



from __future__ import annotations

from collections.abc import Iterable


class 						lowerCamelCase__			:


						def __init__(			self    :	Any   ,							_a    :	Optional[int]   ,							_a    :	str      ):
													a__				,      a__:							Any									=float(snake_case__      ), float(snake_case__      )


						def __eq__(			self    :	List[Any]   ,							_a    :	Any      ):
													return self.x == other.x and self.y == other.y


						def __ne__(			self    :	int   ,							_a    :	Tuple      ):
													return not self == other


						def __gt__(			self    :	Optional[Any]   ,							_a    :	List[str]      ):





													if self.x > other.x:
																				return True
													elif self.x == other.x:
																				return self.y > other.y
													return False


						def __lt__(			self    :	Dict   ,							_a    :	int      ):
													return not self > other


						def __ge__(			self    :	int   ,							_a    :	Optional[Any]      ):





													if self.x > other.x:
																				return True
													elif self.x == other.x:
																				return self.y >= other.y
													return False


						def __le__(			self    :	List[str]   ,							_a    :	Union[str, Any]      ):





													if self.x < other.x:
																				return True
													elif self.x == other.x:
																				return self.y <= other.y
													return False


						def __repr__(			self    :	Union[str, Any]      ):
													return F"({self.x}, {self.y})"







						def __hash__(			self    :	Any      ):
													return hash(self.x      )





def     __lowerCamelCase							(   __magic_name__						:	Optional[int]  ,			):
							a__:							Optional[Any]									=[]
							if list_of_tuples:
														for p in list_of_tuples:
																					if isinstance(a_  ,			a_    ):
																												points.append(a_    )
																					else:
																												try:
																																			points.append(Point(p[0]  ,			p[1]    )    )
																												except (IndexError, TypeError):
																																			print(
																																			    F"Ignoring deformed point {p}. All points"
																																			    " must have at least 2 coordinates."    )
							return points





def     __lowerCamelCase							(   __magic_name__						:	List[str]    ):

							if not hasattr(a_  ,			"__iter__"    ):
														a__:							Tuple									=F"Expecting an iterable object but got an non-iterable type {points}"
														raise ValueError(a_    )

							if not points:
														a__:							Any									=F"Expecting a list of points but got {points}"
														raise ValueError(a_    )

							return _construct_points(a_    )





def     __lowerCamelCase							(   __magic_name__						:	Tuple  ,			__magic_name__						:	Dict  ,			__magic_name__						:	List[Any]    ):
							a__:							List[str]									=(a.x * b.y + b.x * c.y + c.x * a.y) - (a.y * b.x + b.y * c.x + c.y * a.x)
							return det





def     __lowerCamelCase							(   __magic_name__						:	Tuple    ):
							a__:							List[str]									=sorted(_validate_input(a_    )    )
							a__:							Optional[int]									=len(a_    )
							a__:							List[Any]									=set()

							for i in range(n - 1    ):
														for j in range(i + 1  ,			a_    ):
																					a__:							Any									=False
																					a__:							int									=True
																					for k in range(a_    ):
																												if k != i and k != j:
																																			a__:							List[Any]									=_det(points[i]  ,			points[j]  ,			points[k]    )

																																			if det_k > 0:
																																										a__:							Optional[int]									=True
																																			elif det_k < 0:
																																										a__:							Tuple									=True
																																			else:
																																										# point[i], point[j], point[k] all lie on a straight line
																																										# if point[k] is to the left of point[i] or it's to the
																																										# right of point[j], then point[i], point[j] cannot be
																																										# part of the convex hull of A
																																										if points[k] < points[i] or points[k] > points[j]:
																																																	a__:							Any									=False
																																																	break

																												if points_left_of_ij and points_right_of_ij:
																																			a__:							str									=False
																																			break

																					if ij_part_of_convex_hull:
																												convex_set.update([points[i], points[j]]    )

							return sorted(a_    )





def     __lowerCamelCase							(   __magic_name__						:	Any    ):
							a__:							Tuple									=sorted(_validate_input(a_    )    )
							a__:							str									=len(a_    )

							# divide all the points into an upper hull and a lower hull
							# the left most point and the right most point are definitely
							# members of the convex hull by definition.
							# use these two anchors to divide all the points into two hulls,
							# an upper hull and a lower hull.

