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<div class="title">spai.cpp</div> </div>
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<p>This tutorial shows how to use the sparse approximate inverse (SPAI) preconditioner.</p>
<dl class="section warning"><dt>Warning</dt><dd>SPAI is currently only available with the OpenCL backend and is experimental. API-changes may happen any time in the future.</dd></dl>
<p>We start with including the necessary headers: </p>
<div class="fragment"><div class="line"><span class="comment">// enable Boost.uBLAS support</span></div>
<div class="line"><span class="preprocessor">#define VIENNACL_WITH_UBLAS</span></div>
<div class="line"></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">// System headers:</span></div>
<div class="line"><span class="preprocessor">#include <utility></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 <string></span></div>
<div class="line"><span class="preprocessor">#include <cmath></span></div>
<div class="line"><span class="preprocessor">#include <algorithm></span></div>
<div class="line"><span class="preprocessor">#include <stdio.h></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="scalar_8hpp.html">viennacl/scalar.hpp</a>"</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="compressed__matrix_8hpp.html">viennacl/compressed_matrix.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="prod_8hpp.html">viennacl/linalg/prod.hpp</a>"</span></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="inner__prod_8hpp.html">viennacl/linalg/inner_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="norm__2_8hpp.html">viennacl/linalg/norm_2.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"><span class="preprocessor">#include "<a class="code" href="spai_8hpp.html">viennacl/linalg/spai.hpp</a>"</span></div>
<div class="line"></div>
<div class="line"><span class="comment">// Boost headers:</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/matrix.hpp"</span></div>
<div class="line"><span class="preprocessor">#include "boost/numeric/ublas/io.hpp"</span></div>
<div class="line"></div>
<div class="line"><span class="comment">// auxiliary functionality:</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> The following helper routine is used to run a solver with the provided preconditioner and to print the resulting residual norm. </p>
<div class="fragment"><div class="line"><span class="keyword">template</span><<span class="keyword">typename</span> MatrixT, <span class="keyword">typename</span> VectorT, <span class="keyword">typename</span> SolverTagT, <span class="keyword">typename</span> PreconditionerT></div>
<div class="line"><span class="keywordtype">void</span> <a name="a0"></a><a class="code" href="solver_8cpp.html#afadbea4317c8f42f54d4622cf0a1829f">run_solver</a>(MatrixT <span class="keyword">const</span> & A, VectorT <span class="keyword">const</span> & b, SolverTagT <span class="keyword">const</span> & solver_tag, PreconditionerT <span class="keyword">const</span> & precond)</div>
<div class="line">{</div>
<div class="line"> VectorT result = <a name="a1"></a><a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(A, b, solver_tag, precond);</div>
<div class="line"> std::cout << <span class="stringliteral">" * Solver iterations: "</span> << solver_tag.iters() << std::endl;</div>
<div class="line"> VectorT residual = <a name="a2"></a><a class="code" href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">viennacl::linalg::prod</a>(A, result);</div>
<div class="line"> residual -= b;</div>
<div class="line"> std::cout << <span class="stringliteral">" * Rel. Residual: "</span> << <a name="a3"></a><a class="code" href="namespaceviennacl_1_1linalg.html#ae46f15d01c01f92a153b3f555a15096b">viennacl::linalg::norm_2</a>(residual) / <a class="code" href="namespaceviennacl_1_1linalg.html#ae46f15d01c01f92a153b3f555a15096b">viennacl::linalg::norm_2</a>(b) << std::endl;</div>
