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<div id="projectname">ViennaCL - The Vienna Computing Library
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<div class="title">tql2.cpp</div> </div>
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<p>This tutorial explains how one can use the tql-algorithm to compute the eigenvalues of tridiagonal matrices.</p>
<p>We start with including the necessary headers: </p>
<div class="fragment"><div class="line"><span class="comment">// include necessary 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 <limits></span></div>
<div class="line"><span class="preprocessor">#include <string></span></div>
<div class="line"><span class="preprocessor">#include <iomanip></span></div>
<div class="line"></div>
<div class="line"><span class="preprocessor">#define VIENNACL_WITH_UBLAS</span></div>
<div class="line"></div>
<div class="line"><span class="comment">//include basic scalar and vector types of ViennaCL</span></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="scalar_8hpp.html">viennacl/scalar.hpp</a>"</span></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="vector_8hpp.html">viennacl/vector.hpp</a>"</span></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="compressed__matrix_8hpp.html">viennacl/compressed_matrix.hpp</a>"</span></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="matrix__market_8hpp.html">viennacl/io/matrix_market.hpp</a>"</span></div>
<div class="line"></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"><span class="preprocessor">#include "<a class="code" href="qr-method-common_8hpp.html">viennacl/linalg/qr-method-common.hpp</a>"</span></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="host__based_2matrix__operations_8hpp.html">viennacl/linalg/host_based/matrix_operations.hpp</a>"</span></div>
<div class="line"></div>
<div class="line"><span class="comment">// Use the shortcut 'ublas::' instead of 'boost::numeric::ublas::'</span></div>
<div class="line"><span class="keyword">namespace </span>ublas = boost::numeric::ublas;</div>
<div class="line"></div>
<div class="line"><span class="comment">// Run in single precision. Change to double precision if provided by your GPU.</span></div>
<div class="line"><span class="keyword">typedef</span> <span class="keywordtype">float</span> <a name="a0"></a><a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>;</div>
</div><!-- fragment --><p> We generate a symmetric tridiagonal matrix with known eigenvalues, call the tql-algorithm, and then print the results. </p>
<div class="fragment"><div class="line"><span class="keywordtype">int</span> <a name="a1"></a><a class="code" href="tests_2src_2bisect_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>()</div>
<div class="line">{</div>
<div class="line"> std::size_t sz = 10;</div>
<div class="line"> std::cout << <span class="stringliteral">"Compute eigenvalues and eigenvectors of matrix of size "</span> << sz << <span class="stringliteral">"-by-"</span> << sz << std::endl << std::endl;</div>
<div class="line"></div>
<div class="line"> std::vector<ScalarType> d(sz), e(sz);</div>
<div class="line"> <span class="comment">// Initialize diagonal and superdiagonal elements of the tridiagonal matrix</span></div>
<div class="line"> d[0] = 1; e[0] = 0;</div>
<div class="line"> d[1] = 2; e[1] = 4;</div>
<div class="line"> d[2] =-4; e[2] = 5;</div>
<div class="line"> d[3] = 6; e[3] = 1;</div>
<div class="line"> d[4] = 3; e[4] = 2;</div>
<div class="line"> d[5] = 4; e[5] =-3;</div>
<div class="line"> d[6] = 7; e[6] = 5;</div>
<div class="line"> d[7] = 9; e[7] = 1;</div>
<div class="line"> d[8] = 3; e[8] = 5;</div>
<div class="line"> d[9] = 8; e[9] = 2;</div>
</div><!-- fragment --><p> Initialize the matrix Q as the identity matrix. It will hold the eigenvectors. </p>
<div class="fragment"><div class="line"><a name="_a2"></a><a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<ScalarType></a> Q = <a name="_a3"></a><a class="code" href="classviennacl_1_1identity__matrix.html">viennacl::identity_matrix<ScalarType></a>(sz);</div>
</div><!-- fragment --><p> Compute the eigenvalues and eigenvectors </p>
<div class="fragment"><div class="line"><a name="a4"></a><a class="code" href="namespaceviennacl_1_1linalg.html#a3fe3eb20d4dcda794259fd6a6d30afb6">viennacl::linalg::tql2</a>(Q, d, e);</div>
</div><!-- fragment --><p> Print the results: </p>
<div class="fragment"><div class="line">std::cout << <span class="stringliteral">"Eigenvalues: "</span> << std::endl;</div>
<div class="line"><span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i = 0; i < d.size(); i++)</div>
<div class="line"> std::cout << std::setprecision(6) << std::fixed << d[i] << <span class="stringliteral">" "</span>;</div>
<div class="line">std::cout << std::endl;</div>
<div class="line"></div>
<div class="line">std::cout << std::endl;</div>
