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 <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">matrix-free.cpp</div> </div>
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<div class="contents">
<p>This tutorial explains how to use the iterative solvers in ViennaCL in a matrix-free manner, i.e. without explicitly assembling a matrix.</p>
<p>We consider the solution of the Poisson equation <img class="formulaInl" alt="$ \Delta \varphi = -1 $" src="form_138.png"/> on the unit square <img class="formulaInl" alt="$ [0,1] \times [0,1] $" src="form_139.png"/> with homogeneous Dirichlet boundary conditions using a finite-difference discretization. A <img class="formulaInl" alt="$ N \times N $" src="form_140.png"/> grid is used, where the first and the last points per dimensions represent the boundary. For simplicity we only consider the host-backend here. Have a look at custom-kernels.hpp and custom-cuda.cu on how to use custom kernels in such a matrix-free setting.</p>
<dl class="section note"><dt>Note</dt><dd><a class="el" href="matrix-free_8cpp.html">matrix-free.cpp</a> and matrix-free.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">// 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="prod_8hpp.html">viennacl/linalg/prod.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><!-- fragment --><p> ViennaCL imposes two type requirements on a user-provided operator to compute <code>y = prod(A, x)</code> for the iterative solvers:</p>
<ul>
<li>A member function <code>apply()</code>, taking two ViennaCL base vectors <code>x</code> and <code>y</code> as arguments. This member function carries out the action of the matrix to the vector.</li>
<li>A member function <code><a class="el" href="namespaceviennacl_1_1traits.html#aa756f5d6820722094cae0d8b9bb6d5e2" title="Generic routine for obtaining the number of rows of a matrix (ViennaCL, uBLAS, etc.) ">size1()</a></code> returning the length of the result vectors. Keep in mind that you can always wrap your existing classes accordingly to fit ViennaCL's interface requirements.</li>
</ul>
<p>We define a simple class for dealing with the <img class="formulaInl" alt="$ N \times N $" src="form_140.png"/> grid for solving Poisson's equation. It only holds the number of grid points per coordinate direction and implements the <code>apply()</code> and <code><a class="el" href="namespaceviennacl_1_1traits.html#aa756f5d6820722094cae0d8b9bb6d5e2" title="Generic routine for obtaining the number of rows of a matrix (ViennaCL, uBLAS, etc.) ">size1()</a></code> routines. Depending on whether the host, OpenCL, or CUDA is used for the computation, the respective implementation is called. We skip the details for now and discuss (and implement) them at the end of this tutorial. </p>
<div class="fragment"><div class="line"><span class="keyword">template</span><<span class="keyword">typename</span> NumericT></div>
<div class="line"><span class="keyword">class </span>MyOperator</div>
<div class="line">{</div>
<div class="line"><span class="keyword">public</span>:</div>
<div class="line"> MyOperator(std::size_t N) : N_(N) {}</div>
<div class="line"></div>
<div class="line"> <span class="comment">// Dispatcher for y = Ax</span></div>
<div class="line"> <span class="keywordtype">void</span> apply(<a name="_a0"></a><a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> <span class="keyword">const</span> & x, <a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> & y)<span class="keyword"> const</span></div>
<div class="line"><span class="keyword"> </span>{</div>
<div class="line"><span class="preprocessor">#if defined(VIENNACL_WITH_CUDA)</span></div>
<div class="line"> <span class="keywordflow">if</span> (<a name="a1"></a><a class="code" href="namespaceviennacl_1_1traits.html#aad443a796634a9648e19b4156fcd880d">viennacl::traits::active_handle_id</a>(x) == <a name="a2"></a><a class="code" href="namespaceviennacl.html#a00b40450b6b2fd87aad3527d9b2084b8ab58facda25e2c7e20d9fe1b5e62f46d2">viennacl::CUDA_MEMORY</a>)</div>
<div class="line"> apply_cuda(x, y);</div>
<div class="line"><span class="preprocessor">#endif</span></div>
<div class="line"></div>
<div class="line"><span class="preprocessor">#if defined(VIENNACL_WITH_OPENCL)</span></div>
<div class="line"> <span class="keywordflow">if</span> (<a class="code" href="namespaceviennacl_1_1traits.html#aad443a796634a9648e19b4156fcd880d">viennacl::traits::active_handle_id</a>(x) == <a name="a3"></a><a class="code" href="namespaceviennacl.html#a00b40450b6b2fd87aad3527d9b2084b8adb37af613f34867568e4f6cf720c68b1">viennacl::OPENCL_MEMORY</a>)</div>
<div class="line"> apply_opencl(x, y);</div>
<div class="line"><span class="preprocessor">#endif</span></div>
<div class="line"></div>
<div class="line"> <span class="keywordflow">if</span> (<a class="code" href="namespaceviennacl_1_1traits.html#aad443a796634a9648e19b4156fcd880d">viennacl::traits::active_handle_id</a>(x) == <a name="a4"></a><a class="code" href="namespaceviennacl.html#a00b40450b6b2fd87aad3527d9b2084b8a427356f0fb1b8d32b28f37e36b272df4">viennacl::MAIN_MEMORY</a>)</div>
