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<div class="sphx-glr-example-title section" id="creating-extensions-using-numpy-and-scipy">
<span id="sphx-glr-advanced-numpy-extensions-tutorial-py"></span><h1>Creating Extensions Using numpy and scipy<a class="headerlink" href="#creating-extensions-using-numpy-and-scipy" title="Permalink to this headline">ΒΆ</a></h1>
<p><strong>Author</strong>: <a class="reference external" href="https://github.com/apaszke">Adam Paszke</a></p>
<p><strong>Updated by</strong>: <a class="reference external" href="https://github.com/adam-dziedzic">Adam Dziedzic</a></p>
<p>In this tutorial, we shall go through two tasks:</p>
<ol class="arabic">
<li><p>Create a neural network layer with no parameters.</p>
<blockquote>
<div><ul class="simple">
<li><p>This calls into <strong>numpy</strong> as part of its implementation</p></li>
</ul>
</div></blockquote>
</li>
<li><p>Create a neural network layer that has learnable weights</p>
<blockquote>
<div><ul class="simple">
<li><p>This calls into <strong>SciPy</strong> as part of its implementation</p></li>
</ul>
</div></blockquote>
</li>
</ol>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">torch</span>
<span class="kn">from</span> <span class="nn">torch.autograd</span> <span class="kn">import</span> <span class="n">Function</span>
</pre></div>
</div>
<div class="section" id="parameter-less-example">
<h2>Parameter-less example<a class="headerlink" href="#parameter-less-example" title="Permalink to this headline">ΒΆ</a></h2>
<p>This layer doesnβt particularly do anything useful or mathematically
correct.</p>
<p>It is aptly named BadFFTFunction</p>
<p><strong>Layer Implementation</strong></p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">numpy.fft</span> <span class="kn">import</span> <span class="n">rfft2</span><span class="p">,</span> <span class="n">irfft2</span>
<span class="k">class</span> <span class="nc">BadFFTFunction</span><span class="p">(</span><span class="n">Function</span><span class="p">):</span>
<span class="nd">@staticmethod</span>
<span class="k">def</span> <span class="nf">forward</span><span class="p">(</span><span class="n">ctx</span><span class="p">,</span> <span class="nb">input</span><span class="p">):</span>
<span class="n">numpy_input</span> <span class="o">=</span> <span class="nb">input</span><span class="o">.</span><span class="n">detach</span><span class="p">()</span><span class="o">.</span><span class="n">numpy</span><span class="p">()</span>
<span class="n">result</span> <span class="o">=</span> <span class="nb">abs</span><span class="p">(</span><span class="n">rfft2</span><span class="p">(</span><span class="n">numpy_input</span><span class="p">))</span>
<span class="k">return</span> <span class="nb">input</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">result</span><span class="p">)</span>
<span class="nd">@staticmethod</span>
<span class="k">def</span> <span class="nf">backward</span><span class="p">(</span><span class="n">ctx</span><span class="p">,</span> <span class="n">grad_output</span><span class="p">):</span>
<span class="n">numpy_go</span> <span class="o">=</span> <span class="n">grad_output</span><span class="o">.</span><span class="n">numpy</span><span class="p">()</span>
<span class="n">result</span> <span class="o">=</span> <span class="n">irfft2</span><span class="p">(</span><span class="n">numpy_go</span><span class="p">)</span>
<span class="k">return</span> <span class="n">grad_output</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">result</span><span class="p">)</span>
<span class="c1"># since this layer does not have any parameters, we can</span>
<span class="c1"># simply declare this as a function, rather than as an nn.Module class</span>
<span class="k">def</span> <span class="nf">incorrect_fft</span><span class="p">(</span><span class="nb">input</span><span class="p">):</span>
<span class="k">return</span> <span class="n">BadFFTFunction</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="nb">input</span><span class="p">)</span>
</pre></div>
</div>
<p><strong>Example usage of the created layer:</strong></p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">input</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">8</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="n">requires_grad</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">result</span> <span class="o">=</span> <span class="n">incorrect_fft</span><span class="p">(</span><span class="nb">input</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">result</span><span class="p">)</span>
