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| # Copyright (c) 2020-2022 NVIDIA CORPORATION & AFFILIATES. All rights reserved. | |
| # | |
| # NVIDIA CORPORATION, its affiliates and licensors retain all intellectual | |
| # property and proprietary rights in and to this material, related | |
| # documentation and any modifications thereto. Any use, reproduction, | |
| # disclosure or distribution of this material and related documentation | |
| # without an express license agreement from NVIDIA CORPORATION or | |
| # its affiliates is strictly prohibited. | |
| import numpy as np | |
| import os | |
| import sys | |
| import torch | |
| import torch.utils.cpp_extension | |
| from .bsdf import * | |
| from .loss import * | |
| #---------------------------------------------------------------------------- | |
| # C++/Cuda plugin compiler/loader. | |
| _cached_plugin = None | |
| def _get_plugin(): | |
| # Return cached plugin if already loaded. | |
| global _cached_plugin | |
| if _cached_plugin is not None: | |
| return _cached_plugin | |
| # Make sure we can find the necessary compiler and libary binaries. | |
| if os.name == 'nt': | |
| def find_cl_path(): | |
| import glob | |
| for edition in ['Enterprise', 'Professional', 'BuildTools', 'Community']: | |
| paths = sorted(glob.glob(r"C:\Program Files (x86)\Microsoft Visual Studio\*\%s\VC\Tools\MSVC\*\bin\Hostx64\x64" % edition), reverse=True) | |
| if paths: | |
| return paths[0] | |
| # If cl.exe is not on path, try to find it. | |
| if os.system("where cl.exe >nul 2>nul") != 0: | |
| cl_path = find_cl_path() | |
| if cl_path is None: | |
| raise RuntimeError("Could not locate a supported Microsoft Visual C++ installation") | |
| os.environ['PATH'] += ';' + cl_path | |
| # Compiler options. | |
| opts = ['-DNVDR_TORCH'] | |
| # Linker options. | |
| if os.name == 'posix': | |
| ldflags = ['-lcuda', '-lnvrtc'] | |
| elif os.name == 'nt': | |
| ldflags = ['cuda.lib', 'advapi32.lib', 'nvrtc.lib'] | |
| # List of sources. | |
| source_files = [ | |
| 'c_src/mesh.cu', | |
| 'c_src/loss.cu', | |
| 'c_src/bsdf.cu', | |
| 'c_src/normal.cu', | |
| 'c_src/cubemap.cu', | |
| 'c_src/common.cpp', | |
| 'c_src/torch_bindings.cpp' | |
| ] | |
| # Some containers set this to contain old architectures that won't compile. We only need the one installed in the machine. | |
| os.environ['TORCH_CUDA_ARCH_LIST'] = '' | |
| # Try to detect if a stray lock file is left in cache directory and show a warning. This sometimes happens on Windows if the build is interrupted at just the right moment. | |
| try: | |
| lock_fn = os.path.join(torch.utils.cpp_extension._get_build_directory('renderutils_plugin', False), 'lock') | |
| if os.path.exists(lock_fn): | |
| print("Warning: Lock file exists in build directory: '%s'" % lock_fn) | |
| except: | |
| pass | |
| # Compile and load. | |
| source_paths = [os.path.join(os.path.dirname(__file__), fn) for fn in source_files] | |
| torch.utils.cpp_extension.load(name='renderutils_plugin', sources=source_paths, extra_cflags=opts, | |
| extra_cuda_cflags=opts, extra_ldflags=ldflags, with_cuda=True, verbose=True) | |
| # Import, cache, and return the compiled module. | |
| import renderutils_plugin | |
| _cached_plugin = renderutils_plugin | |
| return _cached_plugin | |
| #---------------------------------------------------------------------------- | |
| # Internal kernels, just used for testing functionality | |
| class _fresnel_shlick_func(torch.autograd.Function): | |
| def forward(ctx, f0, f90, cosTheta): | |
| out = _get_plugin().fresnel_shlick_fwd(f0, f90, cosTheta, False) | |
