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<div id="projectname">ViennaCL - The Vienna Computing Library
 <span id="projectnumber">1.7.1</span>
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<div id="projectbrief">Free open-source GPU-accelerated linear algebra and solver library.</div>
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<div class="title">iterative.cpp</div> </div>
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<p>This tutorial explains the use of iterative solvers in ViennaCL.</p>
<dl class="section note"><dt>Note</dt><dd><a class="el" href="iterative_8cpp.html">iterative.cpp</a> and iterative.cu are identical, the latter being required for compilation using CUDA nvcc</dd></dl>
<p>We start with including the necessary system headers: </p>
<div class="fragment"><div class="line"><span class="comment">//</span></div>
<div class="line"><span class="comment">// include necessary system headers</span></div>
<div class="line"><span class="comment">//</span></div>
<div class="line"><span class="preprocessor">#include <iostream></span></div>
<div class="line"></div>
<div class="line"><span class="comment">//</span></div>
<div class="line"><span class="comment">// Necessary to obtain a suitable performance in ublas</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">//</span></div>
<div class="line"><span class="comment">// ublas includes</span></div>
<div class="line"><span class="comment">//</span></div>
<div class="line"><span class="preprocessor">#include <boost/numeric/ublas/io.hpp></span></div>
<div class="line"><span class="preprocessor">#include <boost/numeric/ublas/triangular.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/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/operation.hpp></span></div>
<div class="line"><span class="preprocessor">#include <boost/numeric/ublas/operation_sparse.hpp></span></div>
<div class="line"><span class="preprocessor">#include <boost/numeric/ublas/io.hpp></span></div>
<div class="line"><span class="preprocessor">#include <boost/numeric/ublas/lu.hpp></span></div>
<div class="line"></div>
<div class="line"><span class="comment">// Must be set if you want to use ViennaCL algorithms on ublas objects</span></div>
<div class="line"><span class="preprocessor">#define VIENNACL_WITH_UBLAS 1</span></div>
<div class="line"></div>
<div class="line"></div>
<div class="line"><span class="comment">//</span></div>
<div class="line"><span class="comment">// ViennaCL includes</span></div>
<div class="line"><span class="comment">//</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="coordinate__matrix_8hpp.html">viennacl/coordinate_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="ilu_8hpp.html">viennacl/linalg/ilu.hpp</a>"</span></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="jacobi__precond_8hpp.html">viennacl/linalg/jacobi_precond.hpp</a>"</span></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="cg_8hpp.html">viennacl/linalg/cg.hpp</a>"</span></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="bicgstab_8hpp.html">viennacl/linalg/bicgstab.hpp</a>"</span></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="gmres_8hpp.html">viennacl/linalg/gmres.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"></div>
<div class="line"><span class="comment">// Some helper functions for this tutorial:</span></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="vector-io_8hpp.html">vector-io.hpp</a>"</span></div>
</div><!-- fragment --><p> A shortcut for convience (use <code>ublas::</code> instead of <code>boost::numeric::ublas::</code>) </p>
<div class="fragment"><div class="line"><span class="keyword">using namespace </span>boost::numeric;</div>
</div><!-- fragment --><p> In the <a class="el" href="tests_2src_2bisect_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main()</a> routine we create matrices and vectors using Boost.uBLAS types and fill them with data. Then, ViennaCL types are created and the data is copied from the respective Boost.uBLAS objects. Various preconditioners are set up and finally the iterative solvers get called. </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="keyword">typedef</span> <span class="keywordtype">float</span> <a name="a1"></a><a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>;</div>
</div><!-- fragment --><p> Set up some ublas objects </p>
<div class="fragment"><div class="line">ublas::vector<ScalarType> rhs;</div>
<div class="line">ublas::vector<ScalarType> ref_result;</div>
<div class="line">ublas::vector<ScalarType> result;</div>
<div class="line">ublas::compressed_matrix<ScalarType> ublas_matrix;</div>
</div><!-- fragment --><p> Read system matrix from a matrix-market file </p>
<div class="fragment"><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_matrix, <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"><span class="keywordflow">if</span> (!<a name="a3"></a><a class="code" href="vector-io_8hpp.html#a303954a45833b84192a6dcf3065f85e3">readVectorFromFile</a>(<span class="stringliteral">"../examples/testdata/rhs65025.txt"</span>, rhs))</div>
