



'''simple docstring'''




from dataclasses import dataclass
from typing import Tuple

import numpy as np
import torch







@dataclass
class 	_lowerCAmelCase							:
	__SCREAMING_SNAKE_CASE   :		torch.Tensor  # [batch_size x 3]
	__SCREAMING_SNAKE_CASE   :		torch.Tensor  # [batch_size x 3]
	__SCREAMING_SNAKE_CASE   :		torch.Tensor  # [batch_size x 3]
	__SCREAMING_SNAKE_CASE   :		torch.Tensor  # [batch_size x 3]
	__SCREAMING_SNAKE_CASE   :		int
	__SCREAMING_SNAKE_CASE   :		int
	__SCREAMING_SNAKE_CASE   :		float
	__SCREAMING_SNAKE_CASE   :		float
	__SCREAMING_SNAKE_CASE   :		Tuple[int]


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


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


	def     _a	(self							):
				A_	:						Tuple	=     torch.arange(self.height * self.width							)
				A_	:						int	=     torch.stack(
				    [
				        pixel_indices % self.width,
				        torch.div(lowercase       ,      self.width       ,      rounding_mode="""trunc"""							),
				    ]       ,      axis=1       ,      )
				return coords


	@property
	def     _a	(self							):
				A_,    *A_	:						List[str]	=     self.shape
				A_	:						Optional[Any]	=     int(np.prod(lowercase							)							)

				A_	:						Tuple	=     self.get_image_coords()
				A_	:						List[str]	=     torch.broadcast_to(coords.unsqueeze(0							)       ,      [batch_size * inner_batch_size, *coords.shape]							)
				A_	:						Tuple	=     self.get_camera_rays(lowercase							)

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

				return rays


	def     _a	(self       ,      lowercase							):
				A_,    *A_,    A_	:						Any	=     coords.shape
				assert n_coords == 2
				assert batch_size == self.origin.shape[0]

				A_	:						Dict	=     coords.view(lowercase       ,      -1       ,      2							)

				A_	:						Optional[Any]	=     self.resolution()
				A_	:						int	=     self.fov()

				A_	:						Optional[int]	=     (flat.float() / (res - 1)) * 2 - 1
				A_	:						Tuple	=     fracs * torch.tan(fov / 2							)

				A_	:						List[Any]	=     fracs.view(lowercase       ,      -1       ,      2							)
				A_	:						List[Any]	=     (
				    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_	:						List[Any]	=     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     _a	(self       ,      lowercase       ,      lowercase							):
				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 	a			( lowerCamelCase__    ):
			'''simple docstring'''





			A_	:						Union[str, Any]	=     []
			A_	:						Tuple	=     []
			A_	:						List[str]	=     []
			A_	:						Optional[int]	=     []
			for theta in np.linspace(0						,      2 * np.pi						,      num=20    ):
						A_	:						Optional[int]	=     np.array([np.sin(lowerCamelCase__    ), np.cos(lowerCamelCase__    ), -0.5]    )
						z /= np.sqrt(np.sum(z**2    )    )
						A_	:						int	=     -z * 4
						A_	:						Optional[Any]	=     np.array([np.cos(lowerCamelCase__    ), -np.sin(lowerCamelCase__    ), 0.0]    )
						A_	:						List[str]	=     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'''




import re



def 	a			( lowerCamelCase__    ):
			'''simple docstring'''





			return [char.split() for char in re.split(r"""[^ a-z A-Z 0-9 \s]"""						,      str_    )]



def 	a			( lowerCamelCase__    ):
			'''simple docstring'''





			A_	:						Optional[int]	=     split_input(str_    )
			return "".join(
			    ["""""".join([char.capitalize() for char in sub_str]    ) for sub_str in string_split]    )



def 	a			( lowerCamelCase__						,      lowerCamelCase__						,      lowerCamelCase__    ):
			'''simple docstring'''





			try:
						A_	:						List[Any]	=     split_input(lowerCamelCase__    )
						if upper:
									A_	:						Tuple	=     """""".join(
									    [
									        separator.join([char.upper() for char in sub_str]    )
									        for sub_str in string_split
									    ]    )
						else:
									A_	:						Optional[int]	=     """""".join(
									    [
									        separator.join([char.lower() for char in sub_str]    )
									        for sub_str in string_split
									    ]    )
						return res_str
			except IndexError:
						return "not valid string"



def 	a			( lowerCamelCase__    ):
			'''simple docstring'''





			return to_simple_case(lowerCamelCase__    )



def 	a			( lowerCamelCase__    ):
			'''simple docstring'''





			try:
						A_	:						Tuple	=     to_simple_case(lowerCamelCase__    )
						return res_str[0].lower() + res_str[1:]
			except IndexError:
						return "not valid string"



def 	a			( lowerCamelCase__						,      lowerCamelCase__    ):
			'''simple docstring'''





			return to_complex_case(lowerCamelCase__						,      lowerCamelCase__						,      """_"""    )



def 	a			( lowerCamelCase__						,      lowerCamelCase__    ):
			'''simple docstring'''





			return to_complex_case(lowerCamelCase__						,      lowerCamelCase__						,      """-"""    )


if __name__ == "__main__":
						__import__('''doctest''').testmod()