From d319e029d246743d982d41caf1362392eb47b169 Mon Sep 17 00:00:00 2001
From: Gausshj <kylin_0@qq.com>
Date: Thu, 20 Nov 2025 20:35:30 +0800
Subject: [PATCH] dev(conjugate): add support for conjugation

- Add support for conjugation
- Add some test cases for conjugation
---
 grassmann_tensor/tensor.py |  30 +++++++++++
 tests/conjugate_test.py    | 106 +++++++++++++++++++++++++++++++++++++
 2 files changed, 136 insertions(+)
 create mode 100644 tests/conjugate_test.py

diff --git a/grassmann_tensor/tensor.py b/grassmann_tensor/tensor.py
index 7b9dbb7..7e68fc8 100644
--- a/grassmann_tensor/tensor.py
+++ b/grassmann_tensor/tensor.py
@@ -970,6 +970,36 @@ def identity(self, pairs: tuple[tuple[int, ...], tuple[int, ...]]) -> GrassmannT
 
         return tensor_identity
 
+    def conjugate(self) -> GrassmannTensor:
+        tensor_conj = self.tensor.conj()
+
+        dim = self.tensor.dim()
+        parity = self.parity
+
+        total_parity = functools.reduce(
+            torch.logical_xor,
+            (
+                torch.logical_and(
+                    self._unsqueeze(parity[i], i, dim),
+                    self._unsqueeze(parity[j], j, dim),
+                )
+                for j in range(dim)
+                for i in range(0, j)
+            ),
+            torch.zeros([], dtype=torch.bool, device=self.tensor.device),
+        )
+
+        tensor_conj = torch.where(total_parity, -tensor_conj, tensor_conj)
+
+        return dataclasses.replace(
+            self,
+            _arrow=tuple(not arrow for arrow in self.arrow),
+            _tensor=tensor_conj,
+        )
+
+    def conj(self) -> GrassmannTensor:
+        return self.conjugate()
+
     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()})."
diff --git a/tests/conjugate_test.py b/tests/conjugate_test.py
new file mode 100644
index 0000000..c0263c7
--- /dev/null
+++ b/tests/conjugate_test.py
@@ -0,0 +1,106 @@
+import torch
+import pytest
+from typing import TypeAlias
+
+from grassmann_tensor import GrassmannTensor
+
+Arrow_Edges: TypeAlias = tuple[tuple[bool, ...], tuple[tuple[int, int], ...]]
+
+
+@pytest.fixture(
+    params=[
+        (
+            (True, False),
+            ((2, 2), (2, 2)),
+        ),
+        (
+            (True, False, False),
+            ((2, 2), (2, 2), (2, 2)),
+        ),
+    ]
+)
+def arrow_edges(request: pytest.FixtureRequest) -> Arrow_Edges:
+    return request.param
+
+
+@pytest.fixture(
+    params=[
+        (
+            (True, False),
+            ((4, 0), (4, 0)),
+        ),
+        (
+            (True, False, False),
+            ((4, 0), (4, 0), (4, 0)),
+        ),
+    ]
+)
+def arrow_edges_without_symmetry(request: pytest.FixtureRequest) -> Arrow_Edges:
+    return request.param
+
+
+def create_random_tensor(
+    arrow_edges: Arrow_Edges,
+    *,
+    dtype: torch.dtype,
+) -> GrassmannTensor:
+    arrow, edges = arrow_edges
+    shape = [even + odd for even, odd in edges]
+
+    if dtype == torch.float64:
+        tensor = torch.rand(*shape, dtype=dtype)
+    else:
+        tensor = torch.randn(*shape) + 1j * torch.randn(*shape).to(dtype)
+    return GrassmannTensor(arrow, edges, tensor)
+
+
+@pytest.fixture
+def random_real_tensor(arrow_edges: Arrow_Edges) -> GrassmannTensor:
+    return create_random_tensor(arrow_edges, dtype=torch.float64)
+
+
+@pytest.fixture
+def random_complex_tensor(arrow_edges: Arrow_Edges) -> GrassmannTensor:
+    return create_random_tensor(arrow_edges, dtype=torch.complex128)
+
+
+def test_conjugate_involution_with_complex_tensor(random_complex_tensor: GrassmannTensor) -> None:
+    contrast_a = random_complex_tensor
+    contrast_b = contrast_a.conj().conj()
+    assert contrast_a.arrow == contrast_b.arrow
+    assert torch.allclose(contrast_a.tensor, contrast_b.tensor)
+
+
+def test_conjugate_involution_with_real_tensor(random_real_tensor: GrassmannTensor) -> None:
+    contrast_a = random_real_tensor
+    contrast_b = contrast_a.conj().conj()
+    assert contrast_a.arrow == contrast_b.arrow
+    assert torch.allclose(contrast_a.tensor, contrast_b.tensor)
+
+
+def test_conjugate_reverse_order_of_contraction(
+    arrow_edges: Arrow_Edges,
+) -> None:
+    a = create_random_tensor(arrow_edges, dtype=torch.complex128).update_mask()
+    b = create_random_tensor(arrow_edges, dtype=torch.complex128).update_mask()
+
+    contrast_a = GrassmannTensor.contract(a, b, a.tensor.dim() - 1, 0)
+    contrast_a = contrast_a.conj()
+
+    a_conj = a.conj()
+    b_conj = b.conj()
+
+    contrast_b = GrassmannTensor.contract(a_conj, b_conj, a_conj.tensor.dim() - 1, 0)
+
+    assert contrast_a.arrow == contrast_b.arrow
+    assert torch.allclose(contrast_a.tensor, contrast_b.tensor)
+
+
+def test_conjugate_without_symmetry_equality(
+    arrow_edges_without_symmetry: Arrow_Edges,
+) -> None:
+    a = create_random_tensor(arrow_edges_without_symmetry, dtype=torch.float64)
+    b = create_random_tensor(arrow_edges_without_symmetry, dtype=torch.complex128)
+
+    assert torch.allclose(a.tensor, a.conj().tensor)
+    assert torch.allclose(b.tensor.conj(), b.conj().tensor)