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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)rgwhere)r)b signs_differs r2 _copysignrs)Eq1u%L ;;|R ++rScp[R"U5nUS:n[R"X5X'U$)zO Returns torch.sqrt(torch.max(0, x)) but with a zero subgradient where x is 0. r)rg zeros_likero)rPret positive_masks r2_sqrt_positive_partrs6   1 CEMA$45C JrScURS5S:wdURS5S:wa[SURS35eUSnUSnUSnS [S U-U-U-5-nS [S U-U- U- 5-nS [S U- U-U- 5-nS [S U- U- U-5-n[ XPS US - 5n[ X`S US- 5n [ XpSUS- 5n [ R "XHX4S5$)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). rNr z Invalid rotation matrix shape f.).rr).rr).rrrr).rr).rr).rr).rr).rr).rr)size ValueErrorr!rrrgstack) matrixm00m11m22o0rPrVrWo1o2o3s r2matrix_to_quaternionrs/{{2!v{{2!3;FLL>KLL  C  C  C "1s7S=3#67 7B !!c'C-#"566A !!c'C-#"566A !!c'C-#"566A 1Y'&*;; r0)rgnormatan2abs empty_liker[) quaternionsnorms half_anglesanglesrl small_anglessin_half_angles_over_angless r2quaternion_to_axis_angler5s JJ{37+qb$ GE++ebqb%9:K _F C::<#%L"'"2"26": +m,-}0EE . v#f&::b@@ - sABw "= ==rSc*[[U55$)aW 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)rs r2matrix_to_axis_anglerRs $$8$@ AArSd6cUSSS24USSS24p![R"USS9nX#U-RSSS9U-- n[R"USS9n[R"X4SS9n[R "X4U4SS9$) 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 .Nr rN)rTrer)F normalizerhrgrr)ra1a2b1b2b3s r2rotation_6d_to_matrixrbs RaR["S!"W+ RR B BwmmBm-2 2B RR B R $B ;;| ,,rS)F)g?g?gI@)g#B ;)r8r=numpyrnvdiffrast.torchrgrtorch.nn.functionalnn functionalrr3rLrRrXr`rbTensorrirkrrrrtrrrrrrrrrSr2rs   Tn;|8 7 7 7 .5<<.ELL.U\\.!u||! !!ell5<< ell5<<4&\,$-2>: B -ell-u||-rS