							# all points to the left (above) the line joining the extreme points belong to the
							# upper hull
							# all points to the right (below) the line joining the extreme points below to the
							# lower hull
							# ignore all points on the line joining the extreme points since they cannot be
							# part of the convex hull

							a__:							Dict									=points[0]
							a__:							Tuple									=points[n - 1]

							a__:							Tuple									={left_most_point, right_most_point}
							a__:							Optional[int]									=[]
							a__:							List[Any]									=[]

							for i in range(1  ,			n - 1    ):
														a__:							Optional[int]									=_det(a_  ,			a_  ,			points[i]    )

														if det > 0:
																					upper_hull.append(points[i]    )
														elif det < 0:
																					lower_hull.append(points[i]    )

							_construct_hull(a_  ,			a_  ,			a_  ,			a_    )
							_construct_hull(a_  ,			a_  ,			a_  ,			a_    )

							return sorted(a_    )





def     __lowerCamelCase							(   __magic_name__						:	Any  ,			__magic_name__						:	List[str]  ,			__magic_name__						:	int  ,			__magic_name__						:	str    ):
							if points:
														a__:							Tuple									=None
														a__:							Any									=float("-inf"    )
														a__:							Union[str, Any]									=[]

														for p in points:
																					a__:							Union[str, Any]									=_det(a_  ,			a_  ,			a_    )

																					if det > 0:
																												candidate_points.append(a_    )

																												if det > extreme_point_distance:
																																			a__:							Optional[int]									=det
																																			a__:							Any									=p

														if extreme_point:
																					_construct_hull(a_  ,			a_  ,			a_  ,			a_    )
																					convex_set.add(a_    )
																					_construct_hull(a_  ,			a_  ,			a_  ,			a_    )





def     __lowerCamelCase							(   __magic_name__						:	Tuple    ):
							a__:							Tuple									=sorted(_validate_input(a_    )    )
							a__:							Any									=len(a_    )

							a__:							Any									=points[:2]
							for i in range(2  ,			a_    ):
														a__:							List[str]									=_det(convex_hull[1]  ,			convex_hull[0]  ,			points[i]    )
														if det > 0:
																					convex_hull.insert(0  ,			points[i]    )
																					break
														elif det < 0:
																					convex_hull.append(points[i]    )
																					break
														else:
																					a__:							Tuple									=points[i]
							i += 1

							for j in range(a_  ,			a_    ):
														if (
														    _det(convex_hull[0]  ,			convex_hull[-1]  ,			points[j]    ) > 0
														    and _det(convex_hull[-1]  ,			convex_hull[0]  ,			points[1]    ) < 0
														):
																					# The point lies within the convex hull
																					continue

														convex_hull.insert(0  ,			points[j]    )
														convex_hull.append(points[j]    )
														while _det(convex_hull[0]  ,			convex_hull[1]  ,			convex_hull[2]    ) >= 0:
																					del convex_hull[1]
														while _det(convex_hull[-1]  ,			convex_hull[-2]  ,			convex_hull[-3]    ) <= 0:
																					del convex_hull[-2]

    # `convex_hull` is contains the convex hull in circular order
							return sorted(convex_hull[1:] if len(a_    ) > 3 else convex_hull    )





def     __lowerCamelCase							(   ):
							a__:							Dict									=[
							    (0, 3),
							    (2, 2),
							    (1, 1),
							    (2, 1),
							    (3, 0),
							    (0, 0),
							    (3, 3),
							    (2, -1),
							    (2, -4),
							    (1, -3),
							]
							# the convex set of points is
							# [(0, 0), (0, 3), (1, -3), (2, -4), (3, 0), (3, 3)]
							a__:							List[str]									=convex_hull_bf(a_    )

							a__:							Tuple									=convex_hull_recursive(a_    )
							assert results_bf == results_recursive

							a__:							str									=convex_hull_melkman(a_    )
							assert results_bf == results_melkman

							print(a_    )


if __name__ == "__main__":
		main()







import math
from dataclasses import dataclass
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, logging, randn_tensor
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin


