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<div class="title">power-iter.cpp</div> </div>
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<p>This tutorial demonstrates the calculation of the eigenvalue with largest modulus using the power iteration method.</p>
<p>We start with including the necessary headers: </p>
<div class="fragment"><div class="line"><span class="comment">// Sparse matrices in uBLAS are *very* slow if debug mode is enabled. Disable it:</span></div>
<div class="line"><span class="preprocessor">#ifndef NDEBUG</span></div>
<div class="line"><span class="preprocessor"> #define BOOST_UBLAS_NDEBUG</span></div>
<div class="line"><span class="preprocessor">#endif</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"></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"></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="power__iter_8hpp.html">viennacl/linalg/power_iter.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="comment">// Some helper functions for this tutorial:</span></div>
<div class="line"><span class="preprocessor">#include <iostream></span></div>
<div class="line"></div>
<div class="line"><span class="comment">// Boost includes:</span></div>
<div class="line"><span class="preprocessor">#include <boost/numeric/ublas/matrix.hpp></span></div>
<div class="line"><span class="preprocessor">#include <boost/numeric/ublas/matrix_proxy.hpp></span></div>
<div class="line"><span class="preprocessor">#include <boost/numeric/ublas/matrix_expression.hpp></span></div>
<div class="line"><span class="preprocessor">#include <boost/numeric/ublas/matrix_sparse.hpp></span></div>
<div class="line"><span class="preprocessor">#include <boost/numeric/ublas/vector.hpp></span></div>
<div class="line"><span class="preprocessor">#include <boost/numeric/ublas/operation.hpp></span></div>
<div class="line"><span class="preprocessor">#include <boost/numeric/ublas/vector_expression.hpp></span></div>
</div><!-- fragment --><p> To run the power iteration, we set up a sparse matrix using Boost.uBLAS, transfer it over to a ViennaCL matrix, and then run the algorithm. </p>
<div class="fragment"><div class="line"><span class="keywordtype">int</span> <a name="a0"></a><a class="code" href="tests_2src_2bisect_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>()</div>
<div class="line">{</div>
<div class="line"> <span class="comment">// This example relies on double precision to be available and will provide only poor results with single precision</span></div>
<div class="line"> <span class="keyword">typedef</span> <span class="keywordtype">double</span> <a name="a1"></a><a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>;</div>
</div><!-- fragment --><p> Create the sparse uBLAS matrix and read the matrix from the matrix-market file: </p>
<div class="fragment"><div class="line">boost::numeric::ublas::compressed_matrix<ScalarType> ublas_A;</div>
<div class="line"></div>
<div class="line"><span class="keywordflow">if</span> (!<a name="a2"></a><a class="code" href="namespaceviennacl_1_1io.html#ad934125ed3dbe661e264bcd7d62b1048">viennacl::io::read_matrix_market_file</a>(ublas_A, <span class="stringliteral">"../examples/testdata/mat65k.mtx"</span>))</div>
<div class="line">{</div>
<div class="line"> std::cout << <span class="stringliteral">"Error reading Matrix file"</span> << std::endl;</div>
<div class="line"> <span class="keywordflow">return</span> EXIT_FAILURE;</div>
<div class="line">}</div>
</div><!-- fragment --><p> Transfer the data from the uBLAS matrix over to the ViennaCL sparse matrix: </p>
<div class="fragment"><div class="line"><a name="_a3"></a><a class="code" href="classviennacl_1_1compressed__matrix.html">viennacl::compressed_matrix<ScalarType></a> vcl_A(ublas_A.size1(), ublas_A.size2());</div>
<div class="line"><a name="a4"></a><a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(ublas_A, vcl_A);</div>
</div><!-- fragment --><p> Run the power iteration up until the largest eigenvalue changes by less than the specified tolerance. Print the results of running with uBLAS as well as ViennaCL and exit. </p>
<div class="fragment"><div class="line"><a name="_a5"></a><a class="code" href="classviennacl_1_1linalg_1_1power__iter__tag.html">viennacl::linalg::power_iter_tag</a> ptag(1e-6);</div>
<div class="line"></div>
<div class="line">std::cout << <span class="stringliteral">"Starting computation of eigenvalue with largest modulus (might take about a minute)..."</span> << std::endl;</div>
<div class="line">std::cout << <span class="stringliteral">"Result of power iteration with ublas matrix (single-threaded): "</span> << <a name="a6"></a><a class="code" href="namespaceviennacl_1_1linalg.html#af5002a88fa4cc3fbe65a904797a0ecba">viennacl::linalg::eig</a>(ublas_A, ptag) << std::endl;</div>
<div class="line">std::cout << <span class="stringliteral">"Result of power iteration with ViennaCL (OpenCL accelerated): "</span> << <a class="code" href="namespaceviennacl_1_1linalg.html#af5002a88fa4cc3fbe65a904797a0ecba">viennacl::linalg::eig</a>(vcl_A, ptag) << std::endl;</div>
</div><!-- fragment --><p> You can also obtain the associated <em>approximated</em> eigenvector by passing it as a third argument to <a class="el" href="namespaceviennacl_1_1linalg.html#af5002a88fa4cc3fbe65a904797a0ecba" title="Implementation of the calculation of eigenvalues using lanczos (with and without reorthogonalization)...">eig()</a> Tighten the tolerance passed to ptag above in order to obtain more accurate results. </p>
<div class="fragment"><div class="line"> <a name="_a7"></a><a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> eigenvector(vcl_A.size1());</div>
<div class="line"> <a class="code" href="namespaceviennacl_1_1linalg.html#af5002a88fa4cc3fbe65a904797a0ecba">viennacl::linalg::eig</a>(vcl_A, ptag, eigenvector);</div>
