


def __lowercase     (      lowerCamelCase_  :      Tuple						,					lowerCamelCase_  :      Dict  ):
				return (pointa[0] - pointa[0]) ** 2 + (pointa[1] - pointa[1]) ** 2


def __lowercase     (      lowerCamelCase_  :      Optional[int]						,					lowerCamelCase_  :      str=0  ):
				return sorted(lowerCamelCase_						,					key=lambda lowerCamelCase_  : x[column]  )


def __lowercase     (      lowerCamelCase_  :      Tuple						,					lowerCamelCase_  :      str						,					lowerCamelCase_  :      List[str]=float("inf"  )  ):

				for i in range(points_counts - 1  ):
								for j in range(i + 1						,					lowerCamelCase_  ):
												SCREAMING_SNAKE_CASE__     							=				euclidean_distance_sqr(points[i]						,					points[j]  )
												if current_dis < min_dis:
																SCREAMING_SNAKE_CASE__     							=				current_dis
				return min_dis


def __lowercase     (      lowerCamelCase_  :      int						,					lowerCamelCase_  :      List[Any]						,					lowerCamelCase_  :      Optional[Any]=float("inf"  )  ):

				for i in range(min(6						,					points_counts - 1  )						,					lowerCamelCase_  ):
								for j in range(max(0						,					i - 6  )						,					lowerCamelCase_  ):
												SCREAMING_SNAKE_CASE__     							=				euclidean_distance_sqr(points[i]						,					points[j]  )
												if current_dis < min_dis:
																SCREAMING_SNAKE_CASE__     							=				current_dis
				return min_dis


def __lowercase     (      lowerCamelCase_  :      Union[str, Any]						,					lowerCamelCase_  :      int						,					lowerCamelCase_  :      str  ):

				# base case
				if points_counts <= 3:
								return dis_between_closest_pair(lowerCamelCase_						,					lowerCamelCase_  )

				# recursion
				SCREAMING_SNAKE_CASE__     							=				points_counts // 2
				SCREAMING_SNAKE_CASE__     							=				closest_pair_of_points_sqr(
				    lowerCamelCase_						,					points_sorted_on_y[:mid]						,					lowerCamelCase_  )
				SCREAMING_SNAKE_CASE__     							=				closest_pair_of_points_sqr(
				    lowerCamelCase_						,					points_sorted_on_y[mid:]						,					points_counts - mid  )
				SCREAMING_SNAKE_CASE__     							=				min(lowerCamelCase_						,					lowerCamelCase_  )
				SCREAMING_SNAKE_CASE__     							=				[]
				for point in points_sorted_on_x:
								if abs(point[0] - points_sorted_on_x[mid][0]  ) < closest_pair_dis:
												cross_strip.append(lowerCamelCase_  )

				SCREAMING_SNAKE_CASE__     							=				dis_between_closest_in_strip(
				    lowerCamelCase_						,					len(lowerCamelCase_  )						,					lowerCamelCase_  )
				return min(lowerCamelCase_						,					lowerCamelCase_  )


def __lowercase     (      lowerCamelCase_  :      Optional[Any]						,					lowerCamelCase_  :      Tuple  ):
				SCREAMING_SNAKE_CASE__     							=				column_based_sort(lowerCamelCase_						,					column=0  )
				SCREAMING_SNAKE_CASE__     							=				column_based_sort(lowerCamelCase_						,					column=1  )
				return (
				    closest_pair_of_points_sqr(
				        lowerCamelCase_						,					lowerCamelCase_						,					lowerCamelCase_  )
				) ** 0.5


if __name__ == "__main__":
	_lowerCamelCase     =  [(2, 3), (12, 30), (40, 50), (5, 1), (12, 10), (3, 4)]
	print('Distance:', closest_pair_of_points(points, len(points)))




"""simple docstring"""






# DISCLAIMER: This file is strongly influenced by https://github.com/yang-song/score_sde_pytorch

import math
from typing import Union

import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import randn_tensor
from .scheduling_utils import SchedulerMixin


class 			lowerCamelCase_		(			lowercase       ,  lowercase   ):





				"""simple docstring"""







				_lowerCAmelCase      :      List[Any]      							=					1



				@register_to_config
				def __init__(						self       ,		UpperCAmelCase__=2000       ,		UpperCAmelCase__=0.1       ,		UpperCAmelCase__=20       ,		UpperCAmelCase__=1e-3     ):
								SCREAMING_SNAKE_CASE__     							=				None
								SCREAMING_SNAKE_CASE__     							=				None
								SCREAMING_SNAKE_CASE__     							=				None



				def   lowerCAmelCase__		(						self       ,		UpperCAmelCase__       ,		UpperCAmelCase__ = None     ):
								SCREAMING_SNAKE_CASE__     							=				torch.linspace(1       ,		self.config.sampling_eps       ,		UpperCAmelCase__       ,		device=UpperCAmelCase__     )



				def   lowerCAmelCase__		(						self       ,		UpperCAmelCase__       ,		UpperCAmelCase__       ,		UpperCAmelCase__       ,		UpperCAmelCase__=None     ):
								if self.timesteps is None:
												raise ValueError(
												    "`self.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"     )

								# TODO(Patrick) better comments + non-PyTorch
								# postprocess model score
								SCREAMING_SNAKE_CASE__     							=				(
								    -0.25 * t**2 * (self.config.beta_max - self.config.beta_min) - 0.5 * t * self.config.beta_min
								)
								SCREAMING_SNAKE_CASE__     							=				torch.sqrt(1.0 - torch.exp(2.0 * log_mean_coeff     )     )
								SCREAMING_SNAKE_CASE__     							=				std.flatten()
								while len(std.shape     ) < len(score.shape     ):
												SCREAMING_SNAKE_CASE__     							=				std.unsqueeze(-1     )
								SCREAMING_SNAKE_CASE__     							=				-score / std

								# compute
								SCREAMING_SNAKE_CASE__     							=				-1.0 / len(self.timesteps     )

								SCREAMING_SNAKE_CASE__     							=				self.config.beta_min + t * (self.config.beta_max - self.config.beta_min)
								SCREAMING_SNAKE_CASE__     							=				beta_t.flatten()
								while len(beta_t.shape     ) < len(x.shape     ):
												SCREAMING_SNAKE_CASE__     							=				beta_t.unsqueeze(-1     )
								SCREAMING_SNAKE_CASE__     							=				-0.5 * beta_t * x

								SCREAMING_SNAKE_CASE__     							=				torch.sqrt(UpperCAmelCase__     )
								SCREAMING_SNAKE_CASE__     							=				drift - diffusion**2 * score
								SCREAMING_SNAKE_CASE__     							=				x + drift * dt

								# add noise
								SCREAMING_SNAKE_CASE__     							=				randn_tensor(x.shape       ,		layout=x.layout       ,		generator=UpperCAmelCase__       ,		device=x.device       ,		dtype=x.dtype     )
								SCREAMING_SNAKE_CASE__     							=				x_mean + diffusion * math.sqrt(-dt     ) * noise

								return x, x_mean






				def __len__(						self     ):
								return self.config.num_train_timesteps