<div class="line">{</div>
<div class="line"> std::cout << <span class="stringliteral">"Error reading RHS 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"><span class="keywordflow">if</span> (!<a class="code" href="vector-io_8hpp.html#a303954a45833b84192a6dcf3065f85e3">readVectorFromFile</a>(<span class="stringliteral">"../examples/testdata/result65025.txt"</span>, ref_result))</div>
<div class="line">{</div>
<div class="line"> std::cout << <span class="stringliteral">"Error reading Result file"</span> << std::endl;</div>
<div class="line"> <span class="keywordflow">return</span> EXIT_FAILURE;</div>
<div class="line">}</div>
</div><!-- fragment --><p> Set up some ViennaCL objects </p>
<div class="fragment"><div class="line">std::size_t vcl_size = rhs.size();</div>
<div class="line"><a name="_a4"></a><a class="code" href="classviennacl_1_1compressed__matrix.html">viennacl::compressed_matrix<ScalarType></a> vcl_compressed_matrix;</div>
<div class="line"><a name="_a5"></a><a class="code" href="classviennacl_1_1coordinate__matrix.html">viennacl::coordinate_matrix<ScalarType></a> vcl_coordinate_matrix;</div>
<div class="line"><a name="_a6"></a><a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> vcl_rhs(vcl_size);</div>
<div class="line"><a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> vcl_result(vcl_size);</div>
<div class="line"><a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> vcl_ref_result(vcl_size);</div>
<div class="line"></div>
<div class="line"><a name="a7"></a><a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(rhs.begin(), rhs.end(), vcl_rhs.begin());</div>
<div class="line"><a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(ref_result.begin(), ref_result.end(), vcl_ref_result.begin());</div>
</div><!-- fragment --><p> Transfer ublas-matrix to GPU: </p>
<div class="fragment"><div class="line"><a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(ublas_matrix, vcl_compressed_matrix);</div>
</div><!-- fragment --><p> An alternative way is to use the C++ STL. In such case, the sparse matrix is represented as a std::vector< std::map< unsigned int, ScalarType> > After the instantiation, the data from the uBLAS matrix is copied over to the STL-matrix, which is then copied over to a ViennaCL matrix. This step is just for demonstration purposes. </p>
<div class="fragment"><div class="line">std::vector< std::map< unsigned int, ScalarType> > stl_matrix(rhs.size());</div>
<div class="line"><span class="keywordflow">for</span> (ublas::compressed_matrix<ScalarType>::iterator1 iter1 = ublas_matrix.begin1();</div>
<div class="line"> iter1 != ublas_matrix.end1();</div>
<div class="line"> ++iter1)</div>
<div class="line">{</div>
<div class="line"> <span class="keywordflow">for</span> (ublas::compressed_matrix<ScalarType>::iterator2 iter2 = iter1.begin();</div>
<div class="line"> iter2 != iter1.end();</div>
<div class="line"> ++iter2)</div>
<div class="line"> stl_matrix[iter2.index1()][<span class="keyword">static_cast<</span><span class="keywordtype">unsigned</span> <span class="keywordtype">int</span><span class="keyword">></span>(iter2.index2())] = *iter2;</div>
<div class="line">}</div>
<div class="line">std::vector<ScalarType> stl_rhs(rhs.size()), stl_result(result.size());</div>
<div class="line"><a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">std::copy</a>(rhs.begin(), rhs.end(), stl_rhs.begin());</div>
<div class="line"><a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(stl_matrix, vcl_coordinate_matrix);</div>
<div class="line"><a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(vcl_coordinate_matrix, stl_matrix);</div>
</div><!-- fragment --><p> Set up ILUT preconditioners for ublas and ViennaCL objects: </p>
<div class="fragment"><div class="line">std::cout << <span class="stringliteral">"Setting up preconditioners for uBLAS-matrix..."</span> << std::endl;</div>
<div class="line"><a name="_a8"></a><a class="code" href="classviennacl_1_1linalg_1_1ilut__precond.html">viennacl::linalg::ilut_precond< ublas::compressed_matrix<ScalarType></a> > ublas_ilut(ublas_matrix, <a name="_a9"></a><a class="code" href="classviennacl_1_1linalg_1_1ilut__tag.html">viennacl::linalg::ilut_tag</a>());</div>
<div class="line"><a name="_a10"></a><a class="code" href="classviennacl_1_1linalg_1_1ilu0__precond.html">viennacl::linalg::ilu0_precond< ublas::compressed_matrix<ScalarType></a> > ublas_ilu0(ublas_matrix, <a name="_a11"></a><a class="code" href="classviennacl_1_1linalg_1_1ilu0__tag.html">viennacl::linalg::ilu0_tag</a>());</div>
<div class="line"><a name="_a12"></a><a class="code" href="classviennacl_1_1linalg_1_1block__ilu__precond.html">viennacl::linalg::block_ilu_precond< ublas::compressed_matrix<ScalarType></a>,</div>
