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    <li>How to use Eigen in Paddle</li>
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  <div class="section" id="how-to-use-eigen-in-paddle">
<span id="how-to-use-eigen-in-paddle"></span><h1>How to use Eigen in Paddle<a class="headerlink" href="#how-to-use-eigen-in-paddle" title="Permalink to this headline"></a></h1>
<p>Essentially, a neural network is a compute graph. T data needed for the computation is stored in <code class="docutils literal"><span class="pre">Tensor</span></code>s and its computation procedure is described by <code class="docutils literal"><span class="pre">Operator</span></code>s. An <code class="docutils literal"><span class="pre">Operator</span></code> calls the <code class="docutils literal"><span class="pre">Compute</span></code> interface in its corresponding <code class="docutils literal"><span class="pre">OpKernel</span></code> and operates on the <code class="docutils literal"><span class="pre">Tensor</span></code>.</p>
<div class="section" id="eigen-tensor-module">
<span id="eigen-tensor-module"></span><h2>Eigen Tensor Module<a class="headerlink" href="#eigen-tensor-module" title="Permalink to this headline"></a></h2>
<p>The Eigen Tensor module supports powerful element-wise computation. In addition, a piece of code written using it can be run on both the CPU and the GPU.</p>
<p>Note that Eigen Tensor is still being actively developed, so its tests are not completely covered and its documentation may be sparse.</p>
<p>For details on Eigen Tensor module, please see <a class="reference external" href="https://github.com/RLovelett/eigen/blob/master/unsupported/Eigen/CXX11/src/Tensor/README.md">doc 1</a> and <a class="reference external" href="https://bitbucket.org/eigen/eigen/src/default/unsupported/Eigen/CXX11/src/Tensor/README.md">doc 2</a>.</p>
</div>
<div class="section" id="paddle-framework-tensor">
<span id="paddle-framework-tensor"></span><h2>paddle::framework::Tensor<a class="headerlink" href="#paddle-framework-tensor" title="Permalink to this headline"></a></h2>
<p>Paddle Tensor&#8217;s is defined in the framework directory with the following interface:</p>
<div class="highlight-cpp"><div class="highlight"><pre><span></span><span class="k">class</span> <span class="nc">Tensor</span> <span class="p">{</span>
 <span class="k">public</span><span class="o">:</span>
  <span class="cm">/*! Return a pointer to mutable memory block. */</span>
  <span class="k">template</span> <span class="o">&lt;</span><span class="k">typename</span> <span class="n">T</span><span class="o">&gt;</span>
  <span class="kr">inline</span> <span class="n">T</span><span class="o">*</span> <span class="n">data</span><span class="p">();</span>

  <span class="cm">/**</span>
<span class="cm">   * @brief   Return a pointer to mutable memory block.</span>
<span class="cm">   * @note    If not exist, then allocation.</span>
<span class="cm">   */</span>
  <span class="k">template</span> <span class="o">&lt;</span><span class="k">typename</span> <span class="n">T</span><span class="o">&gt;</span>
  <span class="kr">inline</span> <span class="n">T</span><span class="o">*</span> <span class="n">mutable_data</span><span class="p">(</span><span class="n">platform</span><span class="o">::</span><span class="n">Place</span> <span class="n">place</span><span class="p">);</span>

  <span class="cm">/**</span>
<span class="cm">   * @brief     Return a pointer to mutable memory block.</span>
<span class="cm">   *</span>
<span class="cm">   * @param[in] dims    The dimensions of the memory block.</span>
<span class="cm">   * @param[in] place   The place of the memory block.</span>
<span class="cm">   *</span>
<span class="cm">   * @note      If not exist, then allocation.</span>
<span class="cm">   */</span>
  <span class="k">template</span> <span class="o">&lt;</span><span class="k">typename</span> <span class="n">T</span><span class="o">&gt;</span>
  <span class="kr">inline</span> <span class="n">T</span><span class="o">*</span> <span class="n">mutable_data</span><span class="p">(</span><span class="n">DDim</span> <span class="n">dims</span><span class="p">,</span> <span class="n">platform</span><span class="o">::</span><span class="n">Place</span> <span class="n">place</span><span class="p">);</span>

  <span class="cm">/*! Resize the dimensions of the memory block. */</span>
  <span class="kr">inline</span> <span class="n">Tensor</span><span class="o">&amp;</span> <span class="n">Resize</span><span class="p">(</span><span class="k">const</span> <span class="n">DDim</span><span class="o">&amp;</span> <span class="n">dims</span><span class="p">);</span>

  <span class="cm">/*! Return the dimensions of the memory block. */</span>
  <span class="kr">inline</span> <span class="k">const</span> <span class="n">DDim</span><span class="o">&amp;</span> <span class="n">dims</span><span class="p">()</span> <span class="k">const</span><span class="p">;</span>

