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Running on Zero
Running on Zero
| # Modified for SplatAnything: inference-only release. | |
| import torch | |
| import numpy as np | |
| import torch.nn.functional as F | |
| def quat_to_rotmat(quaternions: torch.Tensor) -> torch.Tensor: | |
| """ | |
| Quaternion Order: XYZW or say ijkr, scalar-last | |
| Convert rotations given as quaternions to rotation matrices. | |
| Args: | |
| quaternions: quaternions with real part last, | |
| as tensor of shape (..., 4). | |
| Returns: | |
| Rotation matrices as tensor of shape (..., 3, 3). | |
| """ | |
| (i, j, k, r) = 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)) | |
| def rotmat_to_quat(matrix: torch.Tensor) -> torch.Tensor: | |
| """ | |
| Convert rotations given as rotation matrices to quaternions. | |
| Args: | |
| matrix: Rotation matrices as tensor of shape (..., 3, 3). | |
| Returns: | |
| quaternions with real part last, as tensor of shape (..., 4). | |
| Quaternion Order: XYZW or say ijkr, scalar-last | |
| """ | |
| if matrix.size(-1) != 3 or matrix.size(-2) != 3: | |
| raise ValueError(f'Invalid rotation matrix shape {matrix.shape}.') | |
| batch_dim = matrix.shape[:-2] | |
| (m00, m01, m02, m10, m11, m12, m20, m21, m22) = torch.unbind(matrix.reshape(batch_dim + (9,)), dim=-1) | |
| q_abs = _sqrt_positive_part(torch.stack([1.0 + m00 + m11 + m22, 1.0 + m00 - m11 - m22, 1.0 - m00 + m11 - m22, 1.0 - m00 - m11 + m22], dim=-1)) | |
| quat_by_rijk = torch.stack([torch.stack([q_abs[..., 0] ** 2, m21 - m12, m02 - m20, m10 - m01], dim=-1), torch.stack([m21 - m12, q_abs[..., 1] ** 2, m10 + m01, m02 + m20], dim=-1), torch.stack([m02 - m20, m10 + m01, q_abs[..., 2] ** 2, m12 + m21], dim=-1), torch.stack([m10 - m01, m20 + m02, m21 + m12, q_abs[..., 3] ** 2], dim=-1)], dim=-2) | |
| flr = torch.tensor(0.1).to(dtype=q_abs.dtype, device=q_abs.device) | |
| quat_candidates = quat_by_rijk / (2.0 * q_abs[..., None].max(flr)) | |
| out = quat_candidates[F.one_hot(q_abs.argmax(dim=-1), num_classes=4) > 0.5, :].reshape(batch_dim + (4,)) | |
| out = out[..., [1, 2, 3, 0]] | |
| out = standardize_quaternion(out) | |
| return out | |
| def _sqrt_positive_part(x: torch.Tensor) -> torch.Tensor: | |
| """ | |
| Returns torch.sqrt(torch.max(0, x)) | |
| but with a zero subgradient where x is 0. | |
| """ | |
| ret = torch.zeros_like(x) | |
| positive_mask = x > 0 | |
| if torch.is_grad_enabled(): | |
| ret[positive_mask] = torch.sqrt(x[positive_mask]) | |
| else: | |
| ret = torch.where(positive_mask, torch.sqrt(x), ret) | |
| return ret | |
| def standardize_quaternion(quaternions: torch.Tensor) -> torch.Tensor: | |
| """ | |
| Convert a unit quaternion to a standard form: one in which the real | |
| part is non negative. | |
| Args: | |
| quaternions: Quaternions with real part last, | |
| as tensor of shape (..., 4). | |
| Returns: | |
| Standardized quaternions as tensor of shape (..., 4). | |
| """ | |
| return torch.where(quaternions[..., 3:4] < 0, -quaternions, quaternions) | |