<div class="line"> std::cout << <span class="stringliteral">"First three entries in eigenvector: "</span> << eigenvector[0] << <span class="stringliteral">" "</span> << eigenvector[1] << <span class="stringliteral">" "</span> << eigenvector[2] << std::endl;</div>
<div class="line"> <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> Ax = <a name="a8"></a><a class="code" href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">viennacl::linalg::prod</a>(vcl_A, eigenvector);</div>
<div class="line"> std::cout << <span class="stringliteral">"First three entries in A*eigenvector: "</span> << Ax[0] << <span class="stringliteral">" "</span> << Ax[1] << <span class="stringliteral">" "</span> << Ax[2] << 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">// Sparse matrices in uBLAS are *very* slow if debug mode is enabled. Disable it:</span></div>
<div class="line"><span class="preprocessor">#ifndef NDEBUG</span></div>
<div class="line"><span class="preprocessor"> #define BOOST_UBLAS_NDEBUG</span></div>
<div class="line"><span class="preprocessor">#endif</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"></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"></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="power__iter_8hpp.html">viennacl/linalg/power_iter.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="comment">// Some helper functions for this tutorial:</span></div>
<div class="line"><span class="preprocessor">#include <iostream></span></div>
<div class="line"></div>
<div class="line"><span class="comment">// Boost includes:</span></div>
<div class="line"><span class="preprocessor">#include <boost/numeric/ublas/matrix.hpp></span></div>
<div class="line"><span class="preprocessor">#include <boost/numeric/ublas/matrix_proxy.hpp></span></div>
<div class="line"><span class="preprocessor">#include <boost/numeric/ublas/matrix_expression.hpp></span></div>
<div class="line"><span class="preprocessor">#include <boost/numeric/ublas/matrix_sparse.hpp></span></div>
<div class="line"><span class="preprocessor">#include <boost/numeric/ublas/vector.hpp></span></div>
<div class="line"><span class="preprocessor">#include <boost/numeric/ublas/operation.hpp></span></div>
<div class="line"><span class="preprocessor">#include <boost/numeric/ublas/vector_expression.hpp></span></div>
<div class="line"></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"> <span class="comment">// This example relies on double precision to be available and will provide only poor results with single precision</span></div>
<div class="line"> <span class="keyword">typedef</span> <span class="keywordtype">double</span> <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>;</div>
<div class="line"></div>
<div class="line"> boost::numeric::ublas::compressed_matrix<ScalarType> ublas_A;</div>
<div class="line"></div>
<div class="line"> <span class="keywordflow">if</span> (!<a class="code" href="namespaceviennacl_1_1io.html#ad934125ed3dbe661e264bcd7d62b1048">viennacl::io::read_matrix_market_file</a>(ublas_A, <span class="stringliteral">"../examples/testdata/mat65k.mtx"</span>))</div>
<div class="line"> {</div>
<div class="line"> std::cout << <span class="stringliteral">"Error reading Matrix file"</span> << std::endl;</div>
<div class="line"> <span class="keywordflow">return</span> EXIT_FAILURE;</div>
<div class="line"> }</div>
<div class="line"></div>
<div class="line"> <a class="code" href="classviennacl_1_1compressed__matrix.html">viennacl::compressed_matrix<ScalarType></a> vcl_A(ublas_A.size1(), ublas_A.size2());</div>
<div class="line"> <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(ublas_A, vcl_A);</div>
<div class="line"></div>
<div class="line"> <a class="code" href="classviennacl_1_1linalg_1_1power__iter__tag.html">viennacl::linalg::power_iter_tag</a> ptag(1e-6);</div>
<div class="line"></div>
<div class="line"> std::cout << <span class="stringliteral">"Starting computation of eigenvalue with largest modulus (might take about a minute)..."</span> << std::endl;</div>
<div class="line"> std::cout << <span class="stringliteral">"Result of power iteration with ublas matrix (single-threaded): "</span> << <a class="code" href="namespaceviennacl_1_1linalg.html#af5002a88fa4cc3fbe65a904797a0ecba">viennacl::linalg::eig</a>(ublas_A, ptag) << std::endl;</div>
<div class="line"> std::cout << <span class="stringliteral">"Result of power iteration with ViennaCL (OpenCL accelerated): "</span> << <a class="code" href="namespaceviennacl_1_1linalg.html#af5002a88fa4cc3fbe65a904797a0ecba">viennacl::linalg::eig</a>(vcl_A, ptag) << std::endl;</div>
<div class="line"></div>
<div class="line"> <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> eigenvector(vcl_A.size1());</div>
<div class="line"> <a class="code" href="namespaceviennacl_1_1linalg.html#af5002a88fa4cc3fbe65a904797a0ecba">viennacl::linalg::eig</a>(vcl_A, ptag, eigenvector);</div>
<div class="line"> std::cout << <span class="stringliteral">"First three entries in eigenvector: "</span> << eigenvector[0] << <span class="stringliteral">" "</span> << eigenvector[1] << <span class="stringliteral">" "</span> << eigenvector[2] << std::endl;</div>
<div class="line"> <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> Ax = <a class="code" href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">viennacl::linalg::prod</a>(vcl_A, eigenvector);</div>
<div class="line"> std::cout << <span class="stringliteral">"First three entries in A*eigenvector: "</span> << Ax[0] << <span class="stringliteral">" "</span> << Ax[1] << <span class="stringliteral">" "</span> << Ax[2] << 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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