<div class="line"> <a class="code" href="classviennacl_1_1linalg_1_1ilu0__tag.html">viennacl::linalg::ilu0_tag</a>> ublas_block_ilu0(ublas_matrix, <a class="code" href="classviennacl_1_1linalg_1_1ilu0__tag.html">viennacl::linalg::ilu0_tag</a>());</div>
<div class="line"></div>
<div class="line">std::cout << <span class="stringliteral">"Setting up preconditioners for ViennaCL-matrix..."</span> << std::endl;</div>
<div class="line"><a class="code" href="classviennacl_1_1linalg_1_1ilut__precond.html">viennacl::linalg::ilut_precond< viennacl::compressed_matrix<ScalarType></a> > vcl_ilut(vcl_compressed_matrix, <a class="code" href="classviennacl_1_1linalg_1_1ilut__tag.html">viennacl::linalg::ilut_tag</a>());</div>
<div class="line"><a class="code" href="classviennacl_1_1linalg_1_1ilu0__precond.html">viennacl::linalg::ilu0_precond< viennacl::compressed_matrix<ScalarType></a> > vcl_ilu0(vcl_compressed_matrix, <a class="code" href="classviennacl_1_1linalg_1_1ilu0__tag.html">viennacl::linalg::ilu0_tag</a>());</div>
<div class="line"><a class="code" href="classviennacl_1_1linalg_1_1block__ilu__precond.html">viennacl::linalg::block_ilu_precond< viennacl::compressed_matrix<ScalarType></a>,</div>
<div class="line"> <a class="code" href="classviennacl_1_1linalg_1_1ilu0__tag.html">viennacl::linalg::ilu0_tag</a>> vcl_block_ilu0(vcl_compressed_matrix, <a class="code" href="classviennacl_1_1linalg_1_1ilu0__tag.html">viennacl::linalg::ilu0_tag</a>());</div>
</div><!-- fragment --><p> set up Jacobi preconditioners for ViennaCL and ublas objects: </p>
<div class="fragment"><div class="line"><a name="_a13"></a><a class="code" href="classviennacl_1_1linalg_1_1jacobi__precond.html">viennacl::linalg::jacobi_precond< ublas::compressed_matrix<ScalarType></a> > ublas_jacobi(ublas_matrix, <a name="_a14"></a><a class="code" href="classviennacl_1_1linalg_1_1jacobi__tag.html">viennacl::linalg::jacobi_tag</a>());</div>
<div class="line"><a class="code" href="classviennacl_1_1linalg_1_1jacobi__precond.html">viennacl::linalg::jacobi_precond< viennacl::compressed_matrix<ScalarType></a> > vcl_jacobi(vcl_compressed_matrix, <a class="code" href="classviennacl_1_1linalg_1_1jacobi__tag.html">viennacl::linalg::jacobi_tag</a>());</div>
</div><!-- fragment --> <h2>Conjugate Gradient Solver</h2>
<div class="fragment"><div class="line">std::cout << <span class="stringliteral">"----- CG Method -----"</span> << std::endl;</div>
</div><!-- fragment --><p> Run the CG method with uBLAS objects. Use a relative tolerance of <img class="formulaInl" alt="$ 10^{-6} $" src="form_111.png"/> and a maximum of 20 iterations when using ILUT or Jacobi preconditioners. You might need higher iteration counts for poorly conditioned systems. </p>
<div class="fragment"><div class="line">result = <a name="a15"></a><a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(ublas_matrix, rhs, <a name="_a16"></a><a class="code" href="classviennacl_1_1linalg_1_1cg__tag.html">viennacl::linalg::cg_tag</a>());</div>
<div class="line">result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(ublas_matrix, rhs, <a class="code" href="classviennacl_1_1linalg_1_1cg__tag.html">viennacl::linalg::cg_tag</a>(1e-6, 20), ublas_ilut);</div>
<div class="line">result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(ublas_matrix, rhs, <a class="code" href="classviennacl_1_1linalg_1_1cg__tag.html">viennacl::linalg::cg_tag</a>(1e-6, 20), ublas_jacobi);</div>
</div><!-- fragment --><p> Run the CG method for ViennaCL objects. The results here should be the same as with uBLAS objects (at least up to round-off error). </p>
<div class="fragment"><div class="line">vcl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(vcl_compressed_matrix, vcl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1cg__tag.html">viennacl::linalg::cg_tag</a>());</div>
<div class="line">vcl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(vcl_compressed_matrix, vcl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1cg__tag.html">viennacl::linalg::cg_tag</a>(1e-6, 20), vcl_ilut);</div>
<div class="line">vcl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(vcl_compressed_matrix, vcl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1cg__tag.html">viennacl::linalg::cg_tag</a>(1e-6, 20), vcl_jacobi);</div>
</div><!-- fragment --><p> Convenience option: Run the CG method by passing STL types. This will use appropriate ViennaCL objects internally. You need to include <a class="el" href="compressed__matrix_8hpp.html" title="Implementation of the compressed_matrix class. ">viennacl/compressed_matrix.hpp</a> and <a class="el" href="vector_8hpp.html" title="The vector type with operator-overloads and proxy classes is defined here. Linear algebra operations ...">viennacl/vector.hpp</a> before <a class="el" href="cg_8hpp.html" title="The conjugate gradient method is implemented here. ">viennacl/linalg/cg.hpp</a> for this to work! </p>
<div class="fragment"><div class="line">stl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(stl_matrix, stl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1cg__tag.html">viennacl::linalg::cg_tag</a>());</div>
