






from dataclasses import dataclass
from typing import Tuple

import numpy as np
import torch
@dataclass
class        a       :



      """simple docstring"""


      a    :					torch.Tensor  # [batch_size x 3]
      a    :					torch.Tensor  # [batch_size x 3]
      a    :					torch.Tensor  # [batch_size x 3]
      a    :					torch.Tensor  # [batch_size x 3]
      a    :					int
      a    :					int
      a    :					float
      a    :					float
      a    :					Tuple[int]
      def       UpperCAmelCase ( self   :     List[Any]   )				-> int:
        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       UpperCAmelCase ( self   :     Union[str, Any]   )				-> List[Any]:
        return torch.from_numpy(np.array([self.width, self.height]						, dtype=np.floataa   )   )
      def       UpperCAmelCase ( self   :     Dict   )				-> Optional[int]:
        return torch.from_numpy(np.array([self.x_fov, self.y_fov]						, dtype=np.floataa   )   )
      def       UpperCAmelCase ( self   :     List[Any]   )				-> torch.Tensor:
        __UpperCAmelCase				:      Optional[Any]	 =    torch.arange(self.height * self.width   )
        __UpperCAmelCase				:      str	 =    torch.stack(
            [
                pixel_indices % self.width,
                torch.div(__lowercase						, self.width						, rounding_mode="""trunc"""   ),
            ]						, axis=1						, )
        return coords
      @property
      def       UpperCAmelCase ( self   :     Tuple   )				-> List[Any]:
        __UpperCAmelCase ,					*__UpperCAmelCase				:      str	 =    self.shape
        __UpperCAmelCase				:      List[str]	 =    int(np.prod(__lowercase   )   )

        __UpperCAmelCase				:      int	 =    self.get_image_coords()
        __UpperCAmelCase				:      Any	 =    torch.broadcast_to(coords.unsqueeze(0   )						, [batch_size * inner_batch_size, *coords.shape]   )
        __UpperCAmelCase				:      int	 =    self.get_camera_rays(__lowercase   )

        __UpperCAmelCase				:      Tuple	 =    rays.view(__lowercase						, inner_batch_size * self.height * self.width						, 2						, 3   )

        return rays
      def       UpperCAmelCase ( self   :     Optional[int]						, __lowercase   :     torch.Tensor   )				-> torch.Tensor:
        __UpperCAmelCase ,					*__UpperCAmelCase ,					__UpperCAmelCase				:      List[str]	 =    coords.shape
        assert n_coords == 2
        assert batch_size == self.origin.shape[0]

        __UpperCAmelCase				:      Tuple	 =    coords.view(__lowercase						, -1						, 2   )

        __UpperCAmelCase				:      Tuple	 =    self.resolution()
        __UpperCAmelCase				:      Any	 =    self.fov()

        __UpperCAmelCase				:      Tuple	 =    (flat.float() / (res - 1)) * 2 - 1
        __UpperCAmelCase				:      Union[str, Any]	 =    fracs * torch.tan(fov / 2   )

        __UpperCAmelCase				:      str	 =    fracs.view(__lowercase						, -1						, 2   )
        __UpperCAmelCase				:      Dict	 =    (
            self.z.view(__lowercase						, 1						, 3   )
            + self.x.view(__lowercase						, 1						, 3   ) * fracs[:, :, :1]
            + self.y.view(__lowercase						, 1						, 3   ) * fracs[:, :, 1:]
        )
        __UpperCAmelCase				:      Optional[int]	 =    directions / directions.norm(dim=-1						, keepdim=__lowercase   )
        __UpperCAmelCase				:      Optional[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       UpperCAmelCase ( self   :     Optional[int]						, __lowercase   :     int						, __lowercase   :     int   )				-> "DifferentiableProjectiveCamera":
        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 							lowerCamelCase__ (       __lowerCamelCase     :	int						):
  __UpperCAmelCase				:      Optional[int]	 =    []
  __UpperCAmelCase				:      List[Any]	 =    []
  __UpperCAmelCase				:      Dict	 =    []
  __UpperCAmelCase				:      Optional[Any]	 =    []
  for theta in np.linspace(0    ,						2 * np.pi    ,						num=20						):
    __UpperCAmelCase				:      Optional[Any]	 =    np.array([np.sin(__lowerCamelCase						), np.cos(__lowerCamelCase						), -0.5]						)
    z /= np.sqrt(np.sum(z**2						)						)
    __UpperCAmelCase				:      Dict	 =    -z * 4
    __UpperCAmelCase				:      Dict	 =    np.array([np.cos(__lowerCamelCase						), -np.sin(__lowerCamelCase						), 0.0]						)
    __UpperCAmelCase				:      Union[str, Any]	 =    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"""






