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 <span id="projectnumber">1.7.1</span>
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<div class="title">qr_method.cpp</div> </div>
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<p>In this tutorial the eigenvalues and eigenvectors of a symmetric 9-by-9 matrix are calculated using the QR-method.</p>
<p>The first step is to include the necessary headers and to define the floating point type used. </p>
<div class="fragment"><div class="line"><span class="comment">// System headers:</span></div>
<div class="line"><span class="preprocessor">#include <iostream></span></div>
<div class="line"><span class="preprocessor">#include <fstream></span></div>
<div class="line"><span class="preprocessor">#include <stdexcept></span></div>
<div class="line"><span class="preprocessor">#include <vector></span></div>
<div class="line"></div>
<div class="line"><span class="comment">// ViennaCL headers:</span></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="matrix_8hpp.html">viennacl/matrix.hpp</a>"</span></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="prod_8hpp.html">viennacl/linalg/prod.hpp</a>"</span></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="qr-method_8hpp.html">viennacl/linalg/qr-method.hpp</a>"</span></div>
</div><!-- fragment --><p> Helper routine for initializing a ViennaCL matrix and returning its associated eigenvalues </p>
<div class="fragment"><div class="line"><span class="keyword">template</span> <<span class="keyword">typename</span> ScalarType></div>
<div class="line"><span class="keywordtype">void</span> initialize(<a name="_a0"></a><a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<ScalarType></a> & A, std::vector<ScalarType> & v)</div>
<div class="line">{</div>
<div class="line"> <span class="comment">// System matrix:</span></div>
<div class="line"> <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> M[9][9] = {{ 4, 1, -2, 2, -7, 3, 9, -6, -2},</div>
<div class="line"> { 1, -2, 0, 1, -1, 5, 4, 7, 3},</div>
<div class="line"> {-2, 0, 3, 2, 0, 3, 6, 1, -1},</div>
<div class="line"> { 2, 1, 2, 1, 4, 5, 6, 7, 8},</div>
<div class="line"> {-7, -1, 0, 4, 5, 4, 9, 1, -8},</div>
<div class="line"> { 3, 5, 3, 5, 4, 9, -3, 3, 3},</div>
<div class="line"> { 9, 4, 6, 6, 9, -3, 3, 6, -7},</div>
<div class="line"> {-6, 7, 1, 7, 1, 3, 6, 2, 6},</div>
<div class="line"> {-2, 3, -1, 8, -8, 3, -7, 6, 1}};</div>
<div class="line"></div>
<div class="line"> <span class="keywordflow">for</span>(std::size_t i = 0; i < 9; i++)</div>
<div class="line"> <span class="keywordflow">for</span>(std::size_t j = 0; j < 9; j++)</div>
<div class="line"> A(i, j) = M[i][j];</div>
<div class="line"></div>
<div class="line"> <span class="comment">// Known eigenvalues:</span></div>
<div class="line"> <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> V[9] = {<a name="a1"></a><a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(12.6005), <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(19.5905), <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(8.06067), <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(2.95074), <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(0.223506),</div>
<div class="line"> <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(24.3642), <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(-9.62084), <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(-13.8374), <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(-18.3319)};</div>
<div class="line"></div>
<div class="line"> <span class="keywordflow">for</span>(std::size_t i = 0; i < 9; i++)</div>
<div class="line"> v[i] = V[i];</div>
<div class="line">}</div>
</div><!-- fragment --><p> Helper routine: Print an STL vector </p>
<div class="fragment"><div class="line"><span class="keyword">template</span> <<span class="keyword">typename</span> ScalarType></div>
<div class="line"><span class="keywordtype">void</span> <a name="a2"></a><a class="code" href="qr__method__func_8cpp.html#afe063343d3b1e9d9665d8cb04dd59c6d">vector_print</a>(std::vector<ScalarType>& v )</div>
<div class="line">{</div>
<div class="line"> <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i = 0; i < v.size(); i++)</div>
<div class="line"> std::cout << std::setprecision(6) << std::fixed << v[i] << <span class="stringliteral">"\t"</span>;</div>
<div class="line"> std::cout << std::endl;</div>
<div class="line">}</div>