<div class="line">stl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(stl_matrix, stl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1cg__tag.html">viennacl::linalg::cg_tag</a>(1e-6, 20), vcl_ilut);</div>
<div class="line">stl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(stl_matrix, stl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1cg__tag.html">viennacl::linalg::cg_tag</a>(1e-6, 20), vcl_jacobi);</div>
</div><!-- fragment --> <h2>Stabilized BiConjugate Gradient Solver</h2>
<div class="fragment"><div class="line">std::cout << <span class="stringliteral">"----- BiCGStab Method -----"</span> << std::endl;</div>
</div><!-- fragment --><p> Run BiCGStab for Boost.uBLAS objects. Parameters are the same as for the CG method. </p>
<div class="fragment"><div class="line">result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(ublas_matrix, rhs, <a name="_a17"></a><a class="code" href="classviennacl_1_1linalg_1_1bicgstab__tag.html">viennacl::linalg::bicgstab_tag</a>()); <span class="comment">//without preconditioner</span></div>
<div class="line">result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(ublas_matrix, rhs, <a class="code" href="classviennacl_1_1linalg_1_1bicgstab__tag.html">viennacl::linalg::bicgstab_tag</a>(1e-6, 20), ublas_ilut); <span class="comment">//with preconditioner</span></div>
<div class="line">result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(ublas_matrix, rhs, <a class="code" href="classviennacl_1_1linalg_1_1bicgstab__tag.html">viennacl::linalg::bicgstab_tag</a>(1e-6, 20), ublas_jacobi); <span class="comment">//with preconditioner</span></div>
</div><!-- fragment --><p> Run the BiCGStab method for ViennaCL objects. The results here should be the same as with uBLAS objects (at least up to round-off error). </p>
<div class="fragment"><div class="line">vcl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(vcl_compressed_matrix, vcl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1bicgstab__tag.html">viennacl::linalg::bicgstab_tag</a>()); <span class="comment">//without preconditioner</span></div>
<div class="line">vcl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(vcl_compressed_matrix, vcl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1bicgstab__tag.html">viennacl::linalg::bicgstab_tag</a>(1e-6, 20), vcl_ilut); <span class="comment">//with preconditioner</span></div>
<div class="line">vcl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(vcl_compressed_matrix, vcl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1bicgstab__tag.html">viennacl::linalg::bicgstab_tag</a>(1e-6, 20), vcl_jacobi); <span class="comment">//with preconditioner</span></div>
</div><!-- fragment --><p> Convenience option: Run the BiCGStab method by passing STL types. This will use appropriate ViennaCL objects internally. You need to include <a class="el" href="compressed__matrix_8hpp.html" title="Implementation of the compressed_matrix class. ">viennacl/compressed_matrix.hpp</a> and <a class="el" href="vector_8hpp.html" title="The vector type with operator-overloads and proxy classes is defined here. Linear algebra operations ...">viennacl/vector.hpp</a> before <a class="el" href="bicgstab_8hpp.html" title="The stabilized bi-conjugate gradient method is implemented here. ">viennacl/linalg/bicgstab.hpp</a> for this to work! </p>
<div class="fragment"><div class="line">stl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(stl_matrix, stl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1bicgstab__tag.html">viennacl::linalg::bicgstab_tag</a>());</div>
<div class="line">stl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(stl_matrix, stl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1bicgstab__tag.html">viennacl::linalg::bicgstab_tag</a>(1e-6, 20), vcl_ilut);</div>
<div class="line">stl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(stl_matrix, stl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1bicgstab__tag.html">viennacl::linalg::bicgstab_tag</a>(1e-6, 20), vcl_jacobi);</div>
</div><!-- fragment --> <h2>GMRES Solver</h2>
<div class="fragment"><div class="line">std::cout << <span class="stringliteral">"----- GMRES Method -----"</span> << std::endl;</div>
</div><!-- fragment --><p> Run GMRES for Boost.uBLAS objects. Parameters are the same as for the CG method. </p>
<div class="fragment"><div class="line">result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(ublas_matrix, rhs, <a name="_a18"></a><a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html">viennacl::linalg::gmres_tag</a>()); <span class="comment">//without preconditioner</span></div>
<div class="line">result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(ublas_matrix, rhs, <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html">viennacl::linalg::gmres_tag</a>(1e-6, 20), ublas_ilut);<span class="comment">//with preconditioner</span></div>
