
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> std::valarray<std::valarray<double>> X = {{-4, 4, 2, 0, -3},</div>
|
||||
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> {4, -4, 4, -3, -1},</div>
|
||||
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> {2, 4, 4, 3, -3},</div>
|
||||
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> {0, -3, 3, -1, -3},</div>
|
||||
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> {-3, -1, -3, -3, 0}};</div>
|
||||
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> <span class="keywordtype">double</span> y[] = {9.27648, -9.26948, 2.0181, -1.03516,</div>
|
||||
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span> -5.98994}; <span class="comment">// corresponding y-values</span></div>
|
||||
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span> </div>
|
||||
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span> std::cout << <span class="stringliteral">"------- Test 2 -------"</span> << std::endl;</div>
|
||||
<div class="line"><a id="l00220" name="l00220"></a><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>
|
||||
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> </div>
|
||||
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> std::cout << X << <span class="stringliteral">"\n"</span></div>
|
||||
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span> << <span class="stringliteral">"Eigen values: "</span> << eig_vals << <span class="stringliteral">"\n"</span>;</div>
|
||||
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span> </div>
|
||||
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < 5; i++) {</div>
|
||||
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span> std::cout << i + 1 << <span class="stringliteral">"/5 Checking for "</span> << y[i] << <span class="stringliteral">" --> "</span>;</div>
|
||||
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</span> <span class="keywordtype">bool</span> result = <span class="keyword">false</span>;</div>
|
||||
<div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < 5 && !result; j++) {</div>
|
||||
<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span> <span class="keywordflow">if</span> (std::abs(y[i] - eig_vals[j]) < 0.1) {</div>
|
||||
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span> result = <span class="keyword">true</span>;</div>
|
||||
<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> std::cout << <span class="stringliteral">"("</span> << eig_vals[j] << <span class="stringliteral">") "</span>;</div>
|
||||
<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span> }</div>
|
||||
<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span> }</div>
|
||||
<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span> assert(result); <span class="comment">// ensure that i^th expected eigen value was computed</span></div>
|
||||
<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span> std::cout << <span class="stringliteral">"found\n"</span>;</div>
|
||||
<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span> }</div>
|
||||
<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span> std::cout << <span class="stringliteral">"Test 2 Passed\n\n"</span>;</div>
|
||||
<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span>}</div>
|
||||
</div>
|
||||
<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span> </div>
|
||||
<div class="foldopen" id="foldopen00243" data-start="{" data-end="}">
|
||||
<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"><a class="line" href="../../de/d75/qr__eigen__values_8cpp.html#a3c04138a5bfe5d72780bb7e82a18e627"> 243</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../dd/d1e/generate__parentheses_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4">main</a>(<span class="keywordtype">int</span> argc, <span class="keywordtype">char</span> **argv) {</div>
|
||||
<div class="line"><a id="l00244" name="l00244"></a><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>
|
||||
<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span> <span class="keywordflow">if</span> (argc == 2) {</div>
|
||||
<div class="line"><a id="l00246" name="l00246"></a><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>
|
||||
<div class="line"><a id="l00247" 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>
|
||||
<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span> <a class="code hl_function" href="../../de/d75/qr__eigen__values_8cpp.html#a1440a7779ac56f47a3f355ce4a8c7da0">test1</a>();</div>
|
||||
<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> <a class="code hl_function" href="../../de/d75/qr__eigen__values_8cpp.html#a0283886819c7c140a023582b7269e2d0">test2</a>();</div>
|
||||
<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> std::cout << <span class="stringliteral">"Usage: ./qr_eigen_values [mat_size]\n"</span>;</div>
|
||||
<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> <span class="keywordflow">return</span> 0;</div>
|
||||
<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> }</div>
|
||||
<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> </div>
|
||||
<div class="line"><a id="l00254" name="l00254"></a><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>
|
||||
<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span> fprintf(stderr, <span class="stringliteral">"Matrix size should be > 2\n"</span>);</div>
|
||||
<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span> <span class="keywordflow">return</span> -1;</div>
|
||||
<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> }</div>
|
||||
<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span> </div>
|
||||
