

"""simple docstring"""





from dataclasses import dataclass
from typing import Tuple

import numpy as np
import torch







@dataclass
class 				SCREAMING_SNAKE_CASE					:






					"""simple docstring"""



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







					def        __lowerCAmelCase (       self			:				Union[str, Any]		):
						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			:				int		):
						return torch.from_numpy(np.array([self.width, self.height]   ,dtype=np.floataa		)		)







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







					def        __lowerCAmelCase (       self			:				str		):
						lowerCAmelCase__	:						Any  				=	torch.arange(self.height * self.width		)
						lowerCAmelCase__	:						str  				=	torch.stack(
						    [
						        pixel_indices % self.width,
						        torch.div(lowercase_   ,self.width   ,rounding_mode='''trunc'''		),
						    ]   ,axis=1   ,)
						return coords







					@property
					def        __lowerCAmelCase (       self			:				int		):
						lowerCAmelCase__				,*lowerCAmelCase__	:						List[Any]  				=	self.shape
						lowerCAmelCase__	:						Optional[int]  				=	int(np.prod(lowercase_		)		)

						lowerCAmelCase__	:						Any  				=	self.get_image_coords()
						lowerCAmelCase__	:						Optional[int]  				=	torch.broadcast_to(coords.unsqueeze(0		)   ,[batch_size * inner_batch_size, *coords.shape]		)
						lowerCAmelCase__	:						str  				=	self.get_camera_rays(lowercase_		)

						lowerCAmelCase__	:						List[str]  				=	rays.view(lowercase_   ,inner_batch_size * self.height * self.width   ,2   ,3		)

						return rays







					def        __lowerCAmelCase (       self			:				List[str]   ,lowercase_			:				torch.Tensor		):
						lowerCAmelCase__				,*lowerCAmelCase__				,lowerCAmelCase__	:						List[Any]  				=	coords.shape
						assert n_coords == 2
						assert batch_size == self.origin.shape[0]

						lowerCAmelCase__	:						Tuple  				=	coords.view(lowercase_   ,-1   ,2		)

						lowerCAmelCase__	:						Union[str, Any]  				=	self.resolution()
						lowerCAmelCase__	:						Tuple  				=	self.fov()

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

						lowerCAmelCase__	:						List[str]  				=	fracs.view(lowercase_   ,-1   ,2		)
						lowerCAmelCase__	:						Optional[int]  				=	(
						    self.z.view(lowercase_   ,1   ,3		)
						    + self.x.view(lowercase_   ,1   ,3		) * fracs[:, :, :1]
						    + self.y.view(lowercase_   ,1   ,3		) * fracs[:, :, 1:]
						)
						lowerCAmelCase__	:						Optional[int]  				=	directions / directions.norm(dim=-1   ,keepdim=lowercase_		)
						lowerCAmelCase__	:						Tuple  				=	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			:				List[str]   ,lowercase_			:				int   ,lowercase_			:				int		):
						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   __SCREAMING_SNAKE_CASE  (      A_ ):
	lowerCAmelCase__	:						List[str]  				=	[]
	lowerCAmelCase__	:						Optional[Any]  				=	[]
	lowerCAmelCase__	:						Any  				=	[]
	lowerCAmelCase__	:						List[str]  				=	[]
	for theta in np.linspace(0						,     2 * np.pi						,     num=20 ):
		lowerCAmelCase__	:						Any  				=	np.array([np.sin(A_ ), np.cos(A_ ), -0.5] )
		z /= np.sqrt(np.sum(z**2 ) )
		lowerCAmelCase__	:						Any  				=	-z * 4
		lowerCAmelCase__	:						Optional[Any]  				=	np.array([np.cos(A_ ), -np.sin(A_ ), 0.0] )
		lowerCAmelCase__	:						Any  				=	np.cross(A_						,     A_ )
		origins.append(A_ )
		xs.append(A_ )
		ys.append(A_ )
		zs.append(A_ )
	return DifferentiableProjectiveCamera(
	    origin=torch.from_numpy(np.stack(A_						,     axis=0 ) ).float()						,     x=torch.from_numpy(np.stack(A_						,     axis=0 ) ).float()						,     y=torch.from_numpy(np.stack(A_						,     axis=0 ) ).float()						,     z=torch.from_numpy(np.stack(A_						,     axis=0 ) ).float()						,     width=A_						,     height=A_						,     x_fov=0.7						,     y_fov=0.7						,     shape=(1, len(A_ ))						,     )







"""simple docstring"""





import random

def   __SCREAMING_SNAKE_CASE  (      A_						,     A_ ):
	lowerCAmelCase__				,lowerCAmelCase__				,lowerCAmelCase__	:						Optional[int]  				=	[], [], []
	for element in data:
		if element < pivot:
			less.append(A_ )
		elif element > pivot:
			greater.append(A_ )
		else:
			equal.append(A_ )
	return less, equal, greater





def   __SCREAMING_SNAKE_CASE  (      A_						,     A_ ):
	# index = len(items) // 2 when trying to find the median
	#   (value of index when items is sorted)

	# invalid input
	if index >= len(A_ ) or index < 0:
		return None

	lowerCAmelCase__	:						str  				=	items[random.randint(0						,     len(A_ ) - 1 )]
	lowerCAmelCase__	:						Optional[Any]  				=	0
	lowerCAmelCase__				,lowerCAmelCase__				,lowerCAmelCase__	:						Any  				=	_partition(A_						,     A_ )
	lowerCAmelCase__	:						str  				=	len(A_ )
	lowerCAmelCase__	:						Optional[Any]  				=	len(A_ )

	# index is the pivot
	if m <= index < m + count:
		return pivot
	# must be in smaller
	elif m > index:
		return quick_select(A_						,     A_ )
	# must be in larger
	else:
		return quick_select(A_						,     index - (m + count) )




