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AlphaFold3  rigid_utils 模块的 rot_matmul 和 rot_vec_mul 函数实现了手动计算两个旋转矩阵的乘法 A×B 以及矩阵-向量乘法 R×t， 避免了直接用矩阵乘法的AMP（Automatic Mixed Precision）问题。

源代码：

def rot_matmul(a: torch.Tensor, b: torch.Tensor
) -> torch.Tensor:"""Performs matrix multiplication of two rotation matrix tensors. Writtenout by hand to avoid AMP downcasting.Args:a: [*, 3, 3] left multiplicandb: [*, 3, 3] right multiplicandReturns:The product ab"""def row_mul(i):return torch.stack([a[..., i, 0] * b[..., 0, 0]+ a[..., i, 1] * b[..., 1, 0]+ a[..., i, 2] * b[..., 2, 0],a[..., i, 0] * b[..., 0, 1]+ a[..., i, 1] * b[..., 1, 1]+ a[..., i, 2] * b[..., 2, 1],a[..., i, 0] * b[..., 0, 2]+ a[..., i, 1] * b[..., 1, 2]+ a[..., i, 2] * b[..., 2, 2],],dim=-1,)return torch.stack([row_mul(0), row_mul(1), row_mul(2),], dim=-2)def rot_vec_mul(r: torch.Tensor, t: torch.Tensor
) -> torch.Tensor:"""Applies a rotation to a vector. Written out by hand to avoid transferto avoid AMP downcasting.Args:r: [*, 3, 3] rotation matricest: [*, 3] coordinate tensorsReturns:[*, 3] rotated coordinates"""x, y, z = torch.unbind(t, dim=-1)return torch.stack([r[..., 0, 0] * x + r[..., 0, 1] * y + r[..., 0, 2] * z,r[..., 1, 0] * x + r[..., 1, 1] * y + r[..., 1, 2] * z,r[..., 2, 0] * x + r[..., 2, 1] * y + r[..., 2, 2] * z,],dim=-1,)

代码解读：

def rot_matmul(a: torch.Tensor, b: torch.Tensor
) -> torch.Tensor:

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