</div><!-- fragment --><p> Create a system of size 9-by-9 with known eigenvalues and compare it with the eigenvalues computed from the QR method implemented in ViennaCL. </p>
<div class="fragment"><div class="line"><span class="keywordtype">int</span> <a name="a3"></a><a class="code" href="tests_2src_2qr__method_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>()</div>
<div class="line">{</div>
<div class="line"> <span class="comment">// Change to 'double' if supported by your hardware.</span></div>
<div class="line"> <span class="keyword">typedef</span> <span class="keywordtype">float</span> <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>;</div>
<div class="line"></div>
<div class="line"> std::cout << <span class="stringliteral">"Testing matrix of size "</span> << 9 << <span class="stringliteral">"-by-"</span> << 9 << std::endl;</div>
<div class="line"></div>
<div class="line"> <a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<ScalarType></a> A_input(9,9);</div>
<div class="line"> <a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<ScalarType></a> Q(9, 9);</div>
<div class="line"> std::vector<ScalarType> eigenvalues_ref(9);</div>
<div class="line"> std::vector<ScalarType> eigenvalues(9);</div>
<div class="line"></div>
<div class="line"> <a name="_a4"></a><a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> vcl_eigenvalues(9);</div>
<div class="line"></div>
<div class="line"> initialize(A_input, eigenvalues_ref);</div>
<div class="line"></div>
<div class="line"> std::cout << std::endl <<<span class="stringliteral">"Input matrix: "</span> << std::endl;</div>
<div class="line"> std::cout << A_input << std::endl;</div>
<div class="line"></div>
<div class="line"> <a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<ScalarType></a> A_input2(A_input); <span class="comment">// duplicate to demonstrate the use with both std::vector and viennacl::vector</span></div>
</div><!-- fragment --><p> Call the function <a class="el" href="namespaceviennacl_1_1linalg.html#a51cbe06645207f9b3054e8725269cc71">qr_method_sym()</a> to calculate eigenvalues and eigenvectors Parameters:</p>
<ul>
<li>A_input - input matrix to find eigenvalues and eigenvectors from</li>
<li>Q - matrix, where the calculated eigenvectors will be stored in</li>
<li>eigenvalues - vector, where the calculated eigenvalues will be stored in <div class="fragment"><div class="line">std::cout << <span class="stringliteral">"Calculation..."</span> << std::endl;</div>
<div class="line"><a name="a5"></a><a class="code" href="namespaceviennacl_1_1linalg.html#a51cbe06645207f9b3054e8725269cc71">viennacl::linalg::qr_method_sym</a>(A_input, Q, eigenvalues);</div>
</div><!-- fragment --> Same as before, but writing the eigenvalues to a ViennaCL-vector: <div class="fragment"><div class="line"><a class="code" href="namespaceviennacl_1_1linalg.html#a51cbe06645207f9b3054e8725269cc71">viennacl::linalg::qr_method_sym</a>(A_input2, Q, vcl_eigenvalues);</div>
</div><!-- fragment --> Print the computed eigenvalues and eigenvectors: <div class="fragment"><div class="line">std::cout << std::endl << <span class="stringliteral">"Eigenvalues with std::vector<T>:"</span> << std::endl;</div>
<div class="line"><a class="code" href="qr__method__func_8cpp.html#afe063343d3b1e9d9665d8cb04dd59c6d">vector_print</a>(eigenvalues);</div>
<div class="line">std::cout << <span class="stringliteral">"Eigenvalues with viennacl::vector<T>: "</span> << std::endl << vcl_eigenvalues << std::endl;</div>
<div class="line">std::cout << std::endl << <span class="stringliteral">"Reference eigenvalues:"</span> << std::endl;</div>
<div class="line"><a class="code" href="qr__method__func_8cpp.html#afe063343d3b1e9d9665d8cb04dd59c6d">vector_print</a>(eigenvalues_ref);</div>
<div class="line">std::cout << std::endl;</div>
<div class="line">std::cout << <span class="stringliteral">"Eigenvectors - each column is an eigenvector"</span> << std::endl;</div>
<div class="line">std::cout << Q << std::endl;</div>
</div><!-- fragment --> That's it. Print a success message and exit. <div class="fragment"><div class="line"> std::cout << std::endl;</div>
<div class="line"> std::cout << <span class="stringliteral">"------- Tutorial completed --------"</span> << std::endl;</div>
<div class="line"> std::cout << std::endl;</div>
<div class="line"></div>
<div class="line"> <span class="keywordflow">return</span> EXIT_SUCCESS;</div>
<div class="line">}</div>
</div><!-- fragment --> <h2>Full Example Code</h2>
