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This is like the standard copysign floating-point operation, but is not careful about negative 0 and NaN. Args: a: source tensor. b: tensor whose signs will be used, of the same shape as a. Returns: Tensor of the same shape as a with the signs of b. r)rpwhere)r b signs_differr r r _copysignsrcCs(t|}|dk}t||||<|S)z[ Returns torch.sqrt(torch.max(0, x)) but with a zero subgradient where x is 0. r)rp zeros_likerw)r]ret positive_maskr r r _sqrt_positive_parts rc Cs|ddks|ddkrtd|jd|d}|d}|d}d td |||}d td |||}d td |||}d td |||}t||d |d }t||d |d} t||d|d} t||| | fdS)z Convert rotations given as rotation matrices to quaternions. Args: matrix: Rotation matrices as tensor of shape (..., 3, 3). Returns: quaternions with real part first, as tensor of shape (..., 4). r[rz Invalid rotation matrix shape f.).rr).rr).rrrr).rr).rr).rr).rr).rr).rr)size ValueErrorr,rrrpstack) matrixm00m11m22o0r]rarbo1o2o3r r r matrix_to_quaternions rcCstj|dddfdddd}t||dddf}d|}d}||k}t|}t||||||<d ||||d ||<|dddf|S) a Convert rotations given as quaternions to axis/angle. Args: quaternions: quaternions with real part first, as tensor of shape (..., 4). Returns: Rotations given as a vector in axis angle form, as a tensor of shape (..., 3), where the magnitude is the angle turned anticlockwise in radians around the vector's direction. .rNrr[T)pdimrogư>r0)rpnormatan2abs empty_likere) quaternionsnorms half_anglesanglesru small_anglessin_half_angles_over_anglesr r r quaternion_to_axis_angle5s  rcCs tt|S)a{ Convert rotations given as rotation matrices to axis/angle. Args: matrix: Rotation matrices as tensor of shape (..., 3, 3). Returns: Rotations given as a vector in axis angle form, as a tensor of shape (..., 3), where the magnitude is the angle turned anticlockwise in radians around the vector's direction. )rr)rr r r matrix_to_axis_angleRs rd6cCs||dddf|dddf}}tj|dd}|||jddd|}tj|dd}tj||dd}tj|||fddS) a Converts 6D rotation representation by Zhou et al. [1] to rotation matrix using Gram--Schmidt orthogonalisation per Section B of [1]. Args: d6: 6D rotation representation, of size (*, 6) Returns: batch of rotation matrices of size (*, 3, 3) [1] Zhou, Y., Barnes, C., Lu, J., Yang, J., & Li, H. On the Continuity of Rotation Representations in Neural Networks. IEEE Conference on Computer Vision and Pattern Recognition, 2019. Retrieved from http://arxiv.org/abs/1812.07035 .Nrr[)rTrnr)F normalizerqrprr)ra1a2b1b2b3r r r rotation_6d_to_matrixbs "r)F)rXrYrZ)rt)rErJnumpyr&nvdiffrast.torchrprtorch.nn.functionalnn functionalrr<rWr_rcrjrlTensorrrrsrrzr{rrrrrrrrr r r r s0  W >.