__a							  =						logging.get_logger(__name__)  # pylint: disable=invalid-name

@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerDiscrete
class        UpperCamelCase__(    lowerCAmelCase__	):

	"""simple docstring"""

	_A  =		42
	_A  =		None


def    UpperCamelCase_ (	a_  ,				a_=0.999  ,				a_="cosine"  ,				)     ->List[Any]:
		if alpha_transform_type == "cosine":

				def alpha_bar_fn(a_		):
						return math.cos((t + 0.008) / 1.008 * math.pi / 2		) ** 2

		elif alpha_transform_type == "exp":

				def alpha_bar_fn(a_		):
						return math.exp(t * -12.0		)

		else:
				raise ValueError(f'''Unsupported alpha_tranform_type: {alpha_transform_type}'''		)

		A				=[]
		for i in range(a_		):
				A				=i / num_diffusion_timesteps
				A				=(i + 1) / num_diffusion_timesteps
				betas.append(min(1 - alpha_bar_fn(a_		) / alpha_bar_fn(a_		)  ,				a_		)		)
		return torch.tensor(a_  ,				dtype=torch.floataa		)






class        UpperCamelCase__(    lowerCAmelCase__						,						lowerCAmelCase__	):

	"""simple docstring"""

	_A  =		[e.name for e in KarrasDiffusionSchedulers]
	_A  =		1







	@register_to_config
	def __init__(      self				:			Any							,			snake_case__				:			int = 10_00							,			snake_case__				:			float = 0.0_001							,			snake_case__				:			float = 0.02							,			snake_case__				:			str = "linear"							,			snake_case__				:			Optional[Union[np.ndarray, List[float]]] = None							,			snake_case__				:			str = "epsilon"							,			snake_case__				:			str = "linear"							,			snake_case__				:			Optional[bool] = False							,			snake_case__				:			str = "linspace"							,			snake_case__				:			int = 0							,			):
			"""simple docstring"""





			if trained_betas is not None:
					A				=torch.tensor(snake_case__							,			dtype=torch.floataa )
			elif beta_schedule == "linear":
					A				=torch.linspace(snake_case__							,			snake_case__							,			snake_case__							,			dtype=torch.floataa )
			elif beta_schedule == "scaled_linear":
					# this schedule is very specific to the latent diffusion model.
					A				=(
					    torch.linspace(beta_start**0.5							,			beta_end**0.5							,			snake_case__							,			dtype=torch.floataa ) ** 2
					)
			elif beta_schedule == "squaredcos_cap_v2":
					# Glide cosine schedule
					A				=betas_for_alpha_bar(snake_case__ )
			else:
					raise NotImplementedError(f'''{beta_schedule} does is not implemented for {self.__class__}''' )

			A				=1.0 - self.betas
			A				=torch.cumprod(self.alphas							,			dim=0 )

			A				=np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5 )
			A				=np.concatenate([sigmas[::-1], [0.0]] ).astype(np.floataa )
			A				=torch.from_numpy(snake_case__ )

			# setable values
			A				=None
			A				=np.linspace(0							,			num_train_timesteps - 1							,			snake_case__							,			dtype=snake_case__ )[::-1].copy()
			A				=torch.from_numpy(snake_case__ )
			A				=False
			A				=use_karras_sigmas







	@property
	def        _a					(      self				:			Dict ):
			"""simple docstring"""





			if self.config.timestep_spacing in ["linspace", "trailing"]:
					return self.sigmas.max()

			return (self.sigmas.max() ** 2 + 1) ** 0.5







	def        _a					(      self				:			str							,			snake_case__				:			torch.FloatTensor							,			snake_case__				:			Union[float, torch.FloatTensor] ):
			"""simple docstring"""





			if isinstance(snake_case__							,			torch.Tensor ):
					A				=timestep.to(self.timesteps.device )
			A				=(self.timesteps == timestep).nonzero().item()
			A				=self.sigmas[step_index]

