




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
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->UnCLIP
class 		__A   (      UpperCamelCase__      ):
						UpperCamelCase      =       42
						UpperCamelCase      =       None




def 		lowerCAmelCase_ (						lowerCamelCase						,  lowerCamelCase=0.9_9_9						,  lowerCamelCase="cosine"						,  ):
				if alpha_transform_type == "cosine":

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

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

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




class 		__A   (      UpperCamelCase__       ,    UpperCamelCase__      ):

						@register_to_config
						def __init__(		self :Union[str, Any]     ,			__snake_case :int = 10_00     ,			__snake_case :str = "fixed_small_log"     ,			__snake_case :bool = True     ,			__snake_case :Optional[float] = 1.0     ,			__snake_case :str = "epsilon"     ,			__snake_case :str = "squaredcos_cap_v2"     ,			):
										'''simple docstring'''

										if beta_schedule != "squaredcos_cap_v2":
														raise ValueError("""UnCLIPScheduler only supports `beta_schedule`: 'squaredcos_cap_v2'"""			)

										__magic_name__						:						Optional[int]										=betas_for_alpha_bar(__snake_case			)

										__magic_name__						:						Dict										=1.0 - self.betas
										__magic_name__						:						Tuple										=torch.cumprod(self.alphas     ,			dim=0			)
										__magic_name__						:						List[str]										=torch.tensor(1.0			)

										# standard deviation of the initial noise distribution
										__magic_name__						:						Optional[int]										=1.0

										# setable values
										__magic_name__						:						str										=None
										__magic_name__						:						List[str]										=torch.from_numpy(np.arange(0     ,			__snake_case			)[::-1].copy()			)

										__magic_name__						:						Dict										=variance_type

						def      A__    (		self :List[str]     ,			__snake_case :torch.FloatTensor     ,			__snake_case :Optional[int] = None			):
										'''simple docstring'''

										return sample

						def      A__    (		self :str     ,			__snake_case :int     ,			__snake_case :Union[str, torch.device] = None			):
										'''simple docstring'''

										__magic_name__						:						Tuple										=num_inference_steps
										__magic_name__						:						List[str]										=(self.config.num_train_timesteps - 1) / (self.num_inference_steps - 1)
										__magic_name__						:						Dict										=(np.arange(0     ,			__snake_case			) * step_ratio).round()[::-1].copy().astype(np.intaa			)
										__magic_name__						:						Union[str, Any]										=torch.from_numpy(__snake_case			).to(__snake_case			)

						def      A__    (		self :List[Any]     ,			__snake_case :str     ,			__snake_case :Any=None     ,			__snake_case :List[Any]=None     ,			__snake_case :Union[str, Any]=None			):
										'''simple docstring'''

										if prev_timestep is None:
														__magic_name__						:						List[Any]										=t - 1

										__magic_name__						:						Any										=self.alphas_cumprod[t]
										__magic_name__						:						List[str]										=self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.one
										__magic_name__						:						int										=1 - alpha_prod_t
										__magic_name__						:						str										=1 - alpha_prod_t_prev

										if prev_timestep == t - 1:
														__magic_name__						:						Union[str, Any]										=self.betas[t]
										else:
														__magic_name__						:						Optional[Any]										=1 - alpha_prod_t / 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
										__magic_name__						:						Optional[Any]										=beta_prod_t_prev / beta_prod_t * beta

										if variance_type is None:
														__magic_name__						:						Dict										=self.config.variance_type

										# hacks - were probably added for training stability
										if variance_type == "fixed_small_log":
														__magic_name__						:						Optional[int]										=torch.log(torch.clamp(__snake_case     ,			min=1E-20			)			)
														__magic_name__						:						Dict										=torch.exp(0.5 * variance			)
										elif variance_type == "learned_range":
														# NOTE difference with DDPM scheduler
														__magic_name__						:						str										=variance.log()
														__magic_name__						:						str										=beta.log()

