


"""simple docstring"""
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


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



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






		'''simple docstring'''

		lowerCamelCase__           =42
		lowerCamelCase__           =None






def 						lowercase				(	_snake_case		: Union[str, Any]	,  _snake_case		: List[str]=0.999	,  _snake_case		: Union[str, Any]="cosine"	,  )	->Union[str, Any]:
	"""simple docstring"""





	if alpha_transform_type == "cosine":

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

	elif alpha_transform_type == "exp":

		def alpha_bar_fn(_snake_case		: Union[str, Any]	):
			return math.exp(t * -12.0	)

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

	__snake_case      :		List[str]         =							[]
	for i in range(_snake_case	):
		__snake_case      :		List[str]         =							i / num_diffusion_timesteps
		__snake_case      :		Optional[int]         =							(i + 1) / num_diffusion_timesteps
		betas.append(min(1 - alpha_bar_fn(_snake_case	) / alpha_bar_fn(_snake_case	)	,  _snake_case	)	)
	return torch.tensor(_snake_case	,  dtype=torch.floataa	)



class      _UpperCAmelCase					(				__snake_case,							__snake_case							):






		'''simple docstring'''

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



		@register_to_config
		def __init__(self							,			a_ = 10_00							,			a_ = 0.0001							,			a_ = 0.02							,			a_ = "linear"							,			a_ = None							,			a_ = "epsilon"							,			a_ = "linear"							,			a_ = False							,			a_ = "linspace"							,			a_ = 0							,			):





			'''simple docstring'''

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

			__snake_case      :		Tuple         =							1.0 - self.betas
			__snake_case      :		Optional[int]         =							torch.cumprod(self.alphas							,			dim=0   )

			__snake_case      :		str         =							np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5   )
			__snake_case      :		Dict         =							np.concatenate([sigmas[::-1], [0.0]]   ).astype(np.floataa   )
			__snake_case      :		List[str]         =							torch.from_numpy(a_   )

			# setable values
			__snake_case      :		List[Any]         =							None
			__snake_case      :		str         =							np.linspace(0							,			num_train_timesteps - 1							,			a_							,			dtype=a_   )[::-1].copy()
			__snake_case      :		int         =							torch.from_numpy(a_   )
			__snake_case      :		int         =							False
			__snake_case      :		Union[str, Any]         =							use_karras_sigmas



		@property
		def 							SCREAMING_SNAKE_CASE    (self   ):





			'''simple docstring'''

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

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



		def 							SCREAMING_SNAKE_CASE    (self							,			a_							,			a_   ):





			'''simple docstring'''

			if isinstance(a_							,			torch.Tensor   ):
				__snake_case      :		Tuple         =							timestep.to(self.timesteps.device   )
			__snake_case      :		int         =							(self.timesteps == timestep).nonzero().item()
			__snake_case      :		List[Any]         =							self.sigmas[step_index]

			__snake_case      :		Any         =							sample / ((sigma**2 + 1) ** 0.5)

			__snake_case      :		Union[str, Any]         =							True
			return sample



		def 							SCREAMING_SNAKE_CASE    (self							,			a_							,			a_ = None   ):





			'''simple docstring'''

			__snake_case      :		Union[str, Any]         =							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":
				__snake_case      :		Tuple         =							np.linspace(0							,			self.config.num_train_timesteps - 1							,			a_							,			dtype=a_   )[
				    ::-1
				].copy()
			elif self.config.timestep_spacing == "leading":
				__snake_case      :		List[str]         =							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
				__snake_case      :		Dict         =							(np.arange(0							,			a_   ) * step_ratio).round()[::-1].copy().astype(a_   )
				timesteps += self.config.steps_offset
			elif self.config.timestep_spacing == "trailing":
				__snake_case      :		Optional[int]         =							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
				__snake_case      :		Union[str, Any]         =							(np.arange(self.config.num_train_timesteps							,			0							,			-step_ratio   )).round().copy().astype(a_   )
				timesteps -= 1
			else:
				raise ValueError(
				    f"""{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'."""   )

			__snake_case      :		Dict         =							np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5   )
			__snake_case      :		Tuple         =							np.log(a_   )

			if self.config.interpolation_type == "linear":
				__snake_case      :		Union[str, Any]         =							np.interp(a_							,			np.arange(0							,			len(a_   )   )							,			a_   )
			elif self.config.interpolation_type == "log_linear":
				__snake_case      :		List[str]         =							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:
				__snake_case      :		str         =							self._convert_to_karras(in_sigmas=a_							,			num_inference_steps=self.num_inference_steps   )
				__snake_case      :		Dict         =							np.array([self._sigma_to_t(a_							,			a_   ) for sigma in sigmas]   )

			__snake_case      :		Optional[Any]         =							np.concatenate([sigmas, [0.0]]   ).astype(np.floataa   )
			__snake_case      :		List[Any]         =							torch.from_numpy(a_   ).to(device=a_   )
			if str(a_   ).startswith('''mps'''   ):
				# mps does not support float64
				__snake_case      :		Dict         =							torch.from_numpy(a_   ).to(a_							,			dtype=torch.floataa   )
			else:
				__snake_case      :		List[str]         =							torch.from_numpy(a_   ).to(device=a_   )



		def 							SCREAMING_SNAKE_CASE    (self							,			a_							,			a_   ):





