



"""simple docstring"""

from dataclasses import dataclass
from typing import Tuple

import numpy as np
import torch




@dataclass
class SCREAMING_SNAKE_CASE__					:
						_lowerCAmelCase							=					4_2  # [batch_size x 3]
						_lowerCAmelCase							=					4_2  # [batch_size x 3]
						_lowerCAmelCase							=					4_2  # [batch_size x 3]
						_lowerCAmelCase							=					4_2  # [batch_size x 3]
						_lowerCAmelCase							=					4_2
						_lowerCAmelCase							=					4_2
						_lowerCAmelCase							=					4_2
						_lowerCAmelCase							=					4_2
						_lowerCAmelCase							=					4_2



						def     lowerCAmelCase__(self							):





													'''simple docstring'''

													assert self.x.shape[0] == self.y.shape[0] == self.z.shape[0] == self.origin.shape[0]
													assert self.x.shape[1] == self.y.shape[1] == self.z.shape[1] == self.origin.shape[1] == 3
													assert len(self.x.shape							) == len(self.y.shape							) == len(self.z.shape							) == len(self.origin.shape							) == 2



						def     lowerCAmelCase__(self							):





													'''simple docstring'''

													return torch.from_numpy(np.array([self.width, self.height]						,     dtype=np.floataa							)							)



						def     lowerCAmelCase__(self							):





													'''simple docstring'''

													return torch.from_numpy(np.array([self.x_fov, self.y_fov]						,     dtype=np.floataa							)							)



						def     lowerCAmelCase__(self							):





													'''simple docstring'''

													__a		:		Union[str, Any]									=       torch.arange(self.height * self.width							)
													__a		:		Tuple									=       torch.stack(
													    [
													        pixel_indices % self.width,
													        torch.div(_lowercase						,     self.width						,     rounding_mode="""trunc"""							),
													    ]						,     axis=1						,     )
													return coords



						@property
						def     lowerCAmelCase__(self							):





													'''simple docstring'''

													__a		:		Union[str, Any]									=       self.shape
													__a		:		int									=       int(np.prod(_lowercase							)							)

													__a		:		Union[str, Any]									=       self.get_image_coords()
													__a		:		List[Any]									=       torch.broadcast_to(coords.unsqueeze(0							)						,     [batch_size * inner_batch_size, *coords.shape]							)
													__a		:		List[str]									=       self.get_camera_rays(_lowercase							)

													__a		:		Union[str, Any]									=       rays.view(_lowercase						,     inner_batch_size * self.height * self.width						,     2						,     3							)

													return rays



						def     lowerCAmelCase__(self						,     _lowercase							):





													'''simple docstring'''

													__a		:		str									=       coords.shape
													assert n_coords == 2
													assert batch_size == self.origin.shape[0]

													__a		:		List[str]									=       coords.view(_lowercase						,     -1						,     2							)

													__a		:		List[Any]									=       self.resolution()
													__a		:		List[Any]									=       self.fov()

													__a		:		List[str]									=       (flat.float() / (res - 1)) * 2 - 1
													__a		:		int									=       fracs * torch.tan(fov / 2							)

													__a		:		Optional[int]									=       fracs.view(_lowercase						,     -1						,     2							)
													__a		:		Optional[int]									=       (
													    self.z.view(_lowercase						,     1						,     3							)
													    + self.x.view(_lowercase						,     1						,     3							) * fracs[:, :, :1]
													    + self.y.view(_lowercase						,     1						,     3							) * fracs[:, :, 1:]
													)
													__a		:		List[str]									=       directions / directions.norm(dim=-1						,     keepdim=_lowercase							)
													__a		:		int									=       torch.stack(
													    [
													        torch.broadcast_to(self.origin.view(_lowercase						,     1						,     3							)						,     [batch_size, directions.shape[1], 3]							),
													        directions,
													    ]						,     dim=2						,     )
													return rays.view(_lowercase						,     *_lowercase						,     2						,     3							)





						def     lowerCAmelCase__(self						,     _lowercase						,     _lowercase							):





													'''simple docstring'''

													assert width * self.height == height * self.width, "The aspect ratio should not change."
													return DifferentiableProjectiveCamera(
													    origin=self.origin						,     x=self.x						,     y=self.y						,     z=self.z						,     width=_lowercase						,     height=_lowercase						,     x_fov=self.x_fov						,     y_fov=self.y_fov						,     )







def       __magic_name__    (   _lowerCamelCase				: int					):
							__a		:		int									=       []
							__a		:		str									=       []
							__a		:		Optional[int]									=       []
							__a		:		Optional[Any]									=       []
							for theta in np.linspace(0  ,       2 * np.pi  ,       num=2_0					):
														__a		:		str									=       np.array([np.sin(_lowerCamelCase					), np.cos(_lowerCamelCase					), -0.5]					)
														z /= np.sqrt(np.sum(z**2					)					)
														__a		:		Any									=       -z * 4
														__a		:		Union[str, Any]									=       np.array([np.cos(_lowerCamelCase					), -np.sin(_lowerCamelCase					), 0.0]					)
														__a		:		Dict									=       np.cross(_lowerCamelCase  ,       _lowerCamelCase					)
														origins.append(_lowerCamelCase					)
														xs.append(_lowerCamelCase					)
														ys.append(_lowerCamelCase					)
														zs.append(_lowerCamelCase					)
							return DifferentiableProjectiveCamera(
							    origin=torch.from_numpy(np.stack(_lowerCamelCase  ,       axis=0					)					).float()  ,       x=torch.from_numpy(np.stack(_lowerCamelCase  ,       axis=0					)					).float()  ,       y=torch.from_numpy(np.stack(_lowerCamelCase  ,       axis=0					)					).float()  ,       z=torch.from_numpy(np.stack(_lowerCamelCase  ,       axis=0					)					).float()  ,       width=_lowerCamelCase  ,       height=_lowerCamelCase  ,       x_fov=0.7  ,       y_fov=0.7  ,       shape=(1, len(_lowerCamelCase					))  ,       )








"""simple docstring"""

def       __magic_name__    (   _lowerCamelCase				: int  ,       _lowerCamelCase				: float  ,       _lowerCamelCase				: float					):
							return round(float(moles / volume					) * nfactor					)





def       __magic_name__    (   _lowerCamelCase				: float  ,       _lowerCamelCase				: float  ,       _lowerCamelCase				: float					):
							return round(float((moles * 0.08_21 * temperature) / (volume)					)					)





def       __magic_name__    (   _lowerCamelCase				: float  ,       _lowerCamelCase				: float  ,       _lowerCamelCase				: float					):
							return round(float((moles * 0.08_21 * temperature) / (pressure)					)					)





def       __magic_name__    (   _lowerCamelCase				: float  ,       _lowerCamelCase				: float  ,       _lowerCamelCase				: float					):
							return round(float((pressure * volume) / (0.08_21 * moles)					)					)


if __name__ == "__main__":
	import doctest

	doctest.testmod()

