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| <h1 id="ndarray-vectorized-tensor-computations-on-cpus-and-gpus">NDArray: Vectorized Tensor Computations on CPUs and GPUs</h1> |
| |
| <p><code>NDArray</code> is the basic vectorized operation unit in MXNet for matrix and tensor computations. |
| Users can perform usual calculations as on an R"s array, but with two additional features:</p> |
| |
| <ul> |
| <li><p>Multiple devices: All operations can be run on various devices including |
| CPUs and GPUs.</p></li> |
| <li><p>Automatic parallelization: All operations are automatically executed in |
| parallel with each other.</p></li> |
| </ul> |
| |
| <h2 id="create-and-initialize">Create and Initialize</h2> |
| |
| <p>Let"s create <code>NDArray</code> on either a GPU or a CPU:</p> |
| <div class="highlight"><pre><code class="language-r" data-lang="r"><span class="n">require</span><span class="p">(</span><span class="n">mxnet</span><span class="p">)</span><span class="w"> |
| </span></code></pre></div><div class="highlight"><pre><code class="language-" data-lang="">## Loading required package: mxnet |
| ## Loading required package: methods |
| </code></pre></div><div class="highlight"><pre><code class="language-r" data-lang="r"><span class="n">a</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.nd.zeros</span><span class="p">(</span><span class="nf">c</span><span class="p">(</span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="m">3</span><span class="p">))</span><span class="w"> </span><span class="c1"># create a 2-by-3 matrix on cpu</span><span class="w"> |
| </span><span class="n">b</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.nd.zeros</span><span class="p">(</span><span class="nf">c</span><span class="p">(</span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="m">3</span><span class="p">),</span><span class="w"> </span><span class="n">mx.cpu</span><span class="p">())</span><span class="w"> </span><span class="c1"># create a 2-by-3 matrix on cpu</span><span class="w"> |
| </span><span class="c1"># c <- mx.nd.zeros(c(2, 3), mx.gpu(0)) # create a 2-by-3 matrix on gpu 0, if you have CUDA enabled.</span><span class="w"> |
| </span></code></pre></div> |
| <p>Typically for CUDA-enabled devices, the device id of a GPU starts from 0. |
| That's why we passed in 0 to the GPU id.</p> |
| |
| <p>We can initialize an <code>NDArray</code> object in various ways:</p> |
| <div class="highlight"><pre><code class="language-r" data-lang="r"><span class="n">a</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.nd.ones</span><span class="p">(</span><span class="nf">c</span><span class="p">(</span><span class="m">4</span><span class="p">,</span><span class="w"> </span><span class="m">4</span><span class="p">))</span><span class="w"> |
| </span><span class="n">b</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.rnorm</span><span class="p">(</span><span class="nf">c</span><span class="p">(</span><span class="m">4</span><span class="p">,</span><span class="w"> </span><span class="m">5</span><span class="p">))</span><span class="w"> |
| </span><span class="n">c</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.nd.array</span><span class="p">(</span><span class="m">1</span><span class="o">:</span><span class="m">5</span><span class="p">)</span><span class="w"> |
| </span></code></pre></div> |
| <p>To check the numbers in an <code>NDArray</code>, we can simply run:</p> |
| <div class="highlight"><pre><code class="language-r" data-lang="r"><span class="n">a</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.nd.ones</span><span class="p">(</span><span class="nf">c</span><span class="p">(</span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="m">3</span><span class="p">))</span><span class="w"> |
| </span><span class="n">b</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">as.array</span><span class="p">(</span><span class="n">a</span><span class="p">)</span><span class="w"> |
| </span><span class="nf">class</span><span class="p">(</span><span class="n">b</span><span class="p">)</span><span class="w"> |
| </span></code></pre></div><div class="highlight"><pre><code class="language-" data-lang="">## [1] "matrix" |
| </code></pre></div><div class="highlight"><pre><code class="language-r" data-lang="r"><span class="n">b</span><span class="w"> |
| </span></code></pre></div><div class="highlight"><pre><code class="language-" data-lang="">## [,1] [,2] [,3] |
| ## [1,] 1 1 1 |
| ## [2,] 1 1 1 |
| </code></pre></div> |
| <h2 id="performing-basic-operations">Performing Basic Operations</h2> |
| |
| <h3 id="elemental-wise-operations">Elemental-wise Operations</h3> |
| |
| <p>You can perform elemental-wise operations on <code>NDArray</code> objects, as follows:</p> |