<div class="line"> apply_host(x, y);</div>
<div class="line"> }</div>
<div class="line"></div>
<div class="line"> std::size_t <a name="a5"></a><a class="code" href="namespaceviennacl_1_1traits.html#aa756f5d6820722094cae0d8b9bb6d5e2">size1</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> N_ * N_; }</div>
<div class="line"></div>
<div class="line"><span class="keyword">private</span>:</div>
<div class="line"></div>
<div class="line"><span class="preprocessor">#if defined(VIENNACL_WITH_CUDA)</span></div>
<div class="line"> <span class="keywordtype">void</span> apply_cuda(<a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> <span class="keyword">const</span> & x, <a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> & y) <span class="keyword">const</span>;</div>
<div class="line"><span class="preprocessor">#endif</span></div>
<div class="line"></div>
<div class="line"><span class="preprocessor">#if defined(VIENNACL_WITH_OPENCL)</span></div>
<div class="line"> <span class="keywordtype">void</span> apply_opencl(<a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> <span class="keyword">const</span> & x, <a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> & y) <span class="keyword">const</span>;</div>
<div class="line"><span class="preprocessor">#endif</span></div>
<div class="line"></div>
<div class="line"> <span class="keywordtype">void</span> apply_host(<a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> <span class="keyword">const</span> & x, <a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> & y) <span class="keyword">const</span>;</div>
<div class="line"></div>
<div class="line"> std::size_t N_;</div>
<div class="line">};</div>
</div><!-- fragment --> <h2>Main Program</h2>
<p>In the <code><a class="el" href="tests_2src_2bisect_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main()</a></code> routine we create the right hand side vector, instantiate the operator, and then call the solver. </p>
<div class="fragment"><div class="line"><span class="keywordtype">int</span> <a name="a6"></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="a7"></a><a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>; <span class="comment">// feel free to change to double (and change OpenCL kernel argument types accordingly)</span></div>
<div class="line"></div>
<div class="line"> std::size_t N = 10;</div>
<div class="line"> <a name="_a8"></a><a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> rhs = <a name="_a9"></a><a class="code" href="structviennacl_1_1scalar__vector.html">viennacl::scalar_vector<ScalarType></a>(N*N, <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(-1));</div>
<div class="line"> MyOperator<ScalarType> op(N);</div>
</div><!-- fragment --><p> Run the CG method with our on-the-fly operator. Use <code><a class="el" href="classviennacl_1_1linalg_1_1bicgstab__tag.html" title="A tag for the stabilized Bi-conjugate gradient solver. Used for supplying solver parameters and for d...">viennacl::linalg::bicgstab_tag()</a></code> or <code><a class="el" href="classviennacl_1_1linalg_1_1gmres__tag.html" title="A tag for the solver GMRES. Used for supplying solver parameters and for dispatching the solve() func...">viennacl::linalg::gmres_tag()</a></code> instead of <code><a class="el" href="classviennacl_1_1linalg_1_1cg__tag.html" title="A tag for the conjugate gradient Used for supplying solver parameters and for dispatching the solve()...">viennacl::linalg::cg_tag()</a></code> to solve using BiCGStab or GMRES, respectively. </p>
<div class="fragment"><div class="line"><a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> result = <a name="a10"></a><a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(op, rhs, <a name="_a11"></a><a class="code" href="classviennacl_1_1linalg_1_1cg__tag.html">viennacl::linalg::cg_tag</a>());</div>
</div><!-- fragment --><p> Pretty-Print solution vector to verify solution. (We use a slow direct element-access via <code>operator[]</code> here for convenience.) </p>
<div class="fragment"><div class="line">std::cout.precision(3);</div>
<div class="line">std::cout << std::fixed;</div>
<div class="line">std::cout << <span class="stringliteral">"Result value map: "</span> << std::endl;</div>
<div class="line">std::cout << std::endl << <span class="stringliteral">"^ y "</span> << std::endl;</div>
<div class="line"><span class="keywordflow">for</span> (std::size_t i=0; i<N; ++i)</div>
<div class="line">{</div>
<div class="line"> std::cout << <span class="stringliteral">"| "</span>;</div>
<div class="line"> <span class="keywordflow">for</span> (std::size_t j=0; j<N; ++j)</div>
<div class="line"> std::cout << result[i * N + j] << <span class="stringliteral">" "</span>;</div>
<div class="line"> std::cout << std::endl;</div>
<div class="line">}</div>
