import torch


def quaternion_to_matrix(quaternions: torch.Tensor) -> torch.Tensor:
    """
    Convert rotations given as quaternions to rotation matrices.
    Args:
        quaternions: quaternions with real part first,
            as tensor of shape (..., 4).
    Returns:
        Rotation matrices as tensor of shape (..., 3, 3).
    """
    r, i, j, k = torch.unbind(quaternions, -1)
    two_s = 2.0 / (quaternions * quaternions).sum(-1)

    o = torch.stack(
        (
            1 - two_s * (j * j + k * k),
            two_s * (i * j - k * r),
            two_s * (i * k + j * r),
            two_s * (i * j + k * r),
            1 - two_s * (i * i + k * k),
            two_s * (j * k - i * r),
            two_s * (i * k - j * r),
            two_s * (j * k + i * r),
            1 - two_s * (i * i + j * j),
        ),
        -1,
    )

    return o.reshape(quaternions.shape[:-1] + (3, 3))