dev/add support for trace

grassmann_tensor/tensor.py

@@ -488,6 +488,47 @@ def matmul(self, other: GrassmannTensor) -> GrassmannTensor:
             _tensor=tensor,
         )
 
+    def trace(self, trace_pair: tuple[int, int]) -> torch.Tensor:
+        assert len(trace_pair) == 2, (
+            f"The length of trace pair must be 2, but got {len(trace_pair)}."
+        )
+
+        assert trace_pair[0] != trace_pair[1], (
+            f"Trace requires two distinct axes but got {trace_pair[0]} and {trace_pair[1]}."
+        )
+
+        assert self.arrow[trace_pair[0]] == self.arrow[trace_pair[1]], (
+            f"Trace requires two different arrows but got {self.arrow[trace_pair[0]]} and {self.arrow[trace_pair[1]]}."
+        )
+
+        tensor = self
+
+        if trace_pair[0] > trace_pair[1]:
+            trace_pair = trace_pair[::-1]
+
+        edge_first, edge_end = self.edges[trace_pair[0]], self.edges[trace_pair[1]]
+        if edge_first != edge_end:
+            raise ValueError(f"Incompatible edges: {edge_first} and {edge_end}.")
+
+        if tensor.arrow[trace_pair[0]] != tensor.arrow[trace_pair[1]]:
+            tensor = tensor.reverse((trace_pair[1],))
+
+        order = list(range(tensor.tensor.dim()))
+        order_first = order.pop(trace_pair[0])
+        order_end = order.pop(trace_pair[1])
+        order[trace_pair[0] : trace_pair[0]] = [order_first, order_end]
+        tensor = tensor.permute(tuple(order))
+
+        shape = tensor.tensor.shape[0] + tensor.tensor.shape[1]
+        tensor.reshape(
+            (
+                shape,
+                *(-1 for _ in range(tensor.tensor.dim() - 2)),
+            )
+        )
+
+        return tensor.tensor[0].trace()
+
     def __post_init__(self) -> None:
         assert len(self._arrow) == self._tensor.dim(), (
             f"Arrow length ({len(self._arrow)}) must match tensor dimensions ({self._tensor.dim()})."

tests/trace_test.py

@@ -0,0 +1,11 @@
+import torch
+from grassmann_tensor.tensor import GrassmannTensor
+
+
+def test_trace() -> None:
+    gt = GrassmannTensor(
+        (False, False, False),
+        ((1, 1), (1, 1), (1, 1)),
+        torch.tensor([[[1, 0], [0, 2]], [[0, 3], [4, 0]]]),
+    )
+    gt.trace((0, 1))