<div class="line">std::cout << <span class="stringliteral">"*---------------------------------------------> x"</span> << std::endl;</div>
</div><!-- fragment --><p> That's it, print a completion message. Read on for details on how to implement the actual compute kernels. </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>Implementation Details </h2>
<p>So far we have only looked at the code for the control logic. In the following we define the actual 'worker' code for the matrix-free implementations.</p>
<h3>Execution on Host </h3>
<p>Since the execution on the host has the smallest amount of boilerplate code surrounding it, we use this case as a starting point. </p>
<div class="fragment"><div class="line"><span class="keyword">template</span><<span class="keyword">typename</span> NumericT></div>
<div class="line"><span class="keywordtype">void</span> MyOperator<NumericT>::apply_host(<a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> <span class="keyword">const</span> & x, <a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> & y)<span class="keyword"> const</span></div>
<div class="line"><span class="keyword"></span>{</div>
<div class="line"> <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> <span class="keyword">const</span> * values_x = viennacl::linalg::host_based::detail::extract_raw_pointer<NumericT>(x.<a name="a12"></a><a class="code" href="classviennacl_1_1vector__base.html#a64e98aea5aa298ad63e3832a04c19648">handle</a>());</div>
<div class="line"> <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> * values_y = viennacl::linalg::host_based::detail::extract_raw_pointer<NumericT>(y.<a class="code" href="classviennacl_1_1vector__base.html#a64e98aea5aa298ad63e3832a04c19648">handle</a>());</div>
<div class="line"></div>
<div class="line"> <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> dx = <a name="a13"></a><a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a>(1) / <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a>(N_ + 1);</div>
<div class="line"> <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> dy = <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a>(1) / <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a>(N_ + 1);</div>
</div><!-- fragment --><p> In the following we iterate over all <img class="formulaInl" alt="$ N \times N $" src="form_140.png"/> points and apply the five-point stencil directly. This is done in a straightforward manner for illustration purposes. Multi-threaded execution via OpenMP can be obtained by uncommenting the pragma below.</p>
<p>Feel free to apply additional optimizations with respect to data access patterns and the like. </p>
<div class="fragment"><div class="line"> <span class="comment">// feel free to use</span></div>
<div class="line"> <span class="comment">// #pragma omp parallel for</span></div>
<div class="line"> <span class="comment">// here</span></div>
<div class="line"> <span class="keywordflow">for</span> (std::size_t i=0; i<N_; ++i)</div>
<div class="line"> <span class="keywordflow">for</span> (std::size_t j=0; j<N_; ++j)</div>
<div class="line"> {</div>
<div class="line"> <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> value_right = (j < N_ - 1) ? values_x[ i *N_ + j + 1] : 0;</div>
<div class="line"> <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> value_left = (j > 0 ) ? values_x[ i *N_ + j - 1] : 0;</div>
<div class="line"> <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> value_top = (i < N_ - 1) ? values_x[(i+1)*N_ + j ] : 0;</div>
<div class="line"> <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> value_bottom = (i > 0 ) ? values_x[(i-1)*N_ + j ] : 0;</div>
<div class="line"> <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> value_center = values_x[i*N_ + j];</div>
<div class="line"></div>
<div class="line"> values_y[i*N_ + j] = ((value_right - value_center) / dx - (value_center - value_left) / dx) / dx</div>
<div class="line"> + ((value_top - value_center) / dy - (value_center - value_bottom) / dy) / dy;</div>
<div class="line"> }</div>
<div class="line">}</div>
</div><!-- fragment --> <h3>Execution via CUDA </h3>
<p>The host-based kernel code serves as a basis for the CUDA kernel. The only thing we have to adjust are the array bounds: We assign one CUDA threadblock per index <code>i</code>. For a fixed <code>i</code>, parallelization across all threads in the block is obtained with respect to <code>j</code>.</p>
<p>Again, feel free to apply additional optimizations with respect to data access patterns and the like... </p>
<div class="fragment"><div class="line"><span class="preprocessor">#if defined(VIENNACL_WITH_CUDA)</span></div>
<div class="line"><span class="keyword">template</span><<span class="keyword">typename</span> NumericT></div>
<div class="line">__global__ <span class="keywordtype">void</span> apply_cuda_kernel(<a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> <span class="keyword">const</span> * values_x,</div>