<div class="line">}</div>
</div><!-- fragment --><p> The main steps in this tutorial are the following:</p>
<ul>
<li>Setup the systems</li>
<li>Run solvers without preconditioner and with ILUT preconditioner for comparison</li>
<li>Run solver with SPAI preconditioner on CPU</li>
<li>Run solver with SPAI preconditioner on GPU</li>
<li>Run solver with factored SPAI preconditioner on CPU</li>
<li>Run solver with factored SPAI preconditioner on GPU</li>
</ul>
<div class="fragment"><div class="line"><span class="keywordtype">int</span> <a name="a4"></a><a class="code" href="tests_2src_2bisect_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> (<span class="keywordtype">int</span>, <span class="keyword">const</span> <span class="keywordtype">char</span> **)</div>
<div class="line">{</div>
<div class="line"> <span class="keyword">typedef</span> <span class="keywordtype">float</span> <a name="a5"></a><a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>;</div>
<div class="line"> <span class="keyword">typedef</span> boost::numeric::ublas::compressed_matrix<ScalarType> MatrixType;</div>
<div class="line"> <span class="keyword">typedef</span> boost::numeric::ublas::vector<ScalarType> VectorType;</div>
<div class="line"> <span class="keyword">typedef</span> <a name="_a6"></a><a class="code" href="classviennacl_1_1compressed__matrix.html">viennacl::compressed_matrix<ScalarType></a> GPUMatrixType;</div>
<div class="line"> <span class="keyword">typedef</span> <a name="_a7"></a><a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> GPUVectorType;</div>
</div><!-- fragment --><p> If you have multiple OpenCL-capable devices in your system, we pick the second device for this tutorial. </p>
<div class="fragment"><div class="line"><span class="preprocessor">#ifdef VIENNACL_WITH_OPENCL</span></div>
<div class="line"> <span class="comment">// Optional: Customize OpenCL backend</span></div>
<div class="line"> <a name="_a8"></a><a class="code" href="classviennacl_1_1ocl_1_1platform.html">viennacl::ocl::platform</a> pf = <a name="a9"></a><a class="code" href="namespaceviennacl_1_1ocl.html#ae1e931f6efd155240b33ca440dfcfef5">viennacl::ocl::get_platforms</a>()[0];</div>
<div class="line"> std::vector<viennacl::ocl::device> <span class="keyword">const</span> & devices = pf.<a name="a10"></a><a class="code" href="classviennacl_1_1ocl_1_1platform.html#afaa563522ebe9ce7b80ef02c40e7fe31">devices</a>();</div>
<div class="line"></div>
<div class="line"> <span class="comment">// Optional: Set first device to first context:</span></div>
<div class="line"> <a name="a11"></a><a class="code" href="namespaceviennacl_1_1ocl.html#add1725d48cfd159ce187e287369d1cdb">viennacl::ocl::setup_context</a>(0, devices[0]);</div>
<div class="line"></div>
<div class="line"> <span class="comment">// Optional: Set second device for second context (use the same device for the second context if only one device available):</span></div>
<div class="line"> <span class="keywordflow">if</span> (devices.size() > 1)</div>
<div class="line"> <a class="code" href="namespaceviennacl_1_1ocl.html#add1725d48cfd159ce187e287369d1cdb">viennacl::ocl::setup_context</a>(1, devices[1]);</div>
<div class="line"> <span class="keywordflow">else</span></div>
<div class="line"> <a class="code" href="namespaceviennacl_1_1ocl.html#add1725d48cfd159ce187e287369d1cdb">viennacl::ocl::setup_context</a>(1, devices[0]);</div>
<div class="line"></div>
<div class="line"> std::cout << <a name="a12"></a><a class="code" href="namespaceviennacl_1_1ocl.html#ac54d59a74deaccec81f64e738b856348">viennacl::ocl::current_device</a>().<a name="a13"></a><a class="code" href="classviennacl_1_1ocl_1_1device.html#a26a424782f982725453808a94763bd19">info</a>() << std::endl;</div>
<div class="line"> <a name="_a14"></a><a class="code" href="classviennacl_1_1context.html">viennacl::context</a> ctx(<a name="a15"></a><a class="code" href="namespaceviennacl_1_1ocl.html#a82c1aba632a7ee0991eee480d5340966">viennacl::ocl::get_context</a>(1));</div>
