



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

import numpy as np
import torch

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

@dataclass
class 			__snake_case   ( SCREAMING_SNAKE_CASE):







							'''simple docstring'''






							UpperCamelCase__					:   torch.FloatTensor
							UpperCamelCase__					:   torch.FloatTensor




def       A_   (						__a  :					Dict			,		__a  :					Optional[int]=0.9_9_9			,		__a  :					Dict="cosine"			,		):

				"""simple docstring"""
				if alpha_transform_type == "cosine":

								def alpha_bar_fn(__a  :					List[Any]		):
												return math.cos((t + 0.0_0_8) / 1.0_0_8 * math.pi / 2		) ** 2

				elif alpha_transform_type == "exp":

								def alpha_bar_fn(__a  :					int		):
												return math.exp(t * -1_2.0		)

				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 			__snake_case   ( SCREAMING_SNAKE_CASE      ,SCREAMING_SNAKE_CASE):







							'''simple docstring'''






							UpperCamelCase__					:   Any       =       1


							@register_to_config
							def __init__(				self	,	a_ = 1_000	,	a_ = 0.0_001	,	a_ = 0.02	,	a_ = "linear"	,	a_ = 0.0	,	a_ = None	,	a_ = True	,	):
											if trained_betas is not None:
															a__					   =		torch.from_numpy(a_		)
											elif beta_schedule == "linear":
															a__					   =		torch.linspace(a_	,	a_	,	a_	,	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	,	a_	,	dtype=torch.floataa		) ** 2
															)
											elif beta_schedule == "squaredcos_cap_v2":
															# Glide cosine schedule
															a__					   =		betas_for_alpha_bar(a_		)
											elif beta_schedule == "sigmoid":
															# GeoDiff sigmoid schedule
															a__					   =		torch.linspace(-6	,	6	,	a_		)
															a__					   =		torch.sigmoid(a_		) * (beta_end - beta_start) + beta_start
											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__					   =		torch.tensor(1.0		)

											a__					   =		torch.tensor(1.0		)

											# standard deviation of the initial noise distribution
											a__					   =		1.0

											# setable values
											a__					   =		None
											a__					   =		torch.from_numpy(np.arange(0	,	a_		)[::-1].copy()		)

											a__					   =		eta


							def _a   (				self	,	a_	,	a_ = None		):
											return sample


							def _a   (				self	,	a_	,	a_ = 10	,	a_ = 10	,	a_ = None	,	):
											a__					   =		min(self.config.num_train_timesteps	,	a_		)
											a__					   =		num_inference_steps

											a__					   =		[]

											a__					   =		{}
											for j in range(0	,	num_inference_steps - jump_length	,	a_		):
															a__					   =		jump_n_sample - 1

											a__					   =		num_inference_steps
											while t >= 1:
															a__					   =		t - 1
															timesteps.append(a_		)

															if jumps.get(a_	,	0		) > 0:
																			a__					   =		jumps[t] - 1
																			for _ in range(a_		):
																							a__					   =		t + 1
																							timesteps.append(a_		)

											a__					   =		np.array(a_		) * (self.config.num_train_timesteps // self.num_inference_steps)
											a__					   =		torch.from_numpy(a_		).to(a_		)


							def _a   (				self	,	a_		):
											a__					   =		t - self.config.num_train_timesteps // self.num_inference_steps

											a__					   =		self.alphas_cumprod[t]
											a__					   =		self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
											a__					   =		1 - alpha_prod_t
											a__					   =		1 - alpha_prod_t_prev

											# For t > 0, compute predicted variance βt (see formula (6) and (7) from
											# https://arxiv.org/pdf/2006.11239.pdf) and sample from it to get
											# previous sample x_{t-1} ~ N(pred_prev_sample, variance) == add
											# variance to pred_sample
											# Is equivalent to formula (16) in https://arxiv.org/pdf/2010.02502.pdf
											# without eta.
											# variance = (1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * self.betas[t]
											a__					   =		(beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)

											return variance


							def _a   (				self	,	a_	,	a_	,	a_	,	a_	,	a_	,	a_ = None	,	a_ = True	,	):
											a__					   =		timestep
											a__					   =		timestep - self.config.num_train_timesteps // self.num_inference_steps

											# 1. compute alphas, betas
											a__					   =		self.alphas_cumprod[t]
											a__					   =		self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
											a__					   =		1 - alpha_prod_t

											# 2. compute predicted original sample from predicted noise also called
											# "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
											a__					   =		(sample - beta_prod_t**0.5 * model_output) / alpha_prod_t**0.5

											# 3. Clip "predicted x_0"
											if self.config.clip_sample:
															a__					   =		torch.clamp(a_	,	-1	,	1		)

											# We choose to follow RePaint Algorithm 1 to get x_{t-1}, however we
											# substitute formula (7) in the algorithm coming from DDPM paper
											# (formula (4) Algorithm 2 - Sampling) with formula (12) from DDIM paper.
											# DDIM schedule gives the same results as DDPM with eta = 1.0
											# Noise is being reused in 7. and 8., but no impact on quality has
											# been observed.

