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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="k">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="k">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([[ 8.6736, 1.2358, 5.3560, 1.9721, 0.0562],
[ 7.3729, 11.8951, 10.5456, 9.1499, 1.6347],
[ 1.8184, 8.7315, 5.0504, 10.0316, 2.0912],
[ 3.3423, 11.2330, 6.3480, 15.5189, 1.6654],
[ 0.1560, 3.5289, 5.1113, 11.7995, 6.4944],
[ 3.3423, 8.0942, 10.8932, 1.5125, 1.6654],
[ 1.8184, 4.5770, 11.9054, 2.5929, 2.0912],
[ 7.3729, 7.5588, 6.2854, 3.7757, 1.6347]],
grad_fn=<BadFFTFunctionBackward>)
tensor([[ 0.1800, 0.7934, 0.4422, -0.6368, -0.3449, 0.2004, 0.2077, -0.4703],
[-1.0612, -0.3385, 0.8267, -1.6585, 0.2592, 1.9034, 0.1304, 0.1986],
[-0.6218, 0.7488, -0.4641, 0.8991, 0.7250, -1.7597, 1.7421, -0.1284],
[ 1.4567, -0.6556, -2.0568, -0.1023, -1.0762, 2.0799, 0.4652, -0.8476],
[-0.2822, 0.0358, -1.1566, -1.3220, 0.8009, 0.2789, -0.5823, -0.8381],
[-0.4374, -0.4081, 0.9506, 2.0388, -0.5236, -1.4160, -1.2250, -0.7342],
[ 1.0212, -0.3772, -0.8089, -0.7906, -0.0171, -1.0157, -1.3611, 0.6435],
[-0.0840, 0.4607, 0.4223, -0.4623, -1.1220, -0.2234, -0.7700, -0.4047]],
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="k">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="k">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="k">import</span> <span class="n">Module</span>
<span class="kn">from</span> <span class="nn">torch.nn.parameter</span> <span class="k">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="nf">__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([[-0.2463, 1.3323, -0.1164],
[-0.6245, -0.5231, 0.8460],
[ 0.0826, -0.8166, 0.3638]], requires_grad=True), Parameter containing:
tensor([[-0.0901]], requires_grad=True)]
Output from the convolution: tensor([[-2.5897, 0.6518, 1.2417, 1.4218, -1.8193, -0.4743, 0.7030, 0.4981],
[-2.7613, -2.2026, 1.6367, -0.1487, -1.9842, -0.0129, -3.9020, -0.5468],
[ 1.4815, -2.2999, -1.7652, 3.1233, -1.8920, -1.3765, -1.7182, -2.1471],
[ 1.9511, 0.1871, -0.7454, 1.1319, 2.2410, 2.2760, 1.7457, -2.3955],
[ 1.1504, -0.4743, -2.1891, 1.2978, -1.0455, -1.9666, 0.5783, -0.3511],
[ 1.4052, 2.5164, -2.1212, -2.4177, 0.6220, 1.6083, -0.6531, 0.6299],
[-0.7015, 1.7152, 0.9506, -2.8316, 0.8645, 0.0554, 3.1653, 0.3533],
[ 2.4109, -2.7415, 2.6173, -2.5184, -1.2031, -0.0455, -0.8362, 0.1678]],
grad_fn=<ScipyConv2dFunctionBackward>)
Gradient for the input map: tensor([[-2.2584e-01, 1.1344e+00, 2.6305e-01, 7.1845e-01, -1.2912e+00,
7.5053e-01, 6.5180e-01, 5.7675e-01, 2.4723e-02, -7.2427e-03],
[-6.9868e-01, -3.3331e-04, 1.8870e-01, 4.2936e-01, 5.9782e-01,
-1.6103e+00, 3.3309e-01, 1.0410e+00, 1.2989e+00, -3.4708e-02],
[-1.8202e-01, -1.3686e+00, 1.4077e+00, -1.5038e+00, 1.0252e-01,
-1.1430e+00, -5.1042e-01, -3.9226e-01, 1.0494e+00, 5.9781e-01],
[ 2.5758e-01, -7.8731e-01, 2.0816e-01, 2.1301e-01, 4.9722e-01,
-3.3538e+00, -2.6648e+00, 6.7924e-01, -1.7320e+00, 8.2427e-01],
[-2.0582e-01, 2.5116e+00, -9.3229e-01, 4.6463e-01, 9.6275e-01,
1.0577e+00, -8.7827e-01, -5.2759e-01, 2.3738e+00, -8.1397e-01],
[-7.2020e-01, -1.0139e+00, 2.2081e+00, -3.3287e-01, -2.8523e+00,
3.7957e+00, -3.2118e+00, -6.8435e-01, 3.0463e-01, 7.7895e-01],
[ 5.6343e-01, -1.3551e+00, 8.9059e-01, 1.9382e+00, -2.1979e-01,
-1.2421e+00, 1.3109e+00, -3.4767e+00, -6.9768e-01, 1.9045e-01],
[ 4.7284e-02, 8.0640e-01, 4.4032e-01, 8.5067e-01, -1.3745e+00,
-2.3654e+00, 4.5101e+00, -6.4339e-01, -1.3063e+00, -4.7751e-01],
[-2.4503e-01, -6.0080e-01, -4.7918e-01, 2.1341e+00, 1.6615e+00,
-2.1002e+00, -1.4106e+00, 3.5176e+00, -7.1833e-01, -5.5931e-01],
[ 2.9193e-02, -2.0045e-01, -7.3381e-01, 1.1288e-01, 1.9373e+00,
-1.6709e-01, -1.6027e+00, 1.2009e+00, 8.0501e-02, -1.6887e-01]])
</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="k">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>
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