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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 class="first">Create a neural network layer with no parameters.</p>
<blockquote>
<div><ul class="simple">
<li>This calls into <strong>numpy</strong> as part of its implementation</li>
</ul>
</div></blockquote>
</li>
<li><p class="first">Create a neural network layer that has learnable weights</p>
<blockquote>
<div><ul class="simple">
<li>This calls into <strong>SciPy</strong> as part of its implementation</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([[ 1.4839, 2.5299, 8.2822, 5.7193, 7.1493],
[13.1836, 6.2973, 2.1584, 3.3738, 5.4185],
[ 9.0299, 7.5143, 5.3861, 2.0743, 7.1462],
[ 5.8116, 2.3906, 16.4799, 5.8820, 5.2063],
[12.2800, 10.6594, 8.1183, 7.6186, 11.3666],
[ 5.8116, 13.5470, 8.5990, 6.2266, 5.2063],
[ 9.0299, 4.6358, 8.8316, 9.7948, 7.1462],
[13.1836, 14.2887, 8.2465, 9.1051, 5.4185]],
grad_fn=<BadFFTFunctionBackward>)
tensor([[ 0.3855, 0.0700, -0.1190, -0.6064, -0.9754, -0.3952, 0.5016, 1.7637],
[ 0.5128, -0.4970, 1.2489, -0.2165, 0.1547, 2.6279, 1.7911, -1.5699],
[ 0.2831, 0.4426, -2.0371, 1.0565, -0.4328, -0.6353, -0.4868, 0.4151],
[-0.4151, 2.0910, 1.6475, 0.3195, -0.4956, -0.1518, 0.4923, 1.7999],
[-0.2763, 1.1863, 1.5218, 0.4156, -0.4060, 0.4382, -0.9364, -1.0928],
[ 0.0849, -1.2389, 0.5403, 0.2296, 1.0621, 0.5837, -1.0333, 0.8809],
[-0.9139, 0.8284, -0.5841, -0.2474, -0.4411, -0.2750, -2.4111, -1.4343],
[-0.8421, -0.6686, -0.1892, -2.0916, -0.1261, 1.6404, 0.0620, -1.3518]],
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([[-0.1720, -0.7576, -1.6202],
[ 1.5514, -0.8969, -1.3046],
[ 1.0487, 0.8901, 0.3066]], requires_grad=True), Parameter containing:
tensor([[-1.1039]], requires_grad=True)]
Output from the convolution: tensor([[ 2.7284e+00, -1.0781e+00, -4.6166e+00, -3.5084e+00, -9.4009e-01,
3.1789e+00, -2.2956e+00, -1.6878e-01],
[ 5.0181e+00, 1.4264e-01, -4.7418e+00, -6.4631e+00, -2.0972e+00,
-4.3795e+00, -2.0129e+00, -2.0045e+00],
[ 6.4642e-01, -1.8545e+00, -2.6823e+00, 1.4252e+00, -3.3383e+00,
-7.2155e+00, -1.8686e+00, -2.1400e+00],
[-1.2089e-02, -6.3965e+00, -5.2462e+00, 2.0544e+00, 8.7603e-01,
2.0844e+00, 1.5275e-01, -1.3878e+00],
[ 5.1333e+00, 1.9333e+00, -3.9424e+00, -4.5664e+00, -3.0176e+00,
1.7561e+00, 1.7851e+00, 2.4229e+00],
[-4.2955e+00, 1.0160e+00, 3.4282e+00, -8.3685e-01, -4.8737e+00,
-1.6821e+00, 3.1652e+00, 1.9694e+00],
[-5.2395e+00, -4.7644e+00, -5.4166e-02, 6.9540e+00, -2.2102e-02,
-2.1887e+00, 2.4923e+00, 3.5662e-01],
[-4.0109e+00, -4.6590e+00, -5.0817e+00, 1.9480e+00, -6.7938e-01,
-7.1298e-03, -6.2676e+00, -1.5256e+00]],
grad_fn=<ScipyConv2dFunctionBackward>)
Gradient for the input map: tensor([[ 0.0914, 0.1965, -0.0791, -2.0378, -0.0382, 0.2970, -0.9849, -2.8354,
2.0823, 0.1265],
[-0.6334, 3.0912, 1.0767, -4.0740, -2.7525, 4.7139, -2.5353, -4.2296,
1.5705, 0.0883],
[-2.0494, 3.8639, 7.5162, 0.6742, -5.3240, 4.4611, 2.4781, -0.4578,
-0.1595, -1.0197],
[-3.1410, -0.6487, 7.3873, 6.1448, -2.4883, -2.6740, -1.0463, 4.8532,
1.1793, -2.1950],
[-2.7853, -4.5591, 0.4704, 3.2774, 4.1224, -4.7943, -5.1322, 0.9542,
0.9345, -0.6701],
[ 0.1206, -4.2960, -5.5900, -0.7649, -3.5847, -1.3652, 2.0133, 3.6330,
2.6749, 2.6340],
[ 2.0359, -0.1915, -1.3882, -1.1300, -7.9716, -7.9863, 3.1647, 3.0609,
1.0697, 0.0287],
[ 1.4820, 2.9842, 2.3103, 4.6084, 3.4339, -6.1782, -5.2677, 0.9434,
-1.9863, -1.1200],
[ 0.5804, 1.6826, -0.4451, 3.4400, 4.5771, -3.5138, -0.7750, 2.2364,
1.4117, 0.8059],
[ 0.1239, 0.1798, -1.3179, -0.6328, 1.4940, 0.0683, -0.8053, -0.8750,
-0.3690, -0.1161]])
</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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<ul>
<li><a class="reference internal" href="#">Creating Extensions Using numpy and scipy</a><ul>
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