
"""simple docstring"""







from dataclasses import dataclass
from typing import Tuple

import numpy as np
import torch






@dataclass
class 				__A    :






 """simple docstring"""




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


 def 				SCREAMING_SNAKE_CASE							(		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 				SCREAMING_SNAKE_CASE							(		self						) ->					Optional[int]:
     return torch.from_numpy(np.array([self.width, self.height]			,   dtype=np.floataa						)						)


 def 				SCREAMING_SNAKE_CASE							(		self						) ->					Union[str, Any]:
     return torch.from_numpy(np.array([self.x_fov, self.y_fov]			,   dtype=np.floataa						)						)


 def 				SCREAMING_SNAKE_CASE							(		self						) ->					torch.Tensor:
     a					=torch.arange(self.height * self.width						)
     a					=torch.stack(
         [
             pixel_indices % self.width,
             torch.div(__A			,   self.width			,   rounding_mode='''trunc'''						),
         ]			,   axis=1			,   )
     return coords


 @property
 def 				SCREAMING_SNAKE_CASE							(		self						) ->					Union[str, Any]:
     a		,				*a					=self.shape
     a					=int(np.prod(__A						)						)

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

     a					=rays.view(__A			,   inner_batch_size * self.height * self.width			,   2			,   3						)

     return rays


 def 				SCREAMING_SNAKE_CASE							(		self			,   __A						) ->					torch.Tensor:
     a		,				*a		,				a					=coords.shape
     assert n_coords == 2
     assert batch_size == self.origin.shape[0]

     a					=coords.view(__A			,   -1			,   2						)

     a					=self.resolution()
     a					=self.fov()

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

     a					=fracs.view(__A			,   -1			,   2						)
     a					=(
         self.z.view(__A			,   1			,   3						)
         + self.x.view(__A			,   1			,   3						) * fracs[:, :, :1]
         + self.y.view(__A			,   1			,   3						) * fracs[:, :, 1:]
     )
     a					=directions / directions.norm(dim=-1			,   keepdim=__A						)
     a					=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 				SCREAMING_SNAKE_CASE							(		self			,   __A			,   __A						) ->					"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=__A			,   height=__A			,   x_fov=self.x_fov			,   y_fov=self.y_fov			,   )

def _A						(						lowercase		):







    """simple docstring"""
    a					=[]
    a					=[]
    a					=[]
    a					=[]
    for theta in np.linspace(0	,   2 * np.pi	,   num=20		):
        a					=np.array([np.sin(lowercase		), np.cos(lowercase		), -0.5]		)
        z /= np.sqrt(np.sum(z**2		)		)
        a					=-z * 4
        a					=np.array([np.cos(lowercase		), -np.sin(lowercase		), 0.0]		)
        a					=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

from typing import Generic, TypeVar

lowerCamelCase_       :       List[Any]      						=  TypeVar("""T""")






class 				__A    (	Generic[T]      ):






 """simple docstring"""




 def __init__(		self			,   __A						) ->					None:
     a					=data
     a					=self
     a					=0






class 				__A    (	Generic[T]      ):






 """simple docstring"""




 def __init__(		self						) ->					None:
     # map from node name to the node object
     a					={}


 def 				SCREAMING_SNAKE_CASE							(		self			,   __A						) ->					None:
     # create a new set with x as its member
     a					=DisjointSetTreeNode(__A						)


 def 				SCREAMING_SNAKE_CASE							(		self			,   __A						) ->					DisjointSetTreeNode[T]:
     # find the set x belongs to (with path-compression)
     a					=self.map[data]
     if elem_ref != elem_ref.parent:
         a					=self.find_set(elem_ref.parent.data						)
     return elem_ref.parent


 def 				SCREAMING_SNAKE_CASE							(		self			,   __A			,   __A						) ->					None:
     # helper function for union operation
     if nodea.rank > nodea.rank:
         a					=nodea
     else:
         a					=nodea
         if nodea.rank == nodea.rank:
             nodea.rank += 1





 def 				SCREAMING_SNAKE_CASE							(		self			,   __A			,   __A						) ->					None:
     # merge 2 disjoint sets
     self.link(self.find_set(__A						)			,   self.find_set(__A						)						)






class 				__A    (	Generic[T]      ):






 """simple docstring"""




 def __init__(		self						) ->					None:
     # connections: map from the node to the neighbouring nodes (with weights)
     a					={}


 def 				SCREAMING_SNAKE_CASE							(		self			,   __A						) ->					None:
     # add a node ONLY if its not present in the graph
     if node not in self.connections:
         a					={}


 def 				SCREAMING_SNAKE_CASE							(		self			,   __A			,   __A			,   __A						) ->					None:
     # add an edge with the given weight
     self.add_node(__A						)
     self.add_node(__A						)
     a					=weight
     a					=weight





 def 				SCREAMING_SNAKE_CASE							(		self						) ->					GraphUndirectedWeighted[T]:
     a					=[]
     a					=set()
     for start in self.connections:
         for end in self.connections[start]:
             if (start, end) not in seen:
                 seen.add((end, start)						)
                 edges.append((start, end, self.connections[start][end])						)
     edges.sort(key=lambda __A						: x[2]						)

     # creating the disjoint set
     a					=DisjointSetTree[T]()
     for node in self.connections:
         disjoint_set.make_set(__A						)

     # MST generation
     a					=0
     a					=0
     a					=GraphUndirectedWeighted[T]()
     while num_edges < len(self.connections						) - 1:
         a		,				a		,				a					=edges[index]
         index += 1
         a					=disjoint_set.find_set(__A						)
         a					=disjoint_set.find_set(__A						)
         if parent_u != parent_v:
             num_edges += 1
             graph.add_edge(__A			,   __A			,   __A						)
             disjoint_set.union(__A			,   __A						)
     return graph