text: """Classify tetris using gate activation function
  
  Implement a equivariant model using gates to fit the tetris dataset
  Exact equivariance to :math:`E(3)`
  
  >>> test()
  """
  import torch
  from torch_cluster import radius_graph
  from torch_geometric.data import Data, DataLoader
  from torch_scatter import scatter
  
  from e3nn import o3
  from e3nn.nn import FullyConnectedNet, Gate
  from e3nn.o3 import FullyConnectedTensorProduct
  from e3nn.math import soft_one_hot_linspace
  
  
  def tetris():
      pos = [
          [(0, 0, 0), (0, 0, 1), (1, 0, 0), (1, 1, 0)],  # chiral_shape_1
          [(0, 0, 0), (0, 0, 1), (1, 0, 0), (1, -1, 0)],  # chiral_shape_2
          [(0, 0, 0), (1, 0, 0), (0, 1, 0), (1, 1, 0)],  # square
          [(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 0, 3)],  # line
          [(0, 0, 0), (0, 0, 1), (0, 1, 0), (1, 0, 0)],  # corner
          [(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 1, 0)],  # L
          [(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 1, 1)],  # T
          [(0, 0, 0), (1, 0, 0), (1, 1, 0), (2, 1, 0)],  # zigzag
      ]
      pos = torch.tensor(pos, dtype=torch.get_default_dtype())
  
      # Since chiral shapes are the mirror of one another we need an *odd* scalar to distinguish them
      labels = torch.tensor([
          [+1, 0, 0, 0, 0, 0, 0],  # chiral_shape_1
          [-1, 0, 0, 0, 0, 0, 0],  # chiral_shape_2
          [0, 1, 0, 0, 0, 0, 0],  # square
          [0, 0, 1, 0, 0, 0, 0],  # line
          [0, 0, 0, 1, 0, 0, 0],  # corner
          [0, 0, 0, 0, 1, 0, 0],  # L
          [0, 0, 0, 0, 0, 1, 0],  # T
          [0, 0, 0, 0, 0, 0, 1],  # zigzag
      ], dtype=torch.get_default_dtype())
  
      # apply random rotation
      pos = torch.einsum('zij,zaj->zai', o3.rand_matrix(len(pos)), pos)
  
      # put in torch_geometric format
      dataset = [Data(pos=pos) for pos in pos]
      data = next(iter(DataLoader(dataset, batch_size=len(dataset))))
  
      return data, labels
  
  
  def mean_std(name, x):
      print(f"{name} \t{x.mean():.1f} ± ({x.var(0).mean().sqrt():.1f}|{x.std():.1f})")
  
  
  class Convolution(torch.nn.Module):
      def __init__(self, irreps_in, irreps_sh, irreps_out) -> None:
          super().__init__()
  
          tp = FullyConnectedTensorProduct(
              irreps_in1=irreps_in,
              irreps_in2=irreps_sh,
              irreps_out=irreps_out,
              internal_weights=False,
              shared_weights=False,
          )
          self.fc = FullyConnectedNet([3, 256, tp.weight_numel], torch.relu)
          self.tp = tp
  
      def forward(self, edge_src, edge_dst, node_features, edge_sh, edge_length_embedded, num_neighbors) -> torch.Tensor:
          weight = self.fc(edge_length_embedded)
          edge_features = self.tp(node_features[edge_src], edge_sh, weight)
          node_features = scatter(edge_features, edge_dst, dim=0).div(num_neighbors**0.5)
          return node_features
  
  
  class Network(torch.nn.Module):
      def __init__(self) -> None:
          super().__init__()
          self.irreps_sh = o3.Irreps.spherical_harmonics(3)
  
          irreps = self.irreps_sh
  
          # First layer with gate
          gate = Gate(
              "16x0e + 16x0o", [torch.relu, torch.abs],  # scalar
              "8x0e + 8x0o + 8x0e + 8x0o", [torch.relu, torch.tanh, torch.relu, torch.tanh],  # gates (scalars)
              "16x1o + 16x1e"  # non-scalars, num_irreps has to match with gates
          )
          self.conv = Convolution(irreps, self.irreps_sh, gate.irreps_in)
          self.gate = gate
          irreps = self.gate.irreps_out
  
          # Final layer
          self.final = Convolution(irreps, self.irreps_sh, "0o + 6x0e")
  
      def forward(self, data) -> torch.Tensor:
          num_neighbors = 3.8  # typical number of neighbors
          num_nodes = 4  # typical number of nodes
  
          edge_src, edge_dst = radius_graph(data.pos, 2.1, data.batch)
          edge_vec = data.pos[edge_src] - data.pos[edge_dst]
          edge_sh = o3.spherical_harmonics(self.irreps_sh, edge_vec, normalization='component', normalize=True)
          edge_length_embedded = soft_one_hot_linspace(edge_vec.norm(dim=1), 1.0, 2.0, 3) * 3**0.5
  
          x = scatter(edge_sh, edge_dst, dim=0).div(num_neighbors**0.5)
  
          x = self.conv(edge_src, edge_dst, x, edge_sh, edge_length_embedded, num_neighbors)
          x = self.gate(x)
          x = self.final(edge_src, edge_dst, x, edge_sh, edge_length_embedded, num_neighbors)
  
          return scatter(x, data.batch, dim=0).div(num_nodes**0.5)
  
  
  def main():
      data, labels = tetris()
      f = Network()
  
      print(f)
  
      optim = torch.optim.Adam(f.parameters(), lr=1e-2)
  
      for step in range(200):
          pred = f(data)
          loss = (pred - labels).pow(2).sum()
  
          optim.zero_grad()
          loss.backward()
          optim.step()
  
          if step % 10 == 0:
              accuracy = pred.round().eq(labels).double().mean().item()
              print(f"{100 * accuracy:.1f}% accuracy")
  
      # Check equivariance
      rotated_data, _ = tetris()
      error = f(rotated_data) - f(data)
      print(f"Equivariance error = {error.abs().max().item():.1e}")
  
  
  if __name__ == '__main__':
      main()
  
  
  def test():
      torch.set_default_dtype(torch.float64)
  
      data, labels = tetris()
      f = Network()
  
      pred = f(data)
      loss = (pred - labels).pow(2).sum()
      loss.backward()
  
      rotated_data, _ = tetris()
      error = f(rotated_data) - f(data)
      assert error.abs().max() < 1e-10
  