<span class="n">result</span><span class="o">.</span><span class="n">backward</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="n">result</span><span class="o">.</span><span class="n">size</span><span class="p">()))</span>
<span class="nb">print</span><span class="p">(</span><span class="nb">input</span><span class="p">)</span>
</pre></div>
</div>
<p class="sphx-glr-script-out">Out:</p>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>tensor([[ 0.2733, 4.7178, 2.1754, 10.7828, 5.9417],
[ 5.6993, 7.8431, 5.5058, 10.6697, 4.5358],
[ 6.7284, 6.4406, 9.7342, 6.4750, 6.2320],
[ 5.0593, 7.2425, 5.3294, 3.0321, 12.6597],
[ 5.4206, 4.7828, 14.6675, 7.2581, 4.0779],
[ 5.0593, 7.2960, 6.9993, 3.6543, 12.6597],
[ 6.7284, 3.3722, 11.8476, 8.0785, 6.2320],
[ 5.6993, 7.6340, 9.9890, 5.4811, 4.5358]],
grad_fn=<BadFFTFunctionBackward>)
tensor([[-0.0052, 1.5592, 0.7096, 0.5321, -2.0388, 1.6087, -0.1862, -0.2872],
[ 0.2383, -0.7734, -0.5612, 1.6329, -0.5915, -0.1637, 1.4101, -0.6295],
[ 0.5098, 0.5700, -1.2098, -0.6402, 0.2011, 1.5179, -0.0935, -1.1632],
[ 0.3459, -0.4139, -0.8139, -0.2018, -0.7975, 0.6402, 1.4969, -0.2749],
[-0.1459, -1.2135, 0.5639, -0.0632, -0.1011, 1.4329, 1.3587, -0.3588],
[-0.9695, -0.9300, -0.2941, 1.0837, -2.4694, -0.1516, -0.8989, 0.0336],
[ 0.9653, 0.3875, 0.5827, -0.8855, 1.2638, -1.2188, -1.4169, 0.1116],
[ 0.0434, -0.7051, -0.9752, 1.0329, 1.0653, -0.3915, -0.0203, 1.4300]],
requires_grad=True)
</pre></div>
</div>
</div>
<div class="section" id="parametrized-example">
<h2>Parametrized example<a class="headerlink" href="#parametrized-example" title="Permalink to this headline">ΒΆ</a></h2>
<p>In deep learning literature, this layer is confusingly referred
to as convolution while the actual operation is cross-correlation
(the only difference is that filter is flipped for convolution,
which is not the case for cross-correlation).</p>
<p>Implementation of a layer with learnable weights, where cross-correlation
has a filter (kernel) that represents weights.</p>
<p>The backward pass computes the gradient wrt the input and the gradient wrt the filter.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">flip</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">scipy.signal</span> <span class="kn">import</span> <span class="n">convolve2d</span><span class="p">,</span> <span class="n">correlate2d</span>
<span class="kn">from</span> <span class="nn">torch.nn.modules.module</span> <span class="kn">import</span> <span class="n">Module</span>
<span class="kn">from</span> <span class="nn">torch.nn.parameter</span> <span class="kn">import</span> <span class="n">Parameter</span>
<span class="k">class</span> <span class="nc">ScipyConv2dFunction</span><span class="p">(</span><span class="n">Function</span><span class="p">):</span>
<span class="nd">@staticmethod</span>
<span class="k">def</span> <span class="nf">forward</span><span class="p">(</span><span class="n">ctx</span><span class="p">,</span> <span class="nb">input</span><span class="p">,</span> <span class="nb">filter</span><span class="p">,</span> <span class="n">bias</span><span class="p">):</span>
<span class="c1"># detach so we can cast to NumPy</span>
<span class="nb">input</span><span class="p">,</span> <span class="nb">filter</span><span class="p">,</span> <span class="n">bias</span> <span class="o">=</span> <span class="nb">input</span><span class="o">.</span><span class="n">detach</span><span class="p">(),</span> <span class="nb">filter</span><span class="o">.</span><span class="n">detach</span><span class="p">(),</span> <span class="n">bias</span><span class="o">.</span><span class="n">detach</span><span class="p">()</span>
<span class="n">result</span> <span class="o">=</span> <span class="n">correlate2d</span><span class="p">(</span><span class="nb">input</span><span class="o">.</span><span class="n">numpy</span><span class="p">(),</span> <span class="nb">filter</span><span class="o">.</span><span class="n">numpy</span><span class="p">(),</span> <span class="n">mode</span><span class="o">=</span><span class="s1">'valid'</span><span class="p">)</span>
<span class="n">result</span> <span class="o">+=</span> <span class="n">bias</span><span class="o">.</span><span class="n">numpy</span><span class="p">()</span>
<span class="n">ctx</span><span class="o">.</span><span class="n">save_for_backward</span><span class="p">(</span><span class="nb">input</span><span class="p">,</span> <span class="nb">filter</span><span class="p">,</span> <span class="n">bias</span><span class="p">)</span>
<span class="k">return</span> <span class="n">torch</span><span class="o">.</span><span class="n">as_tensor</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">input</span><span class="o">.</span><span class="n">dtype</span><span class="p">)</span>