<div class="line"><span class="preprocessor">#else</span></div>
<div class="line"> <a class="code" href="classviennacl_1_1context.html">viennacl::context</a> ctx;</div>
<div class="line"><span class="preprocessor">#endif</span></div>
</div><!-- fragment --><p> Create uBLAS-based sparse matrix and read system matrix from file </p>
<div class="fragment"><div class="line">MatrixType M;</div>
<div class="line"></div>
<div class="line"><span class="keywordflow">if</span> (!<a name="a16"></a><a class="code" href="namespaceviennacl_1_1io.html#ad934125ed3dbe661e264bcd7d62b1048">viennacl::io::read_matrix_market_file</a>(M, <span class="stringliteral">"../examples/testdata/mat65k.mtx"</span>))</div>
<div class="line">{</div>
<div class="line"> std::cerr<<<span class="stringliteral">"ERROR: Could not read matrix file "</span> << std::endl;</div>
<div class="line"> exit(EXIT_FAILURE);</div>
<div class="line">}</div>
<div class="line"></div>
<div class="line">std::cout << <span class="stringliteral">"Size of matrix: "</span> << M.size1() << std::endl;</div>
<div class="line">std::cout << <span class="stringliteral">"Avg. Entries per row: "</span> << double(M.nnz()) / static_cast<double>(M.size1()) << std::endl;</div>
</div><!-- fragment --><p> Use a constant load vector for simplicity </p>
<div class="fragment"><div class="line">VectorType rhs(M.size2());</div>
<div class="line"><span class="keywordflow">for</span> (std::size_t i=0; i<rhs.size(); ++i)</div>
<div class="line"> rhs(i) = <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(1);</div>
</div><!-- fragment --><p> Create the ViennaCL matrix and vector and initialize with uBLAS data: </p>
<div class="fragment"><div class="line">GPUMatrixType gpu_M(M.size1(), M.size2(), ctx);</div>
<div class="line">GPUVectorType gpu_rhs(M.size1(), ctx);</div>
<div class="line"><a name="a17"></a><a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(M, gpu_M);</div>
<div class="line"><a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(rhs, gpu_rhs);</div>
</div><!-- fragment --> <h2>Solver Runs</h2>
<p>We use a relative tolerance of <img class="formulaInl" alt="$ 10^{-10} $" src="form_23.png"/> with a maximum of 50 iterations for each use case. Usually more than 50 solver iterations are required for convergence, but this choice ensures shorter execution times and suffices for this tutorial. </p>
<div class="fragment"><div class="line"><a name="_a18"></a><a class="code" href="classviennacl_1_1linalg_1_1bicgstab__tag.html">viennacl::linalg::bicgstab_tag</a> solver_tag(1e-10, 50); <span class="comment">//for simplicity and reasonably short execution times we use only 50 iterations here</span></div>
</div><!-- fragment --><p> The first reference is to use no preconditioner (CPU and GPU): </p>
<div class="fragment"><div class="line">std::cout << <span class="stringliteral">"--- Reference 1: Pure BiCGStab on CPU ---"</span> << std::endl;</div>
<div class="line">VectorType result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(M, rhs, solver_tag);</div>
<div class="line">std::cout << <span class="stringliteral">" * Solver iterations: "</span> << solver_tag.iters() << std::endl;</div>
<div class="line">VectorType residual = <a class="code" href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">viennacl::linalg::prod</a>(M, result) - rhs;</div>
<div class="line">std::cout << <span class="stringliteral">" * Rel. Residual: "</span> << <a class="code" href="namespaceviennacl_1_1linalg.html#ae46f15d01c01f92a153b3f555a15096b">viennacl::linalg::norm_2</a>(residual) / <a class="code" href="namespaceviennacl_1_1linalg.html#ae46f15d01c01f92a153b3f555a15096b">viennacl::linalg::norm_2</a>(rhs) << std::endl;</div>
<div class="line"></div>
<div class="line">std::cout << <span class="stringliteral">"--- Reference 2: Pure BiCGStab on GPU ---"</span> << std::endl;</div>