| <div class="highlight"><pre><code class="language-r" data-lang="r"><span class="n">a</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.nd.ones</span><span class="p">(</span><span class="nf">c</span><span class="p">(</span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="m">4</span><span class="p">))</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="m">2</span><span class="w"> |
| </span><span class="n">b</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.nd.ones</span><span class="p">(</span><span class="nf">c</span><span class="p">(</span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="m">4</span><span class="p">))</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">8</span><span class="w"> |
| </span><span class="n">as.array</span><span class="p">(</span><span class="n">a</span><span class="p">)</span><span class="w"> |
| </span></code></pre></div><div class="highlight"><pre><code class="language-" data-lang="">## [,1] [,2] [,3] [,4] |
| ## [1,] 2 2 2 2 |
| ## [2,] 2 2 2 2 |
| </code></pre></div><div class="highlight"><pre><code class="language-r" data-lang="r"><span class="n">as.array</span><span class="p">(</span><span class="n">b</span><span class="p">)</span><span class="w"> |
| </span></code></pre></div><div class="highlight"><pre><code class="language-" data-lang="">## [,1] [,2] [,3] [,4] |
| ## [1,] 0.125 0.125 0.125 0.125 |
| ## [2,] 0.125 0.125 0.125 0.125 |
| </code></pre></div><div class="highlight"><pre><code class="language-r" data-lang="r"><span class="n">c</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="w"> |
| </span><span class="n">as.array</span><span class="p">(</span><span class="n">c</span><span class="p">)</span><span class="w"> |
| </span></code></pre></div><div class="highlight"><pre><code class="language-" data-lang="">## [,1] [,2] [,3] [,4] |
| ## [1,] 2.125 2.125 2.125 2.125 |
| ## [2,] 2.125 2.125 2.125 2.125 |
| </code></pre></div><div class="highlight"><pre><code class="language-r" data-lang="r"><span class="n">d</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">5</span><span class="w"> |
| </span><span class="n">as.array</span><span class="p">(</span><span class="n">d</span><span class="p">)</span><span class="w"> |
| </span></code></pre></div><div class="highlight"><pre><code class="language-" data-lang="">## [,1] [,2] [,3] [,4] |
| ## [1,] -3.9375 -3.9375 -3.9375 -3.9375 |
| ## [2,] -3.9375 -3.9375 -3.9375 -3.9375 |
| </code></pre></div> |
| <p>If two <code>NDArray</code>s are located on different devices, we need to explicitly move them to the same one. For instance:</p> |
| <div class="highlight"><pre><code class="language-r" data-lang="r"><span class="n">a</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.nd.ones</span><span class="p">(</span><span class="nf">c</span><span class="p">(</span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="m">3</span><span class="p">))</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="m">2</span><span class="w"> |
| </span><span class="n">b</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.nd.ones</span><span class="p">(</span><span class="nf">c</span><span class="p">(</span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="m">3</span><span class="p">),</span><span class="w"> </span><span class="n">mx.gpu</span><span class="p">())</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">8</span><span class="w"> |
| </span><span class="n">c</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.nd.copyto</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">mx.gpu</span><span class="p">())</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">b</span><span class="w"> |
| </span><span class="n">as.array</span><span class="p">(</span><span class="n">c</span><span class="p">)</span><span class="w"> |
| </span></code></pre></div> |
| <h3 id="loading-and-saving">Loading and Saving</h3> |
| |
| <p>You can save a list of <code>NDArray</code> object to your disk with <code>mx.nd.save</code>:</p> |
| <div class="highlight"><pre><code class="language-r" data-lang="r"><span class="n">a</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.nd.ones</span><span class="p">(</span><span class="nf">c</span><span class="p">(</span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="m">3</span><span class="p">))</span><span class="w"> |
| </span><span class="n">mx.nd.save</span><span class="p">(</span><span class="nf">list</span><span class="p">(</span><span class="n">a</span><span class="p">),</span><span class="w"> </span><span class="s2">"temp.ndarray"</span><span class="p">)</span><span class="w"> |
| </span></code></pre></div> |
| <p>You can load it back easily:</p> |
| <div class="highlight"><pre><code class="language-r" data-lang="r"><span class="n">a</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.nd.load</span><span class="p">(</span><span class="s2">"temp.ndarray"</span><span class="p">)</span><span class="w"> |