| ctx.save_for_backward(f0, f90, cosTheta) | |
| return out | |
| def backward(ctx, dout): | |
| f0, f90, cosTheta = ctx.saved_variables | |
| return _get_plugin().fresnel_shlick_bwd(f0, f90, cosTheta, dout) + (None,) | |
| def _fresnel_shlick(f0, f90, cosTheta, use_python=False): | |
| if use_python: | |
| out = bsdf_fresnel_shlick(f0, f90, cosTheta) | |
| else: | |
| out = _fresnel_shlick_func.apply(f0, f90, cosTheta) | |
| if torch.is_anomaly_enabled(): | |
| assert torch.all(torch.isfinite(out)), "Output of _fresnel_shlick contains inf or NaN" | |
| return out | |
| class _ndf_ggx_func(torch.autograd.Function): | |
| def forward(ctx, alphaSqr, cosTheta): | |
| out = _get_plugin().ndf_ggx_fwd(alphaSqr, cosTheta, False) | |
| ctx.save_for_backward(alphaSqr, cosTheta) | |
| return out | |
| def backward(ctx, dout): | |
| alphaSqr, cosTheta = ctx.saved_variables | |
| return _get_plugin().ndf_ggx_bwd(alphaSqr, cosTheta, dout) + (None,) | |
| def _ndf_ggx(alphaSqr, cosTheta, use_python=False): | |
| if use_python: | |
| out = bsdf_ndf_ggx(alphaSqr, cosTheta) | |
| else: | |
| out = _ndf_ggx_func.apply(alphaSqr, cosTheta) | |
| if torch.is_anomaly_enabled(): | |
| assert torch.all(torch.isfinite(out)), "Output of _ndf_ggx contains inf or NaN" | |
| return out | |
| class _lambda_ggx_func(torch.autograd.Function): | |
| def forward(ctx, alphaSqr, cosTheta): | |
| out = _get_plugin().lambda_ggx_fwd(alphaSqr, cosTheta, False) | |
| ctx.save_for_backward(alphaSqr, cosTheta) | |
| return out | |
| def backward(ctx, dout): | |
| alphaSqr, cosTheta = ctx.saved_variables | |
| return _get_plugin().lambda_ggx_bwd(alphaSqr, cosTheta, dout) + (None,) | |
| def _lambda_ggx(alphaSqr, cosTheta, use_python=False): | |
| if use_python: | |
| out = bsdf_lambda_ggx(alphaSqr, cosTheta) | |
| else: | |
| out = _lambda_ggx_func.apply(alphaSqr, cosTheta) | |
| if torch.is_anomaly_enabled(): | |
| assert torch.all(torch.isfinite(out)), "Output of _lambda_ggx contains inf or NaN" | |
| return out | |
| class _masking_smith_func(torch.autograd.Function): | |
| def forward(ctx, alphaSqr, cosThetaI, cosThetaO): | |
| ctx.save_for_backward(alphaSqr, cosThetaI, cosThetaO) | |
| out = _get_plugin().masking_smith_fwd(alphaSqr, cosThetaI, cosThetaO, False) | |
| return out | |
| def backward(ctx, dout): | |
| alphaSqr, cosThetaI, cosThetaO = ctx.saved_variables | |
| return _get_plugin().masking_smith_bwd(alphaSqr, cosThetaI, cosThetaO, dout) + (None,) | |
| def _masking_smith(alphaSqr, cosThetaI, cosThetaO, use_python=False): | |
| if use_python: | |
| out = bsdf_masking_smith_ggx_correlated(alphaSqr, cosThetaI, cosThetaO) | |
| else: | |
| out = _masking_smith_func.apply(alphaSqr, cosThetaI, cosThetaO) | |
| if torch.is_anomaly_enabled(): | |
| assert torch.all(torch.isfinite(out)), "Output of _masking_smith contains inf or NaN" | |
| return out | |
| #---------------------------------------------------------------------------- | |
| # Shading normal setup (bump mapping + bent normals) | |
| class _prepare_shading_normal_func(torch.autograd.Function): | |
| def forward(ctx, pos, view_pos, perturbed_nrm, smooth_nrm, smooth_tng, geom_nrm, two_sided_shading, opengl): | |
| ctx.two_sided_shading, ctx.opengl = two_sided_shading, opengl | |
| out = _get_plugin().prepare_shading_normal_fwd(pos, view_pos, perturbed_nrm, smooth_nrm, smooth_tng, geom_nrm, two_sided_shading, opengl, False) | |
| ctx.save_for_backward(pos, view_pos, perturbed_nrm, smooth_nrm, smooth_tng, geom_nrm) | |
| return out | |
| def backward(ctx, dout): | |