<div class="line">GPUVectorType gpu_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(gpu_M, gpu_rhs, solver_tag);</div>
<div class="line">std::cout << <span class="stringliteral">" * Solver iterations: "</span> << solver_tag.iters() << std::endl;</div>
<div class="line">GPUVectorType gpu_residual = <a class="code" href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">viennacl::linalg::prod</a>(gpu_M, gpu_result);</div>
<div class="line">gpu_residual -= gpu_rhs;</div>
<div class="line">std::cout << <span class="stringliteral">" * Rel. Residual: "</span> << <a class="code" href="namespaceviennacl_1_1linalg.html#ae46f15d01c01f92a153b3f555a15096b">viennacl::linalg::norm_2</a>(gpu_residual) / <a class="code" href="namespaceviennacl_1_1linalg.html#ae46f15d01c01f92a153b3f555a15096b">viennacl::linalg::norm_2</a>(gpu_rhs) << std::endl;</div>
</div><!-- fragment --><p> The second reference is a standard ILUT preconditioner (only CPU): </p>
<div class="fragment"><div class="line">std::cout << <span class="stringliteral">"--- Reference 2: BiCGStab with ILUT on CPU ---"</span> << std::endl;</div>
<div class="line">std::cout << <span class="stringliteral">" * Preconditioner setup..."</span> << std::endl;</div>
<div class="line"><a name="_a19"></a><a class="code" href="classviennacl_1_1linalg_1_1ilut__precond.html">viennacl::linalg::ilut_precond<MatrixType></a> ilut(M, <a name="_a20"></a><a class="code" href="classviennacl_1_1linalg_1_1ilut__tag.html">viennacl::linalg::ilut_tag</a>());</div>
<div class="line">std::cout << <span class="stringliteral">" * Iterative solver run..."</span> << std::endl;</div>
<div class="line"><a class="code" href="solver_8cpp.html#afadbea4317c8f42f54d4622cf0a1829f">run_solver</a>(M, rhs, solver_tag, ilut);</div>
</div><!-- fragment --> <h2>Step 1: SPAI with CPU</h2>
<div class="fragment"><div class="line">std::cout << <span class="stringliteral">"--- Test 1: CPU-based SPAI ---"</span> << std::endl;</div>
<div class="line">std::cout << <span class="stringliteral">" * Preconditioner setup..."</span> << std::endl;</div>
<div class="line"><a name="_a21"></a><a class="code" href="classviennacl_1_1linalg_1_1spai__precond.html">viennacl::linalg::spai_precond<MatrixType></a> spai_cpu(M, <a name="_a22"></a><a class="code" href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1spai__tag.html">viennacl::linalg::spai_tag</a>(1e-3, 3, 5e-2));</div>
<div class="line">std::cout << <span class="stringliteral">" * Iterative solver run..."</span> << std::endl;</div>
<div class="line"><a class="code" href="solver_8cpp.html#afadbea4317c8f42f54d4622cf0a1829f">run_solver</a>(M, rhs, solver_tag, spai_cpu);</div>
</div><!-- fragment --> <h2>Step 2: FSPAI with CPU</h2>
<div class="fragment"><div class="line">std::cout << <span class="stringliteral">"--- Test 2: CPU-based FSPAI ---"</span> << std::endl;</div>
<div class="line">std::cout << <span class="stringliteral">" * Preconditioner setup..."</span> << std::endl;</div>
<div class="line"><a name="_a23"></a><a class="code" href="classviennacl_1_1linalg_1_1fspai__precond.html">viennacl::linalg::fspai_precond<MatrixType></a> fspai_cpu(M, <a name="_a24"></a><a class="code" href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html">viennacl::linalg::fspai_tag</a>());</div>
<div class="line">std::cout << <span class="stringliteral">" * Iterative solver run..."</span> << std::endl;</div>
<div class="line"><a class="code" href="solver_8cpp.html#afadbea4317c8f42f54d4622cf0a1829f">run_solver</a>(M, rhs, solver_tag, fspai_cpu);</div>
</div><!-- fragment --> <h2>Step 3: SPAI with GPU</h2>
<div class="fragment"><div class="line">std::cout << <span class="stringliteral">"--- Test 3: GPU-based SPAI ---"</span> << std::endl;</div>
<div class="line">std::cout << <span class="stringliteral">" * Preconditioner setup..."</span> << std::endl;</div>