</li>
</ul>
<div class="fragment"><div class="line"><span class="comment">/* =========================================================================</span></div>
<div class="line"><span class="comment"> Copyright (c) 2010-2016, Institute for Microelectronics,</span></div>
<div class="line"><span class="comment"> Institute for Analysis and Scientific Computing,</span></div>
<div class="line"><span class="comment"> TU Wien.</span></div>
<div class="line"><span class="comment"> Portions of this software are copyright by UChicago Argonne, LLC.</span></div>
<div class="line"><span class="comment"></span></div>
<div class="line"><span class="comment"> -----------------</span></div>
<div class="line"><span class="comment"> ViennaCL - The Vienna Computing Library</span></div>
<div class="line"><span class="comment"> -----------------</span></div>
<div class="line"><span class="comment"></span></div>
<div class="line"><span class="comment"> Project Head: Karl Rupp rupp@iue.tuwien.ac.at</span></div>
<div class="line"><span class="comment"></span></div>
<div class="line"><span class="comment"> (A list of authors and contributors can be found in the PDF manual)</span></div>
<div class="line"><span class="comment"></span></div>
<div class="line"><span class="comment"> License: MIT (X11), see file LICENSE in the base directory</span></div>
<div class="line"><span class="comment">============================================================================= */</span></div>
<div class="line"></div>
<div class="line"><span class="comment">// System headers:</span></div>
<div class="line"><span class="preprocessor">#include <iostream></span></div>
<div class="line"><span class="preprocessor">#include <fstream></span></div>
<div class="line"><span class="preprocessor">#include <stdexcept></span></div>
<div class="line"><span class="preprocessor">#include <vector></span></div>
<div class="line"></div>
<div class="line"><span class="comment">// ViennaCL headers:</span></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="matrix_8hpp.html">viennacl/matrix.hpp</a>"</span></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="prod_8hpp.html">viennacl/linalg/prod.hpp</a>"</span></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="qr-method_8hpp.html">viennacl/linalg/qr-method.hpp</a>"</span></div>
<div class="line"></div>
<div class="line"></div>
<div class="line"><span class="keyword">template</span> <<span class="keyword">typename</span> ScalarType></div>
<div class="line"><span class="keywordtype">void</span> initialize(<a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<ScalarType></a> & A, std::vector<ScalarType> & v)</div>
<div class="line">{</div>
<div class="line"> <span class="comment">// System matrix:</span></div>
<div class="line"> <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> M[9][9] = {{ 4, 1, -2, 2, -7, 3, 9, -6, -2},</div>
<div class="line"> { 1, -2, 0, 1, -1, 5, 4, 7, 3},</div>
<div class="line"> {-2, 0, 3, 2, 0, 3, 6, 1, -1},</div>
<div class="line"> { 2, 1, 2, 1, 4, 5, 6, 7, 8},</div>
<div class="line"> {-7, -1, 0, 4, 5, 4, 9, 1, -8},</div>
<div class="line"> { 3, 5, 3, 5, 4, 9, -3, 3, 3},</div>
<div class="line"> { 9, 4, 6, 6, 9, -3, 3, 6, -7},</div>
<div class="line"> {-6, 7, 1, 7, 1, 3, 6, 2, 6},</div>
<div class="line"> {-2, 3, -1, 8, -8, 3, -7, 6, 1}};</div>
<div class="line"></div>
<div class="line"> <span class="keywordflow">for</span>(std::size_t i = 0; i < 9; i++)</div>
<div class="line"> <span class="keywordflow">for</span>(std::size_t j = 0; j < 9; j++)</div>
<div class="line"> A(i, j) = M[i][j];</div>
<div class="line"></div>
<div class="line"> <span class="comment">// Known eigenvalues:</span></div>
<div class="line"> <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a> V[9] = {<a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(12.6005), <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(19.5905), <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(8.06067), <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(2.95074), <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(0.223506),</div>
<div class="line"> <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(24.3642), <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(-9.62084), <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(-13.8374), <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(-18.3319)};</div>
<div class="line"></div>