<div class="line">result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(ublas_matrix, rhs, <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html">viennacl::linalg::gmres_tag</a>(1e-6, 20), ublas_jacobi);<span class="comment">//with preconditioner</span></div>
</div><!-- fragment --><p> Run the GMRES method for ViennaCL objects. The results here should be the same as with uBLAS objects (at least up to round-off error). </p>
<div class="fragment"><div class="line">vcl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(vcl_compressed_matrix, vcl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html">viennacl::linalg::gmres_tag</a>()); <span class="comment">//without preconditioner</span></div>
<div class="line">vcl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(vcl_compressed_matrix, vcl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html">viennacl::linalg::gmres_tag</a>(1e-6, 20), vcl_ilut);<span class="comment">//with preconditioner</span></div>
<div class="line">vcl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(vcl_compressed_matrix, vcl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html">viennacl::linalg::gmres_tag</a>(1e-6, 20), vcl_jacobi);<span class="comment">//with preconditioner</span></div>
</div><!-- fragment --><p> Convenience option: Run the GMRES method by passing STL types. This will use appropriate ViennaCL objects internally. You need to include <a class="el" href="compressed__matrix_8hpp.html" title="Implementation of the compressed_matrix class. ">viennacl/compressed_matrix.hpp</a> and <a class="el" href="vector_8hpp.html" title="The vector type with operator-overloads and proxy classes is defined here. Linear algebra operations ...">viennacl/vector.hpp</a> before <a class="el" href="gmres_8hpp.html" title="Implementations of the generalized minimum residual method are in this file. ">viennacl/linalg/gmres.hpp</a> for this to work! </p>
<div class="fragment"><div class="line">stl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(stl_matrix, stl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html">viennacl::linalg::gmres_tag</a>());</div>
<div class="line">stl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(stl_matrix, stl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html">viennacl::linalg::gmres_tag</a>(1e-6, 20), vcl_ilut);</div>
<div class="line">stl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(stl_matrix, stl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html">viennacl::linalg::gmres_tag</a>(1e-6, 20), vcl_jacobi);</div>
</div><!-- fragment --><p> That's it, the tutorial is completed. </p>
<div class="fragment"><div class="line"> std::cout << <span class="stringliteral">"!!!! TUTORIAL COMPLETED SUCCESSFULLY !!!!"</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">//</span></div>
<div class="line"><span class="comment">// include necessary system headers</span></div>
<div class="line"><span class="comment">//</span></div>
<div class="line"><span class="preprocessor">#include <iostream></span></div>
<div class="line"></div>
<div class="line"><span class="comment">//</span></div>
<div class="line"><span class="comment">// Necessary to obtain a suitable performance in ublas</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">//</span></div>
<div class="line"><span class="comment">// ublas includes</span></div>
<div class="line"><span class="comment">//</span></div>
<div class="line"><span class="preprocessor">#include <boost/numeric/ublas/io.hpp></span></div>
<div class="line"><span class="preprocessor">#include <boost/numeric/ublas/triangular.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/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/operation.hpp></span></div>
<div class="line"><span class="preprocessor">#include <boost/numeric/ublas/operation_sparse.hpp></span></div>
<div class="line"><span class="preprocessor">#include <boost/numeric/ublas/io.hpp></span></div>
<div class="line"><span class="preprocessor">#include <boost/numeric/ublas/lu.hpp></span></div>
<div class="line"></div>
<div class="line"><span class="comment">// Must be set if you want to use ViennaCL algorithms on ublas objects</span></div>
<div class="line"><span class="preprocessor">#define VIENNACL_WITH_UBLAS 1</span></div>
<div class="line"></div>
<div class="line"></div>
<div class="line"><span class="comment">//</span></div>
<div class="line"><span class="comment">// ViennaCL includes</span></div>
<div class="line"><span class="comment">//</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="coordinate__matrix_8hpp.html">viennacl/coordinate_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="ilu_8hpp.html">viennacl/linalg/ilu.hpp</a>"</span></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="jacobi__precond_8hpp.html">viennacl/linalg/jacobi_precond.hpp</a>"</span></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="cg_8hpp.html">viennacl/linalg/cg.hpp</a>"</span></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="bicgstab_8hpp.html">viennacl/linalg/bicgstab.hpp</a>"</span></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="gmres_8hpp.html">viennacl/linalg/gmres.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"></div>