<div class="line"><a class="code" href="classviennacl_1_1linalg_1_1spai__precond.html">viennacl::linalg::spai_precond<GPUMatrixType></a> spai_gpu(gpu_M, <a class="code" href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1spai__tag.html">viennacl::linalg::spai_tag</a>(1e-3, 3, 5e-2));</div>
<div class="line">std::cout << <span class="stringliteral">" * Iterative solver run..."</span> << std::endl;</div>
<div class="line"><a class="code" href="solver_8cpp.html#afadbea4317c8f42f54d4622cf0a1829f">run_solver</a>(gpu_M, gpu_rhs, solver_tag, spai_gpu);</div>
</div><!-- fragment --> <h2>Step 4: FSPAI with GPU</h2>
<div class="fragment"><div class="line">std::cout << <span class="stringliteral">"--- Test 4: GPU-based FSPAI ---"</span> << std::endl;</div>
<div class="line">std::cout << <span class="stringliteral">" * Preconditioner setup..."</span> << std::endl;</div>
<div class="line"><a class="code" href="classviennacl_1_1linalg_1_1fspai__precond.html">viennacl::linalg::fspai_precond<GPUMatrixType></a> fspai_gpu(gpu_M, <a class="code" href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html">viennacl::linalg::fspai_tag</a>());</div>
<div class="line">std::cout << <span class="stringliteral">" * Iterative solver run..."</span> << std::endl;</div>
<div class="line"><a class="code" href="solver_8cpp.html#afadbea4317c8f42f54d4622cf0a1829f">run_solver</a>(gpu_M, gpu_rhs, solver_tag, fspai_gpu);</div>
</div><!-- fragment --><p> That's it! Print success message and exit. </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">// enable Boost.uBLAS support</span></div>
<div class="line"><span class="preprocessor">#define VIENNACL_WITH_UBLAS</span></div>
<div class="line"></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">// System headers:</span></div>
<div class="line"><span class="preprocessor">#include <utility></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 <string></span></div>
<div class="line"><span class="preprocessor">#include <cmath></span></div>
<div class="line"><span class="preprocessor">#include <algorithm></span></div>
<div class="line"><span class="preprocessor">#include <stdio.h></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="scalar_8hpp.html">viennacl/scalar.hpp</a>"</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="compressed__matrix_8hpp.html">viennacl/compressed_matrix.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="prod_8hpp.html">viennacl/linalg/prod.hpp</a>"</span></div>
<div class="line"><span class="preprocessor">#include "<a class="code" href="inner__prod_8hpp.html">viennacl/linalg/inner_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="norm__2_8hpp.html">viennacl/linalg/norm_2.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"><span class="preprocessor">#include "<a class="code" href="spai_8hpp.html">viennacl/linalg/spai.hpp</a>"</span></div>
<div class="line"></div>
<div class="line"><span class="comment">// Boost headers:</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/matrix.hpp"</span></div>
<div class="line"><span class="preprocessor">#include "boost/numeric/ublas/io.hpp"</span></div>
<div class="line"></div>
<div class="line"><span class="comment">// auxiliary functionality:</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">template</span><<span class="keyword">typename</span> MatrixT, <span class="keyword">typename</span> VectorT, <span class="keyword">typename</span> SolverTagT, <span class="keyword">typename</span> PreconditionerT></div>
<div class="line"><span class="keywordtype">void</span> <a class="code" href="solver_8cpp.html#afadbea4317c8f42f54d4622cf0a1829f">run_solver</a>(MatrixT <span class="keyword">const</span> & A, VectorT <span class="keyword">const</span> & b, SolverTagT <span class="keyword">const</span> & solver_tag, PreconditionerT <span class="keyword">const</span> & precond)</div>
<div class="line">{</div>
<div class="line"> VectorT result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(A, b, solver_tag, precond);</div>