<div class="line"> <span class="keywordflow">for</span>(std::size_t i = 0; i < 9; i++)</div>
<div class="line"> v[i] = V[i];</div>
<div class="line">}</div>
<div class="line"></div>
<div class="line"><span class="keyword">template</span> <<span class="keyword">typename</span> ScalarType></div>
<div class="line"><span class="keywordtype">void</span> <a class="code" href="qr__method__func_8cpp.html#afe063343d3b1e9d9665d8cb04dd59c6d">vector_print</a>(std::vector<ScalarType>& v )</div>
<div class="line">{</div>
<div class="line"> <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i = 0; i < v.size(); i++)</div>
<div class="line"> std::cout << std::setprecision(6) << std::fixed << v[i] << <span class="stringliteral">"\t"</span>;</div>
<div class="line"> std::cout << std::endl;</div>
<div class="line">}</div>
<div class="line"></div>
<div class="line"><span class="keywordtype">int</span> <a class="code" href="tests_2src_2qr__method_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>()</div>
<div class="line">{</div>
<div class="line"> <span class="comment">// Change to 'double' if supported by your hardware.</span></div>
<div class="line"> <span class="keyword">typedef</span> <span class="keywordtype">float</span> <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>;</div>
<div class="line"></div>
<div class="line"> std::cout << <span class="stringliteral">"Testing matrix of size "</span> << 9 << <span class="stringliteral">"-by-"</span> << 9 << std::endl;</div>
<div class="line"></div>
<div class="line"> <a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<ScalarType></a> A_input(9,9);</div>
<div class="line"> <a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<ScalarType></a> Q(9, 9);</div>
<div class="line"> std::vector<ScalarType> eigenvalues_ref(9);</div>
<div class="line"> std::vector<ScalarType> eigenvalues(9);</div>
<div class="line"></div>
<div class="line"> <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> vcl_eigenvalues(9);</div>
<div class="line"></div>
<div class="line"> initialize(A_input, eigenvalues_ref);</div>
<div class="line"></div>
<div class="line"> std::cout << std::endl <<<span class="stringliteral">"Input matrix: "</span> << std::endl;</div>
<div class="line"> std::cout << A_input << std::endl;</div>
<div class="line"></div>
<div class="line"> <a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<ScalarType></a> A_input2(A_input); <span class="comment">// duplicate to demonstrate the use with both std::vector and viennacl::vector</span></div>
<div class="line"></div>
<div class="line"></div>
<div class="line"> std::cout << <span class="stringliteral">"Calculation..."</span> << std::endl;</div>
<div class="line"> <a class="code" href="namespaceviennacl_1_1linalg.html#a51cbe06645207f9b3054e8725269cc71">viennacl::linalg::qr_method_sym</a>(A_input, Q, eigenvalues);</div>
<div class="line"></div>
<div class="line"> <a class="code" href="namespaceviennacl_1_1linalg.html#a51cbe06645207f9b3054e8725269cc71">viennacl::linalg::qr_method_sym</a>(A_input2, Q, vcl_eigenvalues);</div>
<div class="line"></div>
<div class="line"> std::cout << std::endl << <span class="stringliteral">"Eigenvalues with std::vector<T>:"</span> << std::endl;</div>
<div class="line"> <a class="code" href="qr__method__func_8cpp.html#afe063343d3b1e9d9665d8cb04dd59c6d">vector_print</a>(eigenvalues);</div>
<div class="line"> std::cout << <span class="stringliteral">"Eigenvalues with viennacl::vector<T>: "</span> << std::endl << vcl_eigenvalues << std::endl;</div>
<div class="line"> std::cout << std::endl << <span class="stringliteral">"Reference eigenvalues:"</span> << std::endl;</div>
<div class="line"> <a class="code" href="qr__method__func_8cpp.html#afe063343d3b1e9d9665d8cb04dd59c6d">vector_print</a>(eigenvalues_ref);</div>
<div class="line"> std::cout << std::endl;</div>
<div class="line"> std::cout << <span class="stringliteral">"Eigenvectors - each column is an eigenvector"</span> << std::endl;</div>
<div class="line"> std::cout << Q << std::endl;</div>
<div class="line"></div>
<div class="line"> std::cout << std::endl;</div>
<div class="line"> std::cout << <span class="stringliteral">"------- Tutorial completed --------"</span> << std::endl;</div>
<div class="line"> std::cout << std::endl;</div>
<div class="line"></div>
<div class="line"> <span class="keywordflow">return</span> EXIT_SUCCESS;</div>
<div class="line">}</div>
<div class="line"></div>
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