			'''simple docstring'''

			__snake_case      :		int         =							np.log(a_   )

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

			# get sigmas range
			__snake_case      :		int         =							np.cumsum((dists >= 0)							,			axis=0   ).argmax(axis=0   ).clip(max=log_sigmas.shape[0] - 2   )
			__snake_case      :		Union[str, Any]         =							low_idx + 1

			__snake_case      :		Union[str, Any]         =							log_sigmas[low_idx]
			__snake_case      :		int         =							log_sigmas[high_idx]

			# interpolate sigmas
			__snake_case      :		int         =							(low - log_sigma) / (low - high)
			__snake_case      :		Optional[int]         =							np.clip(a_							,			0							,			1   )

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



		def 							SCREAMING_SNAKE_CASE    (self							,			a_							,			a_   ):





			'''simple docstring'''

			__snake_case      :		float         =							in_sigmas[-1].item()
			__snake_case      :		float         =							in_sigmas[0].item()

			__snake_case      :		Dict         =							7.0  # 7.0 is the value used in the paper
			__snake_case      :		int         =							np.linspace(0							,			1							,			a_   )
			__snake_case      :		int         =							sigma_min ** (1 / rho)
			__snake_case      :		Dict         =							sigma_max ** (1 / rho)
			__snake_case      :		Any         =							(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
			return sigmas



		def 							SCREAMING_SNAKE_CASE    (self							,			a_							,			a_							,			a_							,			a_ = 0.0							,			a_ = 0.0							,			a_ = float('''inf'''   )							,			a_ = 1.0							,			a_ = None							,			a_ = True							,			):





			'''simple docstring'''

			if (
			    isinstance(a_							,			a_   )
			    or isinstance(a_							,			torch.IntTensor   )
			    or isinstance(a_							,			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(a_							,			torch.Tensor   ):
				__snake_case      :		Tuple         =							timestep.to(self.timesteps.device   )

			__snake_case      :		List[str]         =							(self.timesteps == timestep).nonzero().item()
			__snake_case      :		Optional[Any]         =							self.sigmas[step_index]

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

			__snake_case      :		Optional[int]         =							randn_tensor(
			    model_output.shape							,			dtype=model_output.dtype							,			device=model_output.device							,			generator=a_   )

			__snake_case      :		Union[str, Any]         =							noise * s_noise
			__snake_case      :		str         =							sigma * (gamma + 1)

			if gamma > 0:
				__snake_case      :		Union[str, Any]         =							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":
				__snake_case      :		List[Any]         =							model_output
			elif self.config.prediction_type == "epsilon":
				__snake_case      :		str         =							sample - sigma_hat * model_output
			elif self.config.prediction_type == "v_prediction":
				# * c_out + input * c_skip
				__snake_case      :		Dict         =							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
			__snake_case      :		Union[str, Any]         =							(sample - pred_original_sample) / sigma_hat

			__snake_case      :		Optional[Any]         =							self.sigmas[step_index + 1] - sigma_hat

			__snake_case      :		Union[str, Any]         =							sample + derivative * dt

			if not return_dict:
				return (prev_sample,)

			return EulerDiscreteSchedulerOutput(prev_sample=a_							,			pred_original_sample=a_   )



		def 							SCREAMING_SNAKE_CASE    (self							,			a_							,			a_							,			a_							,			):





			'''simple docstring'''

			__snake_case      :		Any         =							self.sigmas.to(device=original_samples.device							,			dtype=original_samples.dtype   )
			if original_samples.device.type == "mps" and torch.is_floating_point(a_   ):
				# mps does not support float64
				__snake_case      :		Union[str, Any]         =							self.timesteps.to(original_samples.device							,			dtype=torch.floataa   )
				__snake_case      :		Any         =							timesteps.to(original_samples.device							,			dtype=torch.floataa   )
			else:
				__snake_case      :		List[Any]         =							self.timesteps.to(original_samples.device   )
				__snake_case      :		List[Any]         =							timesteps.to(original_samples.device   )

			__snake_case      :		List[Any]         =							[(schedule_timesteps == t).nonzero().item() for t in timesteps]

			__snake_case      :		Dict         =							sigmas[step_indices].flatten()
			while len(sigma.shape   ) < len(original_samples.shape   ):
				__snake_case      :		Union[str, Any]         =							sigma.unsqueeze(-1   )

			__snake_case      :		Optional[Any]         =							original_samples + noise * sigma
			return noisy_samples



		def __len__(self   ):





			'''simple docstring'''

			return self.config.num_train_timesteps






from __future__ import annotations

from collections.abc import Iterable
class 							a_					:






 '''simple docstring'''






 def __init__(     self   :    int     ,       lowercase__   :    Optional[int]     ,       lowercase__   :    List[str]):







        '''simple docstring'''



        lowerCAmelCase__      ,   lowerCAmelCase__	      =   float(lowercase__), float(lowercase__)




 def __eq__(     self   :    int     ,       lowercase__   :    int):