 <span class="k">private</span><span class="o">:</span>
  <span class="cm">/*! holds the memory block if allocated. */</span>
  <span class="n">std</span><span class="o">::</span><span class="n">shared_ptr</span><span class="o">&lt;</span><span class="n">Placeholder</span><span class="o">&gt;</span> <span class="n">holder_</span><span class="p">;</span>

  <span class="cm">/*! points to dimensions of memory block. */</span>
  <span class="n">DDim</span> <span class="n">dim_</span><span class="p">;</span>
<span class="p">};</span>
</pre></div>
</div>
<p><code class="docutils literal"><span class="pre">Placeholder</span></code> is used to delay memory allocation; that is, we can first define a tensor, using <code class="docutils literal"><span class="pre">Resize</span></code> to configure its shape, and then call <code class="docutils literal"><span class="pre">mutuable_data</span></code> to allocate the actual memory.</p>
<div class="highlight-cpp"><div class="highlight"><pre><span></span><span class="n">paddle</span><span class="o">::</span><span class="n">framework</span><span class="o">::</span><span class="n">Tensor</span> <span class="n">t</span><span class="p">;</span>
<span class="n">paddle</span><span class="o">::</span><span class="n">platform</span><span class="o">::</span><span class="n">CPUPlace</span> <span class="n">place</span><span class="p">;</span>
<span class="c1">// set size first</span>
<span class="n">t</span><span class="p">.</span><span class="n">Resize</span><span class="p">({</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">});</span>
<span class="c1">// allocate memory on CPU later</span>
<span class="n">t</span><span class="p">.</span><span class="n">mutable_data</span><span class="p">(</span><span class="n">place</span><span class="p">);</span>
</pre></div>
</div>
</div>
<div class="section" id="paddle-framework-tensor-usage">
<span id="paddle-framework-tensor-usage"></span><h2>paddle::framework::Tensor Usage<a class="headerlink" href="#paddle-framework-tensor-usage" title="Permalink to this headline"></a></h2>
<p><code class="docutils literal"><span class="pre">AddOp</span></code> demonstrates Tensor&#8217;s usage.</p>
<ul class="simple">
<li>InferShape</li>
</ul>
<p>When computing a neural network&#8217;s compute graph, first call every <code class="docutils literal"><span class="pre">Operator</span></code>&#8216;s <code class="docutils literal"><span class="pre">InferShape</span></code> method, and use <code class="docutils literal"><span class="pre">Resize</span></code> to configure the size of the output tensor.</p>
<div class="highlight-cpp"><div class="highlight"><pre><span></span><span class="kt">void</span> <span class="nf">InferShape</span><span class="p">(</span><span class="k">const</span> <span class="n">framework</span><span class="o">::</span><span class="n">InferShapeContext</span> <span class="o">&amp;</span><span class="n">ctx</span><span class="p">)</span> <span class="k">const</span> <span class="k">override</span> <span class="p">{</span>
  <span class="n">PADDLE_ENFORCE_EQ</span><span class="p">(</span><span class="n">ctx</span><span class="p">.</span><span class="n">Input</span><span class="o">&lt;</span><span class="n">Tensor</span><span class="o">&gt;</span><span class="p">(</span><span class="s">&quot;X&quot;</span><span class="p">)</span><span class="o">-&gt;</span><span class="n">dims</span><span class="p">(),</span>
                    <span class="n">ctx</span><span class="p">.</span><span class="n">Input</span><span class="o">&lt;</span><span class="n">Tensor</span><span class="o">&gt;</span><span class="p">(</span><span class="s">&quot;Y&quot;</span><span class="p">)</span><span class="o">-&gt;</span><span class="n">dims</span><span class="p">(),</span>
                    <span class="s">&quot;Two input of Add Op&#39;s dimension must be same.&quot;</span><span class="p">);</span>
  <span class="n">ctx</span><span class="p">.</span><span class="n">Output</span><span class="o">&lt;</span><span class="n">Tensor</span><span class="o">&gt;</span><span class="p">(</span><span class="s">&quot;Out&quot;</span><span class="p">)</span><span class="o">-&gt;</span><span class="n">Resize</span><span class="p">(</span><span class="n">ctx</span><span class="p">.</span><span class="n">Input</span><span class="o">&lt;</span><span class="n">Tensor</span><span class="o">&gt;</span><span class="p">(</span><span class="s">&quot;X&quot;</span><span class="p">)</span><span class="o">-&gt;</span><span class="n">dims</span><span class="p">());</span>
<span class="p">}</span>
</pre></div>
</div>
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<li>Run</li>
</ul>
<div class="highlight-cpp"><div class="highlight"><pre><span></span><span class="kt">void</span> <span class="nf">Compute</span><span class="p">(</span><span class="k">const</span> <span class="n">framework</span><span class="o">::</span><span class="n">ExecutionContext</span><span class="o">&amp;</span> <span class="n">context</span><span class="p">)</span> <span class="k">const</span> <span class="k">override</span> <span class="p">{</span>
  <span class="k">auto</span><span class="o">*</span> <span class="n">input0</span> <span class="o">=</span> <span class="n">context</span><span class="p">.</span><span class="n">Input</span><span class="o">&lt;</span><span class="n">Tensor</span><span class="o">&gt;</span><span class="p">(</span><span class="s">&quot;X&quot;</span><span class="p">);</span>
  <span class="k">auto</span><span class="o">*</span> <span class="n">input1</span> <span class="o">=</span> <span class="n">context</span><span class="p">.</span><span class="n">Input</span><span class="o">&lt;</span><span class="n">Tensor</span><span class="o">&gt;</span><span class="p">(</span><span class="s">&quot;Y&quot;</span><span class="p">);</span>
  <span class="k">auto</span><span class="o">*</span> <span class="n">output</span> <span class="o">=</span> <span class="n">context</span><span class="p">.</span><span class="n">Output</span><span class="o">&lt;</span><span class="n">Tensor</span><span class="o">&gt;</span><span class="p">(</span><span class="s">&quot;Out&quot;</span><span class="p">);</span>