<span class="nd">@staticmethod</span>
<span class="k">def</span> <span class="nf">backward</span><span class="p">(</span><span class="n">ctx</span><span class="p">,</span> <span class="n">grad_output</span><span class="p">):</span>
<span class="n">grad_output</span> <span class="o">=</span> <span class="n">grad_output</span><span class="o">.</span><span class="n">detach</span><span class="p">()</span>
<span class="nb">input</span><span class="p">,</span> <span class="nb">filter</span><span class="p">,</span> <span class="n">bias</span> <span class="o">=</span> <span class="n">ctx</span><span class="o">.</span><span class="n">saved_tensors</span>
<span class="n">grad_output</span> <span class="o">=</span> <span class="n">grad_output</span><span class="o">.</span><span class="n">numpy</span><span class="p">()</span>
<span class="n">grad_bias</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">grad_output</span><span class="p">,</span> <span class="n">keepdims</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">grad_input</span> <span class="o">=</span> <span class="n">convolve2d</span><span class="p">(</span><span class="n">grad_output</span><span class="p">,</span> <span class="nb">filter</span><span class="o">.</span><span class="n">numpy</span><span class="p">(),</span> <span class="n">mode</span><span class="o">=</span><span class="s1">'full'</span><span class="p">)</span>
<span class="c1"># the previous line can be expressed equivalently as:</span>
<span class="c1"># grad_input = correlate2d(grad_output, flip(flip(filter.numpy(), axis=0), axis=1), mode='full')</span>
<span class="n">grad_filter</span> <span class="o">=</span> <span class="n">correlate2d</span><span class="p">(</span><span class="nb">input</span><span class="o">.</span><span class="n">numpy</span><span class="p">(),</span> <span class="n">grad_output</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s1">'valid'</span><span class="p">)</span>
<span class="k">return</span> <span class="n">torch</span><span class="o">.</span><span class="n">from_numpy</span><span class="p">(</span><span class="n">grad_input</span><span class="p">),</span> <span class="n">torch</span><span class="o">.</span><span class="n">from_numpy</span><span class="p">(</span><span class="n">grad_filter</span><span class="p">)</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">float</span><span class="p">),</span> <span class="n">torch</span><span class="o">.</span><span class="n">from_numpy</span><span class="p">(</span><span class="n">grad_bias</span><span class="p">)</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">float</span><span class="p">)</span>
<span class="k">class</span> <span class="nc">ScipyConv2d</span><span class="p">(</span><span class="n">Module</span><span class="p">):</span>
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">filter_width</span><span class="p">,</span> <span class="n">filter_height</span><span class="p">):</span>
<span class="nb">super</span><span class="p">(</span><span class="n">ScipyConv2d</span><span class="p">,</span> <span class="bp">self</span><span class="p">)</span><span class="o">.</span><span class="fm">__init__</span><span class="p">()</span>
<span class="bp">self</span><span class="o">.</span><span class="n">filter</span> <span class="o">=</span> <span class="n">Parameter</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="n">filter_width</span><span class="p">,</span> <span class="n">filter_height</span><span class="p">))</span>
<span class="bp">self</span><span class="o">.</span><span class="n">bias</span> <span class="o">=</span> <span class="n">Parameter</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
<span class="k">def</span> <span class="nf">forward</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="nb">input</span><span class="p">):</span>
<span class="k">return</span> <span class="n">ScipyConv2dFunction</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="nb">input</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">filter</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">bias</span><span class="p">)</span>
</pre></div>
</div>
<p><strong>Example usage:</strong></p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">module</span> <span class="o">=</span> <span class="n">ScipyConv2d</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"Filter and bias: "</span><span class="p">,</span> <span class="nb">list</span><span class="p">(</span><span class="n">module</span><span class="o">.</span><span class="n">parameters</span><span class="p">()))</span>