| </span><span class="n">as.array</span><span class="p">(</span><span class="n">a</span><span class="p">[[</span><span class="m">1</span><span class="p">]])</span><span class="w"> |
| </span></code></pre></div><div class="highlight"><pre><code class="language-" data-lang="">## [,1] [,2] [,3] |
| ## [1,] 1 1 1 |
| ## [2,] 1 1 1 |
| </code></pre></div> |
| <p>We can directly save data to and load it from a distributed file system, such as Amazon S3 and HDFS:</p> |
| <div class="highlight"><pre><code class="language-r" data-lang="r"><span class="n">mx.nd.save</span><span class="p">(</span><span class="nf">list</span><span class="p">(</span><span class="n">a</span><span class="p">),</span><span class="w"> </span><span class="s2">"s3://mybucket/mydata.bin"</span><span class="p">)</span><span class="w"> |
| </span><span class="n">mx.nd.save</span><span class="p">(</span><span class="nf">list</span><span class="p">(</span><span class="n">a</span><span class="p">),</span><span class="w"> </span><span class="s2">"hdfs///users/myname/mydata.bin"</span><span class="p">)</span><span class="w"> |
| </span></code></pre></div> |
| <h2 id="automatic-parallelization">Automatic Parallelization</h2> |
| |
| <p><code>NDArray</code> can automatically execute operations in parallel. Automatic parallelization is useful when |
| using multiple resources, such as CPU cards, GPU cards, and CPU-to-GPU memory bandwidth.</p> |
| |
| <p>For example, if we write <code>a <- a + 1</code> followed by <code>b <- b + 1</code>, and <code>a</code> is on a CPU and |
| <code>b</code> is on a GPU, executing them in parallel improves |
| efficiency. Furthermore, because copying data between CPUs and GPUs are also expensive, running in parallel with other computations further increases efficiency.</p> |
| |
| <p>It's hard to find the code that can be executed in parallel by eye. In the |
| following example, <code>a <- a + 1</code> and <code>c <- c * 3</code> can be executed in parallel, but <code>a <- a + 1</code> and |
| <code>b <- b * 3</code> should be in sequential.</p> |
| <div class="highlight"><pre><code class="language-r" data-lang="r"><span class="n">a</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.nd.ones</span><span class="p">(</span><span class="nf">c</span><span class="p">(</span><span class="m">2</span><span class="p">,</span><span class="m">3</span><span class="p">))</span><span class="w"> |
| </span><span class="n">b</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">a</span><span class="w"> |
| </span><span class="n">c</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">mx.nd.copyto</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">mx.cpu</span><span class="p">())</span><span class="w"> |
| </span><span class="n">a</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="w"> |
| </span><span class="n">b</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="m">3</span><span class="w"> |
| </span><span class="n">c</span><span class="w"> </span><span class="o"><-</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="m">3</span><span class="w"> |
| </span></code></pre></div> |
| <p>Luckily, MXNet can automatically resolve the dependencies and |
| execute operations in parallel accurately. This allows us to write our program assuming there is only a single thread. MXNet will |
| automatically dispatch the program to multiple devices.</p> |
| |
| <p>MXNet achieves this with lazy evaluation. Each operation is issued to an |
| internal engine, and then returned. For example, if we run <code>a <- a + 1</code>, it |
| returns immediately after pushing the plus operator to the engine. This |
| asynchronous processing allows us to push more operators to the engine. It determines |
| the read and write dependencies and the best way to execute them in |
| parallel.</p> |
| |
| <p>The actual computations are finished, allowing us to copy the results someplace else, such as <code>as.array(a)</code> or <code>mx.nd.save(a, "temp.dat")</code>. To write highly parallelized codes, we only need to postpone when we need |
| the results.</p> |
| |
| <h2 id="next-steps">Next Steps</h2> |
| |
| <ul> |
| <li><a href="/api/r/docs/tutorials/symbol">Symbol</a></li> |
| <li><a href="/api/r/docs/tutorials/callback_function">Write and use callback functions</a></li> |
| <li><a href="/api/r/docs/tutorials/five_minutes_neural_network">Neural Networks with MXNet in Five Minutes</a></li> |
| <li><a href="/api/r/docs/tutorials/classify_real_image_with_pretrained_model">Classify Real-World Images with Pre-trained Model</a></li> |
| <li><a href="/api/r/docs/tutorials/mnist_competition">Handwritten Digits Classification Competition</a></li> |
| <li><a href="/api/r/docs/tutorials/char_rnn_model">Character Language Model using RNN</a></li> |
| </ul> |
| </div> |
| </div> |
| |
| </div> |
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