Add similarities file

prototorch/functions/similarities.py

@@ -0,0 +1,18 @@
+"""ProtoTorch similarity functions."""
+
+import torch
+
+
+def cosine_similarity(x, y):
+    """Compute the cosine similarity between :math:`x` and :math:`y`.
+
+    Expected dimension of x is 2.
+    Expected dimension of y is 2.
+    """
+    norm_x = x.pow(2).sum(1).sqrt()
+    norm_y = y.pow(2).sum(1).sqrt()
+    norm_mat = norm_x.unsqueeze(-1) @ norm_y.unsqueeze(-1).T
+    epsilon = torch.finfo(norm_mat.dtype).eps
+    norm_mat.clamp_(min=epsilon)
+    similarities = (x @ y.T) / norm_mat
+    return similarities