| pos, view_pos, perturbed_nrm, smooth_nrm, smooth_tng, geom_nrm = ctx.saved_variables | |
| return _get_plugin().prepare_shading_normal_bwd(pos, view_pos, perturbed_nrm, smooth_nrm, smooth_tng, geom_nrm, dout, ctx.two_sided_shading, ctx.opengl) + (None, None, None) | |
| def prepare_shading_normal(pos, view_pos, perturbed_nrm, smooth_nrm, smooth_tng, geom_nrm, two_sided_shading=True, opengl=True, use_python=False): | |
| '''Takes care of all corner cases and produces a final normal used for shading: | |
| - Constructs tangent space | |
| - Flips normal direction based on geometric normal for two sided Shading | |
| - Perturbs shading normal by normal map | |
| - Bends backfacing normals towards the camera to avoid shading artifacts | |
| All tensors assume a shape of [minibatch_size, height, width, 3] or broadcastable equivalent. | |
| Args: | |
| pos: World space g-buffer position. | |
| view_pos: Camera position in world space (typically using broadcasting). | |
| perturbed_nrm: Trangent-space normal perturbation from normal map lookup. | |
| smooth_nrm: Interpolated vertex normals. | |
| smooth_tng: Interpolated vertex tangents. | |
| geom_nrm: Geometric (face) normals. | |
| two_sided_shading: Use one/two sided shading | |
| opengl: Use OpenGL/DirectX normal map conventions | |
| use_python: Use PyTorch implementation (for validation) | |
| Returns: | |
| Final shading normal | |
| ''' | |
| if perturbed_nrm is None: | |
| perturbed_nrm = torch.tensor([0, 0, 1], dtype=torch.float32, device='cuda', requires_grad=False)[None, None, None, ...] | |
| if use_python: | |
| out = bsdf_prepare_shading_normal(pos, view_pos, perturbed_nrm, smooth_nrm, smooth_tng, geom_nrm, two_sided_shading, opengl) | |
| else: | |
| out = _prepare_shading_normal_func.apply(pos, view_pos, perturbed_nrm, smooth_nrm, smooth_tng, geom_nrm, two_sided_shading, opengl) | |
| if torch.is_anomaly_enabled(): | |
| assert torch.all(torch.isfinite(out)), "Output of prepare_shading_normal contains inf or NaN" | |
| return out | |
| #---------------------------------------------------------------------------- | |
| # BSDF functions | |
| class _lambert_func(torch.autograd.Function): | |
| def forward(ctx, nrm, wi): | |
| out = _get_plugin().lambert_fwd(nrm, wi, False) | |
| ctx.save_for_backward(nrm, wi) | |
| return out | |
| def backward(ctx, dout): | |
| nrm, wi = ctx.saved_variables | |
| return _get_plugin().lambert_bwd(nrm, wi, dout) + (None,) | |
| def lambert(nrm, wi, use_python=False): | |
| '''Lambertian bsdf. | |
| All tensors assume a shape of [minibatch_size, height, width, 3] or broadcastable equivalent. | |
| Args: | |
| nrm: World space shading normal. | |
| wi: World space light vector. | |
| use_python: Use PyTorch implementation (for validation) | |
| Returns: | |
| Shaded diffuse value with shape [minibatch_size, height, width, 1] | |
| ''' | |
| if use_python: | |
| out = bsdf_lambert(nrm, wi) | |
| else: | |
| out = _lambert_func.apply(nrm, wi) | |
| if torch.is_anomaly_enabled(): | |
| assert torch.all(torch.isfinite(out)), "Output of lambert contains inf or NaN" | |
| return out | |
| class _frostbite_diffuse_func(torch.autograd.Function): | |
| def forward(ctx, nrm, wi, wo, linearRoughness): | |
| out = _get_plugin().frostbite_fwd(nrm, wi, wo, linearRoughness, False) | |
| ctx.save_for_backward(nrm, wi, wo, linearRoughness) | |
| return out | |
| def backward(ctx, dout): | |
| nrm, wi, wo, linearRoughness = ctx.saved_variables | |
| return _get_plugin().frostbite_bwd(nrm, wi, wo, linearRoughness, dout) + (None,) | |
| def frostbite_diffuse(nrm, wi, wo, linearRoughness, use_python=False): | |