<div class="line"><span class="comment">// Some helper functions for this tutorial:</span></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="vector-io_8hpp.html">vector-io.hpp</a>"</span></div>
<div class="line"></div>
<div class="line"><span class="keyword">using namespace </span>boost::numeric;</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="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"> ublas::vector<ScalarType> rhs;</div>
<div class="line"> ublas::vector<ScalarType> ref_result;</div>
<div class="line"> ublas::vector<ScalarType> result;</div>
<div class="line"> ublas::compressed_matrix<ScalarType> ublas_matrix;</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_matrix, <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"> <span class="keywordflow">if</span> (!<a class="code" href="vector-io_8hpp.html#a303954a45833b84192a6dcf3065f85e3">readVectorFromFile</a>(<span class="stringliteral">"../examples/testdata/rhs65025.txt"</span>, rhs))</div>
<div class="line"> {</div>
<div class="line"> std::cout << <span class="stringliteral">"Error reading RHS 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"> <span class="keywordflow">if</span> (!<a class="code" href="vector-io_8hpp.html#a303954a45833b84192a6dcf3065f85e3">readVectorFromFile</a>(<span class="stringliteral">"../examples/testdata/result65025.txt"</span>, ref_result))</div>
<div class="line"> {</div>
<div class="line"> std::cout << <span class="stringliteral">"Error reading Result 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"> std::size_t vcl_size = rhs.size();</div>
<div class="line"> <a class="code" href="classviennacl_1_1compressed__matrix.html">viennacl::compressed_matrix<ScalarType></a> vcl_compressed_matrix;</div>
<div class="line"> <a class="code" href="classviennacl_1_1coordinate__matrix.html">viennacl::coordinate_matrix<ScalarType></a> vcl_coordinate_matrix;</div>
<div class="line"> <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> vcl_rhs(vcl_size);</div>
<div class="line"> <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> vcl_result(vcl_size);</div>
<div class="line"> <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> vcl_ref_result(vcl_size);</div>
<div class="line"></div>
<div class="line"> <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(rhs.begin(), rhs.end(), vcl_rhs.<a name="a19"></a><a class="code" href="classviennacl_1_1vector__base.html#a762d98e2f912fc534951f25555b6077f">begin</a>());</div>
<div class="line"> <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(ref_result.begin(), ref_result.end(), vcl_ref_result.<a class="code" href="classviennacl_1_1vector__base.html#a762d98e2f912fc534951f25555b6077f">begin</a>());</div>
<div class="line"></div>
<div class="line"></div>
<div class="line"> <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(ublas_matrix, vcl_compressed_matrix);</div>
<div class="line"></div>
<div class="line"> std::vector< std::map< unsigned int, ScalarType> > stl_matrix(rhs.size());</div>
<div class="line"> <span class="keywordflow">for</span> (ublas::compressed_matrix<ScalarType>::iterator1 iter1 = ublas_matrix.begin1();</div>
<div class="line"> iter1 != ublas_matrix.end1();</div>
<div class="line"> ++iter1)</div>
<div class="line"> {</div>
<div class="line"> <span class="keywordflow">for</span> (ublas::compressed_matrix<ScalarType>::iterator2 iter2 = iter1.begin();</div>
<div class="line"> iter2 != iter1.end();</div>
<div class="line"> ++iter2)</div>
<div class="line"> stl_matrix[iter2.index1()][<span class="keyword">static_cast<</span><span class="keywordtype">unsigned</span> <span class="keywordtype">int</span><span class="keyword">></span>(iter2.index2())] = *iter2;</div>
<div class="line"> }</div>
<div class="line"> std::vector<ScalarType> stl_rhs(rhs.size()), stl_result(result.size());</div>
<div class="line"> <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">std::copy</a>(rhs.begin(), rhs.end(), stl_rhs.begin());</div>
<div class="line"> <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(stl_matrix, vcl_coordinate_matrix);</div>
<div class="line"> <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(vcl_coordinate_matrix, stl_matrix);</div>
<div class="line"></div>
<div class="line"> std::cout << <span class="stringliteral">"Setting up preconditioners for uBLAS-matrix..."</span> << std::endl;</div>
<div class="line"> <a class="code" href="classviennacl_1_1linalg_1_1ilut__precond.html">viennacl::linalg::ilut_precond< ublas::compressed_matrix<ScalarType></a> > ublas_ilut(ublas_matrix, <a class="code" href="classviennacl_1_1linalg_1_1ilut__tag.html">viennacl::linalg::ilut_tag</a>());</div>
