


'''simple docstring'''

def 							__magic_name__(  lowerCamelCase, lowerCamelCase):
						return (pointa[0] - pointa[0]) ** 2 + (pointa[1] - pointa[1]) ** 2

def 							__magic_name__(  lowerCamelCase, lowerCamelCase=0):
						return sorted(A__, key=lambda lowerCamelCase: x[column])

def 							__magic_name__(  lowerCamelCase, lowerCamelCase, lowerCamelCase=float('''inf''')):

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

def 							__magic_name__(  lowerCamelCase, lowerCamelCase, lowerCamelCase=float('''inf''')):

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

def 							__magic_name__(  lowerCamelCase, lowerCamelCase, lowerCamelCase):

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

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

						__lowerCAmelCase											= dis_between_closest_in_strip(
						    A__, len(A__), A__)
						return min(A__, A__)

def 							__magic_name__(  lowerCamelCase, lowerCamelCase):
						__lowerCAmelCase											= column_based_sort(A__, column=0)
						__lowerCAmelCase											= column_based_sort(A__, column=1)
						return (
						    closest_pair_of_points_sqr(
						        A__, A__, A__)
						) ** 0.5


if __name__ == "__main__":
	_UpperCAmelCase :       Dict										= [(2, 3), (1_2, 3_0), (4_0, 5_0), (5, 1), (1_2, 1_0), (3, 4)]
	print("""Distance:""", closest_pair_of_points(points, len(points)))









"""simple docstring"""
from dataclasses import dataclass
from typing import Optional, Tuple, Union

import flax
import jax.numpy as jnp
from jax import random

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput
from .scheduling_utils_flax import FlaxSchedulerMixin







@flax.struct.dataclass
class 			UpperCamelCase_       :
	# setable values
	__magic_name__	      =				None
	__magic_name__	      =				None
	__magic_name__	      =				None  # sigma(t_i)





	@classmethod
	def      _SCREAMING_SNAKE_CASE      (      cls					: List[str]						)						->			Optional[Any]:
				return cls()







@dataclass
class 			UpperCamelCase_       (__A     ):
	__magic_name__	      =				42
	__magic_name__	      =				42
	__magic_name__	      =				42







class 			UpperCamelCase_       (__A				,						__A     ):





	@property
	def      _SCREAMING_SNAKE_CASE      (      self					: Tuple						)						->			str:
				return True





	@register_to_config
	def __init__(      self					: List[str]	,	lowerCAmelCase_					: float = 0.0_2	,	lowerCAmelCase_					: float = 100	,	lowerCAmelCase_					: float = 1.0_0_7	,	lowerCAmelCase_					: float = 80	,	lowerCAmelCase_					: float = 0.0_5	,	lowerCAmelCase_					: float = 50	,	)						->			Union[str, Any]:
				pass





	def      _SCREAMING_SNAKE_CASE      (      self					: Union[str, Any]						)						->			Tuple:
				return KarrasVeSchedulerState.create()





	def      _SCREAMING_SNAKE_CASE      (      self					: Union[str, Any]	,	lowerCAmelCase_					: KarrasVeSchedulerState	,	lowerCAmelCase_					: int	,	lowerCAmelCase_					: Tuple = ()						)						->			KarrasVeSchedulerState:
				UpperCAmelCase_     : Dict			     =					jnp.arange(0	,	lowerCAmelCase_						)[::-1].copy()
				UpperCAmelCase_     : Dict			     =					[
				    (
				        self.config.sigma_max**2
				        * (self.config.sigma_min**2 / self.config.sigma_max**2) ** (i / (num_inference_steps - 1))
				    )
				    for i in timesteps
				]

				return state.replace(
				    num_inference_steps=lowerCAmelCase_	,	schedule=jnp.array(lowerCAmelCase_	,	dtype=jnp.floataa						)	,	timesteps=lowerCAmelCase_	,	)





	def      _SCREAMING_SNAKE_CASE      (      self					: List[str]	,	lowerCAmelCase_					: KarrasVeSchedulerState	,	lowerCAmelCase_					: jnp.ndarray	,	lowerCAmelCase_					: float	,	lowerCAmelCase_					: random.KeyArray	,	)						->			Tuple[jnp.ndarray, float]:
				if self.config.s_min <= sigma <= self.config.s_max:
							UpperCAmelCase_     : Any			     =					min(self.config.s_churn / state.num_inference_steps	,	2**0.5 - 1						)
				else:
							UpperCAmelCase_     : Optional[int]			     =					0

				# sample eps ~ N(0, S_noise^2 * I)
				UpperCAmelCase_     : List[Any]			     =					random.split(lowerCAmelCase_	,	num=1						)
				UpperCAmelCase_     : List[str]			     =					self.config.s_noise * random.normal(key=lowerCAmelCase_	,	shape=sample.shape						)
				UpperCAmelCase_     : Optional[Any]			     =					sigma + gamma * sigma
				UpperCAmelCase_     : Any			     =					sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps)

				return sample_hat, sigma_hat





	def      _SCREAMING_SNAKE_CASE      (      self					: Union[str, Any]	,	lowerCAmelCase_					: KarrasVeSchedulerState	,	lowerCAmelCase_					: jnp.ndarray	,	lowerCAmelCase_					: float	,	lowerCAmelCase_					: float	,	lowerCAmelCase_					: jnp.ndarray	,	lowerCAmelCase_					: bool = True	,	)						->			Union[FlaxKarrasVeOutput, Tuple]:
				UpperCAmelCase_     : Union[str, Any]			     =					sample_hat + sigma_hat * model_output
				UpperCAmelCase_     : List[Any]			     =					(sample_hat - pred_original_sample) / sigma_hat
				UpperCAmelCase_     : Union[str, Any]			     =					sample_hat + (sigma_prev - sigma_hat) * derivative

				if not return_dict:
							return (sample_prev, derivative, state)

				return FlaxKarrasVeOutput(prev_sample=lowerCAmelCase_	,	derivative=lowerCAmelCase_	,	state=lowerCAmelCase_						)





	def      _SCREAMING_SNAKE_CASE      (      self					: List[str]	,	lowerCAmelCase_					: KarrasVeSchedulerState	,	lowerCAmelCase_					: jnp.ndarray	,	lowerCAmelCase_					: float	,	lowerCAmelCase_					: float	,	lowerCAmelCase_					: jnp.ndarray	,	lowerCAmelCase_					: jnp.ndarray	,	lowerCAmelCase_					: jnp.ndarray	,	lowerCAmelCase_					: bool = True	,	)						->			Union[FlaxKarrasVeOutput, Tuple]:
				UpperCAmelCase_     : str			     =					sample_prev + sigma_prev * model_output
				UpperCAmelCase_     : Any			     =					(sample_prev - pred_original_sample) / sigma_prev
				UpperCAmelCase_     : int			     =					sample_hat + (sigma_prev - sigma_hat) * (0.5 * derivative + 0.5 * derivative_corr)

				if not return_dict:
							return (sample_prev, derivative, state)

				return FlaxKarrasVeOutput(prev_sample=lowerCAmelCase_	,	derivative=lowerCAmelCase_	,	state=lowerCAmelCase_						)





	def      _SCREAMING_SNAKE_CASE      (      self					: Union[str, Any]	,	lowerCAmelCase_					: KarrasVeSchedulerState	,	lowerCAmelCase_					: List[Any]	,	lowerCAmelCase_					: List[str]	,	lowerCAmelCase_					: Optional[Any]						)						->			Dict:
				raise NotImplementedError()