  <span class="n">output</span><span class="o">-&gt;</span><span class="n">mutable_data</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">context</span><span class="p">.</span><span class="n">GetPlace</span><span class="p">());</span>

  <span class="k">auto</span> <span class="n">x</span> <span class="o">=</span> <span class="n">EigenVector</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;::</span><span class="n">Flatten</span><span class="p">(</span><span class="o">*</span><span class="n">input0</span><span class="p">);</span>
  <span class="k">auto</span> <span class="n">y</span> <span class="o">=</span> <span class="n">EigenVector</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;::</span><span class="n">Flatten</span><span class="p">(</span><span class="o">*</span><span class="n">input1</span><span class="p">);</span>
  <span class="k">auto</span> <span class="n">z</span> <span class="o">=</span> <span class="n">EigenVector</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;::</span><span class="n">Flatten</span><span class="p">(</span><span class="o">*</span><span class="n">output</span><span class="p">);</span>

  <span class="k">auto</span> <span class="n">place</span> <span class="o">=</span> <span class="n">context</span><span class="p">.</span><span class="n">GetEigenDevice</span><span class="o">&lt;</span><span class="n">Place</span><span class="o">&gt;</span><span class="p">();</span>

  <span class="n">z</span><span class="p">.</span><span class="n">device</span><span class="p">(</span><span class="n">place</span><span class="p">)</span> <span class="o">=</span> <span class="n">x</span> <span class="o">+</span> <span class="n">y</span><span class="p">;</span>
<span class="p">}</span>
</pre></div>
</div>
</div>
<div class="section" id="paddle-framework-tensoreigentensor">
<span id="paddle-framework-tensoreigentensor"></span><h2>paddle::framework::Tensor到EigenTensor的转换<a class="headerlink" href="#paddle-framework-tensoreigentensor" title="Permalink to this headline"></a></h2>
<p>As shown above, in actual computation, we need to transform the input and output <code class="docutils literal"><span class="pre">Tensor</span></code>s into formats Eigen supports. We show some functions in <a class="reference external" href="https://github.com/PaddlePaddle/Paddle/blob/develop/paddle/framework/eigen.h">eigen.h</a> to implement the transformation from <code class="docutils literal"><span class="pre">paddle::framework::Tensor</span></code>to <code class="docutils literal"><span class="pre">EigenTensor/EigenMatrix/EigenVector/EigenScalar</span></code>.</p>
<p>Using EigenTensor as an example:</p>
<div class="highlight-cpp"><div class="highlight"><pre><span></span><span class="n">Tensor</span> <span class="n">t</span><span class="p">;</span>
<span class="kt">float</span><span class="o">*</span> <span class="n">p</span> <span class="o">=</span> <span class="n">t</span><span class="p">.</span><span class="n">mutable_data</span><span class="o">&lt;</span><span class="kt">float</span><span class="o">&gt;</span><span class="p">(</span><span class="n">make_ddim</span><span class="p">({</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">}),</span> <span class="n">platform</span><span class="o">::</span><span class="n">CPUPlace</span><span class="p">());</span>
<span class="k">for</span> <span class="p">(</span><span class="kt">int</span> <span class="n">i</span> <span class="o">=</span> <span class="mi">0</span><span class="p">;</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="mi">1</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="mi">3</span><span class="p">;</span> <span class="n">i</span><span class="o">++</span><span class="p">)</span> <span class="p">{</span>
  <span class="n">p</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="k">static_cast</span><span class="o">&lt;</span><span class="kt">float</span><span class="o">&gt;</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
<span class="p">}</span>