<div class="line"> std::cout << <span class="stringliteral">" * Solver iterations: "</span> << solver_tag.iters() << std::endl;</div>
<div class="line"> VectorT residual = <a class="code" href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">viennacl::linalg::prod</a>(A, result);</div>
<div class="line"> residual -= b;</div>
<div class="line"> std::cout << <span class="stringliteral">" * Rel. Residual: "</span> << <a class="code" href="namespaceviennacl_1_1linalg.html#ae46f15d01c01f92a153b3f555a15096b">viennacl::linalg::norm_2</a>(residual) / <a class="code" href="namespaceviennacl_1_1linalg.html#ae46f15d01c01f92a153b3f555a15096b">viennacl::linalg::norm_2</a>(b) << 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_2bisect_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> (<span class="keywordtype">int</span>, <span class="keyword">const</span> <span class="keywordtype">char</span> **)</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"> <span class="keyword">typedef</span> boost::numeric::ublas::compressed_matrix<ScalarType> MatrixType;</div>
<div class="line"> <span class="keyword">typedef</span> boost::numeric::ublas::vector<ScalarType> VectorType;</div>
<div class="line"> <span class="keyword">typedef</span> <a class="code" href="classviennacl_1_1compressed__matrix.html">viennacl::compressed_matrix<ScalarType></a> GPUMatrixType;</div>
<div class="line"> <span class="keyword">typedef</span> <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> GPUVectorType;</div>
<div class="line"></div>
<div class="line"><span class="preprocessor">#ifdef VIENNACL_WITH_OPENCL</span></div>
<div class="line"> <span class="comment">// Optional: Customize OpenCL backend</span></div>
<div class="line"> <a class="code" href="classviennacl_1_1ocl_1_1platform.html">viennacl::ocl::platform</a> pf = <a class="code" href="namespaceviennacl_1_1ocl.html#ae1e931f6efd155240b33ca440dfcfef5">viennacl::ocl::get_platforms</a>()[0];</div>
<div class="line"> std::vector<viennacl::ocl::device> <span class="keyword">const</span> & devices = pf.<a class="code" href="classviennacl_1_1ocl_1_1platform.html#afaa563522ebe9ce7b80ef02c40e7fe31">devices</a>();</div>
<div class="line"></div>
<div class="line"> <span class="comment">// Optional: Set first device to first context:</span></div>
<div class="line"> <a class="code" href="namespaceviennacl_1_1ocl.html#add1725d48cfd159ce187e287369d1cdb">viennacl::ocl::setup_context</a>(0, devices[0]);</div>
<div class="line"></div>
<div class="line"> <span class="comment">// Optional: Set second device for second context (use the same device for the second context if only one device available):</span></div>
<div class="line"> <span class="keywordflow">if</span> (devices.size() > 1)</div>
<div class="line"> <a class="code" href="namespaceviennacl_1_1ocl.html#add1725d48cfd159ce187e287369d1cdb">viennacl::ocl::setup_context</a>(1, devices[1]);</div>
<div class="line"> <span class="keywordflow">else</span></div>
<div class="line"> <a class="code" href="namespaceviennacl_1_1ocl.html#add1725d48cfd159ce187e287369d1cdb">viennacl::ocl::setup_context</a>(1, devices[0]);</div>
<div class="line"></div>
<div class="line"> std::cout << <a class="code" href="namespaceviennacl_1_1ocl.html#ac54d59a74deaccec81f64e738b856348">viennacl::ocl::current_device</a>().<a class="code" href="classviennacl_1_1ocl_1_1device.html#a26a424782f982725453808a94763bd19">info</a>() << std::endl;</div>
<div class="line"> <a class="code" href="classviennacl_1_1context.html">viennacl::context</a> ctx(<a class="code" href="namespaceviennacl_1_1ocl.html#a82c1aba632a7ee0991eee480d5340966">viennacl::ocl::get_context</a>(1));</div>
<div class="line"><span class="preprocessor">#else</span></div>
<div class="line"> <a class="code" href="classviennacl_1_1context.html">viennacl::context</a> ctx;</div>
<div class="line"><span class="preprocessor">#endif</span></div>