<div class="line"> <a class="code" href="classviennacl_1_1linalg_1_1ilu0__precond.html">viennacl::linalg::ilu0_precond< ublas::compressed_matrix<ScalarType></a> > ublas_ilu0(ublas_matrix, <a class="code" href="classviennacl_1_1linalg_1_1ilu0__tag.html">viennacl::linalg::ilu0_tag</a>());</div>
<div class="line"> <a class="code" href="classviennacl_1_1linalg_1_1block__ilu__precond.html">viennacl::linalg::block_ilu_precond< ublas::compressed_matrix<ScalarType></a>,</div>
<div class="line"> <a class="code" href="classviennacl_1_1linalg_1_1ilu0__tag.html">viennacl::linalg::ilu0_tag</a>> ublas_block_ilu0(ublas_matrix, <a class="code" href="classviennacl_1_1linalg_1_1ilu0__tag.html">viennacl::linalg::ilu0_tag</a>());</div>
<div class="line"></div>
<div class="line"> std::cout << <span class="stringliteral">"Setting up preconditioners for ViennaCL-matrix..."</span> << std::endl;</div>
<div class="line"> <a class="code" href="classviennacl_1_1linalg_1_1ilut__precond.html">viennacl::linalg::ilut_precond< viennacl::compressed_matrix<ScalarType></a> > vcl_ilut(vcl_compressed_matrix, <a class="code" href="classviennacl_1_1linalg_1_1ilut__tag.html">viennacl::linalg::ilut_tag</a>());</div>
<div class="line"> <a class="code" href="classviennacl_1_1linalg_1_1ilu0__precond.html">viennacl::linalg::ilu0_precond< viennacl::compressed_matrix<ScalarType></a> > vcl_ilu0(vcl_compressed_matrix, <a class="code" href="classviennacl_1_1linalg_1_1ilu0__tag.html">viennacl::linalg::ilu0_tag</a>());</div>
<div class="line"> <a class="code" href="classviennacl_1_1linalg_1_1block__ilu__precond.html">viennacl::linalg::block_ilu_precond< viennacl::compressed_matrix<ScalarType></a>,</div>
<div class="line"> <a class="code" href="classviennacl_1_1linalg_1_1ilu0__tag.html">viennacl::linalg::ilu0_tag</a>> vcl_block_ilu0(vcl_compressed_matrix, <a class="code" href="classviennacl_1_1linalg_1_1ilu0__tag.html">viennacl::linalg::ilu0_tag</a>());</div>
<div class="line"></div>
<div class="line"> <a class="code" href="classviennacl_1_1linalg_1_1jacobi__precond.html">viennacl::linalg::jacobi_precond< ublas::compressed_matrix<ScalarType></a> > ublas_jacobi(ublas_matrix, <a class="code" href="classviennacl_1_1linalg_1_1jacobi__tag.html">viennacl::linalg::jacobi_tag</a>());</div>
<div class="line"> <a class="code" href="classviennacl_1_1linalg_1_1jacobi__precond.html">viennacl::linalg::jacobi_precond< viennacl::compressed_matrix<ScalarType></a> > vcl_jacobi(vcl_compressed_matrix, <a class="code" href="classviennacl_1_1linalg_1_1jacobi__tag.html">viennacl::linalg::jacobi_tag</a>());</div>
<div class="line"></div>
<div class="line"> std::cout << <span class="stringliteral">"----- CG Method -----"</span> << std::endl;</div>
<div class="line"></div>
<div class="line"> result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(ublas_matrix, rhs, <a class="code" href="classviennacl_1_1linalg_1_1cg__tag.html">viennacl::linalg::cg_tag</a>());</div>
<div class="line"> result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(ublas_matrix, rhs, <a class="code" href="classviennacl_1_1linalg_1_1cg__tag.html">viennacl::linalg::cg_tag</a>(1e-6, 20), ublas_ilut);</div>
<div class="line"> result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(ublas_matrix, rhs, <a class="code" href="classviennacl_1_1linalg_1_1cg__tag.html">viennacl::linalg::cg_tag</a>(1e-6, 20), ublas_jacobi);</div>
<div class="line"></div>
<div class="line"></div>
<div class="line"> vcl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(vcl_compressed_matrix, vcl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1cg__tag.html">viennacl::linalg::cg_tag</a>());</div>
<div class="line"> vcl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(vcl_compressed_matrix, vcl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1cg__tag.html">viennacl::linalg::cg_tag</a>(1e-6, 20), vcl_ilut);</div>
<div class="line"> vcl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(vcl_compressed_matrix, vcl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1cg__tag.html">viennacl::linalg::cg_tag</a>(1e-6, 20), vcl_jacobi);</div>
<div class="line"></div>
<div class="line"> stl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(stl_matrix, stl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1cg__tag.html">viennacl::linalg::cg_tag</a>());</div>
<div class="line"> stl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(stl_matrix, stl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1cg__tag.html">viennacl::linalg::cg_tag</a>(1e-6, 20), vcl_ilut);</div>
<div class="line"> stl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(stl_matrix, stl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1cg__tag.html">viennacl::linalg::cg_tag</a>(1e-6, 20), vcl_jacobi);</div>
<div class="line"></div>
<div class="line"></div>
<div class="line"> std::cout << <span class="stringliteral">"----- BiCGStab Method -----"</span> << std::endl;</div>
<div class="line"></div>
<div class="line"> result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(ublas_matrix, rhs, <a class="code" href="classviennacl_1_1linalg_1_1bicgstab__tag.html">viennacl::linalg::bicgstab_tag</a>()); <span class="comment">//without preconditioner</span></div>
