


"""simple docstring"""






from dataclasses import dataclass
from typing import Tuple

import numpy as np
import torch


@dataclass
class 			lowerCamelCase_		:





    """simple docstring"""







    _lowerCAmelCase      :      torch.Tensor  # [batch_size x 3]
    _lowerCAmelCase      :      torch.Tensor  # [batch_size x 3]
    _lowerCAmelCase      :      torch.Tensor  # [batch_size x 3]
    _lowerCAmelCase      :      torch.Tensor  # [batch_size x 3]
    _lowerCAmelCase      :      int
    _lowerCAmelCase      :      int
    _lowerCAmelCase      :      float
    _lowerCAmelCase      :      float
    _lowerCAmelCase      :      Tuple[int]



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



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



    def   lowerCAmelCase__		(						self     ):
        SCREAMING_SNAKE_CASE__     							=				torch.arange(self.height * self.width     )
        SCREAMING_SNAKE_CASE__     							=				torch.stack(
            [
                pixel_indices % self.width,
                torch.div(UpperCAmelCase__       ,		self.width       ,		rounding_mode="trunc"     ),
            ]       ,		axis=1       ,		)
        return coords



    @property
    def   lowerCAmelCase__		(						self     ):
        SCREAMING_SNAKE_CASE__							,      *SCREAMING_SNAKE_CASE__     							=				self.shape
        SCREAMING_SNAKE_CASE__     							=				int(np.prod(UpperCAmelCase__     )     )

        SCREAMING_SNAKE_CASE__     							=				self.get_image_coords()
        SCREAMING_SNAKE_CASE__     							=				torch.broadcast_to(coords.unsqueeze(0     )       ,		[batch_size * inner_batch_size, *coords.shape]     )
        SCREAMING_SNAKE_CASE__     							=				self.get_camera_rays(UpperCAmelCase__     )

        SCREAMING_SNAKE_CASE__     							=				rays.view(UpperCAmelCase__       ,		inner_batch_size * self.height * self.width       ,		2       ,		3     )

        return rays



    def   lowerCAmelCase__		(						self       ,		UpperCAmelCase__     ):
        SCREAMING_SNAKE_CASE__							,      *SCREAMING_SNAKE_CASE__							,      SCREAMING_SNAKE_CASE__     							=				coords.shape
        assert n_coords == 2
        assert batch_size == self.origin.shape[0]

        SCREAMING_SNAKE_CASE__     							=				coords.view(UpperCAmelCase__       ,		-1       ,		2     )

        SCREAMING_SNAKE_CASE__     							=				self.resolution()
        SCREAMING_SNAKE_CASE__     							=				self.fov()

        SCREAMING_SNAKE_CASE__     							=				(flat.float() / (res - 1)) * 2 - 1
        SCREAMING_SNAKE_CASE__     							=				fracs * torch.tan(fov / 2     )

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






    def   lowerCAmelCase__		(						self       ,		UpperCAmelCase__       ,		UpperCAmelCase__     ):
        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=UpperCAmelCase__       ,		height=UpperCAmelCase__       ,		x_fov=self.x_fov       ,		y_fov=self.y_fov       ,		)


def __lowercase     (      lowerCamelCase_  :      int  ):
    SCREAMING_SNAKE_CASE__     							=				[]
    SCREAMING_SNAKE_CASE__     							=				[]
    SCREAMING_SNAKE_CASE__     							=				[]
    SCREAMING_SNAKE_CASE__     							=				[]
    for theta in np.linspace(0						,					2 * np.pi						,					num=20  ):
        SCREAMING_SNAKE_CASE__     							=				np.array([np.sin(lowerCamelCase_  ), np.cos(lowerCamelCase_  ), -0.5]  )
        z /= np.sqrt(np.sum(z**2  )  )
        SCREAMING_SNAKE_CASE__     							=				-z * 4
        SCREAMING_SNAKE_CASE__     							=				np.array([np.cos(lowerCamelCase_  ), -np.sin(lowerCamelCase_  ), 0.0]  )
        SCREAMING_SNAKE_CASE__     							=				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 __lowercase     (      lowerCamelCase_  :      List[Any]  ):
				SCREAMING_SNAKE_CASE__     							=				[]
				SCREAMING_SNAKE_CASE__     							=				set({"(", "[", "{"}  )
				SCREAMING_SNAKE_CASE__     							=				set({")", "]", "}"}  )
				SCREAMING_SNAKE_CASE__     							=				{"{": "}", "[": "]", "(": ")"}

				for i in range(len(lowerCamelCase_  )  ):
								if s[i] in open_brackets:
												stack.append(s[i]  )

								elif s[i] in closed_brackets and (
								    len(lowerCamelCase_  ) == 0 or (len(lowerCamelCase_  ) > 0 and open_to_closed[stack.pop()] != s[i])
								):
												return False

				return len(lowerCamelCase_  ) == 0


def __lowercase     (      ):
				SCREAMING_SNAKE_CASE__     							=				input("Enter sequence of brackets: "  )
				if is_balanced(lowerCamelCase_  ):
								print(lowerCamelCase_						,					"is balanced"  )
				else:
								print(lowerCamelCase_						,					"is not balanced"  )


if __name__ == "__main__":
	main()
