




from dataclasses import dataclass
from typing import Tuple

import numpy as np
import torch







@dataclass
class     A:



 '''simple docstring'''


 UpperCamelCase		  =		42  # [batch_size x 3]
 UpperCamelCase		  =		42  # [batch_size x 3]
 UpperCamelCase		  =		42  # [batch_size x 3]
 UpperCamelCase		  =		42  # [batch_size x 3]
 UpperCamelCase		  =		42
 UpperCamelCase		  =		42
 UpperCamelCase		  =		42
 UpperCamelCase		  =		42
 UpperCamelCase		  =		42

 def 							a__					(							self   :    Optional[int]    )  ->      List[Any]:

       """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 							a__					(							self   :    Union[str, Any]    )  ->      List[Any]:

       """simple docstring"""






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

 def 							a__					(							self   :    Dict    )  ->      Union[str, Any]:

       """simple docstring"""






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

 def 							a__					(							self   :    List[Any]    )  ->      torch.Tensor:

       """simple docstring"""






       lowerCamelCase_							=       torch.arange(self.height * self.width    )
       lowerCamelCase_							=       torch.stack(
           [
               pixel_indices % self.width,
               torch.div(A_		,				self.width		,				rounding_mode='trunc'    ),
           ]		,				axis=1		,				)
       return coords

 @property
 def 							a__					(							self   :    List[Any]    )  ->      Dict:

       """simple docstring"""






       lowerCamelCase_	,							*lowerCamelCase_							=       self.shape
       lowerCamelCase_							=       int(np.prod(A_    )    )

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

       lowerCamelCase_							=       rays.view(A_		,				inner_batch_size * self.height * self.width		,				2		,				3    )

       return rays

 def 							a__					(							self   :    int		,				A_   :    torch.Tensor    )  ->      torch.Tensor:

       """simple docstring"""






       lowerCamelCase_	,							*lowerCamelCase_	,							lowerCamelCase_							=       coords.shape
       assert n_coords == 2
       assert batch_size == self.origin.shape[0]

       lowerCamelCase_							=       coords.view(A_		,				-1		,				2    )

       lowerCamelCase_							=       self.resolution()
       lowerCamelCase_							=       self.fov()

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

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





 def 							a__					(							self   :    Any		,				A_   :    int		,				A_   :    int    )  ->      "DifferentiableProjectiveCamera":

       """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=A_		,				height=A_		,				x_fov=self.x_fov		,				y_fov=self.y_fov		,				)

def      _SCREAMING_SNAKE_CASE     (				lowercase      :			int	):


      '''simple docstring'''



      lowerCamelCase_							=       []
      lowerCamelCase_							=       []
      lowerCamelCase_							=       []
      lowerCamelCase_							=       []
      for theta in np.linspace(0      ,				2 * np.pi      ,				num=20	):
            lowerCamelCase_							=       np.array([np.sin(lowercase	), np.cos(lowercase	), -0.5]	)
            z /= np.sqrt(np.sum(z**2	)	)
            lowerCamelCase_							=       -z * 4
            lowerCamelCase_							=       np.array([np.cos(lowercase	), -np.sin(lowercase	), 0.0]	)
            lowerCamelCase_							=       np.cross(lowercase      ,				lowercase	)
            origins.append(lowercase	)
            xs.append(lowercase	)
            ys.append(lowercase	)
            zs.append(lowercase	)
      return DifferentiableProjectiveCamera(
          origin=torch.from_numpy(np.stack(lowercase      ,				axis=0	)	).float()      ,				x=torch.from_numpy(np.stack(lowercase      ,				axis=0	)	).float()      ,				y=torch.from_numpy(np.stack(lowercase      ,				axis=0	)	).float()      ,				z=torch.from_numpy(np.stack(lowercase      ,				axis=0	)	).float()      ,				width=lowercase      ,				height=lowercase      ,				x_fov=0.7      ,				y_fov=0.7      ,				shape=(1, len(lowercase	))      ,				)







"""simple docstring"""




from __future__ import annotations





def       a_ (	lowercase__ :list[float]     ):
			if len(lowercase__     ) < 2:
						raise ValueError("""Monogons and Digons are not polygons in the Euclidean space"""     )
			if any(i <= 0 for i in nums     ):
						raise ValueError("""All values must be greater than 0"""     )
			__lowerCamelCase          =      nums.copy()
			copy_nums.sort()
			return copy_nums[-1] < sum(copy_nums[:-1]     )


if __name__ == "__main__":
					import doctest

					doctest.testmod()