														__magic_name__						:						List[str]										=(predicted_variance + 1) / 2
														__magic_name__						:						str										=frac * max_log + (1 - frac) * min_log

										return variance

						def      A__    (		self :List[str]     ,			__snake_case :torch.FloatTensor     ,			__snake_case :int     ,			__snake_case :torch.FloatTensor     ,			__snake_case :Optional[int] = None     ,			__snake_case :Dict=None     ,			__snake_case :bool = True     ,			):
										'''simple docstring'''

										__magic_name__						:						List[str]										=timestep

										if model_output.shape[1] == sample.shape[1] * 2 and self.variance_type == "learned_range":
														__magic_name__					,			__magic_name__						:						int										=torch.split(__snake_case     ,			sample.shape[1]     ,			dim=1			)
										else:
														__magic_name__						:						str										=None

										# 1. compute alphas, betas
										if prev_timestep is None:
														__magic_name__						:						Optional[Any]										=t - 1

										__magic_name__						:						Union[str, Any]										=self.alphas_cumprod[t]
										__magic_name__						:						Optional[int]										=self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.one
										__magic_name__						:						Dict										=1 - alpha_prod_t
										__magic_name__						:						Optional[int]										=1 - alpha_prod_t_prev

										if prev_timestep == t - 1:
														__magic_name__						:						Optional[Any]										=self.betas[t]
														__magic_name__						:						Any										=self.alphas[t]
										else:
														__magic_name__						:						List[Any]										=1 - alpha_prod_t / alpha_prod_t_prev
														__magic_name__						:						Tuple										=1 - beta

										# 2. compute predicted original sample from predicted noise also called
										# "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
										if self.config.prediction_type == "epsilon":
														__magic_name__						:						Optional[Any]										=(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
										elif self.config.prediction_type == "sample":
														__magic_name__						:						str										=model_output
										else:
														raise ValueError(
														    f"prediction_type given as {self.config.prediction_type} must be one of `epsilon` or `sample`"
														    """ for the UnCLIPScheduler."""			)

										# 3. Clip "predicted x_0"
										if self.config.clip_sample:
														__magic_name__						:						int										=torch.clamp(
														    __snake_case     ,			-self.config.clip_sample_range     ,			self.config.clip_sample_range			)

										# 4. Compute coefficients for pred_original_sample x_0 and current sample x_t
										# See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
										__magic_name__						:						Optional[Any]										=(alpha_prod_t_prev ** 0.5 * beta) / beta_prod_t
										__magic_name__						:						Dict										=alpha ** 0.5 * beta_prod_t_prev / beta_prod_t

										# 5. Compute predicted previous sample µ_t
										# See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
										__magic_name__						:						Any										=pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

										# 6. Add noise
										__magic_name__						:						Any										=0
										if t > 0:
														__magic_name__						:						str										=randn_tensor(
														    model_output.shape     ,			dtype=model_output.dtype     ,			generator=__snake_case     ,			device=model_output.device			)

														__magic_name__						:						Optional[Any]										=self._get_variance(
														    __snake_case     ,			predicted_variance=__snake_case     ,			prev_timestep=__snake_case     ,			)

														if self.variance_type == "fixed_small_log":
																		__magic_name__						:						List[str]										=variance
														elif self.variance_type == "learned_range":
																		__magic_name__						:						int										=(0.5 * variance).exp()
														else:
																		raise ValueError(
																		    f"variance_type given as {self.variance_type} must be one of `fixed_small_log` or `learned_range`"
																		    """ for the UnCLIPScheduler."""			)

														__magic_name__						:						Union[str, Any]										=variance * variance_noise

										__magic_name__						:						str										=pred_prev_sample + variance

										if not return_dict:
														return (pred_prev_sample,)

										return UnCLIPSchedulerOutput(prev_sample=__snake_case     ,			pred_original_sample=__snake_case			)


						def      A__    (		self :List[str]     ,			__snake_case :torch.FloatTensor     ,			__snake_case :torch.FloatTensor     ,			__snake_case :torch.IntTensor     ,			):
										'''simple docstring'''