<div class="line"></div>
<div class="line"> MatrixType M;</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>(M, <span class="stringliteral">"../examples/testdata/mat65k.mtx"</span>))</div>
<div class="line"> {</div>
<div class="line"> std::cerr<<<span class="stringliteral">"ERROR: Could not read matrix file "</span> << std::endl;</div>
<div class="line"> exit(EXIT_FAILURE);</div>
<div class="line"> }</div>
<div class="line"></div>
<div class="line"> std::cout << <span class="stringliteral">"Size of matrix: "</span> << M.size1() << std::endl;</div>
<div class="line"> std::cout << <span class="stringliteral">"Avg. Entries per row: "</span> << double(M.nnz()) / static_cast<double>(M.size1()) << std::endl;</div>
<div class="line"></div>
<div class="line"> VectorType rhs(M.size2());</div>
<div class="line"> <span class="keywordflow">for</span> (std::size_t i=0; i<rhs.size(); ++i)</div>
<div class="line"> rhs(i) = <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(1);</div>
<div class="line"></div>
<div class="line"> GPUMatrixType gpu_M(M.size1(), M.size2(), ctx);</div>
<div class="line"> GPUVectorType gpu_rhs(M.size1(), ctx);</div>
<div class="line"> <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(M, gpu_M);</div>
<div class="line"> <a class="code" href="namespaceviennacl.html#a10b7f8cf6b8864a7aa196d670481a453">viennacl::copy</a>(rhs, gpu_rhs);</div>
<div class="line"></div>
<div class="line"> <a class="code" href="classviennacl_1_1linalg_1_1bicgstab__tag.html">viennacl::linalg::bicgstab_tag</a> solver_tag(1e-10, 50); <span class="comment">//for simplicity and reasonably short execution times we use only 50 iterations here</span></div>
<div class="line"></div>
<div class="line"> std::cout << <span class="stringliteral">"--- Reference 1: Pure BiCGStab on CPU ---"</span> << std::endl;</div>
<div class="line"> VectorType result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(M, rhs, solver_tag);</div>
<div class="line"> std::cout << <span class="stringliteral">" * Solver iterations: "</span> << solver_tag.iters() << std::endl;</div>
<div class="line"> VectorType residual = <a class="code" href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">viennacl::linalg::prod</a>(M, result) - rhs;</div>
<div class="line"> std::cout << <span class="stringliteral">" * Rel. Residual: "</span> << <a class="code" href="namespaceviennacl_1_1linalg.html#ae46f15d01c01f92a153b3f555a15096b">viennacl::linalg::norm_2</a>(residual) / <a class="code" href="namespaceviennacl_1_1linalg.html#ae46f15d01c01f92a153b3f555a15096b">viennacl::linalg::norm_2</a>(rhs) << std::endl;</div>
<div class="line"></div>
<div class="line"> std::cout << <span class="stringliteral">"--- Reference 2: Pure BiCGStab on GPU ---"</span> << std::endl;</div>
<div class="line"> GPUVectorType gpu_result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(gpu_M, gpu_rhs, solver_tag);</div>
<div class="line"> std::cout << <span class="stringliteral">" * Solver iterations: "</span> << solver_tag.iters() << std::endl;</div>
<div class="line"> GPUVectorType gpu_residual = <a class="code" href="namespaceviennacl_1_1linalg.html#aa18d10f8a90e38bd9ff43c650fc670ef">viennacl::linalg::prod</a>(gpu_M, gpu_result);</div>
<div class="line"> gpu_residual -= gpu_rhs;</div>
<div class="line"> std::cout << <span class="stringliteral">" * Rel. Residual: "</span> << <a class="code" href="namespaceviennacl_1_1linalg.html#ae46f15d01c01f92a153b3f555a15096b">viennacl::linalg::norm_2</a>(gpu_residual) / <a class="code" href="namespaceviennacl_1_1linalg.html#ae46f15d01c01f92a153b3f555a15096b">viennacl::linalg::norm_2</a>(gpu_rhs) << std::endl;</div>
<div class="line"></div>
<div class="line"></div>
<div class="line"> std::cout << <span class="stringliteral">"--- Reference 2: BiCGStab with ILUT on CPU ---"</span> << std::endl;</div>
<div class="line"> std::cout << <span class="stringliteral">" * Preconditioner setup..."</span> << std::endl;</div>
