Add code/cube3d/training/check_rotation_flip.py

code/cube3d/training/check_rotation_flip.py

@@ -0,0 +1,49 @@
+import numpy as np
+import itertools
+
+def signed_perm_mats_det_plus_1():
+    """生成所有 3x3 的 ±1 置换矩阵，且 det=+1（24 个）"""
+    mats = []
+    for perm in itertools.permutations(range(3)):  # 6 种列置换
+        P = np.zeros((3,3), int)
+        for r, c in enumerate(perm):
+            P[r, c] = 1
+        for signs in itertools.product([1, -1], repeat=3):  # 行符号
+            R = P * np.array(signs)[:, None]               # 每行乘 ±1
+            if int(round(np.linalg.det(R))) == 1:
+                mats.append(R)
+    # 去重（以 tuple 做 key）
+    uniq = {}
+    for R in mats:
+        key = tuple(R.reshape(-1))
+        uniq[key] = R
+    return list(uniq.values())
+
+def check_transformation_invariance():
+    """严格验证变换后的矩阵仍在群中"""
+    R24 = signed_perm_mats_det_plus_1()  # 使用您的可靠生成器
+    R_z180 = np.array([[-1, 0, 0],
+                       [0, -1, 0],
+                       [0, 0, 1]], dtype=int)  # 确保整数类型
+    
+    failed_cases = []
+    for i, R in enumerate(R24):
+        transformed = R_z180 @ R
+        # 精确匹配（因所有矩阵均为整数）
+        found = any(np.array_equal(transformed, M) for M in R24)
+        if not found:
+            failed_cases.append((i, R, transformed))
+    
+    if not failed_cases:
+        print("✅ 所有24个矩阵经过变换后仍在集合中")
+        return True
+    else:
+        print(f"❌ 发现{len(failed_cases)}个不符合的案例：")
+        for idx, orig, trans in failed_cases:
+            print(f"\n案例 {idx}:")
+            print("原矩阵（行列式={}）:\n{}".format(int(np.linalg.det(orig)), orig))
+            print("变换后（行列式={}）:\n{}".format(int(np.linalg.det(transformed)), trans))
+        return False
+
+# 执行验证
+check_transformation_invariance()