<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span> <span class="comment">// initialize random number generator</span></div>
|
||||
<div class="line"><a id="l00260" name="l00260"></a><span class="lineno"> 260</span> std::srand(std::time(<span class="keyword">nullptr</span>));</div>
|
||||
<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span> </div>
|
||||
<div class="line"><a id="l00262" name="l00262"></a><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>
|
||||
<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span> </div>
|
||||
<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span> std::valarray<std::valarray<double>> A(rows);</div>
|
||||
<div class="line"><a id="l00265" name="l00265"></a><span class="lineno"> 265</span> </div>
|
||||
<div class="line"><a id="l00266" name="l00266"></a><span class="lineno"> 266</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < rows; i++) {</div>
|
||||
<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span> A[i] = std::valarray<double>(columns);</div>
|
||||
<div class="line"><a id="l00268" name="l00268"></a><span class="lineno"> 268</span> }</div>
|
||||
<div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span> </div>
|
||||
<div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span> <span class="comment">/* create a random matrix */</span></div>
|
||||
<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span> <a class="code hl_function" href="../../de/d75/qr__eigen__values_8cpp.html#a9bbf469d5525a816b0d6ca812119093d">create_matrix</a>(&A);</div>
|
||||
<div class="line"><a id="l00272" name="l00272"></a><span class="lineno"> 272</span> </div>
|
||||
<div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</span> std::cout << A << <span class="stringliteral">"\n"</span>;</div>
|
||||
<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span> </div>
|
||||
<div class="line"><a id="l00275" name="l00275"></a><span class="lineno"> 275</span> clock_t t1 = clock();</div>
|
||||
<div class="line"><a id="l00276" name="l00276"></a><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>
|
||||
<div class="line"><a id="l00277" 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>(clock() - t1) / CLOCKS_PER_SEC;</div>
|
||||
<div class="line"><a id="l00278" name="l00278"></a><span class="lineno"> 278</span> </div>
|
||||
<div class="line"><a id="l00279" name="l00279"></a><span class="lineno"> 279</span> std::cout << <span class="stringliteral">"Eigen vals: "</span>;</div>
|
||||
<div class="line"><a id="l00280" name="l00280"></a><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"><a id="l00281" name="l00281"></a><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"><a id="l00282" name="l00282"></a><span class="lineno"> 282</span> </div>
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<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span>}</div>
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</div>
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<div class="ttc" id="agenerate__parentheses_8cpp_html_gae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../dd/d1e/generate__parentheses_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdoc">Main function.</div><div class="ttdef"><b>Definition</b> <a href="../../dd/d1e/generate__parentheses_8cpp_source.html#l00110">generate_parentheses.cpp:110</a></div></div>
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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"><div class="ttname"><a href="../../d2/d3b/namespaceqr__algorithm.html">qr_algorithm</a></div><div class="ttdoc">Functions to compute QR decomposition of any rectangular matrix.</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="#l00098">qr_eigen_values.cpp:98</a></div></div>
|
||||
<div class="ttc" id="anamespaceqr__algorithm_html_a73ce637634fc49e1d10d190eb388ebf1"><div class="ttname"><a href="../../d2/d3b/namespaceqr__algorithm.html#a73ce637634fc49e1d10d190eb388ebf1">qr_algorithm::qr_decompose</a></div><div class="ttdeci">void qr_decompose(const std::valarray< std::valarray< T > > &A, std::valarray< std::valarray< T > > *Q, std::valarray< std::valarray< T > > *R)</div><div class="ttdef"><b>Definition</b> <a href="../../d4/d68/qr__decompose_8h_source.html#l00146">qr_decompose.h:146</a></div></div>
|
||||
<div class="ttc" id="aqr__decompose_8h_html"><div class="ttname"><a href="../../d4/d68/qr__decompose_8h.html">qr_decompose.h</a></div><div class="ttdoc">Library functions to compute QR decomposition of a given matrix.</div></div>
|
||||
<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> <a href="#l00210">qr_eigen_values.cpp:210</a></div></div>
|
||||
<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> <a href="#l00177">qr_eigen_values.cpp:177</a></div></div>
|
||||
<div class="ttc" id="aqr__eigen__values_8cpp_html_a9bbf469d5525a816b0d6ca812119093d"><div class="ttname"><a href="../../de/d75/qr__eigen__values_8cpp.html#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="#l00028">qr_eigen_values.cpp:28</a></div></div>
|
||||
<div class="ttc" id="aqr__eigen__values_8cpp_html_abb8bf4c55e10685a5eb2ad3797fde1ae"><div class="ttname"><a href="../../de/d75/qr__eigen__values_8cpp.html#abb8bf4c55e10685a5eb2ad3797fde1ae">mat_mul</a></div><div class="ttdeci">void mat_mul(const std::valarray< std::valarray< double > > &A, const std::valarray< std::valarray< double > > &B, std::valarray< std::valarray< double > > *OUT)</div><div class="ttdef"><b>Definition</b> <a href="#l00054">qr_eigen_values.cpp:54</a></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> <a href="#l00020">qr_eigen_values.cpp:20</a></div></div>
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