<div class="line"> <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> * values_y,</div>
<div class="line"> std::size_t N)</div>
<div class="line">{</div>
<div class="line"> <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> dx = <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a>(1) / (N + 1);</div>
<div class="line"> <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> dy = <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a>(1) / (N + 1);</div>
<div class="line"></div>
<div class="line"> <span class="keywordflow">for</span> (std::size_t i = blockIdx.x; i < N; i += gridDim.x)</div>
<div class="line"> <span class="keywordflow">for</span> (std::size_t j = threadIdx.x; j < N; j += blockDim.x)</div>
<div class="line"> {</div>
<div class="line"> <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> value_right = (j < N - 1) ? values_x[ i *N + j + 1] : 0;</div>
<div class="line"> <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> value_left = (j > 0 ) ? values_x[ i *N + j - 1] : 0;</div>
<div class="line"> <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> value_top = (i < N - 1) ? values_x[(i+1)*N + j ] : 0;</div>
<div class="line"> <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> value_bottom = (i > 0 ) ? values_x[(i-1)*N + j ] : 0;</div>
<div class="line"> <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> value_center = values_x[i*N + j];</div>
<div class="line"></div>
<div class="line"> values_y[i*N + j] = ((value_right - value_center) / dx - (value_center - value_left) / dx) / dx</div>
<div class="line"> + ((value_top - value_center) / dy - (value_center - value_bottom) / dy) / dy;</div>
<div class="line"> }</div>
<div class="line">}</div>
<div class="line"><span class="preprocessor">#endif</span></div>
<div class="line"></div>
<div class="line"></div>
<div class="line"><span class="preprocessor">#if defined(VIENNACL_WITH_CUDA)</span></div>
<div class="line"><span class="keyword">template</span><<span class="keyword">typename</span> NumericT></div>
<div class="line"><span class="keywordtype">void</span> MyOperator<NumericT>::apply_cuda(<a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> <span class="keyword">const</span> & x, <a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> & y)<span class="keyword"> const</span></div>
<div class="line"><span class="keyword"></span>{</div>
<div class="line"> apply_cuda_kernel<<<128, 128>>>(<a name="a14"></a><a class="code" href="namespaceviennacl.html#ae7d5db0c2c91be75218db5b52c4d13da">viennacl::cuda_arg</a>(x), <a class="code" href="namespaceviennacl.html#ae7d5db0c2c91be75218db5b52c4d13da">viennacl::cuda_arg</a>(y), N_);</div>
<div class="line">}</div>
<div class="line"><span class="preprocessor">#endif</span></div>
</div><!-- fragment --> <h3>Execution via OpenCL </h3>
<p>The OpenCL kernel is almost identical to the CUDA kernel: Only a couple of keywords need to be replaced. Also, the sources need to be packed into a string: </p>
<div class="fragment"><div class="line"><span class="preprocessor">#if defined(VIENNACL_WITH_OPENCL)</span></div>
<div class="line"><span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">char</span> * my_compute_program =</div>
<div class="line"><span class="stringliteral">"typedef float NumericT; \n"</span></div>
<div class="line"><span class="stringliteral">"__kernel void apply_opencl_kernel(__global NumericT const * values_x, \n"</span></div>
<div class="line"><span class="stringliteral">" __global NumericT * values_y, \n"</span></div>
<div class="line"><span class="stringliteral">" unsigned int N) {\n"</span></div>
<div class="line"></div>
<div class="line"><span class="stringliteral">" NumericT dx = (NumericT)1 / (N + 1); \n"</span></div>
<div class="line"><span class="stringliteral">" NumericT dy = (NumericT)1 / (N + 1); \n"</span></div>
<div class="line"></div>
<div class="line"><span class="stringliteral">" for (unsigned int i = get_group_id(0); i < N; i += get_num_groups(0)) \n"</span></div>
<div class="line"><span class="stringliteral">" for (unsigned int j = get_local_id(0); j < N; j += get_local_size(0)) { \n"</span></div>
<div class="line"></div>
<div class="line"><span class="stringliteral">" NumericT value_right = (j < N - 1) ? values_x[ i *N + j + 1] : 0; \n"</span></div>
<div class="line"><span class="stringliteral">" NumericT value_left = (j > 0 ) ? values_x[ i *N + j - 1] : 0; \n"</span></div>
<div class="line"><span class="stringliteral">" NumericT value_top = (i < N - 1) ? values_x[(i+1)*N + j ] : 0; \n"</span></div>
<div class="line"><span class="stringliteral">" NumericT value_bottom = (i > 0 ) ? values_x[(i-1)*N + j ] : 0; \n"</span></div>
<div class="line"><span class="stringliteral">" NumericT value_center = values_x[i*N + j]; \n"</span></div>
<div class="line"></div>
<div class="line"><span class="stringliteral">" values_y[i*N + j] = ((value_right - value_center) / dx - (value_center - value_left) / dx) / dx \n"</span></div>