			A				=sample / ((sigma**2 + 1) ** 0.5)

			A				=True
			return sample







	def        _a					(      self				:			str							,			snake_case__				:			int							,			snake_case__				:			Union[str, torch.device] = None ):
			"""simple docstring"""





			A				=num_inference_steps

			# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
			if self.config.timestep_spacing == "linspace":
					A				=np.linspace(0							,			self.config.num_train_timesteps - 1							,			snake_case__							,			dtype=snake_case__ )[
					    ::-1
					].copy()
			elif self.config.timestep_spacing == "leading":
					A				=self.config.num_train_timesteps // self.num_inference_steps
					# creates integer timesteps by multiplying by ratio
					# casting to int to avoid issues when num_inference_step is power of 3
					A				=(np.arange(0							,			snake_case__ ) * step_ratio).round()[::-1].copy().astype(snake_case__ )
					timesteps += self.config.steps_offset
			elif self.config.timestep_spacing == "trailing":
					A				=self.config.num_train_timesteps / self.num_inference_steps
					# creates integer timesteps by multiplying by ratio
					# casting to int to avoid issues when num_inference_step is power of 3
					A				=(np.arange(self.config.num_train_timesteps							,			0							,			-step_ratio )).round().copy().astype(snake_case__ )
					timesteps -= 1
			else:
					raise ValueError(
					    f'''{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'.''' )

			A				=np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5 )
			A				=np.log(snake_case__ )

			if self.config.interpolation_type == "linear":
					A				=np.interp(snake_case__							,			np.arange(0							,			len(snake_case__ ) )							,			snake_case__ )
			elif self.config.interpolation_type == "log_linear":
					A				=torch.linspace(np.log(sigmas[-1] )							,			np.log(sigmas[0] )							,			num_inference_steps + 1 ).exp()
			else:
					raise ValueError(
					    f'''{self.config.interpolation_type} is not implemented. Please specify interpolation_type to either'''
					    " 'linear' or 'log_linear'" )

			if self.use_karras_sigmas:
					A				=self._convert_to_karras(in_sigmas=snake_case__							,			num_inference_steps=self.num_inference_steps )
					A				=np.array([self._sigma_to_t(snake_case__							,			snake_case__ ) for sigma in sigmas] )

			A				=np.concatenate([sigmas, [0.0]] ).astype(np.floataa )
			A				=torch.from_numpy(snake_case__ ).to(device=snake_case__ )
			if str(snake_case__ ).startswith("mps" ):
					# mps does not support float64
					A				=torch.from_numpy(snake_case__ ).to(snake_case__							,			dtype=torch.floataa )
			else:
					A				=torch.from_numpy(snake_case__ ).to(device=snake_case__ )







	def        _a					(      self				:			Dict							,			snake_case__				:			Dict							,			snake_case__				:			Any ):
			"""simple docstring"""





			A				=np.log(snake_case__ )

			# get distribution
			A				=log_sigma - log_sigmas[:, np.newaxis]

			# get sigmas range
			A				=np.cumsum((dists >= 0)							,			axis=0 ).argmax(axis=0 ).clip(max=log_sigmas.shape[0] - 2 )
			A				=low_idx + 1

			A				=log_sigmas[low_idx]
			A				=log_sigmas[high_idx]

			# interpolate sigmas
			A				=(low - log_sigma) / (low - high)
			A				=np.clip(snake_case__							,			0							,			1 )

			# transform interpolation to time range
			A				=(1 - w) * low_idx + w * high_idx
			A				=t.reshape(sigma.shape )
			return t







	def        _a					(      self				:			List[str]							,			snake_case__				:			torch.FloatTensor							,			snake_case__				:			Dict ):
			"""simple docstring"""





			A				=in_sigmas[-1].item()
			A				=in_sigmas[0].item()