<div class="line"> result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(ublas_matrix, rhs, <a class="code" href="classviennacl_1_1linalg_1_1bicgstab__tag.html">viennacl::linalg::bicgstab_tag</a>(1e-6, 20), ublas_ilut); <span class="comment">//with preconditioner</span></div>
<div class="line"> result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(ublas_matrix, rhs, <a class="code" href="classviennacl_1_1linalg_1_1bicgstab__tag.html">viennacl::linalg::bicgstab_tag</a>(1e-6, 20), ublas_jacobi); <span class="comment">//with preconditioner</span></div>
<div class="line"></div>
<div class="line"> vcl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(vcl_compressed_matrix, vcl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1bicgstab__tag.html">viennacl::linalg::bicgstab_tag</a>()); <span class="comment">//without preconditioner</span></div>
<div class="line"> vcl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(vcl_compressed_matrix, vcl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1bicgstab__tag.html">viennacl::linalg::bicgstab_tag</a>(1e-6, 20), vcl_ilut); <span class="comment">//with preconditioner</span></div>
<div class="line"> vcl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(vcl_compressed_matrix, vcl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1bicgstab__tag.html">viennacl::linalg::bicgstab_tag</a>(1e-6, 20), vcl_jacobi); <span class="comment">//with preconditioner</span></div>
<div class="line"></div>
<div class="line"> stl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(stl_matrix, stl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1bicgstab__tag.html">viennacl::linalg::bicgstab_tag</a>());</div>
<div class="line"> stl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(stl_matrix, stl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1bicgstab__tag.html">viennacl::linalg::bicgstab_tag</a>(1e-6, 20), vcl_ilut);</div>
<div class="line"> stl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(stl_matrix, stl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1bicgstab__tag.html">viennacl::linalg::bicgstab_tag</a>(1e-6, 20), vcl_jacobi);</div>
<div class="line"></div>
<div class="line"></div>
<div class="line"> std::cout << <span class="stringliteral">"----- GMRES Method -----"</span> << std::endl;</div>
<div class="line"></div>
<div class="line"> result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(ublas_matrix, rhs, <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html">viennacl::linalg::gmres_tag</a>()); <span class="comment">//without preconditioner</span></div>
<div class="line"> result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(ublas_matrix, rhs, <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html">viennacl::linalg::gmres_tag</a>(1e-6, 20), ublas_ilut);<span class="comment">//with preconditioner</span></div>
<div class="line"> result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(ublas_matrix, rhs, <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html">viennacl::linalg::gmres_tag</a>(1e-6, 20), ublas_jacobi);<span class="comment">//with preconditioner</span></div>
<div class="line"></div>
<div class="line"> vcl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(vcl_compressed_matrix, vcl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html">viennacl::linalg::gmres_tag</a>()); <span class="comment">//without preconditioner</span></div>
<div class="line"> vcl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(vcl_compressed_matrix, vcl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html">viennacl::linalg::gmres_tag</a>(1e-6, 20), vcl_ilut);<span class="comment">//with preconditioner</span></div>
<div class="line"> vcl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(vcl_compressed_matrix, vcl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html">viennacl::linalg::gmres_tag</a>(1e-6, 20), vcl_jacobi);<span class="comment">//with preconditioner</span></div>
<div class="line"></div>
<div class="line"> stl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(stl_matrix, stl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html">viennacl::linalg::gmres_tag</a>());</div>
<div class="line"> stl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(stl_matrix, stl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html">viennacl::linalg::gmres_tag</a>(1e-6, 20), vcl_ilut);</div>
<div class="line"> stl_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(stl_matrix, stl_rhs, <a class="code" href="classviennacl_1_1linalg_1_1gmres__tag.html">viennacl::linalg::gmres_tag</a>(1e-6, 20), vcl_jacobi);</div>
<div class="line"></div>
<div class="line"></div>
<div class="line"> std::cout << <span class="stringliteral">"!!!! TUTORIAL COMPLETED SUCCESSFULLY !!!!"</span> << 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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