| '''Frostbite, normalized Disney Diffuse bsdf. | |
| All tensors assume a shape of [minibatch_size, height, width, 3] or broadcastable equivalent. | |
| Args: | |
| nrm: World space shading normal. | |
| wi: World space light vector. | |
| wo: World space camera vector. | |
| linearRoughness: Material roughness | |
| use_python: Use PyTorch implementation (for validation) | |
| Returns: | |
| Shaded diffuse value with shape [minibatch_size, height, width, 1] | |
| ''' | |
| if use_python: | |
| out = bsdf_frostbite(nrm, wi, wo, linearRoughness) | |
| else: | |
| out = _frostbite_diffuse_func.apply(nrm, wi, wo, linearRoughness) | |
| if torch.is_anomaly_enabled(): | |
| assert torch.all(torch.isfinite(out)), "Output of lambert contains inf or NaN" | |
| return out | |
| class _pbr_specular_func(torch.autograd.Function): | |
| def forward(ctx, col, nrm, wo, wi, alpha, min_roughness): | |
| ctx.save_for_backward(col, nrm, wo, wi, alpha) | |
| ctx.min_roughness = min_roughness | |
| out = _get_plugin().pbr_specular_fwd(col, nrm, wo, wi, alpha, min_roughness, False) | |
| return out | |
| def backward(ctx, dout): | |
| col, nrm, wo, wi, alpha = ctx.saved_variables | |
| return _get_plugin().pbr_specular_bwd(col, nrm, wo, wi, alpha, ctx.min_roughness, dout) + (None, None) | |
| def pbr_specular(col, nrm, wo, wi, alpha, min_roughness=0.08, use_python=False): | |
| '''Physically-based specular bsdf. | |
| All tensors assume a shape of [minibatch_size, height, width, 3] or broadcastable equivalent unless otherwise noted. | |
| Args: | |
| col: Specular lobe color | |
| nrm: World space shading normal. | |
| wo: World space camera vector. | |
| wi: World space light vector | |
| alpha: Specular roughness parameter with shape [minibatch_size, height, width, 1] | |
| min_roughness: Scalar roughness clamping threshold | |
| use_python: Use PyTorch implementation (for validation) | |
| Returns: | |
| Shaded specular color | |
| ''' | |
| if use_python: | |
| out = bsdf_pbr_specular(col, nrm, wo, wi, alpha, min_roughness=min_roughness) | |
| else: | |
| out = _pbr_specular_func.apply(col, nrm, wo, wi, alpha, min_roughness) | |
| if torch.is_anomaly_enabled(): | |
| assert torch.all(torch.isfinite(out)), "Output of pbr_specular contains inf or NaN" | |
| return out | |
| class _pbr_bsdf_func(torch.autograd.Function): | |
| def forward(ctx, kd, arm, pos, nrm, view_pos, light_pos, min_roughness, BSDF): | |
| ctx.save_for_backward(kd, arm, pos, nrm, view_pos, light_pos) | |
| ctx.min_roughness = min_roughness | |
| ctx.BSDF = BSDF | |
| out = _get_plugin().pbr_bsdf_fwd(kd, arm, pos, nrm, view_pos, light_pos, min_roughness, BSDF, False) | |
| return out | |
| def backward(ctx, dout): | |
| kd, arm, pos, nrm, view_pos, light_pos = ctx.saved_variables | |
| return _get_plugin().pbr_bsdf_bwd(kd, arm, pos, nrm, view_pos, light_pos, ctx.min_roughness, ctx.BSDF, dout) + (None, None, None) | |
| def pbr_bsdf(kd, arm, pos, nrm, view_pos, light_pos, min_roughness=0.08, bsdf="lambert", use_python=False): | |
| '''Physically-based bsdf, both diffuse & specular lobes | |
| All tensors assume a shape of [minibatch_size, height, width, 3] or broadcastable equivalent unless otherwise noted. | |
| Args: | |
| kd: Diffuse albedo. | |
| arm: Specular parameters (attenuation, linear roughness, metalness). | |
| pos: World space position. | |
| nrm: World space shading normal. | |
| view_pos: Camera position in world space, typically using broadcasting. | |
| light_pos: Light position in world space, typically using broadcasting. | |