			A				=7.0  # 7.0 is the value used in the paper
			A				=np.linspace(0							,			1							,			snake_case__ )
			A				=sigma_min ** (1 / rho)
			A				=sigma_max ** (1 / rho)
			A				=(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
			return sigmas







	def        _a					(      self				:			Any							,			snake_case__				:			torch.FloatTensor							,			snake_case__				:			Union[float, torch.FloatTensor]							,			snake_case__				:			torch.FloatTensor							,			snake_case__				:			float = 0.0							,			snake_case__				:			float = 0.0							,			snake_case__				:			float = float("inf" )							,			snake_case__				:			float = 1.0							,			snake_case__				:			Optional[torch.Generator] = None							,			snake_case__				:			bool = True							,			):
			"""simple docstring"""





			if (
			    isinstance(snake_case__							,			snake_case__ )
			    or isinstance(snake_case__							,			torch.IntTensor )
			    or isinstance(snake_case__							,			torch.LongTensor )
			):
					raise ValueError(
					    (
					        "Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to"
					        " `EulerDiscreteScheduler.step()` is not supported. Make sure to pass"
					        " one of the `scheduler.timesteps` as a timestep."
					    )							,			)

			if not self.is_scale_input_called:
					logger.warning(
					    "The `scale_model_input` function should be called before `step` to ensure correct denoising. "
					    "See `StableDiffusionPipeline` for a usage example." )

			if isinstance(snake_case__							,			torch.Tensor ):
					A				=timestep.to(self.timesteps.device )

			A				=(self.timesteps == timestep).nonzero().item()
			A				=self.sigmas[step_index]

			A				=min(s_churn / (len(self.sigmas ) - 1)							,			2**0.5 - 1 ) if s_tmin <= sigma <= s_tmax else 0.0

			A				=randn_tensor(
			    model_output.shape							,			dtype=model_output.dtype							,			device=model_output.device							,			generator=snake_case__ )

			A				=noise * s_noise
			A				=sigma * (gamma + 1)

			if gamma > 0:
					A				=sample + eps * (sigma_hat**2 - sigma**2) ** 0.5

			# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
			# NOTE: "original_sample" should not be an expected prediction_type but is left in for
			# backwards compatibility
			if self.config.prediction_type == "original_sample" or self.config.prediction_type == "sample":
					A				=model_output
			elif self.config.prediction_type == "epsilon":
					A				=sample - sigma_hat * model_output
			elif self.config.prediction_type == "v_prediction":
					# * c_out + input * c_skip
					A				=model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
			else:
					raise ValueError(
					    f'''prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`''' )

			# 2. Convert to an ODE derivative
			A				=(sample - pred_original_sample) / sigma_hat

			A				=self.sigmas[step_index + 1] - sigma_hat

			A				=sample + derivative * dt

			if not return_dict:
					return (prev_sample,)

			return EulerDiscreteSchedulerOutput(prev_sample=snake_case__							,			pred_original_sample=snake_case__ )







	def        _a					(      self				:			Optional[int]							,			snake_case__				:			torch.FloatTensor							,			snake_case__				:			torch.FloatTensor							,			snake_case__				:			torch.FloatTensor							,			):
			"""simple docstring"""





			A				=self.sigmas.to(device=original_samples.device							,			dtype=original_samples.dtype )
			if original_samples.device.type == "mps" and torch.is_floating_point(snake_case__ ):
					# mps does not support float64
					A				=self.timesteps.to(original_samples.device							,			dtype=torch.floataa )
					A				=timesteps.to(original_samples.device							,			dtype=torch.floataa )
			else:
					A				=self.timesteps.to(original_samples.device )
					A				=timesteps.to(original_samples.device )

			A				=[(schedule_timesteps == t).nonzero().item() for t in timesteps]

			A				=sigmas[step_indices].flatten()
			while len(sigma.shape ) < len(original_samples.shape ):
					A				=sigma.unsqueeze(-1 )

			A				=original_samples + noise * sigma
			return noisy_samples







	def __len__(      self				:			Tuple ):
			"""simple docstring"""





			return self.config.num_train_timesteps




