Animate the training loop for the alpha complex example

Creates an animation using matplotlib to visualise how the point cloud forms the required topology over each training loop iteration.

Author: CtrlAltDelirious

torch_topological/examples/alpha_complex_animated.py

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+"""Example demonstrating the computation of alpha complexes.
+
+This simple example demonstrates how to use alpha complexes to change
+the appearance of a point cloud, following the `TopologyLayer
+<https://github.com/bruel-gabrielsson/TopologyLayer>`_ package.
+
+This example is still a **work in progress**.
+"""
+
+from torch_topological.nn import AlphaComplex
+from torch_topological.nn import SummaryStatisticLoss
+
+from torch_topological.utils import SelectByDimension
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+import torch
+
+if __name__ == '__main__':
+    np.random.seed(42)
+    data = np.random.rand(100, 2)
+
+    alpha_complex = AlphaComplex()
+
+    loss_fn = SummaryStatisticLoss(
+        summary_statistic='polynomial_function',
+        p=2,
+        q=0
+    )
+
+    X = torch.nn.Parameter(torch.as_tensor(data), requires_grad=True)
+    opt = torch.optim.Adam([X], lr=1e-2)
+
+    plt.ion()
+    fig, ax = plt.subplots()
+
+    for i in range(100):
+        # We are only interested in working with persistence diagrams of
+        # dimension 1.
+        selector = SelectByDimension(1)
+
+        # Let's think step by step; apparently, AIs like that! So let's
+        # first get the persistence information of our complex. We pass
+        # it through the selector to remove diagrams we do not need.
+        pers_info = alpha_complex(X)
+        pers_info = selector(pers_info)
+
+        # Evaluate the loss; notice that we want to *maximise* it in
+        # order to improve the holes in the data.
+        loss = -loss_fn(pers_info)
+
+        opt.zero_grad()
+        loss.backward()
+        opt.step()
+
+        data = X.detach().numpy()
+        ax.clear()
+        ax.scatter(data[:, 0], data[:, 1])
+        plt.pause(0.2)