<span class="n">EigenTensor</span><span class="o">&lt;</span><span class="kt">float</span><span class="p">,</span> <span class="mi">3</span><span class="o">&gt;::</span><span class="n">Type</span> <span class="n">et</span> <span class="o">=</span> <span class="n">EigenTensor</span><span class="o">&lt;</span><span class="kt">float</span><span class="p">,</span> <span class="mi">3</span><span class="o">&gt;::</span><span class="n">From</span><span class="p">(</span><span class="n">t</span><span class="p">);</span>
</pre></div>
</div>
<p><code class="docutils literal"><span class="pre">From</span></code> is an interfacing method provided by the EigenTensor template, which implements the transformation from a <code class="docutils literal"><span class="pre">paddle::framework::Tensor</span></code> object to an EigenTensor. Since <code class="docutils literal"><span class="pre">rank</span></code> is a template parameter, it needs to be explicitly specified at the time of the transformation.</p>
<p>In Eigen, tensors with different ranks are different types, with <code class="docutils literal"><span class="pre">Vector</span></code> bring a rank-1 instance. Note that <code class="docutils literal"><span class="pre">EigenVector&lt;T&gt;::From</span></code> uses a transformation from an 1-dimensional Paddle tensor to a 1-dimensional Eigen tensor while <code class="docutils literal"><span class="pre">EigenVector&lt;T&gt;::Flatten</span></code> reshapes a paddle tensor and flattens it into a 1-dimensional Eigen tensor. Both resulting tensors are still typed EigenVector.</p>
<p>For more transformations, see the <a class="reference external" href="https://github.com/PaddlePaddle/Paddle/blob/develop/paddle/framework/eigen_test.cc">unit tests</a> in the <code class="docutils literal"><span class="pre">eigen_test.cc</span></code> file.</p>
</div>
<div class="section" id="implementing-computation">
<span id="implementing-computation"></span><h2>Implementing Computation<a class="headerlink" href="#implementing-computation" title="Permalink to this headline"></a></h2>
<p>While computing, the device interface is needed from the EigenTensors on the left hand side of the assignments. Note that the computation between EigenTensors only changes the data originally inthe Tensor and does not change all the shape information associated with the Tensor.</p>
<div class="highlight-cpp"><div class="highlight"><pre><span></span><span class="k">auto</span> <span class="n">x</span> <span class="o">=</span> <span class="n">EigenVector</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;::</span><span class="n">Flatten</span><span class="p">(</span><span class="o">*</span><span class="n">input0</span><span class="p">);</span>
<span class="k">auto</span> <span class="n">y</span> <span class="o">=</span> <span class="n">EigenVector</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;::</span><span class="n">Flatten</span><span class="p">(</span><span class="o">*</span><span class="n">input1</span><span class="p">);</span>
<span class="k">auto</span> <span class="n">z</span> <span class="o">=</span> <span class="n">EigenVector</span><span class="o">&lt;</span><span class="n">T</span><span class="o">&gt;::</span><span class="n">Flatten</span><span class="p">(</span><span class="o">*</span><span class="n">output</span><span class="p">);</span>
<span class="k">auto</span> <span class="n">place</span> <span class="o">=</span> <span class="n">context</span><span class="p">.</span><span class="n">GetEigenDevice</span><span class="o">&lt;</span><span class="n">Place</span><span class="o">&gt;</span><span class="p">();</span>
<span class="n">z</span><span class="p">.</span><span class="n">device</span><span class="p">(</span><span class="n">place</span><span class="p">)</span> <span class="o">=</span> <span class="n">x</span> <span class="o">+</span> <span class="n">y</span><span class="p">;</span>
</pre></div>
</div>
<p>In this code segment, input0/input1/output can be Tensors of arbitrary dimension. We are calling Flatten from EigenVector, transforming a tensor of any dimension into a 1-dimensional EigenVector. After completing computation, input0/input1/output will retain the same shape information, and they can be resized using the <code class="docutils literal"><span class="pre">Resize</span></code> interface.</p>
<p>Because the Eigen Tensor module is under-documented, please refer to <code class="docutils literal"><span class="pre">OpKernel</span></code>&#8216;s computation code in TensorFlow&#8217;s <a class="reference external" href="https://github.com/tensorflow/tensorflow/tree/master/tensorflow/core/kernels">kernel module documentation</a>.</p>
</div>
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