											# 5. Add noise
											a__					   =		model_output.device
											a__					   =		randn_tensor(model_output.shape	,	generator=a_	,	device=a_	,	dtype=model_output.dtype		)
											a__					   =		self.eta * self._get_variance(a_		) ** 0.5

											a__					   =		0
											if t > 0 and self.eta > 0:
															a__					   =		std_dev_t * noise

											# 6. compute "direction pointing to x_t" of formula (12)
											# from https://arxiv.org/pdf/2010.02502.pdf
											a__					   =		(1 - alpha_prod_t_prev - std_dev_t**2) ** 0.5 * model_output

											# 7. compute x_{t-1} of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
											a__					   =		alpha_prod_t_prev**0.5 * pred_original_sample + pred_sample_direction + variance

											# 8. Algorithm 1 Line 5 https://arxiv.org/pdf/2201.09865.pdf
											a__					   =		(alpha_prod_t_prev**0.5) * original_image + ((1 - alpha_prod_t_prev) ** 0.5) * noise

											# 9. Algorithm 1 Line 8 https://arxiv.org/pdf/2201.09865.pdf
											a__					   =		mask * prev_known_part + (1.0 - mask) * prev_unknown_part

											if not return_dict:
															return (
															    pred_prev_sample,
															    pred_original_sample,
															)

											return RePaintSchedulerOutput(prev_sample=a_	,	pred_original_sample=a_		)


							def _a   (				self	,	a_	,	a_	,	a_=None		):
											a__					   =		self.config.num_train_timesteps // self.num_inference_steps

											for i in range(a_		):
															a__					   =		self.betas[timestep + i]
															if sample.device.type == "mps":
																			# randn does not work reproducibly on mps
																			a__					   =		randn_tensor(sample.shape	,	dtype=sample.dtype	,	generator=a_		)
																			a__					   =		noise.to(sample.device		)
															else:
																			a__					   =		randn_tensor(sample.shape	,	generator=a_	,	device=sample.device	,	dtype=sample.dtype		)

															# 10. Algorithm 1 Line 10 https://arxiv.org/pdf/2201.09865.pdf
															a__					   =		(1 - beta) ** 0.5 * sample + beta**0.5 * noise

											return sample


							def _a   (				self	,	a_	,	a_	,	a_	,	):
											raise NotImplementedError("""Use `DDPMScheduler.add_noise()` to train for sampling with RePaint."""		)







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


from __future__ import annotations

from collections.abc import Iterable







class      SCREAMING_SNAKE_CASE__					:

       def __init__(							self					:     Optional[Any]			,			_lowerCAmelCase					:     Tuple			,			_lowerCAmelCase					:     Tuple			):
           __snake_case			, __snake_case       :				str 			=    float(_lowerCAmelCase			), float(_lowerCAmelCase			)

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

       def __ne__(							self					:     Any			,			_lowerCAmelCase					:     Optional[Any]			):
           return not self == other

       def __gt__(							self					:     Union[str, Any]			,			_lowerCAmelCase					:     int			):
           if self.x > other.x:
               return True
           elif self.x == other.x:
               return self.y > other.y
           return False

       def __lt__(							self					:     List[str]			,			_lowerCAmelCase					:     List[str]			):
           return not self > other

       def __ge__(							self					:     List[Any]			,			_lowerCAmelCase					:     List[Any]			):
           if self.x > other.x:
               return True
           elif self.x == other.x:
               return self.y >= other.y
           return False

       def __le__(							self					:     List[Any]			,			_lowerCAmelCase					:     List[Any]			):
           if self.x < other.x:
               return True
           elif self.x == other.x:
               return self.y <= other.y
           return False

       def __repr__(							self					:     str			):
           return f'''({self.x}, {self.y})'''





       def __hash__(							self					:     List[str]			):
           return hash(self.x			)







def 					__lowerCAmelCase				(		__SCREAMING_SNAKE_CASE       :					list[Point] | list[list[float]] | Iterable[list[float]]		,							):







    '''simple docstring'''
    __snake_case       :				list[Point] 			=    []
    if list_of_tuples:
        for p in list_of_tuples:
            if isinstance(__SCREAMING_SNAKE_CASE		,							__SCREAMING_SNAKE_CASE   ):
                points.append(__SCREAMING_SNAKE_CASE   )
            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				(		__SCREAMING_SNAKE_CASE       :					list[Point] | list[list[float]]   ):