| min_roughness: Scalar roughness clamping threshold | |
| bsdf: Controls diffuse BSDF, can be either 'lambert' or 'frostbite' | |
| use_python: Use PyTorch implementation (for validation) | |
| Returns: | |
| Shaded color. | |
| ''' | |
| BSDF = 0 | |
| if bsdf == 'frostbite': | |
| BSDF = 1 | |
| if use_python: | |
| out = bsdf_pbr(kd, arm, pos, nrm, view_pos, light_pos, min_roughness, BSDF) | |
| else: | |
| out = _pbr_bsdf_func.apply(kd, arm, pos, nrm, view_pos, light_pos, min_roughness, BSDF) | |
| if torch.is_anomaly_enabled(): | |
| assert torch.all(torch.isfinite(out)), "Output of pbr_bsdf contains inf or NaN" | |
| return out | |
| #---------------------------------------------------------------------------- | |
| # cubemap filter with filtering across edges | |
| class _diffuse_cubemap_func(torch.autograd.Function): | |
| def forward(ctx, cubemap): | |
| out = _get_plugin().diffuse_cubemap_fwd(cubemap) | |
| ctx.save_for_backward(cubemap) | |
| return out | |
| def backward(ctx, dout): | |
| cubemap, = ctx.saved_variables | |
| cubemap_grad = _get_plugin().diffuse_cubemap_bwd(cubemap, dout) | |
| return cubemap_grad, None | |
| def diffuse_cubemap(cubemap, use_python=False): | |
| if use_python: | |
| assert False | |
| else: | |
| out = _diffuse_cubemap_func.apply(cubemap) | |
| if torch.is_anomaly_enabled(): | |
| assert torch.all(torch.isfinite(out)), "Output of diffuse_cubemap contains inf or NaN" | |
| return out | |
| class _specular_cubemap(torch.autograd.Function): | |
| def forward(ctx, cubemap, roughness, costheta_cutoff, bounds): | |
| out = _get_plugin().specular_cubemap_fwd(cubemap, bounds, roughness, costheta_cutoff) | |
| ctx.save_for_backward(cubemap, bounds) | |
| ctx.roughness, ctx.theta_cutoff = roughness, costheta_cutoff | |
| return out | |
| def backward(ctx, dout): | |
| cubemap, bounds = ctx.saved_variables | |
| cubemap_grad = _get_plugin().specular_cubemap_bwd(cubemap, bounds, dout, ctx.roughness, ctx.theta_cutoff) | |
| return cubemap_grad, None, None, None | |
| # Compute the bounds of the GGX NDF lobe to retain "cutoff" percent of the energy | |
| def __ndfBounds(res, roughness, cutoff): | |
| def ndfGGX(alphaSqr, costheta): | |
| costheta = np.clip(costheta, 0.0, 1.0) | |
| d = (costheta * alphaSqr - costheta) * costheta + 1.0 | |
| return alphaSqr / (d * d * np.pi) | |
| # Sample out cutoff angle | |
| nSamples = 1000000 | |
| costheta = np.cos(np.linspace(0, np.pi/2.0, nSamples)) | |
| D = np.cumsum(ndfGGX(roughness**4, costheta)) | |
| idx = np.argmax(D >= D[..., -1] * cutoff) | |
| # Brute force compute lookup table with bounds | |
| bounds = _get_plugin().specular_bounds(res, costheta[idx]) | |
| return costheta[idx], bounds | |
| __ndfBoundsDict = {} | |
| def specular_cubemap(cubemap, roughness, cutoff=0.99, use_python=False): | |
| assert cubemap.shape[0] == 6 and cubemap.shape[1] == cubemap.shape[2], "Bad shape for cubemap tensor: %s" % str(cubemap.shape) | |
| if use_python: | |
| assert False | |
| else: | |
| key = (cubemap.shape[1], roughness, cutoff) | |
| if key not in __ndfBoundsDict: | |
| __ndfBoundsDict[key] = __ndfBounds(*key) | |
| out = _specular_cubemap.apply(cubemap, roughness, *__ndfBoundsDict[key]) | |
| if torch.is_anomaly_enabled(): | |
| assert torch.all(torch.isfinite(out)), "Output of specular_cubemap contains inf or NaN" | |
| return out[..., 0:3] / out[..., 3:] | |
| #---------------------------------------------------------------------------- | |
| # Fast image loss function | |
| class _image_loss_func(torch.autograd.Function): | |
| def forward(ctx, img, target, loss, tonemapper): | |