<div class="line"><span class="stringliteral">" + ((value_top - value_center) / dy - (value_center - value_bottom) / dy) / dy; \n"</span></div>
<div class="line"><span class="stringliteral">" } \n"</span></div>
<div class="line"><span class="stringliteral">" } \n"</span>;</div>
<div class="line"><span class="preprocessor">#endif</span></div>
</div><!-- fragment --><p> Before the kernel is called for the first time, the OpenCL program containing the kernel needs to be compiled. We use a simple singleton using a static variable to achieve that.</p>
<p>Except for the kernel compilation at the first invocation, the OpenCL kernel launch is just one line of code just like for CUDA. Refer to <a class="el" href="custom-kernels_8cpp.html">custom-kernels.cpp</a> for some more details. </p>
<div class="fragment"><div class="line"><span class="preprocessor">#if defined(VIENNACL_WITH_OPENCL)</span></div>
<div class="line"><span class="keyword">template</span><<span class="keyword">typename</span> NumericT></div>
<div class="line"><span class="keywordtype">void</span> MyOperator<NumericT>::apply_opencl(<a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> <span class="keyword">const</span> & x, <a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> & y)<span class="keyword"> const</span></div>
<div class="line"><span class="keyword"> </span>{</div>
<div class="line"> <a name="_a15"></a><a class="code" href="classviennacl_1_1ocl_1_1context.html">viennacl::ocl::context</a> & ctx = <span class="keyword">const_cast<</span><a class="code" href="classviennacl_1_1ocl_1_1context.html">viennacl::ocl::context</a> &<span class="keyword">></span>(viennacl::traits::opencl_handle(x).context());</div>
<div class="line"> <span class="keyword">static</span> <span class="keywordtype">bool</span> first_run = <span class="keyword">true</span>;</div>
<div class="line"> <span class="keywordflow">if</span> (first_run) {</div>
<div class="line"> ctx.<a name="a16"></a><a class="code" href="classviennacl_1_1ocl_1_1context.html#a9094ac71f0cdf80df698c0c84ebb483d">add_program</a>(my_compute_program, <span class="stringliteral">"my_compute_program"</span>);</div>
<div class="line"> first_run = <span class="keyword">false</span>;</div>
<div class="line"> }</div>
<div class="line"> <a name="_a17"></a><a class="code" href="classviennacl_1_1ocl_1_1kernel.html">viennacl::ocl::kernel</a> & my_kernel = ctx.<a name="a18"></a><a class="code" href="classviennacl_1_1ocl_1_1context.html#afe68ad8c2df449f40f45db6605038946">get_kernel</a>(<span class="stringliteral">"my_compute_program"</span>, <span class="stringliteral">"apply_opencl_kernel"</span>);</div>
<div class="line"></div>
<div class="line"> <a name="a19"></a><a class="code" href="namespaceviennacl_1_1ocl.html#a5f2022f653ea1cf364d20e3ff84dcada">viennacl::ocl::enqueue</a>(my_kernel(x, y, static_cast<cl_uint>(N_)));</div>
<div class="line"> }</div>
<div class="line"><span class="preprocessor">#endif</span></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">// 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="prod_8hpp.html">viennacl/linalg/prod.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"></div>
<div class="line"><span class="keyword">template</span><<span class="keyword">typename</span> NumericT></div>
<div class="line"><span class="keyword">class </span>MyOperator</div>
<div class="line">{</div>
<div class="line"><span class="keyword">public</span>:</div>
<div class="line"> MyOperator(std::size_t N) : N_(N) {}</div>
<div class="line"></div>
<div class="line"> <span class="comment">// Dispatcher for y = Ax</span></div>
<div class="line"> <span class="keywordtype">void</span> apply(<a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> <span class="keyword">const</span> & x, <a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> & y)<span class="keyword"> const</span></div>
<div class="line"><span class="keyword"> </span>{</div>
<div class="line"><span class="preprocessor">#if defined(VIENNACL_WITH_CUDA)</span></div>
<div class="line"> <span class="keywordflow">if</span> (<a class="code" href="namespaceviennacl_1_1traits.html#aad443a796634a9648e19b4156fcd880d">viennacl::traits::active_handle_id</a>(x) == <a class="code" href="namespaceviennacl.html#a00b40450b6b2fd87aad3527d9b2084b8ab58facda25e2c7e20d9fe1b5e62f46d2">viennacl::CUDA_MEMORY</a>)</div>
<div class="line"> apply_cuda(x, y);</div>
<div class="line"><span class="preprocessor">#endif</span></div>
<div class="line"></div>
<div class="line"><span class="preprocessor">#if defined(VIENNACL_WITH_OPENCL)</span></div>
<div class="line"> <span class="keywordflow">if</span> (<a class="code" href="namespaceviennacl_1_1traits.html#aad443a796634a9648e19b4156fcd880d">viennacl::traits::active_handle_id</a>(x) == <a class="code" href="namespaceviennacl.html#a00b40450b6b2fd87aad3527d9b2084b8adb37af613f34867568e4f6cf720c68b1">viennacl::OPENCL_MEMORY</a>)</div>
<div class="line"> apply_opencl(x, y);</div>