<span class="nb">input</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="n">requires_grad</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">output</span> <span class="o">=</span> <span class="n">module</span><span class="p">(</span><span class="nb">input</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"Output from the convolution: "</span><span class="p">,</span> <span class="n">output</span><span class="p">)</span>
<span class="n">output</span><span class="o">.</span><span class="n">backward</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">8</span><span class="p">,</span> <span class="mi">8</span><span class="p">))</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"Gradient for the input map: "</span><span class="p">,</span> <span class="nb">input</span><span class="o">.</span><span class="n">grad</span><span class="p">)</span>
</pre></div>
</div>
<p class="sphx-glr-script-out">Out:</p>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>Filter and bias: [Parameter containing:
tensor([[-0.3535, -0.3607, -1.2605],
[ 0.3209, -0.8493, 0.6655],
[-1.0012, 1.1931, -1.7587]], requires_grad=True), Parameter containing:
tensor([[-0.0306]], requires_grad=True)]
Output from the convolution: tensor([[ -4.0675, 1.3104, 0.5629, -3.7993, 1.8225, -10.2257, 3.5116,
-7.3815],
[ 3.2081, 5.5051, -1.8760, 3.9300, 0.0912, 6.4329, -3.6189,
4.1120],
[ 1.7241, -3.1719, 1.6780, -3.4582, 5.3718, -2.4910, 2.3587,
-8.0891],
[ -8.0555, 5.4626, 2.6618, -0.0119, -0.1193, 3.6653, -0.5059,
6.1946],
[ 7.2719, -2.0581, 0.9481, -1.0228, -1.5216, -1.6020, 1.0148,
-1.2701],
[ 0.8911, -1.4974, 1.2182, -0.8256, -2.6953, 3.9136, 1.1159,
-0.0987],
[ 1.0162, 2.0385, 1.2889, 1.2850, 2.8959, -6.1096, -0.4603,
-1.4425],
[ 2.3807, 0.9308, -0.2695, 0.6634, -3.5688, 2.7815, -1.6980,
-3.1248]], grad_fn=<ScipyConv2dFunctionBackward>)
Gradient for the input map: tensor([[-3.4096e-01, -9.1705e-01, -2.2859e+00, -2.6787e+00, -1.6059e+00,
-1.2994e-01, 1.5016e+00, 7.1582e-01, 1.2297e+00, -7.8701e-02],
[ 6.3099e-01, 2.4377e-01, 9.5901e-01, 7.5480e-01, -1.2390e-01,
1.8727e+00, 1.4054e-01, 3.5836e+00, -1.6047e-01, 4.3205e-01],
[-1.2248e+00, 1.5279e-01, -7.9226e-01, -1.9629e+00, -1.4980e-03,
-1.4512e+00, 3.2129e+00, 1.1967e-01, 1.8305e+00, 6.5689e-01],
[ 8.9605e-01, -1.2795e-02, 8.5167e-01, 3.8157e+00, 3.4823e-01,
2.4066e+00, -1.9342e-01, 2.0934e+00, -5.8531e-01, -1.1626e+00],
[ 3.5303e-01, -2.2945e-02, 2.4130e+00, -9.9097e-01, -9.3822e-01,
1.1022e+00, -2.6235e+00, 2.3530e+00, 4.9177e-02, 2.9527e+00],
[ 2.1249e-01, 2.9596e+00, 8.9114e-01, 5.3807e+00, -3.0829e+00,
4.1247e+00, -2.5109e+00, 2.8002e+00, 1.8017e+00, -7.5350e-01],
[ 3.9816e-01, -1.8299e-01, 3.5922e+00, -2.6653e+00, 4.9914e+00,
-4.3308e+00, 1.7477e+00, -2.0365e-01, 2.2252e+00, 7.9312e-01],
[ 1.0914e+00, 5.2782e-01, -2.9234e+00, 7.3035e+00, -3.6218e+00,
3.6365e+00, 1.8854e+00, -8.4757e-01, 8.7292e-01, 2.7866e+00],
[ 8.7442e-02, 1.1606e+00, -1.3734e+00, 2.2743e+00, 5.0627e-01,
1.8080e+00, -6.7569e-01, -1.5551e+00, 2.6815e+00, -2.0371e-01],
[-2.6183e-01, -7.2607e-01, 1.2376e+00, -9.2589e-01, 8.4368e-02,
8.8597e-01, 2.0842e+00, 1.7161e-01, -1.2514e+00, 1.2657e+00]])
</pre></div>
</div>
<p><strong>Check the gradients:</strong></p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">torch.autograd.gradcheck</span> <span class="kn">import</span> <span class="n">gradcheck</span>
<span class="n">moduleConv</span> <span class="o">=</span> <span class="n">ScipyConv2d</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
<span class="nb">input</span> <span class="o">=</span> <span class="p">[</span><span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">20</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">double</span><span class="p">,</span> <span class="n">requires_grad</span><span class="o">=</span><span class="kc">True</span><span class="p">)]</span>
<span class="n">test</span> <span class="o">=</span> <span class="n">gradcheck</span><span class="p">(</span><span class="n">moduleConv</span><span class="p">,</span> <span class="nb">input</span><span class="p">,</span> <span class="n">eps</span><span class="o">=</span><span class="mf">1e-6</span><span class="p">,</span> <span class="n">atol</span><span class="o">=</span><span class="mf">1e-4</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"Are the gradients correct: "</span><span class="p">,</span> <span class="n">test</span><span class="p">)</span>
</pre></div>
</div>
<p class="sphx-glr-script-out">Out:</p>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>Are the gradients correct: True
</pre></div>
</div>
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