| ctx.loss, ctx.tonemapper = loss, tonemapper | |
| ctx.save_for_backward(img, target) | |
| out = _get_plugin().image_loss_fwd(img, target, loss, tonemapper, False) | |
| return out | |
| def backward(ctx, dout): | |
| img, target = ctx.saved_variables | |
| return _get_plugin().image_loss_bwd(img, target, dout, ctx.loss, ctx.tonemapper) + (None, None, None) | |
| def image_loss(img, target, loss='l1', tonemapper='none', use_python=False): | |
| '''Compute HDR image loss. Combines tonemapping and loss into a single kernel for better perf. | |
| All tensors assume a shape of [minibatch_size, height, width, 3] or broadcastable equivalent unless otherwise noted. | |
| Args: | |
| img: Input image. | |
| target: Target (reference) image. | |
| loss: Type of loss. Valid options are ['l1', 'mse', 'smape', 'relmse'] | |
| tonemapper: Tonemapping operations. Valid options are ['none', 'log_srgb'] | |
| use_python: Use PyTorch implementation (for validation) | |
| Returns: | |
| Image space loss (scalar value). | |
| ''' | |
| if use_python: | |
| out = image_loss_fn(img, target, loss, tonemapper) | |
| else: | |
| out = _image_loss_func.apply(img, target, loss, tonemapper) | |
| out = torch.sum(out) / (img.shape[0]*img.shape[1]*img.shape[2]) | |
| if torch.is_anomaly_enabled(): | |
| assert torch.all(torch.isfinite(out)), "Output of image_loss contains inf or NaN" | |
| return out | |
| #---------------------------------------------------------------------------- | |
| # Transform points function | |
| class _xfm_func(torch.autograd.Function): | |
| def forward(ctx, points, matrix, isPoints): | |
| ctx.save_for_backward(points, matrix) | |
| ctx.isPoints = isPoints | |
| return _get_plugin().xfm_fwd(points, matrix, isPoints, False) | |
| def backward(ctx, dout): | |
| points, matrix = ctx.saved_variables | |
| return (_get_plugin().xfm_bwd(points, matrix, dout, ctx.isPoints),) + (None, None, None) | |
| def xfm_points(points, matrix, use_python=False): | |
| '''Transform points. | |
| Args: | |
| points: Tensor containing 3D points with shape [minibatch_size, num_vertices, 3] or [1, num_vertices, 3] | |
| matrix: A 4x4 transform matrix with shape [minibatch_size, 4, 4] | |
| use_python: Use PyTorch's torch.matmul (for validation) | |
| Returns: | |
| Transformed points in homogeneous 4D with shape [minibatch_size, num_vertices, 4]. | |
| ''' | |
| if use_python: | |
| out = torch.matmul(torch.nn.functional.pad(points, pad=(0,1), mode='constant', value=1.0), torch.transpose(matrix, 1, 2)) | |
| else: | |
| out = _xfm_func.apply(points, matrix, True) | |
| if torch.is_anomaly_enabled(): | |
| assert torch.all(torch.isfinite(out)), "Output of xfm_points contains inf or NaN" | |
| return out | |
| def xfm_vectors(vectors, matrix, use_python=False): | |
| '''Transform vectors. | |
| Args: | |
| vectors: Tensor containing 3D vectors with shape [minibatch_size, num_vertices, 3] or [1, num_vertices, 3] | |
| matrix: A 4x4 transform matrix with shape [minibatch_size, 4, 4] | |
| use_python: Use PyTorch's torch.matmul (for validation) | |
| Returns: | |
| Transformed vectors in homogeneous 4D with shape [minibatch_size, num_vertices, 4]. | |
| ''' | |
| if use_python: | |
| out = torch.matmul(torch.nn.functional.pad(vectors, pad=(0,1), mode='constant', value=0.0), torch.transpose(matrix, 1, 2))[..., 0:3].contiguous() | |
| else: | |
| out = _xfm_func.apply(vectors, matrix, False) | |
| if torch.is_anomaly_enabled(): | |
| assert torch.all(torch.isfinite(out)), "Output of xfm_vectors contains inf or NaN" | |
| return out | |