<div class="line"><span class="preprocessor">#endif</span></div>
<div class="line"></div>
<div class="line"> <span class="keywordflow">if</span> (<a class="code" href="namespaceviennacl_1_1traits.html#aad443a796634a9648e19b4156fcd880d">viennacl::traits::active_handle_id</a>(x) == <a class="code" href="namespaceviennacl.html#a00b40450b6b2fd87aad3527d9b2084b8a427356f0fb1b8d32b28f37e36b272df4">viennacl::MAIN_MEMORY</a>)</div>
<div class="line"> apply_host(x, y);</div>
<div class="line"> }</div>
<div class="line"></div>
<div class="line"> std::size_t <a class="code" href="namespaceviennacl_1_1traits.html#aa756f5d6820722094cae0d8b9bb6d5e2">size1</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> N_ * N_; }</div>
<div class="line"></div>
<div class="line"><span class="keyword">private</span>:</div>
<div class="line"></div>
<div class="line"><span class="preprocessor">#if defined(VIENNACL_WITH_CUDA)</span></div>
<div class="line"> <span class="keywordtype">void</span> apply_cuda(<a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> <span class="keyword">const</span> & x, <a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> & y) <span class="keyword">const</span>;</div>
<div class="line"><span class="preprocessor">#endif</span></div>
<div class="line"></div>
<div class="line"><span class="preprocessor">#if defined(VIENNACL_WITH_OPENCL)</span></div>
<div class="line"> <span class="keywordtype">void</span> apply_opencl(<a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> <span class="keyword">const</span> & x, <a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> & y) <span class="keyword">const</span>;</div>
<div class="line"><span class="preprocessor">#endif</span></div>
<div class="line"></div>
<div class="line"> <span class="keywordtype">void</span> apply_host(<a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> <span class="keyword">const</span> & x, <a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> & y) <span class="keyword">const</span>;</div>
<div class="line"></div>
<div class="line"> std::size_t N_;</div>
<div class="line">};</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>; <span class="comment">// feel free to change to double (and change OpenCL kernel argument types accordingly)</span></div>
<div class="line"></div>
<div class="line"> std::size_t N = 10;</div>
<div class="line"> <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> rhs = <a class="code" href="structviennacl_1_1scalar__vector.html">viennacl::scalar_vector<ScalarType></a>(N*N, <a class="code" href="fft__1d_8cpp.html#ad5c19ca4f47d3f8ec21232a5af2624e5">ScalarType</a>(-1));</div>
<div class="line"> MyOperator<ScalarType> op(N);</div>
<div class="line"></div>
<div class="line"> <a class="code" href="classviennacl_1_1vector.html">viennacl::vector<ScalarType></a> result = <a class="code" href="namespaceviennacl_1_1linalg.html#a6e9b329b64ac782e6a5687ad2fc47a2a">viennacl::linalg::solve</a>(op, rhs, <a class="code" href="classviennacl_1_1linalg_1_1cg__tag.html">viennacl::linalg::cg_tag</a>());</div>
<div class="line"></div>
<div class="line"> std::cout.precision(3);</div>
<div class="line"> std::cout << std::fixed;</div>
<div class="line"> std::cout << <span class="stringliteral">"Result value map: "</span> << std::endl;</div>
<div class="line"> std::cout << std::endl << <span class="stringliteral">"^ y "</span> << std::endl;</div>
<div class="line"> <span class="keywordflow">for</span> (std::size_t i=0; i<N; ++i)</div>
<div class="line"> {</div>
<div class="line"> std::cout << <span class="stringliteral">"| "</span>;</div>
<div class="line"> <span class="keywordflow">for</span> (std::size_t j=0; j<N; ++j)</div>
<div class="line"> std::cout << result[i * N + j] << <span class="stringliteral">" "</span>;</div>
<div class="line"> std::cout << std::endl;</div>
<div class="line"> }</div>
<div class="line"> std::cout << <span class="stringliteral">"*---------------------------------------------> x"</span> << std::endl;</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>
<div class="line"></div>
<div class="line"></div>
<div class="line"></div>
<div class="line"><span class="keyword">template</span><<span class="keyword">typename</span> NumericT></div>
<div class="line"><span class="keywordtype">void</span> MyOperator<NumericT>::apply_host(<a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> <span class="keyword">const</span> & x, <a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> & y)<span class="keyword"> const</span></div>
<div class="line"><span class="keyword"></span>{</div>
<div class="line"> <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> <span class="keyword">const</span> * values_x = viennacl::linalg::host_based::detail::extract_raw_pointer<NumericT>(x.<a class="code" href="classviennacl_1_1vector__base.html#a64e98aea5aa298ad63e3832a04c19648">handle</a>());</div>
