from nanotorch.tensor import Tensor # Test 1: Simple multiplication (no broadcasting) print("Test 1 - No broadcasting:") a = Tensor([2.0, 3.0, 4.0]) b = Tensor([5.0, 6.0, 7.0]) c = a * b # [10, 18, 28] c.backward() print(f"c.data: {c.data}") print(f"a.grad: {a.grad}") # Should be [5, 6, 7] (b's values) print(f"b.grad: {b.grad}") # Should be [2, 3, 4] (a's values) # Test 2: Broadcasting case print("\nTest 2 - Broadcasting:") a = Tensor([[1.0, 2.0, 3.0]]) # shape (1, 3) b = Tensor([[2.0], [3.0]]) # shape (2, 1) c = a * b # shape (2, 3) c.backward() print(f"c.data:\n{c.data}") print(f"a.grad shape: {a.grad.shape}, values: {a.grad}") # Should be (1,3) with [[5, 5, 5]] print(f"b.grad shape: {b.grad.shape}, values: {b.grad}") # Should be (2,1) with [[6], [6]] # Test 3: Chain rule test (addition + multiplication) print("\nTest 3 - Chain rule:") x = Tensor([2.0, 3.0]) y = Tensor([4.0, 5.0]) z = x * y # [8, 15] w = z + z # [16, 30] w.backward() print(f"w.data: {w.data}") print(f"x.grad: {x.grad}") # Should be [8, 10] (2 * y, because w = 2*x*y) print(f"y.grad: {y.grad}") # Should be [4, 6] (2 * x)