        '''simple docstring'''



        return self.x == other.x and self.y == other.y




 def __ne__(     self   :    Tuple     ,       lowercase__   :    List[Any]):







        '''simple docstring'''



        return not self == other




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







        '''simple docstring'''



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




 def __lt__(     self   :    str     ,       lowercase__   :    List[str]):







        '''simple docstring'''



        return not self > other




 def __ge__(     self   :    List[Any]     ,       lowercase__   :    Any):







        '''simple docstring'''



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




 def __le__(     self   :    Dict     ,       lowercase__   :    str):







        '''simple docstring'''



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




 def __repr__(     self   :    List[str]):







        '''simple docstring'''



        return F"""({self.x}, {self.y})"""




 def __hash__(     self   :    Dict):







        '''simple docstring'''



        return hash(self.x)






def  __lowerCamelCase						(		lowerCAmelCase__      ,    ):
       lowerCAmelCase__	      =   []
       if list_of_tuples:
              for p in list_of_tuples:
                     if isinstance(lowerCAmelCase__      ,    lowerCAmelCase__      ):
                            points.append(lowerCAmelCase__      )
                     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						(		lowerCAmelCase__      ):

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

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

       return _construct_points(lowerCAmelCase__      )






def  __lowerCamelCase						(		lowerCAmelCase__      ,    lowerCAmelCase__      ,    lowerCAmelCase__      ):
       lowerCAmelCase__	      =   (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						(		lowerCAmelCase__      ):
       lowerCAmelCase__	      =   sorted(_validate_input(lowerCAmelCase__      )      )
       lowerCAmelCase__	      =   len(lowerCAmelCase__      )
       lowerCAmelCase__	      =   set()

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

                                   if det_k > 0:
                                          lowerCAmelCase__	      =   True
                                   elif det_k < 0:
                                          lowerCAmelCase__	      =   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]:
                                                 lowerCAmelCase__	      =   False
                                                 break

                            if points_left_of_ij and points_right_of_ij:
                                   lowerCAmelCase__	      =   False
                                   break

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

       return sorted(lowerCAmelCase__      )






def  __lowerCamelCase						(		lowerCAmelCase__      ):
       lowerCAmelCase__	      =   sorted(_validate_input(lowerCAmelCase__      )      )
       lowerCAmelCase__	      =   len(lowerCAmelCase__      )

       # 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

       lowerCAmelCase__	      =   points[0]
       lowerCAmelCase__	      =   points[n - 1]

       lowerCAmelCase__	      =   {left_most_point, right_most_point}
       lowerCAmelCase__	      =   []
       lowerCAmelCase__	      =   []

       for i in range(1      ,    n - 1      ):
              lowerCAmelCase__	      =   _det(lowerCAmelCase__      ,    lowerCAmelCase__      ,    points[i]      )

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

       _construct_hull(lowerCAmelCase__      ,    lowerCAmelCase__      ,    lowerCAmelCase__      ,    lowerCAmelCase__      )
       _construct_hull(lowerCAmelCase__      ,    lowerCAmelCase__      ,    lowerCAmelCase__      ,    lowerCAmelCase__      )

       return sorted(lowerCAmelCase__      )






def  __lowerCamelCase						(		lowerCAmelCase__      ,    lowerCAmelCase__      ,    lowerCAmelCase__      ,    lowerCAmelCase__      ):
       if points:
              lowerCAmelCase__	      =   None
              lowerCAmelCase__	      =   float('-inf'      )
              lowerCAmelCase__	      =   []

              for p in points:
                     lowerCAmelCase__	      =   _det(lowerCAmelCase__      ,    lowerCAmelCase__      ,    lowerCAmelCase__      )

                     if det > 0:
                            candidate_points.append(lowerCAmelCase__      )

                            if det > extreme_point_distance:
                                   lowerCAmelCase__	      =   det
                                   lowerCAmelCase__	      =   p

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






def  __lowerCamelCase						(		lowerCAmelCase__      ):
       lowerCAmelCase__	      =   sorted(_validate_input(lowerCAmelCase__      )      )
       lowerCAmelCase__	      =   len(lowerCAmelCase__      )

       lowerCAmelCase__	      =   points[:2]
       for i in range(2      ,    lowerCAmelCase__      ):
              lowerCAmelCase__	      =   _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:
                     lowerCAmelCase__	      =   points[i]
       i += 1

       for j in range(lowerCAmelCase__      ,    lowerCAmelCase__      ):
              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(lowerCAmelCase__      ) > 3 else convex_hull      )






def  __lowerCamelCase						(		):
       lowerCAmelCase__	      =   [
           (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)]
       lowerCAmelCase__	      =   convex_hull_bf(lowerCAmelCase__      )

       lowerCAmelCase__	      =   convex_hull_recursive(lowerCAmelCase__      )
       assert results_bf == results_recursive

       lowerCAmelCase__	      =   convex_hull_melkman(lowerCAmelCase__      )
       assert results_bf == results_melkman

       print(lowerCAmelCase__      )


if __name__ == "__main__":
    main()