<div class="line"> <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> * values_y = viennacl::linalg::host_based::detail::extract_raw_pointer<NumericT>(y.<a class="code" href="classviennacl_1_1vector__base.html#a64e98aea5aa298ad63e3832a04c19648">handle</a>());</div>
<div class="line"></div>
<div class="line"> <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> dx = <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a>(1) / <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a>(N_ + 1);</div>
<div class="line"> <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> dy = <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a>(1) / <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a>(N_ + 1);</div>
<div class="line"></div>
<div class="line"> <span class="comment">// feel free to use</span></div>
<div class="line"> <span class="comment">// #pragma omp parallel for</span></div>
<div class="line"> <span class="comment">// here</span></div>
<div class="line"> <span class="keywordflow">for</span> (std::size_t i=0; i<N_; ++i)</div>
<div class="line"> <span class="keywordflow">for</span> (std::size_t j=0; j<N_; ++j)</div>
<div class="line"> {</div>
<div class="line"> <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> value_right = (j < N_ - 1) ? values_x[ i *N_ + j + 1] : 0;</div>
<div class="line"> <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> value_left = (j > 0 ) ? values_x[ i *N_ + j - 1] : 0;</div>
<div class="line"> <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> value_top = (i < N_ - 1) ? values_x[(i+1)*N_ + j ] : 0;</div>
<div class="line"> <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> value_bottom = (i > 0 ) ? values_x[(i-1)*N_ + j ] : 0;</div>
<div class="line"> <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> value_center = values_x[i*N_ + j];</div>
<div class="line"></div>
<div class="line"> values_y[i*N_ + j] = ((value_right - value_center) / dx - (value_center - value_left) / dx) / dx</div>
<div class="line"> + ((value_top - value_center) / dy - (value_center - value_bottom) / dy) / dy;</div>
<div class="line"> }</div>
<div class="line">}</div>
<div class="line"></div>
<div class="line"></div>
<div class="line"><span class="preprocessor">#if defined(VIENNACL_WITH_CUDA)</span></div>
<div class="line"><span class="keyword">template</span><<span class="keyword">typename</span> NumericT></div>
<div class="line">__global__ <span class="keywordtype">void</span> apply_cuda_kernel(<a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> <span class="keyword">const</span> * values_x,</div>
<div class="line"> <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> * values_y,</div>
<div class="line"> std::size_t N)</div>
<div class="line">{</div>
<div class="line"> <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> dx = <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a>(1) / (N + 1);</div>
<div class="line"> <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> dy = <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a>(1) / (N + 1);</div>
<div class="line"></div>
<div class="line"> <span class="keywordflow">for</span> (std::size_t i = blockIdx.x; i < N; i += gridDim.x)</div>
<div class="line"> <span class="keywordflow">for</span> (std::size_t j = threadIdx.x; j < N; j += blockDim.x)</div>
<div class="line"> {</div>
<div class="line"> <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> value_right = (j < N - 1) ? values_x[ i *N + j + 1] : 0;</div>
<div class="line"> <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> value_left = (j > 0 ) ? values_x[ i *N + j - 1] : 0;</div>
<div class="line"> <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> value_top = (i < N - 1) ? values_x[(i+1)*N + j ] : 0;</div>
<div class="line"> <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> value_bottom = (i > 0 ) ? values_x[(i-1)*N + j ] : 0;</div>
<div class="line"> <a class="code" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> value_center = values_x[i*N + j];</div>
<div class="line"></div>
<div class="line"> values_y[i*N + j] = ((value_right - value_center) / dx - (value_center - value_left) / dx) / dx</div>
<div class="line"> + ((value_top - value_center) / dy - (value_center - value_bottom) / dy) / dy;</div>
<div class="line"> }</div>
<div class="line">}</div>
<div class="line"><span class="preprocessor">#endif</span></div>
<div class="line"></div>
<div class="line"></div>
<div class="line"><span class="preprocessor">#if defined(VIENNACL_WITH_CUDA)</span></div>
<div class="line"><span class="keyword">template</span><<span class="keyword">typename</span> NumericT></div>
<div class="line"><span class="keywordtype">void</span> MyOperator<NumericT>::apply_cuda(<a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> <span class="keyword">const</span> & x, <a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> & y)<span class="keyword"> const</span></div>
<div class="line"><span class="keyword"></span>{</div>