    '''simple docstring'''

    if not hasattr(__SCREAMING_SNAKE_CASE		,							"""__iter__"""   ):
        __snake_case       :				List[str] 			=    F'''Expecting an iterable object but got an non-iterable type {points}'''
        raise ValueError(__SCREAMING_SNAKE_CASE   )

    if not points:
        __snake_case       :				Tuple 			=    F'''Expecting a list of points but got {points}'''
        raise ValueError(__SCREAMING_SNAKE_CASE   )

    return _construct_points(__SCREAMING_SNAKE_CASE   )







def 					__lowerCAmelCase				(		__SCREAMING_SNAKE_CASE       :					Point		,							__SCREAMING_SNAKE_CASE       :					Point		,							__SCREAMING_SNAKE_CASE       :					Point   ):







    '''simple docstring'''
    __snake_case       :				List[Any] 			=    (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				(		__SCREAMING_SNAKE_CASE       :					list[Point]   ):







    '''simple docstring'''
    __snake_case       :				List[Any] 			=    sorted(_validate_input(__SCREAMING_SNAKE_CASE   )   )
    __snake_case       :				Optional[Any] 			=    len(__SCREAMING_SNAKE_CASE   )
    __snake_case       :				Dict 			=    set()

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

                    if det_k > 0:
                        __snake_case       :				str 			=    True
                    elif det_k < 0:
                        __snake_case       :				List[Any] 			=    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]:
                            __snake_case       :				Any 			=    False
                            break

                if points_left_of_ij and points_right_of_ij:
                    __snake_case       :				int 			=    False
                    break

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

    return sorted(__SCREAMING_SNAKE_CASE   )







def 					__lowerCAmelCase				(		__SCREAMING_SNAKE_CASE       :					list[Point]   ):







    '''simple docstring'''
    __snake_case       :				Union[str, Any] 			=    sorted(_validate_input(__SCREAMING_SNAKE_CASE   )   )
    __snake_case       :				Any 			=    len(__SCREAMING_SNAKE_CASE   )

    # 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

    __snake_case       :				Tuple 			=    points[0]
    __snake_case       :				Optional[Any] 			=    points[n - 1]

    __snake_case       :				Optional[Any] 			=    {left_most_point, right_most_point}
    __snake_case       :				Optional[int] 			=    []
    __snake_case       :				List[str] 			=    []

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

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

    _construct_hull(__SCREAMING_SNAKE_CASE		,							__SCREAMING_SNAKE_CASE		,							__SCREAMING_SNAKE_CASE		,							__SCREAMING_SNAKE_CASE   )
    _construct_hull(__SCREAMING_SNAKE_CASE		,							__SCREAMING_SNAKE_CASE		,							__SCREAMING_SNAKE_CASE		,							__SCREAMING_SNAKE_CASE   )

    return sorted(__SCREAMING_SNAKE_CASE   )







def 					__lowerCAmelCase				(		__SCREAMING_SNAKE_CASE       :					list[Point]		,							__SCREAMING_SNAKE_CASE       :					Point		,							__SCREAMING_SNAKE_CASE       :					Point		,							__SCREAMING_SNAKE_CASE       :					set[Point]   ):







    '''simple docstring'''
    if points:
        __snake_case       :				List[str] 			=    None
        __snake_case       :				Tuple 			=    float("""-inf"""   )
        __snake_case       :				List[Any] 			=    []

        for p in points:
            __snake_case       :				Union[str, Any] 			=    _det(__SCREAMING_SNAKE_CASE		,							__SCREAMING_SNAKE_CASE		,							__SCREAMING_SNAKE_CASE   )

            if det > 0:
                candidate_points.append(__SCREAMING_SNAKE_CASE   )

                if det > extreme_point_distance:
                    __snake_case       :				List[str] 			=    det
                    __snake_case       :				List[str] 			=    p

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







def 					__lowerCAmelCase				(		__SCREAMING_SNAKE_CASE       :					list[Point]   ):







    '''simple docstring'''
    __snake_case       :				Tuple 			=    sorted(_validate_input(__SCREAMING_SNAKE_CASE   )   )
    __snake_case       :				str 			=    len(__SCREAMING_SNAKE_CASE   )

    __snake_case       :				Optional[int] 			=    points[:2]
    for i in range(2		,							__SCREAMING_SNAKE_CASE   ):
        __snake_case       :				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:
            __snake_case       :				Union[str, Any] 			=    points[i]
    i += 1

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







def 					__lowerCAmelCase				(		):







    '''simple docstring'''
    __snake_case       :				str 			=    [
        (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)]
    __snake_case       :				Optional[Any] 			=    convex_hull_bf(__SCREAMING_SNAKE_CASE   )

    __snake_case       :				List[Any] 			=    convex_hull_recursive(__SCREAMING_SNAKE_CASE   )
    assert results_bf == results_recursive

    __snake_case       :				Tuple 			=    convex_hull_melkman(__SCREAMING_SNAKE_CASE   )
    assert results_bf == results_melkman

    print(__SCREAMING_SNAKE_CASE   )


if __name__ == "__main__":
     main()