from copy import deepcopy



class     UpperCAmelCase    :



   def __init__(       self    :	Optional[Any]							,       __lowerCamelCase    :	list[int] | None = None							,       __lowerCamelCase    :	int | None = None				):



     """simple docstring"""

     if arr is None and size is not None:
       _snake_case   	=      size
       _snake_case   	=      [0] * size
     elif arr is not None:
       self.init(__lowerCamelCase				)
     else:
       raise ValueError('''Either arr or size must be specified'''				)



   def    __UpperCAmelCase    (       self    :	Any							,       __lowerCamelCase    :	list[int]				):



     """simple docstring"""
     _snake_case   	=      len(__lowerCamelCase				)
     _snake_case   	=      deepcopy(__lowerCamelCase				)
     for i in range(1							,       self.size				):
       _snake_case   	=      self.next_(__lowerCamelCase				)
       if j < self.size:
         self.tree[j] += self.tree[i]



   def    __UpperCAmelCase    (       self    :	Union[str, Any]				):



     """simple docstring"""
     _snake_case   	=      self.tree[:]
     for i in range(self.size - 1							,       0							,       -1				):
       _snake_case   	=      self.next_(__lowerCamelCase				)
       if j < self.size:
         arr[j] -= arr[i]
     return arr



   @staticmethod
   def    __UpperCAmelCase    (       __lowerCamelCase    :	int				):



     """simple docstring"""
     return index + (index & (-index))



   @staticmethod
   def    __UpperCAmelCase    (       __lowerCamelCase    :	int				):



     """simple docstring"""
     return index - (index & (-index))



   def    __UpperCAmelCase    (       self    :	Dict							,       __lowerCamelCase    :	int							,       __lowerCamelCase    :	int				):



     """simple docstring"""
     if index == 0:
       self.tree[0] += value
       return
     while index < self.size:
       self.tree[index] += value
       _snake_case   	=      self.next_(__lowerCamelCase				)



   def    __UpperCAmelCase    (       self    :	List[str]							,       __lowerCamelCase    :	int							,       __lowerCamelCase    :	int				):



     """simple docstring"""
     self.add(__lowerCamelCase							,       value - self.get(__lowerCamelCase				)				)



   def    __UpperCAmelCase    (       self    :	Optional[Any]							,       __lowerCamelCase    :	int				):



     """simple docstring"""
     if right == 0:
       return 0
     _snake_case   	=      self.tree[0]
     right -= 1  # make right inclusive
     while right > 0:
       result += self.tree[right]
       _snake_case   	=      self.prev(__lowerCamelCase				)
     return result



   def    __UpperCAmelCase    (       self    :	str							,       __lowerCamelCase    :	int							,       __lowerCamelCase    :	int				):



     """simple docstring"""
     return self.prefix(__lowerCamelCase				) - self.prefix(__lowerCamelCase				)



   def    __UpperCAmelCase    (       self    :	List[str]							,       __lowerCamelCase    :	int				):



     """simple docstring"""
     return self.query(__lowerCamelCase							,       index + 1				)





   def    __UpperCAmelCase    (       self    :	Optional[int]							,       __lowerCamelCase    :	int				):



     """simple docstring"""
     value -= self.tree[0]
     if value < 0:
       return -1

     _snake_case   	=      1  # Largest power of 2 <= size
     while j * 2 < self.size:
       j *= 2

     _snake_case   	=      0

     while j > 0:
       if i + j < self.size and self.tree[i + j] <= value:
         value -= self.tree[i + j]
         i += j
       j //= 2
     return i


if __name__ == "__main__":
     import doctest

     doctest.testmod()