										__magic_name__						:						str										=self.alphas_cumprod.to(device=original_samples.device     ,			dtype=original_samples.dtype			)
										__magic_name__						:						Union[str, Any]										=timesteps.to(original_samples.device			)

										__magic_name__						:						List[Any]										=alphas_cumprod[timesteps] ** 0.5
										__magic_name__						:						Dict										=sqrt_alpha_prod.flatten()
										while len(sqrt_alpha_prod.shape			) < len(original_samples.shape			):
														__magic_name__						:						Union[str, Any]										=sqrt_alpha_prod.unsqueeze(-1			)

										__magic_name__						:						List[Any]										=(1 - alphas_cumprod[timesteps]) ** 0.5
										__magic_name__						:						str										=sqrt_one_minus_alpha_prod.flatten()
										while len(sqrt_one_minus_alpha_prod.shape			) < len(original_samples.shape			):
														__magic_name__						:						Union[str, Any]										=sqrt_one_minus_alpha_prod.unsqueeze(-1			)

										__magic_name__						:						List[str]										=sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
										return noisy_samples










from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean




def 		lowerCAmelCase_ (						lowerCamelCase ):

				# A local function to see if a dot lands in the circle.
				def is_in_circle(lowerCamelCase						,  lowerCamelCase ) -> bool:
								__magic_name__						:						Dict										=sqrt((x**2) + (y**2) )
								# Our circle has a radius of 1, so a distance
								# greater than 1 would land outside the circle.
								return distance_from_centre <= 1

				# The proportion of guesses that landed in the circle
				__magic_name__						:						Union[str, Any]										=mean(
				    int(is_in_circle(uniform(-1.0						,  1.0 )						,  uniform(-1.0						,  1.0 ) ) )
				    for _ in range(lowerCamelCase ) )
				# The ratio of the area for circle to square is pi/4.
				__magic_name__						:						List[Any]										=proportion * 4
				print(F"The estimated value of pi is {pi_estimate}" )
				print(F"The numpy value of pi is {pi}" )
				print(F"The total error is {abs(pi - pi_estimate )}" )




def 		lowerCAmelCase_ (						lowerCamelCase						,  lowerCamelCase						,  lowerCamelCase = 0.0						,  lowerCamelCase = 1.0						,  ):
				return mean(
				    function_to_integrate(uniform(lowerCamelCase						,  lowerCamelCase ) ) for _ in range(lowerCamelCase ) ) * (max_value - min_value)




def 		lowerCAmelCase_ (						lowerCamelCase						,  lowerCamelCase = 0.0						,  lowerCamelCase = 1.0 ):

				def identity_function(lowerCamelCase ) -> float:
								return x

				__magic_name__						:						Optional[int]										=area_under_curve_estimator(
				    lowerCamelCase						,  lowerCamelCase						,  lowerCamelCase						,  lowerCamelCase )
				__magic_name__						:						str										=(max_value * max_value - min_value * min_value) / 2

				print("""******************""" )
				print(F"Estimating area under y=x where x varies from {min_value} to {max_value}" )
				print(F"Estimated value is {estimated_value}" )
				print(F"Expected value is {expected_value}" )
				print(F"Total error is {abs(estimated_value - expected_value )}" )
				print("""******************""" )




def 		lowerCAmelCase_ (						lowerCamelCase ):

				def function_to_integrate(lowerCamelCase ) -> float:
								return sqrt(4.0 - x * x )

				__magic_name__						:						Dict										=area_under_curve_estimator(
				    lowerCamelCase						,  lowerCamelCase						,  0.0						,  2.0 )

				print("""******************""" )
				print("""Estimating pi using area_under_curve_estimator""" )
				print(F"Estimated value is {estimated_value}" )
				print(F"Expected value is {pi}" )
				print(F"Total error is {abs(estimated_value - pi )}" )
				print("""******************""" )


if __name__ == "__main__":
							import doctest

							doctest.testmod()