<div class="line"> apply_cuda_kernel<<<128, 128>>>(<a class="code" href="namespaceviennacl.html#ae7d5db0c2c91be75218db5b52c4d13da">viennacl::cuda_arg</a>(x), <a class="code" href="namespaceviennacl.html#ae7d5db0c2c91be75218db5b52c4d13da">viennacl::cuda_arg</a>(y), N_);</div>
<div class="line">}</div>
<div class="line"><span class="preprocessor">#endif</span></div>
<div class="line"></div>
<div class="line"></div>
<div class="line"></div>
<div class="line"></div>
<div class="line"><span class="preprocessor">#if defined(VIENNACL_WITH_OPENCL)</span></div>
<div class="line"><span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">char</span> * my_compute_program =</div>
<div class="line"><span class="stringliteral">"typedef float NumericT; \n"</span></div>
<div class="line"><span class="stringliteral">"__kernel void apply_opencl_kernel(__global NumericT const * values_x, \n"</span></div>
<div class="line"><span class="stringliteral">" __global NumericT * values_y, \n"</span></div>
<div class="line"><span class="stringliteral">" unsigned int N) {\n"</span></div>
<div class="line"></div>
<div class="line"><span class="stringliteral">" NumericT dx = (NumericT)1 / (N + 1); \n"</span></div>
<div class="line"><span class="stringliteral">" NumericT dy = (NumericT)1 / (N + 1); \n"</span></div>
<div class="line"></div>
<div class="line"><span class="stringliteral">" for (unsigned int i = get_group_id(0); i < N; i += get_num_groups(0)) \n"</span></div>
<div class="line"><span class="stringliteral">" for (unsigned int j = get_local_id(0); j < N; j += get_local_size(0)) { \n"</span></div>
<div class="line"></div>
<div class="line"><span class="stringliteral">" NumericT value_right = (j < N - 1) ? values_x[ i *N + j + 1] : 0; \n"</span></div>
<div class="line"><span class="stringliteral">" NumericT value_left = (j > 0 ) ? values_x[ i *N + j - 1] : 0; \n"</span></div>
<div class="line"><span class="stringliteral">" NumericT value_top = (i < N - 1) ? values_x[(i+1)*N + j ] : 0; \n"</span></div>
<div class="line"><span class="stringliteral">" NumericT value_bottom = (i > 0 ) ? values_x[(i-1)*N + j ] : 0; \n"</span></div>
<div class="line"><span class="stringliteral">" NumericT value_center = values_x[i*N + j]; \n"</span></div>
<div class="line"></div>
<div class="line"><span class="stringliteral">" values_y[i*N + j] = ((value_right - value_center) / dx - (value_center - value_left) / dx) / dx \n"</span></div>
<div class="line"><span class="stringliteral">" + ((value_top - value_center) / dy - (value_center - value_bottom) / dy) / dy; \n"</span></div>
<div class="line"><span class="stringliteral">" } \n"</span></div>
<div class="line"><span class="stringliteral">" } \n"</span>;</div>
<div class="line"><span class="preprocessor">#endif</span></div>
<div class="line"></div>
<div class="line"><span class="preprocessor">#if defined(VIENNACL_WITH_OPENCL)</span></div>
<div class="line"><span class="keyword">template</span><<span class="keyword">typename</span> NumericT></div>
<div class="line"><span class="keywordtype">void</span> MyOperator<NumericT>::apply_opencl(<a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> <span class="keyword">const</span> & x, <a class="code" href="classviennacl_1_1vector__base.html">viennacl::vector_base<NumericT></a> & y)<span class="keyword"> const</span></div>
<div class="line"><span class="keyword"> </span>{</div>
<div class="line"> <a class="code" href="classviennacl_1_1ocl_1_1context.html">viennacl::ocl::context</a> & ctx = <span class="keyword">const_cast<</span><a class="code" href="classviennacl_1_1ocl_1_1context.html">viennacl::ocl::context</a> &<span class="keyword">></span>(viennacl::traits::opencl_handle(x).context());</div>
<div class="line"> <span class="keyword">static</span> <span class="keywordtype">bool</span> first_run = <span class="keyword">true</span>;</div>
<div class="line"> <span class="keywordflow">if</span> (first_run) {</div>
<div class="line"> ctx.<a class="code" href="classviennacl_1_1ocl_1_1context.html#a9094ac71f0cdf80df698c0c84ebb483d">add_program</a>(my_compute_program, <span class="stringliteral">"my_compute_program"</span>);</div>
<div class="line"> first_run = <span class="keyword">false</span>;</div>
<div class="line"> }</div>
<div class="line"> <a class="code" href="classviennacl_1_1ocl_1_1kernel.html">viennacl::ocl::kernel</a> & my_kernel = ctx.<a class="code" href="classviennacl_1_1ocl_1_1context.html#afe68ad8c2df449f40f45db6605038946">get_kernel</a>(<span class="stringliteral">"my_compute_program"</span>, <span class="stringliteral">"apply_opencl_kernel"</span>);</div>
<div class="line"></div>
<div class="line"> <a class="code" href="namespaceviennacl_1_1ocl.html#a5f2022f653ea1cf364d20e3ff84dcada">viennacl::ocl::enqueue</a>(my_kernel(x, y, static_cast<cl_uint>(N_)));</div>
<div class="line"> }</div>
<div class="line"><span class="preprocessor">#endif</span></div>
<div class="line"></div>
<div class="line"></div>
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