<div class="line"> <a class="code" href="classviennacl_1_1linalg_1_1ilut__precond.html">viennacl::linalg::ilut_precond<MatrixType></a> ilut(M, <a class="code" href="classviennacl_1_1linalg_1_1ilut__tag.html">viennacl::linalg::ilut_tag</a>());</div>
<div class="line"> std::cout << <span class="stringliteral">" * Iterative solver run..."</span> << std::endl;</div>
<div class="line"> <a class="code" href="solver_8cpp.html#afadbea4317c8f42f54d4622cf0a1829f">run_solver</a>(M, rhs, solver_tag, ilut);</div>
<div class="line"></div>
<div class="line"></div>
<div class="line"> std::cout << <span class="stringliteral">"--- Test 1: CPU-based SPAI ---"</span> << std::endl;</div>
<div class="line"> std::cout << <span class="stringliteral">" * Preconditioner setup..."</span> << std::endl;</div>
<div class="line"> <a class="code" href="classviennacl_1_1linalg_1_1spai__precond.html">viennacl::linalg::spai_precond<MatrixType></a> spai_cpu(M, <a class="code" href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1spai__tag.html">viennacl::linalg::spai_tag</a>(1e-3, 3, 5e-2));</div>
<div class="line"> std::cout << <span class="stringliteral">" * Iterative solver run..."</span> << std::endl;</div>
<div class="line"> <a class="code" href="solver_8cpp.html#afadbea4317c8f42f54d4622cf0a1829f">run_solver</a>(M, rhs, solver_tag, spai_cpu);</div>
<div class="line"></div>
<div class="line"> std::cout << <span class="stringliteral">"--- Test 2: CPU-based FSPAI ---"</span> << std::endl;</div>
<div class="line"> std::cout << <span class="stringliteral">" * Preconditioner setup..."</span> << std::endl;</div>
<div class="line"> <a class="code" href="classviennacl_1_1linalg_1_1fspai__precond.html">viennacl::linalg::fspai_precond<MatrixType></a> fspai_cpu(M, <a class="code" href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html">viennacl::linalg::fspai_tag</a>());</div>
<div class="line"> std::cout << <span class="stringliteral">" * Iterative solver run..."</span> << std::endl;</div>
<div class="line"> <a class="code" href="solver_8cpp.html#afadbea4317c8f42f54d4622cf0a1829f">run_solver</a>(M, rhs, solver_tag, fspai_cpu);</div>
<div class="line"></div>
<div class="line"> std::cout << <span class="stringliteral">"--- Test 3: GPU-based SPAI ---"</span> << std::endl;</div>
<div class="line"> std::cout << <span class="stringliteral">" * Preconditioner setup..."</span> << std::endl;</div>
<div class="line"> <a class="code" href="classviennacl_1_1linalg_1_1spai__precond.html">viennacl::linalg::spai_precond<GPUMatrixType></a> spai_gpu(gpu_M, <a class="code" href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1spai__tag.html">viennacl::linalg::spai_tag</a>(1e-3, 3, 5e-2));</div>
<div class="line"> std::cout << <span class="stringliteral">" * Iterative solver run..."</span> << std::endl;</div>
<div class="line"> <a class="code" href="solver_8cpp.html#afadbea4317c8f42f54d4622cf0a1829f">run_solver</a>(gpu_M, gpu_rhs, solver_tag, spai_gpu);</div>
<div class="line"></div>
<div class="line"> std::cout << <span class="stringliteral">"--- Test 4: GPU-based FSPAI ---"</span> << std::endl;</div>
<div class="line"> std::cout << <span class="stringliteral">" * Preconditioner setup..."</span> << std::endl;</div>
<div class="line"> <a class="code" href="classviennacl_1_1linalg_1_1fspai__precond.html">viennacl::linalg::fspai_precond<GPUMatrixType></a> fspai_gpu(gpu_M, <a class="code" href="classviennacl_1_1linalg_1_1detail_1_1spai_1_1fspai__tag.html">viennacl::linalg::fspai_tag</a>());</div>
<div class="line"> std::cout << <span class="stringliteral">" * Iterative solver run..."</span> << std::endl;</div>
<div class="line"> <a class="code" href="solver_8cpp.html#afadbea4317c8f42f54d4622cf0a1829f">run_solver</a>(gpu_M, gpu_rhs, solver_tag, fspai_gpu);</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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