<div class="line">std::cout << <span class="stringliteral">"Eigenvectors corresponding to the eigenvalues above are the columns: "</span> << std::endl << std::endl;</div>
<div class="line">std::cout << Q << std::endl;</div>
</div><!-- fragment --><p> That's it. Print success message and exit. </p>
<div class="fragment"><div class="line"> std::cout << std::endl <<<span class="stringliteral">"--------TUTORIAL COMPLETED----------"</span> << 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>
<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">// include necessary 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 <limits></span></div>
<div class="line"><span class="preprocessor">#include <string></span></div>
<div class="line"><span class="preprocessor">#include <iomanip></span></div>
<div class="line"></div>
<div class="line"><span class="preprocessor">#define VIENNACL_WITH_UBLAS</span></div>
<div class="line"></div>
<div class="line"><span class="comment">//include basic scalar and vector types of ViennaCL</span></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="scalar_8hpp.html">viennacl/scalar.hpp</a>"</span></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="vector_8hpp.html">viennacl/vector.hpp</a>"</span></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="compressed__matrix_8hpp.html">viennacl/compressed_matrix.hpp</a>"</span></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="matrix__market_8hpp.html">viennacl/io/matrix_market.hpp</a>"</span></div>
<div class="line"></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"><span class="preprocessor">#include "<a class="code" href="qr-method-common_8hpp.html">viennacl/linalg/qr-method-common.hpp</a>"</span></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="host__based_2matrix__operations_8hpp.html">viennacl/linalg/host_based/matrix_operations.hpp</a>"</span></div>
<div class="line"></div>
<div class="line"><span class="comment">// Use the shortcut 'ublas::' instead of 'boost::numeric::ublas::'</span></div>
<div class="line"><span class="keyword">namespace </span>ublas = boost::numeric::ublas;</div>
<div class="line"></div>
<div class="line"><span class="comment">// Run in single precision. Change to double precision if provided by your GPU.</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"><span class="keywordtype">int</span> <a class="code" href="tests_2src_2bisect_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>()</div>
<div class="line">{</div>
<div class="line"> std::size_t sz = 10;</div>
<div class="line"> std::cout << <span class="stringliteral">"Compute eigenvalues and eigenvectors of matrix of size "</span> << sz << <span class="stringliteral">"-by-"</span> << sz << std::endl << std::endl;</div>
<div class="line"></div>
<div class="line"> std::vector<ScalarType> d(sz), e(sz);</div>
<div class="line"> <span class="comment">// Initialize diagonal and superdiagonal elements of the tridiagonal matrix</span></div>
<div class="line"> d[0] = 1; e[0] = 0;</div>
<div class="line"> d[1] = 2; e[1] = 4;</div>
<div class="line"> d[2] =-4; e[2] = 5;</div>
<div class="line"> d[3] = 6; e[3] = 1;</div>
<div class="line"> d[4] = 3; e[4] = 2;</div>
<div class="line"> d[5] = 4; e[5] =-3;</div>
<div class="line"> d[6] = 7; e[6] = 5;</div>
<div class="line"> d[7] = 9; e[7] = 1;</div>
<div class="line"> d[8] = 3; e[8] = 5;</div>
<div class="line"> d[9] = 8; e[9] = 2;</div>
<div class="line"></div>
<div class="line"> <a class="code" href="classviennacl_1_1matrix.html">viennacl::matrix<ScalarType></a> Q = <a class="code" href="classviennacl_1_1identity__matrix.html">viennacl::identity_matrix<ScalarType></a>(sz);</div>
<div class="line"></div>
<div class="line"> <a class="code" href="namespaceviennacl_1_1linalg.html#a3fe3eb20d4dcda794259fd6a6d30afb6">viennacl::linalg::tql2</a>(Q, d, e);</div>
<div class="line"></div>
<div class="line"> std::cout << <span class="stringliteral">"Eigenvalues: "</span> << std::endl;</div>
<div class="line"> <span class="keywordflow">for</span> (<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> i = 0; i < d.size(); i++)</div>
<div class="line"> std::cout << std::setprecision(6) << std::fixed << d[i] << <span class="stringliteral">" "</span>;</div>
<div class="line"> std::cout << std::endl;</div>
<div class="line"></div>
<div class="line"> std::cout << std::endl;</div>
<div class="line"> std::cout << <span class="stringliteral">"Eigenvectors corresponding to the eigenvalues above are the columns: "</span> << std::endl << std::endl;</div>
<div class="line"> std::cout << Q << std::endl;</div>
<div class="line"></div>
<div class="line"> std::cout << std::endl <<<span class="stringliteral">"--------TUTORIAL COMPLETED----------"</span> << std::endl;</div>
<div class="line"></div>
<div class="line"> <span class="keywordflow">return</span> EXIT_SUCCESS;</div>
<div class="line">}</div>
</div><!-- fragment --> </div><!-- contents -->
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